MMAE- Solids
-
Upload
eduardo-villanueva -
Category
Documents
-
view
220 -
download
0
description
Transcript of MMAE- Solids
-
7/21/2019 MMAE- Solids
1/23
-
7/21/2019 MMAE- Solids
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/ -
7/21/2019 MMAE- Solids
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/ -
7/21/2019 MMAE- Solids
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/ -
7/21/2019 MMAE- Solids
5/23
Solid Rockets II
St Roberts Law
http://www.iit.edu/~armour/ -
7/21/2019 MMAE- Solids
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
*
http://www.iit.edu/~armour/ -
7/21/2019 MMAE- Solids
7/23
Lesson 21 7
Solid Rockets IISRM $esi%n #rocess
-ission 5esign67 and mpayload
8hoosing finertIsp minitial9 mpropellant :et step; detailed design to determine
Po & Pa
grain geometry (e.g. a simple cylindrical port) propellant formulation case outer diameter case material properties insulation properties
turn thrust & !eight no""le information Predicted #$
http://www.iit.edu/~armour/ -
7/21/2019 MMAE- Solids
8/23
Lesson 21 8
Solid Rockets IISRM $esi%n #rocess
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
-
7/21/2019 MMAE- Solids
9/23
Lesson 21 9
Solid Rockets IISRM $esi%n #rocess
=' >se the R,( code to analy
-
7/21/2019 MMAE- Solids
10/23
Lesson 21 10
Solid Rockets IISRM $esi%n #rocess
)' 5etermine the propellant graininformation
/o!+ calculate the initial mass flo! rate
0gIV
initial
finalspe
mm
=
finalinitialprop mmm =
0gI
Fmsp
=
http://www.iit.edu/~armour/ -
7/21/2019 MMAE- Solids
11/23
Lesson 21 11
Solid Rockets IISRM $esi%n #rocess
&' 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
=
http://www.iit.edu/~armour/ -
7/21/2019 MMAE- Solids
12/23
Lesson 21 12
Solid Rockets IISRM $esi%n #rocess
@' ind the length of the grain
Know for a cylindrical grain" the burn area is
rom S,(5" 12n 3.A)
where Bv$ volumetric loading efficiency %C.DC.4D'
propv
prop
case
mV
=
LrA ib 2
=
http://www.iit.edu/~armour/ -
7/21/2019 MMAE- Solids
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
Solid Rockets IISRM $esi%n #rocess
( )( )
+= 1/
46
3 DLDVcase
DD
LL
=
DLLcyl =
cylgrain LL =
http://www.iit.edu/~armour/ -
7/21/2019 MMAE- Solids
14/23
Lesson 21 14
Solid Rockets IISRM $esi%n #rocess
3' ind the inner radius of the cylindricalport
A' Si
-
7/21/2019 MMAE- Solids
15/23
Lesson 21 15
Solid Rockets IISRM $esi%n #rocess
3se the %PA code or stagnation relations to find the
epansion ratio
+=
120
2
11
M
p
p
=
11
2
1
0
eexit
P
PM
)1(21
2
2
11
1
21 +
+
+
=
e
exit
MM
http://www.iit.edu/~armour/ -
7/21/2019 MMAE- Solids
16/23
-
7/21/2019 MMAE- Solids
17/23
Lesson 21 17
Solid Rockets IISRM &rn Si!lation
D' 5etermine the burn time of the motor his is !here the geometry of the port comes into play
3se a spreadsheet or 7ata to e*aluate ho! the geometry and
performance *ary o*er time
Consider an internal cylindrical port as an eample
t
%sec'
,o
%pa'
ri
%m'
(b
%m)'
rb
%m/s'
m dot
%!g/s'
0hrust
%:'
C ,oo rio )Erio+ a,oon (b# rb m dot
Isp go
tF#t.
.
.
t$tburn
,o=$mGdot
cH/(t
ri=$rioFrb#t
8ontinueuntil
ri5/)
)Eri=+ a,o=n
(b# rb m dotIsp go
http://www.iit.edu/~armour/ -
7/21/2019 MMAE- Solids
18/23
Lesson 21 18
Solid Rockets IISRM $esi%n #rocess
4' 5etermine the mass of the no
-
7/21/2019 MMAE- Solids
19/23
Lesson 21 19
Solid Rockets IISRM $esi%n #rocess
=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=
http://www.iit.edu/~armour/ -
7/21/2019 MMAE- Solids
20/23
Lesson 21 20
Solid Rockets IISRM $esi%n #rocess
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 +=
http://www.iit.edu/~armour/ -
7/21/2019 MMAE- Solids
21/23
Lesson 21 21
Solid Rockets IISRM $esi%n #rocess
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
-
7/21/2019 MMAE- Solids
22/23
Lesson 21 22
Solid Rockets IISRM $esi%n #rocess
==' :ow find the actual 67 using thesemasses
his #$ 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 +++++=
http://www.iit.edu/~armour/ -
7/21/2019 MMAE- Solids
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