MMAE- Solids

7/21/2019 MMAE- Solids

1/23


2/23

Lesson 21 2

Solid Rockets IIObjectives

Objectives

Introduce St. Roberts law

Know how to predict/simulate thrust for asolid motor given the grain geometry

Know how to do a detailed preliminary solidmotor design

Reading

SPAD: Ch. 6.2 & 6.6
http://www.iit.edu/~armour/


3/23

Lesson 21 3

Solid Rockets II

Mass Flow Rate

or a solid roc!et" the mass flow ratehas the relation

#prop $ propellant density%!g/m&'

(burn $ burn surface area %m)

' r $ burn rate %m/s'

%the rate at which the propellant surface isconsumed measured normal tothe surface'

sec)/(kgrAm burnprop=
http://www.iit.edu/~armour/http://www.iit.edu/~armour/


4/23

Lesson 21 4

Solid Rockets II

St Roberts Law

*urn rate comes from St Roberts +aw

,c $ chamber pressure %-,a' a $ burn rate coefficient %cm/sec/-,a)' n $ burn rate eponent

a and n are found from eperimental data

rate is measured at different chamber pressuresdata plotted as the natural log of the burn rate vs thenatural log of the chamber pressure

yais intercept is the natural log of a and theslope of thebestfit line is n %net slide'

n

caPr=
http://www.iit.edu/~armour/http://www.iit.edu/~armour/


5/23

Solid Rockets II

St Roberts Law


6/23

Lesson 21 6

Solid Rockets II

Steady State L!"ed #ara!eter Reslt

rom conservation of mass the total massflow rate in the chamber is constant insteady state

0hus" m dot of the burning propellant $ mdot

leaving through the throat So

Solve for ,c to get12 3.)4%remember ,c$,o'

n

c

ctoutburnpropburn

aPrwith

c

PAmrAm

=

===*

( )n

t

burnprop

cA

cAaP

=

11

*


7/23

Lesson 21 7

Solid Rockets IISRM $esi%n #rocess

-ission 5esign67 and mpayload

8hoosing finertIsp minitial9 mpropellant :et step; detailed design to determine

Po & Pa

grain geometry (e.g. a simple cylindrical port) propellant formulation case outer diameter case material properties insulation properties

turn thrust & !eight no""le information Predicted #$


8/23

Lesson 21 8


0he following approach wor!s well for constantthrust and Isp over a burn

If thrust" ,o" and ,a change over time" pic! adesign point with no


9/23

Lesson 21 9


=' >se the R,( code to analy


10/23

Lesson 21 10


)' 5etermine the propellant graininformation

/o!+ calculate the initial mass flo! rate

0gIV

initial

finalspe

mm

=

finalinitialprop mmm =

0gI

Fmsp

=


11/23

Lesson 21 11


&' ind the propellant regression rate %StRoberts +aw'

?' :ow use the regression rate to get theburn area from the mass flow rate

c

n

b PPaPr = 00 ,

bprop

b

r

mA

=


12/23

Lesson 21 12


@' ind the length of the grain

Know for a cylindrical grain" the burn area is

rom S,(5" 12n 3.A)

where Bv$ volumetric loading efficiency %C.DC.4D'

propv

prop

case

mV

=

LrA ib 2

=


13/23

Lesson 21 13

(lso" from S,(5" 12n 3.A& %+/5 usually given'

his e0uation can e sol*ed for the case internal diameter (assumes the

domes of the case are spherical)

1rom this !e can use the gi*en 'D to get

he length of the cylindrical section of the case is found y

he length of the propellant grain e0uals the length of the cylindricalsection


( )( )

+= 1/

46

3 DLDVcase

DD

LL

=

DLLcyl =

cylgrain LL =


14/23

Lesson 21 14


3' ind the inner radius of the cylindricalport

A' Si


15/23

Lesson 21 15


3se the %PA code or stagnation relations to find the

epansion ratio

+=

120

2

11

M

p

p

=

11

2

1

0

eexit

P

PM

)1(21

2

2

11

1

21 +

+

+

=

e

exit

MM


16/23


17/23

Lesson 21 17

Solid Rockets IISRM &rn Si!lation

D' 5etermine the burn time of the motor his is !here the geometry of the port comes into play

3se a spreadsheet or 7ata to e*aluate ho! the geometry and

performance *ary o*er time

Consider an internal cylindrical port as an eample

t

%sec'

,o

%pa'

ri

%m'

(b

%m)'

rb

%m/s'

m dot

%!g/s'

0hrust

%:'

C ,oo rio )Erio+ a,oon (b# rb m dot

Isp go

tF#t.

.

.

t$tburn

,o=$mGdot

cH/(t

ri=$rioFrb#t

8ontinueuntil

ri5/)

)Eri=+ a,o=n

(b# rb m dotIsp go


18/23

Lesson 21 18


4' 5etermine the mass of the no


19/23

Lesson 21 19


=C' ind masses for the motor case and theinsulation 1irst+ find the urst pressure for the motor case

!here Pcma maimum epected chamer pressure (Pa)

's factor of safety

he thic;ness of the case is (40n. 6.96 in SPAD)

!here 1tu ultimate tensile strength

scburst

fPP max=

tu

burstcs

F

DPt

2=


20/23

Lesson 21 20


he mass of the pressure *essel is (40n. 6.99 in SPAD)

he mass of the thrust s;irt is (40n. 6.95 in SPAD)

o account for the aft polar oss+ increase the total case

mass of the thrust s;irt and pressure *essel y 8 in SPAD)

+=

D

LDtm

cyl

cscspv 12

2Dtm cscsskirt =

)(1.1 skpvcase mmm +=


21/23

Lesson 21 21


1ind the insulation mass

he eposed !all surface in the motor case is (40n. 6.5< in

SPAD )

he mass of the insulation can e found from (40n. 6.86)

and the thic;ness of the insulation from (40n. 6.52)

!here All masses are in ;g

su is a fraction of 8


22/23

Lesson 21 22


==' :ow find the actual 67 using thesemasses

his #$ should e close to the gi*en re0uirement. ,f not+ there may e some changes needed to the design

propif

mmm

=

=

f

i

spm

mgIV ln0

propskirtpvnozinsulcsi mmmmmmm +++++=


23/23

23

Solid Rockets II

SRM $esi%n #rocess

-ay have to iterate/redesign as necessaryuntil inert mass" propellant mass meetre2uirements.

Jood idea to use ideal roc!et e2uation with

si

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MMAE- Solids