Thermo-structural analysis of regenerative cooling thrust chamber cylinder segment based on experimental data

CJA 1418 15 October 2019 Chinese Journal of Aeronautics, (2019), xxx(xx): xxx–xxx

No. of Pages 15

1

Chinese Society of Aeronautics and Astronautics & Beihang University

Chinese Journal of Aeronautics [email protected] www.sciencedirect.com

5

Thermo-structural analysis of regenerative cooling thrust chamber cylinder segment based on experimental data

6

Di LIU a, Bing SUN a, Taiping WANG a, Jiawen SONG b, Jianwei ZHANG a,*

3

4

7 8

9

a b

School of Astronautics, Beihang University, Beijing 100083, China The 9th Designing, China Aerospace Science and Industry Corporation, Wuhan 430040, China

Received 19 September 2018; revised 14 March 2019; accepted 21 April 2019

10

12 13

KEYWORDS

14

Finite element analysis; Rocket engine; Regenerative cooling; Structural analysis; Thrust chamber; Thermal analysis

15 16 17 18 19

20

Abstract To evaluate the structural failure risk of the regenerative cooling thrust chamber cylinder segment, a Finite Element Method (FEM) based on experimental data was developed. The methodology was validated and utilized to reveal the thermal response and the nonlinear deformation behavior of the cylinder segment phase by phase. The conclusions of the research are as follows: The 2D heat flux distribution caused by the injector determines the uneven temperature distribution on the gas-side wall and leads to the temperature disparity between various cooling channels; The reason for the accumulation of residual strain is that the tensile strain generated in the post-cooling phase is greater than the compressive strain produced in the hot run phase; Through the single-cycle simulation, two potential failure locations with conspicuous deformations were found, but it is difficult to determine which point is more dangerous. However, the multi-cycle thermo-structural analysis gives the evolution of the stress-strain curve and gradually discloses that the low-temperature corner of a particular channel is the most likely location to fail, rather than the maximum residual strain point of the gas-side wall. The damage analysis for dangerous point indicates that the quasistatic damage accounts for the majority of the total damage and is the main factor limiting the service life. Ó 2019 Production and hosting by Elsevier Ltd. on behalf of Chinese Society of Aeronautics and Astronautics. This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/ licenses/by-nc-nd/4.0/).

* Corresponding author. E-mail address: [email protected] (J. ZHANG). Peer review under responsibility of Editorial Committee of CJA.

Production and hosting by Elsevier

1. Introduction

21

The excellent reusable performance of rockets engine has always been the goal of engineers and scientists.1 ‘‘Falcon 9” and ‘‘New Shepard”, which have been successfully recovered several times, make the pursuit increasingly urgent. As a critical component of the rocket engine, regeneratively cooling thrust chamber suffers the extremely severe thermal load and pressure load, which caused by hot gas and cryogenic cool-

22

https://doi.org/10.1016/j.cja.2019.09.023 1000-9361 Ó 2019 Production and hosting by Elsevier Ltd. on behalf of Chinese Society of Aeronautics and Astronautics. This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/4.0/). Please cite this article in press as: LIU D et al. Thermo-structural analysis of regenerative cooling thrust chamber cylinder segment based on experimental data, Chin J Aeronaut (2019), https://doi.org/10.1016/j.cja.2019.09.023

23 24 25 26 27 28

CJA 1418 15 October 2019

No. of Pages 15

2 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75

D. LIU et al.

ant.2–4 After several cyclic processes of pre-cooling, hot run, post-cooling and relaxation, the plastic strain accumulates continuously, also, the inner wall of thrust chamber thins gradually and bulges irreversibly toward the centerline of the thrust chamber, resulting in structural failure known as ‘‘doghouse” effect indicated in Ref. 5 and Fig. 1. To explore the failure mechanism of thrust chamber, many scientists and engineers have carried out plenty of experiments and simulations. From the 1970s to the 2000s, a series of experiments and simulations were performed at NASA Lewis Research Center (LRC) to analyze the thermo-structural response of thrust chamber. According to the experimental results of plug nozzle, Armstrong6,7 suggested that the failure reason of OxygenFree-High-Conductivity copper (OFHC) thrust chamber wall was creep rupture that accelerated by ratchet effect rather than low cycle fatigue, while the failure of Zirconium-copper alloy (Amzirc) thrust chamber wall took the form of low cycle fatigue and the actual service life was dramatically shorter than predicted life. In an experimental scheme proposed by Quentmeyer,8 21 thrust chambers were thermally cyclic loaded to failure to investigate the low cycle thermal fatigue. All the failures were characterized by bulging toward the centerline and eventual failure by tensile rupture. These results showed that service life was closely related to the hot run test conditions, the temperature difference between the inner and outer walls as well as the ratio of the height to width of the channel. Hannum et al.9,10 carried out a test program, where thrust chambers made by different materials were cycled, to study the deformation of thrust chamber wall. A linear relationship between wall thickness and failure site deformation was discovered based on data and rupture phenomenon, furthermore, the potential crack point could be detected near half-life by means of nondestructive method. Over the last two decades, the research on the thermostructural response of thrust chamber was increasingly thorough due to the progress made in the field of the solid mechanics and the new materials. Yang et al.11 utilized a viscoplastic model to study the influence of the start-up time and the shutdown time of the liquid rocket engine on the stress-strain response, and the damage process of throat section was explained phase by phase. Kimura et al.12 investigated the effects of material types and Thermal Barrier Coatings (TBC) on the deformation of regenerative cooling thrust chamber with a nonlinear finite element method, and then, some practical methods for extending the lifetime of the thrust chamber are proposed. Aiming to improve reusable performance of the Vulcain engine, the German Aerospace Center

Fig. 1

Structural failure of regeneratively cooling channel.5

(DLR) studied the thermo-structural problem of thrust chamber in depth. A concept of Thermo-Mechanical Fatigue (TMF) bench was utilized by Gernoth et al.13 to approximate the extreme conditions which thrust chamber suffered from, and the experimental results provided verification data for structural simulations. Subsequently, Thiede et al.14 coupled damage and thermal aging into a viscoplastic model and simulated the deformation of the TMF panel under cyclic loadings. The actual failure position observed on the panel was consistent with the maximum damage position predicted by simulation. In summary, most thermo-structural analysis about thrust chamber focus on the throat section, but the deformation of cylinder segment especially near the injector head15 is not sufficiently emphasized. For a thrust chamber with a long cylinder segment, the maximum temperature of cylinder wall is almost equal to or higher than throat,16 because that the gas temperature in the cylinder segment is the highest and the cooling capacity of the coolant is decreased after the coolant passes through the throat. Thus, the working conditions of the thrust chamber cylindrical section are atrocious, but there has been lack of exact information in literature concerning the potential fatigue risk of cylinder segment. The principal objective of this work is to elucidate the thermo-structural response of thrust chamber cylinder segment. The nonlinear deformation behavior caused by thermal and mechanical load is studied phase by phase with a Finite Element Method (FEM), in which the boundary conditions is defined by applying the experimental results for making the simulation more realistic. The stress-strain histories at the more severely deformed positions quantitatively explain the mechanism of residual strain generation. The multi-cycle evolution of stress-strain process reveals the location where the failure is most likely to occur, which provides a reference for the design of rocket engine thrust chamber.

76

2. Cylinder segment and working process

111

2.1. Cylinder segment

112

The experimental thrust chamber investigated in this paper consists of four parts, including the injector head, the heat sink segment, the regenerative cooling cylinder segment and the nozzle segment. The assembly diagram of the entire thrust chamber is demonstrated in our previous work.15 Among these four parts, only the injector head and the regenerative cooling cylinder segment demonstrated in Fig. 2 are related to the presented study. As shown in Fig. 2(a), seven coaxial shear injector elements are embedded in the injector head, and the central injector element is different from the other six because a torch igniter is inserted through it. The gaseous hydrogen and gaseous oxygen are chosen as fuel and oxidant to produce the thermal condition and pressure environment in the thrust chamber. The diameter of the cylinder segment is 77.8 mm. The circumferential position of 0°, 30° and 60° are also marked in Fig. 2(a). The cylinder segment assembled by jacket and liner is the main research object of this paper as exhibited in Fig. 2(b). The total length of the cylinder segment is 150 mm. The other necessary parameters of the cylinder segment are given in Fig. 2(c). By applying the diffusion welding technology, the

113

Please cite this article in press as: LIU D et al. Thermo-structural analysis of regenerative cooling thrust chamber cylinder segment based on experimental data, Chin J Aeronaut (2019), https://doi.org/10.1016/j.cja.2019.09.023

77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105 106 107 108 109 110

114 115 116 117 118 119 120 121 122 123 124 125 126 127 128 129 130 131 132 133

CJA 1418 15 October 2019

No. of Pages 15

Thermo-structural analysis of regenerative cooling thrust chamber cylinder segment based on experimental data

Fig. 2

134 135 136 137 138 139 140 141 142 143 144 145 146 147 148

Injector head and regenerative cooling cylinder segment.

OFHC liner and the stainless steel jacket were welded together. 36 cooling channels are milled on the OFHC liner. To prevent the coolant from leaking into the thrust chamber and exploding during hot run, the distilled water with a temperature of 290 K is selected as coolant for safety reasons, although the actual thrust chamber is cooled by hydrogen. Two flanges serving as inlet and outlet manifolds were welded together with the jacket. At circumferential position of 0° and 30°, thermocouples were arranged along the axis to measure the transient temperature, then an inverse heat conduction method17 based on the measured temperatures is applied to get the flux distribution. The geometric model to be simulated in this study is simplified from the regenerative cooling cylinder segment, the inlet as well as outlet flanges are neglected. Considering that the

Fig. 3

3

Cross section of 3D calculation domain.

Fig. 4

Diagram of working process.

arrangement of the injection unit will affect the thermal load on the thrust chamber wall, the calculation domain is taken by 60° as presented in Fig. 3, which can take the inhomogeneity of thermal load caused by a complete injection unit into account. The welding surface between OFHC liner and the jacket did not break during the test, which meant that the welding strength was enough for the current experiment. Therefore, the type of connection between the OFHC liner and the jacket is defined as Bonded in ANSYS, which means that no sliding or separation between faces or edges is allowed. Also, the mesh nodes on the welding surface are matched to each other.

149

2.2. Working process

161

A complete working process of the experimental thrust chamber including four phases of pre-cooling, hot run, post-cooling

162

Please cite this article in press as: LIU D et al. Thermo-structural analysis of regenerative cooling thrust chamber cylinder segment based on experimental data, Chin J Aeronaut (2019), https://doi.org/10.1016/j.cja.2019.09.023

150 151 152 153 154 155 156 157 158 159 160

163

CJA 1418 15 October 2019

No. of Pages 15

4

D. LIU et al. @T ¼ rðkrTÞ @t

191

and relaxation is analyzed in this paper. To comprehend the thermo-structural response of the cylinder segment, it is necessary to introduce in detail how each phase is. Fig. 4 gives the diagram of these four phases. In the pre-cooling phase, only coolant flowed in the cooling channels to keep the thrust chamber at a lower temperature. The pressure and mass flow rate of the coolant remained unchanged. There was no hot gas exists in the thrust chamber. In the hot run phase, the cylinder segment was simultaneously subjected to cooling of the coolant and heating of the hot gas. The supply of coolant was the same as that in the pre-cooling phase. The mass flow rate of oxygen and hydrogen was designed to be 372.908 g/s and 62.151 g/s, respectively. In the post cooling phase, the fuel and oxidant were cut off and the cylinder segment was only cooled by coolant Also, the pressure and the mass flow rate of the coolant had no difference with that in pre-cooling phase. After the post-cooling phase, the thrust chamber entered the relaxation phase. The entire thrust chamber shut down and the coolant is no longer supplied, but some cooling water remained in the cooling channels. The experiments were carried out in winter, and the thrust chamber was fixed in an open and ventilated laboratory where the temperature was below 273 K. In order to prevent the cooling water from freezing and blocking the cooling channels, some heating equipment was placed around the thrust chamber to heat it and keep it warm. The temperature of the thrust chamber was approximately stable at 317 K.

192

3. Analysis method

where D denotes stiffness matrix, r is stress. T and Tref are current temperature and reference temperature, respectively. The two metallic materials studied in this paper are assumed to be isotropic, and a is thermal expansion coefficient changing with temperature. When the material produces plastic deformation, the strain increments are divided into elastic and plastic strain increments and the evolution of plastic strain obeys the flow rule as Eq. (9) describes, which means that the plastic strain increases along the gradient of the yield surface.

193

3.1. Governing equation

de ¼ deel þ depl

164 165 166 167 168 169 170 171 172 173 174 175 176 177 178 179 180 181 182 183 184 185 186 187 188 189 190

194 195 196 197 198 200 201 203 204

The turbulent flow process of distilled water in cooling channels is calculated by finite volume method in CFD program Ansys Fluent. The mass, momentum and energy equations are given by: @q þ r  ðqvÞ ¼ 0 @t

ð1Þ

 @ðqvÞ  þ r  ðqvvÞ ¼ rp þ r  ðs Þ @t

ð2Þ

 X @ðqEÞ  hj Jj þ ðs eff  vÞÞ þ r  ðvðqE þ pÞÞ ¼ rðkeff rT  @t j

206

ð3Þ

207

where q is density, t is time, v is velocity vector, p is static pres-

208 209 210 211 212 213 214 215 216 217 218 219 220

 

sure, s is stress tensor of fluid, E is energy of fluid, keff is effective conductivity, T is temperature, hj is enthalpy of species j, Jj is diffusion flux of species j. The more detailed descriptions and discussions about Eqs. (1) to (3) are given in Ref. 18. The Reynolds-Averaged Navier-Stokes (RANS) equations are closed by the standard k-e model.18 The temperature distribution of regenerative cooling cylinder segment is obtained by transient-state thermal analysis. The heat conduction in the solid domain including OFHC liner and stainless steel jacket is govern by transient-state heat conduction differential equation without internal heat source term:

qc

ð4Þ

where c is specific heat capacity. In Eq. (4), q, c and k are parameters depending on the type of materials as well as varying with temperature. Considering the thermal expansion and contraction of the structure, the total strain is decomposed into three parts as Eq. (5) describes: e¼e þ e þe el

pl

ð5Þ

th

where e is total strain, e is elastic strain, e is plastic strain and eth is the thermal strain. Among them, the elastic stress-strain relationship submits the generalized Hooke’s law and the thermal strain that only result in normal strain is regulated by thermal expansion coefficient as well as temperature difference between reference temperature and current temperature: el

pl

r ¼ De

ð6Þ

eth ¼ aðT  Tref Þ  ½111000T

ð7Þ

el

222 223 224 225 226 227 228 229 231 232 233 234 235 236 237 238 240 241

ð8Þ ð9Þ

where dk is the magnitude of the plastic strain increment and f is the is the expression of the yield surface and the field function in Chaboche model19 is defined as Eq. (10): pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi f ¼ 1:5ðs  aÞ : ðs  aÞ  ry ¼ 0 ð10Þ where s is deviatoric stress tensor, a is back stress tensor that represents the center of field surface and ry is yield stress that denotes the size of yield surface. The back stress tensor is given by the superposition of 3 kinematic back stress tensors. The evolution rule of each back stress term is presented in Eq. (12): 3 X

ai

ð11Þ

i ¼1

2 dai ¼ Ci depl  ci ai 3

244 245 246 247 248 249 250 251 252 253 254 256 257

@f de ¼ dk @r pl

a¼

243

rffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 2 pl de : depl 3

259 260 261 262 263 265 266 267 268 269 270 271

273 274

ð12Þ

where Ci and ci are material parameters obtained by curve fitting process.

276 277 278

3.2. Boundary conditions based on experimental data

279

For making the simulation as close as possible to the actual working conditions of the cylinder segment, most of the boundary conditions are defined by experimental data. The data is measured from the experiment that demonstrated in

280

Please cite this article in press as: LIU D et al. Thermo-structural analysis of regenerative cooling thrust chamber cylinder segment based on experimental data, Chin J Aeronaut (2019), https://doi.org/10.1016/j.cja.2019.09.023

281 282 283

CJA 1418 15 October 2019

No. of Pages 15

Thermo-structural analysis of regenerative cooling thrust chamber cylinder segment based on experimental data

Fig. 5

284 285 286 287 288 289 290 291 292 293 294 295

5

Experimental data for boundary conditions.

Fig. 5(a), and the data used to define boundary conditions is summarized in Fig. 5(c)-(e). In experiments, the pre-cooling phase is from the 1 s to 11 s, the hot-run phase is from the 11 s to the 16 s, and the post-cooling phase is from the 16 s to 23 s. The detailed description about relaxation phase has been given in Chapter 2.2. In Fig. 5(b), the temperature histories of a measuring point under different working conditions are demonstrated. As can be seen in Fig. 5(b), the temperature of the measuring point is substantially stable before the end of each phase. Therefore, the time of each phase is sufficient for the temperature of the thrust chamber to reach a steady state. During

the relaxation phase, some heating equipment is used to heat the thrust chamber and keep it around 317 K, the temperature variation in relaxation phase is not recorded in the temperature histories. In Fig. 5(c), the coolant pressure and mass flow rate in precooling phase (1 s-11 s), hot run phase (11 s-16 s) and postcooling (16 s-23 s) are measured. Simultaneously, the chamber pressure during hot run phase is also gauged by pressure sensor. The mass flow rate of cooling water, inlet pressure and outlet pressure are 0.882 kg/s, 3.15 MPa and 3.0 MPa, respectively. The chamber pressure during the hot run phase is 2.98 MPa.

Please cite this article in press as: LIU D et al. Thermo-structural analysis of regenerative cooling thrust chamber cylinder segment based on experimental data, Chin J Aeronaut (2019), https://doi.org/10.1016/j.cja.2019.09.023

296 297 298 299 300 301 302 303 304 305 306 307

CJA 1418 15 October 2019

No. of Pages 15

6 308 309 310 311 312 313 314 315 316 317 318 319 320 321 322 323 324 325 326 327 328 329 330 331 332 333 334 335 336 338 339 340 342 343 344 346 347 348 349 350 351 352 353 354 355 356 357 358 359 360 361 362 363 364 365 366 367 368 369

D. LIU et al.

In Fig. 5(d), the heat flux axial distributions at the circumferential position of 0° and 30° is measured with the inverse heat conduction method.17 Assuming that the heat flux axis distribution at 0° is the same with that at 60°, heat flux from 0° to 30° and 30° to 60° is obtained by interpolation. The heat flux 2D distribution based on experimental data is obtained finally and is shown in Fig. 5(e), this flux distribution is suitable for applying as the boundary condition of thermal analysis. Fig. 5(f) demonstrates a photograph of the OFHC liner gas-side wall, and a black curve is marked on it. Within the area drawn by the curve, the color of the OFHC liner is relatively fresh. However, outside the curve area, the color of the inner wall is black, which means that the surface oxidation is more serious. This phenomenon matches the horseshoe-like heat flux mark illustrated in Fig. 5(e) very well, which indicates that the heat flux 2D distribution interpolated by experimental data is convincing. The thermo-structural boundaries of the cooling segment including cooling surface, hot gas surface, symmetry and jacket outer surface are shown in Fig. 6. Because that the simulation consists of thermal analysis and structural analysis, the boundary conditions that divided into thermal and structural boundary conditions need to be defined separately. Based on the available data demonstrated in Fig. 5, the thermal analysis boundary conditions for different surfaces are defined as follows: On the jacket outer surface and symmetry: qn¼0

ð13Þ

On the cooling surface: q  n ¼ hðTcoolant  Tsurface Þ

ð14Þ

On the hot gas surface: q  n ¼ qexp

ð15Þ

where q is heat flux, n is the external normal vector for the solid surface, Tcoolant is the known coolant temperature while Tsurface is unknown cooling channels surface temperature to be calculated. qexp is the heat flux imposed on the OFHC liner gas-side wall by hot gas, which is already shown in Fig. 5(e). h denotes the distribution of convective heat transfer coefficient that can’t gain directly by experimental data. In this paper, the distribution of convective heat transfer coefficient h is obtained by simulating the process of coolant turbulent flow with the CFD tool ANSYS Fluent. The coolant mass flow rate and the coolant outlet pressure that shown in Fig. 5(c) are utilized in ANSYS Fluent as the fluid inlet and outlet conditions. The h calculated in ANSYS Fluent is extracted and imported into the thermal analysis. It should be noted that the mass flow rate through each channel is different in the actual situation. However, the distribution of mass flow rate is assumed to be uniform in this study, which may have a certain impact on the simulation results. Therefore, some additional simulations that are not shown in this paper are carried out to analyze the difference between uniform distribution and uneven distribution of mass flow rate. The maximum difference in mass flow rate is 5.9%. Thus, the assumption that the mass flow rate is uniform is acceptable in this paper.

Fig. 6

Boundaries schematic.

The boundary conditions of structural analysis are delimited in Eqs. (16)–(19). On the symmetries: un¼0

ð16Þ ð17Þ

376 377 379

ð18Þ

380 381 383

ð19Þ

384 385 387

On the hot gas surface: n  r  n ¼ pchamber On the jacket outer surface: nrn¼0

371 372 373 375

On the cooling surfaces: n  r  n ¼ pcoolant

370

where u is displacement vector, pcoolant and pchamber are coolant and chamber pressure gauged during experiment, respectively. The data of pcoolant and pchamber has been exhibited in Fig. 5(c). On the basis of Eqs. (16) and (19), normal displacement of symmetric surface is fixed to zero and it is noteworthy that the pressure load on the jacket outer surface is environmental pressure that can be neglected compared to pcoolant and pchamber. 3.3. Material parameters and mechanical properties In the Chaboche model19 adopted by this study, there are six parameters such as Ci(i = 1,2,3) and ci(i = 1,2,3) that need to be determined. For the sake of making the model represent the deformation of the material as accurate as possible, these parameters need to be defined reasonably through curving fitting processes. In view of that the mechanical properties of the materials are affected tremendously by temperature, the uniaxial tensile test data at different temperature20 is applied for fitting processes. With the initial value estimated as input, the optimized parameter values can be obtained. All the fitted parameters are presented in Table 1. Note that the value of c3 in Table 1 is not optimal because the uniaxial cyclic tension–compression data is more appropriate for fitting c3 instead of the uniaxial tensile data, however, the available cyclic loading data about OFHC is hardly seen in published literature. According to our previous published study21 that involved the influence of c3, the value of it was set to be 5 for Narloy-Z liner. The ratchet effect of OFHC is more pronounced than that of Narloy-Z, thus, the value of c3 for OFHC is fixed at 30, which is greater than 5 and is within the range of 10 to 100. As shown in Fig. 7, these implemented parameters of Chaboche model19 are validated to be

Please cite this article in press as: LIU D et al. Thermo-structural analysis of regenerative cooling thrust chamber cylinder segment based on experimental data, Chin J Aeronaut (2019), https://doi.org/10.1016/j.cja.2019.09.023

388 389 390 391 392 393 394 395

396

397 398 399 400 401 402 403 404 405 406 407 408 409 410 411 412 413 414 415 416 417 418

CJA 1418 15 October 2019

No. of Pages 15

Thermo-structural analysis of regenerative cooling thrust chamber cylinder segment based on experimental data Table 1

Chaboche model parameters.

Temperature (K)

ry (MPa)

C1 (MPa)

c1

C2 (MPa)

c2

C3 (MPa)

c3

27.6 294.3 533.1 755.4

55 47 38 29

69,900 22,543 63,980 16,990

41,654 16,181 22,669 10,303

16,997 1841 5331 2002

5768 295 470 277

1865 1614 531 701

30 30 30 30

Fig. 7

OFHC stress-strain curves.

420

reasonable by contrasting the simulated stress–strain curve with tensile data at several diverse temperatures.

421

4. Validation

419

422

423 424 425 426 427

7

4.1. Grid independence Fig. 8(a) illustrates the mesh distribution of the OFHC liner. The simulation is carried out at different grid densities as summarized in Table 2. Case 1 and Case 2 are relatively sparse grids, adopted mesh is the grid used in this study and the grid density of Case 3 is twice as high as that of adopted mesh.

Fig. 8

The circumferential normal stress-strain histories of the identical location on the inner wall for diverse mesh levels are compared with each other in Fig. 8(b). It can be seen from stress-strain curves that the absolute value of strain obtained by Case 1 and Case 2 are distinctly less than that from Case 3 and adopted mesh. Although the element number of Case 3 is remarkably greater than adopted mesh, the dissimilarity in stress-strain histories calculated from them is almost unrecognizable. Considering the simulation time cost and calculation precision comprehensively, the employed grid in this paper is deemed acceptable.

428

4.2. Method verification

439

The rationality of thermo-structural analysis method for deformation behavior of regeneratively cooled segment is verified by using the Thermo-Mechanical Fatigue (TMF) panel tests22 performed at DLR. The TMF panel is a simplified structure of regeneratively cooling thrust chamber and the 3D mesh of it is demonstrated in Fig. 9. The panel is heated by high energy laser beams and cooled by mixture of cryogenic liquid nitrogen and gaseous nitrogen. The mechanical properties of TMF panel are given in reference.23 The experimental conditions of TMF panel listed in reference22,24 are utilized in our analysis methods to obtain the deformation behavior caused by thermal and mechanical load. Fig. 10 compares deformation of heated surface as well as final destruction form of TMF panel with thermo-structural simulation results. As exhibited in Fig. 10(a)22 and 9(c), the maximum normal mechanical strain of the laser loaded surface

440

Grid independent validation.

Please cite this article in press as: LIU D et al. Thermo-structural analysis of regenerative cooling thrust chamber cylinder segment based on experimental data, Chin J Aeronaut (2019), https://doi.org/10.1016/j.cja.2019.09.023

429 430 431 432 433 434 435 436 437 438

441 442 443 444 445 446 447 448 449 450 451 452 453 454 455

CJA 1418 15 October 2019

No. of Pages 15

8

D. LIU et al. Table 2

Element layout.

Case

Element number

Case 1 Case 2 Adopted mesh Case 3

Fig. 9

a

b

c

d

e

4 6 10 20

4 6 10 20

4 6 8 16

5 6 7 14

30 40 60 120

TMF panel mesh for method validation.

471

appears at the bottom of the ribs on both sides of the middle channel, which means that the bulging phenomenon toward the laser source is the most palpable at these zones as illustrated in Fig. 10(c).22 Meanwhile, the ultimate destruction position of the TMF is located near the corner of the middle channel. In Fig. 9(b) and 8(d), the numerical results show the consistency with the experimental results: The maximum normal strain zones of the heated surface are closed to TMF test results and the bulging tendency of the fin areas is reproduced clearly in simulation. In addition, the maximum accumulative Von-Mises equivalent strain position overlaps the failure location observed in Fig. 10(c).22 The coincidences between numerical results and experimental results indicate that the thermo-structural method employed in this paper is reliable to describe the deformation behavior under the thermo-mechanical load.

472

5. Results and discussion

473

478

Taking the experimental data as boundary conditions, the thermo-structural analysis methods explicated previously in Chapter 3 are applicated to achieve the temperature field and the stress-strain histories of the regenerative cooling cylinder segment. The simulated results are demonstrated and discussed in this chapter.

479

5.1. Thermal analysis results

456 457 458 459 460 461 462 463 464 465 466 467 468 469 470

474 475 476 477

480 481 482 483

As described in Chapter 2.2, thrust chamber of a rocket engine goes through four stages in a complete working process. Fig. 11 gives the temperature fields of the regenerative cooling thrust chamber cylinder segment at the end of each phase.

Fig. 10

Comparison of TMF panel tests and simulation.

As can be seen from Fig. 11, the cylinder segment in the pre-cooling phase is sufficiently cooled by the coolant so that the temperature distribution of the entire structure is uniform and almost the same as the coolant temperature (290 K). While in the hot run stage, under the combined effect of the high-

Please cite this article in press as: LIU D et al. Thermo-structural analysis of regenerative cooling thrust chamber cylinder segment based on experimental data, Chin J Aeronaut (2019), https://doi.org/10.1016/j.cja.2019.09.023

484 485 486 487 488

CJA 1418 15 October 2019

No. of Pages 15

Thermo-structural analysis of regenerative cooling thrust chamber cylinder segment based on experimental data

Fig. 11

489 490 491 492 493 494 495 496 497 498 499 500 501 502 503 504 505 506 507 508 509 510

9

Temperature field in four stages.

temperature gas and the coolant, the difference between the highest and lowest temperatures on the liner gas-side wall exceeds 200 K. Similar to the heat flux distribution demonstrated in Fig. 5(e), a temperature peak zone above 650 K followed by a horseshoe-like temperature mark is observed on the inner gas-side wall. In the post-cooling phase, the cylinder segment is no longer subject to the heating of the hot gas and is only cooled fully by coolant. Thus, the temperature returns to 290 K from a high value. In the final relaxation phase, the thrust chamber recovers to 317 K due to the heating by some heating equipment. In order to quantitatively investigate the temperature nonuniformity, the temperature distribution on the gas-side wall is demonstrated in Fig. 11(e). The circumferential positions of the injector elements are 30°, 90°, 150°, 210°, 270°, and 330°, respectively. And, the axial length of the cylinder segment is 150 mm. As shown in Fig. 11(e), the injector element causes notable temperature peak at axial position of 0 mm, 25 mm, and 50 mm. However, when the axial distance is between 80 mm and 120 mm, the temperature at the position corresponding to injector element is lower than the surrounding region. This phenomenon indicates that the uneven heat flux

distribution caused by the arrangement of the injectors leads to a noticeable nonuniform temperature distribution on the gas-side wall along both the axial and circumferential direction. To investigate the temperature distribution inside the metal region, several cross sections including the maximum temperature cross section are given in Fig. 11(f). As Fig. 11(f) shows, the temperature disparity between cooling channels is the most remarkable on the maximum temperature cross section and the temperature distribution in a cooling channel is not bilaterally symmetric. The farther away from the maximum temperature cross section, the smaller the temperature distinction between the channels. This indicates that the complex 2D heat flux distribution shown in Fig. 5(e) not only largely determines the temperature distribution on the gas side, but also deeply affects the various channels inside the solid domain.

511

5.2. Structural analysis results

527

In the process of the structural analysis, the temperature fields calculated in Chapter 5.1 are applied as body loads, meanwhile, the coolant and the chamber pressure data shown in

528

Please cite this article in press as: LIU D et al. Thermo-structural analysis of regenerative cooling thrust chamber cylinder segment based on experimental data, Chin J Aeronaut (2019), https://doi.org/10.1016/j.cja.2019.09.023

512 513 514 515 516 517 518 519 520 521 522 523 524 525 526

529 530

CJA 1418 15 October 2019

No. of Pages 15

10

D. LIU et al.

533

Fig. 5(c) are used as surface loads. These loads are added into the FEM to analyze the thermo-mechanical deformation of the cylinder segment.

534

5.2.1. Deformation of the gas-side wall

531 532

535 536 537 538 539 540 541 542 543 544 545 546 547 548 549 550 551

According to the analysis results from reference,5 the gas-side wall of the liner is the key zone with more severe deformation. Compared with the other surfaces of the OFHC liner, the gasside wall is in direct contact with the hot gas and need to be analyzed firstly. Fig. 12 depicts the circumferential mechanical strain distributions of the gas-side wall in four phases. During pre-cooling phase, due to the 3.1 MPa coolant pressure in channels, the bottom of the cooling channels has the tendency to protrude toward the centerline of the cylinder segment, so these areas are subjected to tensile strain. Because that the the coolant pressure is not too high, so the strain on the gas-side wall is small, the magnitude of it is only 0.0001. During the hot run phase, the inner wall of the OFHC liner tends to swell because of the heating by high-temperature gas. However, the structure is symmetrical, the temperature of the steel jacket is much lower than that of the OFHC liner and the coefficient of thermal expansion of steel jacket is less than

Fig. 12

OFHC liner, so the expansion of the liner inner wall is constrained. Thus, the entire gas-side wall bears the compressive strain and the position of maximum compressive strain is located within the higher-temperature zone that already shown in thermal analysis results. In the post-cooling phase, the cylinder segment is cooled from a high temperature to 290 K by coolant, and the OFHC has a tendency to contract. Nevertheless, the contraction trend is restricted due to the symmetrical structure and the smaller expansion coefficient of stainless steel. The largest tensile strain that up to 0.0021 emerges near the zone where the highest temperature has occurred, because the temperature drop at this location is the maximum (654 K to 290 K). In the relaxation phase, the cylinder segment returns to 317 K from 290 K. The thermal load difference between post-cooling phase and relaxation phase is not significant (290 K to 317 K). Therefore, as shown in Fig. 12(c) and (d), there is no obvious disparity in term of the circumferential mechanical strain distribution. The maximum of the tensile strain (0.002072) in this phase is just slightly smaller than that in post-cooling phase, which means that most of the strain produced in post-cooling phase still remains in relaxation phase.

Circumferential mechanical strain distribution.

Please cite this article in press as: LIU D et al. Thermo-structural analysis of regenerative cooling thrust chamber cylinder segment based on experimental data, Chin J Aeronaut (2019), https://doi.org/10.1016/j.cja.2019.09.023

552 553 554 555 556 557 558 559 560 561 562 563 564 565 566 567 568 569 570 571 572 573

CJA 1418 15 October 2019

No. of Pages 15

Thermo-structural analysis of regenerative cooling thrust chamber cylinder segment based on experimental data

585

For further detailed study, the position with the largest residual strain on the gas-side wall is accurately located in Fig. 12(e) and its stress-strain history is also given in Fig. 12 (e). As Fig. 12(e) shows, this point is subjected to compressive stress in hot run phase but endures the tensile stress during the post-cooling phase. It is clearly that the strain generated under tensile stress is much greater than that generated under compressive stress, this is why noticeable tensile strain occurs at the end of the post-cooling phase. In addition, the strain produced in the post-cooling phase is hardly removed after the relaxation phase. This is the reason for the residual tensile strain after a complete working process.

586

5.2.2. Deformation of the OFHC liner

574 575 576 577 578 579 580 581 582 583 584

587 588 589 590 591 592 593 594 595 596 597 598 599 600 601 602 603 604 605 606 607 608 609 610 611 612 613 614 615 616 617 618 619 620 621 622 623 624 625 626 627 628 629 630 631 632 633

According to the TMF panel test22 carried out in DLR, the failure first occurs on the bottom surface of the cooling channels in some cases. For safety reasons, the deformation on the other surfaces of the OFHC liner is also investigated. The Fig. 13(a) exhibits the residual circumferential mechanical strain distribution of the OFHC liner after a complete working process. Along the circumferential direction, three channels are defined as Channel 1, Channel 2 and Channel 3, respectively. The maximum residual strain point is located near the right corner of the Channel 2 and the maximum residual strain at the right corner of Channel 2 (0.00221) is slightly larger than that on the gas-side wall (0.00207), which may imply that the right corner of the Channel 2 is another possible position of destruction besides the position of maximum residual strain on the gas-side wall. Another obvious phenomenon in Fig. 13(a) is that a palpable difference is observed in term of the residual strain between the left and right corners of Channel 2. To understand how the residual strain difference between the left and right corner of the channel is generated, the circumferential mechanical strain distributions of the cross section where maximum residual strain appears are demonstrated phase by phase in Fig. 13(b) to (e). As Fig. 13(b) to (e) shows, the strain distributions at left and right corners of channel are nearly same with each other in the pre-cooling phase. However, the difference begins to appear in the hot run phase. As the black circles marked in Fig. 13(c), the compressive strain at the left corners of Channel 2 and Channel 3 are more pronounced than that at the right corners. This phenomenon can be explicated if combined with the temperature distribution shown in Fig. 11(f). For each channel from 0° to 30°, the temperature of the left corners is higher than the right corners, which means that the tendency of thermal expansion at the left corners is more intense. However, the expansion is constrained by the steel jacket and the symmetrical structure, so the compressive strain at the left corners is more conspicuous. In the post-cooling and relaxation phases, the disparity of strain distribution between left and right corners of channels is not eliminated, though the temperature distribution is uniform as shown in Fig. 11(c) and (d). The right corners of these channels have the more evident tensile strain contrast to the left corner and the maximum residual strain point is situated at the right corner of the Channel 2 at the end of the relaxation phase. For the sake of quantificationally studying the distinction between the left and right corners of the channel in term of deformation, Fig. 13(f) gives the stress-strain histories of the

11

left and right corners of Channel 2. As demonstrated in Fig. 13(f), the compressive strain generated at the right corner is significantly smaller than that generated at the left corner during the hot run phase, which makes the right corner more easily produce the tensile strain that greater than 0 in the post-cooling phase. This phenomenon explains why the residual strain at the right corner of Channel 2 is larger than the left corner.

634

5.2.3. Stress-strain evolutions

642

Based on the analysis results of Chapter 5.2.1 and Chapter 5.2.2, two severely deformed locations were selected for subsequent analysis. One of them is the maximum residual strain point on the gas-side wall (named round point for convenience) and the other is the right corner of the Channel 2 (named square point for convenience). Fig. 14(a) compares the stress-strain histories of the two points after the first working process. As can be seen in Fig. 14(a), the residual strain at the square point is just slightly larger than that at the round point, however, the distinction can hardly be seen. The reusable launch vehicle is demanded to work several times, and the thrust chamber needs to go through many working cycles. The multi-cycle thermo-structural response of the cylinder segment must be considered, thus, the stress-strain histories of the round and square points during ten working cycles are also given in the Fig. 14(b). As illustrated in Fig. 14(b), the stress-strain curves of every working cycle are similar to each other, and these curves roll forward ceaselessly as the working cycle progresses. Unlike the situation after the first working cycle, the residual strain of the square point after the ten cycles is distinctly greater than the round point. The multi-cycle evolutions of the stress-strain curves imply that as the working cycle progresses, the deformation of the square point is progressively more severe than that of the round point, although the disparity between them is almost undetectable at the end of the first working cycle. Finally, the right corner of Channel 2 is considered to be the most likely location for structural failure. In the relevant theory of local strain method, the service life of the entire structure is dominated by that of dangerous point, therefore, a post-processing damage analysis is conducted for the dangerous point to predict the service life of thrust chamber cylinder segment. Considering two damage factors: fatigue damage Df and quasi static damage Dq, the total damage Dtotal during a working cycle is the summation of these two damages as expressed in Eq. (17).

643

Dtotal ¼ Df þ Dq

ð20Þ

Fatigue damage Df during a working cycle is calculated according to Eq. (18), where Nf is determined by the strain range during a working cycle and is obtained from e-N curve that plot in Ref. 19. Df ¼

1 Nf

ð21Þ 25

Based on Riccius et al.’s work, the quasi-static damage during a cycle is defined as a function of cumulative residual tensile strain according to equation (19), where eend is the residual strain after the end of the cycle, ebegine is the initial strain before a cycle, and ef is the ultimate strain from the tensile experiment data.19

Please cite this article in press as: LIU D et al. Thermo-structural analysis of regenerative cooling thrust chamber cylinder segment based on experimental data, Chin J Aeronaut (2019), https://doi.org/10.1016/j.cja.2019.09.023

635 636 637 638 639 640 641

644 645 646 647 648 649 650 651 652 653 654 655 656 657 658 659 660 661 662 663 664 665 666 667 668 669 670 671 672 673 674 675 676 677 678 679 681 682 683 684 685 686 688 689 690 691 692 693 694 695

CJA 1418 15 October 2019

No. of Pages 15

12

D. LIU et al.

Fig. 13

697 698 699 700

Dq ¼

  max 0; eend  ebegine ef

Deformation of OFHC.

ð22Þ

According to the needs of the post-processing, the strain range and the residual strain of every cycle is given in Fig. 15(a) for damage analysis. The strain range is defined as

the difference between the maximum strain and the minimum strain, which is illustrated in the upper part of Fig. 15(a). In Fig. 15(a), the strain range hardly changes as the cycle number increases, because the maximum and minimum strain increase with the progress of the working cycle. However, the residual

Please cite this article in press as: LIU D et al. Thermo-structural analysis of regenerative cooling thrust chamber cylinder segment based on experimental data, Chin J Aeronaut (2019), https://doi.org/10.1016/j.cja.2019.09.023

701 702 703 704 705

CJA 1418 15 October 2019

No. of Pages 15

Thermo-structural analysis of regenerative cooling thrust chamber cylinder segment based on experimental data

Fig. 14

Fig. 15

706 707 708 709 710 711 712 713 714 715 716

13

Evolution of stress-strain curves.

Post-processing for damage analysis.

strain grows with the increasing of cycle number, which indicates that the deformation at the dangerous point of the entire structure becomes more and more serious as the working cycle progresses. Applying the results in Fig. 15(a) to the post-processing procedure described above, the cumulative quasi-static damage, cumulative fatigue damage and cumulative total damage at the dangerous point during ten cycles are obtained and given in Fig. 15(b). As can be seen from Fig. 15(b), both cumulative fatigue damage and cumulative quasi-static damage increases with the progress of the working cycle, however,

the total damage is mainly derived from quasi static damage because the fatigue damage is relatively small. Therefore, it can be considered that as the working cycle progresses, the failure form of the cylinder segment is a quasi-static failure rather than a fatigue failure. The deformation tendency after 10 cycles resembles ‘‘dog-house” effect shown in Fig. 1. Since the total damage revealed in Fig. 15(b) is almost linearly increasing, a curve of Damage-Cycle number, which is fitted based on the total damage data of the first 10 cycles, is also illustrated in Fig. 15(b) to estimate the life of the cylinder segment. According to the fitted Damage-Cycle number curve,

Please cite this article in press as: LIU D et al. Thermo-structural analysis of regenerative cooling thrust chamber cylinder segment based on experimental data, Chin J Aeronaut (2019), https://doi.org/10.1016/j.cja.2019.09.023

717 718 719 720 721 722 723 724 725 726 727

CJA 1418 15 October 2019

No. of Pages 15

14

D. LIU et al.

737

the Dtotal < 1.0 when cycle number is equal to 312, while, the Dtotal > 1.0 if the cycle number is 313. Thus, the life of the regenerative cooling thrust chamber cylinder segment is deemed to be 312 cycles. This result of life prediction is slightly longer than expected, most likely due to ample coolant supply, which makes the maximum temperature of the cylindrical section only above 650 K. In addition, the coolant pressure (3.15 MPa) is only higher a little than the combustion chamber pressure (3.0 MPa), which also plays a role in extending the life of the cylinder segment.

738

6. Conclusions

728 729 730 731 732 733 734 735 736

740 739 741 742 743 744 745 746 747 748 749 750 751 752 753 754 755 756 757 758 759 760 761 762 763 764 765 766 767 768 769 770 771 772 773 774 775 776 777 778 779 780 781 782 783 784 788 785 786 789 787 790

(1) The 2D heat flux distribution caused by the arrangement of the injectors not only leads to the noticeable temperature inhomogeneity on the gas-side wall along axial and circumferential direction, but also makes temperature distribution in a cooling channel not bilaterally symmetric inside the solid domain. (2) On the gas-side wall, the residual circumferential tensile strain is greater in areas where higher temperatures had occurred after a complete working process including pre-cooling, hot run, post-cooling and relaxation. The reason for the residual strain is that the strain generated under the tensile stress in the post-cooling phase is greater than the strain caused by the compressive stress in the hot run phase. (3) The deformation analysis for OFHC liner shows that the residual strain at the low-temperature corner of a specific channel is significantly larger than that at the hightemperature corner. The reason for this dissimilarity between them is that the compressive strain generated at the low-temperature corner is smaller than that generated at the low-temperature corner during the hot run phase, which makes the low-temperature corner more easily produce the notable tensile strain in the postcooling phase. (4) The low-temperature corner of the specific channel and the maximum residual strain point on the gas-side wall are considered to be two potential failure locations, because that the difference in residual strain at these two locations is barely visible after a complete working process. However, after ten working cycles, the deformation at the low-temperature corner of the specific channel is more serious than that at the maximum residual strain point of the gas-side wall. The low-temperature corner of the specific channel becomes the most likely location to fail. (5) The simulation indicates that the fatigue damage accounts for only a small part of the total damage. However, the quasi-static damage controlled directly by the accumulative rate of residual tensile strain is largely determine the total damage, and it was the main factor that affected the life span of the cylinder segment. (6) According to the analyses and discussions in the present study, the deformation of the gas-side wall and the channel corner is more serious. To decrease the residual strain, covering the Thermal Barrier Coating (TBC) on the gas-side wall and chamfering at the channel corner may be the effective means to extend the service life of the thrust chamber.

References

791

1. Song J, Sun B. Damage localization effects of the regenerativelycooled thrust chamber wall in LOX/methane rocket engines. Chin J Aeronaut 2018;31(8):1667–78. 2. Yan D, He G, Li W, Zhang D, Qin F. Thermal analysis of regenerative-cooled pylon in multi-mode rocket based combined cycle engine. Acta Astronaut 2018;148:121–31. 3. Tao Z, Hu X, Zhu J, Wu H. Numerical investigation of pyrolysis effects on heat transfer characteristics and flow resistance of ndecane under supercritical pressure. Chin J Aeronaut 2018;31 (6):1249–57. 4. Song J, Sun B. Coupled numerical simulation of combustion and regenerative cooling in LOX/Methane rocket engines. Appl Therm Eng 2016;106:762–73. 5. Riccius JR, Haidn OJ, Zametaev EB. Influence of time dependent effects on the estimated life time of liquid rocket combustion chamber walls. Reston: AIAA; 2004. Report No.: AIAA-20043670. 6. Armstrong WH, Brogren EW. Thrust chamber life prediction, vol. 2. Plug nozzle centerbody and cylinder life analysis. Washington, D.C.: NASA; 1975. Report No.: NASA-CR-134822. 7. Armstrong WH, Brogren EW. Thrust chamber life prediction, vol. 3. Fatigue life parametric study, Washington, D.C.: NASA; 1975. Report No.: NASA-CR-134823. 8. Quentmeyer RJ. Experimental fatigue life investigation of cylindrical thrust chambers. Reston: AIAA; 1977. Report No.: AIAA1977-0893. 9. Hannum NP, Kasper HJ, Pavli AJ. Experimental and theoretical investigation of fatigue life in reusable rocket thrust chambers. Reston: AIAA; 1976. Report No.: AIAA-1976-0685. 10. Hannum NP, Quentmeyer RJ, Kasper HJ. Some effects of cyclic induced deformation in rocket thrust chambers. Reston: AIAA; 1979. Report No.: AIAA-1979-0911. 11. Yang J, Chen T, Jin P, Cai G. Influence of the startup and shutdown phases on the viscoplastic structural analysis of the thrust chamber wall. Aerosp Sci Technol 2014;34:84–91. 12. Kimura T, Moriya S, Takahashi M. Effects of heat treatments to inner liner material, thermal barrier coating and outer shell material on lifetime of a combustion chamber. Acta Astronaut 2019;158:244–52. 13. Gernoth A, Riccius JR, Haidn OJ, Brummer L, Mewes B, Quering K. TMF panel tests: close-to-reality simulation of thermomechanical fatigue processes in heat-loaded walls. Reston: AIAA; 2008. Report No.: AIAA-2008-5237. 14. Thiede R, Riccius JR, Reese S. Life prediction of rocket combustion-chamber-type thermomechanical fatigue panels. J Propuls Power 2017;33(1):1–14. 15. Wang T, Sun B, Liu D, Xiang J. Experimental investigation of two-dimensional wall thermal loads in the near-injector region of a film-cooled combustion chamber. Appl Therm Eng 2018;138:913–23. 16. Yang W, Sun B. Numerical simulation of liquid film and regenerative cooling in a liquid rocket. Appl Therm Eng 2013;54:460–9. 17. Coy E. An efficient method for calculating surface temperature and heat flux based on embedded temperature sensors. Reston: AIAA; 2008. Report No.: AIAA-2008-3952. 18. ANSYS Inc. ANSYS theory reference release 14.5. Canonsburg (PA): ANSYS Inc.; 2012. 19. Chaboche JL. Constitutive equations for cyclic plasticity and cyclic viscoplasticity. Int J Plast 1989;5(3):247–302. 20. Esposito JJ, Zabora RF. Thrust chamber life prediction, vol. I. Mechanical and physical properties of high-performance rocket nozzle materials. Washington, D.C.: NASA; 1975. Report No.: NASA-CR-134806.

792

Please cite this article in press as: LIU D et al. Thermo-structural analysis of regenerative cooling thrust chamber cylinder segment based on experimental data, Chin J Aeronaut (2019), https://doi.org/10.1016/j.cja.2019.09.023

793 794 795 796 797 798 799 800 801 802 803 804 805 806 807 808 809 810 811 812 813 814 815 816 817 818 819 820 821 822 823 824 825 826 827 828 829 830 831 832 833 834 835 836 837 838 839 840 841 842 843 844 845 846 847 848 849 850 851 852 853 854 855

CJA 1418 15 October 2019

No. of Pages 15

Thermo-structural analysis of regenerative cooling thrust chamber cylinder segment based on experimental data 856 857 858 859 860 861 862 863

21. Song J, Sun B. Thermal-structural analysis of regenerativelycooled thrust chamber wall in reusable LOX/Methane rocket engines. Chin J Aeronaut 2017;30(3):1043–53. 22. Riccius JR. Cyclic laser heating and optical measurement of combustion chamber wall structures. Reston: AIAA; 2012. Report No.: AIAA-2012-4011. 23. Riccius JR, Gernoth A, Schlechtriem S. TMF tests: Optical heating, thermography and deformation measurement of combus-

15

tion chamber wall structures. Reston: AIAA; 2011. Report No.: AIAA-2011-5780. 24. Riccius JR, Bouajila W, Zametaev EB, Comparison of finite element analysis and experimental results of a combustion chamber type TMF panel test. Reston: AIAA; 2013. Report No.: AIAA-2013-3846. 25. Riccius JR, Zametaev EB, Haidn OJ, Gugu C. LRE Chamber wall optimization using plane strain and generalized plane strain models. Reston: AIAA; 2006. Report No.: AIAA-2006-4366.

864 865 866 867 868 869 870 871 872 873

Please cite this article in press as: LIU D et al. Thermo-structural analysis of regenerative cooling thrust chamber cylinder segment based on experimental data, Chin J Aeronaut (2019), https://doi.org/10.1016/j.cja.2019.09.023