[American Institute of Aeronautics and Astronautics 39th AIAA/ASME/SAE/ASEE Joint Propulsion...

A Subscale-Based Life Prediction Methodology For Rocket Engine Combustors

I-K Sungdagger BG Northcuttdagger KS Rubeldagger WE AndersonDagger School of Aeronautics and Astronautics Purdue University

West Lafayette Indiana 47906

ABSTRACT α = Thermal expansion coefficient micromm-K

δ = Kronecker delta function ε = Strain A small scale experimental annular plug nozzle

thruster was designed built and tested to failure The test article was a water-cooled 200 psia combustor that used decomposed hydrogen peroxide as the oxidizer and JP-8 as the fuel Conventional and visco-plastic models were used to predict life cycle due to low cycle thermal stress transient effects and creep rupture damage To validate the prediction methods which predicted cyclic failure due to thermal ratcheting between 50 and 320 cycles the combustor was tested cyclically at the Advanced Propellants and Combustion Laboratory at Purdue University The first surface cracks in the corner of the milled channels of the copper liner appeared after 90 cycles Testing was stopped after 140 cycles due to an unpredicted failure mechanism in the location where failure was predicted

ξ η = Dummy variables in the integration θ0 = Original ligament thickness θcr = Critical ligament thickness θ = Thermal diffusivity ν = Poissonrsquos ratio σ = Stress τ = Nomalized ligament thinning Subscripts 1 = Coolant side surface of the channel ligament 2 = Hot gas side surface of the channel ligament i j = Indices of stress and strain tensor Superscripts e = Elastic part

NOMENCLATURE in = Inelastic part th = Thermal part A = Cross section area of the thin face = Denotes time derivative a = Distance between channels B = Back stress INTRODUCTION D = Drag stress

NASA and the US Air Force have put a heavy emphasis on the need for reusable propulsion systems Order-of-magnitude increases in life are the stated goals To achieve these goals one of the biggest challenges that must be overcome is the life extension of the propulsion system hot sections ndash pre-burners gas generators turbine stages main combustion chambers and nozzles

d1 d2 = Distance between the centroids of the thin faces to the beam midplane E = Youngrsquos modulus ℓ = Half length of the ligament p = Pressure S = stress T = Temperature w = Radial deflection at the midplane of the

beam Much work needs to be done before the ambitious life-cycle goals can be approached In long-life systems new materials and manufacturing processes probably will be used component configurations will probably be different and different propulsion system cycles eg combined rocket-airbreathing cycles will probably be employed Health monitoring will have to be integrated into the design To predict the propulsion system life which depends on an ever-expanding variety of materials and manufacturing processes component functional designs and engine cycles accurate life characterization and prediction methodologies are critical

x = Cartesian coordinate Z = Zener-Hollomon parameter 1 Greek Letters This work was funded by NASA Marshall Space Flight Center dagger Graduate Students School of Aeronautics and Astronautics Student Members AIAA Dagger Assistant Professor School of Aeronautics and Astronautics Member AIAA

American Institute of Aeronautics and Astronautics

1

39th AIAAASMESAEASEE Joint Propulsion Conference and Exhibit20-23 July 2003 Huntsville Alabama

AIAA 2003-4900

Copyright copy 2003 by In-Kyung Sung Published by the American Institute of Aeronautics and Astronautics Inc with permission

The long-term goal of the work described here is the development of a test-bed for the evaluation of long-life technologies including analytical approaches innovative functional designs advanced materials and integrated health monitoring The near-term goal is to develop an integrated analyticalexperimental approach for life prediction using prototypical subscale combustors The advantage of using a subscale prototypical combustor for life prediction is that the tests can be accomplished for a fraction of the cost of full-scale tests Thus many more configurations can be tested before a full-scale design is determined Manufacturing variability can be examined parametrically through tests which would be impractical with full scale hardware Finally the aversion to a test-to-failure philosophy due to high full scale hardware costs and risks to valuable test facilities could be overcome The specific objectives of this study were three-fold to qualitatively predict the expected failure mechanism of the gradual thinning of the cooling passage and the so-called ldquodog houserdquo effect by using a visco-plastic model to verify theoretical life estimation by using test data and to provide students with the experience of a ldquodesign build and testrdquo rocket engine combustor project First a brief review of previous work in life prediction is presented with an emphasis on studies that used subscale test hardware An analysis based on the viscoplastic treatment of stress and strain is then presented Then the experimental hardware is described along with the test approach used in this study Finally the results are discussed and compared to the analytical predictions

BACKGROUND

In modern high-thrust liquid rocket engines like the SSME the temperature and pressure of the combustion gas are around 3600 K (6000 F) and 20 MPa (3000 psi) and the heat flux at throat region of combustor chamber rises up to 115-130 Wm2 (70-80 Btuin2-s) At present there is no material to withstand this temperature without losing structural strength Thermal stress is an important factor in the material selection To relieve high thermal stress and ensure useful life at these harsh conditions materials with high thermal conductivity such as oxygen free high conductivity (OFHC) are used Due to its low melting point (1350 K) the copper wall temperature should be kept below 860 K (1100 F) In the SSME case the thickness of the wall between hot gas side and coolant side is 076 mm (003 in) and the temperature difference is about 200 K (360 F) Because the stress due to this thermal gradient is about 100-150

MPa it can be seen that most of stress range is within the plastic region according to the stress-strain curve of the copper alloy For most metals an increase in temperature results in a reduction in the yield stress and cyclic loading results in strain hardening before steady state is reached At low temperatures for most metals crack initiation and propagation will occur when cyclic loading is applied As temperature increases the material softens and finally melts and burns out Creep is the dominant factor at this phase Also buckling due to high axial pressure loads may occur because of the weakened material strength at elevated temperature Corrosion and abrasion can also be expected when the combustor is fired either for long time or for repeated operations When the operation time is sufficiently long at elevated temperatures creep is more important than other factors but when the cyclic period is too short to reach a steady state fatigue is more important To make matters worse two mechanisms can interact to result in plastic ratcheting or cyclic-dependent creep This process results in progressive deformation and thinning of coolant channel wall Successive tests of small thrusters by Quentmeyer1 and Jankovsky et al2 at the NASA Lewis Research Center showed that combustor life is determined not only by fatigue but by creep-fatigue interaction corrosion and sometimes ductile rupture Kasper3 used a cyclic fatigue and creep analysis approach to estimate combustor life Porowski et al4 attempted a simplified structural model of the coolant channel ligament as a rectangular beam for life prediction Dai and Ray5 improved this method by introducing the concepts of sandwich beam model approximation and a time-dependent visco-plastic model Robinson and Arnold6 also developed and investigated the influence of loading cycle duration and verified the effects of thinning and bulging by using a viscoplastic model Presently the viscoplastic model represents the state of the art for modeling stress and strain and combustor life at typical rocket conditions Since there is no universal viscoplastic model which covers all the possible phenomena of material behavior models specified for different materials and features have to be chosen Classical theory is only applicable to steady state situations Simple rheological models describe creep and relaxation in a first order approximation However unified models show that they can deal with all the inelastic time dependent phenomena In unified models internal variables describe the different material behavior during loading via evolutionary functions The viscoplastic model is made up of flow


2

rules and evolutionary laws which describes inelastic strain rate and hardening and recovery processes for cyclic loading respectively A detailed explanation for viscoplastic models are given in References 6 and 8

2 22

2

2 20 0 01 2

( )( )6 4

12

xin in

Cx p t xw x t x

x I d I d dd d

ηξ ξ η

= minus +

+ minus + int int int

(4)

The design of the small scale combustor used in this project is meant to reproduce the same ldquodog-houserdquo effect due to plastic ratcheting observed by Quentmeyer1 A test section was designed on the basis of simple one-dimensional thermal models and empirical stress-strain life curves Preliminary analysis was used to fabricate a test section that could be tested to failure within a reasonable number of cycles without burnout The simple thermal analysis was updated using coolant temperature rise data and a detailed life analysis was conducted based on the ideas of Dai and Ray5 and Freedrsquos visco-plastic model8 to compute the inelastic strain rate Cyclic testing with periodic test article inspection was conducted to verify the predictions The analytical and experimental approaches are described in the following sections along with the experimental results

where subscripts 1 and 2 denote coolant and hot side thin faces of the sandwich beam model respectively and

1 1 2 22

1 2 1 2 1 2( )A E A EC

A A E E d d+

=+

2 2in in inI 1ε ε= minus

and p(t) = distributed force per unit length

ℓ = half length of the ligament x = ligament width A1 A2 = cross section area of sandwich beam 1 and 2 E1 E2 = Youngrsquos modulus of face 1 and 2 d1 d2 = distance between the thin faces

The first term on the right hand side of Eq (4) shows the reversible components of the radial deflection and the second term represents the permanent bulging and progressive thinning of the coolant channel wall With this radial deflection w(t) at the midplane of the ligament the normalized thinning rate is expressed as

ANALYTICAL APPROACH

The method developed by Dai and Ray5 is based on the concepts of sandwich beam model and viscoplasticity to represent progressive bulging and thinning phenomena in the coolant channel of rocket engine This is a brief description about prediction methodology

0

4 1 ( )( )

4 2 1

w tat

a a

τϑ

+ = +

(5) The total strain rate is the sum of elastic and inelastic strain

e iij ij ij

nε ε ε= + (1) where a is the distance between channels and θ0 is the original ligament thickness

Each strain can be obtained by the integration of the elastic and inelastic strain rate

Finally life was computed as (1 )e

ij ij kk ijE Eν νε σ σ+

= minus δ (2)

0

( )crLife

tθ θτminus

= (6) thij Tε α= (3)

and critical thickness by To compute the inelastic strain rate the Freed

viscoplastic model was introduced From this inelastic strain pressure distribution and geometric configuration of the cooling channel the time-dependent radial deflection at the midplane of the hot wall can be obtained

0 exp( )cr qθ θ= minus (7)) where q = 02[(Su-Sy)Sy]06 Su = ultimate stress Sy = yield stress


3

Freed8 developed a phenomenologically based viscoplastic model for copper Two internal state variables are introduced the back stress Bij for kinematic anisotropic hardening and the drag stress D for isotropic hardening

Finally the recovery function r is defined as

0

0

0( )

( )D D

r GR G D D

== gt

(13)

where The flow law equation represents the strain rate

associated with metal deformation which can be modeled by a power law at lower stresses and an exponential law at the higher stresses [ ]

1 1( )

exp ( 1) 1

nAG GR G

A n G G G

minus le= minus ge

(14)

2

ijinij Zε θ

Σ=

Σ (8)

with the constraint

221 2

Br Z F

G LD

ge minus +

(15) The thermal diffusivity function θ is a temperature dependent effect largely due to the thermal diffusivity parameter11 Dislocation climb dominates at higher temperatures while dislocation gliding acts at lower temperatures

where 212

in inij jiI ε ε= L

S D=

minusG 2F

DΣ

=

exp 05

2exp ln 1 052

Q T TmkT

TQ m T TmkT Tm

θ

minus ge = minus + le

(9)

212 ij jiB B= B 1

3ij ij kk ijS σ σ δ= minus

ij ij ijS BΣ = minus 212 ij jiΣ = Σ Σ

The main purpose of this model is to simplify the physics and extend its intended application to a wide range of temperature for ductile material such as copper The material constants can be obtained from isothermal experiment data By the comparison with experimental data it was shown that this model was good for the hot end of a loading cycle but over-predicted the stress at the cold end of the cycle8

where k = Boltzman constant 1381E-23 JK Q = activation energy 200000 Jmol Tm = melting temperature 1356 K The Zener-Hollomon parameter Z is defined by the ratio of inelastic strain rate and thermal diffusivity parameter

EXPERIMENTAL APPROACH

1

exp[ ( 1)] 1

nAF FZ

A n F F le

= minus ge

(10) A small scale combustion chamber was designed built and tested by senior and first year graduate level students in the School of Aeronautics and Astronautics at Purdue University The students derived specific design requirements from the following top-level requirements

The back stress Bij accounts for the kinematic or flow-induced anisotropic hardening when a cyclic load is applied - a low cycle fatigue failure mechanism had to be

demonstrated within a reasonable number of cycles (lt200)

2ijin

ij ij

BB H I

Lε

= minus

(11) - the experiment had to verify a life prediction analysis from conventional modeling approaches

- the environments in the test section had to be well-characterized and results from the thermal analysis had to be verifiable

The drag stress D represents the isotropic hardening of the material

- the water cooled liner could not melt prior to the LCF failure 2 ( )

ID h r G

Gθ = minus

(12) - conventional design analysis methods were used

- all parts had to be manufactured in the Aerospace Sciences Laboratory at Purdue


4

The main components of the test article (Figure 1 from top to bottom) were a catalyst bed to decompose 90 by weight hydrogen peroxide a fuel injector a copper heat sink precombustor with sufficient volume to provide complete combustion and mixing of the decomposed oxidizer and fuel and the test section which comprised a plug nozzle and a water-cooled oxygen-free high-conductivity (CU102) copper liner This configuration is similar to that used at NASA Lewis Research Center12 The combustor assembled on the test stand is shown in Figure 2 Design and operating parameters are given in Table 1

P_Oxcatoutfrac14rdquo AN Fitting200 psi

T_Catout116rdquo Swagelok Fitting1200 degrees F

P_Chamber2frac14rdquo AN Fitting200 psi


T_PrecombustorWelded260 degrees F

P_CBinfrac14rdquo AN Fitting100 psi

P_Jackinfrac14rdquo AN Fitting100 psi

T_Jackin116rdquo Swagelok Fitting

71 degrees F

P_Jackoutfrac14rdquo AN Fitting80-100 psi

T_Jackout1116rdquo Swagelok Fitting150 degrees F


To Ox Main Valve500 psi 90 H202frac12rdquo AN Fitting

To Fuel Main Valve250 psi RP-112rdquo AN Fitting

To Water Main Valve200 psi H2012rdquo AN Fitting

Engine Mount Bolts to (4) Unitstrut L-bracketsOn Test Stand w(4) frac12rdquo bolts

The cooled liner channel geometry was based on standard channel wall designs The hot wall thickness was set at 0030 in (which is within the design range for typical designs as well as being machinable in the Aerospace Sciences Laboratory machine shop) and the land width was set at 0103 in The channel width was 0125 in and the channel height was 006 in These channel geometries were determined to result in a failure within a reasonable number of cycles at the available combustor conditions

A simple one-dimensional code using the

Bartz and Seider-Tate equations9 for hot- and coolant-side heat transfer coefficients respectively was developed and applied The coolant flow rate was set to maintain a safe margin from a calculated burnout heat flux of 654 Btuin2-s De-ionized water was used as coolant for both the center body and the chamber liner which was dumped into the plume Figures 3 and 4 show the predicted heat flux variation and wall temperatures along the chamber and nozzle Detailed analysis of the temperature stress and strain field around the cooling channel was done using finite element analysis codes namely ABAQUS and ANSYS

Figure 1 Test article schematic and interfaces A catalyst bed is used to decompose hydrogen peroxide which is then sent to the precombustor to burn with JP-8 to produce a well-mixed hot gas The hot gas enters the test section composed of the water-cooled liner and centerbody The throat of the test section is formed by the diverging centerbody

Figures 5 6 and 7 show the assembly upstream of the nozzle the water-cooled chamber liner and the water-cooled center-body The chamber liner was designed to fit tightly within a stainless steel combustor case (not shown) The center-body was coated with thermal barrier coating (TBC) To avoid cracks due to differential thermal expansion an aluminumbronze bond layer was applied between the copper and the Rokide a Zirconium Oxide TBC Rokide is made up of 95 copper and 5 aluminum and was applied to a thickness of 001 in After 140 firings the coating was still intact on the most critical part of the center-body the throat However a TBC failure did occur on the point between the three center-body support ribs due to stagnation point heating Pre- and post-failure pictures can be seen in Figures 8 and 9 respectively Loss of the TBC however did not result in a loss of functionality of the part

Figure 2 Test article assembly on test stand


5

Table 1 Operating and Design Parameters Parameter Value Propellant Mixture Ratio (OF) 40 Oxidizer Mass Flow Rate 10 lbs Fuel Mass Flow Rate 025 lbs Chamber Pressure (Pc) 200 psia Characteristic Velocity (C) 4961 fts Specific Impulse (Isp) 2051 s Chamber Temperature (Tc) 3900 degR Expansion Ratio (ε) 28 Nozzle Throat Area (At) 0915 in2 Nozzle Exit Area (Ae) 256 in2 Nozzle Throat Diameter (Dt) 108 in Chamber Diameter (Dc) 35 in Contraction Ratio (CR) 105 Characteristic Length (L) 70 Chamber Volume (Vc) 64 in3

Chamber Length (Lc) 60 in Injector Diameter (Din) 230 in Number of Injector Holes 12 Injector Hole Diameter (Dinh) 0032 in

20

25

30

35

40

45

50

55

60

65

-25 -20 -15 -10 -05 00 05 10 15Axis [in]

q [B

tuin

^2-s

]

Figure 3 Predicted chamber heat flux as function of chamber length Throat is at 00 location

Testing was conducted in the Advanced Propellant and Combustion Laboratory (APCL) at Purdue University (httpengrpurdueeduAAEResearchPropulsionFacilitiesapcl) An image of a representative test firing is shown in Figure 10 The project took advantage of the major hardware previously installed in the test cell Modifications were made to accommodate the requirements of this project For instance a 650 psia water tank was installed to provide water to both the center-body and the cooling liner The flow timing sequence was automatically controlled with LABVIEW (National Instruments) which controlled the pneumatically actuated valves and the data acquisition system

450

500

550

600

650

700

-25 -20 -15 -10 -05 00 05 10 15

Axis [in]

Twg

amp T

wl [

K]

TwgTwl

Figure 4 Predicted gas-side and coolant-side wall temperature as function of test section length Throat is at 00 location

On average each cycle comprised a 05 s H2O2 lead with a 10 s bipropellant (both fuel and oxidizer) firing a 15 s H2O2 lag and then a 20 s pause to allow the cooling channels to return to their initial temperatures The lead and lag time were implemented to insure complete H2O2 decomposition and to burn any residual fuel left in the engine This cycle was repeated (on average) twelve times for every test Cooling water was flowed continuously throughout the cyclic testing Figures 11 and 12 show chamber pressure and propellant mass flow rates typical of a series of cycles The five pulses shown at the beginning of the test were monopropellant cycles used to raise the temperature of the catalyst bed prior to the bipropellant tests to ensure that the oxidizer was completely decomposed before it entered the precombustor Figure 13 shows the C efficiency of the engine indicating that nearly complete combustion was occurring in the precombustor and that the gas environment in the test section could be closely characterized by one-dimensional equilibrium calculations Figures 14 and 15 represent coolant temperatures and pressures at the inlet and the outlet water ports respectively These measurements were the primary means used to verify the thermal analysis which served as a basis for the life prediction analysis described later The rocket was disassembled after every ten or so cycles depending on the amount of propellant loaded The cooling jacket was then visually inspected as well as dye-penetrant inspected Notes were taken and pictures were taken to document the condition of the hardware


6

Figure 5 Assembly of injector and pre-combustor with a test nozzle

Figure 8 Center-body in pre-test condition View is forward looking aft Three struts hold centerbody

Figure 9 Post-failure center-body showing spalling of thermal barrier coating

Figure 6 Chamber liner before testing

Figure 10 Representative bipropellant hot fire test in APCL

Figure 7 Center-body after TBC coating


7

Figure 11 Experimental chamber pressure during

Figure 13 C efficiency measured in precombustor

cyclic testing

Figure 14 Coolant temperature during cyclic

Figure 12 Experimental propellant mass flow

testing rate during cyclic testing


8

temperature as a function of channel length

300

305

310

315

320

325

330

335

340

345

-25 -20 -15 -10 -05 00 05 10 15Axis [in]

Tw_p

red

amp T

w-c

orr [

K]

Tw_predTw_corr

Figure 16 Predicted and measured coolant

Figure 15 Coolant pressure during cyclic testing From the calculated temperature distribution and

pressure loading the thermo-mechanical stress and strain were obtained Figure 18 depicts total strain for the throat region at steady state conditions as computed by ANSYS The maximum strain computed analytically and the ANSYS prediction was in agreement at about 20 From the strain life (S-N) curve of OFHC10 Figure 19 the number of cycles to failure was predicted to be 115 cycles

DETAILED ANALYSIS A detailed finite element analysis was performed after the first set of data was obtained to provide verification data for the thermal analysis Data reduction was performed by a MATLAB code written by the students For verification of the thermal analysis results the temperature rise of the coolant was measured Figure 16 shows that the temperature rise predicted initially was somewhat lower than that which was measured This may have been due to the fact that the simple thermal analysis only considered the heat flux at the bottom surface of the channel ie the effect of side wall heat transfer was neglected To determine actual liner conditions for input to the life analysis the coolant temperature variation was corrected on the basis of the coolant temperature measurements

Thermal and mechanical stress and strain were then computed using the corrected wall temperature values that were derived from the coolant water temperature measurements To further verify the analytical values more detailed analyses using ANSYS and ABAQUS were used Figure 17 shows the predicted temperature distribution in the wall at the throat region indicating a maximum temperature of 714 K (825 F) and a temperature gradient of 1920 Fin

Figure 17 Wall temperature distribution around rectangular cooling channel Maximum temperature (790 K) was occurred at the middle of the ligament


9

Figure 18 Total strain predicted by ANSYS around rectangular cooling channel Highest strain occurred at the corner of cooling channel

Figure 19 Strain-life curve for OHFC10

The method of Porowski4 and the viscoplastic method estimated life to be between 51 and 260 cycles A deformation in the throat region was noted at approximately the 90th cycle To validate the viscoplastic prediction method the nozzle test section deformation was measured The thickness of the throat section that did not show deformation was partially increased The original thickness of the throat was 0030 in The average thickness of the throat section where it was not deformed was changed to 0032rdquo after 140 cycles The thickness of the deformed region was 0029 in so the reduced thickness was 0003 in Therefore the thinning rate was calculated as 0003 in140 = 25E-5 incycle The critical wall thickness beyond which the crack growth rate became infinity was computed to be 00242rdquo by Eq (7) The cycles to failure can be calculated using Eq(6) Finally life was

determined to be 270 cycles which shows good agreement with the visco-plastic estimation Figure 20 shows the equivalent plastic strain Since ABAQUS starts zero strain at the yield point the total strain (12) is the sum of plastic (10) and elastic strain (02) Total strain gives a life of 320 cycles from Figure 19 To see the progressive deformation and thinning of the wall the throat region was modeled via ABAQUS and cyclic loading was applied up to 100 times based on the loading history that was used Figures 21 ndash 24 show the deformation of the wall in increments of 20 cycles (starting at 40 cycles)

Figure 20 Equivalent plastic strain in region around rectangular cooling channel Highest strain (12) occurred at the middle of the hot side ligament

Figure 21 Deformation of channel wall at 40 cycles


10



Figure 24 Deformation of channel wall at 100 cycles From Figures 21 ndash 24 it can be seen that deformation was predicted to begin at around 60 cycles However thinning was not observed in these simulations This is due to the fact that temperature dependent experimental plastic stress strain data were

implemented instead of using visco-plastic modeling to compute fatigue deformation Table 2 contains a summary of predicted results and measured result Table 2 Summary of Predicted and Measured Life

Prediction Method Predicted No of cycle

Measured No of cycle

Effective stress-strain 115 Poroski method 51 Viscoplastic model 260 FEM ndash ANSYS 115 FEM ndash ABAQUS 320

270

EXPERIMENTAL RESULTS

After the first 20 cycles the liner had two purple spots indicating local overheating At the same time it was noted that several o-rings in the fuel injector were melting and causing the fuel to leak into the chamber To remedy this another copper spacer was machined and inserted between the injector and the pre-combustor This spacer acted as a block between the hot combustion gases and the fuel injector as well as a relatively large sink that would assist in dissipating residual heat Later tests proved that this fix helped greatly In addition to this extra spacer Teflon O-rings were used to replace Viton O-rings After 60 cycles two dime-sized silver spots indicating local temperatures approaching 1400 F were observed at the throat region as shown in Figures 25 and 26 At that same time the inner surface of the liner had noticeable surface roughening very similar to that noticed by Quentmeyer1

Figure 25 Picture of silver spot 1 in liner near throat plane


11

Figure 26 Picture of silver spot 2 in liner neat throat plane

Inspection after cycle 119 showed that the two spots had merged into one large silver spot with considerable radial (inward) deformation (see Figures 27 and 28) The large deformation observed was not the type of failure that was predicted a crack was expected that would eventually propagate and lead to a coolant flow pressure loss A small crack did appear at the end of the 90th cycle but no changes were noted in subsequent tests One more set of cycles were conducted to increase the total number of cycles to 140

Figure 27 Close-up of extreme deformation and silver spot enlarged The size of this spot is 15rdquo times 06rdquo in A speculated failure mechanism is that the weakest portion (due to material inconsistencies or a hot spot) of the liner at the throat began to deform as normally expected by the bulging out of the coolant wall towards the interior of the chamber However since the liner was not fixed to the stainless steel casing the inward

bulging created a void between the copper liner and the stainless steel casing which potentially led to a lower coolant flow velocity and increased local heating A structural analysis performed early in the design phase indicated that the free-standing liner had the strength to withstand buckling at the elevated temperature Another possible failure mechanism is the circumferential buckling due to difference of stress direction Thermal loads cause compressive stress on the hot side wall and tensile stress on the coolant side It is speculated that the weakest portion could not sustain its original shape at the high temperature and high coolant pressure This process could have propagated very quickly during a set of 12 cycles

Figure 28 Interior surface deformation showing roughening around ribs

SUMMARY AND CONCLUSIONS Presently life prediction of rocket hot sections is a heavily empirical practice requiring safety factors that are higher than those used in conventional thermo-structural analysis Furthermore the mechanisms that limit the life of the combustor are not necessarily well-understood a priori Important factors that could lead to early failure include the effects of thermo-fluid cycling and the specific design and manufacturing of the chamber A small-scale rocket combustor was designed and tested to verify life prediction models for low cycle fatigue and fatigue-creep interaction In this paper several life prediction methods were applied to predict combustor life and were compared with test results Viscoplastic modeling showed better agreement than conventional methods in predicting the life cycle failure when both low cycle fatigue and elevated temperature


12


13

loads were applied Possible improvements that could eliminate some uncertainty in the failure mechanism would be to fix the liner lands to the structural jacket

ACKNOWLEDGEMENTS This work was funded by the NASA Marshall Space Flight Center Grant NAG8-1876 with Mr Huu Trinh as Technical Monitor and by the School of Aeronautics and Astronautics at Purdue University The authors wish to thank the staff at the Aerospace Sciences Laboratory for their excellent fabrication of the test articles Messrs Jim Sisco BJ Austin and Scott Meyer for their advice in test article design and testing and Mr Brian Hoyt of Metal Technologies in Lebanon IN for his help in applying thermal barrier coatings to the plug nozzle Finally the authors would like to acknowledge the outstanding work of John Gedmark Jason Gromski Joshua Jung Matthew Stout Daisuke Hiroka Dentcho Genov and Emily Vaughn members of the student team who designed built and tested the combustor as part of a Design Build Test project at Purdue

REFERENCES

[1] Quentmeyer RJ ldquoExperimental Fatigue Life Investigation of Cylindrical Thrust Chambersrdquo presented at the AIAA Thirteenth Propulsion Conference Orlando FL July 11-13 1977 NASA TM X-73665

[2] Jankovsky RS Arya V K Kazaroff JM Halford GR ldquoStructurally Compliant Rocket Engine Combustion Chamber-Experimental and Analytical Validationrdquo NASA TP 3431 1994

[3] Kasper H J ldquoThrust Chamber Life Predictionrdquo NASA CP-2372 pp 36-43 1984

[4] Porowski JS OrsquoDonnell WJ Badlani ML Kasraie B and Kasper HJ ldquoSimplified Design and Life Prediction of Rocket Thrust Chambersrdquo AIAA Journal Vol 2 No 2 March 1985

[5] Dai X and Ray A ldquoLife Prediction of the Thrust Chamber Wall of a Reusable Rocket Enginerdquo J of Propulsion and Power Vol 11 No 6 1995

[6] Robinson DN and Arnold SM ldquoEffects of State Recovery on Creep Buckling Under Variable Loadingrdquo J of Applied Mechanics Vol 57 1990

[7] Arya V K Arnold SM ldquoViscoplastic Analysis of an Experimental Cylindrical Thrust Chamber Linerrdquo AIAA Journal Vol 30 No 3 1992

[8] Freed A D Verrilli M J ldquoA Viscoplastic Theory Applied to Copperrdquo NASA TM-100831 1988

[9] Huzel D K Huang D H ldquoModern Engineering for Design of Liquid-Propellant Rocket Enginesrdquo NASA SP-125 1992

[10] Esposito J J and Zabora R F ldquoThrust Chamber Life Prediction Volume I - Mechanical and Physical Properties of High Performance Rocket Nozzle Materialsrdquo NASA CR-134806 1975

[11] Miller A K ldquoA Unified Phenomenological Model for the Monotonic Cyclic and Creep Deformation of Strongly Work-Hardening Materialsrdquo PhD Thesis Stanford University 1975 pp 36-41

The long-term goal of the work described here is the development of a test-bed for the evaluation of long-life technologies including analytical approaches innovative functional designs advanced materials and integrated health monitoring The near-term goal is to develop an integrated analyticalexperimental approach for life prediction using prototypical subscale combustors The advantage of using a subscale prototypical combustor for life prediction is that the tests can be accomplished for a fraction of the cost of full-scale tests Thus many more configurations can be tested before a full-scale design is determined Manufacturing variability can be examined parametrically through tests which would be impractical with full scale hardware Finally the aversion to a test-to-failure philosophy due to high full scale hardware costs and risks to valuable test facilities could be overcome The specific objectives of this study were three-fold to qualitatively predict the expected failure mechanism of the gradual thinning of the cooling passage and the so-called ldquodog houserdquo effect by using a visco-plastic model to verify theoretical life estimation by using test data and to provide students with the experience of a ldquodesign build and testrdquo rocket engine combustor project First a brief review of previous work in life prediction is presented with an emphasis on studies that used subscale test hardware An analysis based on the viscoplastic treatment of stress and strain is then presented Then the experimental hardware is described along with the test approach used in this study Finally the results are discussed and compared to the analytical predictions

BACKGROUND

In modern high-thrust liquid rocket engines like the SSME the temperature and pressure of the combustion gas are around 3600 K (6000 F) and 20 MPa (3000 psi) and the heat flux at throat region of combustor chamber rises up to 115-130 Wm2 (70-80 Btuin2-s) At present there is no material to withstand this temperature without losing structural strength Thermal stress is an important factor in the material selection To relieve high thermal stress and ensure useful life at these harsh conditions materials with high thermal conductivity such as oxygen free high conductivity (OFHC) are used Due to its low melting point (1350 K) the copper wall temperature should be kept below 860 K (1100 F) In the SSME case the thickness of the wall between hot gas side and coolant side is 076 mm (003 in) and the temperature difference is about 200 K (360 F) Because the stress due to this thermal gradient is about 100-150

MPa it can be seen that most of stress range is within the plastic region according to the stress-strain curve of the copper alloy For most metals an increase in temperature results in a reduction in the yield stress and cyclic loading results in strain hardening before steady state is reached At low temperatures for most metals crack initiation and propagation will occur when cyclic loading is applied As temperature increases the material softens and finally melts and burns out Creep is the dominant factor at this phase Also buckling due to high axial pressure loads may occur because of the weakened material strength at elevated temperature Corrosion and abrasion can also be expected when the combustor is fired either for long time or for repeated operations When the operation time is sufficiently long at elevated temperatures creep is more important than other factors but when the cyclic period is too short to reach a steady state fatigue is more important To make matters worse two mechanisms can interact to result in plastic ratcheting or cyclic-dependent creep This process results in progressive deformation and thinning of coolant channel wall Successive tests of small thrusters by Quentmeyer1 and Jankovsky et al2 at the NASA Lewis Research Center showed that combustor life is determined not only by fatigue but by creep-fatigue interaction corrosion and sometimes ductile rupture Kasper3 used a cyclic fatigue and creep analysis approach to estimate combustor life Porowski et al4 attempted a simplified structural model of the coolant channel ligament as a rectangular beam for life prediction Dai and Ray5 improved this method by introducing the concepts of sandwich beam model approximation and a time-dependent visco-plastic model Robinson and Arnold6 also developed and investigated the influence of loading cycle duration and verified the effects of thinning and bulging by using a viscoplastic model Presently the viscoplastic model represents the state of the art for modeling stress and strain and combustor life at typical rocket conditions Since there is no universal viscoplastic model which covers all the possible phenomena of material behavior models specified for different materials and features have to be chosen Classical theory is only applicable to steady state situations Simple rheological models describe creep and relaxation in a first order approximation However unified models show that they can deal with all the inelastic time dependent phenomena In unified models internal variables describe the different material behavior during loading via evolutionary functions The viscoplastic model is made up of flow


2


2 22

2

2 20 0 01 2

( )( )6 4

12

xin in

Cx p t xw x t x

x I d I d dd d

ηξ ξ η

= minus +


(4)



1 1 2 22

1 2 1 2 1 2( )A E A EC

A A E E d d+

=+





ANALYTICAL APPROACH


0

4 1 ( )( )

4 2 1

w tat

a a

τϑ

+ = +


e iij ij ij





= minus δ (2)

0

( )crLife

tθ θτminus

= (6) thij Tε α= (3)





3



0

0

0( )

( )D D

r GR G D D

== gt

(13)



1 1( )

exp ( 1) 1

nAG GR G

A n G G G

minus le= minus ge

(14)

2

ijinij Zε θ

Σ=

Σ (8)

with the constraint

221 2

Br Z F

G LD

ge minus +


where 212


S D=

minusG 2F

DΣ

=

exp 05

2exp ln 1 052

Q T TmkT

TQ m T TmkT Tm

θ


(9)

212 ij jiB B= B 1






1

exp[ ( 1)] 1

nAF FZ

A n F F le

= minus ge




2ijin

ij ij

BB H I

Lε

= minus





ID h r G

Gθ = minus




4










71 degrees F















5



20

25

30

35

40

45

50

55

60

65

-25 -20 -15 -10 -05 00 05 10 15Axis [in]

q [B

tuin

^2-s

]



450

500

550

600

650

700

-25 -20 -15 -10 -05 00 05 10 15

Axis [in]

Twg

amp T

wl [

K]

TwgTwl




6








7



cyclic testing





8


300

305

310

315

320

325

330

335

340

345

-25 -20 -15 -10 -05 00 05 10 15Axis [in]

Tw_p

red

amp T

w-c

orr [

K]

Tw_predTw_corr








9








10








270





11








12


13



REFERENCES













2 22

2

2 20 0 01 2

( )( )6 4

12

xin in

Cx p t xw x t x

x I d I d dd d

ηξ ξ η

= minus +


(4)



1 1 2 22

1 2 1 2 1 2( )A E A EC

A A E E d d+

=+





ANALYTICAL APPROACH


0

4 1 ( )( )

4 2 1

w tat

a a

τϑ

+ = +


e iij ij ij





= minus δ (2)

0

( )crLife

tθ θτminus

= (6) thij Tε α= (3)





3



0

0

0( )

( )D D

r GR G D D

== gt

(13)



1 1( )

exp ( 1) 1

nAG GR G

A n G G G

minus le= minus ge

(14)

2

ijinij Zε θ

Σ=

Σ (8)

with the constraint

221 2

Br Z F

G LD

ge minus +


where 212


S D=

minusG 2F

DΣ

=

exp 05

2exp ln 1 052

Q T TmkT

TQ m T TmkT Tm

θ


(9)

212 ij jiB B= B 1






1

exp[ ( 1)] 1

nAF FZ

A n F F le

= minus ge




2ijin

ij ij

BB H I

Lε

= minus





ID h r G

Gθ = minus




4










71 degrees F















5



20

25

30

35

40

45

50

55

60

65

-25 -20 -15 -10 -05 00 05 10 15Axis [in]

q [B

tuin

^2-s

]



450

500

550

600

650

700

-25 -20 -15 -10 -05 00 05 10 15

Axis [in]

Twg

amp T

wl [

K]

TwgTwl




6








7



cyclic testing





8


300

305

310

315

320

325

330

335

340

345

-25 -20 -15 -10 -05 00 05 10 15Axis [in]

Tw_p

red

amp T

w-c

orr [

K]

Tw_predTw_corr








9








10








270





11








12


13



REFERENCES














0

0

0( )

( )D D

r GR G D D

== gt

(13)



1 1( )

exp ( 1) 1

nAG GR G

A n G G G

minus le= minus ge

(14)

2

ijinij Zε θ

Σ=

Σ (8)

with the constraint

221 2

Br Z F

G LD

ge minus +


where 212


S D=

minusG 2F

DΣ

=

exp 05

2exp ln 1 052

Q T TmkT

TQ m T TmkT Tm

θ


(9)

212 ij jiB B= B 1






1

exp[ ( 1)] 1

nAF FZ

A n F F le

= minus ge




2ijin

ij ij

BB H I

Lε

= minus





ID h r G

Gθ = minus




4










71 degrees F















5



20

25

30

35

40

45

50

55

60

65

-25 -20 -15 -10 -05 00 05 10 15Axis [in]

q [B

tuin

^2-s

]



450

500

550

600

650

700

-25 -20 -15 -10 -05 00 05 10 15

Axis [in]

Twg

amp T

wl [

K]

TwgTwl




6








7



cyclic testing





8


300

305

310

315

320

325

330

335

340

345

-25 -20 -15 -10 -05 00 05 10 15Axis [in]

Tw_p

red

amp T

w-c

orr [

K]

Tw_predTw_corr








9








10








270





11








12


13



REFERENCES





















71 degrees F















5



20

25

30

35

40

45

50

55

60

65

-25 -20 -15 -10 -05 00 05 10 15Axis [in]

q [B

tuin

^2-s

]



450

500

550

600

650

700

-25 -20 -15 -10 -05 00 05 10 15

Axis [in]

Twg

amp T

wl [

K]

TwgTwl




6








7



cyclic testing





8


300

305

310

315

320

325

330

335

340

345

-25 -20 -15 -10 -05 00 05 10 15Axis [in]

Tw_p

red

amp T

w-c

orr [

K]

Tw_predTw_corr








9








10








270





11








12


13



REFERENCES














20

25

30

35

40

45

50

55

60

65

-25 -20 -15 -10 -05 00 05 10 15Axis [in]

q [B

tuin

^2-s

]



450

500

550

600

650

700

-25 -20 -15 -10 -05 00 05 10 15

Axis [in]

Twg

amp T

wl [

K]

TwgTwl




6








7



cyclic testing





8


300

305

310

315

320

325

330

335

340

345

-25 -20 -15 -10 -05 00 05 10 15Axis [in]

Tw_p

red

amp T

w-c

orr [

K]

Tw_predTw_corr








9








10








270





11








12


13



REFERENCES



















7



cyclic testing





8


300

305

310

315

320

325

330

335

340

345

-25 -20 -15 -10 -05 00 05 10 15Axis [in]

Tw_p

red

amp T

w-c

orr [

K]

Tw_predTw_corr








9








10








270





11








12


13



REFERENCES














cyclic testing





8


300

305

310

315

320

325

330

335

340

345

-25 -20 -15 -10 -05 00 05 10 15Axis [in]

Tw_p

red

amp T

w-c

orr [

K]

Tw_predTw_corr








9








10








270





11








12


13



REFERENCES













300

305

310

315

320

325

330

335

340

345

-25 -20 -15 -10 -05 00 05 10 15Axis [in]

Tw_p

red

amp T

w-c

orr [

K]

Tw_predTw_corr








9








10








270





11








12


13



REFERENCES



















10








270





11








12


13



REFERENCES



















270





11








12


13



REFERENCES



















12


13



REFERENCES













13



REFERENCES












[American Institute of Aeronautics and Astronautics 39th AIAA/ASME/SAE/ASEE Joint Propulsion...

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Transcript of [American Institute of Aeronautics and Astronautics 39th AIAA/ASME/SAE/ASEE Joint Propulsion...