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Flow and thermal analyses of regenerative cooling in non-uniform channels for combustion chamber
Accepted Manuscript Flow and thermal analyses of regenerative cooling in non-uniform channels for combustion chamber Tingting Jing, Guoqiang He, Wenqiang Li, Fei Qin, Xianggeng Wei, Yang Liu, Zhiyuan Hou PII: DOI: Reference:
S1359-4311(16)34275-2 http://dx.doi.org/10.1016/j.applthermaleng.2017.03.062 ATE 10066
To appear in:
Applied Thermal Engineering
Received Date: Revised Date: Accepted Date:
26 December 2016 7 March 2017 14 March 2017
Please cite this article as: T. Jing, G. He, W. Li, F. Qin, X. Wei, Y. Liu, Z. Hou, Flow and thermal analyses of regenerative cooling in non-uniform channels for combustion chamber, Applied Thermal Engineering (2017), doi: http://dx.doi.org/10.1016/j.applthermaleng.2017.03.062
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Flow and thermal analyses of regenerative cooling in non-uniform channels for combustion chamber Tingting Jing, Guoqiang He, Wenqiang Li*, Fei Qin, Xianggeng Wei, Yang Liu, Zhiyuan Hou Science and Technology on Combustion, Internal Flow and Thermal-structure Laboratory, Northwestern Polytechnical University, Xi’an, China, 710072 *Corresponding author: E-mail address: [email protected] Abstract: Regenerative cooling is considered one of the most prospective thermal protection techniques in hypersonic vehicles. However, the non-uniform flow distribution in the cooling channels has the potential to lead the combustion chamber to overheat. In the present study, the regenerative cooling channels designed in a variety of non-uniform patterns are proposed. The conjugated flow and heat transfer behaviors of coolant and solid combustion chamber are numerically investigated. The scaling factor (Ω), i.e., height/width ratio, channel inlet/outlet manifold configuration, and relative angle (ω) of the inlet/outlet tube on flow and heat transfer characteristics are discussed. The numerical prediction is in reasonable agreement with previous numerical and experimental data. Results reveal that the basic configuration (Ω=1) contributes dramatic non-uniform flow in the channels near the inlet tube. The non-uniformity becomes more evident in the case of ω=60°. The scaling factor (Ω) exerts stronger influence on flow distribution in channels and the reformed case of =0.9 for Ch-1~4 gives the best flow uniformity and temperature distribution. The flow distribution is less sensitive to the outlet manifold than the inlet manifold. Keywords: Thermal protection; Engine; Regenerative cooling; Flow uniformity; Conjugated heat transfer Nomenclature cp
Specific heat at constant pressure, J/(kg·K)
Ch
Cooling channel
DL,ij
Molecular diffusion
DT,ij
Turbulent diffusion
Fx, Fy, Fz
Body force of x, y, z axis, N
Fij
Production by system rotation
1
Gij
Buoyancy production
m
Mass flow rate, kg/s
n
Channel number
N
Total number of cooling channels
p
Static pressure, Pa
pinlet
Pressure along the centerline of the inlet manifold, Pa
poutlet
Pressure along the centerline of the outlet manifold, Pa
Pij
Stress production
q
Heat flux, W/m2
Qi
Volume flow rate for ith tube, m3/s
Q
Total volume flow rate, m3/s
Sh
Volumetric heat sources, W/m3
t
Time,s
T
Temperature, K
u, v, w
Velocity magnitudes of x, y, z axis, m/s
V
Overall velocity vector, m/s
X
Tolerance of the arithmetic progression, mm
Greek symbols
Angle between the nth channel and the inlet, degree
ij
Dissipation
Angle of the channel, degree
Thermal conductivity, W/m·K
Dynamic viscosity, m2/s
Density, kg/m3
ij
Pressure strain
Coefficient of non-uniformity
Angle between one set of inlet and outlet, degree
Scaling factors of channels
Subscripts ave
Average 2
c
Coolant
w
Wall
1.
Introduction The increasing demands of higher altitude and speed have motivated the propulsion system
of hypersonic vehicle providing higher combustion pressure and more efficient thrust[1]. However, the hot gas generated from propellant in the combustion chamber has dramatically increased the thermal load of chamber jacket. In some extreme circumstances (Ma>6) of rocket or scramjet, the combustion chamber and nozzle tend to withstand the temperature over 3000K[2]. Confronted with this challenge, sorts of thermal protection techniques have been proposed in order to sustain more stable operation and realize the reusability of hypersonic vehicle[3]. The thermal protection techniques can be broadly classified as passive cooling and active cooling. Passive thermal protection technique, mainly utilized in solid rocket motor or air-breathing engine working in low Mach number, prevented the vehicle from thermal failure by sacrificing thermal protection material at combustor surface to keep the surface temperature at the ablative point. Active cooling is more suitable for high-speed vehicles working in the long term and regenerative cooling is considered as a prospective thermal protection technique due to its high efficiency and structural simplicity. The propellant of the engine is generally selected as the coolant, such as liquid hydrogen and hydrocarbon fuel. During the working cycle, the coolant (hydrocarbon fuel) flows through the cooling channel, absorbs the heat flux of the combustor and decomposes into small hydrocarbons which are more susceptible to ignition before injected to the combustion chamber[4]. Xu[5] conducted numerical simulation of turbulent fluid flow and heat transfer of cryogenic methane in ribbed cooling tubes at 8MPa. Results revealed that the ribbed tube could enhance the heat transfer and weaken the heat transfer deterioration compared with the smooth cooling tube. Rajagopal[6] investigated the regenerative cooling behaviors of a cryogenic rocket engine using liquid hydrogen or oxidizer as the cooling medium. Yan[7] compared the heat transfer of hydrocarbon fuel experimentally under steady states and pressure-transient states, and concluded that the thermal margin for a regenerative cooling system could be increased by approximately 25%. Negishi[8] conducted conjugated numerical studies for full-scale regenerative cooled thrust chambers. The research mainly focused on the flow and thermal characteristics in the combustion field and the individual channel. 3
It was noted in the published literatures[9][13] that the identical value of flow rate was imposed on each inlet of multiple cooling channels for calculation convenience without considering the non-uniformity of mass flow rate in multiple channels. In the actual fuel supply system, the coolant is initially pumped to primary delivery tubes, congested in a manifold, and then distributed to the subordinate cooling channels. The hypothesis of uniform inlet flow condition tended to be an impossible task in realistic engineering, because the velocity distributions of these channel inlets become non-uniform attributed to different flow resistance of each channel[14],[15]. Qin et al.[16] and Jiang et al.[17] investigated the flow rate distribution of cracked hydrocarbon fuel in parallel pipes with a two-parallel-pipe system, the supercritical hydrocarbon fuel has a more complex distribution in parallel channels and the research on two-parallel system could help to decrease the loss of coolant’s heat sink and avoid over-temperature in hypersonic vehicles. Eventually, the non-uniform inlet flow may result in local overheat problem especially with the increased channels. In this paper, the turbulent flows in sectorial cross-section cooling channels of water at atmospheric pressure and conjugate heat transfer with consideration of coupled heat conduction in the solid walls are numerically studied. The present study conducts detailed investigations of the effects of several key influential parameters on flow and thermal behaviors, including geometric parameters of manifold structure, scaling factor of parallel channels and relative position of the inlet and outlet tubes. 2. 2.1.
Model Problem description Fig.1 depicts the basic configuration of simplified axisymmetric combustion chamber with
180 fan-shaped cooling channels along the circumference. Two flanges with three sets of manifold inlet and outlet are welded at two ends of the chamber. Both inlet and outlet are averagely positioned around the flange. For the basic configuration, each set of inlet and outlet is located at the same radical position, i.e., =0o. Considering the relative positions of the coolant entrance and exit are often restricted with installation, we also investigate the influence of the relative position ( = 60o) of the inlet and outlet, as shown in Fig.2(a). To simplify the numerical model and speed up the computation, only one-sixth of the model is adopted for computational domain, as shown in Fig.2. Figs.2(b)~2(c) describe the cooling channels of combustion chamber with 4
non-uniform channel width. A scaling factor, i.e. =n/n+1, is employed to characterize the geometric non-uniformity defined as the width ratio of the nth channel(n) to its adjacent channel(n+1) which is away from the inlet. Fig.3 shows the redesigned concave/convex channel entrance/exit structures. The channel structure features that the lengths of the channels are in arithmetic progression from the central tube to either side of inlet tube with the tolerance of X=0.2 mm. Table 1 lists the cases with various channel configurations for simulation. 2.2.
Mathematical formulation To simplify the numerical model and focus on the influence of the panel configuration, the
following assumptions are made: (1) thermophysical properties of the working coolant and solid material are assumed to be constant; (2) no phase change occurs in the cooling channels, i.e. the coolant maintains liquid phase in the whole process; (3) the external walls are assumed to be adiabatic, except for the heated walll; (4) the influence of buoyancy force of coolant is neglected. Based on the above assumptions, the governing equations consisted of continuous, momentum and energy equations for 3-D steady state flow are written in Eqs(1)~(3)[18]. Notably, energy conservation equation integrates the convective heat transfer of the coolant and heat conduction through the solid walls. Mass Conservation Equation:
div V 0
(1)
Momentum Conservation Equation: div uV div gradu
p Fx x
(2-1)
div vV div gradv
p Fy y
(2-2)
div wV div gradw
p Fz z
(2-3)
Energy Conservation Equation: div( c pVT ) div(gradT ) Sh
(3)
For the turbulence model, the Reynolds stress model (RSM)[19],[20] is adopted as the turbulence model because the RSM model abandons the isotropic eddy-viscosity hypothesis and is more suitable to the stress-induced secondary flows in ducts. The transport equations for the Reynolds stresses can be written as Eq.(4), in which the parameters on the right hand of can be 5
checked in Ref.[19][20].
uiuj uk uiuj DT ,ij DL,ij Pij Gij ij ij Fij S h t xk 2.3.
(4)
Boundary conditions In order to study the single effects of the channels’ geometric parameters on the flow
characteristics, the simulation firstly focuses on the flow pattern and eliminates the influence of heat transfer. Thus, only fluid region is simulated and the conjugated interface is imposed with the constant heat flux of qw=1 MW/m2. Liquid water is selected as the coolant. The mass flow rate of each inlet is 1 kg/s. The ambient pressure (101325 Pa) is set to the outlet. In the second part of simulation that the conjugated heat transfer between solid structure and fluid is considered. The steel is employed as the solid material. The temperature of inlet coolant equals to 300 K. The inner surface is heated under constant heat flux of qw=1 MW/m2. The outside walls exposed to the surroundings are set adiabatic[21],[22]. The boundary conditions for the governing equations are listed in Table 2. 2.4.
Numerical method The RSM turbulence model is solved by the pressure-based solver, and the gradient is
computed according to the Least Squares Cell-Based method and the discretization scheme of second order upwind is chosen for the convection terms of momentum equations. The grid density is clustered at the vicinity of the coupling interface for a good resolution of the boundary layer and stress-induced secondary flows. The grids with more than 5 million nodes are generated using the software ICEM. The combined equations are solved with Couple algorithm packed in commercial software of Fluent. 3. 3.1.
Results and Discussions Code validation The validation of accuracy of simulation is necessary to guarantee the feasibility of the
numerical model. To accomplish the verification, the current model is applied to the “Z-type” compact parallel flow heat exchangers shown in Ref.[23], [24]. Fig.4 shows the comparison results of flow ratios of tubes among the present solutions with RSM, experimental data[23]and Huang’s solutions with stand k- model[24]. The flow ratio used to evaluate the flow distribution is defined as Qi/Q, where Qi represents volumetric flow rate (m3/s) for ith tube and Q is total 6
volume flow rate. It can be seen that both numerical predictions agree well with the experimental data. Moreover, for the forepart tubes (No.1-2), we obtain a more reasonable prediction with the RSM model probably because the present model is more suitable to simulate stress-induced secondary flows and complex configurations. 3.2.
Effects of the relative position of the inlets and outlets To quantify the flow non-uniformity in the parallel channels, the non-uniformity coefficient is
defined as the difference between mass flux ratio of the nth channel ( mn / mave ) versus average value (1), as shown in Eq.(5)
n /m ave 1 m
(5-1)
N
mave mn / N
(5-2)
n 1
First, we focus on the influence of the relative position, i.e. the angle between the inlet and outlet tubes on the flow patterns. Fig. 5(a) compares the non-uniformity coefficients of the cooling channels for Config-1 ( =0°) and Config-2 ( =60°). Config-1 presents a dramatic non-uniform flow distribution in the initial channels (Ch-1~5) near the inlet, and switches to a gentle increase since Ch-6. Compared with Config-2, the mass flow rate for Config-1 is slightly higher owing to more friction drag. Compared with Config-1, the non-uniformity coefficient varies significantly for =60°, from -0.35 to 0.65. This means that the case of =0° can stabilize the flow although its mass flux is lower than that of =0° in the channels of Ch-16~31. Overall, the flow is more homogenized in Config-1 at expense of sudden increase of non-uniformity near the inlet. Thus, it is still needed to balance the inlet pressure and mass flow rate of different channels. For the pressure distribution in the manifold for Config-1 shown in Fig.5(b), the pressure at the vicinity of the inlet tube(Ch-1~4) increases drastically (x=10 mm) due to flow impingement, then decreases to a further extent (x=6 mm), which stimulates the non-uniformity of Ch-1~4 higher than zero [see Fig.5(a)]. Then, as shown in Fig.5(b), low pressure covers the area in the manifold near Ch-5~9. This is caused by the flow recirculation [Fig.5(c)] mainly due to the reflection from the manifold bottom which tends to cause pressure loss and lower flow rate for Ch-5~9. In addition, to analyze the reason of the non-uniformity, the pressure difference of the centerlines in the inlet (x=10 mm) and outlet manifold (x=290 mm) is showed in Fig. 5(d), the definition of pressure difference in Fig.5(d) is defined by subtracting the pressure values along the 7
centerline of the outlet manifold from that of the inlet manifold, as shown in Eq.(6):
p pinlet poutlet
(6)
It can be seen that the pressure difference of Config-2 fluctuates more strongly in different channels than Config-1, which leads to less uniformity in the channels of Config-2, as indicated in Fig. 5(a). Consequently, the non-uniformity becomes more evident in the case of =60°, which demonstrates that arrangement of inlets and outlets in different angle is not recommended in the regenerative cooling system in combustion chamber. 3.3.
Effects of geometric parameters of the parallel channels In this section, the scaling factors with three sets of width gradients, i.e. =0.90, 0.95, 1.10
are selected to quantify the impacts of height-to-width ratio on the flow rates of the channels. Considering that the channel number changes for different width ratios, we employ a relative angle to refer to the position of a channel. It can be seen in Fig. 6(a) that the scaling factor exerts more impact on the flow uniformity of channels for Config-5 () than the other scaling factors. This means that more coolant is accumulated near the inlet due to the less flow resistance for the expanded cross-section area of the channels near the tube inlet. However, this dramatic increase is achieved at the expenses of the remarkable shrinkage of flow rate of other channels, which has potential of causing temperature deviation in the cooling channels. Comparatively, in Configs-3~4 (), the mass flow rate is lower than the average value () for the channels within <30° and the highest mass flow rate is observed at the channel with largest cross section area (=60°). The result implies that the expanded area of channels of >30° exerts more dominated role in flow distribution than that of higher entrance pressure of frontal channels (<30°). Therefore, this type of channel configuration (Configs-3~4) can distribute extra coolant to the adjacent channels. Fig.6(b) illustrates the area-weighted velocity of at the exit of each channel for different scaling factors (=0.90, 0.95, 1.10). It is noted that the maximum velocities are discovered at Ch-1 for the four cases although the maximum mass flow rates are not in Ch-1 for Configs-3~5 [see Fig.6(a)]. The result indicates that channel velocity is determined by both mass rate and cross section area. Besides, it can be seen that the case of =0.95 (Config-4) provides the smallest velocity difference between inlet channel and the channel of =60°, which means that this channel 8
configuration obtains best velocity uniformity. From the analysis of Fig.6(a), the cases with scaling factors of =0.90 and 0.95 have improved the flow uniformity before < 30°. However, this uniformity is disrupted after = 30°. To gain better distributions in the entire channels, we propose another two reformed configurations based on the Configs-3~4, but differently applying the scaling factors of = 0.95 and = 0.9 only on Ch-1~4, labeled as Configs-10~11. As seen from Fig.7(a), compared to the basic configuration, both of the two reformed configurations improve the mass flow rate distributions in the cooling channels. Fig.7(b) illustrates the area-weighted velocity at the exit of each channel for Config-10 and Config-11. It is noted that with the help of small velocity difference of Config-11 and the variation of the cross section area, the mass flow rate distribution of Config-11 has been greatly improved by applying minor change on scaling factor for the channels whose non-uniformity are larger than 1.0. For the entire channels, the mean values of non-uniformity for Configs-1, 10 11 are calculated as 0.01, 0.0049 and 0.0002, and the deviations are 0.16, 0.07 and 0.03 respectively. Moreover, it is observed that Config-11 not only manipulates the flow rates in Ch-1~2 more close to the averaged value, but also has more uniform flow distributions in the rest channels ( > 30°). 3.4.
Effects of the manifold geometric structure The manifold shape is one of the vital parameters in the design of regenerative cooling
channels. In practical scramjet and RBCC, the inlet and outlet tubes are mounted normal to the combustor wall and form an “I-type” arrangement which has a symmetric flow rate distribution and larger pressure drop than other arrangements such as “U-type”, “C-type”[23],[24]. In order to make the current research more suitable for the practical application, the “I-type” arrangement with larger pressure drop is chosen to be the research model. Fig.8 depicts the non-uniform coefficients of cooling channels for Config-1 and Configs-6~9 with different entrance/exit structure. As shown in Fig.8, the flow distributions of Configs-6~8 present dramatic non-uniform in the initial channels (Ch-1~12) similar to that in Config-1. Comparatively, the non-uniform value and its coverage zone decrease in Config-9 with convex channel entrance. The non-uniformity of the Config-9 with convex entrance has been improved from the basic configuration which is attributed to a larger flow recirculation area compared with Config-1 in the channel entrance near the inlet, as shown in Fig.9. Config-6 with concave entrance 9
has worse flow distribution and no distinction of non-uniformity is observed between Configs-7~8 and the basic configuration. The result indicates that the inlet manifold plays a more significant role than the outlet manifold in the mass flow rate distribution and a convex entrance is more preferred. Fig.10 illustrates the pressure drop and temperature rise from inlet tube to outlet tube of Configs-1~11. It can be observed that temperature rise varies significantly in Configs-3~5, whereas maintains at nearly 25K in the rest cases. This result means that the temperature rise is closely related to the cooling channel number (see Table 1). Configs-3~5 owning the less heat transfer area (fewer channels) than other configurations lead to lower fin efficiency and smaller temperature rise. For the pressure drop, the similar trend as the temperature rise is found in the pressure drop for different channel configurations due to the influence of channel number. However, the pressure drop does not decrease strictly as the channel number increases, particularly in Configs-3~5. In addition, it is found that concave/convex structures of channel entrance/exit have little impact on the temperature rise and total pressure drop. 3.5.
Conjugated heat transfer characteristics of the improved configuration The purpose of improving the flow uniformity of cooling channels is to get more uniform
heat transfer efficiency in the RBCC combustor. In order to validate the above discussions, the temperature distributions in the combustor for the basic (Config-01) and optimized configuration (Config-11) are shown in Fig.11. As seen in Fig.11(a), the maximum temperature difference of the basic configuration is 18.21 K, whereas the value of the reformed case is 7.02 K. For the temperature contour in combustor, the reformed configuration[Fig.11(c)] obtains a more uniform temperature distribution than the basic configuration[Fig.11(b)] in the cooling channels. The temperature difference has decreased by 61.45%. As can be seen from Fig.11(c), there still exists local high temperature region in the central forepart of combustor (12° < < 16°) due to the decreases of mass flow rate and area-weighted average velocity in the range 12° < < 16°, as shown in Fig.7. 4.
Conclusions Flow and thermal behaviors of regenerative cooling in non-uniform channels are numerically
studied. The effects of several influential parameters, including the geometric parameters of manifold structure, scaling factor of parallel channels and relative position of the inlets and outlets, 10
on flow and heat transfer characteristics are investigated in detail. The following conclusions are obtained: 1.
The basic configuration (Ω=1) presents a dramatic non-uniform flow pattern in the channels near the inlet tube.
2.
The cases where the scaling factor Ω covers all the channels unified the channels near the inlet tube, but intensifies the non-uniformity in the rest channels. Comparatively, the most uniform flow rate and temperature distribution are achieved as the scaling factor of Ω=0.9 only covering channels of Ch-1~4.
3.
The angle between a set of the inlet and outlet tube, , influences the mass flow distribution significantly, and arrangement of inlets and outlets in different angle is not recommended in the regenerative cooling system.
4.
The convex entrance manifold influences the mass flow rate distributions significantly with increasing pressure lose because of the growing recirculation area in the channel entrance.
Acknowledgment This study is financially supported by the National Natural Science Foundation of China (NSFC) under Grant No. 51506180 and No. 51276150. The authors would like to thank NSFC for the sponsorship. Reference [1] Y.J. Wang, J. Li, F. Qin, G.Q. He, L. Shi, Study of thermal throat of RBCC combustor based on one-dimensional analysis, Acta Astronautica 117 (2015) 130-141. [2] N.R. Council, Review and Evaluation of the Air Force Hypersonic Technology Program, Washington, D.C., 1998. [3] N.R. Council, Evaluation of the National Aerospace Initiative, Washington, D.C., 2004. [4] Z.Y. Hou, G.Q. He, W.Q. Li, F. Qin, X.G. Wei, T.T. Jing, Numerical investigation on thermal behaviors of active-cooled strut in RBCC engine, Appl. Therm. Eng. 113 (2017) 822-830. [5] K.K. Xu, L. Tang, H. Meng, Numerical study of supercritical-pressure fluid flows and heat transfer of methane in ribbed cooling tubes, Int. J. Heat Mass Transfer 84 (2015) 346-358. [6] M. Rajagopal, Numerical Modeling of Regenerative Cooling System for Large Expansion Ratio Rocket Engines, J. Thermal Sci. Eng. Appl. 7 (2015) 011012-011012-8. [7] J.G. Yan, Z.H. Liu, Q.C. Bi, Y. Guo, Z.Q. Yang, Heat Transfer of Hydrocarbon Fuel Under 11
Steady States and Pressure-Transient States, J. Propul. Power 32 (2015) 1-8. [8] H. Negishi, Y. Daimon, H. Kawashima, N. Yamanishi, Conjugated Combustion and Heat Transfer Modeling for Full-Scale Regeneratively Cooled Thrust Chambers, in: 49th Joint Propulsion Conference, San Jose, CA, (2013) 3997. [9] Y.D. Kang, B. Sun, Numerical Simulation of Liquid Rocket Engine Thrust Chamber Regenerative Cooling, J. Thermophys Heat Transfer 25 (2012) 155-164. [10] M. Naraghi, R. Quentmeyer, D. Mohr, Effect of a blocked channel on the wall temperature of a regeneratively cooled rocket thrust chamber, in: 37th Joint Propulsion Conference and Exhibit, Salt Lake City, UT, U.S.A., (2001)3406. [11] W. Bao, X.L. Li, J. Qin, W.X. Zhou, D.R. Yu, Efficient utilization of heat sink of hydrocarbon fuel for regeneratively cooled scramjet, Appl. Therm. Eng. 33-34 (2012) 208-218. [12] F. Yu, J. Qin, B. Wen, Q.C. Yang, H.Y. Huang, Z.Q. Wang, Numerical analysis of convective heat transfer characteristics of supercritical hydrocarbon fuel in cooling panel with local flow blockage structure, J Supercrit. Fluids88 (2014) 8-16. [13] M. Pizzarelli, B. Betti, F. Nasuti, Cooling Channel Analysis of a LOX/LCH4 Rocket Engine Demonstrator, in: 50th Joint Propulsion Conference, Cleveland, OH, (2014)4004. [14] C.H. Huang, C.H. Wang, The study on the improvement of system uniformity flow rate for U-type compact heat exchangers, Int. J. Heat Mass Transfer 63 (2013) 1-8. [15] X.Q. Liu, J.L. Yu, Numerical study on performances of mini-channel heat sinks with non-uniform inlets, Appl. Therm. Eng. 93 (2016) 856-864. [16] J. Qin, Y.G. Jiang, Y. Feng, X.J. Li, H.W. Li, Y.X. Xu, W. Bao, S.L. Zhang, J.C. Han, Flow rate distribution of cracked hydrocarbon fuel in parallel pipes, Fuel 161(2015)105-112. [17] Y.G. Jiang, S.L. Zhang, Y. Feng, J. Cao, J. Qin, W. Bao, A control method for flow rate distribution of cracked hydrocarbon fuel in parallel channels, Appl. Therm. Eng. 105 (2016) 521-536. [18] J.D. Anderson, Computational fluid dynamics: the basics with applications, McGraw-Hill, 1995. [19] B.E. Launder, G.J. Reece, W. Rodi, Progress in the development of a Reynolds-stress turbulence closure, J. Fluid Mech. 68 (1975) 537-566. [20] M.M. Gibson, B.E. Launder, Ground effects on pressure fluctuations in the atmospheric 12
boundary layer, J. Fluid Mech. 86 (1978) 491-511. [21] M. Pizzarelli, F. Nasuti, R. Paciorri, M. Onofri, A Numerical Model for Supercritical Flow in Rocket Engines Applications, in: 43td Joint Propulsion Conference, Cincinnati, OH, (2007)5501. [22] S.L. Zhang, J. Qin, K.L. Xie, Y. Feng, W. Bao, Thermal Behavior Inside Scramjet Cooling Channels at Different Channel Aspect Ratios, J. Propul. Power 32 (2016) 57-70. [23] C.C. Wang, K.S. Yang, J.S. Tsai, I.Y. Chen, Characteristics of flow distribution in compact parallel flow heat exchangers, part I: Typical inlet header, Appl. Therm. Eng. 31 (2011) 3226-3234. [24] C.H. Huang, C.H. Wang, The design of uniform tube flow rates for Z -type compact parallel flow heat exchangers, Int. J. Heat Mass Transfer 57 (2013) 608-622.
13
Table 1 Geometric properties of the basic and reformed configurations Config
Inlet and outlet position
Scaling factors
Channel entrance
Channel number
No.
and exit
N
1
0o
1
/
31
2
60o
1
/
31
3
0o
0.90
/
17
4
0o
0.95
/
22
5
0o
1.10
/
18
6
0o
1
Concave entrance
31
7
0o
1
Concave exit
31
8
0o
1
Convex exit
31
9
0o
1
Convex entrance
31
14
Table 2 Boundary Conditions Inlet
Outlet
(kg/s) m
T(K)
P(Pa)
1
300
101325
Heating wall Position Conjugate
Model only for fluid
qw(W/m2)
Outer wall
1.0×106
Adiabatic
1.0×106
Adiabatic
interface Conjugated model
1
300
101325
15
Inner wall
Figure captions Fig. 1 Schematic of basic configuration Fig. 2 Cross-sections of configurations with different inlet/outlet position and scaling factor Fig. 3 Schematic of configurations with different manifold Fig. 4 Comparison of flow ratios of present solution with previous experimental data, and numerical results Fig.5 The influence of relative position of inlet and outlet tubes Fig. 6 Effect of scaling factor on the non-uniformity and velocities in the channels Fig. 7 The coefficient of non-uniformity of cooling channels with different scaling factors Fig. 8 Non-uniformity coefficients of cooling channels with different entrance and exit structures Fig. 9 Streamlines on the symmetric boundary conditions of Config-1 and Config-9 Fig. 10 Pressure drop and temperature rise of inlet/outlet tube of Configs-1~11 Fig. 11 Temperature distributions of the basic and reformed configurations
16
Fig. 1 Schematic of basic configuration
17
(a) =60o, =1
(b) =0o, <1
(c)=0o, >1
Fig. 2 Cross-sections of configurations with different inlet/outlet position and scaling factor
18
(a) Concave entrance
(b) Concave exit
(c) Convex exit (d) Convex entrance Fig. 3 Schematic of configurations with different manifold
19
Fig. 4 Comparison of flow ratios of present solution with previous experimental data[23], and numerical results[24]
20
(a)Influence of relative position of inlet and outlet on non-uniformity coefficients
(b) Pressure Distribution in the Inlet Manifold of Config-1
21
(c) Streamline in the Inlet Manifold of Config-1(x=10 mm)
(d) Pressure difference in the manifolds of Configs-1~2 Fig.5 The influence of relative position of inlet and outlet tubes on the (a)non-uniformity coefficient, (b)Pressure distribution,(c)Streamlines in the manifold, (d)Pressure difference in the manifolds
22
(a) The non-uniformity coefficients of cooling channels
(b) Area-weighted average velocity of cooling channel exits Fig. 6 Effect of scaling factor on the non-uniformity and velocities in the channels
23
(a) The coefficient of non-uniformity of cooling channels with different scaling factors
(b) Area-weighted average velocity of cooling channel exits Fig. 7 Effects of different scaling factor on the non-uniform and velocities in the channels
24
Fig. 8 Non-uniformity coefficients of cooling channels with different entrance and exit structures
25
(a) Streamlines on the symmetric boundary conditions of Config-1
(b) Streamlines on the symmetric boundary conditions of Config-9 Fig. 9 Streamlines on the symmetric boundary conditions of Config-1 and Config-9
26
Fig. 10 Pressure drop and temperature rise of inlet/outlet tube of Configs-1~11
27
(a) Temperature distributions of the basic and reformed configurations
(b) Contour of temperature distribution of Config-1
(c) Contour of temperature distribution of Config-11 Fig. 11 Temperature distributions of the basic and reformed configurations
28
S1359-4311(16)34275-2 http://dx.doi.org/10.1016/j.applthermaleng.2017.03.062 ATE 10066
To appear in:
Applied Thermal Engineering
Received Date: Revised Date: Accepted Date:
26 December 2016 7 March 2017 14 March 2017
Please cite this article as: T. Jing, G. He, W. Li, F. Qin, X. Wei, Y. Liu, Z. Hou, Flow and thermal analyses of regenerative cooling in non-uniform channels for combustion chamber, Applied Thermal Engineering (2017), doi: http://dx.doi.org/10.1016/j.applthermaleng.2017.03.062
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Flow and thermal analyses of regenerative cooling in non-uniform channels for combustion chamber Tingting Jing, Guoqiang He, Wenqiang Li*, Fei Qin, Xianggeng Wei, Yang Liu, Zhiyuan Hou Science and Technology on Combustion, Internal Flow and Thermal-structure Laboratory, Northwestern Polytechnical University, Xi’an, China, 710072 *Corresponding author: E-mail address: [email protected] Abstract: Regenerative cooling is considered one of the most prospective thermal protection techniques in hypersonic vehicles. However, the non-uniform flow distribution in the cooling channels has the potential to lead the combustion chamber to overheat. In the present study, the regenerative cooling channels designed in a variety of non-uniform patterns are proposed. The conjugated flow and heat transfer behaviors of coolant and solid combustion chamber are numerically investigated. The scaling factor (Ω), i.e., height/width ratio, channel inlet/outlet manifold configuration, and relative angle (ω) of the inlet/outlet tube on flow and heat transfer characteristics are discussed. The numerical prediction is in reasonable agreement with previous numerical and experimental data. Results reveal that the basic configuration (Ω=1) contributes dramatic non-uniform flow in the channels near the inlet tube. The non-uniformity becomes more evident in the case of ω=60°. The scaling factor (Ω) exerts stronger influence on flow distribution in channels and the reformed case of =0.9 for Ch-1~4 gives the best flow uniformity and temperature distribution. The flow distribution is less sensitive to the outlet manifold than the inlet manifold. Keywords: Thermal protection; Engine; Regenerative cooling; Flow uniformity; Conjugated heat transfer Nomenclature cp
Specific heat at constant pressure, J/(kg·K)
Ch
Cooling channel
DL,ij
Molecular diffusion
DT,ij
Turbulent diffusion
Fx, Fy, Fz
Body force of x, y, z axis, N
Fij
Production by system rotation
1
Gij
Buoyancy production
m
Mass flow rate, kg/s
n
Channel number
N
Total number of cooling channels
p
Static pressure, Pa
pinlet
Pressure along the centerline of the inlet manifold, Pa
poutlet
Pressure along the centerline of the outlet manifold, Pa
Pij
Stress production
q
Heat flux, W/m2
Qi
Volume flow rate for ith tube, m3/s
Q
Total volume flow rate, m3/s
Sh
Volumetric heat sources, W/m3
t
Time,s
T
Temperature, K
u, v, w
Velocity magnitudes of x, y, z axis, m/s
V
Overall velocity vector, m/s
X
Tolerance of the arithmetic progression, mm
Greek symbols
Angle between the nth channel and the inlet, degree
ij
Dissipation
Angle of the channel, degree
Thermal conductivity, W/m·K
Dynamic viscosity, m2/s
Density, kg/m3
ij
Pressure strain
Coefficient of non-uniformity
Angle between one set of inlet and outlet, degree
Scaling factors of channels
Subscripts ave
Average 2
c
Coolant
w
Wall
1.
Introduction The increasing demands of higher altitude and speed have motivated the propulsion system
of hypersonic vehicle providing higher combustion pressure and more efficient thrust[1]. However, the hot gas generated from propellant in the combustion chamber has dramatically increased the thermal load of chamber jacket. In some extreme circumstances (Ma>6) of rocket or scramjet, the combustion chamber and nozzle tend to withstand the temperature over 3000K[2]. Confronted with this challenge, sorts of thermal protection techniques have been proposed in order to sustain more stable operation and realize the reusability of hypersonic vehicle[3]. The thermal protection techniques can be broadly classified as passive cooling and active cooling. Passive thermal protection technique, mainly utilized in solid rocket motor or air-breathing engine working in low Mach number, prevented the vehicle from thermal failure by sacrificing thermal protection material at combustor surface to keep the surface temperature at the ablative point. Active cooling is more suitable for high-speed vehicles working in the long term and regenerative cooling is considered as a prospective thermal protection technique due to its high efficiency and structural simplicity. The propellant of the engine is generally selected as the coolant, such as liquid hydrogen and hydrocarbon fuel. During the working cycle, the coolant (hydrocarbon fuel) flows through the cooling channel, absorbs the heat flux of the combustor and decomposes into small hydrocarbons which are more susceptible to ignition before injected to the combustion chamber[4]. Xu[5] conducted numerical simulation of turbulent fluid flow and heat transfer of cryogenic methane in ribbed cooling tubes at 8MPa. Results revealed that the ribbed tube could enhance the heat transfer and weaken the heat transfer deterioration compared with the smooth cooling tube. Rajagopal[6] investigated the regenerative cooling behaviors of a cryogenic rocket engine using liquid hydrogen or oxidizer as the cooling medium. Yan[7] compared the heat transfer of hydrocarbon fuel experimentally under steady states and pressure-transient states, and concluded that the thermal margin for a regenerative cooling system could be increased by approximately 25%. Negishi[8] conducted conjugated numerical studies for full-scale regenerative cooled thrust chambers. The research mainly focused on the flow and thermal characteristics in the combustion field and the individual channel. 3
It was noted in the published literatures[9][13] that the identical value of flow rate was imposed on each inlet of multiple cooling channels for calculation convenience without considering the non-uniformity of mass flow rate in multiple channels. In the actual fuel supply system, the coolant is initially pumped to primary delivery tubes, congested in a manifold, and then distributed to the subordinate cooling channels. The hypothesis of uniform inlet flow condition tended to be an impossible task in realistic engineering, because the velocity distributions of these channel inlets become non-uniform attributed to different flow resistance of each channel[14],[15]. Qin et al.[16] and Jiang et al.[17] investigated the flow rate distribution of cracked hydrocarbon fuel in parallel pipes with a two-parallel-pipe system, the supercritical hydrocarbon fuel has a more complex distribution in parallel channels and the research on two-parallel system could help to decrease the loss of coolant’s heat sink and avoid over-temperature in hypersonic vehicles. Eventually, the non-uniform inlet flow may result in local overheat problem especially with the increased channels. In this paper, the turbulent flows in sectorial cross-section cooling channels of water at atmospheric pressure and conjugate heat transfer with consideration of coupled heat conduction in the solid walls are numerically studied. The present study conducts detailed investigations of the effects of several key influential parameters on flow and thermal behaviors, including geometric parameters of manifold structure, scaling factor of parallel channels and relative position of the inlet and outlet tubes. 2. 2.1.
Model Problem description Fig.1 depicts the basic configuration of simplified axisymmetric combustion chamber with
180 fan-shaped cooling channels along the circumference. Two flanges with three sets of manifold inlet and outlet are welded at two ends of the chamber. Both inlet and outlet are averagely positioned around the flange. For the basic configuration, each set of inlet and outlet is located at the same radical position, i.e., =0o. Considering the relative positions of the coolant entrance and exit are often restricted with installation, we also investigate the influence of the relative position ( = 60o) of the inlet and outlet, as shown in Fig.2(a). To simplify the numerical model and speed up the computation, only one-sixth of the model is adopted for computational domain, as shown in Fig.2. Figs.2(b)~2(c) describe the cooling channels of combustion chamber with 4
non-uniform channel width. A scaling factor, i.e. =n/n+1, is employed to characterize the geometric non-uniformity defined as the width ratio of the nth channel(n) to its adjacent channel(n+1) which is away from the inlet. Fig.3 shows the redesigned concave/convex channel entrance/exit structures. The channel structure features that the lengths of the channels are in arithmetic progression from the central tube to either side of inlet tube with the tolerance of X=0.2 mm. Table 1 lists the cases with various channel configurations for simulation. 2.2.
Mathematical formulation To simplify the numerical model and focus on the influence of the panel configuration, the
following assumptions are made: (1) thermophysical properties of the working coolant and solid material are assumed to be constant; (2) no phase change occurs in the cooling channels, i.e. the coolant maintains liquid phase in the whole process; (3) the external walls are assumed to be adiabatic, except for the heated walll; (4) the influence of buoyancy force of coolant is neglected. Based on the above assumptions, the governing equations consisted of continuous, momentum and energy equations for 3-D steady state flow are written in Eqs(1)~(3)[18]. Notably, energy conservation equation integrates the convective heat transfer of the coolant and heat conduction through the solid walls. Mass Conservation Equation:
div V 0
(1)
Momentum Conservation Equation: div uV div gradu
p Fx x
(2-1)
div vV div gradv
p Fy y
(2-2)
div wV div gradw
p Fz z
(2-3)
Energy Conservation Equation: div( c pVT ) div(gradT ) Sh
(3)
For the turbulence model, the Reynolds stress model (RSM)[19],[20] is adopted as the turbulence model because the RSM model abandons the isotropic eddy-viscosity hypothesis and is more suitable to the stress-induced secondary flows in ducts. The transport equations for the Reynolds stresses can be written as Eq.(4), in which the parameters on the right hand of can be 5
checked in Ref.[19][20].
uiuj uk uiuj DT ,ij DL,ij Pij Gij ij ij Fij S h t xk 2.3.
(4)
Boundary conditions In order to study the single effects of the channels’ geometric parameters on the flow
characteristics, the simulation firstly focuses on the flow pattern and eliminates the influence of heat transfer. Thus, only fluid region is simulated and the conjugated interface is imposed with the constant heat flux of qw=1 MW/m2. Liquid water is selected as the coolant. The mass flow rate of each inlet is 1 kg/s. The ambient pressure (101325 Pa) is set to the outlet. In the second part of simulation that the conjugated heat transfer between solid structure and fluid is considered. The steel is employed as the solid material. The temperature of inlet coolant equals to 300 K. The inner surface is heated under constant heat flux of qw=1 MW/m2. The outside walls exposed to the surroundings are set adiabatic[21],[22]. The boundary conditions for the governing equations are listed in Table 2. 2.4.
Numerical method The RSM turbulence model is solved by the pressure-based solver, and the gradient is
computed according to the Least Squares Cell-Based method and the discretization scheme of second order upwind is chosen for the convection terms of momentum equations. The grid density is clustered at the vicinity of the coupling interface for a good resolution of the boundary layer and stress-induced secondary flows. The grids with more than 5 million nodes are generated using the software ICEM. The combined equations are solved with Couple algorithm packed in commercial software of Fluent. 3. 3.1.
Results and Discussions Code validation The validation of accuracy of simulation is necessary to guarantee the feasibility of the
numerical model. To accomplish the verification, the current model is applied to the “Z-type” compact parallel flow heat exchangers shown in Ref.[23], [24]. Fig.4 shows the comparison results of flow ratios of tubes among the present solutions with RSM, experimental data[23]and Huang’s solutions with stand k- model[24]. The flow ratio used to evaluate the flow distribution is defined as Qi/Q, where Qi represents volumetric flow rate (m3/s) for ith tube and Q is total 6
volume flow rate. It can be seen that both numerical predictions agree well with the experimental data. Moreover, for the forepart tubes (No.1-2), we obtain a more reasonable prediction with the RSM model probably because the present model is more suitable to simulate stress-induced secondary flows and complex configurations. 3.2.
Effects of the relative position of the inlets and outlets To quantify the flow non-uniformity in the parallel channels, the non-uniformity coefficient is
defined as the difference between mass flux ratio of the nth channel ( mn / mave ) versus average value (1), as shown in Eq.(5)
n /m ave 1 m
(5-1)
N
mave mn / N
(5-2)
n 1
First, we focus on the influence of the relative position, i.e. the angle between the inlet and outlet tubes on the flow patterns. Fig. 5(a) compares the non-uniformity coefficients of the cooling channels for Config-1 ( =0°) and Config-2 ( =60°). Config-1 presents a dramatic non-uniform flow distribution in the initial channels (Ch-1~5) near the inlet, and switches to a gentle increase since Ch-6. Compared with Config-2, the mass flow rate for Config-1 is slightly higher owing to more friction drag. Compared with Config-1, the non-uniformity coefficient varies significantly for =60°, from -0.35 to 0.65. This means that the case of =0° can stabilize the flow although its mass flux is lower than that of =0° in the channels of Ch-16~31. Overall, the flow is more homogenized in Config-1 at expense of sudden increase of non-uniformity near the inlet. Thus, it is still needed to balance the inlet pressure and mass flow rate of different channels. For the pressure distribution in the manifold for Config-1 shown in Fig.5(b), the pressure at the vicinity of the inlet tube(Ch-1~4) increases drastically (x=10 mm) due to flow impingement, then decreases to a further extent (x=6 mm), which stimulates the non-uniformity of Ch-1~4 higher than zero [see Fig.5(a)]. Then, as shown in Fig.5(b), low pressure covers the area in the manifold near Ch-5~9. This is caused by the flow recirculation [Fig.5(c)] mainly due to the reflection from the manifold bottom which tends to cause pressure loss and lower flow rate for Ch-5~9. In addition, to analyze the reason of the non-uniformity, the pressure difference of the centerlines in the inlet (x=10 mm) and outlet manifold (x=290 mm) is showed in Fig. 5(d), the definition of pressure difference in Fig.5(d) is defined by subtracting the pressure values along the 7
centerline of the outlet manifold from that of the inlet manifold, as shown in Eq.(6):
p pinlet poutlet
(6)
It can be seen that the pressure difference of Config-2 fluctuates more strongly in different channels than Config-1, which leads to less uniformity in the channels of Config-2, as indicated in Fig. 5(a). Consequently, the non-uniformity becomes more evident in the case of =60°, which demonstrates that arrangement of inlets and outlets in different angle is not recommended in the regenerative cooling system in combustion chamber. 3.3.
Effects of geometric parameters of the parallel channels In this section, the scaling factors with three sets of width gradients, i.e. =0.90, 0.95, 1.10
are selected to quantify the impacts of height-to-width ratio on the flow rates of the channels. Considering that the channel number changes for different width ratios, we employ a relative angle to refer to the position of a channel. It can be seen in Fig. 6(a) that the scaling factor exerts more impact on the flow uniformity of channels for Config-5 () than the other scaling factors. This means that more coolant is accumulated near the inlet due to the less flow resistance for the expanded cross-section area of the channels near the tube inlet. However, this dramatic increase is achieved at the expenses of the remarkable shrinkage of flow rate of other channels, which has potential of causing temperature deviation in the cooling channels. Comparatively, in Configs-3~4 (), the mass flow rate is lower than the average value () for the channels within <30° and the highest mass flow rate is observed at the channel with largest cross section area (=60°). The result implies that the expanded area of channels of >30° exerts more dominated role in flow distribution than that of higher entrance pressure of frontal channels (<30°). Therefore, this type of channel configuration (Configs-3~4) can distribute extra coolant to the adjacent channels. Fig.6(b) illustrates the area-weighted velocity of at the exit of each channel for different scaling factors (=0.90, 0.95, 1.10). It is noted that the maximum velocities are discovered at Ch-1 for the four cases although the maximum mass flow rates are not in Ch-1 for Configs-3~5 [see Fig.6(a)]. The result indicates that channel velocity is determined by both mass rate and cross section area. Besides, it can be seen that the case of =0.95 (Config-4) provides the smallest velocity difference between inlet channel and the channel of =60°, which means that this channel 8
configuration obtains best velocity uniformity. From the analysis of Fig.6(a), the cases with scaling factors of =0.90 and 0.95 have improved the flow uniformity before < 30°. However, this uniformity is disrupted after = 30°. To gain better distributions in the entire channels, we propose another two reformed configurations based on the Configs-3~4, but differently applying the scaling factors of = 0.95 and = 0.9 only on Ch-1~4, labeled as Configs-10~11. As seen from Fig.7(a), compared to the basic configuration, both of the two reformed configurations improve the mass flow rate distributions in the cooling channels. Fig.7(b) illustrates the area-weighted velocity at the exit of each channel for Config-10 and Config-11. It is noted that with the help of small velocity difference of Config-11 and the variation of the cross section area, the mass flow rate distribution of Config-11 has been greatly improved by applying minor change on scaling factor for the channels whose non-uniformity are larger than 1.0. For the entire channels, the mean values of non-uniformity for Configs-1, 10 11 are calculated as 0.01, 0.0049 and 0.0002, and the deviations are 0.16, 0.07 and 0.03 respectively. Moreover, it is observed that Config-11 not only manipulates the flow rates in Ch-1~2 more close to the averaged value, but also has more uniform flow distributions in the rest channels ( > 30°). 3.4.
Effects of the manifold geometric structure The manifold shape is one of the vital parameters in the design of regenerative cooling
channels. In practical scramjet and RBCC, the inlet and outlet tubes are mounted normal to the combustor wall and form an “I-type” arrangement which has a symmetric flow rate distribution and larger pressure drop than other arrangements such as “U-type”, “C-type”[23],[24]. In order to make the current research more suitable for the practical application, the “I-type” arrangement with larger pressure drop is chosen to be the research model. Fig.8 depicts the non-uniform coefficients of cooling channels for Config-1 and Configs-6~9 with different entrance/exit structure. As shown in Fig.8, the flow distributions of Configs-6~8 present dramatic non-uniform in the initial channels (Ch-1~12) similar to that in Config-1. Comparatively, the non-uniform value and its coverage zone decrease in Config-9 with convex channel entrance. The non-uniformity of the Config-9 with convex entrance has been improved from the basic configuration which is attributed to a larger flow recirculation area compared with Config-1 in the channel entrance near the inlet, as shown in Fig.9. Config-6 with concave entrance 9
has worse flow distribution and no distinction of non-uniformity is observed between Configs-7~8 and the basic configuration. The result indicates that the inlet manifold plays a more significant role than the outlet manifold in the mass flow rate distribution and a convex entrance is more preferred. Fig.10 illustrates the pressure drop and temperature rise from inlet tube to outlet tube of Configs-1~11. It can be observed that temperature rise varies significantly in Configs-3~5, whereas maintains at nearly 25K in the rest cases. This result means that the temperature rise is closely related to the cooling channel number (see Table 1). Configs-3~5 owning the less heat transfer area (fewer channels) than other configurations lead to lower fin efficiency and smaller temperature rise. For the pressure drop, the similar trend as the temperature rise is found in the pressure drop for different channel configurations due to the influence of channel number. However, the pressure drop does not decrease strictly as the channel number increases, particularly in Configs-3~5. In addition, it is found that concave/convex structures of channel entrance/exit have little impact on the temperature rise and total pressure drop. 3.5.
Conjugated heat transfer characteristics of the improved configuration The purpose of improving the flow uniformity of cooling channels is to get more uniform
heat transfer efficiency in the RBCC combustor. In order to validate the above discussions, the temperature distributions in the combustor for the basic (Config-01) and optimized configuration (Config-11) are shown in Fig.11. As seen in Fig.11(a), the maximum temperature difference of the basic configuration is 18.21 K, whereas the value of the reformed case is 7.02 K. For the temperature contour in combustor, the reformed configuration[Fig.11(c)] obtains a more uniform temperature distribution than the basic configuration[Fig.11(b)] in the cooling channels. The temperature difference has decreased by 61.45%. As can be seen from Fig.11(c), there still exists local high temperature region in the central forepart of combustor (12° < < 16°) due to the decreases of mass flow rate and area-weighted average velocity in the range 12° < < 16°, as shown in Fig.7. 4.
Conclusions Flow and thermal behaviors of regenerative cooling in non-uniform channels are numerically
studied. The effects of several influential parameters, including the geometric parameters of manifold structure, scaling factor of parallel channels and relative position of the inlets and outlets, 10
on flow and heat transfer characteristics are investigated in detail. The following conclusions are obtained: 1.
The basic configuration (Ω=1) presents a dramatic non-uniform flow pattern in the channels near the inlet tube.
2.
The cases where the scaling factor Ω covers all the channels unified the channels near the inlet tube, but intensifies the non-uniformity in the rest channels. Comparatively, the most uniform flow rate and temperature distribution are achieved as the scaling factor of Ω=0.9 only covering channels of Ch-1~4.
3.
The angle between a set of the inlet and outlet tube, , influences the mass flow distribution significantly, and arrangement of inlets and outlets in different angle is not recommended in the regenerative cooling system.
4.
The convex entrance manifold influences the mass flow rate distributions significantly with increasing pressure lose because of the growing recirculation area in the channel entrance.
Acknowledgment This study is financially supported by the National Natural Science Foundation of China (NSFC) under Grant No. 51506180 and No. 51276150. The authors would like to thank NSFC for the sponsorship. Reference [1] Y.J. Wang, J. Li, F. Qin, G.Q. He, L. Shi, Study of thermal throat of RBCC combustor based on one-dimensional analysis, Acta Astronautica 117 (2015) 130-141. [2] N.R. Council, Review and Evaluation of the Air Force Hypersonic Technology Program, Washington, D.C., 1998. [3] N.R. Council, Evaluation of the National Aerospace Initiative, Washington, D.C., 2004. [4] Z.Y. Hou, G.Q. He, W.Q. Li, F. Qin, X.G. Wei, T.T. Jing, Numerical investigation on thermal behaviors of active-cooled strut in RBCC engine, Appl. Therm. Eng. 113 (2017) 822-830. [5] K.K. Xu, L. Tang, H. Meng, Numerical study of supercritical-pressure fluid flows and heat transfer of methane in ribbed cooling tubes, Int. J. Heat Mass Transfer 84 (2015) 346-358. [6] M. Rajagopal, Numerical Modeling of Regenerative Cooling System for Large Expansion Ratio Rocket Engines, J. Thermal Sci. Eng. Appl. 7 (2015) 011012-011012-8. [7] J.G. Yan, Z.H. Liu, Q.C. Bi, Y. Guo, Z.Q. Yang, Heat Transfer of Hydrocarbon Fuel Under 11
Steady States and Pressure-Transient States, J. Propul. Power 32 (2015) 1-8. [8] H. Negishi, Y. Daimon, H. Kawashima, N. Yamanishi, Conjugated Combustion and Heat Transfer Modeling for Full-Scale Regeneratively Cooled Thrust Chambers, in: 49th Joint Propulsion Conference, San Jose, CA, (2013) 3997. [9] Y.D. Kang, B. Sun, Numerical Simulation of Liquid Rocket Engine Thrust Chamber Regenerative Cooling, J. Thermophys Heat Transfer 25 (2012) 155-164. [10] M. Naraghi, R. Quentmeyer, D. Mohr, Effect of a blocked channel on the wall temperature of a regeneratively cooled rocket thrust chamber, in: 37th Joint Propulsion Conference and Exhibit, Salt Lake City, UT, U.S.A., (2001)3406. [11] W. Bao, X.L. Li, J. Qin, W.X. Zhou, D.R. Yu, Efficient utilization of heat sink of hydrocarbon fuel for regeneratively cooled scramjet, Appl. Therm. Eng. 33-34 (2012) 208-218. [12] F. Yu, J. Qin, B. Wen, Q.C. Yang, H.Y. Huang, Z.Q. Wang, Numerical analysis of convective heat transfer characteristics of supercritical hydrocarbon fuel in cooling panel with local flow blockage structure, J Supercrit. Fluids88 (2014) 8-16. [13] M. Pizzarelli, B. Betti, F. Nasuti, Cooling Channel Analysis of a LOX/LCH4 Rocket Engine Demonstrator, in: 50th Joint Propulsion Conference, Cleveland, OH, (2014)4004. [14] C.H. Huang, C.H. Wang, The study on the improvement of system uniformity flow rate for U-type compact heat exchangers, Int. J. Heat Mass Transfer 63 (2013) 1-8. [15] X.Q. Liu, J.L. Yu, Numerical study on performances of mini-channel heat sinks with non-uniform inlets, Appl. Therm. Eng. 93 (2016) 856-864. [16] J. Qin, Y.G. Jiang, Y. Feng, X.J. Li, H.W. Li, Y.X. Xu, W. Bao, S.L. Zhang, J.C. Han, Flow rate distribution of cracked hydrocarbon fuel in parallel pipes, Fuel 161(2015)105-112. [17] Y.G. Jiang, S.L. Zhang, Y. Feng, J. Cao, J. Qin, W. Bao, A control method for flow rate distribution of cracked hydrocarbon fuel in parallel channels, Appl. Therm. Eng. 105 (2016) 521-536. [18] J.D. Anderson, Computational fluid dynamics: the basics with applications, McGraw-Hill, 1995. [19] B.E. Launder, G.J. Reece, W. Rodi, Progress in the development of a Reynolds-stress turbulence closure, J. Fluid Mech. 68 (1975) 537-566. [20] M.M. Gibson, B.E. Launder, Ground effects on pressure fluctuations in the atmospheric 12
boundary layer, J. Fluid Mech. 86 (1978) 491-511. [21] M. Pizzarelli, F. Nasuti, R. Paciorri, M. Onofri, A Numerical Model for Supercritical Flow in Rocket Engines Applications, in: 43td Joint Propulsion Conference, Cincinnati, OH, (2007)5501. [22] S.L. Zhang, J. Qin, K.L. Xie, Y. Feng, W. Bao, Thermal Behavior Inside Scramjet Cooling Channels at Different Channel Aspect Ratios, J. Propul. Power 32 (2016) 57-70. [23] C.C. Wang, K.S. Yang, J.S. Tsai, I.Y. Chen, Characteristics of flow distribution in compact parallel flow heat exchangers, part I: Typical inlet header, Appl. Therm. Eng. 31 (2011) 3226-3234. [24] C.H. Huang, C.H. Wang, The design of uniform tube flow rates for Z -type compact parallel flow heat exchangers, Int. J. Heat Mass Transfer 57 (2013) 608-622.
13
Table 1 Geometric properties of the basic and reformed configurations Config
Inlet and outlet position
Scaling factors
Channel entrance
Channel number
No.
and exit
N
1
0o
1
/
31
2
60o
1
/
31
3
0o
0.90
/
17
4
0o
0.95
/
22
5
0o
1.10
/
18
6
0o
1
Concave entrance
31
7
0o
1
Concave exit
31
8
0o
1
Convex exit
31
9
0o
1
Convex entrance
31
14
Table 2 Boundary Conditions Inlet
Outlet
(kg/s) m
T(K)
P(Pa)
1
300
101325
Heating wall Position Conjugate
Model only for fluid
qw(W/m2)
Outer wall
1.0×106
Adiabatic
1.0×106
Adiabatic
interface Conjugated model
1
300
101325
15
Inner wall
Figure captions Fig. 1 Schematic of basic configuration Fig. 2 Cross-sections of configurations with different inlet/outlet position and scaling factor Fig. 3 Schematic of configurations with different manifold Fig. 4 Comparison of flow ratios of present solution with previous experimental data, and numerical results Fig.5 The influence of relative position of inlet and outlet tubes Fig. 6 Effect of scaling factor on the non-uniformity and velocities in the channels Fig. 7 The coefficient of non-uniformity of cooling channels with different scaling factors Fig. 8 Non-uniformity coefficients of cooling channels with different entrance and exit structures Fig. 9 Streamlines on the symmetric boundary conditions of Config-1 and Config-9 Fig. 10 Pressure drop and temperature rise of inlet/outlet tube of Configs-1~11 Fig. 11 Temperature distributions of the basic and reformed configurations
16
Fig. 1 Schematic of basic configuration
17
(a) =60o, =1
(b) =0o, <1
(c)=0o, >1
Fig. 2 Cross-sections of configurations with different inlet/outlet position and scaling factor
18
(a) Concave entrance
(b) Concave exit
(c) Convex exit (d) Convex entrance Fig. 3 Schematic of configurations with different manifold
19
Fig. 4 Comparison of flow ratios of present solution with previous experimental data[23], and numerical results[24]
20
(a)Influence of relative position of inlet and outlet on non-uniformity coefficients
(b) Pressure Distribution in the Inlet Manifold of Config-1
21
(c) Streamline in the Inlet Manifold of Config-1(x=10 mm)
(d) Pressure difference in the manifolds of Configs-1~2 Fig.5 The influence of relative position of inlet and outlet tubes on the (a)non-uniformity coefficient, (b)Pressure distribution,(c)Streamlines in the manifold, (d)Pressure difference in the manifolds
22
(a) The non-uniformity coefficients of cooling channels
(b) Area-weighted average velocity of cooling channel exits Fig. 6 Effect of scaling factor on the non-uniformity and velocities in the channels
23
(a) The coefficient of non-uniformity of cooling channels with different scaling factors
(b) Area-weighted average velocity of cooling channel exits Fig. 7 Effects of different scaling factor on the non-uniform and velocities in the channels
24
Fig. 8 Non-uniformity coefficients of cooling channels with different entrance and exit structures
25
(a) Streamlines on the symmetric boundary conditions of Config-1
(b) Streamlines on the symmetric boundary conditions of Config-9 Fig. 9 Streamlines on the symmetric boundary conditions of Config-1 and Config-9
26
Fig. 10 Pressure drop and temperature rise of inlet/outlet tube of Configs-1~11
27
(a) Temperature distributions of the basic and reformed configurations
(b) Contour of temperature distribution of Config-1
(c) Contour of temperature distribution of Config-11 Fig. 11 Temperature distributions of the basic and reformed configurations
28