NUMERICAL COMPUTATIONS AND MEASUREMENTS

Abstract

O F TRANSONIC FLOW IN A

SLOTTED-WALL WIND TUNNEL

Nada Agrell, Bj6m Pcttcrsson AQ /

FFA, S-161 11 Bromma, Swcden J/I 0 I 'md I

Yngvc C-J. Scdin SAAB-SCANIA AB, S-581 88 Linkgping, Swedcn

Numerical simulation of transonic flow around a sim- ple wingbody combination in a rectangular test sec- tion, provided by 4 slots on each wall, has been car- ried out. Comparisons between the computational re- sults and the recently available experimental data have been performed. The experimental data include wall pressure- and total force measurements on the model. The basically inviscid numerical method treats the flow through each individual slot and couples this to the flow in the test section. The inviscid theoretical slot- flow model is qualitatively corrected for viscous slot flow losses and viscous wall boundary layers. The slot- flow equations consist of basically two equations, one mass-flux equation and one pressure equation imposing the constant plenum pressure. The interior test-section flow in the wind tunnel is described by the non-linear small perturbation potential equation. The test model is blocking 0.5% of the wind tunnel cross section area which is 0.5x0.5m2. Numerical and experimental re- sults are shown for two Mach numbers at two angles of attack. Considering the rather small test model produc- ing small disturbances at the walls the computed wall pressure distributions agree quite well with the mea- surement s.

Introduction

A numerical method(lJ) has been developed for tran- sonic tunnels with slotted walls and rectangular test sections in order to study:

1) the influence of the wind tunnel walls on the model tested, and 2) the possibility to minimize this influence by optimiz- ing the shape of the slots and to make proper choices of parameters for the wind tunnel runs.

A reasonable blockage for the model tested in a wind tunnel should, in general, be less than 0.5% in order to avoid too large interference effects in transonic flow. The method that has been developed is hoped to be a valuable tool in order to give guidelines into getting low wall interference and making good predictions when the blockage ratio is up to 1.5%. This is hoped to be a considerable improvement concerning the possibility of

Copyright @ American Institute of Aeronautics and Astronautics, Inc., 1987. All rights reserved.

testing large size models in e.g. existing wind tunnels and when designing new wind tunnel facilities.

Recently a model has been tested(3) in the TVM 500 tunnel at FFA in order to provide some experimen- tal data for the further development and verification of the method. The blockage of the used model was around 0.5%. Total forces on the test model and pres- sures along the centrelines of the test section walls were measured.

Description of the Method

The slot flow is schematically shown in Fig. 1. The physical model is basically inviscid and based on a 2D cross-flow theory(4). Two reduction factors, 7, for the slot with a(x) and 7, for the axial velocity U are used in order to correct for viscous effects. Typical values for these factors, which are assumed to be constants, are 0.6-0.8(~). The slot flow consist of two relations, one essentially based on the 2D cross-flow mass flux equation to determine the plenum pressure surface YP(x) and the other to give the pressure differ- ence across the slot in terms of the slot flux q(x) per unit length, the slot width a(x) and the plenum sur- face position Yp(x). The slot flux q is a priori unknown and must be determined as a part of the total solution including the interaction with the interior test section flow generated in the wind tunnel.

Plenum chcmber

\ A Y / Velocity u

1 k!& Reduced slot widih ?,.a

Slci width a

Fig. 1. Slot flow model.

The field equation for the interior test section flow is given by the non-linear small perturbation potential equation:

Here 4 is the disturbance potential and M, the nomi- nal reference Mach number labelling the tunnel run.7 is the specific heat ratio for air. (x, y, r ) is a fixed Carte- sian coordinate system with x pointing downstream in the direction of the tunnel axis. Equation (1) written in finite-difference form is solved by an over-relaxation procedure. No-through-flow conditions are imposed on the wind tunnel test model. No boundary layer calcu- lation is performed for the test model. On the walls be- tween the slot strips, which are as many as the slots but wider (see Fig. 2), the normal velocities are given by the turbulent wall boundary layer displacement thick- ness and the existing wall inclination.

On the slot strips a local slot boundary condition(') is applied giving #(x, 0,z) in terms of the slot flux (see Fig. 2). The slot flux q is found assuming a mass flux balance for each slot. The slot flux q is evaluated in terms of the normal flow velocities as computed from Eq. (1) and integrated across the wall strip. It is cor- rected for the wall boundary layer.

Inner @ slot flow

Wall b' layer +

displacement b y Outer test wail inclination' 0 ) ~ sect ion . flow: 9 Ix,o,z) given by slot eqs.

Fig. 2. Local slot boundary condition.

Descrivtion of the Test Case

A small 55-degree swept delta wing with cylindrical body (ogive nose) and a NACA 64A005 profile has been tested in a tunnel at FFA, see Fig. 3. The test section of the used TVM 500 tunnel has quadratic cross section (each side is 0.5m) and is 1.4m in length. The walls of this tunnel are provided with 4 slots each and the to- tal ventilation is 4% at the location of the model. The blockage of the tested model in this tunnel was around 0.5%. The pressure measurements have been performed along centrelines of the walls, at positions A, B and F as can be seen in Fig. 5. In the same Fig. the location of the model in the wind tunnel can be seen. Consid- ering the smallness of the model the flow disturbances at the walls can be expected to be small.

1

- 198

- N

A l l dimensions in 10 m t

Fig. 3. Tested model.

The computational mesh in the vicinity of the model projected on the wing mean plane can be seen in Fig. 4. The actual mesh size, when solving the small perturba- tion equation with the finite difference procedure in the tunnel, was 6 6 x 3 3 ~ 6 6 points. The model support was simulated by a constant diameter sting , which is not quite correct a bit further downstream. When solving the slot flow equations 130 equally spaced points have been used along the length of the tunnel. The viscous

Fig. 4. Computational grid in the vicinity of the model.

573

PLENUM CHAMBER

FLOW r

TEST SECTION

slot wall pressure

SLOT SHAPE 1 /

.p.p-l * 6.95

4

correction parameters used have been 0.7 for both 17, and qu Approximately 90 points describe each surface of the wing in the computations. Consequently the res- olution of the modcl in the computational grid is prob- ably not sufficient. The fuselage is also represented by correspondingly too few points. A better agreement be- tween computed and measured forces on the configura- tion could be expected with more computatonal points on the model.

]

Results

.05 Al l dimensions in lo-' rn

Fig. G shows the comparison of measured and computed pressure distributions for the empty wind tunnel along the centrelines of the bottom, top and side walls in the wind tunnel at &I, = 0.95 . This corresponds to the calibration configuration for the tunnel with the plenum Cp being -0.014. The scatter in the experimental data can be estimated to 0.01 in Cp, which corresponds to half a percent of the air speed in the test section. If thc plenum Cp in the computations is incrcased by 0.01 a much better agreement is obtained with experiments. From the experiments shown in Figs. 6 and 7 one can see some asymmetric behaviour in flow between bottom and top wdIs and with respect to the vertical symme- try plane of the actual empty tunnel. The secondary flow asymmetry(6) seems to be around ACp = 0.01. This is specially demonstrated in Fig. 7 where pressure coefficients are given as measured at the teat section position x = 0.92m symmetrically on both sides of the centrelincs on the bottom and top walls.

Fig. 5. Test section with the model.

Fig. 8 shows the same type of comparison as Fig. G but with the model in the tunnel at a very close to 0'. Almost no difference can be seen in the computational results between the bottom and top walls for such a small a. However, the experimental values show much larger differences for these two walls, indicating scc- ondary flow. The coefficients as measured at x = 0.92m can be seen in Fig. 9. The Cp-level from the empty wind tunnel has been decreased and more lateral asym- metry can be seen.

Fig. 10 demonstrates a comparison between experi- ments and computations carried out at two different plenum suction values at M, = 0.95 and a = 3.38'. The solid line represents a computational result at a plenum Cp as obtained at the calibration of the tunnel, while the dashed line is a corresponding result at an adjusted lower suction level.

Figs. 11 and 12 represent comparison between exper- iments and computations at M , = 0.7 for a = 0.02' and a = 2.95'. The plenum pressure used in the com- putations was the same as was obtained at the calibra- tion occasion and which was then used in the experi- ment with the model in the wind tunnel.

Fig. 13 shows the computed slot flux q along the test section in two of the slots at M, = 0.95 and a = 3.38'. Two different plenum Cp have been applied in the com- putations. The lower suction in the slots results in the flow reentering the test section (slot 2) much earlier than the higher suction. This Fig. should specially be compared with Fig. 10.

Pos. A

.02 0 l $1 EX^, Plenum Cp =-.OIL

- Calc.. - , I - - ,, - --- Cak. . - I / - cp=-.OOL

-.02 r

Fig. G. C,, distribution along the tunnel walls - empty tunnel at &Im = 0.95.

Bottom Slot 1

Fig. 7. Cp distribution at x = 0.92m on both sides of the centreline at M, = 0.95 - empty tunnel.

Bottom Slot 1

& -1. 0. 1. Y

Fig. 8. Cp distribution along the tunnel walls - model in the tunnel at M, = 0.95, (Y = 0.05' and plenum Cp = -0.0142

- caic.

Fig. 9. Cp distribution at x = 0.92m on both sides of the centreline at Mm = 0.95 - model in the tunnel.

- Calc., - - - ., - - -- ~ a l c . , - " - c p = - .OOLO

-.02 , A

Fig. 10. Cp distribution along the tunnel walls - model in the tunnel at M, = 0.95, (Y = 3.38' and two different plenum C,.

1 -.021 Pos. A rn

- Calc. -.02 - cp Pos. B

A 0.

Fig. 11. Cp distribution along the tunnel walls - model in the tunnel at M , = 0.7, a = 0.02' and plenum Cp = -0.0108.

Fig. 13. Computed slot flux q(x) in slots 1 and 2 at M, = 0.95, a = 3.3s' for two different plenum Cp.

Finally in Fig. 14 CL, and C,, as a function of M, can be studied. The computed CL, and C,, are some- what lower than the measured values for all Mach num- bers investigated. Considering that no boundary layer has been applied to the model in the computations and keeping in mind the relatively low numerical resolution in terms of the number of grid points on the model, the results are quite satisfactory.

Conclusions

As can be seen from Cp-distributions the disturbances for our small model blocking only 0.5% are very small

-.02 - Pos A CP 13

0.- 13

I I

11.

.02-1 [I]

-. 02 A - 1 Pos. F

Fig. 12. Cp distribution along the tunnel walls - model in the tunnel at M, = 0.7, ct = 2.95Oand plenum Cp = -0.0114.

Fig. 14. CL, and Cmp as functions of M,.

demanding a very high resolution in both experimen- tal measurements and in the numerical method. The largest absolute Cp-value on the walls in the experi- ments is around 0.04 while the scatter in Cp is at the same time around 0.01 or around 25% of the largest value.

The slopes of the Cp-distributions at the upstream part of the test section are mainly due to the displace- ment effects of the wall-boundary layer. The agreement with respect to the slopes is there quite good for all cases shown i.e. in a wide range of Mach numbers.

Considering specially Cp values at the bottom and top walls in Figs. 8 and 11 at the downstream part of the

tunnel, we can see that even if a is very close to 0' for the model in both Figs. the Cp-values are different at the two walls. Whether this is due to asymmetric flow in the tunnel or has to do with the equipment just downstream of the test section or possibly depends on the structural obstructions in the plenum chamber is very hard to say. The plenum pressure was measured only at one location at the most upstream end of the plenum chamber.

Computationally a higher plenum pressure tends to de- crease the C,-level in the upstream part while it in- creases this level in the downstre'un part of the wind tunnel, which is physically reasonable. This is to a ccrtnin dcgrec n. desirable trcnd at h/l, = 0.95 in or- der to obtain a better agrecmcnt with the experiments. Experimentally the combination of Mach number and plenum pressure have been obtained on the occasion of calibration when the wind tunnel is empty. When the model is inserted into the wind tunnel the combination of Mach number and plenum pressure can not be the same as in the empty tunnel case. At M, = 0.95 the scatter of 0.01 in Cp corresponds to the scatter of 0.005 in Mach number. Even when the model is blocking only 0.5% of the cross sectional area of the wind tun- nel it still is quite possible that the Mach number can be misjudged by 0.5% compared to the empty tunnel calibration case.

A similar method(5) was developed earlier for cylindri- cal test sections. A relatively large model creating more pronounced flow disturbances on the walls was tested and good agreement between computations and exper- iments was obtained. Similar results can be expected in cases of rectangular test sections.

References

Sedin, Y. C-J., Agrell, N. and Zhang, N.: Computation of Transonic Wall-Interference in Slotted-Wall Test Sections of Wind Tunnels, ISCFD, Tokyo, Sept 1985.

Agrell, N., Pettersson, B. and Scdin, Y. C-J.: Numerical Design Parameter Study for Slotted Walls in Transonic Wind Tunnels, ICAS Paper 86-1.6.2, 1986.

Iderfelt, H.: Private Comunication, FFA, Project no AU-2431.

Berndt, S. B.: Inviscid Theory of Wall Interference in Slotted Test Sections, AIAA J., Vol 15, Sept 1977, pp 1278-1287.

Sedin, Y. C-J. and Sorensen, H.: Computed and Measured Wall Interference in a Slotted Transonic Test Section, AIAA J., Vol 24, March 1986, pp.444-450.

Wu, J . M., Collins, F. G. and Bhat, M. I<.: Three-Dimensional Flow Studies on Slotted Transonic Wind Tunnel Wall, AIAA J . , Vol 21, No 7,July 1983.