NASA TECHNICAL NOTE NASA TN D-8243 · 2013-08-31 · NASA TECHNICAL NOTE NASA TN D-8243 M u- cy w n z c AERODYNAMIC DESIGN GUIDELINES AND COMPUTER PROGRAM FOR ESTIMATION OF SUBSONIC

NASA TECHNICAL NOTE NASA TN D-8243 -

M u- cy w n z c

AERODYNAMIC DESIGN GUIDELINES AND COMPUTER PROGRAM FOR ESTIMATION OF SUBSONIC WIND TUNNEL PERFORMANCE

William T. Eckert, Kemeth K? Mort, and Jeau Jope

Ames Research Center und U S . Army Air Mobility RGD Laboratory

doL"T1o&

Moffett Field, Cali$ 94035 v "., '>76 ,916 +is

N A T I O N A L A E R O N A U T I C S A N D S P A C E A D M I N I S T R A T I O N W A S H I N G T O N , 0. C. O C T O B E R 1976

https://ntrs.nasa.gov/search.jsp?R=19770005050 2020-05-07T05:30:01+00:00Z

1. Report No. TN D-8243

William T. Eckert,* Kenneth W. Mort, and Jean Jope

9 Performing Organization Name and Address NASA Ames Research Lenter

Ames Directorate,U.S. Army Air Mobility R&D Laboratory Moffett Field, CA 94035

12 Sponsoring Agency Name and Address National Aeronautics and Space Administration Washington, D. C. 20546 and U.S. Army Air Mobility R&D Laboratory, Moffett Field, CA 94035

and

I 5 Supplementary Notes

2. Government Accession No. 3. Recipient's Catalog No.

A-5944 10. Work Unit No.

505-06-31

4. Title and Subtitle AERODYNAMIC DESIGN GUIDELINES AND COMPUTER PROGRAM FOR ESTIMATION OF SUBSONIC WIND TUNNEL PERFORMANCE

7. Author(s1

11. Contract or Grant No.

5. Report Date

6. Performing Ormnizrtion Code October 1976

8. Performing Organization Report No.

13. Type of Report and Period Covered

Technical Note

Wind tunnel design (subsonic) Wind tunnel (subsonic) Duct flow Energy use analysis Duct losses Power consumption Wind tunnel performance analysis Aircraft testing

14. Sponsoring Agency Coda .

Unlimited

STAR Category - 02

*Ames Directorate, U.S. Army Air Mobility R&D Laboratory, Moffett Field, CA 94035

19 Security Classif. (of this report) 20 Security Classif. (of this page)

Unclassified Unclassified

16. Abstract

This report brings together and refines the previously scattered and over-simplified techniques for the aerodynamic design and loss prediction of the components of subsonic wind tunnels. General guidelines are given for the design of diffusers, contractiohs, corners, and the inlets and exits of non-return tunnels. A system of equations, reflecting the current technology, has been compiled and assembled into a computer program (a user's manual for this program is included) for determining the total pressure losses. The formulation presented is applicable to compressible flow through most closed- or open-throat, single-, double-, or non-return wind tunnels. A comparison of estimated performance with that actually achieved by several existing facilities produced generally good agreement.

21. No. of Pages 22. Rice'

197 $7.00

t

17. Key Words (Suggested by Authorls)) 18. Distribution Statement

'For sale by the National Technical Information Service. Springfield,'Virginia 22161

TABLE

NOTATION (Engineering Symbols) . . . SUMMARY . . . . . . . . . . . . . . INTRODUCTION . . . e . CAUTIONARY DESIGN GUIDELINES . . . . Diffusers . . . . . . . . . . . . Contractions . . . . . . . . . . . Corners . . . . . . . . . . . . . Non-Return Wind Tunnels . . . . .

PERFORMANCE ESTIMATION . . . . . . . General Approach . . . . . . . . . Problem Restrictions . . . . . . . Computation Formulas . . . . . . . Flow-state parameters . . . . . Local conditions . . . . . . . . Section pressure losses . . . .

COMPUTER PROGRAM DESCRIPTION . . . . Method of Solution . . . . . . . . Computing Equipment Required . . . Hardware and machine components Software . . . . . . . . . . . .

Source Code . . . . . . . . . . . Operating Instructions . . . . . . Input . . . . . . . . . . . . . output . . . . . . . . . . . . . Computer system restrictions . . Optional inputs . . . . . . . . Diagnostic messages . . . . . .

Test Case . . . . . . . . . . . . DISCUSSION AND APPLICATIONS . . . . Results . . . . . . . . . . . . . Evaluation . . . . . . . . . . . .

Programming Techniques . . . . . .

OF CGYTENTS

APPENDIX A . NON-STANDARD FUNCTIONAL FORMS Local Flow-State Parameters . . . . . . Mach number . . . . . . . . . . . . . Reynolds number . . . . . . . . . . . Friction coefficient . . . . . . . . .

Section Pressure Losses . . . . . . . . Corners (constant area) . . . . . . . Corners (diffusing) . . . . . . . . . Diffusers . . . . . . . . . . . . . . Exit . . . . . . . . . . . . . . . . . Flow straighteners: airfoil members (thick) Internal flow obstruction: drag item . . . Vaned diffusers . . . . . . . . . . . . . . Loss value transferred to reference location Wall pressure differential . . . . . . . . . Input power required . . . . . . . . . . . .

Page

1 1 2 2 3 3 4 4 4 5 5 5 5 6 11 11 12 12 13 14 15 15 15 16 17 18 18 21 22 23 24 26 26 26 27 27 27 27 28 29 30 31 32 32 32 33 34

V

iii

TABLE OF CONTENTS . C o n c l u d e d

APPENDIX B . NUMERICAL FUNCTION-APPROXTMATIONS C o r n e r s . . . . . . . . . . . . . . . . . . D i f f u s e r s . . . . . . . . . . . . . . . . . . Mesh S c r e e n . . . . . . . . . . . . . . . . V a n e d D i f f u s e r s . . . . . . . . . . . . . .

APPENDIX C . COMPUTER PROGRAM F0RTRAN CODES . N o t a t i o n (F0RTRAN) . . . . . . . . . . . . . PERF0RM . . . . . . . . . . . . . . . . . . DATACK . . . . . . . . . . . . . . . . . . . FRICTN . . . . . . . . . . . . . . . . . . . 0UTPUT . . . . . . . . . . . . . . . . . . . . P L g T I T . . . . . . . . . . . . . . . . . . .

APPENDIX D . INPUT .AND OUTPUT FOR SAMPLE CASES

TABLES . . . . . . . . . . . . . . . . . . . .

SPEED . . . . . .

REFERENCES 6 . . . . . FIGURES . . . . .

Page

. . . . . . . . . . . . . 35 . . . . . . . . . . . . . 35 . . . . . . . . . . . . . 35 . . . . . . . . . . . . . 38 . . . . . . . . . . . . . 38 . . . . . . . . . . . . . 39 . . . . . . . . . . . . . 40 . . . . . . . . . . . . . 52 . . . . . . . . . . . . . 79 . . . . . . . . . . . . . 97 . . . . . . . . . . . . . 98 . . . . . . . . . . . . . 99 . . . . . . . . . . . . . 104 . . . . . . . . . . . . . 107 . . . . . . . . . . . . . . 142 . . . . . . . . . . . . . 144 . . . . . . . . . . . . . 153

. t

iv

NOTATION

(Engineering Symbols)

Symbol

A

Anow A0

A1

A2

AR

aT

B

cV

D

Del

F0RTRAN name

A

AL

A0

A1

A2

ASTAR

AR

AT

AS0

CD

CHdRI)

D

Description

cross-sectional area of local section, m2 (ft2)

total cross-sectional flow area at drive fan(s), m (ft2)

cross-sectional area of local flow, m2 (ft2)

cross-sectional flow area of test section at upstream end, m2 (ft2)

cross-sectional flow area of section at upstream end, m2 (ft2)

3, cross-sectional flow area of section at i- downstream end, m2 (ft2)

cross-sectional area for sonic flow at specified flow conditions, m2 (ft2)

cross-sectional flow area ratio of upstream

speed of sound in still gas, computed at total

and downstream ends of section

(stagnation) conditions, m/sec (ft/sec)

speed of sound in moving flow at upstream end of test section, m/sec (ft/sec)

dummy constraint used in defining the friction term of turning vane loss function

drag coefficient of flow obstructions: drag/@

chord of turning vanes, m (ft) .

cross-sectional diameter of circular duct, m (ft)

cross-section diameter at the upstream end of an equivalent circular duct with equal area, m (ft)

'Note that in this section, as throughout the report, all letter 0's occurring in FfiRTRAN names are shown with slashes, as 8 ; all number zeros are shown without slashes.

v

Symbol

De2

Dh

ER

f (d)

K

KCONTRACTION

KDIFFUSION

KEXP

KEXPAdd it ional

KEaSquare

F~RTRAN name

DH

ER

FKTVl FKTV2

EK

EKCNTR

EKD

EKEXP

EKADD

EKBASE

EKC

EK2DR

EKS

EK2DCS

Description

cross-section diameter at the downstream end of an equivalent circular duct with equal area,

(ft)

4 x (cross-sectional area) hydraulic diameter: perimeter 9

energy ratio: ratio of energy of flow at the test section to the output energy of the fans

function defining turning vane loss parameter KTV

local total pressure l o s s coefficient of sec-

*PT tion: - 9

local total pressure loss coefficient from contracting portion of thick-airfoil flow straighteners

local total pressure loss coefficient from diffusing portion of multi-loss-type sections

net expansion loss coefficient for diffusers

additional diffuser expansion l o s s coefficient due only to more diffusion in one plane than the other

basic diffuser expansion l o s s factor coefficient for three-dimensional diffusion

expansion l o s s coefficient for conical diffusers

expansion loss coefficient for a two- dimensional, rectangular cross-section diffuser

expansion l o s s coefficient for three- dimensional expansion in square cross-section diffusers

estimated expansion loss value for a two- dimensional diffuser (one with expansion in only one plane) with cross-section shape of some square/circular hybrid

vi

Symbo 1

KExp2DCir cul ar

KEXPANSION

KFRICT ION

KFRICTION (CONI CALI

KMESH

KRef. 9

KRN

KROTATION

KTV

KTV90

K,

KVANED DIFFUSER

KO

FQRTRAN name

EKZDC

EKCSAV

EKMESH

EKTV

EKTV90

EKV

EKO

Description

estimated expansion loss value for a hypothetical two-dimensional diffuser with circular sides :

K~~ c ir cu lar 2DRe c t angul ar

KEXP

estimated expansion loss coefficient for three- dimensional, combination circular and square cross-section diffuser

diffuser loss coefficient due to expansion:

(ARi '>2 turning vane loss due to friction

diffuser loss due to friction for the equivk- lent conical diffuser

mesh screen-type loss parameter

diffuser loss factor presented in reference 9: Ap/q

[(AR - 1)/ARI2 mesh screen Reynolds number sensitivity factor

turning vane loss coefficient due to rotation

turning vane loss coefficient

turning vane l o s s parameter for given vanes at a 90' turn

local total pressure loss coefficient for vaned diffusers

local total pressure loss coefficient €or vaned 2

diffuser, K, I)

section total pressure loss coefficient referred to test section conditions: APT QO

-

vi i

FdRTRAN Symbol name Description

L

II

M

Mo N

P~~~

PINPUT

PIN PUT^^^

PREQUIRED

P

PT

TATM P

PTSC

9

R

R e

EL

flow obstruction (drag item) total pressure loss coefficient referred to test section conditions

centerline length of section, m (ft)

characteristic dimension on which Reynolds number is based

AMACH local Mach number

EM0 Mach number at upstream end of test section

N section assigned sequence number for order of occurrewe in circuit

power loss due to drag of flow obstruction, w (hP)

PWRIP tunnel drive power required to be input to flow by the fans, W (hp)

power input required to overcome drag of flow obstruction, W (hp)

PmdP total fan motor output power required to drive wind tunnel at specified speed, W (hp)

PT

PATM

QO

R

local static pressure, N/m2 (lb/ft2)

tunnel total (stagnation) pressure, 'N/m2 (lb/f t2)

atmospheric (barometric) pressure, N/m2 ' (lb/ft2)

total (stagnation) pressure in the circuit

local dynamic pressure: - pv2 2 , N/m2 (lb/ft2)

, N/m2 test section dynamic pressure: -

settling chamber, N/m2 (lb/ft2)

povo2

gas constant, m2/sec2 O K (ft2/sec2 OR)

2 (lb/ft2)

- equivalent' radius: dA/n , m (ft)

viii

Symbol

RN

S

S

s?

T

TT

V

vF

V~~~~~~

X

Y

A

AER

APF

APT

F@RTRAN

RN

name

RNREF

TT

V

vo

G

RUFNE S

Description pVR . Reynolds number: - !J

reference Reynolds number at which turning vane 90" loss parameter, K T V ~ ~ , was determined

drag area of flow obstruction (i.e., area for which CD is determined), m2 (ft2)

distance along diffuser wall, m (ft)

length of diffuser, taken along wall, m (ft)

tunnel temperature in moving flow, OK ( O R )

tunnel total (stagnation) temperature, OK ( O R )

local flow velocity, m/sec (ft/sec) I :a

flow velocity at the drive fan(s), mysec (f t Isec)

flow velocity in a multiple-duct section, mlsec (f t/sec)

test sec'tion upstream-end flow velocity, m/sec (f t/sec)

location of inflection point in contraction. wall (distance from upstream end), m (ft)

specific heat ratio of gas

surface roughness in honeycomb cells, m (ft)

difference between estimated and true circuit .

energy ratios; i.e., error in energy ratio es t ima t e

static pressure rise across the fan(s), N/m2 ( l b / f t2)

total pressure drop through a section, N/m2 (lb/f t2)

total pressure drop through a single duct of a

total pressure rise across the fan(s), N/m2

multiple-duct section, N/m2 (lb/ft2)

(lb/ft2)

ix

F~RTRAN Symbol name Description

APTFDUCT average total pressure rise across a single fan, N/m2 (lb/ft2)

total pressure drop through a multiple-duct section, N/m2 (lb/ft2)

APTTOTAL summation of all total pressure drops through the wind tunnel circuit, N/m2 (lb/ft2)

DELP local pressure difference across wind tunnel wall, N/m2 (lb/ft2)

A~REQUIRED difference between true and estimated required drive power levels for given levels of operating velocity and fan efficiency; i.e., error in required power estimate, W (hp)

AVO difference between estimated and true test section operating velocity for given power and fan efficiency levels; i.e., error in operating velocity estimate, m/sec (ft/sec)

AE increment of flow-obstruction downstream influence factor greater than unity: E - 1 (greater than or equal to zero)

diffuser side length ratio: ratio of change in height to change in width from upstream to downstream end, or its inverse, whichever is l ess than o r equal to unity

SLR

flow-obstruction downstream influence coefficient (greater than or equal to unity)

EP S E

drive motor electrical efficiency, percent

ETAFAN fan aerodynamic efficiency, percent

TH diffuser half-angle, rad

SLAMDA friction coefficient for smooth pipes

EMU flow viscosity, N sec/m2 (lb sec/ft2)

EMUSTD standard-day value of viscosity, N sec/m2 ( l b sec/ft2)

h

u

Ustd

EMUT reference viscosity at a known temperature, computed for still gas (stagnation conditions), N sec/m2 ( l b sec/ft2)

X

Symbol

V

P

PF

P O

N

i= 1

9

28

F8KT?&!? name

ENU

R H ~ S

RHdSF

RH@T

RHOSO

SUMEKO

SUMEL

PHI

T H 2

Description

kinetic viscosity of gas, m2/sec (ft2/sec)

local static density, N sec2/m4 (lb sec2/ft4)

static densit at the fan(s), N sec2/m4 (lb sec2/ft x )

density computed for total (stagnation) conditions, N sec2/m4 (lb sec2/ft4)

static density at upstream end of test section, N sec2/m4 (lb sec2/ft4)

summation of section total pressure losses referenced to test section conditions

summation of section centerline lengths, m (ft)

corner flow turning angle, deg

diffuser equivalent cone angle:

xi

AERODYNKiXXC DESXGX GUIEELINES fi'E COMFLTER PROGRAM FOR ESTIMATION

OF SUBSONIC WIND TUNNEL PERFORMANCE

William T. Eckert, Kenneth W. Mort, and Jean Jope

Ames Research Center and

Ames Directorate, U.S. Army Air Mobility R&D Laboratory

SUMMARY

This report brings together and refines the previously scattered and over-

General guidelines are given for the simplified techniques for the aerodynamic design and loss prediction of the components of subsonic wind tunnels. design of diffusers, contractions, corners, and the inlets and exits of non- return tunnels. A system of equations, reflecting the current technology, has been compiled and assembled into a computer program (a user's manual for this program is included) for determining the total pressure losses. The formulation presented is applicable to compressible flow through most closed- or open- throat, single-, double-, or non-return wind tunnels. A comparison of estimated performance with that actually achieved by several existing facilities produced generally good agreement.

INTRODUCTION

In the past, most of the work on the design of ducts and wind tunnels and on the determination of their pressure (and power) losses has been either highly specialized, considering only one type of component, or over-simplified, covering several types of components but giving only a superficial idea of what parameters are important. However, for the recent NASA studies directed toward new and modified wind tunnel facilities, it has been necessary to do a careful job of estimating, easily and quickly, the performance of all circuit components. This report brings together, revises, and updates the techniques for the aerodynamic design and performance prediction of subsonic wind tunnels.

The basic procedures and guidelines for the aerodynamic design of critical wind tunnel components, as presented in references 1 through 3, have been revised and updated, as required. curves developed and suggested herein show the relative design points for several existing facilities. recent NASA studies on end treatments for non-return wind tunnels.

The diffuser and contraction design

Also provided are recommendations derived from

The method of loss analysis presented is a synthesis of theoretical and empirical techniques. Generally, the algorithms used were those substantiated by experimental results. The methods of references 4 through 11 for predic- ting componen; losses have been refined and incorporated. The performance

calculations, based on user-selected flow conditions at the test section, assume that the circuit geometry has been predetermined.

The comparison of the actual and predicted performance for several existing wind tunnel facilities shows generally good agreement.

CAUTIONARY DESIGN GUIDELINES

This report presents the means for rapidly estimating the performance of a wind tunnel circuit after its geometry has been determined. However, an improper design of any of its several components (diffusers, contractions, or corners, for example) could result in performance penalties caused by inter- action with the flow in other components; such penalties cannot be predicted. In addition, improper design could cause poor test-section flow quality which would not be indicated by the performance analysis. Therefore, the purposes of this section are to point out critical areas of concern in wind tunnel design and to attempt to establish proper design criteria.

Diffusers

Diffusers, especially those just downstream of high-speed sections, are very sensitive to design errors which may cause flow separation. The equivalent cone angle and area ratio must be properly selected to avoid steady-state or intermittent separation of the flow from the diffuser walls. (This separation can cause vibration, oscillatory fan loading, oscillations in test section velocity, and higher losses in downstream components.) Generally, proper diffuser design requires that, for a given area ratio, the equivalent cone angle be constrained below a certain value. nary conical section with length and with inlet and exit areas identical to the actual section.) for diffusers with sharp corners than for those with a rounded cross section.

("Equivalent" denotes an imagi-

This cone angle should probably be held 0.5" to 1' lower

Since the portion of the wind tunnel between the test section and the fans is usually the higher-loss segment, it is the most critical in affecting circuit performance. Therefore, it was used as a basis for establishing recommended design limits as a guide to diffuser selection. It was assumed that the fans serve to reenergize the boundary layer of downstream sections and that the fans and the upstream and downstream components have no inter- action that affects their losses; this may or may not be true (see ref. 12). The overall area ratio and cone angle between the test section and fan contraction were examined for several wind tunnels. This analysis used the centerline lengths o f all intervening components, including corners. (The actual effect of corners is unknown: they may alter the onset of separation somewhat.) Figure l(a) compares curves for the first appreciable stall for flows with thin inlet boundary layers, from references 1 and 2, with the design points of selected existing wind tunnels. These. curves were used to aid in defining the separation trend; good correlation with the symbols is not necessarily expected. Figure l(a) shows that most of these wind tunnels were designed beyond (above) the two-dimensional stall curve but below the conical stall

2

curve. (Snme of these diffusers are f a r from conical.) The recommeiided design region, shown in figure l(b), was positioned with the prior knowledge that the NASA-Ames 7- by 10-Foot Wind Tunnel has a partially separated diffuser just downstream of the test section, and that the NASA-Ames 4G- by 8O-Foot Wind Tunnel has some local separation in the corners of the primary diffuser. The upper portion of the design region is recommended for diffusers with rounded corners, and the lower portion for diffusers with sharp corners.

Contract ions

Contracting sections are subject to separation in the same manner as diffusers; however, the penalties are usually much less severe in the contracting sections. Separation of the flow can occur if the contraction is too short for the amount of area reduction. Figure 2(a) presents the general wall shapes suggested in reference 3 and figure 2(b) shows the design boundary for these shapes in comparison with the designs of several selected wind tunnel facilities.

From this comparison it is evident that, while some facilities were designed more conservatively than others, no design severely exceeds the design boundary. Since none of the facilities considered has shown significant contraction-caused flow problems, the design boundary may be considered empirically reasonable. Further, reference 1 3 generally tends to support the positioning of the suggested design curve. However, the criteria of reference 13 are more conservative due to consideration of viscous effects which were neglected in the study of reference 3 .

Corners

The corner losses in a wind tunnel can be large. To minimize them, turning vanes should be used for more efficient turning. Also, as with any other high-loss item corners should, where possible, be located in a large-area section where the flow speed is low. Corner vane losses can be minimized in two additional ways: (1) by selecting an efficient vane cross-sectional shape and adjusting it for proper alignment with the flow, and (2) by choosing the best chord-to-gap spacing.

With reference to item (l), turning vane shapes can vary from bent plates to highly-cambered airfoils. Some sources favor airfoil vanes as being more efficient (ref. 4 , p. 63) while others claim that thin vanes can have lower losses (ref. 5, p. 9 3 ) . But airfoil vanes with blunted leading edges may be more forgiving of misalignment with the flow. The thicker vanes may, therefore, hold some advantage.

When considering item (2), the best chord-to-gap ratio depends on the vane type. For thick vanes, a ratio of about 2.5-to-1 is recommended (ref. 4 , p . 62) and for thin vanes a ratio of about 4-to-1 is suggested (ref. 5, p. 92).

3

Non-Return Wind Tunnels

Non-return wind tunnels have presented some interesting problems in tunnel design. This type of wind tunnel has the advantages of less structure (and therefore lower construction costs) and of no exhaust-gas-purging or air- exchange requirement. Careful design can make the non-return circuit operating power competitive with that of closed-return wind tunnels (the corner losses can be traded for inlet and exit losses). However, an area of concern for the non-return tunnel is its potential sensitivity to external winds which could affect both the required power and the test section flow quality.

A recent series of NASA studies, which dealt with wind s.nsitivity problems, showed that a non-return wind tunnel should have three 2atures: (1) a vertical exit system, (2) a horizontal inlet, and (3 ) an enclused area of protection, with a solid roof, at the inlet. References 14 and 15 detail the development work for the end treatment considered in those studies.

Reference 16 describes an inlet geometry that was developed to reduce the effects of w.ind. (This reference also presents a set of test-section flow- quality requirements by which the characteristics of any inlet treatment may be evaluated.) Although the end treatment designs shown in references 14 through 16 could be revised-or refined for additional wind protection, any additional inlet treatment would increase the structural cost and could increase the power requirement.

PERFORMANCE ESTIMATION I Although the performance analysis presented in this report was systema-

tized and automated for rapid calculation of numerous cases or iterations (by the computer program described in the following sections), the equations presented are equally amenable to manual calculation methods.

General Approach

The equations were derived in forms that use the most common and conveni- The equations are listed and explained below and may ent defining parameters.

be used for component after component, each in turn.

The total pressure losses (proportional to power losses) of each component are calculated and summed to give the total circuit loss and operating power required. The computation technique is applicable to either closed- or non-return circuit types made up of any combination of standard wind tunnel components in any order. and 'stagnation temperature and pressure) and the external atmospheric pressure are variable as required.

The flow conditions in the test section (velocity,

4

Problsin Restrictions

Three restrictions were found to be necessary in order to allow rapid solution of most cases with a minimum amount of effort. First, the cross- sectional geometries were limited to the most common shapes: circular, rectangular, and flat-oval (semi-circular side walls with flat floor and ceiling). Second, air exchangers were omitted from this analysis due to lack of uniform- ity of configuration and a lack of definition as to the proper method of computing the losses. Finally, the drive system was assumed to be located in one or more parallel, annular ducts.

3

’ i Computation Formulas - The equations used in this performance analysis were synthesized from

various sources. Some were used in their original (source) form and others were modified to make them more convenient for use in this analysis. The equations used are presented below.

Flow-state parameters- The basic flow-state parameters were determined from input information about the reference control station and the test section. These parameters were derived from standard relationships for compressible flow.

aT = JVRTT 0.76

PT = USID(%)

aT a, =

PT

(ref. 17, p. 8)

(ref. 17, p. 51)

(ref. 18, p . 19)

(ref. 18, p. 4 )

(ref. 18, p. 4 )

2(Y-1)

A* = { 2 [1+ y + l (+ M:)] }* (appendix A) (appendix A)

Local conditions- The local flow conditions were determined for each end of each section.

5

1. Mach number: The local Mach number was found from a Newton's-method solution of the relationship

(appendix A)

J 2 . Reynolds number: The Reynolds number based on the characteristic

length R, usually the local hydraulic diameter, was determined from

0.76 (appendix A)

3. Friction coefficient: A Newton's-method solution was used to determine the friction coefficient for smooth walls from the expression

[logl,(XRN2) - 0.8]-2 - A = 0 (appendix A)

Section pressure Zosses- The l o s s in total pressure caused by each section was calculated in a form non-dimensionalized by local dynamic pressure: K = ApT/q. (In this study the smallest-area end of each section was used as the local reference position.) The individual losses were based on the nature of the section, local flow conditions, and input geometry and parameter information. The most appropriate l o s s forms for typical wind tunnel sections are catalogued on the following pages. The nonstandard formulas, those which are not directly attributable to the literature, are developed in appendix A. The precise equations, which were developed from various curve-fitting and inter- polation techniques based on the plots presented in certain figures, are given in appendix B.

1. Constant-area ducts: For closed, constant-area sections the pressure loss due t o friction is given by

(ref. 7, p. 5 3 ) XL Dh

K = -

2 . Open-throat duct: The losses from an open-throat test section may be found from the expression

K = 0.0845 - - 0.0053 (<r Dh

(ref. 7, p. 150)

3. Contractions: In contracting sections, where the major part of the losses is due to friction, the local loss may be approximated as

AL K = 0.32 - Dh

(ref. 6 , p. 528)

6

4 . Corners with no net area change ("constant area"): A duct can change direction with or without the aid of flow guide vanes. For a constant-area turn employing turning vanes for efficiency, with a 'hormal" number of vanes (ref. 7, p. 241), and with chord-to-gap ratios between 2-to-1 and 4-to-1, the losses resulting from friction and rotation caused by the vanes are

2 . 5 8 loglo REF

= KTV 3 [2 + ( loglo m ) 3 (appendix A)

The "Reynolds number used for the turning vane l o s s should be based on vane chord. The turning vane loss parameter K T ~ is plotted as a function of turning angle in figure 3(a), with the assumption that value for a 90' corner. Corners without turning vanes are less efficient and the loss function may be approximated by a sixth-order polynomial as shown in figure 3(b) :

KTV = 0.15 is a reasonable

K = 4.313761~10-~ - 6.021515~10-~ $ + 1.693778~10-~ $' - 2.755078~10-~ ( p 3

+2.323170~10-~ $4 - 3.775568~10-~ $5 + 1.796817~10-~~ $6

(appendix B)

This function assumes a l o s s value of about K = 1.8 for a 90' turn. The foregoing losses are those associated with the turning of the flow only. The losses for a corner system (with or without vanes), with the walls of the duct to be considered as well, requires an additional term for the frictional loss of the constant-area duct based on the centerline length.

5. Corners (diffusing): Corners with diffusion may well employ longer vanes in order to improve the efficiency of the diffusion process. For this reason they were treated as vaned diffusers with the addition of the rotational loss term of the turning vane function:

(appendix A)

where parameter is defined as for a constant-area corner. This loss function includes the effects of friction.

u(20 - 21.5') is the unit step function and the turning vane loss

6. Diffusers: Diffusion produces both expansion and friction losses in the duct given by

A AR + l)](AR-; l)! = CKEXp + (8 sin 0 AR - 1

(appendix A)

7

where t h e expansion parameter v a l u e s , KEXP, are p l o t t e d a g a i n s t equ iva len t cone a n g l e i n f i g u r e 4 and t h e technique used f o r e s t i m a t i n g t h e desc r ibed i n appendix A.

KEXP va lues is

( I t should be noted t h a t t h e r e are more s o p h i s t i c a t e d techniques f o r e s t i m a t i n g d i f f u s e r performance than t h e one presented here . However, they r e q u i r e boundary-layer c a l c u l a t i o n s ; f o r example, see r e f e r e n c e 19. Experience wi th bo th the s imple technique descr ibed h e r e i n and more complex techniques i n d i c a t e s t h a t t h e two produce comparable r e s u l t s . Genera l ly , l i t t l e i s gained by t h e s i g n i f i c a n t a d d i t i o n a l e f f o r t r equ i r ed t o use t h e more complex approaches. )

7. Exit : o r of any expel led flow, i s due t o t h e l o s s of t h e k i n e t i c energy of t h e e x i t - i n g flow. This i s given by

The t o t a l p r e s s u r e l o s s a t t h e e x i t of a non-return wind tunnel ,

Y

(appendix A)

8. Fan (power) s e c t i o n : Fan d r i v e s e c t i o n s are commonly made up of con- t r a c t i o n s , constant-area annular d u c t s , and d i f f u s e r s . Analys is should be handled by d i v i d i n g t h e f a n s e c t i o n i n t o t h e s e t h r e e component p a r t s .

9 . Flow s t r a i g h t e n e r s - honeycomb ( t h i n w a l l s ) : The l o s s through t h i n f low-s t ra ightener o r honeycomb systems may be expressed as

where t h e hydrau l i c diameter i s t h a t of t h e honeycomb c e l l . The f r i c t i o n c o e f f i c i e n t i s determined from a Reyriolds number based on t h e s u r f a c e roughness of t h e honeycomb:

f o r RN 5 2 7 5 ,

and f o r RN > 2 7 5 ,

10. Flow s t r a i g h t e n e r s - a i r f o i l members ( t h i c k w a l l s ) : Flow through a d j a c e n t a i r f o i l s w i l l f i r s t c o n t r a c t and then d i f f u s e . It w a s assumed t h a t t h e p o i n t of minimum d i s t a n c e between p a r a l l e l members would be a t 30 percent of t h e s t r a i g h t e n e r l eng th back from t h e l e a d i n g edge. The forward 30 pe rcen t w a s t r e a t e d as a c o n t r a c t i o n and t h e a f t 7 0 percen t a s a vaned d i f f u s e r . Thus,

(appendix A)

8

where t h e hydrau l i c diameter is t h a t of each c e l l of t h e f low s t r a i g h t e n e r , t h e f r i c t i o n c o e f f i c i e n t is determined from a Reynolds number based on t h a t hydrau l i c d iameter , t h e area r a t i o and equiva len t cone ang le a re based on t h e ex i t and minimum flow areas, and u(28 - 21.5') is t h e u n i t s t e p func t ion .

11. I n t e r n a l f low o b s t r u c t i o n - drag i t e m : The l o s s due t o t h e d r a g of i n t e r n a l s t r u c t u r e such as s t r u t s o r models has t h e form

(appendix A)

1 2 . Pe r fo ra t ed p l a t e : Pe r fo ra t ed p l a t e w i t h sharp-edged o r i f i c e s , used as p r o t e c t i o n sc reen o r as sc reen around the i n l e t of a non-return tunne l , produces l o s s e s given by

13. Mesh screen: The l o s s e s produced by a mesh sc reen may be expressed as

K = K R N K ~ S H (1 - 7) AFLOW + (" - 1)2 ( r e f . 7 , p. 308) AFLOW

where t h e Reynolds number i n f l u e n c e f a c t o r , KRN, i s p l o t t e d a g a i n s t Reynolds number (based on mesh d iameter ) i n f i g u r e 5, and t h e mesh cons t an t , KMEsH, i s 1 .3 f o r average c i r c u l a r me ta l w i r e , 1 .0 f o r new metal w i r e , and 2 .1 f o r s i l k thread .

1 4 . Sudden expansion: For a sudden expansion w i t h duc t ing downstream ( t o a l low reat tachment of t h e f low and maximize t h e p r e s s u r e recovery) t h e l o s s i s

( r e f . 7 , p. 128)

15. Vaned d i f f u s e r s : The p r e s s u r e l o s s of a vaned d i f f u s e r , one i n which s p l i t t e r vanes are used t o improve the performance of a s h o r t d i f f u s e r by dec reas ing t h e e f f e c t i v e equ iva len t cone ang le of each chamber, may be determined from

K = (0 .3+ [0.006(2e - 21.50) 1}(AR& '> 2

(appendix A)

where u(28 - 21.5') i s t h e u n i t s t e p funct ion. (See f i g . 6 . )

16. Fixed, known l o s s : For a f i x e d l o s s i t e m where t h e p r e s s u r e l o s s v a l u e i s known, t h a t v a l u e may be used d i r e c t l y by d e f i n i t i o n :

9

17. Multiple ducts: In a system of multiple ducts, where the local flow

Some of passes through two or more separate, identical passages at the same time, the losses have the same value as those for the same type of single duct. the pertinent parameters, such as hydraulic diameter and equivalent cone angle, should be based on the geometry of one of the individual ducts. the system of ducts may then be determined from the l o s s for a single duct:

The loss for

18. Loss value transferred to reference location: Each local loss parameter is calculated based on local conditions at the smallest-area end of each section and may then be referenced to the test section conditions by the formula

(appendix A)

13. Overall and summary performance: The energy ratio of the wind tunnel under consideration is given by

1 N

i= 1

ER = (ref. 4 , p. 69)

The pressure difference across the wind tunnel walls, determining the minimum required structural strength for each section, is given by

The power required to be input into the flow in order to drive the flow through the wind tunnel at a specified test section speed is expressed as

(appendix A)

The actual drive power required is dependent on the efficiency of the fan/motor system:

10

COMPUTER PROGRAM DESCRIPTION

The computer program was written in FORTRAN IV language. It consists of a main program which calls five subroutines and/or six library routines, as required. Two of the subroutines are optional and may be abbreviated and simulated in order to save execution time and/or memory storage space.

Method of Solution

The general technique used is outlined in the computer program functional flow chart in figure 7. The program was developed in six functional units: a main program and five specialized subroutines. The main program retains general control over the computational flow and calls the subprograms as required.

In the main portion (designated PERFQRM), at first entry into the program, various section-shape geometry relationships and certain semi-empirical diffuser, turning vane, and honeycomb l o s s functions are defined. The case title card is read and checked for validity by specified code. The tunnel master data control card is then read, checked for validity, and checked for content of pertinent data by the data-checking subroutine. either of these two preliminary cards, error messages will be printed. Although detected errors will not abort the computer run (unless a card of improper format is encountered where not expected), the case under current consideration will not be computed - only the checking of input errors will then be performed on each section card. the units of measure (International System or U.S. Customary System) to be used for the particulai- case are read. These units of measure are used as the basis for the development of the appropriate flow parameters and test section conditions.

If any errors are found in

Prior to reading the section cards,

The section cards are read and operated on one at a time. They are checked for validity and input errors by the data-checking subroutine (called DATACK) and the input information, if sufficiently complete, is then used in the computation of the section upstream- and downstream-end geometries. Adjustments to these geometry calculations are made for any multiple-ducted sections. input by the user, that parameter is generated from predefined functions. Branching of the computational flow then transfers control to the appropriate block of instructions for the remainder of the calculations which are peculiar to the particular section under consideration.

For diffusing sections where the ex7ansion loss parameter was not

After all section cards have been read in and operated on, each in turn, a case termination card is encountered. The termination card specifies the optional summary operations to be performed. The encounter of this card

11

signals the end of a case and triggers the final calculations. The codes contained on this card determine the printing of velocity-optimizing and circuit summary information, the plottitg of the summary information, and the return to the beginning for another case.

The data-checking subroutine evaluates the master and section input cards for completeness of data (based on the requirements for the type of section). Then, if any error was detected during computation of a case or if the appropriate termination code was specified by the user, the complete set of input data is tabulated. Messages about errors, omissions, or superfluous information are included.

The subroutine SPEED computes the local Mach number based on local cross- sectional area and determines the local flow velocity.

The subroutine FRICTN calculates the local Reynolds number, usually based on the local duct hydraulic diameter, and the local friction coefficient for smooth pipes.

The subroutine dUTPUT accepts the calculated section parameters along with the section type codes describing the types of information to be output and prints the section information according to the appropriate format.

The subroutine PLdTIT plots the summary information (cummulative total

The plot is scaled for centimeter or inch plot paper, pressure losses and/or wall pressure differential) versus circuit centerline length if requested. determined by whether International or U.S. Customary units are used for computation.

The program is terminated after the last operations on a case for which a no-return instruction on the termination card was given by the user.

Computing Equipment Required

Hardware and machine components- Although this program was written for

No magnetic tapes were use on an IBM 360/67 with TSS Monitor, batch mode, an attempt was made to keep it compatible with any system that uses FQRTRAN IV. used. In this version, input is made by cards and the data to be plotted are stored on a disc file for plotting at a later time in an off-line mode. How- ever, it is possible to use a typewriter-type terminal for conversational or real-time computation, typing the data by card-image format, and plotting immediately after the computation has been completed for a case.

The total core required for compilation on the IBM 360/67 was approximately 82 000 (decimal) bytes. If necessary this figure can be reduced by eliminating two subroutines, DATACK and PLQTIT. and of each subroutine were approximately as follows:

The sizes of the main program

12

PERF@M 38 800 bytes DATACK 25 700 SPEED 800 FRICTN 900 OUTPUT 12 900 PL0TIT 2 900

The program was executed on an IBM 360/67, writing plot data on a disc, logical unit 10. second binary-coded-decimal terminal and plotted on a Zeta plotter with 0.005-in. step increments. The plot page size was programmed not to exceed 25 by 38 cm (or 10 by 15 in.).

Later the data file was accessed from a 14.8 character-per-

Sof twee- This program was written for use on any computer with sufficient core and with a standard FgRTRAN IV compiler.

The Zeta plotter routines, with minor exceptions, are compatible with the Calcomp routines. The subroutines AXIS, FACTgR, LINE, PLflT, SCALE and SYMBQL are alike in both Calcomp and Zeta plotting.

CALL AXIS - draws the axis line and annotates the divisions at every two centimeters or each inch (depending on the units of measure specified).

CALL FACTflR - enables the user to produce normal size drawings with plotters which have either 0.01- or 0.005-in. increment size. The variable FACT must be set to 1.0 for 0.01-in. increments and to 2.0 for 0.005-in. increment plotters.

CALL LINE - plots centered squares connected by straight lines through the coordinate pairs of data values.

CALL PLflT - is used to establish a new point of origin for the pen and paper movements. Before plotting commences, the pen must be positioned where desired along the X-axis. Y-axis. which are equated to 25 and 38 cm or 10 and 15 in., as required.

The program will position it along the The plot-page size is defined by the values of YLEN and XLEN

CALL PLgTF - is an alternate plotting initialization routine which is available in the Zeta but not Calcomp plot package. It is used in place of PLOTS whenever deferred plotting is desired. The first argument in the call statement indicates the speed of the terminal with which the plotter is interfaced. The second argument is the logical-device number of the plot file.

CALL SCALE - examines the data and determines the proper scaling for the given dimensions of the plotter paper, 25 by 38 cm or 10 by 15 in.

CALL SMflDE - is available only in the Zeta plot package. It permits the user

In this program the options have been set equal to the usage to choose from extensive capabilities which affect several of the plotter routines. found in the Calcomp routines, and therefore, if Zeta plotter routines are not available, the call to SM@DE should be eliminated.

I 13

CALL SYMB@L - prints the input case title at the top left of each plot page as it appears in columns 2 through 80 of the title card. For reference purposes, it also draws a small plus sign at the origin of the plot.

The library routines used are standard F@RTEUN routines:

ABS - Absolute value

AL@G10 - Common logarithm, base ten

ATAN - Arctangent (result in radians)

EXP - Exponential of the natural number e

IFIX - Convert from real number to integer

SIN - Trigonometric sine (argument in radians)

SQRT - Square root

Programming Techniques

It was intended that this program be usable on as many different computer systems as possible. Therefore, in order to make them applicable to some machines, certain statements were forced into particular forms which would be less efficient on other systems (e.g., Hollerith instead of literals in format statements).

C@MM@N and DATA statements were used as much as possible to simplify the definition of parameter values. In the main program, arithmetic statement functions were used for three purposes: (1) for the definition of section hydraulic diameter, area, and equivalent cone angle geometry functions; ( 2 ) for the conversion function from local to reference-section pressure losses; and ( 3 ) for the definition of the least-squares-polynomial-curve-fit functions. The last group of functions includes: (1) the corner turning-loss parameters as functions of turning angle (see fig. 3 ) ; ( 2 ) the diffuser expansion loss parameters for the different cross-section shapes as functions of equivalent cone angle (see fig. 4 ) ; and (3 ) the mesh screen Reynolds number sensitivity factor as a function of mesh-diameter-based Reynolds number (see fig. 5 ) .

Certain functions not easily solvable in closed form were solved itera- tively (some by Newton's method) to 0.01 percent accuracy. These functions include test section Mach number, local section Mach number, and local section friction coefficient.

Numeric codes were used for specifying such things as section type, section end-shape types, and system of computational units; for decisions on requirements for inputs to each section type; and for case-termination procedures and outputs desired. The various important input codes are listed in tables 1 and 4 . All sections of the multiple-ducted type were assigned high code numbers for simplicity in selecting them for special handling. The

14

various s e c t i o n types were grouped in code decades for reasonable association of section code and component function. Where possible, the second digit of the code (if that second digit is not zero) reflects the basic characteristic of the section: constant area, contracting, or diffusing.

The information input fields on the master data and section cards were arranged in three basic groups: (1) qualitatrve information (type and shape); (2) quantitative geometry information (number of ducts, cross-sectional end dimensions, and length); and (3) loss-related parameters. The case termination card employs the same format as the section cards so that it may be encountered at random intervals without causing a program crash. For the tabulation of the input data (for error-location and record-keeping purposes), object- time formatting was used to compile the combination input and annotation data set for a convenient output.

Much of the output of the program was set up on a demand (i.e., optional) basis. A section-by-section performance analysis is automatically provided. A brief summary of the variation of selected parameters through the circuit, and plots of those parameters, may be selected if desired. An annotated listing of the inputs may be requested or, if errors are detected, the listing is internally forced in order to provide a simple means of error-detection and correction and/or simplified record-keeping of case data.

Source Code

A source code listing of the performance estimation program is provided in appendix C along with the associated notation definitions. The source code includes the use of comment cards throughout the program for identification of the operations carried out by each set of instructions.

Operating Instructions

The basic source program deck arrangement is shown in figure 8 .

Input- Sample coding forms for the four types of input cards required are presented in figure 9. The special symbols required in the first columns of the title and master data cards are included.

1. Title card: For the title labeling card, with the exception of the first column which must contain an asterisk (* I , the entire card may be used as desired. This title was programmed to appear at the top of each page of the case to which the title refers, including the plots. Only one title card per case may be used.

2. Master card: The tunnel master control data card provides sufficient information for defining conditions in the test section (which is the reference section for all calculations) and conditions of the surrounding external atmosphere. Table 2 details the inputs included on the master data card. The first column must contain a minus sign in order to identify the card as a valid master card. The remainder of the inputs should be positive, with

15

columns 2 through 6 containing five fields of integers only (no decimal points). Columns 7 through 10 were not used on this card and should be left blank. Columns 11 through 50 should contain floating-point numbers. were divided into eight parameters of five columns each, including decimal point.

These columns

3 . Section cards: The individual section information cards were based on the same format as the master card, except that the section cards require no special identifying code. Table 3 details the inputs contained on the section cards. The first six columns, containing four data fields, require integer inputs. The remaining 74 columns were divided into two real number fields of two columns each (with the assumed default decimal points to the right of the second columns), and 14 real number fields of five columns each (with the assumed default decimal point between the third and fourth columns of each field) .

Although the input parameter requirements vary from section to section, certain requirements are basic to all sections. (1) the section type code, (2) the section end shape codes, and ( 3 ) the section dimensions (end height(s) and width(s) and/or diameter(s) and usually length). detailed list of the additional, specialized requirements for each section is presented in table 4 .

These items include:

A

Although not mandatory in order to obtain a correct total power estimation, it is advisable to input the section data cards in the actual section order so that the summary calculations and plots have relevance to the,actual circuit.

4 . Termination card: The case termination card, which signals the end of the section inputs for a particular case, is identified by the constraint of blanks in card columns 3 and 4 . The numbers contained on this card are used strictly as task codes; table 5 shows the details of these codes. In the event of a request for plotted information, the code determines the type(s) of information to be presented. yes/no decision.

For all other tasks the codes dictate a simple

As many cases as desired may be input in a single job submission. same system of units need not be used in all cases. Any parameters may be changed as desired from case-to-case since there are no forced carry-overs (except the specific heat ratio, y, which is fixed at the time of program compilation).

The

Output- Based on the foregoing input information the results may be calculated and tabulated in five different types of information groups.

1. Section performance analysis: The section performance tabulation fully describes the performance-related parameters of the wind tunnel circuit. Atmospheric and test section flow reference conditions are stated at the top of the first page. The various parameters are tabulated for each section in the order of computation with the upstream end information on the first and the downstream information on the second of the two lines for each section. The section sequence number and type (a translation of the code) and the end

16

shapes are given first. presented next, followed by the section length and calculated total pressure loss values.

The geometry and local velocity information are

2 . Overall performance: If no input errors are encountered during the analysis of a case, overall performance values are presented at the end of the section performance tabulation. This includes the total circuit length, the total pressure losses and energy ratio for the circuit, and the total operating power required.

3 . Summary characteristics: If requested on the termination card and barring any errors, a summary of the circuit characteristics is tabulated on a separate page. This tabulation includes section sequence numbers, Mach numbers, cumulative pressure losses, and local wall pressures, all as functions of distance through the circuit.

4 . Plots: Under proper condition codes, the cumulative pressure losses and/or the wall pressure differentials will be plotted as functions of distance through the circuit (centerline length). The straight lines that appear on the plots connecting the points are for reference only and do not represent the actual distribution in a component.

5 . Input data tabulation: Finally, if an input error was encountered during the analysis of the circuit, or if such information was requested by the user, the input cards are tabulated with annotations regarding missing or superfluous inputs. A careful look at this section should allow the user to discover why a given set of input data did not produce the expected type of results.

All of the foregoing types of output are shown for the test case.

Computer system restrictions- Certain restrictions and/or assumptions had to be imposed on the computer system and its methods and abilities in order to perform the performance analysis within reasonable time, effort, and money constraints.

1. Hardware: This analysis was programmed for a moderate-sized system with common components. No special hardware is required with the exception of a plotter if the plotting option is used. The output printing device is assumed to have available a minimum capacity of 120 characters per line, but the number of lines per page may be set by means of the LINEMX parameter in the main program. (Barring any special requirements, 45 lines for an 8.5-in. page or 60 lines for an 11-in. page are recommended.)

2. Software: Certain software restrictions were imposed simply as a starting point to the problem solution. The input card formats were fixed as shown in figure 9. The specific heat ratio (y) and the number of lines per output page were fixed for each compilation of the source deck, although changes can be made by altering the values of G and/or LINEMX, respectively, near the beginning of the main program.

17

For reasons of possible memory limitations on smaller systems, the number of wind tunnel components in each circuit case was limited to 30 sections. This limit may be changed by assigning a new value to LMTSEC in the main program and by re-dimensioning the following variables as denoted by "XX"' . the main program (PERF@RM), DELP(XX+2), SEKO(XX) , SEL(XX), SMACH(XX) , SSUMEL(XX+2) and SSUMKO(XX+2); in the data-checking subroutine (DATACK), ENDATA(XX,20), NCHECK(XX,20) and NDATA(XX,4); and in the plotting subroutine (PLOTIT), DELP(XX+2), SSUMEL(XX+2) and SSUMKO(XX+2). If memory limitations are a severe problem and/or if computer-controlled plotting facilities are not available to the user, the data-checking and/or plotting subroutines may be 11 removed" by inserting dummy, one-card subroutines with the same arguments which would have no effect on the calculations. This would decrease the util- ity and power of the program, but would retain the basic performance estimation capabilities without crippling them altogether.

in

I 18

The plotting routines were written according to the requirements for a plotter with 0.005-in. increments.

Optional inputs- Certain of the parameter inputs are designated as optional and have built-in assumed default values in the event that the user knows no better values than the ones provided in the sources referenced herein. These optional parameters are shown in tables 2 through 4 .

On the master card (see table 2), the units of measure should be specified and an error message will be given if they are specified erroneously (other than as type 1 or 2). However, the units code will default to 1 (the International System) and case execution will continue. The test section and atmospheric total pressures will default to one atmosphere if not specified.

On the section cards (see table 3), the number of items in the duct will default to unity if not specified. The expansion loss parameter for diffusers defaults to a value based on figure 4. (It is computed by determining the shape of each end, the extent to which the diffuser is two-dimensional in nature (i.e., changing cross-sectional size in height or width only), and the equivalent cone angle, and then interpolating between the curves of figure 4. See appendix A . ) an average-condition metal mesh screen (ref. 6, p. 527), and the reference Reynolds number for turning vanes defaults to 0.5 million (ref. 6, p. 527). The surface roughness for honeycombs defaults to the appropriate equivalent of 0.00001 my the value for new, commercially smooth, non-steel pipe (ref. 7, p. 62). The factor for the additional influence of a blockage on downstream sections ( A E ) defaults to zero.

The mesh screen loss constant defaults to 1.3, the value for

Diagnostic messages- There are a limited number of error diagnostic messages which were built in to handle many, but not all, of the potential user errors. The causes and appropriate corrections of these errors should be evident in each message.

1. Title card: If a card is in the position of a title card and does not begin with an asterisk as required, the following message will appear:

rnTrnT LLLLO m ('...(invalid title)...') IS IXCGRRECT GR IWROPER AS IT EXISTS. THE FIRST CARD COLUMN MUST CONTAIN AN ASTERISK (*) TO BE IDENTIFIED AS A VALID TITLE CARD.

2. Master card: An invalid master card is denoted by:

MASTER CONTROL DATA ('...(card image)...') IS INCORRECT OR IMPROPER AS IT EXISTS. THE FIRST TWO CARD COLUMNS MUST CONTAIN A NEGATIVE NUMBER (-1 TO -9) TO BE IDENTIFIED AS A VALID MASTER CARD. THIS CASE WILL BE SKIPPED.

A general omission from the master card of required information produces:

CRITICAL OMISSION(S) IN TUNNEL MASTER CONTROL DATA PREVENT EXECUTION OF THIS CASE. ANY SUCCEEDING CASES WILL NOT BE AFFECTED.

Two master cards, back-to-back, for a given case are identified by:

MORE THAN ONE MASTER CONTROL CARD EXISTS FOR THIS CASE OR INPUT CARDS ARE OUT OF ORDER. CHECK DECK SET-UP. THE LAST MASTER CARD ENCOUNTERED WILL BE ASSUMED AS THE CORRECT MASTER CARD FOR THE SECTION O S WHICH FOLLOW.

Encountering a master card where not expected (generally indicating missing case termination and title cards) causes this message:

MASTER CONTROL CARD HAS BEEN ENCOUNTERED BEFORE CASE TERMINATION AND TITLE CARDS. CHECK DECK SET-UP. ERROR-MESSAGE TITLE WILL BE GENER- ATED AND SUMMARY OUTPUT, NO-PLOT, INPUT DATA TABULATION, AND NEXT-CASE RETURN TERMINATION PARAMETERS WILL BE ASSUMED.

If an invalid test section upstream end shape geometry is specified, one which the program cannot handle, an error results:

**ERROR -- INVALID TEST SECTION UPSTREAM END SHAPE CODE WAS SPECIFIED AS (code used) (SHOULD BE 1, 2 OR 3). THIS CASE CANNOT BE EXECUTED.

If an invalid units code is specified the message is:

THE UNITS OF MEASURE CODE IS IMPROPERLY SPECIFIED AS (code used), (SHOULD BE 1 OR 2). CHECK MASTER CARD (COLUMN 4 ) . SEE THE DATA TABULATION AT THE END OF THIS CASE. THE INTERNATIONAL SYSTEM OF UNITS WILL BE ASSUMED FOR THIS CASE.

If the termination code requests power-matching but the input power value is such that the calculation would be meaningless, a diagnostic of the following form is printed:

**ALTHOUGH VELOCITY-OPTIMIZING WAS REQUESTED BY TERMINATION CODE, THE

NO VELOCITY-OPTIMIZING IS POSSIBLE. RECHECK INPUT VALUE ON MASTER INPUT POWER VALUE IS ILLEGAL (LESS THAN OR EQUAL TO ZERO). THEREFORE,

DATA CARD.

19

3. Section card: A general omission of required data from a section card will cause this message:

**ERROR -- CRITICAL OMISSION(S) I N SECTION INPUT DATA. SEE DATA TABULATION AT END OF OUTPUT FOR T H I S CASE.**

If an invalid section shape code is specified it is not possible for the program to properly compute section end geometries; as a result an error occurs :

**ERROR -- INVALID SECTION SHAPE CODE WAS SPECIFIED AS (input code) (SHOULD BE 1, 2 OR 3 ) . T H I S SECTION WILL BE SKIPPED.

An error which arises during computation and causes a non-positive total pressure loss for a given section prevents completion of the case analysis and gives rise to an error message:

**ERROR -- SOME INCORRECT COMBINATION OF INPUTS OR UNANTICIPATED SITUATION HAS CAUSED AN INVALID (NON-POSITIVE) TOTAL LOSS LEVEL. RECHECK SECTION (section number) INPUT DATA.

If the maximum allowable number of circuit sections written into the program is exceeded by placing too many section cards together in one case, or without termination, title, and master cards between cases, this diagnostic will appear:

MAXIMUM LIMIT ON THE NUMBER OF SECTIONS (...(maximum allowable number of section) ...) HAS BEEN REACHED. EITHER A CASE TERMINATION CARD HAS BEEN OMITTED (ALONG WITH TITLE AND MASTER CARDS TO BEGIN A NEW CASE) OR THIS CASE I S TOO LONG FOR THE PROGRAMMED ALLOWABLE NUMBER OF SECTIONS. THE CASE HAS BEEN TERMINATED AT THIS POINT.

In this instance, the inputs from the group of sections for which the limit was exceeded will be tabulated and the remaining section inputs will be evaluated and tabulated. I f the user fails to cause the test section blockage amounts specified on the master control card to coincide with that of the test section card, erroneous analysis may result since inconsistent flow areas would be calculated. The section card value will be used (since the discrep- ancy may be desired) and this notice is given:

**NOTE -- TEST SECTION BLOCKAGE FROM SECTION CARD INPUT (...(section input value) ... PERCENT) DOES NOT EQUAL THAT OF THE MASTER CARD INPUT (...(master input value) ... PERCENT). CHECK DATA DECK. SECTION CARD VALUE WILL BE ASSUMED AS CORRECT AND EXECUTION WILL CONTINUE.

An invalid section type code will cause a section to be skipped and a message to be printed:

*ERROR -- INPUT SECTION TYPE CODE (CARD COLUMNS 3 AND 4 ) CALLS INVALID SECTION TYPE. DATA CARD IGNORED.**

20

Any iiipilt errors were deemed justifiable came for judgment as an incmplete case. As a result, reliable overall and summary information cannot be calculated. To assist the user in locating the error(s), the input values will be forced to be tabulated and the following explanation appears:

A complete list of the test case inputs and computed information outputs are presented in figure 11. The machine computing time for this test case

, I (without plots) was about 7 sec on an IBM 360/67.

***DUE TO ERROR(S) IN INPUT CARD(S), VALID SUMMARY INFORMATION IS NOT AVAILABLE. REFER TO THE TABULATION OF INPUT DATA ON THE FOLLOWING PAGES. CORRECT THE ERROR(S) AND RESUBMIT THIS CASE. SUBSEQUENT CASES WILL NOT BE AFFECTED.

4 . Possible errors lacking diagnostics: Certain potential problem areas remain unprotected by diagnostic and error-recovery systems.

No special provision was made for two test sections in the same circuit case. from the master card, no message will be printed. In any event, the execution will not be terminated. The test section shapes and dimensions from the master card are not checked against those of the test section card. a mismatch of these values could cause a mass-flow error, including and enforcing such a check could inhibit any meaningful tandem-test section cases. These problems could be avoided, however, by naming only one working section as a test section and referring to the other by general type.

As long as the blockage values for both test sections match the one

Although

Also, there was no provision for checking the specified tunnel type against the types of sections actually used (e.g., checking a non-return, or open-test-section tunnel for exit or open-throat test section input cards). This check is not critical and was left to the user.

One error-check was not included due to the program complications which would have resulted. If a case termination card is omitted at the end of a case and a computer-system control card or a title card is encountered, the error will be disastrous due to mismatched format types. Execution and calculations will be immediately aborted by the computer.

Test Case

The NASA-Ames Research Center 40- by 80-Foot Wind Tunnel was used as an example of a typical wind tunnel. This tunnel, illustrated in figure 10, is of the single-return, closed-test-section, continuous-running type. It has a flat-oval test section 12.2 m (40 ft) high by 24.4 m (80 ft) wide and is powered by six 12.2-m (40 ft) diameter, six-bladed fans. It has an eight-to- one overall contraction ratio and uses multiple-circular-arc type turning vanes in each of the four 90' corners.

Although this test case was not an exhaustive exercise of all possible tunnel components, it does include most of the basic section types: diffusing test section, single-duct contraction and diffuser, constant-area single duct,

21

constant-area co rne r w i th t u r n i n g vanes, and mult iple-duct f a n s e c t i o n s ( c o n t r a c t i o n , constant-area annulus, and d i f f u s e r ) . Examples of o t h e r t ypes of components a r e shown i n t h e sample c a s e s which fol low.

DISCUSSION AND APPLICATIONS

Wind tunnel energy r a t i o , r equ i r ed power, and o p e r a t i n g v e l o c i t y are

The r equ i r ed d r i v e power, i n f luenced interdependent . of v e l o c i t y on t h e Reynolds number. d i r e c t l y by o p e r a t i n g v e l o c i t y and i n v e r s e l y by energy r a t i o , is a l s o con- t r o l l e d by t h e f a n system e f f i c i e n c y which i s o f t e n only an e s t ima ted q u a n t i t y . Any e s t ima te of o p e r a t i n g v e l o c i t y f o r a given power l e v e l i s , then, dependent on t h e bas i c e f f i c i e n c y of t h e c i r c u i t (energy r a t i o ) and d r i v e system e f f i - c i ency , assuming t h e b e s t power estimate a v a i l a b l e t o be t h a t d e l i v e r e d t o t h e f a n s . This interdependency means t h a t an e r r o r i n t h e p r e d i c t i o n of energy r a t i o (and/or i n t h e e s t ima t ion of f a n e f f i c i e n c y ) w i l l cause corresponding e r r o r s i n power and v e l o c i t y estimates.

The energy r a t i o is a f f e c t e d by v e l o c i t y through t h e e f f e c t

These e r r o r s r e s u l t i n g from an erroneous p r e d i c t i o n of t h e c i r c u i t energy r a t i o can b e found from t h e r e l a t i o n s h i p governing r e q u i r e d power, test sec- t i o n v e l o c i t y , and energy r a t i o , assuming given motor electrical and f a n e f f i c i e n c i e s . For a f i x e d test s e c t i o n v e l o c i t y ,

- 1 a P ~ ~ ~ ~ ~ ~ ~ - - 1 PREQUIRED 1 - - AER

ER

and, f o r constant power, an e r r o r i n energy r a t i o y i e l d s t h e performance p e n a l t y

1/3 - = AVO VO +-E)

The expected t r u e power and v e l o c i t y levels can thus b e ob ta ined from t h e performance estimate:

f o r a given set of test s e c t i o n c o n d i t i o n s , and from

1 / 3

"E s t i m a t e

f o r a given l e v e l of r equ i r ed power.

22

This adjustment of the estimated performance values is pointless for a known, existing wind tunnel, but necessary for new, or proposed facilities. Before the adjustment can be made the probable error in the energy ratio estimate must be determined. It is desirable, therefore, to consider several existing facilities of different circuit types in order to gain a degree of confidence in the performance estimation routine.

Results

The input parameters and output performance values for the several sample cases, other than the test case shown in figure 11, are compiled in appendix D. The estimated energy ratios for the seven sample wind tunnels are presented in table 6 . The corresponding sketches for all these sample tunnel circuits are shown in figures 10 and 12.

The actual energy ratios for the first three wind tunnels presented in table 6 were estimated from the best available information on fan and electrical efficiencies from known input power levels. The actual performance of the other four facilities was taken from measured data.

The test case and first sample case was the circuit of the NASA-Ames Research Center 40- by 80-Foot Wind Tunnel as described previously in the test case discussion. The predicted energy ratio for this rather conventional tunnel was only 1 percent higher than the actual value when new.

The performance of the NASA-Ames 7- by 10-Foot Tunnel was predicted at a slightly optimistic level. However, this tunnel is one with several known problems which complicate the prediction process. With the air exchanger operating, the primary diffuser is known to have some local flow separation, having been designed at a 6 O equivalent cone angle, an angle too great for its cross-sectional shape and length (see fig. 1). Also, the drive fan is stalled from the centerbody out to about 45 percent of the fan radius, causing some back-flow along the nacelle centerbody. efficiency has only been estimated; it was assumed that the fan efficiency would suffer by about an additional 10 percent.) In spite of these things, the predicted energy ratio was only about 3 percent too high relative to the original value of approximately 7.85, both values taken in the zero-air- exchange configuration. This agreement may indicate that much of the above- mentioned off-design performance is triggered by the air exchanger operation and is not as significant with the air exchanger closed. ent data are available to resolve this question, the fact remains that the prediction accuracy, for the stated conditions, was good.

(The impact of the stall on the fan

Although insuffici-

The Lockheed-Georgia Low-Speed Wind Tunnel employs a tandem test section design. For this analysis, the larger, V/STOL test section was used as the only reference station. Because of the two area restrictions to cross sections smaller than that of the reference area (those of the smaller test section and of the fan), the tunnel efficiency would be expected to be low. (This in no way reflects on the tunnel's usefulness as a research tool or on its design or capabilities. point of reference used in the calculations.) In other than these features

The ''low efficiency" value results only from the

23

the facility is basically of conventional design. performance prediction was in error by less than 2 percent from the true value of about 1.10.

The computerized

The Indian Institute of Science 14- by 9-Foot Tunnel at Bangalore stands out among non-return wind tunnels as a facility with an unusually high energy ratio. Although the determination of circuit dimensions for the program input was somewhat hampered by the limitations of small drawings, the estimated energy ratio was within 1 percent of the true facility value of 6.85. It is interesting to note that the fan performance data of reference 23 would indicate a fan design efficiency of about 69 percent. lations based on energy ratio and test section maximum velocity, however, show that the fan efficiency must be higher than was expected; in fact, greater than 90 percent.

The power requirement calcu-

The Hawker Siddeley 15-Foot V/STOL Tunnel at Hatfield, England was con- structed under economy constraints and is a compact, cost-effective facility. The estimated performance was about 1.6 energy ratios higher (i.e., more optimistic) than the actual value of 2 . 3 8 . This is an error of about 67 percent. The primary performance difference was probably caused by the fan system. The losses of the ducting in this area are difficult to predict because the area changes are not gradual and are even difficult to define.

The University of Washington 8- by 12-Foot Double-Return Tunnel has a surprisingly high measured energy ratio of 8 . 3 . carefully designed circuit powered by carefully designed fans. The performance estimate produced by the computer program is lower than the actual energy ratio by about 13 percent, showing that the achieved performance level is higher than would normally be expected.

This would indicate a very

The NASA-Langley Research Center 30- by 60-Foot Open-Throat Tunnel is unusual in configuration, having a double-return system with the twin fans located less than two fan-diameters downstream of the test section. The location of the data point for this tunnel on the diffuser design curves of figure 1 would not indicate that any diffuser-related problems should be expected forward of the fans. The diffuser between the fans and the first corner, however, does have a rather large equivalent cone angle (more than 8 ' ) . fans cause or contribute to diffuser flow problems (see the Cautionary Design Guidelines for Diffusers) and if those problems lead to corner flow ineffici- ency in a region critical to overall performance, then the circuit energy ratio may be well below the normal estimated level. Although it is not clear whether this is the case in the NASA-Langley 30-by60-Foot Tunne1,the performance estimate was about 27 percent higher than the actual value of about 3.71.

If the

Evaluation

To summarize what may be learned from the sample cases:

1. The Ames 40- by 80-Foot and 7- by 10-Foot Tunnels and the Lockheed- Georgia Low-Speed Tunnel, although at opposite ends of the energy ratio

24

spectrum, are all basically standard, single return, closed-test-section facilities; the computer program estimates of actual performance were good.

2. The Indian Institute of Science Bangalore tunnel, being of the non- return variety, is a different and less common type of facility; the computer program closely estimated its actual performance.

3 . circuit type; the program produced a reasonably accurate prediction of its performance.

The University of Washington double-return tunnel is a third major

4. examples of facilities which may have flow problems due to too-rapid area changes and, as a result, lower than optimum performance levels for their respective circuit types. For these tunnels, because of their flow quality and not because of their circuit types, the program provided a poor estimate of actual performance.

The Hawker Siddeley V/STOL and Langley 30- by 60-Foot Tunnels are

Based on these results one thing is immediately clear: the performance of a wind tunnel of conventional, conservative design can be evaluated accu- rately. On the other hand, the performance of a tunnel whose design generates or contributes to flow problems (separation or grossly non-uniform) will be overestimated by the loss equations and computer program.

Flow peculiarities and off-optimum designs, even though seemingly only slight, can cause operational performance to fall significantly below the predicted levels. Such problems can be expensive whether considered in terms of modifying the facility or in such terms as reduced testing capability and increased power costs. Judicious, iterative use of the estimation techniques presented in this report, simplified by computerized automation, can lead to the improvement of an existing facility through guidance of design changes or to the optimization of a proposed new wind tunnel design.

Ames Research Center National Aeronautics and Space Administration

Moffett Field, California 94035, January 8, 1976

25

~

APPENDIX A

1 NON-STANDARD FUNCTIONAL FORMS

I

I Local Flow-State Parameters

Due t o the nature of this analysis, certain of the local flow-state, section loss, and summary parameter formulas were used in a form more convenient than that usually found in the literature. altered or derived are outlined on the following pages.

The relationships which were

I Solv ing f o r the area for choked flow, knowing the test section area and Mach number ,

The calculation of several local parameters was based on the local Mach number, determined from the relationship between the local area and the area for choked flow:

v+l 2 ( Y - 1 ) + 1

2 [1+ (9 MO2)]

Mach nwnber- Another form of the same area relationship,

3%

can be rewritten to produce a polynomial equation in Mach number which may be solved by Newton's method if the areas are known:

y-l

M)9] +- 2 = Y - 1

26

ReynoZds number- The local Reynolds number was calculated based on other, known, local conditions and from basic principles:

m = - P u

(conservation of mass)

(ref. 18, p. 19)

(ref. 18, p . 4 )

Friction coefficient- The Reynolds number-friction coefficient function used was

- 1 = 2 loglo(RNfi) - 0.8 (ref. 6 , p. 70) fi

A Newton's method solution was performed on a rewritten form of the equation:

[log10(ARN2) - 0.8]-2 - X = 0

Section Pressure Losses

The losses for some types of sections were derived in forms not found in the literature. For others, a curve-fit of data points or a simplification of analysis was performed.

Corners (constant area)- The frictional and rotational losses through turning vanes are additive: K = K~ICTION + KROTATION. Also,

Assuming that the frictional loss value has a form similar to that for a flat plate, then at 90":

(ref.6, p.527) - 0.455B - 1 KFRICTION = 7 K T V ~ ~

RN) Z 58 (1ogl0

27

Thus, t h e cons t an t B i s dependent on t h e t u r n i n g vane l o s s cons t an t and t h e r e f e r e n c e Reynolds number a t which t h a t cons t an t w a s determined:

2.58 1 7 KTVgO(log10 RNREF)

0.455 B =

Therefore , I 1 log lo RNREF

KFRICTION = 7 KTVgO ( loglo RN

Since t h e r o t a t i o n a l term i s assumed independent of Reynolds number, KROTATION = (2/3)KTvgo. t i o n w i t h t u r n i n g ang le i s p resen ted i n f i g u r e 3 f o r a l o s s parameter a t 90' equa l t o 0.15. r e f e r e n c e l o s s c o n s t a n t s i s l i n e a r :

The a d d i t i o n a l complicat ion of l o s s parameter varia-

It w a s assumed t h a t t h e r e l a t i o n s h i p between t h e a c t u a l and

where f ( $ ) i s t h e f u n c t i o n a l r e l a t i o n s h i p p l o t t e d i n f i g u r e 3. t u r n i n g vane l o s s f u n c t i o n then becomes

The complete

Corners (diffusing)- Dif fus ing c o r n e r s were t r e a t e d as vaned d i f f u s e r s The wi th t h e a d d i t i o n of r o t a t i o n a l l o s s e s dependent on t h e t u r n i n g angle .

expansion and f r i c t i o n a l l o s s e s used were those f o r a vaned d i f f u s e r :

The r o t a t i o n a l l o s s i s as f o r a constant-area co rne r where I 2 -

KROTATION - 7 KTv =

The d i f f u s i n g co rne r l o s s func t ion i s then

where u(28 - 21.5') is t h e u n i t s t e p func t ion .

28

,R*fft?aers- The diffuser lmses are due to both friction and expansion. The friction term may be derived theoretically from

Making the simplifying assumptions that the density and the friction coefficient are approximately constant and applying conservation of mass,

which, for a conical diffuser, becomes

KFRICTION - - ,2

and transforming variables from surface to centerline distances,

dx

Completing this integration the friction loss becomes

The influence of the expansion term is given by

K = KEXPANSION + KFRICTION

Thus, it may be rewritten:

(1 - KEXPANSION + KFRICTION K =

29

The expansion loss parameter curves shown in figure 4 were determined using the approximation

K - KFRICTION (CONICAL) '>' =

and figure 5(a) of reference 9, which shows complete diffuser losses plotted as functions of equivalent cone angle and independent of area ratio for circular, square and rectangular, and two-dimensional diffusers. assumption that the expansion part of the losses is dependent only on cross- sectional shape, the extent to which the diffusion takes place in only one direction, and the equivalent cone angle.) diffusers is given as

(This implies an

Thus, the complete loss for

using KED from figure 4 .

Exit- The kinetic energy loss at an exit of a non-return wind tunnel was derived from basic compressibility relationships and with the assumptions that the exit flow static pressure is equal to the atmospheric pressure and that the exit velocity is uniform.

Rewriting, the local total pressure is V

(rewritten fromref.17,p.53)

Also, since ApT = pT - - - p, the total loss parameter is PTATM - PT

since

I 1 = 2 pv2 = - 2 YPM2 (ref.17,~. 55)

Simplifying, the exit loss becomes

F Z m straighteners: a i r f o i l members (thick)- Thick flow straightener losses were assumed to be made up of two parts: diffusion:

contraction and subsequent

The contraction was estimated as being about 30 percent of the length of the straighteners:

0.32h (0.30L) Dh

KCONTRACTION =

The diffusion portion was based on the aft 70 percent of the length and on the exit and minimum areas for the computation of the area ratio and equivalent cone angle. As for a vaned diffuser,

Hence the l o s s for thick flow straighteners becomes

31

Internal flow obstruction: drag item- The loss due to internal structure may be derived from the relationships governing power losses:

K~~~~ P 0 2 ~ 0 ~ 0 3

2pF - - P I N P U T ~ ~ G

and PDWG = tional effec becomes

DVE = (1/2)pv3scDE, where E is the factor accounting for addi- ts on downstream sections. Since PIN PUT^^^ = PDMG, the loss

and therefore

Since in general the flow density at the fans is unknown at the time a given section l o s s is calculated, and since for incompressible flow the density ratio is unity, the ratio of the densities at the fan and the local station was assumed as unity for the analysis. an assumption, an approximation of the ratio may be made by way of a change in the downstream influence factor E.) The loss due to a flow obstruction is

(If the user prefers not to make such

Vaned d i f fusers - The expansion and friction losses for vaned diffusers were combined into one parameter which is reasonably independent of area ratio and is presented in figure 6 . The loss curves shown were approximated by a two-segment, straight-line curve fit so that, for vaned diffusers

where u(28 - 21.5') is the unit step function.

Loss value transferred t o reference location- The change of reference for l o s s values is defined as

32

Using the law of conservation of mass, this may be rewritten in terms of areas and Mach numbers:

1 pv2 AoV a = = -

Qo - 1 p V 2 AVO 2 0 0

and

Wall pressure differential- The pressure across a section of wall was determined from the exterior atmospheric pressure, internal static pressure, and cumulative pressure losses through the circuit. Since the wall pressure differential for a given section is Apwi = p~~~~ - pi and

PT:

and, using the test section as the reference location,

The wall pressure differential may be written as

33

Input power required- The power inpu t t o t h e flow r e q u i r e d f o r o p e r a t i o n of a wind tunne l c i r c u i t having predetermined l o s s e s w a s c a l c u l a t e d from t h e p r e s s u r e rise requ i r ed a t t h e f a n s , w i th t h e s impl i fy ing assumption t h a t t h e s t a t i c and t o t a l p r e s s u r e rises a c r o s s t h e f a n are equal .

Fp oAovo PINPUT = APT~AFVF PFPoAoVo

Considering conse rva t ion of mass,

Also, N

Thus,

34

APPENDIX B

NUMERICAL FUNCTION-APPROXIMATIONS

The formulas t h a t fo l low r e s u l t e d from c u r v e - f i t t i n g and/or i n t e r p o l a t i o n techniques a p p l i e d t o c e r t a i n func t ions a r i s i n g from t h e l o s s a n a l y s i s .

Corners

The co rne r loss parameters f o r corners w i th and wi thout t u r n i n g vanes are shown i n f i g u r e 3. c u r v e - f i t t i n g techniques, t h e t u r n i n g vane l o s s f u n c t i o n of f i g u r e 3(a) becomes, f o r 0" I 8 I 30":

For a corner wi th vanes, u s ing l eas t - squa res polynomial

KTV = 1.395066X10-2 + 5 . 6 7 2 6 4 9 ~ 1 0 - ~ (8

+7.081591~10 '~ g2 + 1 . 3 9 4 6 8 5 ~ 1 0 - ~ g3

-4. 885101X10-8 O4 (B1)

and f o r 30" < 8 I 90":

KTV = -1.605670X10-1 4- 1.446753X10-2

-2 .570748~10-~ d2 + 2 . 0 6 6 2 0 7 ~ 1 0 - ~ g3

-6.335764~10-' d4 032)

For a corner without t u rn ing vanes t h e l o c a l l o s s f u n c t i o n of f i g u r e 3(b) w a s found us ing a leas t - squares polynomial technique and is given by

K = 4 . 3 1 3 7 6 1 ~ 1 0 - ~ - 6 . 0 2 1 5 1 5 ~ 1 0 - ~ 8

+1 .693778~10-~ a2 - 2.755078~10+ 83

+2 .323170~10-~ f14 - 3 . 7 7 5 5 6 8 ~ 1 0 - ~ g5

+1.796817~10-~ ' f16 (B3)

For a l l t h e above equat ions , 8 i s t h e flow tu rn ing ang le i n degrees .

D i f fuse r s

The de termina t ion of t h e d i f f u s e r l o s s parameter i s a complex opera t ion . It depends on t h e c ros s - sec t iona l shape and equ iva len t cone ang le of t h e sec- t i o n . For a c o n i c a l d i f f u s e r t h e expansion func t ions a r e , f o r 3' L 20 I 10':

35

= 1. 70925x10-1 - 5. 84932X10'2 (20) KEXPCircular +8 .14936~10 '~ (20)2 + 1 . 3 4 7 7 7 ~ 1 0 - ~ (20)3

- 5 . 6 7 2 5 8 ~ 1 0 - ~ (20) - 4 . 1 5 8 7 9 ~ 1 0 - ~ (20)

+ 2 . 1 0 2 1 9 ~ 1 0 - ~ (20) 034)

for 0" < 20 < 3":

= 1 . 0 3 3 3 9 5 ~ 1 0 - ~ - 1 . 1 9 4 6 5 ~ 1 0 - ~ ( 2 0 ) (B5 1 K E n c ir cu 1 ar and for 28 > 10":

= - 9 . 6 6 1 3 5 ~ 1 0 - ~ + 2 . 3 3 6 1 3 5 ~ 1 0 - ~ (20) (B6) KEXPCir cular For a square cross-section diffuser the expressions are, for 3" I 2 0 I 1 0 " :

= 1 . 2 2 1 5 6 ~ 1 0 ' ~ - 2 . 2 9 4 8 0 ~ 1 0 - ~ (20) KE*Square

+ 5 . 5 0 7 0 4 ~ 1 0 - ~ ( 2 € 1 ) ~ - 4 . 0 8 6 4 4 ~ 1 0 - ~ ( 2 0 )

- 3 . 8 4 0 5 6 ~ 1 0 - ~ (20) + 8 . 7 4 9 6 9 ~ 1 0 - ~ (20)

- 3 . 6 5 2 1 7 ~ 1 0 - ~ (20) (B7 1

for 0" < 20 < 3":

= 9 . 6 2 2 7 4 ~ 1 0 ' ~ - 2 . 0 7 5 8 2 ~ 1 0 ' ~ (20) (B8) KExp square

and for 28 > 10":

= -1 .321685~10 '~ + 2 . 93315X10-2 (20) 0 9 ) KEXPSquare

For a two-dimensional diffuser with a square upstream-end cross section the expansion l o s s functions are, for 3" 5 20 I 9":

= 3.23334~10-1 - 5. 82939X10'2 (20) KEXP 2DRectangular

-4 .97151~10 '~ (20) + 1 . 9 9 0 9 3 ~ 1 0 ' ~ (20)

- 1 . 9 8 6 3 0 ~ 1 0 - ~ (20)4 + 2 . 0 6 8 5 7 ~ 1 0 ' ~ (2015

+3.81387~10+ (20) 15 (BIOI

= 5.72853 - 1.21832 (20) KEXP 2DRec tangular

+7 .08483~10 '~ (20)

36

= 1.0~10-~ - 5.333333~10'~ (29) KEXP2DRec t angular

and for 28 > 10':

Since the expansion function for a two-dimensional diffuser with circular sides was not given (and is not defined), it was assumed for computational purposes that this value would be the same fraction of that for a two- dimensional rectaFlgular diffuser as the loss of a conical is of that for a three-dimensional square diffuser:

KEXP 2DRec t angular - -

2% ir cul ar KEXP

For cross-section shapes somewhere between rectangular and circular, such as flat oval (flat ceiling and floor with semi-circular sidewalls), or for diffusers which have one end rectangular and one end either circular or flat oval, a loss value between that for circular and rectangular may be more appropriate; thus ,

'"Circular KEXP + KEXI? - 2DRec t angular -

K EXP2DAverage 2

and

- - KEaSquare + KEmCircular KEXP DAverag e 2

The extent to which a diffuser is planar in nature was computed from the ratio of the changes in size of the two characteristic dimensions from end to end :

h2 - h l or w2 - w1 h2 - hl 6, = smaller of

w2 - w1

or if the ratio is negative,

6, = 0 Then, based on the geometries of each end, the basic loss constant, KEDBasicy

and the addi- may be selected Erom K E X P ~ ~ ~ ~ ~ ~ ~ ~ , KEXP 3DAverage or KEmSquare tional l o s s fact. may be selected from the corresponding KEXPAdditional '

37

. F i n a l l y , t h e a p p l i c a b l e 2DRec t angu la r

Or 2DAverage 3 KEXP

2% i r c u ~ ar KEXP

d i f f u s e r expansion loss c o e f f i c i e n t i s g iven by

Mesh Screen

The mesh sc reen Reynolds number s e n s i t i v i t y f a c t o r p l o t t e d i n f i g u r e 5 can be expressed i n f u n c t i o n a l form as, f o r 0 I RJ < 400:

78.5(1 - 7s~;) RN

+ 1.01 100 Km =

and f o r RN 1 4 0 0 :

Vaned D i f f u s e r s

The vaned d i f f u s e r loss c o e f f i c i e n t func t ions p l o t t e d i n f i g u r e 6 were approximated by two l i n e segments; f o r 28 < 21.5':

Kv = 0.3

and for 21.5' L 28 I_ 90':

K, = 0 . 3 + [0.006(28 - 21.5')] Thus, over t h e e n t i r e range of equ iva len t cone ang le s of i n t e r e s t ,

K, = 0.3+ [0.006(28 - 2 1 . 5 ' ) ~ ( 2 8 - 21.5'11

where u(28 - 21.5') i s t h e u n i t s t e p func t ion .

38

!l??E?!DIX c

COMPUTER PROGRAM FdRTRAN CODES

The following pages contain the F8RTRAN codes developed to implement the wind tunnel performance analysis techniques presented in this report.

The Notation section explains the variable names used in the program. (Note that in the notation sections, as throughout this report, all letter 0 ' s occurring in FflRTRAN names are shown with slashes, as 8 ; all number zeros are shown unslashed.) symbols presented in the main body of the report, but this section was changed in two respects. name. Second, it was expanded to include many variable names which were not used elsewhere and which have significance only in the context of the computer program. The "titles" shown in parentheses in the first column of this notation section are column heading titles which appear on the program output pages.

This notation section is similar to that for engineering

First, it was rearranged alphabetically by F8RTRAN variable

Immediately following the Notation are the listings of the six actual FORTRAN program codes: (DATACK, SPEED, FRICTN, OUTPUT, AND PL8TIT). Each program routine page is titled and numbered for clarity. The last seven columns of each line on each page contain a two-letter program routine name abbreviation and a line sequence number (in ten-count increments). Thus, the user can know at a glance to which routine (and where within that routine) any given line or instruction belongs. Each instruction line in the program is uniquely identified.

the main program (PERF8RM) and the five subroutines

39

NOTATION (FflRTRAN)

F~~RTRAN name and/or (title)

A

A I 1

A I 2

AL

AMACH

AMACHl (MACH1)

AMACH2 (MACH2)

AR (AR, CR)

ASL

ASTAR

A S 0

AT

AVGPWR

A 0

A 1 (AREA1)

40

Engineering symbol Description

A cross-sectional area of local section, m2 (ft2)

AFLOW

M

AR

cross-sectional area of individual duct at upstream end, m2 (ft2)

cross-sectional area of individual duct at downstream end, m2 (ft2)

cross-sectional area of local flow, m2 Ut2)

local Mach number

Mach number at section upstream end

Mach number at section downstream end

ratio of cross-sectional areas at upstream and downstream ends of section

speed of sound in moving flow at local section, m/sec (ftlsec)

cross-sectional area for sonic flow at specified flow conditions, m2 (f t2)

speed of sound in moving flow at upstream end of test section, m/sec (ft/sec)

speed of sound in still gas, computed at total (stagnation) conditions, m/sec (f t/sec)

average power consumed by each drive fan at specified conditions: PWR(?JP/ENFAN, w (hP)

cross-sectional flow area of test section at upstream end, m2 (ft2)

cross-sectional flow area of section at upstream end, m2 (ft2)

F@RT” R ~ U Y A n1 name and/or (title)

Alt8AO (Al/AO)

A2 (AREA2)

A20AO (A2/AO)

BLKAGE

(BLKGE)

CD

CH#RD

D

DATA

DELP

(D EPS)

DFAN

DH

DHL


ratio of local section upstream area to test section area, m2 (ft2)

A2

CD

cV

D

APWi

AE

Dh

cross-sectional flow area of section at downstream end, m2 (ft2)

ratio of local section downstream area to test section area, m2 (ft2)

blockage to flow in local section (at upstream end for all applicable sections except fan contraction, for which it is at downstream end), fraction of local area

blockage to flow in local section (at upstream end for all applicable sections except fan contraction, for which it is at downstream end), percent of local area

drag coefficient of flow obstruction,

chord of turning vanes, m (ft)

diameter of circular duct, m (ft)

data array of master, section, and termination card floating-point inputs

local pressure difference across wind tunnel wall, N/m2 (lb/ft2)

increment of flow-obstruction downstream influence factor greater than unity: E - 1, (greater than or equal to zero)

drive fan diameter, m (ft)

hydraulic diameter: 4 x (cross-sectional area)

perimeter ¶ m (ft)

hydraulic diameter of single cell in flow straightener, m (ft)

41

F ~ R T R A N name and/or (title)

DHUB


diameter of drive fan hub and/or spinner, m (ft)

DHO

DH1

DH2

DMESH

D1

D2

EKADD

EKBASE

EKC

EKCNTR

EKCSAV

EKD

EKEXP 1

K

hydraulic diameter of test section, m (ft)

hydraulic diameter of upstream end of local section, m (ft)

hydraulic diameter of downstream end of local section, m (ft)

diameter of mesh element in woven-mesh screen, m (ft)

diameter of upstream end of circular section, m (ft)

diameter of downstream end of circular section, m (ft)

local total pressure loss of section:

KEXPAddit ional

KEXP 3DAverage

KD I FFU s ION

additional diffuser expansion l o s s factor due to more diffusion in one plane than in another (i.e., partially two- dimensional diffusion)

basic diffuser expansion loss factor for purely three-dimensional diffusion

expansion l o s s value for conical diffusers

local total pressure loss from contracting portion of thick-airfoil flow straighteners

estimated expansion loss coefficient for three-dimensional, combination circular and square cross-section diffuser

local total pressure loss from diffusing portion of multi-loss-type sections

net expansion l o s s coefficient for diffusers

42

F~RTRAN and/or (title)

EKMESH (KMESH)

EKS

EKSTRT

EKTE

EKTE90 (KT 90)

EKTV

EKTV90 (KT 90)

EKV

EKi

EK2

EK2DC

EK2DCS

Engineering symbols Description

KMESH mesh screen-type loss constant

expansion loss value for three- dimensional expansion in square cross- section diffusers

KE*Square

KO

local total pressure loss coefficient due to strut drag in fan section

local total pressure loss parameter for corners without turning vanes

vaneless-corner loss parameter for given corner at a 90" turn

turning vane loss coefficient

turning vane loss parameter for given vanes at a 90" turn

local total pressure loss coefficient for vaned diffusers

section total pressure loss referred to

test section conditions: - q0

local cotal pressure loss coefficient due to diffusion and vanes in a diffusing corner

local total pressure loss coefficient due to rotational flow in a diffusiing corner

estimated expansion loss coefficient for KEXP2~C ir c ular hypothetical, two-dimensional diffusion

with circular sides :

KEXP c ir cular 2DRectangular

K E D

estimated expansion loss coefficient for

section shape of some square/circular hybrid

KEXP2DAverage two-dimensional diffuser with cross-

4 3

NRTRAN name and/or (title)

EK2DR

Engineering symbo 1 Description

expansion loss coefficient for two- dimensional rectangular cross-section diffusers

2DRectangular KEXP

centerline length of section, m (ft) EL (L)

ELC

L

length of contracting portion of thick- airfoil flow straighteners, m (ft)

length of diffusing portion of thick- airfoil flow straighteners, m (ft)

ELD

length-to-hydraulic-diameter ratio of flow straightener cell

EMDH (L/DH)

EMDATA data array containing master-card floating-point inputs

Mach number at the fan section EMF

EMU

EMUSTD

flow viscosity, N sec/m2 (lb sec/ft2) lJ

pstd standard-day value of viscosity, N sec/m2 (lb sec/ft2)

reference viscosity at a known temperature, computed for a still gas (stagnation conditions), N sec/m2 (lb sec/ft2)

EMUT lJT

EMWRIT master card output array containing data and/or annotation(s)

Mach number at upstream end of test sect ion

EM0 MO

data array containing section-card floating-point input

ENDATA

ENDUCT

ENFAN

ENITEM

number of ducts in multiple-duct sections

number of fans in fan drive section

number of drag or blockage items in each local duct

kinematic viscosity of gas, m2/sec ( f t /set)

ENU V

44

FgRTRAN name and/or (title)

ENWRIT

EPS

ER

ETAFAN (ETA)

ETWRIT

FAC

FACT

FAF0

FAR

FDHC

FDHF0

FDHR

FEKC

FEKCH

Engineering system Description

section-card output array containing data and/or annotation(s)

E:

ER

flow-obstruction downstream influence factor (greater than or equal to unity)

energy ratio: ratio of energy of flow at test section to the output energy of the fans

fan aerodynamic efficiency, percent

case termination-card output array containing termination request de-codings

function defining the area of sections with circular cross sections

scaling factor for plot size

function defining the area of sections with flat-oval cross sections (flat floor and ceiling, semi-circular walls)

function defining the area of sections with rectangular cross sections

function defining the hydraulic diameter of sections with circular cross sect ions

function defining the hydraulic diameter of sections with flat-oval cross sections

function defining the hydraulic diameter of sections with rectangular cross sections

function defining the diffuser expansion loss for three-dimensional, circular cross-section diffusers

function defining the diffuser expansion loss for three-dimensional, circular cross-section diffusers at high diffusion angles (TH2 > 10')

A - 5 9 4 4 45

F@RTRAN name Engineering and/or (title) system Description

FEKCS function defining the diffuser expansion loss for three-dimensional, circular cross-section diffusers at small diffusion angles (TH2 < 3')

FEKS

FEKSH

FEKS S

FEKO

FEK2DL

FEK2DU

FKTE

FKTVl

K T V 2

FTH

f (0)

f (0)

function defining the diffuser expansion l o s s for three-dimensional, square cross-section diffusers

function defining the diffuser expansion loss for three-dimensional, cross- section diffusers at high diffusion angles (TH2 > 10")

function defining the diffuser expansion loss for three-dimensional, square cross-section diffusers at small diffusion angles (TH2 < 3')

function defining the change-of-reference station for total pressure losses from local section to test section

function defining "two-dimensional" (rectangular) diffuser expansion loss for low diffuser angle range (TH2 < 9")

function defining "two-dimensional" (rectangular) diffuser expansion l o s s for high diffuser angle range ( T H 2 2 9 ' )

function defining corner turning loss parameter EKTE for corners without turning vanes (based on a value of EKTE = 1.80 at P H I = 90")

function defining turning vane loss parameter EKTV (based on a value of EKTV = 0.15 at P H I = 90") for lower turning angle range (PHI I30")

function defining turning vane loss parameter EKTV (based on a value of EKTV = 0.15 at P H I = 90") for upper turning angle range (30" < P H I I 90")

function converting diffuser equivalent cone angle, TH2, in degrees to half- angle, THY in radians

46

n A ryJRTRAN naiiie and/or (title)

FTH2

G

H1

H2

IFLAG

IPL0T

IPRINT

ISEC

ISEQ

ISHAPl

I SHAF' 2

ITITLA

ITITLE

1 T U " L

ITYPE

IU

LINEMX

LMTSEC

Y

hl

h2

E- r r : -A,.-.. l15LllccL ing symbol Description

function defining diffuser equivalent cone angle, TH2

specific heat ratio of gas

height at the upstream end of a non- circular section

height at the downstream end of a non- circular section

parameter indicating the sequence number assigned to the fan section

decision parameter for selecting which (if any) plots are to be plotted

decision parameter for requesting or omitting output of summary characteristics page

section type-description code

input section sequence number

section upstream-end cross-sectional shape code

section downstream-end cross-sectional shape code

assumed case-title array in the event the title card is omitted

input case-title array

wind tunnel circuit-type code

code for type of output format required for printing section information

units-of-measure type code

maximum number of output lines per page

limit for maximum number of sections in any given case

47

F~RTRAN name and/or (title)

MCHECK

MDATA

MF#RMT

MWRITE

N

NCHECK

NDATA

NF#RMT

NN

NWRITE

P

PA

PHI

PI

PRSTY

PT

PWRI

Engineering system Description

master-card input-requirement checking code array

N

’TATM

PT

master-card integer input data array

master-card output format array

master-card output array containing data and /or anno tat ion (s)

section assigned sequence number for order of occurrence in circuit

section-card input-requirement checking code array

section-card integer input data array

section-card output format array

section type number for printing proper section title

section-card output array containing data and /or annot at ion ( s)

input tunnel total (stagnation) pressure, standard atmospheres

input atmospheric (barometric) pressure, standard atmospheres

atmos heric (barometric) pressure, N/m Y (lb/ft2)

corner flow turning angle, deg

ratio of the area of a circle to the square of its radius

porosity of certain non-solid flow obstructions: AL/A

tunnel total (stagnation) pressure, N/m2 (lb/f t2)

decision parameter for requesting or omitting the matching of power consumption with given input value

48

F$RT?AY name Engineering and /o r ( t i t l e ) system Desc r ip t ion PWRIP power r equ i r ed t o be i n p u t t o f low i n

order t o d r i v e wind t u n n e l a t s p e c i f i e d speed, W (hp)

PWRMCH

PwRdP

QO

RHdSF

R H ~ S O

RHdT

RN

RNREF

RNV

RUFNES

(RUFNES)

SEKO

R

P

PF

P O

PT

RN

R N ~ ~ ~

t o t a l power va lue f o r which t h e maximum test s e c t i o n v e l o c i t y is t o b e d e t e r - mined ( i f r eques t ed ) , W (hp)

t o t a l f a n motor output power r equ i r ed t o d r ive wind tunne l a t s p e c i f i e d speed, w (hP)

t e s t s e c t i o n upstream-end dynamic

pressure: , N/m2 ( l b / f t 2 ) povo2 2

gas cons t an t , m2/sec2 OK ( f t 2 / s e c 2 OR)

l o c a l s t a t i c d e n s i t y , N sec2/m4 ( l b s e c 2 / f t 4 )

s t a t i c d e n s i t a t t h e f a n s , N sec2/m4 ( l b sec2/ f t r )

s t a t i c d e n s i t y a t u stream end of test s e c t i o n , N sec2/m t ( l b s e c 2 / f t 4 )

dens i ty computed f o r t o t a l ( s t a n a t i o n ) cond i t ions , N sec2/m4 ( l b sec 8 / f t 4 )

Reynolds number : pVR u

r e fe rence Reynolds number a t which turn- i ng vane 90°-loss cons t an t , EKTV90, was determined

Reynolds number f o r t u r n i n g vanes based PVCV

on vane chord: - u

surface roughness i n honeycomb cel ls , m ( f t )

surface roughness i n honeycomb ce l l s , 10-6 m (10-6 f t )

s ec t ion t o t a l p r e s s u r e l o s s a r r a y ( r e f e r - enced t o t es t s e c t i o n cond i t ions ) used i n summary c a l c u l a t i o n s

49

F~RTRAN name Engineering and/or (title) symbol

SEL

SERRgR

SLAMDA

SLMDAE

SLMDAl

SLMDA2

SLR

SMACH

SSUMEL

SSUMKO

SUMEKO

SUMEL

T

TH

50

N c KO; I i= 1

5 Li i= 1

0

Description

section centerline length array used in summary calculations, m (ft)

section input error occurrence code

friction coefficient for smooth pipes

calculated friction coefficient in test section at the requested power-matching condi.tion

friction coefficient at section upstream end

friction coefficient at section downstream end

diffuser side length ratio: ratio of change in height to change in width from upstream to downstream end, or its inverse, whichever is less than or equal to unity

section downstream-end Mach number array used in summary calculations

ratio of flow-obstruction drag area to local flow area

summation array of total centerline length from start of circuit to end of local section

summation array of total pressure losses from start of circuit to end of local section

summation of all section total pressure losses referenced to test section conditions

summation of all section centerline lengths (total circuit flow length), m (ft)

tunnel total (stagnation) temperature, *C (OF)

diffuser half-angle, rad

F(?!?.T?AA r?aEe and/or (title) TH2 (2 THETA)

T L I S T

T L I S T I

TRETRN

TSBLKG

TT

V

voc

VOK

v1

v2

w1

w2


28 diffuser equivalent cone angle, deg

TT

V

W1

w2

case-fatal error occurrence code

decision parameter for requesting or omitting tabulation of input data

decision parameter for requesting return for additional case or final termination

test section blockage used for computation of basic test section conditions, percent of test section cross-sectional area

tunnel total (stagnation) temperature, OK (OR)

local flow velocity, m/sec (ft/sec)

calculated test section velocity at adjusted power level, m/sec (ft/sec)

test section flow velocity at input conditions, knots

section upstream-end flow velocity, m/sec (ft/sec)

section downstream-end flow velocity, m/sec (ft/sec)

width of upstream end of non-circular section, m (ft)

width of downstream end of non-circular section, m (ft)

51

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INPUT AND OUTPUT FOR SAMPLE CASES

Six wind tunnels were used, in addition to the test case (fig. ll), as I

sample cases to establish the reliability and accuracy of the computer program analysis technique for the various types of duct components and wind tunnel circuits. Each case included here is titled with the appropriate wind tunnel name and its pages are numbered. The performance analyses are presented on the first two to three pages of each case. The summary characteristics tabulations and the plotted information were omitted. The annotated tabulations of the input data were included for reference.

The results of the performance analyses are summarized in table 6 . They are discussed and critiqued in the Results and Evaluation sections of this report.

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REFERENCES

1. McDonald, Alan T.; and Fox, Robert W.: Incompressible Flow in Conical Diffusers. Tech. Rep. No. 1, Army Research Office (Durham), Project No. 4332, 1964. (Available from Armed Services Technical Information Agency, U.S. Department of Defense.)

2. Reneau, L. R.; Johnston, J. P.; and Kl.ine, S. J.: Performance and Design of Straight, Two-Dimensional Diffusers. Trans. ASME, Journal of Basic Engineering, Vol. 89, March 1967, pp. 141-150.

3 . Rouse, Hunter; and Hassan, M. M.: Cavitation-Free Inlets and Contrac- tions. Mechanical Engineering, Vol. 71, March 1949, pp. 213-216.

4. Pope, Alan; and Harper, John J.: Low-Speed Wind Tunnel Testing. John Wiley & Sons, Inc., N. Y., 1966.

5. Pankhurst, R. C.; and Holder, D. W.: Wind-Tunnel Technique. Sir Isaac Pitman & Sons Ltd., 1952.

6 . Wattendorf, Frank L.: Factors Influencing the Energy Ratio of Return Flow Wind Tunnels. Fifth International Congress for Applied Mechanics, Cambridge, 1938, pp. 526-530.

7. Idel’chik, I. E.: Handbook of Hydraulic Resistance. AEC-TR-6630, The Israel Program for Scientific Translations Ltd., 1966. (Available from Clearinghouse for Federal Scientific and Technical Information, U.S. Department of Commerce. )

8. KrEber, G.; (translated by Dwight M. Miner): Guide Vanes for Deflecting Fluid Currents With Small Loss of Energy. NACA TM-722, 1933. (Transl. into Engligh of “Schaufelgitter zur Umlenkung von Fliissigkeitsstromungen mit geringem Energi everl.ust ) ” TngPnieur--Arkiv, Vol - 3, 1932, pp. 516-541.)

9. Henry, John R.; Wood, Charles C. ; and Wilbur, Stafford W.: Summary of Subsonic-Diffuser Data. NACA RM L56F05, 1956.

10. Moore, Carl A., Jr.; and Kline, Stephen J.: Some Effects of Vanes and of Turbulence in Two-Dimensional Wide-Angle Subsonic Diffusers. NACA TN 4080, 1958.

11. Cochran, D. L . ; and Kline, S. . J . : I J se of Short Flat Vanes for Producing Efficient Wide-Angle Two-Dimensional Sub-sonic Diffusers. NASA TN 4309, 1958.

12. Wallis, R. A. : Axial Flow Fans. Academic Press , N. Y. , 1961.

13. Chmielewski, G . E.: Boundary-Layer Considerations in the Design of Aero- dynamic Contractions. J. o f Aircraft, Vol. 11, No. 8, Aug. 1974, pp. 435-438.

14 2

14. Eckert, William T.; Mort, Kenneth W.; and Piazza, J. E.: Wind- Sensitivity Studies of a Non-Return Wind Tunnel With a 216- by 432-mm (8.5- by 17.0-in.) Test Section - Phase I. NASA TM X-62,171, 1972.

15. Eckert, William T.; Mort, Kenneth W.; and Piazza, J. E.: Wind- Sensitivity Studies of a Non-Return Wind Tunnel With a 216- by 432-mm (8.5- by 17.0-in.) Test Section - Phase 11. NASA TM X-62,307, 1973.

16. Mort, K. W.; Eckert, W. T.; and Kelly, M. W.: The Steady-State Flow Quality of an Open Return Wind Tunnel Model. Space Journal, Vol. 18, No. 9, Nov. 1972, pp. 285-289. (Also NASA TM X-62,170, 1972.)

Canadian Aeronautics and

17. Liepmann, H. W.; and Roshko, A.: Elements of Gasdynamics. John Wiley & Sons, Inc., N. Y., 1957.

18. Staff of Ames Research Center: Equations, Tables, and Charts for Compressible Flow. NACA Report 1135, 1953.

19. Sovran, Gino; and Klomp, Edward D.: Experimentally Determined Optimum Geometries for Rectilinear Diffusers with Rectangular, Conical or Annular Cross-Section. Fluid Mechanics of Internal Flow, Gin0 Sovran, ed., Elsevier Publishing Co., Amsterdam, 1967, pp. 270-319.

20. Annon: Low-Speed Wind Tunnel User Manual. Lockheed-Georgia Company, ER-11,000, 1970.

21. Krishnaswamy, T. N.; Ramachandra, S. M.; and Krishnamoorthy, V.: Design and Characteristics of the 14' x 9' Open Circuit Wind Tunnel. Proc. of the 11th Seminar on Aeronautical Sciences, National Aeronautics Lab., Bangalore, 1961, pp. 417-434.

22. Krishnaswamy, T. N.: Selection of the Electric Drive for the 14' x 9' Wind Tunnel. Journal of the Aeronautical Society of India, Vol. 7, No. 2, May 1955, pp. 19-28.

23. Krishnaswamy, T. N.; and Ramachandra, S. M.: Fan System of the 14' x 9' Open Circuit Wind Tunnel of the Indian Institute of Science. of the Aeronautical Society of India, Vol. 18, No. 2, May 1966,

Journal

pp. 47-61.

24. Kirk, J. A.: Experience With a V/STOL Tunnel. Journal of the Royal Aeronautical Society, Vol. 71, Sept. 1967, pp. 606-622.

25. DeFrance, Smith J.: The N.A.C.A. Full-scale Wind Tunnel. NACA Report 459, 1933.

143

TABLE 1.- NUMERIC INPUT CODE DEFINITIONS

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Code type

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0 u a, 7 a a a, U (d C .rl

a, U

a, v) (d U

a C (d

a a, a a

-r(

2

E

%

147

TABLE 4.- ADDITIONAL, SECTION-DEPENDENT INPUT REQUIREMENTS

Sec t ion

Type d e s c r i p t i o n

S i n g l e ducts: Test s e c t i o n , c losed , cons t an t

T e s t s ec t ion , c losed , cons t an t a r e a , empty

a r e a wi th model

T e s t s e c t i o n , c losed , d i f f u s i n g , empty

T e s t s e c t i o n , c losed d i f f u s i n g , w i t h model

T e s t s e c t i o n , open-throat,

T e s t s e c t i o n , open-throat, empty

wi th model

Constant-area duct Contract i o n Corner, constant-area, t u r n i n g

vanes only

Corner, constant-area, w i t h t u r n i n g vanes and w a l l s

Corner, constant-area, w i th walls and without t u r n i n g vanes

tu rn ing vanes and w a l l s Corner, d i f f u s i n g , w i th

Di f fuse r E x i t k i n e t i c energy from flow

dump Sudden expansion

148

- YPe 3de -

3 1

32

33

04

05

06

10 20 30

32

33

34

40 45

46 -

d d i t i o n a l i n p u t

t i t l e ( s )

--- SIAL BLKGE CD D EPS KEXP

SIAL BLKGE KEXP CD D EPS ---

s IAL BLKGE CD D EPS --- ---

CHORD PHI KT 90 RNREF CHORD PHI KT 90 RNREF PHI KT 90

CHORD PHI KT 90 RNRE F KEXP --- -- -

2quir emen t ? a

Required Optional Required Optional Defau l t

Required Optional Defau l t Required Optional

Required Optional Required Optional

Required Required Defau l t Defau l t Required Required Defau l t Defau l t Required Defaul t

Required Required Defau l t Defau l t Defaul t

Card column ( s )

36-40 46-50 61-65 76-80 56-60

36-40 46-50 56-60 61-65 76-80

36-40 46-50 61-65 76-80

41-45 51-55 56-60 66-70 41-45 51-55 56-60 66-70 51-55 56-60

41-45 51-55 56-60 66-70 56-60

TABLE 4 - AZDITIClNAL, SECTION-DEPENDENT INPUT REQUIREMENTS - Contftlued . Section

Type description

Flow straighteners, thin honeycomb

Flow straighteners, thick airfoils

Perforated plate with sharp- edged orifices

Woven mesh screen

Internal structure (drag item(s)) at upstream end of section

Fixed, known local loss item at upstream end of section

Multiple ducts: Constant-area ducts Contractions Corners, constant-area; turning vanes only

Corners, constant-area, with turning vanes and only one side-wall each

Corners, constant-area, with turning vanes and walls

Corners, constant-area, with walls and without turning vanes

turning vanes and only one. side-wall each

Corners, diffusing, with

Type code

51

52

53

54

56

57

61 62 70

71

72

73

74

ddit ional input title (s)

L/DH PRSTY RUFNESS L/DH PRSTY PRSTY

DMESH PRSTY U4ESH ITEMS S/AL BLKGE CD D EPS K

DUCTS DUCTS DUCTS CHORD PHI KT 90 RNREF DUCTS CHORD PHI KT 90 RNREF DUCTS CHORD PHI KT 90 RNREF DUCTS PHI KT 90 DUCTS CHORD PHI KT 90 RNREF

Requirement ? a

Required Required Def au 1 t Default Required Required

Required Required Default Default Required Optional Required Optional Required

Required Required Required Required Required Default Default Required Required Required Default Default Required Required Required Default Default Required Required Default Required Required Required Default Default

Card column (s)

~

36-40 46-50 66-70 36-40 46-50 46-50

41-45 46-50 56-60 9-10 36-40 46-50 61-65 75-80 61-65

7-8 7-8 7-8 41-45 51-55 56-60 66-70 7-8 41-45 51-55 56-60 66-70 7-8 41-45 51-55 56-60 66-70 7-8 51-55 56-60 7-8 41-45 51-.55 56-60 66-70

149

TABLE 4.- ADDITIONAL, SECTION-DEPENDENT INPUT REQUIREMENTS - Concluded.

Section

Type description ~~

Corners, diffusing, with turning vanes and walls

Diffusers

Vaned diffuser Sudden expansion from multiple ducts to single duct

Sudden expansion from multiple ducts to multiple ducts

Fan, constant-area annular duct(s) with motor-support strut ( s )

Fan contraction(s) to annular duct(s) with motor-support strut (s)

Fan diffuser(s) from annular duct(s), each with tapering, cone-shaped centerbody

Internal structure (drag item(s)) at upstream end of each duct

Fixed, known local loss item at upstream end of each duct

Type code

75

84

85 86

87

91

92

94

96

97

Additional input title(s)

DUCTS CHORD PHI KT 90 RNREF DUCTS KEXP

DUCTS

DUCTS

DUCTS ITEMS

DHUB BLKGE CD ETA D EPS DUCTS ITEMS DHUB BLKGE DUCTS DHUB BJXGE KEXP DUCTS ITEMS S/AL BLKGE CD D EPS DUCTS K

---

s /AL

Required Required Required Default Default Required Default

Required

Required

Default Default Required Required Optional Required Default Optional Default Default Required Optional Default Required Optional Default Required Default Required Optional Required Optional Required Required

Card column(s)

7-8 41-45 51-55 56-60 66-70 7-8 56-60

7-8

7-8

7-8 9-10 36-40 41-45 46-50 61-65 71-75 75-80 7-8 9-10 41-45 46-50 7-8 41-45 46-50 56-60 7-8 9-10 36-40 46-50 61-65 7 5-80 7-8 61-65

'"Default" indicates the input is optional and has a default value if omitted

"Optional" indicates the input may be selected and included as desired. "Required" indicates the input must be non-zero and included for all sections

of the specified type or the section will be skipped and the case not completed due to input error.

(see table 3 ) .

150

TABLE 5 . - CASE TEWTNATION TASK DESCRIPTIONS

Card column (s)

3-4 6

7-8

9-10

11-15

16-20

Input type

Blanks Integer

Real

Real

Real

Real

Input value

Blanks

0 #O

30.0 1. 2 .

>2.

0.0

fO .0

0.0 fO.0

0.0 fO.0

Task description

Case termination card identification Summary characteristics page(s) : Non-pr int Print

of distance through circuit: N o plots Cumulative pressure loss Wall pressure differential Cumulative pressure loss and wall pressure

Plotting of summary information as a function

differential Complete, annotated tabulation of input values : No print unless internally forced by

" C ho sen" tabula t ion

specified power level) :

omission of required inputs

Power-matching (optimizing velocity for a

No velocity optimization Velocity optimization Return to beginning for evaluation of another case : No return, program termination Return

151

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Main Program (PERF0RM)

fead Title Card

Subroutine DATACK -------

Skip Analysis, Only

-------

nits Basic Parameters Measure Parameters

Test

Section Flow

Card Error, Transfer to

Section Geometry

U

v n

Default Valve for Diffuser Expansion Loa

to Section

(a) Main program.

Figure 7.- Basic functional flow chart.

162

a al a 1 rl

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163

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Checking and Setting Error Codes

d

A Tabulation of Section Card Checking Input Data

Card Checkina 4 - # Assignment of Fixed

Determination Required General of of Determination Required "I Format Parameters Inputs

_ _ -

w

I Checking Requirements and Filling Arrays with Data or Message 1

Checking and Setting Error Codes

(b) Data-checking subroutine.

Figure 7.- Continued.

164

Local Speed Subroutine (SPEED)

(3 Start

Local Mach Number and Velocity

1

1 Return

Local Reynolds Number and Friction Coefficient Subroutine (F R ICTN)

P 1

Start

1

1 Reynolds Number

Friction I Coefficient

Return T ( c ) Local speed and Reynolds n u m b e r / f r i c t i o n c o e f f i c i e n t sub rou t ines .

F i g u r e 7.- Continued.

165

Section Analysis Information

output Subroutine (OUTPUT)

Start D Section Titles

Summary Information Plotting Subroutine

(PL0TIT)

Definition of Plot Titles and Parameters

Units of us

Section Type

SI

Modify Parameters for SI Plots

Q Typical Section

Section Information

Pressure Losses

Plot Wall Pressures

* 1

No Plot Pressure Losses

*

Return

1

(d) Section information output and plotting subroutines.

Figure 7.- Concluded.

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NASA TECHNICAL NOTE NASA TN D-8243 · 2013-08-31 · NASA TECHNICAL NOTE NASA TN D-8243 M u- cy w n z c AERODYNAMIC DESIGN GUIDELINES AND COMPUTER PROGRAM FOR ESTIMATION OF SUBSONIC