Investigation of RBCC performance improvements based on a variable geometry ramjet combustor

Accepted Manuscript Investigation of RBCC performance improvements based on a variable geometry ramjet combustor Jinying Ye, Hongliang Pan, Fei Qin, Yajun Wang, Duo Zhang PII:

S0094-5765(18)30699-4

DOI:

10.1016/j.actaastro.2018.07.032

Reference:

AA 7013

To appear in:

Acta Astronautica

Received Date: 17 April 2018 Revised Date:

10 July 2018

Accepted Date: 21 July 2018

Please cite this article as: J. Ye, H. Pan, F. Qin, Y. Wang, D. Zhang, Investigation of RBCC performance improvements based on a variable geometry ramjet combustor, Acta Astronautica (2018), doi: 10.1016/ j.actaastro.2018.07.032. This is a PDF file of an unedited manuscript that has been accepted for publication. As a service to our customers we are providing this early version of the manuscript. The manuscript will undergo copyediting, typesetting, and review of the resulting proof before it is published in its final form. Please note that during the production process errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain.

ACCEPTED MANUSCRIPT

Investigation of RBCC performance improvements based

2

on a variable geometry ramjet combustor

3

Jinying Ye, Hongliang Pan*, Fei Qin, Yajun Wang, Duo Zhang

4

Science and Technology on Combustion, Internal Flow and Thermo-structure

5

Laboratory, Northwestern Polytechnical University, Xi’an Shaanxi 710072, PR China

RI PT

1

6 7

*

8

Name: Hongliang Pan

9

E-mail: [email protected]

M AN U

SC

Corresponding Author

10

Postal Address: School of Astronautics, Northwestern Polytechnical University, Xi’an

11

Shaanxi 710072, PR China

AC C

EP

TE D

12

1

ACCEPTED MANUSCRIPT Nomenclature

14

Variables

15

A

Pre-exponential factor, (kmol/m3)1-ηF-ηO/s

16

Ae

Cross-sectional area at the exit of the combustor, Dimensionless

17

Ai

Cross-sectional area at the inlet of the combustor, Dimensionless

18

At

Cross-sectional area at the geometric throat, Dimensionless

19

b

Temperature exponent, Dimensionless

20

E

Activation energy, J/kmol

21

Er

Fuel equivalent ratio, Dimensionless

22

F

Thrust of the combustor, N

23

go

Gravitational acceleration, m/s2

24

H

Altitude of the isolator, Dimensionless

25

Isp

Specific impulse, s

26

k

Specific heat ratio, Dimensionless

27

K

Constant, Dimensionless

28

m&

Mass flow rate of inflow, kg/s

29

m& fuel ,total

Mass flow rate of total fuel, kg/s

30

Ma

Mach number, Dimensionless

31

Mae

Mach number at the exit of the combustor, Dimensionless

32

Maflight

Flight Mach number, Dimensionless

33

Mai

Mach number at the inlet of the combustor, Dimensionless

34

Maisolator

Mach number at the inlet of the isolator, Dimensionless

AC C

EP

TE D

M AN U

SC

RI PT

13

2

ACCEPTED MANUSCRIPT p

Static pressure, Pa

36

p0

Total pressure at the inlet of the isolator, Pa

37

pt

Total pressure, Pa

38

pte

Total pressure at the exit of the combustor, Pa

39

pti

Total pressure at the inlet of the combustor, Pa

40

TAFT

Adiabatic flame temperature, K

41

Tt

Total temperature, K

42

Tte

Total temperature at the exit of the combustor, K

43

Tti

Total temperature at the inlet of the combustor, K

M AN U

SC

RI PT

35

44

Greek symbols

46

ηe

Combustion efficiency, Dimensionless

47

ηF

Exponent of the fuel mole fraction, Dimensionless

48

ηO

Exponent of the oxidizer mole fraction, Dimensionless

49

τe

Heating ratio, Dimensionless

EP

TE D

45

51 52

AC C

50

Abstract

The use of a variable geometry combustor is one of the most effective methods to

53

improve the performance of a rocket-based combined-cycle (RBCC) engine over a

54

wide range of operating conditions. This paper aims to study the capabilities of a

55

variable geometry combustor operating over a wide range of conditions and determine

56

the performance of the combustor under various inflow conditions. Based on the 3

ACCEPTED MANUSCRIPT inflow conditions, the configuration parameters of the combustor were adjusted.

58

Ground direct-connect experiments were conducted under the inflow conditions of

59

Ma 2, Ma 3, Ma 4, and Ma 6, and numerical simulations were performed under the

60

conditions of Ma 3 and Ma 6. The direct-connect experiments showed that the

61

primary rocket operating at a low flow rate can reliably ignite the secondary fuel and

62

maintain a stable and efficient combustion in a variable geometry combustor. Under

63

the inflow conditions of both Ma 4 and Ma 6, smooth transitions of the variable

64

geometry combustor from rocket-ramjet mode to ramjet mode were achieved, and the

65

specific impulses were greatly improved and reached 28.2% and 37.1% of the

66

amplitude, respectively. The numerical simulation showed that the variable geometry

67

combustor can effectively control the combustion heat release region and greatly

68

improve the performance of the combustor. The specific impulse in the combustor

69

increased by 18.6% and 26.2% compared with that in the fixed geometry combustor

70

under Ma 3 and Ma 6 inflow conditions, respectively. It is therefore strongly believed

71

that the variable geometry combustor has significant performance advantages under a

72

wide range of operating conditions.

SC

M AN U

TE D

EP

AC C

73

RI PT

57

74

Keywords

75

Rocket-based combined-cycle; Variable geometry; Geometric throat; Combustor;

76

Performance

77

_____________________________________________________________________

78 4

ACCEPTED MANUSCRIPT 79

1. Introduction A rocket-based combined-cycle (RBCC) engine is a combined propulsion system

81

that operates over a wide range of conditions and can be used in multiple missions. An

82

RBCC engine integrates a rocket engine with a high thrust-to-weight ratio and a low

83

specific impulse and a dual-mode ramjet (DMR) engine with a low thrust-to-weight

84

ratio and a high specific impulse into one flow path. RBCC engines enable an aircraft

85

to take off from zero speed to hypersonic flight and represent one of the major

86

propulsion solutions for space transportation and hypersonic flight vehicles in near

87

space. RBCC engines can be used as the first stage of two-stage-to-orbit (TSTO)

88

vehicles and are expected to achieve single-stage-to-orbit (SSTO) operation in the

89

future [1-4].

M AN U

SC

RI PT

80

The RBCC engine mainly undergoes four operating modes depending on the

91

flight state: the ejector mode, the ramjet mode, the scramjet mode and the rocket

92

mode. For engines operating in such a wide range of conditions with multiple modes,

93

the change of inflow parameters inevitably results in changes in the engine design

94

parameters. The combustor is a major component of the engine, and its performance is

95

directly related to the overall performance of the engine. Previous schemes have

96

generally employ a fixed geometry combustor in an expanded configuration, and the

97

continuous and stable operation of the combustor requires thermal throat conditioning

98

techniques in the ejector and ramjet modes [5] for the coordination of the multiple

99

modes and the stability of the RBCC engine. For fixed geometry combustors, a large

100

number of studies have been performed concerning the flow and combustion

AC C

EP

TE D

90

5

ACCEPTED MANUSCRIPT mechanisms in the combustor [6-11]. Li [12] conducted a study on the fixed geometry

102

RBCC combustor in the ramjet mode and found that the engine performance loss in

103

the designed state enabled improvement of the engine performance in the off-designed

104

state. Wang [13] devised an RBCC flow path configuration that appropriately

105

sacrifices some of the engine performance and can accommodate both high and low

106

Mach numbers, with a better performance observed at Ma 3-6 and proper function

107

observed at Ma 2 and Ma 7. To optimize the multi-mode performance and allow for

108

operation in a wide range of conditions, considerable attention has been focused on

109

variable geometry RBCC research.

M AN U

SC

RI PT

101

As an air-breathing engine, the ram effect dominates after the inlet starts, which

111

operates in a typical Brayton cycle [14]. As shown in Fig. 1(a), the conventional

112

ramjet (CRJ) engine [15] must form normal shock deceleration pressurization in the

113

diffuser section to match the higher combustor pressure, and it also must accelerate

114

the high temperature burned gas at the outlet of the combustor to supersonic through

115

the geometric throat. For a dual-mode ramjet (DMR) engine [16, 17] with a thermal

116

throat, an isolator section matches with the higher combustor pressure to ensure the

117

stability of the inlet work as shown in Fig. 1 (b). For an engine that can operate over a

118

wide range of conditions, the geometry of the combustor is adjusted according to the

119

combustion organization principles of the CRJ and DMR engines. At low flight Mach

120

numbers, a high expansion ratio combustor with the geometric throat configuration is

121

adopted to reduce the total pressure loss in the combustor, in which subsonic

122

combustion is adjusted to improve the engine performance. At high flight Mach

AC C

EP

TE D

110

6

ACCEPTED MANUSCRIPT numbers, a low expansion ratio combustor with a straight and diverging configuration

124

is used to ensure the smooth transition from subsonic combustion to supersonic

125

combustion. If an ejector rocket is placed in the isolator section, the engine becomes a

126

typical RBCC engine. Therefore, the flow path of the combustor must be divergent to

127

achieve supersonic combustion in the scramjet mode, and efficient combustion

128

requires a convergent-divergent section in the ejector and ramjet modes [2]. Moreover,

129

as the flight Mach number increases, the heating ratio is gradually reduced, and the

130

expansion ratio of the combustor must be reduced accordingly to obtain better engine

131

performance [18].

M AN U

SC

RI PT

123

(a) RBCC in a CRJ engine

AC C

EP

TE D

132

(b) RBCC in a DMR engine Fig. 1 Schematics for fixed geometry configurations of CRJ and DMR engines 7

ACCEPTED MANUSCRIPT 133

The corresponding variable geometry combustor has many applications in DMR

135

engines. For example, the French wide-range ramjet (WRR) engine [19], with fully

136

variable combustor profiles, shows high performance over the entire range of

137

operating Mach numbers from Ma 2 to Ma12, in which hydrogen fuel is used. The

138

PIAF engine [20] achieves a wide range operation through changing the geometry of

139

the combustor by cowl translation. Feng [21-23] et al. adopted the PIAF variable

140

geometry combustor configuration to experimentally and numerically study the

141

performance of the combustor with different expansion ratios and fuel equivalence

142

ratios. However, the detailed flow field and performance parameters of the relevant

143

wide-range variable geometry combustor have not been previously reported.

M AN U

SC

RI PT

134

For the multi-mode RBCC engine, the variable geometry combustor can

145

overcome the contradiction of the combustor area requirements in different modes and

146

different flight states and can ensure optimal engine performance in all modes. The

147

performances of different combustor configurations in the ramjet mode were

148

compared between numerical simulations and experimental tests [24], and the results

149

showed that through the variable geometry, the combustor forms a geometric throat

150

that can allow the fuel to burn more efficiently, thereby substantially improving

151

engine performance. Moreover, the geometric throat can improve the combustion

152

quality of Ma 6.5 and Ma 7 to improve the engine performance and can effectively

153

extend the range of the geometric throat to Ma 7 [25].

154

AC C

EP

TE D

144

The performance of an RBCC engine that employs a variable geometry 8

ACCEPTED MANUSCRIPT combustor and that operates in a wide range of Mach numbers is studied through

156

numerical simulations and ground direct-connect experiments in this paper. The aim is

157

to study the functions of the geometric throat and the ability of these throats to

158

improve the performance of RBCC engines. First, the experimental and numerical

159

simulation methods are introduced, and the accuracy of the numerical simulation

160

method is validated. Next, the combustion organization under different inflow

161

conditions is obtained experimentally, and the performance of the variable geometry

162

combustor is estimated. Subsequently, the mechanisms underlying the geometric

163

throat and thermal throat are compared in detail via numerical simulations. The

164

performances of variable geometry and fixed geometry combustors under the same

165

combustion organization method are compared.

166

2. Experimental facility

167

2.1. Combustor configurations

TE D

M AN U

SC

RI PT

155

The designed RBCC variable geometry combustor adjusts its expansion angle and

169

geometric throat area in accordance with the inflow conditions and heat release to

170

achieve high efficiency and stable operations of the combustor under a wide range of

171

inflow conditions from Ma 2-7. With changes in the flight Mach numbers, the inlet

172

parameters of the combustor changes greatly as well. Therefore, the configuration of

173

the combustor is adjusted accordingly. The design principle of the combustor

174

configuration is given below.

AC C

EP

168

175

Based on the basic assumption of isobaric heating, the airflow velocity in the

176

combustor remains constant and is obtained by integrating the differential equations 9

ACCEPTED MANUSCRIPT 177

of total temperature and Mach number, where τ e = Tte Tti . Mae   k − 1   k −1 = τ e  1 + Mai 2  − Mai 2  Mai   2 2  

178

−1/2

(1)

According to Eq. (1), if the inlet Mach number and the heating ratio of the

180

combustor are known, then the viscous drag of the combustor and the mass adding

181

effect of the secondary fuel are ignored and the area change of the combustor is given

182

by Eq. (2).

RI PT

179

184

The ratio of the total pressure at the combustor inlet to that at the outlet is given

(2)

M AN U

185

SC

183

Ae  k −1  k −1 = τ e 1 + Mai 2  − Mai 2 Ai 2   2

by Eq. (3).

k

189 190

TE D

188

With the known parameters of the combustor inlet, the geometric throat area can be obtained according to equations (1) to (3) using the gas flow rate formula.

EP

187

(3)

At =

m& Tte Kpte

(4)

AC C

186

k −1 k −1  2  pte  1 + 2 Mae  =  pti  1 + k − 1 Ma 2  i  2 

Table 1 shows the design parameters of the combustor at different Mach numbers.

191

The expansion ratio of the combustor and the area of the geometric throat in the range

192

of Ma 2-6 gradually decrease as the flight Mach number increases. Moreover, the

193

combustor transits from a configuration with a geometric throat to an expanded

194

configuration over Ma 6. Fig. 2 shows the schematic diagram of the variable geometry

195

combustor and the internal geometry layout of the variable section of the combustor. 10

ACCEPTED MANUSCRIPT The movable part of the combustor is connected by four rods, the two ends are fixed

197

hinge supports, and the middle three parts are constrained by the cylinder hinges. The

198

two parallel hydraulic actuators can meet the changes of the combustor configuration

199

during the experiment.

200

Maflight

τe

Ae Ai

2

3.5

3.2

3

3

2.8

2.1

4

2.5

2.4

1.8

6

1.7

1.7

1.5

7

1.5

1.7

/

SC

At Ai

M AN U

2.4

203 204

AC C

EP

202

Table 1 Variable geometry combustor configuration parameters

TE D

201

RI PT

196

Fig. 2 Variable geometry combustor assembly

205 206

2.2. Experimental system

207

The experiments are conducted on the RBCC direct-connect test bench of

208

Northwestern Polytechnical University in China. The inflow air is heated by a 11

ACCEPTED MANUSCRIPT gas-oxygen-alcohol generator, and it is capable of simulating the total temperature

210

conditions at different Mach numbers. Additional oxygen is supplied to maintain its

211

mass fraction 0.23 in the heated products. The heated high enthalpy air accelerates

212

through the facility nozzle to achieve the desired combustor inlet Mach numbers. Fig.

213

3 shows a schematic diagram of the model engine, which consists of a facility nozzle,

214

an isolator section, a primary rocket, a rectangular combustor and an inner nozzle.

215

The primary rocket is located in the central strut. The straight flow path on both sides

216

of the strut serves as an isolator section to avoid being affected by the pressure rise of

217

the combustion chamber and thus avoid inlet unstart. The combustor is composed of a

218

straight section, a fixed section and a variable section, and the fuel pylons are located

219

in the fixed section. The geometric throat is located at the junction between the

220

combustion chamber and the inner nozzle. Through the configuration transition, the

221

expansion structure with no geometric throat formed in the variable section is the

222

fixed geometry combustor. In the direction of the engine set, a series of pressure

223

sensors are used to obtain the pressure distribution of the engine wall to conduct

224

engine performance evaluations. The pressure sensors provide a full range of -0.1∼1

225

MPa, an uncertainty of 0.25% of full scale, and a maximum sampling frequency of

226

1000 Hz.

SC

M AN U

TE D

EP

AC C

227

RI PT

209

12

SC

RI PT

ACCEPTED MANUSCRIPT

M AN U

Fig. 3 Model engine and pressure measurement point distribution diagram 228

The ground direct-connect experiments are conducted for the flight Mach

230

numbers of 2, 3, 4 and 6. The corresponding inflow parameters are shown in Table 2,

231

wherein the flow rate of the primary rocket is 0.12 kg/s, the oxygen-fuel ratio is

232

approximately 1.0, and the chamber pressure is 1.5 MPa. The primary rocket works at

233

a low flow rate, with a maximum of no more than 5% of the flow rate at Ma 2.

234

Secondary fuel is injected through the flow direction vortex pylons, whose

235

equivalence ratio is listed in Table 2. Fig. 4 shows the schematic of the operation

236

sequence for the test facility. First, the secondary fuel is supplied, which is followed

237

by the primary rocket operation and secondary fuel ignition, and then the primary

238

rocket is turned off to achieve a rocket-ramjet to a ramjet combustion mode transition.

AC C

EP

TE D

229

239

Table 2 Experimental flow parameters

240

Maflight

m& (kg/s)

Tt (K)

pt (MPa) 13

Maisolator

Er

ACCEPTED MANUSCRIPT 2.8

400

0.3

1.3

0.6

3

4.7

600

0.6

1.6

0.6

4

4.0

880

0.9

2.0

0.7

6

3.3

1650

1.3

2.5

1.0

RI PT

2

M AN U

SC

241

Fig. 1 Schematic of the operation sequence for the test facility

244

3. Numerical methods

References [8, 23, 26]

showed that Reynolds-averaged Navier-Stokes

EP

243

TE D

242

(RANS)-based CFD modeling is widely used for dual-mode scramjets and RBCC

246

engines. In this paper, the nonlinear RANS equations were solved by using the cubic

247

k-ε turbulence model in CFD++, an unstructured three-dimensional fluid calculation

248

software [27]. In [26, 28, 29], this model was used to simulate the combustor of the

249

HIRIRE-2 scramjet engine, and the model results were consistent with the

250

experimental data.

AC C

245

251

The Eulerian Dispersed Phase (EDP) model is utilized to simulate the spray of

252

liquid kerosene as the secondary fuel in a gaseous medium. In this paper. 14

ACCEPTED MANUSCRIPT turbulence-chemistry interactions were neglected. As a result, certain deficiencies may

254

occur in the prediction of ignition delay times; however, steady state simulations were

255

used in this study. Therefore, turbulence-chemistry interactions should not play a

256

crucial role. In the present work, C10H20 [30] was selected as kerosene, and a

257

multi-step quasi-global chemical kinetics model proposed by Westbrook [31] was

258

used for the chemical kinetic calculations. This model consists of 10 species and 12

259

finite rate reactions, as listed in Table 3.

SC

RI PT

253

Table 3 Quasi-global chemical kinetics model for kerosene fuel [31] A [(kmol/m3)1-ηF-ηO/s]

b

E (J/kmol)

ηF

ηO

C10H20+5O2=>10CO+10H2

4.50E+09

0

1.256E+08

0.25

1.5

H+O2=O+OH

2.20E+11

0

7.032E+07

1.0

1.0

1.80E+07

1

3.725E+07

1.0

1.0

6.80E+10

0

7.702E+07

1.0

1.0

OH+H2=H+H2O

2.20E+10

0

2.135E+07

1.0

1.0

CO+OH=CO2+H

1.50E+04

1.3 -3.349E+06

1.0

1.0

H2+O=H+OH

EP

O+H2O=OH+OH

TE D

Reaction

AC C

261

M AN U

260

CO+O2=CO2+O

3.10E+08

0

1.574E+08

1.0

1.0

CO+O+M=CO2+M

5.90E+09

0

1.716E+07

1.0

1.0

OH+M=O+H+M

8.00E+16

-1

4.341E+08

1.0

1.0

O2+M=O+O+M

5.10E+12

0

4.814E+08

1.0

1.0

H2+M=H+H+M

2.20E+11

0

4.018E+08

1.0

1.0

H2O+M=H+OH+M

2.20E+13

0

4.395E+08

1.0

1.0

15

ACCEPTED MANUSCRIPT 262

In a previous work, a grid-independence verification of the RBCC fixed geometry

264

combustor under the simulated inflow Ma 5.5 was conducted, and the results also

265

verified the accuracy of the numerical simulation method in the RBCC fixed

266

combustor [32]. To verify the accuracy of this method in a variable geometry

267

combustor, experimental pressures at the combustor wall under Ma 3 and Ma 6 inflow

268

will be compared with three-dimensional numerical pressures. The computational

269

domain covers the entire test facility, from the entrance of the facility nozzle to the

270

combustor exit. Only one-half of the flow path is considered to save computational

271

time. At the inlet of the facility nozzle, the static temperature and mass flow rate are

272

set equal to the experimentally measured values. All the inlet boundary conditions are

273

enumerated in Table 2. The primary rocket inlet species and temperature are

274

calculated by the Chemical Equilibrium with Applications (CEA) code from NASA

275

[33, 34]. The mass fractions of the main gas species in the primary rocket chamber are

276

listed in Table 4, and the mass flow rate and temperature are set as the boundary

277

conditions. Moreover, the mass flow rate and temperature values for the secondary

278

fuel injector obtain from the experimental measurements are used as boundary

279

conditions. Furthermore, the outlet of the combustor is specified as supersonic

280

outflow boundary. The walls are considered no-slip and adiabatic, and the center plane

281

of the combustor is set as a symmetric boundary. The computational mesh was

282

established using the ICEM software. A computational grid of 1.2 million nodes was

283

selected for this study. The boundary-layer cells, particularly the first cell height, play

AC C

EP

TE D

M AN U

SC

RI PT

263

16

ACCEPTED MANUSCRIPT a significant role; therefore, the height of the first cell center above the test-section

285

floor was chosen to be 0.01 mm with a maximum combustor y+ of 30. The structured

286

core cell spacing was generally uniform with modest gradients to smooth the

287

transition to the boundary-layer cells. Each case was run on 64 processors and

288

required approximately 5 days of run time.

RI PT

284

289

Table 4 Mass fractions of the main gas species and the gas parameters in the primary

291

rocket chamber Species

M AN U

SC

290

CO2 H2O H2

Mass fraction (%)

0.1

5.7 94.1

1,850

Chamber pressure (MPa)

1.5

TE D

Chamber temperature (K)

Mass flow rate (kg/s) 292

0.1

CO

0.12

Fig. 5 shows a comparison of the pressure on the sidewall of the combustor

294

between the numerical simulation and the experiment. The pressure curve obtained by

295

the numerical simulation well fits the measured data of the experiment. Moreover, the

296

tendency of the pressure curve obtained by the numerical simulation reflected at each

297

characteristic position is also consistent with the experiment and shows a slight

298

oscillation of the pressure at the fuel pylons and a slight decrease of the pressure

299

caused by heat release. The numerical method adopted in this paper is feasible and

300

can accurately reflect the actual flow field.

AC C

EP

293

17

ACCEPTED MANUSCRIPT

SC

RI PT

301

(a) Inflow of Ma 3

(b) Inflow of Ma 6

302 303

4. Results and discussion

M AN U

Fig. 5 Numerical simulation pressure validation against the experiment

The typical ramjet mode conditions at Ma 2, Ma 3, Ma 4 and Ma 6 are studied in

305

this paper. When the Mach number is low, the total temperature of inflow is relatively

306

low and the primary rocket operates at a low flow rate to ignite the secondary fuel and

307

stabilize the flame. As the Mach number increases, the total temperature increases, at

308

which time, the primary rocket turns off. The flame is stabilized through the

309

combination of the central strut and fuel pylons.

311

EP

AC C

310

TE D

304

4.1. Experimental results

312

Fig. 6 shows the static pressure curves of the combustor in direct-connect

313

experiments under the conditions of Ma 2 [Fig. 6(a)], Ma 3 [Fig. 6(b)], Ma 4 [Fig.

314

6(c)] and Ma 6 [Fig. 6(d)]. In Fig. 6(a) and Fig. 6(b), the wall pressure gradually

315

decreases in the cold flow state; moreover, it increases slightly because of the friction 18

ACCEPTED MANUSCRIPT in the straight isolator section. After exiting the isolator, the pressure in the combustor

317

suddenly decreases because of the expansion wave. Next, the pressure rises via the

318

squeezing effect of the fuel pylons on the flow path. At the same time, the shock

319

caused by the high-speed airflow strikes the leading edge of the fuel pylons, leading to

320

pressure oscillations. Afterwards, the pressure in front of the throat increases slightly

321

via the restriction of the geometric throat. Finally, the pressure at the exit of the

322

combustor is close to atmospheric pressure. The secondary fuel cannot be reliably

323

ignited without an ignition source. When the primary rocket operates at a low flow

324

rate, small molecular plume operates as a pilot flame that provides a continuous

325

source of ignition, which greatly reduces the ignition delay time and enhances the

326

reaction speed of the fuel. With a stable supply of secondary kerosene fuel, the

327

pressure in the combustor rises after the primary rocket begins to operate. The high

328

pressure generated in the combustor causes a separation of the boundary layer. When

329

the adverse pressure gradient is large enough, a stable normal shock train is generated

330

in the isolator. At this time, the gas flow at the entrance of the combustor is reduced to

331

subsonic speed and the combustor works in the ramjet mode. Because of the

332

geometric throat effect, the entire combustor can maintain an isobaric combustion.

SC

M AN U

TE D

EP

AC C

333

RI PT

316

In Fig. 6(c) and Fig. 6(d), the pressure distribution of the combustor for the cold

334

flow is basically the same as that of Ma 3. The pressure in the combustor increases

335

with the ignition of the primary rocket; moreover, its higher combustor pressure

336

separates the boundary layer in the isolator section, which results in a precombustion

337

shock train. The pressure in the combustor decreases slightly after the primary rocket 19

ACCEPTED MANUSCRIPT is turned off. The precombustion shock train moves toward the combustor and

339

stabilizes in the isolator section. At this time, the secondary kerosene fuel can

340

maintain a stable combustion, and the transition from rocket-ramjet mode to ramjet

341

mode is realized.

RI PT

338

(b) Inflow of Ma 3

AC C

EP

TE D

(a) Inflow of Ma 2

M AN U

SC

342

(c) Inflow of Ma 4

(d) Inflow of Ma 6

Fig. 6 Pressure distribution of the combustor in direct-connect experiments

343 344

Fig. 7(a) and Fig. 7(b) show the outlet flame of the combustor under Ma 2 and Ma

345

3 inflow conditions, respectively. The variable geometry combustor can work stably 20

ACCEPTED MANUSCRIPT in the rocket-ramjet mode of Ma 2 and Ma 3 inflow. Fig. 7(c) and Fig. 7(e) show the

347

outlet flame of the combustor operating in the rocket-ramjet combustion mode of Ma

348

4 and Ma 6 inflow, respectively. Fig. 7(d) and Fig. 7(f) show the outlet flame of the

349

ramjet combustion mode of Ma 4 and Ma 6 inflow, respectively. The variable

350

geometry combustor can achieve the smooth transition from the rocket-ramjet mode

351

to the ramjet mode at Ma 4 and Ma 6 inflow. The combustor outlet forms a bright

352

flame in different combustion organization modes, indicating that the secondary fuel

353

in the combustor is in a good combustion state. In the ramjet mode after the rocket is

354

turned off, the combustor outlet forms a bright Mach disk. This is because the fuel in

355

the ramjet mode is more fully burned, and the gas pressure is higher than the

356

atmospheric pressure at the combustor outlet; therefore, the gas continues to expand in

357

the atmosphere, forming a Mach disk.

SC

M AN U

TE D EP AC C

358

RI PT

346

(a) Ma 2 in rocket-ramjet mode

(b) Ma 3 in rocket-ramjet mode

21

ACCEPTED MANUSCRIPT (d) Ma 4 in ramjet mode

(e) Ma 6 in rocket-ramjet mode

(f) Ma 6 in ramjet mode

RI PT

(c) Ma 4 in rocket-ramjet mode

SC

Fig. 7 Flame photographs at the combustor outlet

360

M AN U

359

Specific impulse and combustion efficiency are both key parameters to evaluate

361

the performance of the combustor. The specific impulse is defined as I sp =

362

The combustion efficiency is given as ηb =

F g0 m& fuel ,total

.

TE D

Tt ( x) − Tti . TAFT − Tti

Because of the inability to measure the internal drag of the combustor during the

364

experiment, the drag force of the combustor is evaluated via numerical simulations.

365

The pressure force is obtained by integrating the wall pressure. The test facility also

366

cannot measure the total temperature in the combustor. However, because of the

367

existence of the geometric throat in the variable geometry combustor, if the

368

combustion chamber functions properly, then the throat will inevitably become

369

choked, and the Mach number will be 1 at this moment. The total pressure of the

370

throat can be obtained from the static pressure of the throat, and the total temperature

371

can be obtained by determining the mass flow rate of the combustor. The theoretical

372

adiabatic flame temperature in the combustor can be calculated via CEA. Table 5

AC C

EP

363

22

ACCEPTED MANUSCRIPT presents the performance parameters of the combustor for different inflow

374

experiments. Under Ma 4 and Ma 6 inflow conditions, switching on the primary

375

rocket can achieve a transition from a higher thrust rocket-ramjet mode to a higher

376

specific impulse ramjet mode. The thrust of the combustor decreased by

377

approximately 10.8% and 12.2% after the rocket was turned off for Ma 4 and Ma 6

378

inflow conditions, respectively. However, the specific impulse increased significantly

379

by 28.2% and 37.1% for Ma 4 and Ma 6 inflow conditions, respectively. The results

380

also show that the combustion efficiency can be improved by turning off the primary

381

rocket. The overall equivalent ratio in the combustor is reduced after the primary

382

rocket in the fuel-rich state is turned off, and the secondary fuel is more fully in

383

contact with the oxygen in the incoming flow. Thus, the combustion efficiency is

384

improved in an appropriate combustion organization.

TE D

M AN U

SC

RI PT

373

385

Table 5 Performance parameters of the combustor for different inflow experiments Pressure

Drag

Thrust

Specific

Combustion

status

force (N)

force (N)

(N)

impulse (s)

efficiency

EP

Maflight

Rocket

AC C

386

Ma 2

on

2044

-235

1809

730

0.713

Ma 3

on

3705

-257

3367

1103

0.927

on

3650

-340

3310

1011

0.898

off

3292

-340

2952

1408

0.947

on

3086

-471

2737

808

0.890

off

2752

-471

2403

1026

0.966

Ma 4

Ma 6

23

ACCEPTED MANUSCRIPT 387 388

4.2. Numerical results To further reveal the mechanisms of the geometric throat, the flow field in

390

different structural combustors obtained by the numerical simulations will be

391

analyzed in detail below to obtain the details of the different combustion flow fields in

392

the geometric throat and the thermal throat combustor.

4.2.1. Flow field analysis of Ma 3 inflow

M AN U

394

SC

393

RI PT

389

Fig. 8 presents a comparison of the heat release distribution [Fig. 8(a)] and the

396

static temperature distribution [Fig. 8(b)] between the variable geometry combustor

397

(the upper part of Fig. 8(a) and Fig. 8(b)) and the fixed geometry combustor (the

398

lower part of Fig. 8(a) and Fig. 8(b)) under the Ma 3 inflow condition. The

399

distribution of heat release is calculated directly from the chemical kinetic equation in

400

units of W/m3. A comparison of the heat release of the variable geometry and the

401

fixed geometry combustor shows that the combustion heat release starts from the

402

shear layer formed by the primary rocket plume and the supersonic inflow. Because

403

the rocket high temperature plume is a small molecule rich fuel gas, the reaction rate

404

in the shear layer is obviously faster. The secondary fuel reacts rapidly under the pilot

405

of the rocket's high temperature plume and forms a pronounced exothermic region

406

behind the fuel pylons. Because of the role of the geometric throat, the exothermic

407

area is concentrated between the fuel pylons and the geometric throat, and it is 20%

408

shorter than that of the fixed geometry combustor, making it more beneficial to the

AC C

EP

TE D

395

24

ACCEPTED MANUSCRIPT thermal protection of the combustor. The heat release is faster and the region is

410

broader in the variable geometry combustor than the fixed geometry combustor. The

411

static temperature distribution of the combustion chamber shows that the high

412

temperature region of the variable geometry combustor expands into the entire

413

combustor, and its temperature distribution is more uniform than that of the fixed

414

geometry combustor. Furthermore, the secondary fuel and air mix better in variable

415

geometry combustors, leading to more heat release and higher temperatures.

416

Therefore, because of the role of the geometric throat, the heat release performance of

417

the combustor is obviously improved compared with that of the fixed geometry

418

combustor.

M AN U

SC

RI PT

409

TE D

419

AC C

EP

(a) Heat release distribution

(b) Static temperature distribution

Fig. 8 Comparison of the heat release distribution and the static temperature distribution between the variable geometry and the fixed geometry combustors under the Ma 3 inflow condition 25

ACCEPTED MANUSCRIPT 420

Fig. 9 shows a comparison of the mass weighted average pressure of the cross

422

section along the flow path between the variable geometry and fixed geometry

423

combustors under the Ma 3 inflow condition. The variable combustor with a

424

geometric throat maintains isobaric combustion. However, because of the small

425

expansion angle (2 degrees) in the fixed geometry combustor, the pressure rapidly

426

increases via the heat release of rich fuel by the primary rocket before the secondary

427

fuel injection. Behind the secondary fuel injection position, the combustion of the

428

secondary fuel cannot well counteract the expansion effect of the combustor, which

429

causes the pressure to decrease gradually.

M AN U

SC

RI PT

421

AC C

EP

TE D

430

Fig. 9 Numerical comparison of the static pressure along the flow path under the Ma 3 inflow condition 431 432

Fig. 10 shows a comparison of the Mach number distribution between the variable 26

ACCEPTED MANUSCRIPT geometry and fixed geometry combustors under the Ma 3 inflow condition; in Fig. 10

434

(b), the black line is a sonic line (Ma=1). Both combustors are in the ramjet mode

435

because of the large adverse pressure gradient in the combustor, which generates a

436

normal shock deceleration at the exit of the facility nozzle. Therefore, the gas speed at

437

the combustor entrance is decelerated to subsonic. For the variable geometry

438

combustor, choking occurs because of the presence of the geometric throat. The fixed

439

geometry combustor also forms a thermal choke. From the sonic surface, the thermal

440

throat is found to have a complex three-dimensional structure. For a fixed geometry

441

combustor, because of its large quantity of heat release at the thermal throat and based

442

on the distribution of heat release, the Mach number here is higher than that in the

443

combustor, which inevitably leads to a higher total pressure loss. This pressure loss is

444

unfavorable to the operation of the nozzle.

SC

M AN U

TE D EP AC C

445

RI PT

433

(a) Combustor Ma≥1 field

27

ACCEPTED MANUSCRIPT

M AN U

SC

RI PT

(b) Mach number distribution

TE D

(c) Mass weighted average of the Mach number distribution Fig. 10 Comparison of the Mach number distributions between the variable geometry

447 448

4.2.2. Flow field analysis of Ma 6 inflow

AC C

446

EP

and fixed geometry combustors under the Ma 3 inflow condition

Fig. 11 presents a comparison of the heat release distribution [Fig. 11(a)] and

449

static temperature distribution [Fig. 11(b)] between the variable geometry and fixed

450

geometry combustors under the Ma 6 inflow condition. In Fig. 11a, the exothermic

451

region of the variable geometry combustor is concentrated between the fuel pylons

452

and the geometric throat because of the role of the geometric throat. In addition, its

453

heat release is obviously faster than that of the fixed geometry combustor, and the 28

ACCEPTED MANUSCRIPT exothermic region of the variable geometry combustor is larger than that of the fixed

455

geometry combustor. Although the primary rocket is turned off, the low velocity

456

recirculation zone behind the rocket also causes the flame to propagate upstream,

457

resulting in a certain amount of heat release there as well. Similar to the Ma 3 inflow,

458

the high temperature area of the variable geometry combustor diffuses to the entire

459

combustor, and its temperature distribution is also more uniform than the fixed

460

geometry combustor, the heat release is more sufficient, and the combustor

461

temperature is higher. Compared with the temperature distribution of Ma 3, the total

462

temperature of the inflow increases and the diffusion of the high temperature region in

463

the combustor advances ahead of time, indicating that the secondary fuel evaporating

464

atomization distance is significantly shortened. Moreover, the heat release

465

performance of the combustor is significantly higher than that of the fixed geometry

466

because of the role of the geometric throat.

SC

M AN U

TE D

EP AC C

467

RI PT

454

(a) Heat release distribution

(b) Static temperature distribution 29

ACCEPTED MANUSCRIPT Fig. 11 Comparison of the heat release distribution and static temperature distribution between the variable geometry and fixed geometry combustors under the Ma 6 inflow condition

RI PT

468

The large amount of heat released in the combustor will inevitably lead to an

470

increase of pressure. Fig. 12 shows a comparison of the mass weighted average

471

pressure of the cross section along the flow path under the Ma 6 inflow condition. The

472

pressure of the variable geometry combustor is obviously higher than that of the fixed

473

geometry. Because of the existence of geometric throat, the secondary fuel releases a

474

large amount of concentrated heat in the variable geometry combustor, and the

475

pressure increases rapidly. Concurrently, an isobaric platform is formed in the

476

expansion section. The pressure of the fixed geometry combustor is relatively low,

477

which leads to the simultaneous occurrence of subsonic and supersonic areas in the

478

combustor. The pressure in the combustor fluctuates slightly. In the variable geometry

479

combustor, the adverse pressure gradient is large and the pressure is transmitted to the

480

entrance of the isolator section. However, the pressure in the fixed geometry

481

combustor is lower and the pressure only affects the outlet of the isolator section.

M AN U

TE D

EP

AC C

482

SC

469

30

SC

RI PT

ACCEPTED MANUSCRIPT

M AN U

Fig. 12 Numerical comparison of the static pressure along the flow path under the Ma 6 inflow condition 483

Fig. 13 shows a comparison of the Mach number distribution between the variable

485

geometry and fixed geometry combustors under the Ma 6 inflow condition. Under the

486

action of a geometric throat, a precombustion shock train forms in the isolator section

487

via the violent combustion heat release in the variable geometry combustor. The

488

airflow at the entrance of the combustor is decelerated to subsonic and the entire

489

combustor operates in the ramjet mode. Although the Mach number distribution of the

490

fixed geometry combustor still remains supersonic at the entrance of the combustor,

491

the Mach number outside the pylons is greater than 1. The subsonic region is

492

obviously less than the variable geometry combustor, and ramjet-scramjet mixed

493

mode is observed.

AC C

EP

TE D

484

494

31

M AN U

SC

(a) Combustor Ma≥1 field

RI PT

ACCEPTED MANUSCRIPT

AC C

EP

TE D

(b) Mach number distribution

(c) Mass weighted average Mach number distribution

Fig. 13 Comparison of the Mach number distribution between the variable geometry and fixed geometry combustors under the Ma 6 inflow condition 495 32

ACCEPTED MANUSCRIPT 496

4.3. Variable geometry combustor performance improvement results The performance of different combustion chamber configurations is compared

498

based on the total pressure recovery coefficient, which is defined as the ratio of the

499

mass weighted average total pressure pt at different sections of the combustor to the

500

total pressure p0 at the inlet. Fig. 14 shows a comparison of the total pressure recovery

501

coefficient along the flow path. The total pressure of the combustion chamber

502

decreases rapidly in the isolator section via the influence of the precombustion shock

503

train and decreases with the total pressure loss during the combustion process in the

504

combustor. Because a stronger precombustion shock train is observed in the isolator

505

section of the variable geometry combustor, a larger total pressure loss is observed.

506

However, the Mach number in the variable geometry combustor is lower than that of

507

the fixed geometry combustor, and the total pressure loss caused by combustion is

508

also significantly smaller. Therefore, the total pressure recovery coefficient at the

509

outlet of the variable geometry combustor is higher than that of the fixed geometry

510

combustor. The total pressure recovery coefficient at the outlet of the combustor with

511

different configurations at Ma 3 was 0.63 and 0.58, respectively, thus indicating an

512

increase of 8.6%. The total pressure recovery coefficient at the outlet of the combustor

513

with different configurations in Ma 6 was 0.32 and 0.24, respectively, thus indicating

514

an increase of 33.3%. These results also show that the stronger isolator compression

515

combined with the lower combustor Mach number produces a higher total pressure

516

recovery coefficient.

AC C

EP

TE D

M AN U

SC

RI PT

497

517 33

RI PT

ACCEPTED MANUSCRIPT

(b) Inflow of Ma 6

SC

(a) Inflow of Ma 3

Fig. 14 Comparison of the total pressure recovery coefficient along the flow path

M AN U

518

Fig. 15 shows the combustion efficiency along the flow path for Ma 3 [Fig. 15(a)]

520

and Ma 6 [Fig. 15(b)]. Fig. 15(a) shows that the combustion heat release starts at the

521

rocket exit (x/H=10) and the combustion efficiency rises rapidly after the secondary

522

fuel addition (x/H=14), with the highest combustion efficiency at the exit of the

523

combustor. The combustion efficiency of a variable geometry combustor is 0.90,

524

which is higher than that of a fixed geometry combustor of 0.81. Fig. 15(b) shows that

525

the combustion heat release begins at the secondary fuel injection position and

526

releases heat more rapidly than the Ma 3 inflow after the fuel addition. This finding

527

indicates that the higher total temperature of the inflow is beneficial to the evaporation

528

and atomization of liquid kerosene and shortens the mixing distance. The combustion

529

efficiency of a variable geometry combustor is 0.92, which is higher than that of a

530

fixed geometry combustor (0.78).

AC C

EP

TE D

519

531

34

RI PT

ACCEPTED MANUSCRIPT

(b) Inflow of Ma 6

SC

(a) Inflow of Ma 3

Fig. 15 Comparison of the combustion efficiency along the flow path

M AN U

532

The thrust of the combustor is shown in Table 6. The thrust of the variable

534

geometry combustor is increased by 18.6% and 26.2% for Ma 3 and Ma 6,

535

respectively. The significant increase in the thrust performance also lead to a higher

536

specific impulse performance. It can be seen that under the influence of the geometric

537

throat, the fuel burns and releases heat at a lower Mach number, which leads to a

538

lower total pressure loss and a higher combustor pressure. On the other hand, the

539

combustion of the secondary fuel in the variable geometry combustor is more

540

complete, and the combustion efficiency is higher. By combining these two

541

advantageous effects, the variable geometry combustor produces better thrust and

542

achieves better specific impulse performance.

AC C

EP

TE D

533

543 544

Table 6 Comparison of the performance parameters of combustors with different

545

inflows and configurations

35

ACCEPTED MANUSCRIPT Inflow

Pressure

Drag force

force (N)

(N)

Fixed

3163

-274

2889

924

Variable

3684

-257

3427

1096

Fixed

2427

-582

1845

805

Variable

2849

-471

2378

1016

Configuration condition

Specific Thrust (N) impulse (s)

Ma 6

5. Conclusions

M AN U

547

SC

546

RI PT

Ma 3

In this paper, an RBCC variable geometry combustor was designed that can

549

operate in the range of Ma 2-7, in which kerosene fuel is used. The performance of

550

the RBCC variable geometry combustor operating at Ma 2-6 was studied using

551

ground direct-connect experiments. A comparison of the performance with a fixed

552

geometry combustor was studied using numerical simulations under the Ma 3 and Ma

553

6 inflow conditions. Based on the results, the following conclusions were obtained.

TE D

548

(1) The experiments showed that reliable ignition and stable high-efficiency

555

combustion of secondary fuel can be achieved by the primary rocket operating at a

556

low flow rate under a wide range of inflow conditions from Ma 2-6. The performance

557

of the variable geometry combustor was obtained via direct-connect experiments. The

558

transition from the rocket-ramjet mode to the ramjet mode under the conditions of Ma

559

4 and Ma 6 inflow were realized. The specific impulse was greatly improved by

560

28.2% and 37.1% through the transition of the combustion mode under Ma 4 and Ma

561

6 inflow conditions, respectively.

AC C

EP

554

36

ACCEPTED MANUSCRIPT (2) The heat release region of the variable geometry combustor was concentrated

563

between the fuel pylons and the geometric throat, resulting in better combustion of the

564

secondary fuel than in the fixed geometry combustor. Under the Ma 3 inflow

565

condition, the length of the heat release region of the variable geometry combustor

566

was shortened by 20% compared with that of the fixed geometry combustor and thus

567

was more conducive to the thermal protection of the combustor

RI PT

562

(3) The variable geometry combustor achieved better combustor performance

569

than that of the fixed geometry combustor under the same inflow conditions. The

570

studies showed that the combustion efficiency of the variable geometry combustor

571

reached 0.9 under Ma 3-6 inflow conditions. The total pressure recovery coefficients

572

were increased by 8.6% and 33.3% under the Ma 3 and Ma 6 inflow conditions,

573

respectively. The specific impulses were increased by 18.6% and 26.2% under the Ma

574

3 and Ma 6 inflow conditions, respectively. The increase in performance was due to

575

the dual effects of a lower Maher number and a higher combustion efficiency in the

576

variable geometry combustor. Therefore, variable geometry combustors show

577

significant performance advantages under a wide range of operating conditions and

578

thus represent an important direction of research for further improving engine

579

performance in the future.

580

References

581

[1] C. Clark, K. Kloesel, N. Ratnayake, A Technology Pathway for Airbreathing,

582

Combined-Cycle, Horizontal Space Launch Through SR-71 Based Trajectory

583

Modeling, in: 17th AIAA International Space Planes and Hypersonic Systems and

AC C

EP

TE D

M AN U

SC

568

37

ACCEPTED MANUSCRIPT Technologies Conference, San Francisco, California (2011).

585

[2] R. Daines, C. Segal, Combined Rocket and Airbreathing Propulsion Systems for

586

Space-Launch Applications, J. Propul. Power, 14 (1998), pp. 605-612.

587

[3] K.W. Flaherty, K.M. Andrews, G.W. Liston, Operability Benefits of Airbreathing

588

Hypersonic Propulsion for Flexible Access to Space, J Spacecraft Rockets, 47 (2010),

589

pp. 280-287.

590

[4] M. Kodera, H. Ogawa, S. Tomioka, S. Ueda, Multi-Objective Design and

591

Trajectory Optimization of Space Transport Systems with RBCC Propulsion via

592

Evolutionary Algorithms and Pseudospectral Methods, in: 52nd Aerospace Sciences

593

Meeting, National Harbor, Maryland (2014).

594

[5] Y.-j. Wang, J. Li, F. Qin, G.-q. He, L. Shi, Study of thermal throat of RBCC

595

combustor based on one-dimensional analysis, Acta Astronaut., 117 (2015), pp.

596

130-141.

597

[6] L. Shi, G.Q. He, P.J. Liu, F. Qin, X.G. Wei, J. Liu, L.L. Wu, A rocket-based

598

combined-cycle

599

compatibility and effective mode transition, Acta Astronaut., 128 (2016), pp. 350-362.

600

[7] L. Shi, X. Liu, G. He, F. Qin, X. Wei, B. Yang, L. Wu, Numerical Investigation of

601

Cowl Lip Adjustments for a Rocket-Based Combined-Cycle Inlet in Takeoff Regime,

602

Int. J. Turbo Jet Engines, 33 (2016), pp. 293-307.

603

[8] L. Shi, X.W. Liu, G.Q. He, F. Qin, X.G. Wei, B. Yang, J. Liu, Numerical analysis

604

of flow features and operation characteristics of a rocket-based combined-cycle inlet

605

in ejector mode, Acta Astronaut., 127 (2016), pp. 182-196.

TE D

M AN U

SC

RI PT

584

prototype

demonstrating

comprehensive

component

AC C

EP

engine

38

ACCEPTED MANUSCRIPT [9] B.-b. Lin, H.-l. Pan, L. Shi, J.-y. Ye, Effect of Primary Rocket Jet on

607

Thermodynamic Cycle of RBCC in Ejector Mode, Int. J. Turbo Jet Engines, (2017).

608

[10] R. Xue, G.Q. He, X.G. Wei, C.B. Hu, X. Tang, C. Weng, Experimental study on

609

combustion modes of a liquid kerosene fueled RBCC combustor, Fuel, 197 (2017), pp.

610

433-444.

611

[11] Z.W. Huang, G.Q. He, F. Qin, R. Xue, X.G. Wei, L. Shi, Combustion oscillation

612

study in a kerosene fueled rocket-based combined-cycle engine combustor, Acta

613

Astronaut., 129 (2016), pp. 260-270.

614

[12] Y. Li, Thermal Adjustment Mechanism Research on Ejector and Ramjet Mode of

615

RBCC (Ph.D Dissertation), Northwestern Polytechnical University, Xi'an (2008).

616

[13] W. Yajun, Investigation of Ramjet Mode in RBCC for Wide Adaptability based

617

on Thermal Adjustment (Ph.D Dissertation), Northwestern Polytechnical University,

618

Xi'an (2017).

619

[14] W.H. Heiser, D.T. Pratt, Hypersonic airbreathing propulsion, AIAA, 1994.

620

[15] M. Ou, L. Yan, J.F. Tang, W. Huang, X.Q. Chen, Thermodynamic performance

621

analysis of ramjet engine at wide working conditions, Acta Astronaut., 132 (2017), pp.

622

1-12.

623

[16] W. Huang, L. Yan, J.-g. Tan, Survey on the mode transition technique in

624

combined cycle propulsion systems, Aerosp. Sci. Technol., 39 (2014), pp. 685-691.

625

[17] Y. Tian, B. Xiao, S. Zhang, J. Xing, Experimental and computational study on

626

combustion performance of a kerosene fueled dual-mode scramjet engine, Aerosp. Sci.

627

Technol., 46 (2015), pp. 451-458.

AC C

EP

TE D

M AN U

SC

RI PT

606

39

ACCEPTED MANUSCRIPT [18] Y.P. Gounko, V.V. Shumskiy, Characteristics of dual-combustion ramjet,

629

Thermophys. Aeromech., 21 (2014), pp. 499-508.

630

[19] M. Bouchez, P. Genevieve, V. Levine, D. Davidenko, V. Avrashkov, Airbreathing

631

space launcher interest of a fully variable geometry propulsion system and

632

corresponding French-Russian partnership, in: 36th AIAA/ASME/SAE/ASEE Joint

633

Propulsion Conference and Exhibit, Las Vegas,NV (2000).

634

[20] F. Falempin, L. Serre, LEA Flight Test Program: First Step to an Operational

635

Application of High-Speed Airbreathing Propulsion, in: 12th AIAA International

636

Space Planes and Hypersonic Systems and Technologies, Norfolk, Virginia (2003).

637

[21] S. Feng, J.T. Chang, C.L. Zhang, Y.Y. Wang, J.C. Ma, W. Bao, Experimental and

638

numerical investigation on hysteresis characteristics and formation mechanism for a

639

variable geometry dual-mode combustor, Aerosp. Sci. Technol., 67 (2017), pp.

640

96-104.

641

[22] S. Feng, J.T. Chang, J.L. Zhang, C.L. Zhang, W. Bao, Numerical and

642

experimental investigation of improving combustion performance of variable

643

geometry dual-mode combustor, Aerosp. Sci. Technol., 64 (2017), pp. 213-222.

644

[23] S. Feng, J.T. Chang, Y.S. Zhang, C.L. Zhang, Y.Y. Wang, W. Bao, Numerical

645

studies for performance improvement of a variable geometry dual mode combustor by

646

optimizing deflection angle, Aerosp. Sci. Technol., 68 (2017), pp. 320-330.

647

[24] J. Ye, H. Pan, F. Qin, Combustor Performance of Wide Range Variable Geometry

648

RBCC, in: 8th National Conference on Hypersonic Technology, Harbin, China (2015).

649

[25] J. Ye, H. Pan, F. Qin, Investigation on the Applicable Scope of Geometrical

AC C

EP

TE D

M AN U

SC

RI PT

628

40

ACCEPTED MANUSCRIPT Throat in RBCC Variable Structure Combustion Chamber, J. Northwest. Polytech.

651

Univ., 35 (2017), pp. 975-982.

652

[26] R.J. Yentsch, D.V. Gaitonde, Numerical Investigation of Dual-Mode Operation in

653

a Rectangular Scramjet Flowpath, J. Propul. Power, 30 (2014), pp. 474-489.

654

[27] METACOMP, CFD++ & CAA User Manual, in: M. Technologies (ed.), Agoura

655

Hills, CA, 2011.

656

[28] J. Liu, M. Gruber, Preliminary Preflight CFD Study on the HIFiRE Flight 2

657

Experiment, in: 17th AIAA International Space Planes and Hypersonic Systems and

658

Technologies Conference, (2011).

659

[29] A. Storch, M. Bynum, J. Liu, M. Gruber, Combustor Operability and

660

Performance Verification for HIFiRE Flight 2, in: 17th AIAA International Space

661

Planes and Hypersonic Systems and Technologies Conference, Francisco, California

662

(2011).

663

[30] B. Franzelli, E. Riber, M. Sanjosé, T. Poinsot, A two-step chemical scheme for

664

kerosene–air premixed flames, Combust. Flame, 157 (2010), pp. 1364-1373.

665

[31] C.K. Westbrook, F.L. Dryer, Simplified Reaction Mechanisms for the Oxidation

666

of Hydrocarbon Fuels in Flames, Combust. Sci. Technol., 27 (1981), pp. 31-43.

667

[32] J. Ye, H. Pan, F. Qin, X.g. Wei, X. Tang, S.k. Zhang, Simulation of Kerosene

668

Combustion Sustaining with Cavities in a Strut-Based RBCC Engine, in: 51st

669

AIAA/SAE/ASEE Joint Propulsion Conference, Orlando, FL (2015).

670

[33] S. Gordon, B.J. McBride, Computer program for calculation of complex

671

chemical equilibrium compositions and applications. Part 1: Analysis, in, 1994.

AC C

EP

TE D

M AN U

SC

RI PT

650

41

ACCEPTED MANUSCRIPT 672

[34] B.J. McBride, S. Gordon, Computer Program for Calculation of Complex

673

Chemical Equilibrium Compositions and Applications II. Users Manual and Program

674

Description, in, 1996.

RI PT

675

List of Captions for the Figures and Tables

677

Fig. 1 Schematics for fixed geometry configurations of CRJ and DMR engines: (a)

678

RBCC in a CRJ engine, (b) RBCC in a DMR engine

679

Fig. 2 Variable geometry combustor assembly

680

Fig. 3 Model engine and pressure measurement point distribution diagram

681

Fig. 4 Schematic of the operation sequence for the test facility

682

Fig. 5 Numerical simulation pressure validation against the experiment: (a) Inflow of

683

Ma 3, (b) Inflow of Ma 6

684

Fig. 6 Pressure distribution of the combustor in direct-connect experiments: (a) Inflow

685

of Ma 2, (b) Inflow of Ma 3, (c) Inflow of Ma 4, (d) Inflow of Ma 6

686

Fig. 7 Flame photographs at the combustor outlet: (a) Ma 2 in rocket-ramjet mode, (b)

687

Ma 3 in rocket-ramjet mode, (c) Ma 4 in rocket-ramjet mode, (d) Ma 4 in ramjet mode,

688

(e) Ma 6 in rocket-ramjet mode, (f) Ma 6 in ramjet mode

689

Fig. 8 Comparison of the heat release distribution and the static temperature

690

distribution between the variable geometry and fixed geometry combustors under the

691

Ma 3 inflow condition: (a) Heat release distribution, (b) Static temperature

692

distribution

693

Fig. 9 Numerical comparison of the static pressure along the flow path under the Ma 3

AC C

EP

TE D

M AN U

SC

676

42

ACCEPTED MANUSCRIPT inflow condition

695

Fig. 10 Comparison of the Mach number distributions between the variable geometry

696

and fixed geometry combustors under the Ma 3 inflow condition: (a) Combustor

697

Ma≥1 field, (b) Mach number distribution, (c) Mass weighted average of the Mach

698

number distribution

699

Fig. 11 Comparison of the heat release distribution and static temperature distribution

700

between the variable geometry and fixed geometry combustors under the Ma 6 inflow

701

condition: (a) Heat release distribution, (b) Static temperature distribution

702

Fig. 12 Numerical comparison of the static pressure along the flow path under the Ma

703

6 inflow condition

704

Fig. 13 Comparison of the Mach number distributions between the variable geometry

705

and fixed geometry combustors under the Ma 6 inflow condition: (a) Combustor

706

Ma≥1 field, (b) Mach number distribution, (c) Mass weighted average of the Mach

707

number distribution

708

Fig. 14 Comparison of the total pressure recovery coefficient along the flow path: (a)

709

Inflow of Ma 3, (b) Inflow of Ma 6

710

Fig. 15 Comparison of the combustion efficiency along the flow path: (a) Inflow of

711

Ma 3, (b) Inflow of Ma 6

SC

M AN U

TE D

EP

AC C

712

RI PT

694

713

Table 1 Variable geometry combustor configuration parameters

714

Table 2 Experimental flow parameters

715

Table.3 Quasi-global chemical kinetics model for kerosene fuel [31] 43

ACCEPTED MANUSCRIPT Table 4 Mass fractions of the main gas species and the gas parameters in the primary

717

rocket chamber

718

Table 5 Performance parameters of the combustor for different inflow experiments

719

Table 6 Comparison of the performance parameters of combustors with different

720

inflows and configurations

RI PT

716

AC C

EP

TE D

M AN U

SC

721

44

ACCEPTED MANUSCRIPT Highlights

AC C

EP

TE D

M AN U

SC

RI PT

A RBCC variable geometry combustor is designed. The performance of the combustor operating at Ma 2-6 is studied. The performance of the variable geometry combustor is obtained via experiments. The heat release region is concentrated between the pylons and the geometric throat. A variable geometry combustor presents significant performance advantages.