Effect of geometry parameters on the hydrocarbon fuel flow rate distribution in pyrolysis zone of SCRamjet cooling channels

International Journal of Heat and Mass Transfer 141 (2019) 1114–1130

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International Journal of Heat and Mass Transfer journal homepage: www.elsevier.com/locate/ijhmt

Effect of geometry parameters on the hydrocarbon fuel flow rate distribution in pyrolysis zone of SCRamjet cooling channels Yuguang Jiang a, Jiang Qin b,⇑, Khaled Chetehouna c, Nicolas Gascoin c, Wen Bao b a

School of Power and Energy, Northwestern Polytechnical University, Xi’an 710072, PR China Key Laboratory of Aerospace Thermophysics, MIIT, Harbin Institute of Technology, Harbin 150001, PR China c INSA Centre Val de Loire, University Orléans, PRISME, EA 4229, F-18020 Bourges, France b

a r t i c l e

i n f o

Article history: Received 27 January 2019 Received in revised form 17 June 2019 Accepted 10 July 2019

Keywords: Flow distribution Parallel channels Pyrolysis Hydrocarbon fuel Geometry design

a b s t r a c t Hypersonic air-breathing propulsion (>Mach 5) based on SCRamjet promotes the revolutions of both military and civilian applications. However, the engine thermal protection is seriously challenged due to high Mach number. One of the key problems is mal-distribution of hydrocarbon fuel in regenerative cooling channels under the complex thermal boundaries and channel geometry, which may cause structural failure. To improve the cooling channel design and achieve better fuel flow distribution, the effect of channel geometry parameters on flow distribution in pyrolysis zone is numerically studied. Both geometry induced and heat flux induced flow mal-distribution are concerned. The study indicates that the flow and heat transfer features in pyrolysis zone of parallel channels differs with those in non-pyrolysis zone. The flow distribution deviations in pyrolysis zone are lower. When the channel aspect ratio varies, thermal stratification dominates flow distribution more than the variation of heat flux on heated surface in pyrolysis zone, which is opposite of that in non-pyrolysis zone. Besides, thinner rib and smaller total flow area achieve better cooling performance while consuming less fuel chemical heat sink. The results help to conclude possible references to the design of cooling channels with fuel pyrolysis considered. Ó 2019 Published by Elsevier Ltd.

1. Introduction SCRamjet is a very promising aerospace engine in air-breathing hypersonic flights [1–6]. The high flight Mach number (usually > Mach 5) makes SCRamjet applicable for both military and civil applications. However, under hypersonic flight Mach number, the inlet mainstream becomes too hot to be used as coolant. Regenerative cooling using hydrocarbon fuel brings new hope to engine cooling [7–9], in which hydrocarbon fuel cracks at high temperature and provides extra chemical heat sink [10–12]. Unfortunately, the fuel onboard is too limited when considering the thermal load. What’s worse, due to the non-uniform heat flux and other irregular geometric structures in the cooling system, the fuel flow mal-distribution is likely to occur, which may trigger serious waste of the limited fuel cooling capacity [13–16] and structure failure. So the study regarding the cooling channel design to achieve better flow distribution is in urgent need. There are many published papers studying the cooling channel design of aerospace engines like rocket engine and SCRamjet. D. ⇑ Corresponding author at: No. 92, West Da-Zhi Street, Harbin, Heilongjiang 150001, PR China. E-mail address: [email protected] (J. Qin). https://doi.org/10.1016/j.ijheatmasstransfer.2019.07.054 0017-9310/Ó 2019 Published by Elsevier Ltd.

Parris et al. investigated the effect of tube geometry and bend on the regenerative cooling performance of supercritical hydrogen fueled rocket engine [17]. Refs. [18–22] introduced the applications of high aspect ratio cooling channels. Wang et al. numerically investigated the conjugate heat transfer of cryogenic methane in three-dimensional rectangular cooling channel at supercritical pressures [23]. Zhang et al. numerically researched the thermal behaviors in cooling channels of SCRamjet with different aspect ratios [24,25]. Hydrocarbon fuel pyrolysis has also been one of the interests in the research of cooling channel design. Refs. [26– 28] focused on the detail chemical reaction kinetics. Refs. [29– 33] experimentally investigated the pyrolysis of hydrocarbon fuel, which helped uncover the pyrolysis characteristics and support the development of chemical reaction models. However, the above mentioned papers mainly focus on the flow and heat transfer in single channel. The flow distribution characteristic in parallel channels, which is non-negligible when designing the cooling channels, is not the research interest. In fact, the flow mal-distribution is a commonly seen problem in various kinds of heat exchangers, including boiler, steam generator [34,35], condenser [36], nuclear reactor [37], fuel cell [38,39], heat exchanger [40,41], etc. The studies on flow distribution include the header design and modification [42–44], the effects

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Nomenclature A AR b cp et H L m; mf nc P; p Q q qf sw T tw u b k

l q s

area, m2 aspect ratio channel width, m specific heat , J=ðkg  KÞ total internal energy, J=kg channel height, m channel length, m mass flow rate, kg=s channel number pressure, Pa flow rate, m3 =s heat absorption rate, W the heat flux, W=m2 heated wall thickness, m temperature, K rib thickness, m velocity of fuel, m=s mass flow rate deviation coefficient thermal conductivity, W=ðm  KÞ

£m £C £Tf DP

dynamic viscosity, Pa  s density, kg=m3 viscous stress mass flow rate deviation conversion rate deviation fuel temperature deviation pressure drop, Pa

Subscripts average average values c critical state eff effective HE heat exchange i channel number index m mole; mixture side side surfaces t total w wall

of boundary conditions [45,46], the fluid properties [47–49], the transient features [50,51], etc. The working fluids are mostly water and refrigerants. The operating conditions are generally ambient temperature and pressure. However, the cooling channels of SCRamjet are faced with high temperature and high pressure (normally supercritical pressure of the hydrocarbon fuel) conditions [52–54], which are quite different with above mentioned applications. Regarding the flow distribution problem in cooling channels of SCRamjet, Fu et al. [55] and Qin et al. [15] investigated the flow distribution characteristics in two parallel tubes experimentally. Jiang et al. brought up a flow deviation control method based on tandem flow restriction and validated it experimentally in two parallel tubes [16]. Jing et al. designed a mini-structure between two/ three parallel channels to adjust the flow distribution selfadaptively [56]. It is noted that two/three-parallel-tube layouts were adopted in these papers, which are very simple parallel configurations. In practical cooling system, the channel number is much larger. Chen et al. numerically and experimentally studied the control effect of branch throttle on flow mal-distribution in multi-parallel-channel layout [14,57]. Jiang et al. numerically studied the heat transfer and flow distribution under different channel geometries and flow mal-distribution patterns, in which the channel number ranges from 6 to 32 [58–60]. In addition, Jiang et al. proposed the variable channel sectional area design to adjust the flow distribution [61]. However, the specific effect of fuel pyrolysis on channel geometry parameter design is not considered in these multi-parallel-channel studies. Once pyrolysis occurs, fuel components and properties vary with temperature and pressure, which in turn closely couple with the flow and heat transfer process. The coupling between flow distribution characteristic and channel geometry becomes different and more complex. As listed in Table 1,

the current published papers in this field do not cover the coupling between flow distribution and channel geometry design in pyrolysis zone. The literatures about the effect of channel geometry on flow distribution of reactive hydrocarbon fuel are hardly found. In this paper, the effect of cooling channel geometry on the flow distribution in pyrolysis zone is studied to support the design of cooling channels to obtain a better flow distribution and cooling performance. A 3D numerical model of the heat transfer and pyrolysis of n-Decane in multi-parallel cooling channels is developed. The pyrolysis of n-Decane is considered with the PPD model developed by Ward et al. [62]. The cooling channel parameters in the fuel pyrolysis zone are studied. The flow distribution and cooling performance are set as the main indicators to evaluate different channel designs. 2. Model description 2.1. Geometry description In the cooling channels of SCRamjet, the fuel temperature could be as high as 1000 K. Significant pyrolysis occurs when the fuel temperature exceeds 770 K [63]. As mentioned in Ref. [25], to reduce the design difficulty, the representative cooling channels can be divided into two zones: non-pyrolysis zone and pyrolysis zone. Considering the non-pyrolysis zone has been studied in our previous work [58,59], this paper focuses on the pyrolysis zone. The schematic of the cooling channels of SCRamjet is shown in Fig. 1, which is decided by referring to the real engine configuration in Ref. [64]. The channel geometry and thermal boundary are two main inducements of flow mal-distribution, both of which are considered in this paper. As shown in Fig. 1, U-type-inlet/

Table 1 Literature survey about the flow distribution and channel geometry in SCRamjet cooling system. Investigators

Tf

Pressure

Working fluid

Channel No.

Research method

Main conclusions

Pyrolysis coupling

Chen et al. [14,57] Qin et al. [15] Jiang et al. [16] Fu et al. [55] Jing et al. [56] Jiang et al. [58–61]

400–900 K 300–950 K 300–1000 K 400–700 K 400–1500 K 300–950 K

3 MPa 2.5/3.0/3.5 MPa 2.7 MPa 3/4/5MPa 5 MPa 3 MPa

n-Decane RP-3 RP-3 RP-3 HF-1 n-Decane

5 2 2 2 2–3 6–32

Num.&Exp. Experimental Experimental Experimental Numerical Numerical

①② ①② ② ①② ①② ①②③

No Yes Yes No Yes No

Note: ①basic/detail flow distribution features; ②flow deviation control method; ③channel geometry parameters design.

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Fig. 1. The schematic of cooling channels.

outlet-header-setup (introduced in Ref. [39]) is used to represent the geometry non-uniformity, in which the flow directions of the inlet and outlet are opposite. While in the non-uniform heat flux cases, a 50 mm long ideal header is set, which ensures a uniform initial flow distribution. The computing domain is 20 mm in width. The length of the heated section is 350 mm. The material of the solid used is high temperature alloy GH 3128, the properties of which come from Ref. [65]. As shown in Fig. 1, the cross section of the parallel cooling channels is described by the channel width (b), channel height (H), rib thickness (t w ), and wall thickness (sw ¼ 1 mm). From the origin in the y direction, the channels are numbered from 1 to nc.






r  q! u ¼0


ð4Þ



! r  q! u u ¼ rp þ r  seff

ð5Þ

Standard enthalpy of formation is used to describe the energy variation caused by chemical reaction. The energy conservation equation can be presented as Eq. (6) without the energy source term. Considering the relatively low flow velocity in this paper, the term related to viscous dissipation is neglected.















! r  q! u et ¼ r  keff rT  r  p u

ð6Þ

The species mass fraction equation is presented as follow:



2.2. Principles of the channel geometry parameters configuration The study on the coupling between cooling channel geometry parameters and flow distribution needs a reasonable principle of parameter configuration [66,67]. In this paper, the SCRamjet combustor working conditions from Ref. [4] are used and similar constraints with our previous work [58,59] are adopted. The mass flow rate of engine coolant is set to be 232 g/s, which is the rounded value of the fuel mass flow rate for combustion at Mach 5 in Ref. [4]. The total mass flow rate for the computing domain is calculated to be 16.5 g/s. The channel aspect ratio is defined as:

AR ¼ H=b

ð1Þ

The heated wall area is kept constant:

nc ðb þ tw Þ ¼ const

ð2Þ

When studying the effects of aspect ratio and rib thickness, the total flow section area is kept constant as the following equation. (When studying the effects of total flow section area, it varies.) 2

nc  AR  b ¼ const



r  ðqY i uÞ ¼ r  qY i ud;i þ Si

ð3Þ

The rib thickness tw and total flow area are set to be 2 mm and 10:125 mm2 respectively as initial values for the parameters determination. According to the constraints above, for given mass flow rate mf ¼ 16:5g=s and aspect ratio AR, the geometric parameters (H; b; nc ) can be calculated. The calculated value of the channel number may not be an integer, which needs to be rounded. The rib thickness is recalculated based on the rounded value of the channel number. Therefore, in the section of aspect ratio, the rib thickness is close to instead of equal to the initial value 2 mm . 2.3. Governing equations The continuity, momentum conservation equations for the fluid region are listed below:

ð7Þ

The mass fraction source term Si is expressed as follow:

Si ¼ xi  M wi

ð8Þ

The thermal conduction equation is numerically solved inside the wall of the channels:

r  ðkrT Þ ¼ 0

ð9Þ

All the variables in these equations are defined in the nomenclature. 2.4. Chemical reaction mechanisms One-step proportional product distribution (PPD) chemical model proposed by Ward et al. [62] is adopted in this paper to describe the pyrolysis of n-Decane. The effect of pressure on the pyrolysis products was studied experimentally in Ref. [63] to obtain a general reaction mechanism, which is adopted in this paper as shown in Eq. (10).

C 10 H22 ! 0:151H2 þ 0:143CH4 þ 0:256C 2 H4 þ 0:126C 2 H6 þ 0:230C 3 H6 þ 0:180C 3 H8 þ 0:196C 4 H8 þ 0:102C 4 H10 þ 0:171C 5 H10 þ 0:124C 5 H12 þ 0:195C 6 H12 þ 0:089C 6 H14 þ 0:169C 7 H14 þ 0:072C 7 H16 þ 0:152C 8 H16 þ 0:012C 8 H18 þ

0:053C 9 H18 þ 0:003C 9 H20 ð10Þ

According to Arrhenius expression, the reaction rate constant k can be expressed as follow:

k¼Ae

Ea RT

f

ð11Þ

The values of A and Ea from several researches are listed in Table 2. Since the pressure and temperature conditions in this paper are similar to Zhou et al. [68], the parameters from Zhou et al. are adopted.

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bm ¼

2.5. Fuel properties

X

ð20Þ

xi b i

i

In cooling channels of SCRamjet, the fuel properties are strongly affected both by temperature and pressure, especially in the pseudo-critical region. The Peng-Robinson (PR) equation of state is used to predict the density of fluid considering its wide range of validity and ease of implementation [70].

p¼

ð12Þ

The R is the universal gas constant and V m is the mole volume. The parameters a and b can be calculated by the following equations, where the T c , Pc and x are the critical temperature, critical pressure and the acentric factor respectively. 2

ð13Þ

2

a0 ¼ 0:457247R T c =Pc

ð14Þ

n ¼ 0:37464 þ 1:54226x  0:26992x2

ð15Þ

b ¼ 0:07780RT c =Pc

ð16Þ

2

The specific heat cp is calculated from the ideal specific heat cpideal and the departure functions cpdep as follow

cpdep ¼ cpideal  cp

ð17Þ

where cpdep can be calculated from the equation of state. And the cpideal is calculated as a function of temperature,

cpideal ¼ Rða0 þ a1 T þ a2 T 2 þ a3 T 3 þ a4 T 4 Þ

ð18Þ

where the a0 a1 a2 a3 a4 are the coefficients to calculate the cpideal . The viscosity and thermal conductivity are calculated by the method of Chung et al. [70]. The influences of high pressure and high density are taken into consideration in this method to avoid large error. The method calculating the properties of n-Decane and its products has been validated with NIST data in Ref. [71]. However, when pyrolysis occurs, the fuel becomes a mixture. It is necessary to calculate the real properties of the mixture. A pseudocritical method in Ref. [72] is used in this paper for the computation of properties in a real-gas mixture. In this method, the behavior and properties of a real gas mixture are treated as a pure component. Appropriate critical constants (called pseudocritical constants) are assigned to this ‘‘pure component”. Eq. (12) is also applied for mixtures, where the critical temperature, critical pressure, critical specific volume, and acentric factor, are replaced by the corresponding mixture parameters. The mixing rules adopted are one-fluid van der Waals mixing rules [73]. In order to apply the equation of state models to the mixture, coefficients a and b in Eq. (12) are replaced by the following compositiondependent expressions:

a0:5 m ¼

X

 T cm ¼

  2 T ci x i 0:5 i P ci P
T ci  i xi P

P

ð21Þ

ci

RT a  V m  b V m ðV m þ bÞ þ bðV m  bÞ

a ¼ a0 ½1 þ nð1  ðT=T c Þ0:5 Þ

The critical parameters of the mixture can be calculated as:

xi ðai Þ0:5

T cm  Pcm ¼ P
T ci i xi P

ð22Þ

ci

V cm ¼

X xi Pci V ci T cm  T ci

ð23Þ

P cm

All the variables in these equations are defined in the nomenclature. 2.6. Model validation This paper studies the reactive flow and heat transfer in parallel channels. However, there is no corresponding experimental data. So the model validation is divided into two aspects: 1. the flow and heat transfer of reactive flow in cooling channel at supercritical pressure; 2. the flow distribution in parallel channels. 2.6.1. Validation of solution strategies for reactive flow and heat transfer at supercritical pressure The experimental data in Ref. [24] is used to validate the model’s prediction of flow and heat transfer in pyrolysis zone. Some basic information of the validation case is listed in Table 3. A 3-dimensional domain is adopted in the numerical model. As shown in Fig. 2, the computing domain includes inlet section, heated section and outlet section. The inlet section is set to obtain a fully developed flow. ‘‘Mass flow inlet” and ‘‘pressure outlet” are set as the inlet boundary and outlet boundary conditions respectively. As shown in Table 4, different heat sources are imposed in the solid domain to simulate different heating powers in the experiments. Considering no thermal insulation is set for the heating tube, heat flux boundary conditions in Table 5 are imposed on the outer wall of the test section wall to describe the heat loss. Regarding the outlet section, a constant heat flux of 11550W=m2 is set to account for the heat loss. The grid convergence analysis is carried out with case Run 3. Three mesh sizes are set for the computing domain. The mesh refinement is carried out by increasing the cell number to its 1.105 times in each coordinate direction and the total mesh size

Table 3 Basic information of the validation case.

ð19Þ

Fuel

Pb (MPa)

Tfin (K)

mfin (g/s)

n-Decane

3

727

0.96

i

Table 2 Reaction rate constants.

Zhou et al. [68]

Pressure (MPa)

Temperature (K)

Ea (kcal/mol)

3

770–940

60.2

A (s1 ) 1:8  1015:2

4

1:8  1015:3

5

1:8  1015:4

6

2:0  1015:5

Ward et al. [62]

3.45

773–873

63

Ward et al. [63]

3.45–11.38

823–873

63

1:6  1015:0

Stewart et al. [69]

2.96

712–809

642.4

1:1  1015:91:5

2:1  1015:0

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Fig. 2. The computing domain of the chemical model validation.

Table 4 The heat sources imposed on the test section wall. Experimental case No.

Run1

Heat source (W=m3 )

3:3398  108

Run2

Table 6 Grid convergence analysis of the chemical model validation. Run3

2:6454  108

Run4

2:1534  108

1:6929  108

of the domain increases about to its 1.35 times. The Generalized Richardson Extrapolation method [74] is adopted to calculate the extrapolated numerical solution and the order of accuracy. The grid in the near wall region of fluid domain is refined to ensure the calculation accuracy of boundary layer. The thickness of first row is set to be 0.001 mm to keep yþ < 1. As presented in Table 6, the maximum discrepancy between the medium grid and extrapolation value is 0.77722%, which proves the medium size mesh is good enough to study this problem. The outlet fuel temperature and conversion of n-Decane are shown in Table 7. The largest relative error of fuel temperature is 5.16%, which proves the model predicting the fuel temperature well. As to the prediction of conversion rate, the largest relative error of conversion rate is 9.91% in Run 1. It is because the PPD mechanism mainly applies to low conversion cases. Considering the detailed mechanism is not the research target of this paper and the largest relative error of the other three cases is 8.40%, the prediction of fuel conversion is considered acceptable. The heat transfer in the pyrolysis zone is another important indicator of the model. The comparison of the outer wall temperature of the test section is shown in Fig. 3. The maximum relative error is lower than 7%. The model predicts the heat transfer in pyrolysis zone well. 2.6.2. Validation of the solution strategies for flow distribution The validation of the model’s capability of predicting the flow distribution in parallel channels has been done in our previous work [58]. The experimental data in Ref. [75] is used to validate the prediction of flow distribution. The classical U-type configuration and square headers are used in the experiments, which are similar to the geometry of this paper. Water is used as working fluid, the temperature of which is 25 °C. The system consists of 9 branch tubes, 3 mm in diameter and 400 mm in length. The tube closest to the inlet of the header is defined as No. 1 and the others are defined successively to No.9. 3D simulations using the same geometry with the experiment are done. The flow ratio bref i of flow rate distribution defined in Ref. [75] is listed.

Fluid test

Dp, Pa

Tf , K

Conversion (%)

uout ; m=s

Coarse grid (857696) Medium grid (1156270) Fine grid (1563660) Extrapolation Discrepancy (%)

279330.06 282243.34 282644.22 284454.16 0.77722

936.085 936.255 936.256 936.261 0.00059

32.8613 33.0539 33.0540 33.0545 0.00167

33.4211 33.4246 33.4260 33.4323 0.02309

bref i ¼ Q i =Q

ð24Þ

The inlet/outlet boundary conditions are ‘‘mass flow inlet” and ‘‘pressure outlet” respectively. The inlet temperature and pressure are 298.15 K and 0.115 MPa respectively. The P out is set to be 101325 Pa. The wall is defined as no slip wall. In the validating case, the fluid is not heated. The grid convergence analysis of this validation could be found in previous work [58], which is not presented here. The uncertainty of the experimental results bref i shown in Fig. 4 is 2% according to Ref. [75]. The model compares well with the experimental data. The maximum errors of bref are 10.66%, 12.28% and 11.15% respectively for three flow rate conditions. It can be seen from the comparison that it is not a perfect match but the model is workable for the analysis of the distribution of flow rate and temperature. 2.7. Solution strategy The commercial software ANSYS 16.0 FLUENT is used. The k  xSST turbulence model is used [11]. The SIMPLEC algorithm and pressure based solver are adopted. The inlet and outlet boundary conditions are set to be ‘‘mass flow inlet” condition and ‘‘pressure outlet” conditions respectively. The inlet fluid temperature is set to be 700 K to make sure all the pyrolysis zone is included. The back pressure is 3 MPa, which is higher than the critical pressure of n-Decane.

Dqf ¼ qfmax =qfmin

ð25Þ

In geometry induced cases with U-type parallel set up, a uniform heat flux 3 MW=m2 is imposed on the heated surface. In the non-uniform heat flux induced flow mal-distribution cases, non-uniform heat flux distribution is imposed. The average heat flux is 3 MW=m2 . The heat flux deviation (defined in Eq. (25)) is set to be 1.5 according to the experimental data of SCRamjet com-

Table 5 The heat loss on the test section wall. Experimental case No.

P1

P2 7

P3

P4

P5

0.65486

70.174

26780

8:1739  104

0.52087

66.688

25043

5:7441  104

0.3738

48.592

23138

0.26716

34.491

21269

3

Run1

5:606  10

1:095  10

Run2

4:0281  107

Run3

2:8122  107

Run4

2:0919  107 4:1648  104 y ¼ P 1  x4 þ P 2  x3 þ P 3  x2 þ P 4  x þ P 5 ; xðmmÞ; yðW=m2 Þ

Formula of the heat flux

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Y. Jiang et al. / International Journal of Heat and Mass Transfer 141 (2019) 1114–1130 Table 7 The comparison between the numerical and experimental results of fuel temperature and conversion. Experimental case No.

T fout , K (Experimental)

T fout , K (Numerical)

Relative error (%)

Conversion (%) (Experimental)

Conversion (%) (Numerical)

Relative error (%)

Run Run Run Run

948 913 893 873

996.92 956.30 936.37 911.14

5.16 4.74 4.86 4.37

76.69 55.25 34.36 18.68

84.29 51.30 33.07 17.11

9.91 7.15 3.79 8.40

1 2 3 4

Fig. 5. The heat flux distribution on heated surface.

Fig. 3. The outer wall temperature comparison of Run 3.

domain increases to about 2.2 times. The Dp, T w;av erage and Y C 10 H22 are selected to be the indicators of the fluid domain. As for the solid domain, T w;av erage is selected since it is the only parameter in solid domain. The parameters calculated using Generalized Richardson Extrapolation method [74] show asymptotic behaviors. The discrepancies between the medium grid tests and the extrapolation values are 0.13%, 0.25%, 3.85% and 0.22% respectively. Considering the accuracy and computing time, the medium size mesh is selected for both fluid and solid domains. 3. Results and discussions

Fig. 4. Validation of the flow distribution prediction capability from our previous work [58].

bustor in Ref. [76]. The heat flux distributions are presented in Fig. 5. The other side of the wall is set adiabatic. The solutions are considered as converged when the residuals reach the minimum values after falling for more than two orders of magnitude and the differences of outlet fuel temperature of all branch channels is less than 0.1 K in continuous iterations. In all cases, the difference of inlet and outlet mass flow rate is less than 1  105 kg=s. The buoyancy effect is neglected considering the small horizontal channel and sufficiently high velocity. 2.8. Grid convergence analysis As shown in Table 8, three different mesh sizes are set for the fluid domain and solid domain respectively. The grid of near wall region in fluid domain is refined to ensure the calculation accuracy of boundary layer. The thickness of first row is set to be 0.001 mm and all the yþ values are lower than 3. For each domain, the mesh refinement is carried out by increasing the cell number to its 1.3 times in each coordinate direction. The total mesh size of the

Considering the basic flow distribution features of hydrocarbon fuel is uncovered in our previous work, different channel geometry parameters and flow mal-distribution inducements are compared to present the relationship among flow distribution, cooling performance and channel geometry, which supports the channel design. The definitions in Eqs. (26)–(31) are used to evaluate the flow rate distribution in parallel channels. The mass flow rate deviation coefficient is defined as follow:

bi ¼

mi  m m

ð26Þ

where mi is the mass flow rate of the channel i and m is the average mass flow rate of all the channels. To evaluate the mass flow rate distribution uniformity generally, the Relative Standard Deviation method (RSD) is used in this paper to describe the degree of dispersion. The RSD of mass flow rate is defined:

vffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi u n u1 X £m ¼ t b2 nc i¼1 i

ð27Þ

where nc is the number of the channels. The RSD of fuel temperature is defined as follow:

vffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi !2ffi u n u1 X T  T fouti fout £Tf ¼ t nc i¼1 T fout

ð28Þ

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Table 8 Grid-convergence analysis. Fluid test

Dp, Pa

T w;av erage ; K

Y C 10 H22

Solid test

T w;av erage ; K

Coarse grid (641706) Medium grid (1393750) Fine grid (3161202) Extrapolation Spatial order of accuracy Discrepancy (%)

3174098.5 3166241.2 3164583.5 3162181.0 5.9307 0.13

1231.22 1233.82 1235.11 1236.98 2.6889 0.25

0.72355 0.70755 0.69683 0.68130 1.5254 3.85

Coarse grid (905472) Medium grid (2079000) Fine grid (4707300) Extrapolation Spatial order of accuracy Discrepancy (%)

1230.61 1231.91 1233.01 1234.60 0.6753 0.22

where T fouti is the mass flow rate averaged outlet fuel temperature of channel i and T fout is the mean value of T fouti . The fuel conversion rate deviation coefficient is defined as follow:

b0 i ¼

Ci  C

ð29Þ

C

where C i is the fuel conversion rate of the channel i and C is the average fuel conversion rate of all channels. The RSD of fuel conversion rate is defined as:

vffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi u n u1 X £C ¼ t b0 2 nc i¼1 i

ð30Þ

Table 9 Channel geometry parameters in the study of geometry induced flow mal-distribution. AR

H (mm)

b (mm)

SR

Dh (mm)

DP ratio (%)

C 10 H22 (%)

nc

mf (g/s)

1 2 4 8

1.270 1.270 2.260 3.090

1.270 0.850 0.565 0.386

1.05 1.35 1.77 2.30

1.27 1.13 0.90 0.69

39.04 17.90 9.33 4.18

69.71 69.78 69.42 71.06

6 7 8 9

16.5

Fig. 6. Flow distribution results of U-type inlet/outlet headers setup: a. fuel temperature; b. mass flow rate deviation coefficient; c. fuel cooling capacity deviation coefficient; d. conversion rate deviation coefficient.

Y. Jiang et al. / International Journal of Heat and Mass Transfer 141 (2019) 1114–1130

where nc is the number of the channels. The total heat exchange area between the fluid domain and solid domain is defined as:

AHE ¼ 2nc ðH þ bÞL

ð31Þ

The hydrocarbon fuel flow distribution problems in the engine cooling can be classified into two typical types: (1). the geometry induced flow mal-distribution; (2). the heat flux induced flow mal-distribution, which are based on the practical scenario. Type (1) is abstracted from the walls of inlet/isolator/nozzle of SCRamjet, the heat flux deviations of which are relatively small. As for Type (2), it is abstracted from the wall of combustor, which is faced with evident heat flux deviation because of the combustion organization. In the following parts, each type of the problem will be studied. In Ref. [58], type (1) was focused. The initial flow maldistribution induced by geometry is also the source of flow maldistribution in heated status. Once the geometry setup benefits the initial flow distribution uniformity, fuel is distributed more even in heated status. Generally, higher aspect ratio, thinner rib and smaller total flow area improves the flow distribution and cooling performance. In Ref. [59], type (2) was focused. In nonuniformly heated channels, thermal stratification and the heat flux on heated surface dominates the flow and heat transfer. Higher channel aspect ratio lowers wall heat flux, which is good for flow

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distribution, while aggravating thermal stratification, which is bad for flow distribution. On the whole, it improves the flow distribution and cooling performance. Besides, rib thickness and total flow area hardly influence the flow distribution, which mainly affect cooling performance. However, in these two previous papers, the authors focus on the parallel cooling channels in non-pyrolysis zone. In this paper, pyrolysis zone is studied, which will be compared with the results of non-pyrolysis zone in our previous works [58,59] to uncover the difference of cooling channel design in different temperature zones.

3.1. The geometry induced flow mal-distribution in pyrolysis zone As introduced in Section 2.1, U-type-inlet/outlet-header-setup is used to represent the geometry non-uniformity. A uniform heat flux of 3 MW/m2 is imposed on the heated surface. The inlet velocity is set to be 2.25 m/s and the rib thickness is around 2 mm. The total flow area of the branch channels is maintained the same. The geometry parameters are listed in Table 9. The distribution results are shown in Fig. 6. As shown in the mass flow distribution of case ‘‘AR1 without heating” in Fig. 6.b, the flow distribution deviation occurs even if there is no heating,

Fig. 7. Wall temperature in the U-type-pyrolysis-parallel setup. Fig. 9. Velocity contours in the hottest channel of different cases.

Fig. 8. Mass fraction contours of n-Decane in the hottest channel of different cases.

Fig. 10. Heat transfer coefficient on the top surface of the hottest channel in different cases.

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which is induced by the distributing header. The distributing header is the source of flow deviation. When the heat flux is imposed (case ‘‘AR1”), the flow deviation is larger, which is the combined effect of header and fuel properties variation. If this source is suppressed, the amplification effect from fuel properties on the flow deviation weakens and the flow distribution improves. Taking DP ratio ¼ DPheader =DPbranch to explain the flow distribution. If DPratio ¼ 0, the mass flow rate in each channel will be the same. So, usually a smaller DP ratio leads to a more even flow distribution. From the analysis in Ref. [58], it is known that smaller Dh and larger SR both leads to smaller DP ratio . Besides, larger nc also decreases DPratio . So the variations of Dh , SR and nc with channel aspect ratio in Table 9 all decrease the DP ratio , which improve the mass flow rate distribution. The effect of aspect ratio on the mass flow rate distri-

Table 10 Channel geometries in pyrolysis cases with non-uniform heat flux. AR

H (mm)

b (mm)

t (mm)

AHE (m2)

nc

mf (g/s)

0.5 1 2 4 8

1.000 1.270 1.700 2.260 3.090

2.000 1.270 0.850 0.565 0.386

2.000 2.063 2.007 1.935 1.836

10.50  103 10.67  103 12.50  103 15.82  103 21.90  103

5 6 7 8 9

16.5

bution is quite similar to the non-pyrolysis zone, which is thus introduced very briefly. However, the hydrocarbon flow distribution in pyrolysis zone does have its own uniqueness. The first different point compared with non-pyrolysis zone is the degree of flow mal-distribution. The flow distribution is more uniform in the pyrolysis zone. It is strongly related to the difference between property variations in the pseudo-critical region and the pyrolysis region. The former variation is much more violent, which results in severer flow mal-distribution in the non-pyrolysis zone. The second different point is temperature distribution. For example, when channel aspect ratio varies from 1 to 8, in the channel No.1, the mass flow rate keeps falling. However, the temperature in channel No.1 doesn’t keep increasing all the time, which begins to fall from case AR4 to case AR8. It is because in pyrolysis zone, mass flow rate distribution and chemical conversion jointly affect the temperature distribution. From case AR1 to AR8, the conversion in channel No.1 keeps increasing, which helps lower the fuel temperature. From case AR4, the influence of chemical conversion outweighs the variation of mass flow rate, which leads to the turning point in the temperature variation. The third different point is the cooling performance variation versus aspect ratios. As shown in Fig. 7, the flow distribution improves with the increase of aspect ratio. Yet the maximum wall temperature does not behave in a similar way. It falls a little from

Fig. 13. Flow distributions in the non-uniformly heated parallel channels with pyrolysis. Fig. 11. Mass fraction of C10H22 on the central planes in non-uniformly heated pyrolysis case.

Fig. 12. Density contours on the central planes in non-uniformly heated pyrolysis case.

Fig. 14. Velocity contour on the central plane of the hottest channel in different pyrolysis cases.

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Fig. 15. Heat transfer coefficient on the top surface of the hottest channel in different pyrolysis cases.

Fig. 16. Heat flux on the top surface of the hottest channel in different pyrolysis cases.

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case AR = 1 to case AR = 2, which becomes higher in cases AR = 4 and AR = 8. The velocity and pyrolysis conversion results are used to explain this phenomenon. As we can see in Figs. 8 and 9, the cross section parameters become more non-uniform with larger aspect ratio and serious thermal stratification occurs. The heat transfer from the top wall to the central fluid is more difficult. The fuel near the top wall is overheated, which cracks greatly as shown in Fig. 8. The velocity in this region is much higher, forming a half M-shape velocity, which causes heat transfer deterioration. As shown in Fig. 10, the heat transfer coefficient in the hottest channel falls with the increase of aspect ratio. The heat transfer deterioration seriously limits the application of large aspect ratio channel. In the current setup, AR = 2 achieves the best cooling performance. In summary, although the large aspect ratio design benefits flow distribution, it cannot be applied because of the poor heat transfer performance. In geometry induced flow mal-distribution problems of pyrolysis zone, low aspect ratio channel design fits better. Considering the characteristics of flow mal-distribution in pyrolysis zone are quite similar with non-pyrolysis zone, in which

Fig. 18. Temperature contour on the central plane of the hottest channel in different pyrolysis cases.

Fig. 17. Flow distribution in pyrolysis cases with non-uniform heat flux: (a). Fuel temperature; (b). Mass flow rate coefficient.

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the source of flow distribution is the header, the effects of rib and flow area are not analyzed in this part. 3.2. The non-uniform heat flux induced flow mal-distribution in pyrolysis zone 3.2.1. The flow and heat transfer characteristics in parallel channels The channel geometry parameters are listed in Table 10. The case AR = 1 is selected as an example to present the main flow mal-distribution and heat transfer features of cooling channels in pyrolysis zone. As shown in Figs. 11 and 12, when imposed non-uniform heat flux boundary, the pyrolysis conversion differs in different channels. In channels with higher heat flux, fuel cracks more violently

and the density is much lower. Lower density leads to higher velocity and larger flow resistance in higher heat flux channels, which lowers the flow capacity and mass flow rate. The flow maldistribution occurs (shown in Fig. 13). It follows a positive feedback like in non-pyrolysis zone (Ref. [59]), except that the density variation is caused by pyrolysis instead of trans-critical process. However, the density variation caused by chemical reaction is not as sharp as the trans-critical process. The flow redistribution of the fuel in pyrolysis zone is thus gentler. Besides the flow mal-distribution among parallel channels, the parameter non-uniformity inside each channel is also noteworthy as shown in Figs. 11 and 12. The reaction conversion rate is higher and the density is lower in the region near to the heated wall (top wall), which is the result of thermal stratification. This phenomenon is more evident in channels with higher heat flux. So the hottest channel in each case (channel No. 5 when AR = 0.5, channel No. 6 when AR = 1, channel No. 7 when AR = 2, channel No. 8 when AR = 4 and channel No. 9 when AR = 8) is taken as an example for analysis. The density non-uniformity leads to the half M-shape velocity profile, as shown in Fig. 14. A zero velocity gradient in the near wall region arises, which triggers heat transfer deterioration as shown in Fig. 15. In high aspect ratio cases, the Mshape velocity profile is more distinct and the heat transfer is

Fig. 19. n-Decane mass fraction contours in the hottest channel in different pyrolysis cases.

Fig. 21. Wall temperature in different pyrolysis cases with non-uniform heat flux.

Fig. 20. Density contours in the hottest channel in different pyrolysis cases.

Fig. 22. Total conversion rate at the outlet of parallel channels.

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worse. On the other side, high aspect ratio design also brings benefits. The heat exchange area between fluid and solid is larger. More heat is transferred through lateral walls and the heat flux of the heated wall (the most dangerous wall) lowers (as shown in Fig. 16). It helps relieving thermal stratification and improving flow distribution. The overall effect on cooling performance will be co-decided by these two aspects. 3.2.2. The effects of channel aspect ratio The flow distribution results are shown in Fig. 17. The fuel temperature distribution is more uniform with higher aspect ratio, which is opposite of the result in non-pyrolysis zone. While the mass flow rate distribution stays nearly the same when aspect

Table 11 Channel geometry parameters in the rib thickness study with non-uniform heat flux. AR 1

H (mm) 0.82 1.00 1.10 1.27 1.40 1.60

b (mm) 0.82 1.00 1.10 1.27 1.40 1.60

t (mm) 0.50 1.00 1.40 2.06 2.60 3.40

AHE (m2) 3

17.25  10 14.00  103 12.30  103 10.67  103 9.80  103 8.96  103

nc

mf (g/s)

15 10 8 6 5 4

16.5

Fig. 23. Flow distribution non-uniformities under different rib thicknesses.

Fig. 24. Fuel conversion rate under different rib thicknesses.

Fig. 25. Wall temperature contours under different rib thicknesses.

Fig. 26. Heat flux on heated surface of the hottest channel under different rib thicknesses.

Fig. 27. Mass fraction of C10H22 on the central plane of hottest channel under different rib thicknesses.

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Table 12 Channel geometry parameters in the flow area study with non-uniform heat flux. AR 1

At (mm2) 12.00 10.13 8.00 6.00

H (mm)

b (mm) 2

92.58  10 82.16  102 68.60  102 56.20  102

t (mm) 2

92.58  10 82.16  102 68.60  102 56.20  102

0.50 0.50 0.49 0.49

AHE (m2) 3

18.10  10 17.25  103 16.30  103 14.90  103

nc

mf (g/s)

14 15 17 19

16.5

Fig. 28. Flow distribution non-uniformities under different total flow areas.

keeps deteriorating as the aspect ratio increases. The heat transfer from heated wall to the core flow becomes extremely difficult. It means the fuel in near heated wall region is faced with nearly all the thermal load, which almost completely cracks (as presented in Fig. 19). The fuel chemical heat sink is used up and @T f =@h rises fast. As a result, the fuel temperature in the near heated wall region becomes excessively high. The uniformity of fuel temperature distribution worsens with the increase of channel aspect ratio. Secondly, the mass flow rate distribution result is analyzed. As shown in Figs. 19 and 20, density stratification occurs and worsens due to the stratification of conversion rate as the aspect ratio increases. However, it should be noted the density span is much smaller than that of non-pyrolysis zone. There is no serious low density zone in the near wall region compared to the central zone. As discussed in last section, the flow redistribution in pyrolysis zone is much gentler. So when AR varies, the density stratification is not as serious as non-pyrolysis zone. The flow distribution is thus not obviously affected. Wall temperature is the direct indicator of thermal protection and fuel cooling performance. Obtaining reasonable wall temperature and avoiding over-temperature are the final aims of flow distribution study. As shown in Fig. 21, wall temperature in high aspect ratio cases is higher. On one hand, it is directly affected by the fuel temperature distribution, which is worse with higher aspect ratios. On the other hand, it is also result of heat transfer deterioration caused by high aspect ratio. The combination of higher fuel temperature and lower heat transfer coefficient leads to the higher wall temperature. Besides, as presented in Fig. 22, the total conversion rate of n-Decane increases with the aspect ratio, which means high aspect ratio design consumes more fuel heat sink while achieving worse cooling performance. All these analyses prove the high aspect ratio design doesn’t fit the pyrolysis zone.

Fig. 29. Distribution of fuel conversion rate under different total flow areas.

Fig. 30. Fuel temperature distribution under different total flow areas.

ratio varies, which also differs with the feature in non-pyrolysis zone. Firstly, the temperature distribution result is analyzed. It is noted the mass flow distributions are similar under different aspect ratios. So the fuel temperature distribution is mainly affected by the heat transfer process. As we know from last section, the heat flux of the heated wall falls as aspect ratio increases, which is expected to relieve thermal stratification and improve temperature distribution. However, it doesn’t outweigh the effect of high aspect ratio geometry. As shown in Fig. 18, taking the hottest channel in each case as an example, the thermal stratification

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3.2.3. The effect of rib thickness Rib thickness is another important geometry parameter influencing the cooling performance. The AR = 1 is selected considering its good flow distribution and cooling performance. The channel geometry parameters are listed in Table 11. The rib thickness varies from 0.5 mm to 3.4 mm, which is the commonly used range in SCRamjet design. As shown in Fig. 23, the mass flow rate distribution improves only slightly when the rib thickness decreases. The fuel temperature and conversion rate distribution doesn’t show obvious pattern with the rib thickness. The variation of rib mainly affects the cooling performance and total fuel conversion rate. As shown in Figs. 24 and 25, the total chemical conversion rate and wall temperature both decrease with the reduction of rib thickness, which means thinner rib achieves better cooling performance while consuming less fuel chemical heat sink. As the rib thickness decreases, the total heat exchange area increases. As a result, in Fig. 26, the heat flux on the heated wall

Fig. 31. Heat transfer coefficient of the heated surface of the hottest channel.

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falls which improves the cooling performance. Meanwhile, as shown in Fig. 27, the initial position of the pyrolysis gets earlier when the rib is thicker, which is affected by the heat flux variation. It explains the total conversion rate variation with the rib thickness. 3.2.4. The effect of total flow area AR = 1 and t = 0.5 mm are selected to study the effect of flow area on flow distribution of hydrocarbon fuel. The channel geometry parameters are listed in Table 12. As shown in Fig. 28, with the increase of total flow area, £m keeps increasing and £T f keeps decreasing. The increase of flow area lowers the velocity and the fuel residential time in the channel becomes longer. Longer residential time promotes the chemical reaction. While, as shown in Fig. 29, the pyrolysis is quite limited in channels with lower heat flux. So the influence of residential time affects high heat flux channels more. The pyrolysis becomes more violent and the density is lower in high heat flux channels, which explains the increase of £m . What’s more, higher conversion rate in high heat flux channels releases more fuel heat sink and lowers fuel temperature as shown in Fig. 30. As a result, £T f decreases. The other influence of the increase of flow area is heat transfer deterioration. As shown in Fig. 31, the heat transfer coefficient of the heated wall falls when the total flow area increases. So the final cooling performance is the balance of the effect on heat transfer and pyrolysis. Besides, it is noted that local heat transfer enhancement occurs around the x/L = 0.75 in case At = 6 mm2. To explain the phenomena, the variations of density and velocity along the  direction are shown in Fig. 32. In the zone of heat transfer enhancement, a sharp increase of velocity occurs. Meanwhile, the density falls quickly in the same zone and a local extreme value of @D=@x exits, which indicate the pyrolysis is violent here. Under the influences of both dramatic variations of velocity and density, the flow in this zone is more turbulent, as presented in Fig. 33. The heat transfer in this zone is thus enhanced. As shown in Fig. 34, wall temperature rises when the total flow area increase, which indicates the effect on heat transfer dominates. Lower flow

Fig. 32. Density and velocity variation along x direction in hottest channel of case At = 6 mm2.

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Fig. 33. Streamlines of central plane in hottest channel of case At = 6 mm2.

Fig. 34. Wall temperature contours under different total flow areas.

area design is better for cooling performance as long as the cost of pressure drop and fabrication is acceptable. 4. Conclusions In this paper, the effect of the channel geometry parameters on the hydrocarbon fuel flow distribution in the pyrolysis zone is investigated numerically. The numerical model has been validated by comparing 3D simulations with experimental results. The flow distribution and cooling performance in non-uniformly heated cooling channels under supercritical pressure are the research focuses. Two types of flow distribution problems are included. Wall temperature is selected as the indicator of the cooling performance. In general, the results of pyrolysis zone are quite different with non-pyrolysis zone. In the geometry induced flow mal-distribution in pyrolysis zone, the flow mal-distribution source comes from the initial flow deviation caused by the header. Then the density decrease caused by pyrolysis enlarges the flow mal-distribution. The nonuniformities of flow distribution are lower than those of nonpyrolysis zone. While the effect of aspect ratio on flow distribution is similar in both zones. The flow distribution improves with the

increase of channel aspect ratio. Because the increase of aspect ratio improves the initial flow distribution deviation. Regarding the fuel temperature distribution variation versus channel aspect ratio, a different point is found. The temperature in channel No.1 doesn’t keep increasing all the time with the fall of mass flow rate, which begins to fall from case AR4 to case AR8. Because in pyrolysis zone, mass flow rate distribution and chemical conversion jointly affect the temperature distribution. From case AR4, the influence of chemical conversion outweighs the variation of mass flow rate, which leads to the turning point in the temperature variation. Regarding the cooling performance, the heat transfer deterioration seriously limits the application of large aspect ratio channel. In the current setup, AR = 2 achieves the best cooling performance despite that case AR = 8 achieves the best flow distribution. In the non-uniform heat flux induced flow mal-distribution, the non-uniformities of flow distribution are lower than those of nonpyrolysis zone. However, the influence pattern is different. First, the mass flow rate distribution hardly varies with aspect ratio. The span of the density is much smaller than that of nonpyrolysis zone. And the flow redistribution in pyrolysis zone is much gentler. Second, the fuel temperature distribution worsens with the increase of channel aspect ratio, which is opposite of non-pyrolysis zone. Because the effect of thermal stratification outweighs the decrease of heat flux under high aspect ratio. Finally, the wall temperature increases with channel aspect ratio. Low aspect ratio channel design fits the non-uniformly heated pyrolysis zone. Further, the effects of rib thickness and total flow area are studied. Thinner rib achieves better heat transfer performance and cooling performance while consuming less fuel chemical heat sink. The total flow area changes the fuel velocity, which mainly affects the residential time and heat transfer performance. In current setup, the effect on heat transfer dominates. So smaller flow area achieves better cooling performance. In addition, local heat transfer enhancement is observed in the zone near x/L = 0.75 because of the variations of velocity and density along with pyrolysis. This paper focuses on the effects of geometry parameters on the flow distribution and cooling performance in the pyrolysis zone and compares with the result in non-pyrolysis zone. It offers possible reference for the cooling channel design of advanced aeroengines like SCRamjets.

Y. Jiang et al. / International Journal of Heat and Mass Transfer 141 (2019) 1114–1130

Declaration of Competing Interest The authors declared that there is no conflict of interest.

Acknowledgement This research work is supported by Program of National Natural Science Foundation of China (No. 51606051, No. 51876048).

References [1] E.T. Curran, SCRamjet engines: the first forty years, J. Propul. Power 17 (6) (2001) 1138–1148. [2] N. Gascoin, P. Gillard, A. Mangeot, A. Navarro-Rodriguez, Literature survey for a first choice of a fuel-oxidiser couple for hybrid propulsion based on kinetic justifications, J. Anal. Appl. Pyrol. 94 (2012) 1–9. [3] D. Zhang, S. Yang, S. Zhang, et al., Thermodynamic analysis on optimum performance of SCRamjet engine at high Mach numbers, Energy 90 (2015) 1046–1054. [4] Q. Yang, K. Chetehouna, N. Gascoin, et al., Experimental study on combustion modes and thrust performance of a staged-combustor of the SCRamjet with dual-strut, Acta Astronaut. 122 (2016) 28–34. [5] Q. Yang, W. Bao, K. Chetehouna, et al., Thermal behavior of an isolator with mode transition inducing back-pressure of a dual-mode SCRamjet, Chin. J. Aeronaut. 30 (2) (2017) 595–601. [6] D. Zhang, Y. Feng, S. Zhang, et al., Quasi-one-dimensional model of SCRamjet combustor coupled with regenerative cooling, J. Propul. Power (2016) 687– 697. [7] L. Taddeo, N. Gascoin, I. Fedioun, et al., Dimensioning of automated regenerative cooling: setting of high-end experiment, Aerosp. Sci. Technol. 43 (2015) 350–359. [8] L. Taddeo, N. Gascoin, K. Chetehouna, et al., Experimental study of pyrolysis– combustion coupling in a regeneratively cooled combustor: system dynamics analysis, Aerosp. Sci. Technol. 67 (2017) 473–483. [9] Y. Feng, J. Qin, S. Zhang, et al., Modeling and analysis of heat and mass transfers of supercritical hydrocarbon fuel with pyrolysis in mini-channel, Int. J. Heat Mass Transf. Vol. 91 (2015) 520–531, SCI, IF=3.458. [10] S. Liu, Y. Feng, Y. Cao, et al., Numerical simulation of supercritical catalytic steam reforming of aviation kerosene coupling with coking and heat transfer in mini-channel, Int. J. Therm. Sci. 137 (2019) 199–214. [11] Y. Zhu, B. Liu, P. Jiang, Experimental and numerical investigations on n-decane thermal cracking at supercritical pressures in a vertical tube, Energy Fuels 28 (1) (2013) 466–474. [12] K. Xu, H. Meng, Modeling and simulation of supercritical-pressure turbulent heat transfer of aviation kerosene with detailed pyrolytic chemical reactions, Energy Fuels (2015). [13] Y. Fu, Z. Tao, G. Xu, et al., Experimental study of flow distribution for aviation kerosene in parallel helical tubes under supercritical pressure, Appl. Therm. Eng. 90 (12) (2015) 102–109. [14] Y. Chen, Y. Wang, Z. Bao, et al., Numerical investigation of flow distribution and heat transfer of hydrocarbon fuel in regenerative cooling panel, Appl. Therm. Eng. 98 (2016) 628–635. [15] J. Qin, Y. Jiang, Y. Feng, et al., Flow rate distribution of cracked hydrocarbon fuel in parallel pipes, Fuel 161 (2015) 105–112. [16] Y. Jiang, S. Zhang, Y. Feng, et al., A control method for flow rate distribution of cracked hydrocarbon fuel in parallel channels, Appl. Therm. Eng. 105 (2016) 531–536. [17] D. Parris, D. Landrum, Effect of tube geometry on regenerative cooling performance, Proceedings of the 41st AIAA/ASME/SAE/ASEE Joint Propulsion Conference, AIAA Paper, 2005. [18] J. Wennerberg, H. Jung, R. Schuff, W. Anderson, C. Merkle, Study of simulated fuel flows in high aspect ratio cooling channels, Proceedings of the 42nd AIAA/ ASME/SAE/ASEE Joint Propulsion Conference, AIAA Paper 2006–4708, July 2006, 2006. [19] O. Knab, A. Fröhlich, D. Wennerberg, W. Haslinger, Advanced cooling circuit layout for the vinci expander cycle thrust chamber, Proceedings of the 38th AIAA/ASME/SAE/ASEE Joint Propulsion Conference, AIAA Paper 2002–4005, July 2002, 2002. [20] M. Pizzarelli, F. Nasuti, R. Paciorri, M. Onofri, Numerical analysis of threedimensional flow of supercritical fluid in cooling channels, AIAA J. 47 (11) (2009) 2534–2543. [21] M. Pizzarelli, F. Nasuti, M. Onofri, CFD analysis of transcritical methane in rocket engine cooling channels, J. Supercrit. Fluids 62 (2012) 79–87. [22] A. Ulas, E. Boysan, Numerical analysis of regenerative cooling in liquid propellant rocket engines, Aerosp. Sci. Technol. 24 (1) (2013) 187–197. [23] L. Wang, Z. Chen, H. Meng, Numerical Study of conjugate heat transfer of cryogenic methane in rectangular engine cooling channels at supercritical pressures, Appl. Therm. Eng. 54 (1) (2013) 237–246. [24] S. Zhang, Y. Feng, Y. Jiang, et al., Thermal behavior in the cracking reaction zone of scramjet cooling channels at different channel aspect ratios, Acta Astronaut. 127 (1) (2016) 41–56.

1129

[25] S. Zhang, J. Qin, K. Xie, et al., Thermal behavior inside SCRamjet cooling channels at different channel aspect ratios, J. Propul. Power 32 (1) (2015) 57– 70. [26] Z. Jia, Z. Wang, Z. Cheng, et al., Experimental and modeling study on pyrolysis of n-decane initiated by nitromethane, Combust. Flame 165 (3) (2016) 246– 258. [27] B. Jin, K. Jing, J. Liu, et al., Pyrolysis and coking of endothermic hydrocarbon fuel in regenerative cooling channel under different pressures, J. Anal. Appl. Pyrol. 125 (5) (2017) 117–126. [28] H. Wang, S. Gong, L. Wang, et al., High pressure pyrolysis mechanism and kinetics of a strained-caged hydrocarbon fuel quadricyclane, Fuel 239 (2019) 935–945. [29] H. Li, G. Liu, R. Jiang, et al., Experimental and kinetic modeling study of exo-TCD pyrolysis under low pressure, Combust. Flame 162 (5) (2015) 2177– 2190. [30] Y. Zhu, B. Liu, P. Jiang, Experimental and numerical investigations on decane thermal cracking at supercritical pressures in a vertical tube, Energy Fuels 28 (1) (2014) 466–474. [31] Y. Xing, W. Fang, W. Xie, et al., Thermal cracking of JP-10 under pressure, Ind. Eng. Chem. Res. 47 (24) (2008) 10034–10040. [32] C. Gong, H. Ning, J. Xu, et al., Experimental and modeling study of thermal and catalytic cracking of n-decane, J. Anal. Appl. Pyrol. 110 (2014) 463–469. [33] B. Ruan, H. Meng, V. Yang, Simplification of pyrolytic reaction mechanism and turbulent heat transfer of n-decane at supercritical pressures, Int. J. Heat Mass Transf. 69 (2) (2014) 455–463. [34] J. Zhou, S. Wang, L. Gao, et al., Study on flow instability inside multiple parallel pipes of direct steam generation, Energy Procedia 69 (2015) 259–268. [35] F. Bava, J. Dragsted, S. Furbo, A numerical model to evaluate the flow distribution in a large solar collector field, Sol. Energy 143 (2017) 31–42. [36] M.H. Shojaeefard, J. Zare, S.D. Nourbakhsh, Developing a hybrid procedure of one dimensional finite element method and CFD simulation for modeling refrigerant flow mal-distribution in parallel flow condenser, Int. J. Refrig. 73 (2016) 39–53. [37] T. Xiong, X. Yan, Z. Xiao, et al., Experimental study on flow instability in parallel channels with supercritical water, Ann. Nucl. Energy 48 (2) (2012) 60– 67. [38] S. Maharudrayya, S. Jayanti, A.P. Deshpande, Flow distribution and pressure drop in parallel-channel configurations of planar fuel cells, J. Power Sources 144 (1) (2005) 94–106. [39] J.Y. Wang, Pressure drop and flow distribution in parallel-channel configurations of fuel cells: U-type arrangement, Int. J. Hydrogen Energy 33 (21) (2008) 6339–6350. [40] C.C. Wang, K.S. Yang, J.S. Tsai, et al., Characteristics of flow distribution in compact parallel flow heat exchangers, Part II: Modified inlet header, Appl. Therm. Eng. 31 (16) (2011) 3235–3242. [41] J. Yue, R. Boichot, L. Luo, et al., Flow distribution and mass transfer in a parallel microchannel contactor integrated with constructal distributors, AIChE J. 56 (2) (2010) 298–317. [42] C. Pistoresi, Y. Fan, L. Luo, Numerical study on the improvement of flow distribution uniformity among parallel mini-channels, Chem. Eng. Process. Process Intensif. 95 (2015) 63–71. [43] M. Wei, Y. Fan, L. Luo, et al., CFD-based evolutionary algorithm for the realization of target fluid flow distribution among parallel channels, Chem. Eng. Res. Des. 100 (2015) 341–352. [44] R.M. Kumaran, G. Kumaraguruparan, T. Sornakumar, Experimental and numerical studies of header design and inlet/outlet configurations on flow mal-distribution in parallel micro-channels, Appl. Therm. Eng. 58 (1) (2013) 205–216. [45] U. Minzer, D. Barnea, Y. Taitel, Flow rate distribution in evaporating parallel pipes-modeling and experimental, Chem. Eng. Sci. 61 (22) (2006) 7249–7259. [46] M. Baikin, Y. Taitel, D. Barnea, Flow rate distribution in parallel heated pipes, Int. J. Heat Mass Transf. 54 (19) (2011) 4448–4457. [47] Q.M. Zhang, P.S. Hrnjak, T.A. Newell, An Experimental Investigation of R134a Flow Distribution in Horizontal Microchannel Manifolds, Air Conditioning and Refrigeration Center. College of Engineering. University of Illinois at UrbanaChampaign, 2003. [48] N.H. Kim, D.Y. Kim, J.P. Cho, et al., Effect of flow inlet or outlet direction on airwater two-phase distribution in a parallel flow heat exchanger header, International Journal of Air-Conditioning and Refrigeration 16 (2) (2008) 37– 43. [49] N.-H. Kim, D.Y. Kim, H.W. Byun, Effect of inlet configuration on the refrigerant distribution in a parallel flow minichannel heat exchanger, Int. J. Refrig. 34 (2011) 1209–1221. [50] Y. Taitel, D. Barnea, Transient solution for flow of evaporating fluid in parallel pipes using analysis based on flow patterns, Int. J. Multiph. Flow 37 (5) (2011) 469–474. [51] T.J. Zhang, J.T. Wen, A. Julius, et al., Stability analysis and mal-distribution control of two-phase flow in parallel evaporating channels, Int. J. Heat Mass Transf. 54 (25) (2011) 5298–5305. [52] K. Xu, H. Meng, Numerical study of fluid flows and heat transfer of aviation kerosene with consideration of fuel pyrolysis and surface coking at supercritical pressures, Int. J. Heat Mass Transf. 95 (2016) 806–814. [53] Z. Tao, X. Hu, J. Zhu, et al., Numerical study of flow and heat transfer of ndecane with pyrolysis and pyrolytic coking under supercritical pressures, Energy Fuels 31 (8) (2017) 8698–8707.

1130

Y. Jiang et al. / International Journal of Heat and Mass Transfer 141 (2019) 1114–1130

[54] J. Zhu, Z. Tao, H. Deng, et al., Numerical investigation of heat transfer characteristics and flow resistance of kerosene RP-3 under supercritical pressure, Int. J. Heat Mass Transf. 91 (2015) 330–341. [55] Y. Fu, Z. Tao, G. Xu, et al., Experimental study of flow distribution for aviation kerosene in parallel helical tubes under supercritical pressure, Appl. Therm. Eng. 90 (2015) 102–109. [56] T. Jing, G. He, F. Qin, et al., An innovative self-adaptive method for improving heat sink utilization efficiency of hydrocarbon fuel in regenerative thermal protection system of combined cycle engine, Energy Convers. Manage. 178 (2018) 369–382. [57] C. Yu, L. Bin, L. Zhiliang, et al., A control method for flow distribution in fuelcooled plate based on choked flow effect, Appl. Therm. Eng. 142 (2018) 127– 137. [58] Y. Jiang, Y. Xu, S. Zhang, et al., Parametric study on the distribution of flow rate and heat sink utilization in cooling channels of advanced aero-engines, Energy 138 (2017) 1056–1068. [59] Y. Jiang, J. Qin, C. Khaled, et al., Parametric study on the hydrocarbon fuel flow rate distribution and cooling performance in non-uniformly heated parallel cooling channels, Int. J. Heat Mass Transf. 126 (2018) 267–276. [60] Y. Jiang, Y. Xu, J. Qin, et al., The flow rate distribution of hydrocarbon fuel in parallel channels with different cross section shapes, Appl. Therm. Eng. 137 (2018). [61] Y. Jiang, J. Qin, Y. Xu, et al., The influences of variable sectional area design on improving the hydrocarbon fuel flow distribution in parallel channels under supercritical pressure, Fuel 233 (2018) 442–453. [62] T. Ward, S. Zabarnick, J. Ervin, et al., Simulations of flowing mildly-cracked normal alkanes incorporating proportional product distributions, J. Propul. Power 20 (3) (2004) 394–402. [63] T.A. Ward, J.S. Ervin, S. Zabarnick, et al., Pressure effects on flowing mildlycracked n-decane, J. Propul. Power 21 (2) (2005) 344–355. [64] D. Wishart, T. Fortin, D. Guinan, et al., Design, fabrication and testing of an actively cooled scramjet propulsion system, 41st Aerospace Sciences Meeting and Exhibit, 2003.

[65] [66]

[67]

[68] [69]

[70] [71]

[72] [73] [74] [75]

[76]

The Committee of China Aeronautical Materials Handbook, China Aeronautical Materials Handbook, China Standard Press, 2002. Pizzarelli Marco, Francesco Nasuti, Marcello Onofri, Effect of channel aspect ratio on rocket thermal behavior, J. Thermophys. Heat Transf. 28 (3) (2014) 410–416. L. Valdevit, N. Vermaak, K. Hsu, et al., Design of actively cooled panels for SCRamjets, in: 14th AIAA/AHI Space Planes and Hypersonic Systems and Technologies Conference, 2006, p. 8069. W. Zhou, Z. Jia, J. Qin, et al., Experimental study on effect of pressure on heat sink of n-decane, Chem. Eng. J. 243 (4) (2014) 127–136. J. Stewart, K. Brezinsky, I. Glassman, Supercritical pyrolysis of decalin, tetralin, and N-decane at 700–800K. Product distribution and reaction mechanism, Combust. Sci. Technol. 136 (1–6) (1998) 373–390. B.E. Poling, J.M. Prausnitz, J.P. O’Connell, The Properties of Gases and Liquids, vol. 5, MCGRAW-HILL, 2000. B. Wen, S. Zhang, Q. Jiang, et al., Numerical analysis of flowing cracked hydrocarbon fuel inside cooling channels in view of thermal management, Energy 67 (4) (2014) 149–161. ANSYS FLUENT User’s Guide, Release 13.0, November 2010. O. Redlich, J.N.S. Kwong, On the thermodynamics of solutions. V. An equation of state. Fugacities of gaseous solutions, Chem. Rev. 44 (1) (1949) 233–244. C.J. Roy, Grid convergence error analysis for mixed-order numerical schemes, AIAA J. 41 (4) (2003) 595–604. C.C. Wang, K.S. Yang, J.S. Tsai, et al., Characteristics of flow distribution in compact parallel flow heat exchangers, part I: typical inlet header, Appl. Therm. Eng. 31 (16) (2011) 3226–3234. C. Zhang, Z. Yao, J. Qin, et al., Experimental study on measurement and calculation of heat flux in supersonic combustor of scramjet, J. Therm. Sci. 24 (3) (2015) 254–259.