 Open Access
 Total Downloads : 515
 Authors : Santhini S Lal, A. K. Asraff, Shobha Elizebath Thomas
 Paper ID : IJERTV4IS080439
 Volume & Issue : Volume 04, Issue 08 (August 2015)
 DOI : http://dx.doi.org/10.17577/IJERTV4IS080439
 Published (First Online): 22082015
 ISSN (Online) : 22780181
 Publisher Name : IJERT
 License: This work is licensed under a Creative Commons Attribution 4.0 International License
Thermostructural Analysis of Rocket Engine Thrust Chamber
Santhini S Lal
Graduate Student, Department of Civil Engg,
Sree Buddha College of Engg, Pattoor, Alappuzha
A. K. Asraff
Group Director,
Structural Dynamics & Analysis Group, Liquid Propulsion Systems Centre, Valiamala
Shobha Elizebath Thomas Assistant Professor, Department of Civil Engg
Sree Buddha College of Engg, Pattoor, Alappuzha
Abstract: High performance rockets are developed using cryogenic technology. High thrust cryogenic rocket engines operating at elevated temperatures and pressures are the backbone of such rockets. The thrust chambers of such engines which produce the thrust for the propulsion of the rocket can be considered as structural elements. Often double walled construction is employed for these chambers for better cooling and enhanced performance. The double walled rocket engine thrust chamber investigated here has its hot inner wall fabricated out of a high thermal conductive material like copper alloy and outer wall made of stainless steel. Inner wall is subjected to high thermal and pressure loads during operation of engine due to which it will be in the plastic regime. Major reasons for the failure of such thrust chambers are low cycle fatigue, creep and thermal ratcheting. Elasto plastic material models are required to simulate the above effects through a cyclic stress analysis. This paper gives the details of cyclic stress analysis carried out for a block using the Chaboche nonlinear kinematic hardening plasticity model. The reliable results available from the block is used for the analysis of thrust chamber.
1. INTRODUCTION
Thrust chamber is one of the main components of a cryogenic rocket engine. It is the subassembly of rocket engine in which propellants are injected, mixed and burned to form hot gas products which are accelerated and ejected at high velocity. The thrust chamber investigated in this work is double walled and regeneratively cooled using Liquid Hydrogen. The inner wall of the thrust chamber is made up with a special copper alloy whereas the outer wall
is fabricated from stainless steel.During operation, both the walls experience severe thermal and pressure loads. The inner copper wall has to take care of two contradictory functional requirements. The wall thickness has to be optimised to offer least resistance for heat transfer rate and thereby limit thermal gradients. The inner wall also should have sufficient thickness to withstand the pressure and mechanical loads exerted by coolant pressures and combustion gas pressures. Normally an engine has to undergo repeated cycles of operation before putting to actual use in the flight. Hence cyclic stress analysis of the thrust chamber is of paramount importance so that its structural integrity during flight is ensured. Stress analysis predicts the manner in which a mechanical component will perform structurally under anticipated working conditions. The goal is to design an element with sufficient, but not excessive, strength in every detail. Cyclic stress analysis of a rocket engine thrust chamber using Chaboche model is reported in this work. Failure of a double walled thrust chamber occurs due to bulging and fracture of inner wall. One of the major reasons for its failure is ratchetting. Ratchetting decides the number of times the engine can be hot tested which is one of the major engine operating parameter. Chaboche model is a nonlinear kinematic hardening model which can predict ratcheting more accurately unlike the conventionally used linear kinematic hardening models and isotropic hardening models.
Linear isotropic hardening models
These models are appropriate for large strain, proportional loading situations. They are less preferred for cyclic loading. Isotropic hardening model alone is incapable of describing a cyclic behaviour that includes repeated cyclic deformation, however these models are capable of simulating complex cyclic behaviours when combined with kinematic hardening models.
Linear kinematic hardening models
They follow a linear hardening curve in cyclic loading situations. The hardening rule is given by
ij
dij = c dp
Fig. 1. Progressive failure of a double walled thrust chamber cross section
= incremental back stress
= incremental plastic strain
They can describe stable loops in cyclic loading, including the Bauschinger effect. For a prescribed uniaxial stress cycle with a mean stress, they fail to distinguish between shapes of the loading and reverse loading hysterisis curves and consequently produces a closed loop with no ratchetting.
Non linear kinematic hardening models
They follow follow a smooth non linear hardening curve in cyclic loading situations. The hardening rule is given b
dij = 2 c dp
3 ij
Fig. 2. Dog house effect
PLASTICITY MODELS
Development of models for inelastic behavior of materials has been an area of substantial development over the past 2030 years and is still a very active research area. New models are developed even recently. Todays FE codes provide models for the analysis of plastic deformation of metallic materials, even though the most recent models are yet to be implemented. Plasticity models provide a mathematical relationship that characterizes the elasto plastic response of materials. Choice of plasticity model depends on thexperimental data available to fit the material constants
The basic requirements of a plasticity model are

Yield criterion

Flow rule

Hardening rule
Conventional plasticity models are

Linear isotropic hardening models

Linear kinematic hardening models
= back stress
They siimulate ratchetting and shakedown in a FEA simulation. Nonlinear kinematic hardening implies a shift (or movement) of the yield surface along a nonlinear path. It is similar to linear kinematic hardening except for the fact that the evolution law has a non linear term called recall term. Non linear kinematic hardening does not have a linear relationship between hardening and plastic strain. The non linear term is associated with the translation of the yield surface.
CHABOCHE MODEL
The Chaboche model is a type of non linear kinematic hardening model commonly used to simulate the plastic deformation of metals. It was added in ANSYS 6.0 to complement the existing isotropic and kinematic hardening rules. Chaboche model is based on von Mises yield criterion. The yield function for the non linear kinematic hardening model is
F = [3 ({S} {} ) [] ({S} { })]1/2 – = 0
2
{S} = deviatoric stress tensor
{} = back stress tensor
[M] = matrix containing information on different yield strengths in different directionsR = yield stress
Experimental data and a curve fitting tool are used to determine a set of material parameters for the Chaboche kinematic hardening model in ANSYS 15.A third order Chaboche kinematic hardening model is generally used, as it provides sufficient variation to calibrate the non linear behavior of the metal.
Chaboche model is expressed as
=
=1
3
= 2
= plastic strain
c, = Chaboche material parameters
The first term in the equation is the hardening modulus and the second term is the recall term that produces a non linear effect. The recall term incorporates the fading memory effect of the strain path and essentially makes the rule non inear in nature. The material parameter controls the rate at which hardening modulus decreases with increasing plastic strain.
A stable hysterisis curve can be divided into three critical segments: the initial high modulus at the onset of yielding, the constant modulus segment at a higher strain range and the transient non linear segment (knee of the hysterisis curve). Chaboche initially proposed to use three decomposed hardening rules to improve the simulation of the hysterisis loops in these three segments. He suggested that the first rule (1) should start hardening with a very large modulus and stabilize very quickly. The second rule (2) should simulate the transient non linear portion of the stable hysterisis curve. Finally, the third rule (3) should be a linear hardening rule ( 3 = 0 ) to represent the subsequent linear part of the ratcheting curve at a high strain range. The resulting yield surface center is
= 1 + 2 + 3
Ratchetting predictions can be improved by introducing a slight non linearity in the third rule by assigning a small value to 3 , keeping other parameters the same. This small value does not introduce any noticeable change in the strain controlled stable hysterisis loop simulation. A non zero 3 does not have any effect on 1, but it changes the course of
3 and thereby of 2, which improve the uniaxial ratcheting simulation and prevent shakedown. The higher the value of
3 , the third rule would reach its limiting state and, consequently, the earlier the steady rate of ratcheting would start. Fig. 3, shows the details of third order Chaboche model
Fig. 3. Details of third order Chaboche model
CYCLIC STRESS ANALYSIS OF A SIMPLE BLOCK
Cyclic stress analysis of a simple block is carried out to simulate the cyclic hardening behaviour occuring under symmetric pressure as well as displacement loading conditions.
Analysis is done using the following models

MISO (Multilinear isotropic hardening) model

BISO (Bilinear isotropic hardening) model

KINH (Multilinear kinematic hardening ) model

BKIN(Bilinear kinematic hardening) model

Chaboche model

MISO+ Chaboche model
Analysis is done under pressure as well as displacement loading conditions separately.
ELEMENT CHOSEN FOR ANALYSIS
To capture the cyclic behavior, a single SOLID185 element is used with quarter symmetry boundary conditions and uniaxial displacement in the Y direction. Elastic properties for copper alloy are a Youngs modulus of 110660 MPa and poissons ratio of 0.3. Fig 4 shows the FE model of a simple block.
Fig 4: FE model of simple block
Non linear material properties are input via graphical user interface. Chaboche parameters for strain range Â±0.75% at 900 K is used. Table 1 shows the Chaboche model parameters for copper alloy.
Stress strain points for multi linear isotropic hardening model option as well as multilinear kinematic hardening option are obtained from the tension test data for copper
alloy at 900 K. Fig 7.2 shows the graph comparing true stress true strain and and true stresstrue strain fit and Fig 7.3shows the graph comparing true stress truestrain fit and MISO curve . Table 7.2 shows the MISO points. The same points are used for KINH model. A yield strength of 76N/mm2 and a tangent modulus of 3000 N/mm2 is taken for BISO and BKIN models.
Sl no
True strain
True stress
1
0.00053576
76
2
0.019
88
3
0.035
96
4
0.045
100
5
0.1
111
6
0.13
115
7
0.17
120
8
0.26
127
9
0.3
129
10
0.4
134
11
0.7
144
12
0.92
150
VALU
Table 1: Chaboche model parameters for copper alloy
Sl. No.
Parameter
Final value
1
C1
329433.77
2
1
200987.64
3
C2
40220.46
4
2
1107.84
5
C3
163.77
6
3
9
7
o
32
Table 2: MISO points
CYCLIC STRESS ANALYSIS RESULTS
Different stress strain graphs were obtained as a result of the cyclic stress analysis conducted on a simple block. The Figures given below show Axial stressstrain variation.
PRESSURE LOADING
APR 6 2015
22:08:26
1
MISO model
POST26
SY_2
160
140
120
100
80
60
40
20
0
TRUE
STRESS TRUE STRAIN
TRUESTRE
SSTRUE STRAIN FIT
0 0.2 0.4 0.6 0.8 1
Strain,mm/mm
Stress (N/sq.mm)
Stress (N/sq.mm)
Fig 5: Graph comparing true stress true strain
160
140
120
100
80
60
40
20
0
TRUESTRESS
TRUE STRAIN FIT MISO CURVE
0
0.5
Strain,mm/mm
1
Fig 6: Graph comparing true stress true and true stresstrue strain fits train fit and MISO curve
1
MKIN model
POST26
SY_2
125
100
75
50
25
VALU
0
25
50
75
100
125
125
100
75
50
25
0
25
50
75
100
125
(x10**2)
0 .4 .8 1.2 1.6 2
.2 .6
1 1.4 1.8
TIME
Fig 7 :Axial stress strain variation
APR 7 2015
08:13:12
(x10**2)
.4 .4 1.2 2
1.6 .8 0 .8 1.6
TIME
2 1.2
Fig 8 :Axial stress strain variation
100
80
60
40
20
APR 7 2015
07:25:02
1
VALU
100
80
60
40
20
1
BISO model KINH model
POST26
SY_2
POST26
SY_2
APR 7 2015
08:07:52
0 .4 .8 1.2 1.6 2
.2 .6 1 1.4 1.8
TIME
APR 7 2015
07:07:07
1
BKIN model
Fig 9 :Axial stress strain variation
625
500
375
250
125
1
0
VALU
125
100
75
50
25
BISO model
(x10**2)
0
20
40
60
80
100
VALU
1
.6
.2 .2
TIME
.6
(x10**2)
0 .4 .8 1.2
.4
.8
0
20
40
60
80
100
Fig 12 :Axial stress strain variation
POST26
SY_2
APR 7 2015
08:13:12
POST26
SY_2
.6
.2 .2
TIME
.6
1
MISO model
Fig 10 :Axial stress strain variation
(x10**2)
.8 .4 0 .4 .8 1.2
625
125
250
375
500
0
VALU
1.6
.8
.8 0
TIME
.4 .4 1.2 2
2 1.2
1.6
(x10**2)
25
50
75
100
125
DISPLACEMENT LOADING
120
100
80
60
40VALU 20
0
20
40
60
80
APR 6 2015
19:23:58
POST26
SY_2
0
VALU
200
160
120
80
40
APR 6 2015
08:32:19
1
BKIN model
Fig 13 :Axial stress strain variation
POST26
SY_2
1
Cyclic stress analysis,displacment loading, Mises model (elastic perfectly plast
.6 .2 .2 .6 1
TIME
(x10**2)
0 .4 .8 1.2
.8 .4
1
.6
.2 .2
TIME
.6
(x10**2)
.8 .4 0 .4 .8 1.2
200
40
80
120
160
Fig 11 :Axial stress strain variation
Fig 14 Axial stress strain variation
60
40
20
10
0.005
– 0.
40
60
CHABOCHE MODEL
Stress,Mpa
0.
80
0
000 0.005 0.010

MISO +Chaboche showed cyclic response clearly, Cyclic hardening was observed
DISCUSSION
MISO + Chaboche model is the best model considered for simulating the cyclic hardening behaviour. All other models considered is not able to capture the behaviour properly. Cyclic hardening is a complex material behaviour with expansion and translation of yield surface. MISO model captures yield surface expansion whereas Chaboche model captures yield surface translation. Non linear response of chaboche model is due to the two additional non linear rules
Total strain,mm/mm
Fig 19 :Axial stress strain variation
MISO + Chaboche model
150
100
50
010 0.005 – 0.
50
100
150
200
present compared to other models. Based on the studies conducted on MISO+CHAB model under displacement loading conditions, it is seen that, (CHAB stabilized stress yield strength) + MISO stabilized stress = (MISO+CHAB) stabilized stress .Studies conducted using MISO+CHAB models under pressure loading conditions indicate the ineffectiveness of MISO model except for its help in cyclic hardening modelling. MISO+CHAB model starts with CHAB pattern initially and subsequently shows hardening trend .
Stress,MPa
0.
0
200
000 0.005 0.010
REFERENCES

Asraff , A.K., Jomon Joseph, T., Joshua, F.P., Sadasiva Rao, Y.V.K., (2002), ElastoPlastic Stress Analysis & Life Prediction of an Indigenously Designed Cryogenic Rocket Thrust Chamber, Proceedings of 6th International Symposium on Propulsion for Space Transportation of the XXIst Century, France.
Total strain,mm/mm
Fig 20 :Axial stress strain variation
OBSERVATIONS
FOR PRESSURE LOADING


MISO model did not show cyclic response

KINH model beautifully (nonlinear fashion) showed cyclic responseBISO model did not show cyclic response

BKIN model showed cyclic response in linear fashion. No cyclic hardening

Chaboche showed non linear cyclic response

MISO + Chaboche showed cyclic response with cyclic hardening
FOR DISPLACEMENT LOADING

MISO model showed cyclic hardening in linear fashion

KINH model showed cyclic response in a linear manner but did not show any cyclic hardening

BISO model showed cyclic hardening in linear fashion

BKIN model showed cyclic response in linear fashion. No cyclic hardening

Chaboche showed cyclic response clearly, Cyclic hardening was not observed

Jorg Riccius, R., Oskar Haidn, J.,(2003), Determination of Linear and Nonlinear Parameters of Combustion Chamber Wall Materials, Proceedings of American Institute of Aeronautics and Astronautics, Germany.

Sunil, S., Asraff, A.K., Sarathchandra Das, M.R., (2005), Creep Based Stress Analysis of a Cryogenic Rocket Thrust Chamber, Proceedings of 6th National Conference on Technological Trends, College of Engineering, Trivandrum.

Sunil, S., Asraff, A.K., Muthukumar, R., Ramanathan, T.J., (2006), New Concepts in Structural Analysis and Design of Double Walled LPRE Thrust Chambers, Proceedings of 42nd AIAA/ASME/SAE/ASEE Joint Propulsion Conference, Sacremento, USA.

Sunil, S., Asraff, A.K., Muthukumar, R., Ramanathan, T.J., (2008), Stress Analysis and Life Prediction of A Cryogenic Rocket Engine Thrust Chamber Considering Low Cycle Fatigue, Creep and Thermal Ratchetting, Proceedings of 5th International Conference on Creep, Fatigue and CreepFatigue Interaction, Kalpakkam.

Schwartz, w., Schwub, S., Quering, K., Wiedmann, D., Hoppel, H.W., Goken, M.,(2011)," Life Prediction of Thermally Highly Loaded Components: Modelling the Damage Process of a Rocket Combustion Chamber Hot Wall", CEAS Space Journal, pp 8397.