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Investigation on cooling effect with a combinational opposing jet and platelet transpiration concept in hypersonic flow
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Investigation on cooling effect with a combinational opposing jet and platelet transpiration concept in hypersonic flow
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BinXian Shen , Liang Yin , XiaoLi Zhang , WeiQiang Liu
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Science and Technology on Scramjet Laboratory, College of Aerospace Science and Engineering, National University of Defense Technology, Changsha 410073, China b Jiuquan Satellite Launch Center, Jiuquan 732750, China
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Article history: Received 21 June 2018 Received in revised form 7 November 2018 Accepted 9 November 2018 Available online xxxx
A platelet transpiration is introduced to strengthen the cooling effect in reattachment region for opposing jet in hypersonic flow. This introduced means can strengthen the local thermal protection performance without leading to an overall enhanced cooling intensity, being helpful on saving the total cooling gas. The two-equation SST k–ω turbulence model has been utilized to study the heat reduction and flow fields of the simplified combinational nose-tip in hypersonic flow. At first, the influence of individual pore are analyzed. The obtained results show that transpiration gas forms a cooling film adhering to the body surface which isolates the serious aerodynamic heating. The transpiration pores which are located on upstream margin of the reattachment point exhibit the best cooling effect. Then, the combination nose-tip is improved. A limited amount of pores are arranged in the reattachment region merely to strengthen the local cooling efficiency. The cooling capacity is obviously promoted with transpiration gas in contrast to that without transpiration. The peak heat flux reduces more than 12% with the mass flux of total cooling gas only promotes by 7.5%. Finally, the study demonstrates that the simplified model with limited amount of pores promote the cooling efficiency in contrast to that without transpiration. © 2018 Published by Elsevier Masson SAS.
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Keywords: Hypersonic vehicle Opposing jet Platelet transpiration Cooling effect
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1. Introduction
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The enormous aerodynamic heating has been a crucial factor which imposes restrictions on the practicability of hypersonic vehicles. The aerodynamic heating in stagnation point increases sharply with the increase of free-stream Mach number [1]. The excessive heating can bring out inestimable effect on the performance of hypersonic vehicle, for example, burning out the vehicles material or leading to the malfunction of onboard electronic systems [2]. Either could result in a failure mission. Therefore, an available Thermal Protection System (TPS) which can protect vehicles from the aerodynamic heating is of great importance for hypersonic vehicles. The protective capacity of traditional passive TPS was limited by their slowly elevating ultimate temperature of structural material or thickness of insulating materials. The ultra-high temperature ceramics (UHTCs) which has high-temperature capability also suffers both mechanical challenges and oxidation limitations that prevent them from being a practical material for aerospace applications [3]. Consequently, the passive TPS can’t acclimate the excessive heating for hypersonic vehicles [4]. A variety of active TPS have been
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E-mail address: [email protected] (L. Yin). https://doi.org/10.1016/j.ast.2018.11.021 1270-9638/© 2018 Published by Elsevier Masson SAS.
explored to control the flow-field structure in front of the vehicle. The flow-field, or shock wave structures can be modified by a special blunt structure, such as, an aerodisk/aerospike assemblies for large-angle blunt cones [5,6], a forward-facing cavity in the stagnation zone of a blunt body [7] and an electron transpiration cooling method [8]. The shock wave structures can also be changed by a Lorentz force introduced by a introduced Magneto hydrodynamic heat shield system [9]. Of course, the opposing jet in the stagnation zone, which has got increasing attention among the researchers, is also a simple and effective technique [10] to achieve the thermal protect of hypersonic vehicle. The excellent thermal protection performance of opposing jet has been demonstrated in hypersonic flows [11]. Considerable heat flux reduction was measured in the Hayashi’s experiment about opposing jet in hypersonic flow [12,13]. Two different flow modes were also observed in his experiment results, including an oscillation motions emerging in lower jet to free-stream total pressure ratio and a steady flow type appearing in a higher total pressure ratio. The two modes were respectively called Short Penetration Mode (SPM) and Long Penetration Mode (LPM) by Bibi et al. [14] and Zhou and Ji [15]. The results were also obtained by other researcher’s experimental or numerical works. The factors that de-
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Fig. 1. Theory on opposing jet.
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2. Structures of a combinational opposing jet and platelet transpiration cooling nose-tip
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Platelet devices, called platelets, are created by bonding thin metals together by diffusion welding. This bonding process produces an intricate and precise matrix of coolant passages in the interior of structures and injections at the structural wall by permuting the platelets that contain chemically etched coolant passages. The platelet thermal management devices possess excellent thermal control capacity, especially in solving complicated flow and local thermal issues. Aerojet introduced platelet devices into the aerospace field and manufactured various platelet applications, such as a platelet transpiration cooled combustion chamber [31] and a platelet transpiration nose-tip [32]. Fig. 2 shows the combinational opposing jet and platelet transpiration cooling nose-tip structure. As shown in Fig. 2(a), various platelets are precisely stacked together in an alternating pattern depending on their radial groove configuration to form the nosetip with a radius denoted as R n . Another special platelet without grooves is placed on top of the nose-tip, and the nozzle exit of the opposing jet is located at the center of the platelet. The radius of the nozzle exit is denoted as R opp . As shown in Fig. 2(b), the hole space in the center of the platelet is used for coolant channel, and the pipe in the middle of the central channel is used for the opposing jet. As shown in Fig. 2(c), each platelet has N radial grooves as narrow sectors, and the width of the outlet and the thickness of the plate are denoted as W s and L s , respectively. The adjacent platelets are disposed in a staggered manner, and the cross-bedded angle is denoted as θ . Every M platelet forms a permutation period. W s and θ are calculated as follows:
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termined the process of the flow-field transform from the SPM to LPM had been a core study. How to promote the heat flux reduction of opposing jet is another hot study [16]. Eyi et al. [17] developed a reliable and efficient design optimization method for hypersonic vehicles that produces minimum drag, subject to the constraints on heat transfer, temperature and pressure. Li et al. [18] amended the injection orifice shape, and investigated the influence of multiple injection shapes. The study showed that the pentacle shape enhanced the heat flux reduction of opposing jet. The single jet orifice was replaced by an array of forward-facing micro-jets in Sciram and Barzegar’ instructive idea [19,20]. The performance of an array of spaced distribution micro-jets was much better than the traditional single jet. The dispersive momentum flux could make it easier to cover the whole blunt surface. Surely, the intensity of opposing jet was a key factor which determined the capacity of TPS. Many factors, such as a stronger pressure, a larger injection orifice, a higher jet Mach number, and lighter gas with smaller molecular weight, could strengthen the intensity of the opposing jet [21]. At the same time, all of the corresponding factors could promote the cooling performance. Tamada and Aso [22] combined these factors into a parameter that is the momentum ratio, which stands for the intensity of opposing jet. It could help to predict the flow field and heat flux performance of opposing jet. Rong’s job of R pa had similar results with Tamada. It showed that the same shock wave position and similar total heat load can be obtained with the same R pa [23]. The flow field of the opposing jet in hypersonic flow can be described as follows. Seen in Fig. 1, a bow shock is pushed away from the blunt surface with the interaction of introduced jet stream and incoming free-stream. As a result, a recirculation region appears around the jet protrusion. The free-stream flows along the free shear layer and bypasses the recirculation region, then, causes a recompressed shock on the outer margin of the recirculation region boundary. For the aerodynamic heating, the stagnation zone as well as its’ surrounding region is covered by the cooling injection gas. The crucial aerodynamic heating is quarantined by the injection gas or recirculation flow. On the contrary, the surface called reattachment region which is stricken by the recompressed shock wave suffers an excessive heating. Though the recompressed shock is much weaker than the bow shock wave without jets, and the reattachment temperature is also lower than the stagnation temperature without jets, the heat flux introduced by the recompressed shock can produce undesirable effect in hypersonic flying condition. Geng’s research [24] indicated that a hot-spot may occur on the shoulder of the axi-symmetrical sphere cone because of the influenced of recompressed shock, with the local heat-transfer is much higher than that without injection. The hot-spot weakens
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and even die away if the jet-to-freestream total pressure ratio is enhanced sufficient. On the basis of the research, the strengthened jet intensity can eliminate the hot-spot on the shoulder of the sphere body, however, it results in incremental jet mass flux. The strengthened jet intensity enhances the whole thermal protection capacity but a high-efficient local thermal protection technique is in requirement of eliminating hot-spot. A simplex opposing jet can’t conquer this problem, therefore, several novel combinatorial strategies between the opposing jet and other means have been put forward including the combination of opposing jet and forward-facing cavity [25], the combination of opposing jet and an aerospike [26], the combination of opposing jet and an aerodisk [27], the combination of opposing jet and energy deposition [28]. These combinatorial configurations are conductive to eliminate the hot-spot at the shoulder of the blunt body and economize the jet mass flux. Based on the constructive idea above, an array of micro jets which has been used on the mixing of fuel in the cavity flame holder of the scramjet are introduced to ameliorate the local thermal protection capacity of opposing jet blunt body [29]. In this paper, a combinational opposing jet and platelet transpiration cooling nose-tip is designed for hypersonic vehicles [30]. On the working flying condition, the opposing jet can protect the stagnation zone from the grievous aerodynamic heating while the micro-jets from platelet structures can cool the local high heat flux region apart from the stagnation zone. The purpose of this paper is to investigate the cooling efficiency of the combinational opposing jet and platelet transpiration cooling nose-tip in hypersonic flow and demonstrate that the combinational none-tip can strengthen the thermal protection capacity.
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Fig. 3. Simplified structures.
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C 1 is related to the radius of the nose-tip and the transpiration injection design methods. L o is the distance from the upper surface of the platelet to the stagnation point. 3. Physical model and numerical approach
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Table 1 Parameters of the combinational structures.
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Fig. 2. Structures of combinatorial opposing jet and platelet transpiration thermal protection system.
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3.1. Physical model
The combinational opposing jet and platelet transpiration model delineated in Fig. 2 is simplified to facilitate the numerical simulation for determining the influence of transpiration on the flow-field and heat transfer. The simplified model is shown in Fig. 3. The number of pores for transpiration is reduced, whereas the size of pores is magnified. The structure of the nose-tip is a spherical model with a radius of 25 mm. Table 1 lists the other structure parameters. The transpiration pores are processed in four representative locations by
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Parameter
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Table 2 Parameters of the platelets.
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stacking the programming platelets in a predetermined sequence. Table 2 presents the thicknesses and locations of the platelets. The first transpiration pore, called Tran A, is located on the recirculation region. The second transpiration pore, called Tran B, is located on the upstream of the reattachment point and the downstream of the recirculation region. Trans C and D, representing the third and fourth transpiration pores, respectively, are located on the upstream margin of the reattachment point and the downstream of the reattachment point, respectively. Trans A–D correspond to platelets A–D (Fig. 3).
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3.2. Numerical method
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The 3D Reynolds-averaged Navier–Stokes (RANS) equations are employed as governing equations to simulate the flow-field and heat transfer of the combinational sphere nose-tip. The essential equations are briefly introduced as follows:
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(1) Equation of mass conservation:
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(2) Equation of momentum conservation:
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∂u j ∂ ui + ∂xj ∂ xi
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μt =
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Ω is the strain rate magnitude, and the coefficient α ∗ causes a low Reynolds number correction for turbulent viscosity. σk and σω are the turbulent Prandtl numbers for k and ω , respectively. They are evaluated by
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Fig. 4. Grids and boundary condition of the local model.
Table 3 Boundary conditions.
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δi j
where k and ω stand for the turbulence kinetic energy and specific dissipation rate in compressible turbulent flow, respectively. G k and G ω denote the generation of turbulence kinetic energy due to mean velocity gradients and the generation of ω respectively. Y k and Y ω represent the dissipation of k and ω due to turbulence, respectively. D ω indicates the cross-diffusion term. S k and S ω are the user-defined source terms. Γk and Γω denote the effective diffusivity of k and ω , respectively, which are defined as follows:
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The turbulence equations are described by the Menter’s k–ω shear stress transport (SST) model with compressible correction, which has been employed in published works on opposing jet configurations in hypersonic flow and transverse injection of the micro jet [33,34]. The turbulent equations are presented as follows [35]:
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(3) Equation of energy conversation
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σω,1 = 2.0,
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The equations presented above are solved with a density-based (coupled) double precision solver. And the second spatially accurate upwind scheme (SOU) with the advection upstream splitting method (AUSM) flux vector splitting is adopted. The Courant– Friedrichs–Levy number is set to 0.25 initially to ensure a stable convergence flow and then increased gradually to 4 to quicken convergence speed. Finally, the governing equations are solved in The ANSYS Fluent 16.0 working in a Dell workstation at Science and technology on Scramjet Laboratory which can provide a parallel computing environment for flow solutions.
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3.3. Boundary conditions
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Fig. 4 and Table 3 show the boundary conditions. The numerical simulations of the combinational opposing jet and platelet transpiration model contain three kinds of inlet boundaries including a far-field boundary condition to describe the free-stream, a pressure inlet boundary condition on the opposing jet, and a mass-flow boundary condition on the transpiration pores. The operation gas for three inlet boundaries is air, which is assumed to be thermally and calorically perfect gas. The free-stream condition is obtained in accordance with the flying condition at a height of 25 km with the total pressure and total temperature of 4.02 MPa and 1815 K, respectively. Correspondingly, the flying Mach number is 6. The Mach number of the opposing jet is 1, and its total temperature is 300 K. Its pressure is related to the jet-to-freestream total pressure ratio PR, which is helpful in describing the relationship between opposing jet and free stream. PR is defined as follows:
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F 1 and F 2 are the blending functions, they determine which turbulence model, the original k–ω model or the standard k–ε model, is chosen in different location of flow-field. In addition, their values are related to the distance from the wall. Other parameters with their values are listed as follows:
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∂ τi j ∂ ∂p ∂ (ρ u i ) + (ρ u i u j ) = − + ∂t ∂xj ∂ xi ∂xj
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Table 4 Grid system conditions.
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Grid 1 Grid 2 Grid 3
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Fig. 6. Comparisons of y + for different grids.
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Table 5 Freestream and jet conditions of experiment.
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Fig. 5. Comparisons of wall St for different grids.
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where p 0, j and p 0,∞ refer to the total pressure of the jet and free stream, respectively. The PR is set to be 0.1 in this condition for guaranteeing the stable short jet penetration mode (SPM) of the flow around the combinational model. The mass-flow rate of the transpiration is approximately 0.01mjet . mjet stands for the mass flux of the opposing jet. The surface of the blunt is prescribed as non-slip for velocity, zero normal gradient of pressure and as isothermal at a temperature of 295 K. The flow is hypersonic at the outlet. Thus, the physical information of the outlet is extrapolated from the internal flow-field. Rotational periodic boundary is adopted to reduce the computer resource of the simplified model.
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4. Code validation
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4.1. Grid independence
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In this work, 1/12 model is analyzed because of flow symmetry. Fig. 4 shows the divided grid system that adopts the commercial software ICEM 16.0. The space is filled with hexahedron elements that are efficient in obtaining meshes. Proper grid organization is a pivotal factor to obtain accurate and receivable results. Accurate predictions of the heat transfer near the surface require a strict grid arrangement. Hence, the mesh used must be evaluated to eliminate errors introduced by meshes. Three meshes, namely Grids 1–3, are utilized to perform the grid independency analysis with a stretching factor of 1.05. Table 4 shows the grid information. The opposing orifice, transpiration pore, the bow shock wave region and wall boundary layer are arranged with detailed cells. Fig. 5 shows the comparison of the wall Stanton number (St), which is defined as follows:
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St =
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where q w represents the wall heat flux, T aw stands for the adiabatic wall temperature, and T w stands for the wall temperature. ρ∞ , u ∞ , T ∞ , and Ma∞ denote the essential free-stream parameters respectively. c p ∞ indicates the specific heat, P r w represents the Prandtl number, and γ represents the ratio of specific heats. The comparisons of St in Fig. 5 show that St distributions exhibit good agreement in Grids 2 and 3, whereas the distributions are higher than those in Grid 1. Fig. 6 shows the variations in y + along the body surface. y + should be less than 1 in accordance with the SST k–ω model to ensure a credible prediction. Hence, Grid 2 is considered in the subsequent simulation because its y + is kept below 1 and its St reaches convergence.
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T aw
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( T aw − T w )ρ∞ c p ∞ u ∞
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4.2. Validation of numerical models
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The numerical methods are validated against the available experimental data by using Hayashi’s test [12]. The model structures and boundary conditions are the same as those in Hayashi’s work. The freestream and jet condition are given in Table 5. The cases with PR = 0.4, 0.6, 0.8 can guarantee the stable jet-freestream interactive flow-field. Besides, the case with PR = 0 means a simple blunt-body flow-field without opposing jet. In Fig. 7, the comparisons between the predicted results and experimental data are presented. At each PR, predicted results exhibit the reasonable variation trend to that obtained in the experiment. The predicted St is slightly lower than that of experimental data with PR = 0. For the cases with PR = 0.4, 0.6, 0.8, the predicted St achieves good coincidence with the experimental data except several individual points. The errors may be related to counting error, experimental measurement and assumption of simulation models. Generally, the comparisons of heat transfer distributions exhibits good qualitative coincidence between the predicted results and experimental data, thereby confirming that the numerical methods are credible to predict the surface heat transfer in opposing jet flow.
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Fig. 7. Comparisons between predicted results and experimental data.
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5. Results and discussions 5.1. Feature of the flow-field
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The flow structure around the combinational opposing jet and platelet transpiration nose-tip is discussed, and the stream-lines of Surfaces A and B are illustrated in Figs. 8 and 9, respectively. Surface A is the section that crosses Tran A, Tran C, and the opposing
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Fig. 8. The stream-lines distributions of Surface A.
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orifice, whereas Surface B is the section that crosses Tran B, Tran D, and the opposing orifice. In this case, the flow-field around nose-tip is caused by the interaction of free-stream, opposing jet, and transpiration gas. Figs. 8(a) and 9(a) show the whole stream-lines of Surfaces A and B, respectively. As shown in the figures, the flow-field is composed of a bow shock wave, a reattach shock wave, a Mack disk, a recirculation region, and a contact surface. The feature of the flow-field and the location of the characteristic structures are in accordance with that without transpiration, and the influence of the transpiration gas is not obvious in the whole flow-fields because of its low intensity. The local stream-lines at the transpiration pores are illustrated below. The transpiration gas is injected into the external flow-field along the radial direction of the platelet. However, the transpiration gas cannot penetrate into the far flow-field because its intensity is less powerful than that of the opposing jet. The transpiration gas can only adheres to the wall surface because it is squeezed by the recirculation or reattachment flow. As a result, the transpiration film emerges along the outer flow. Transpiration film cooling is an active thermal protection means that can isolate serious aerodynamic heating. Fig. 8(b) depicts the local stream-lines of Tran A, which is located on the recirculation region. The transpiration gas from Tran A flows into stagnation of the nose-tip with the force of the recirculation flow. Fig. 9(b) shows the local stream-lines of Tran B. A large proportion of gas interacts with the reattachment flow and then flows downstream along the wall surface. The rest of the gas is affected by the recirculation flow and flows into the stagnation regions, such as Tran A. Figs. 8(c) and 9(c) show the lo-
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Fig. 9. The stream-lines distributions of Surface B.
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Fig. 10. Influence of Tran A on wall St distributions.
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5.2. Cooling effect of transpiration pore The transpiration gases of Tran A–D exhibit unique flow characteristics which leads to different cooling effect. In this section, the cooling effect of each transpiration injection is analyzed. To eliminate the interference of adjacent pores, only a group of pores in same platelet are permitted to inject gas, and other transpiration pores are dealt with wall surface. Figs. 10–13 show the influence of Trans A–D on St distributions. The transpiration gas of Tran A, which is influenced by recirculation flow, can only cool the inner side (the side near the stagnation point) of the pores. Fig. 10 shows that St reduced in the outer side of the pore, but the cooling gas of Tran A has no effect on the reattachment point where the peak flux occurs. The transpiration gas of Tran B can strengthen the cooling effect in its downstream region. As shown in Fig. 11, the cooling effect gradually weakens as θ increases. The influence of Tran B on the reattachment point nearly disappears. Thus, the peak flux decreases by around 1.1%. Tran C, where the transpiration gas covers the reattachment point, can improve the extremely aerodynamic heating environment on the reattachment point, and the peak flux declines by 8.6%. The transpiration gas of Tran D considerably influences the downstream region, but it does not affect the cooling of the reattachment point. Consequently, the peak flux has slight changes compared with that in the arrangement without transpiration. Overall, the transpiration pore, such as Tran C located on the upstream margin of reattachment point, is an optimum position to strengthen the cooling capacity of the local high heat flux region.
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Fig. 13. Influence of Tran D on wall St distributions.
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cal stream-lines of Trans C and D, respectively. Both of them are influenced by the reattachment flow and flow downstream. The reattachment flow clings to the solid surface and forms a stable boundary layer without the influence of transpiration gas. In the flow-field of combinational nose-tip, the reattachment flow bypasses the transpiration pore in front of the pore and then reattaches away from the pore. The transpiration gas insulates the reattachment flow with high temperature and strengthens the thermal protection capacity.
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Fig. 11. Influence of Tran B on wall St distributions.
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A large amount of tiny pores may interact to ensure that the transpiration gas can cover the whole reattachment region in the real manufacture of nose-tip. However, this arrangement results in
enormous workload. In this section, the structures of the combinational opposing jet and platelet transpiration are improved. Fig. 14 shows the optimized simplified structure. The transpiration pores are mainly arranged in the reattachment region to enhance the local cooling effect because of its high efficiency in reducing
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Fig. 14. Optimized simplified structures.
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Table 6 Parameters of the combinational structures.
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Fig. 16. Temperature distributions with combination nose-tip.
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Fig. 15. Temperature distributions without transpiration.
the peak heat flux. The tiny transpiration pores are replaced with narrow gaps such as Trans E and F, as shown in the figure. The distance from the upper surface of the first platelet to the stagnation point is 2.7 mm. Table 6 lists the other structure parameters. The flow-field and heat transfer of the improved combinational nose-tip are numerically simulated, PR is 0.1, and the total mass flow rate of the transpiration gas is 0.075 mjet . Other boundary conditions are present in Table 3. Fig. 15 shows the temperature distributions without transpiration, and Fig. 16 shows the temperature distributions with the combinational nose-tip. The whole flow-field and temperature dis-
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Fig. 17. Temperature distributions without transpiration on local region A.
tributions of the combinational nose-tip show no obvious difference from that without transpiration. The intensity of the transpiration gas is too weak to affect the whole flow-field and local flowfield around the gaps. Fig. 18 shows the local temperature around the transpiration gaps, and Fig. 17 shows that without transpiration. As shown in Fig. 17, a thin smooth boundary layer adheres to the body surface on the force of reattachment flow. Different from Fig. 17, the transpiration gases hit against the reattachment flow and destroy the boundary layer in Fig. 18. An embossment forms and covers the gaps with the interaction of the transpiration gas and reattachment flow. The temperature gradient in this region decreases. The embossment fades away due to the feeble intensity of transpiration gas with the distance increasing away from the gap, and the temperature gradient increases gradually until the next gap. Then, a new embossment is produced, and a new circulation begins. Fig. 19 shows the comparison of St contour between the nosetip without transpiration and combinational nose-tip. The heat flux
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between two gaps. However, the heat flux exhibits an obvious reduction with transpiration contrary to that without transpiration. Fig. 20 shows the St comparisons between nose-tip without transpiration and combinational nose-tip. Surface A is the section that crosses Tran E and the opposing orifice, whereas Surface B is the section that crosses Tran F and the opposing orifice. The peak St of Surface A decreases by 10.46%, whereas it declines by 12.15% in Surface B compared with that without transpiration. At the same time, the mass flux of total cool gas only increases by 7.5%. Overall, the combinational nose-tip strengthens the cooling effect of the reattachment region without leading to an identical addition of cool gas. Moreover, the simplified model for the simulation differs from the real structures of the combinational nosetip. The number of transpiration pores is decreased, and the size of pores is enlarged. These factors adversely affect the cooling efficiency. This study shows that the simplified model can promote the cooling efficiency compared with that of without transpiration.
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Fig. 18. Temperature distributions with combination nose-tip on local region B.
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without transpiration distributes annularly, whereas it is disturbed by the transpiration gas in the combinational nose-tip. All transpiration gaps are arranged outside of the recirculation region and cannot be affected by the recirculation flows. The transpiration gases flow into the downstream of the gaps and mainly cool the reattachment region. In the inner part of the first loop of gaps, the heat flux distributes annularly. The same condition is observed in that of without transpiration. In the outer part of the first loop of gaps, the transpiration gas destroys the temperature boundary layer, thereby reducing the temperature gradient and the heat flux. Then, the temperature boundary recovers gradually with the influence of the outer attached flow. As a result, the temperature gradient increases and the heat flux rises again. Finally, a sharp decreasing trend of heat flux is observed owing to the effect of the low enthalpy transpiration gas from the next gap. The heat flux increases first and then declines with the increase in the distance
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In this work, a combinational opposing jet and platelet transpiration nose-tip is introduced for hypersonic vehicles to enhance the cooling effect. Moreover, a numerical study on heat flux reduction in hypersonic flow with the combinational nose-tip is conducted. On this basis, the flow-field and heat transfer are obtained. The major works are summarized as follows. The transpiration gas flow adheres to the body surface with the force of the outer flows (recirculation or reattachment flow) and forms the transpiration cooling film. The cooling capacity of the pores varies with different pore locations. The transpiration pore, which is located on the upstream margin of the reattachment point, exerts the optimum cooling effect on the local peak heat flux region. The heat flux exhibits an obvious reduction with transpiration contrary to that of without transpiration. The peak heat flux decreases by more than 12%, whereas the mass flux of total cool gas increases by 7.5% only. The simplified model for simulation reduces the number of pores and enlarges the size of pores compared with real combinational nose-tip. These factors lead to adverse cooling efficiency.
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Fig. 19. Comparisons of St contour between nose-tip without transpiration and combination nose-tips.
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Fig. 20. Comparisons of St between nose-tip without transpiration and combination nose-tips.
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This study shows that the simplified model with a limited number of pores can promote the cooling efficiency compared with that without transpiration.
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Conflict of interest statement
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The authors declare there is not conflict of interest regarding the publication of this paper.
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Acknowledgements
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The authors would like to express their thanks for the support from the National Natural Science Foundation of China (No. 11802340) and the National Science Foundation of Jiangsu Province, China (BK20130084). Also, the authors thank the anonymous reviewers for some very critical and constructive recommendations on this paper.
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[1] J.A. Fay, Riddell, Theory of stagnation point heat transfer in dissociated air, J. Aeronaut. Sci. 25 (2) (1958) 73–85. [2] Y. Qiang, W. Xie, Z. Peng, New concepts and trends in development of thermal protection design and analysis technology, Acta Aeronaut. Astronaut. Sin. 36 (9) (2015) 2981–2991 (in Chinese). [3] D. Glass, Physical challenges and limitations confronting the use of UHTCs on hypersonic vehicles, in: 17th AIAA International Space Planes and Hypersonic Systems and Technologies Conference, AIAA 2011-2304. [4] Y. Liu, Z. Jiang, Concept of non-ablative thermal protection system for hypersonic vehicles, AIAA J. 51 (3) (2013) 584–590. [5] M.B. Gerdroodbary, S.M. Hosseinalipour, Numerical simulation of hypersonic flow over highly blunted cones with spike, Acta Astronaut. 67 (2010) 180–193. [6] M. Ou, Y. Li, W. Huang, Detailed parametric investigations on drag and heat flux reduction induced by a combinational spike and opposing jet concept in hypersonic flows, Int. J. Heat Mass Transf. 126 (2018) 10–31. [7] X.D. Li, Z.M. Hu, Z.L. Jiang, Numerical investigation on the thermal protection mechanism for blunt body with forward-facing cavity, Sci. China, Technol. Sci. 59 (7) (2016) 1120–1129. [8] K.M. Hanquist, K. Hara, I.D. Boyd, Detailed modeling of electron emission for transpiration cooling of hypersonic vehicles, J. Appl. Phys. 121 (2017) 053302.
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[12] K. Hayashi, S. Aso, Y. Tani, Numerical study of thermal protection system by opposing jet, in: 43rd AIAA Aerospace Sciences Meeting and Exhibit, 2005, AIAA 2005-188. [13] K. Hayashi, S. Aso, Y. Tani, Experimental study on thermal protection system by opposing jet in supersonic flow, J. Spacecr. Rockets 43 (1) (2015) 233–235. [14] A. Bibi, A. Maqsood, S. Sherbaz, L. Dala, Drag reduction of supersonic blunt bodies using opposing jet and nozzle geometric variations, Aerosp. Sci. Technol. 69 (2017) 244–256. [15] C.Y. Zhou, W.Y. Ji, A three-dimensional numerical investigation on drag reduction of a supersonic spherical body with an opposing jet, Proc. IMechE. Part G: J. Aerosp. Eng. 228 (2) (2014) 163–177. [16] B. Shen, W. Liu, L. Yin, Drag and heat reduction efficiency research on opposing jet in supersonic flows, Aerosp. Sci. Technol. 77 (2018) 696–703. [17] S. Eyi, K.M. Hanquist, K. Hara, I.D. Boyd, Aerothermodynamic design optimization of hypersonic vehicles, in: Multidisciplinary Analysis and Optimization Conference, 2018. [18] S.B. Li, Z.G. Wang, W. Huang, Effect of the injector configuration for opposing jet on the drag and heat reduction, Aerosp. Sci. Technol. 51 (2016) 78–86. [19] M.B. Gerdroodbary, M. Imani, D.D. Ganji, Investigation of film cooling on nose cone by a forward facing array of micro-jets in hypersonic flow, Int. Commun. Heat Mass Transf. 64 (2015) 42–49. [20] R. Sriram, G. Jagadeesh, Film cooling at hypersonic Mach numbers using forward facing array of micro-jets, Int. J. Heat Mass Transf. 52 (15) (2009) 3654–3664. [21] B. Shen, W. Liu, Thermal protection performance of opposing jet generating with solid fuel, Acta Astronaut. 144 (2018) 90–96. [22] Isao Tamada, Shigeru Aso, Reducing aerodynamic heating by the opposing jet in supersonic and hypersonic flows, in: 48th AIAA Aerospace Sciences Meeting Including the New Horizons Forum and Aerospace Exposition, 2010, AIAA 2010-991. [23] Y. Rong, Drag reduction research in supersonic flow with opposing jet, Acta Astronaut. 91 (10) (2013) 1–7. [24] X.R. Geng, Y.W. Gui, A.L. Wang, Numerical investigation on drag and heattransfer reduction using 2-D planar and axisymmetrical forward facing jet, Acta Aerodyn. Sin. 24 (1) (2006) 85–89 (in Chinese). [25] H. Lu, W. Liu, Thermal protection efficiency of forward-facing cavity and opposing jet combinational configuration, J. Therm. Sci. 21 (4) (2012) 342–347. [26] L. Zhu, X. Chen, Y. Li, Investigation of drag and heat reduction induced by a novel combinational lateral jet and spike concept in supersonic flows based on conjugate heat transfer approach, Acta Astronaut. 142 (2018) 300–313. [27] M.B. Gerdroodbary, M. Imani, D.D. Ganji, Heat reduction using conterflowing jet for a nose cone with aerodisk in hypersonic flow, Aerosp. Sci. Technol. 39 (2014) 652–665. [28] J.H. Kim, A. Matsuda, T. Sakai, Wave drag reduction with acting spike induced by laser-pulse energy depositions, AIAA J. 49 (9) (2015) 2076–2078. [29] K. Fallah, M.B. Gerdroodbary, A. Ghaderi, J. Alinejad, The influence of micro air jets on mixing augmentation of fuel in cavity flame Holder at supersonic flow, Aerosp. Sci. Technol. 76 (2018) 187–193. [30] Y. Rong, Y. Wei, Research on thermal protection by opposing jet and transpiration for high speed vehicle, Aerosp. Sci. Technol. 48 (2016) 322–327. [31] H.H. Mueggenburg, J.W. Hidahl, E.L. Kessler, Platelet actively cooled thermal management devices, in: 28th Joint Propulsion Conference and Exhibit, 1992, AIAA 92-3127. [32] B.A. Robbers, B.J. Anderson, W.A. Hayes, Platelet devices-limited only by one’s imagination, in: 42nd Joint Propulsion Conference and Exhibit, 2006, AIAA 2006-4542. [33] M.B. Gerdroodbary, Y. Amini, D.D. Ganji, M.R. Takam, The flow feature of transverse hydrogen jet in presence of micro air jets in supersonic flow, Adv. Space Res. 59 (2017) 1330–1340. [34] M.B. Gerdroodbary, K. Fallah, H. Pourmirzaagha, Characteristics of transverse hydrogen jet in presence of multi air jets within scramjet combustor, Acta Astronaut. 132 (2017) 25–32. [35] F.R. Menter, Two-equation eddy-viscosity turbulence models for engineering applications, AIAA J. 32 (8) (2012) 1598–1605.
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[9] K. Li, W.Q. Liu, Analysis of the magnetohydrodynamic heat shield system for hypersonic vehicles, Acta Phys. Sin. 65 (6) (2016). [10] W. Huang, A survey of drag and heat reduction in supersonic flows by a counter flowing jet and its combinations, J. Zhejiang Univ-Sci. A (Appl. Phys. & Eng.) 16 (7) (2015) 551–561. [11] J. Guo, G. Lin, X. Bu, Parametric study on the heat transfer of a blunt body with counterflowing jets in hypersonic flows, Int. J. Heat Mass Transf. 121 (2018) 84–96.
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Investigation on cooling effect with a combinational opposing jet and platelet transpiration concept in hypersonic flow
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BinXian Shen , Liang Yin , XiaoLi Zhang , WeiQiang Liu
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Article history: Received 21 June 2018 Received in revised form 7 November 2018 Accepted 9 November 2018 Available online xxxx
A platelet transpiration is introduced to strengthen the cooling effect in reattachment region for opposing jet in hypersonic flow. This introduced means can strengthen the local thermal protection performance without leading to an overall enhanced cooling intensity, being helpful on saving the total cooling gas. The two-equation SST k–ω turbulence model has been utilized to study the heat reduction and flow fields of the simplified combinational nose-tip in hypersonic flow. At first, the influence of individual pore are analyzed. The obtained results show that transpiration gas forms a cooling film adhering to the body surface which isolates the serious aerodynamic heating. The transpiration pores which are located on upstream margin of the reattachment point exhibit the best cooling effect. Then, the combination nose-tip is improved. A limited amount of pores are arranged in the reattachment region merely to strengthen the local cooling efficiency. The cooling capacity is obviously promoted with transpiration gas in contrast to that without transpiration. The peak heat flux reduces more than 12% with the mass flux of total cooling gas only promotes by 7.5%. Finally, the study demonstrates that the simplified model with limited amount of pores promote the cooling efficiency in contrast to that without transpiration. © 2018 Published by Elsevier Masson SAS.
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Keywords: Hypersonic vehicle Opposing jet Platelet transpiration Cooling effect
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1. Introduction
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The enormous aerodynamic heating has been a crucial factor which imposes restrictions on the practicability of hypersonic vehicles. The aerodynamic heating in stagnation point increases sharply with the increase of free-stream Mach number [1]. The excessive heating can bring out inestimable effect on the performance of hypersonic vehicle, for example, burning out the vehicles material or leading to the malfunction of onboard electronic systems [2]. Either could result in a failure mission. Therefore, an available Thermal Protection System (TPS) which can protect vehicles from the aerodynamic heating is of great importance for hypersonic vehicles. The protective capacity of traditional passive TPS was limited by their slowly elevating ultimate temperature of structural material or thickness of insulating materials. The ultra-high temperature ceramics (UHTCs) which has high-temperature capability also suffers both mechanical challenges and oxidation limitations that prevent them from being a practical material for aerospace applications [3]. Consequently, the passive TPS can’t acclimate the excessive heating for hypersonic vehicles [4]. A variety of active TPS have been
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E-mail address: [email protected] (L. Yin). https://doi.org/10.1016/j.ast.2018.11.021 1270-9638/© 2018 Published by Elsevier Masson SAS.
explored to control the flow-field structure in front of the vehicle. The flow-field, or shock wave structures can be modified by a special blunt structure, such as, an aerodisk/aerospike assemblies for large-angle blunt cones [5,6], a forward-facing cavity in the stagnation zone of a blunt body [7] and an electron transpiration cooling method [8]. The shock wave structures can also be changed by a Lorentz force introduced by a introduced Magneto hydrodynamic heat shield system [9]. Of course, the opposing jet in the stagnation zone, which has got increasing attention among the researchers, is also a simple and effective technique [10] to achieve the thermal protect of hypersonic vehicle. The excellent thermal protection performance of opposing jet has been demonstrated in hypersonic flows [11]. Considerable heat flux reduction was measured in the Hayashi’s experiment about opposing jet in hypersonic flow [12,13]. Two different flow modes were also observed in his experiment results, including an oscillation motions emerging in lower jet to free-stream total pressure ratio and a steady flow type appearing in a higher total pressure ratio. The two modes were respectively called Short Penetration Mode (SPM) and Long Penetration Mode (LPM) by Bibi et al. [14] and Zhou and Ji [15]. The results were also obtained by other researcher’s experimental or numerical works. The factors that de-
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Fig. 1. Theory on opposing jet.
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2. Structures of a combinational opposing jet and platelet transpiration cooling nose-tip
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Platelet devices, called platelets, are created by bonding thin metals together by diffusion welding. This bonding process produces an intricate and precise matrix of coolant passages in the interior of structures and injections at the structural wall by permuting the platelets that contain chemically etched coolant passages. The platelet thermal management devices possess excellent thermal control capacity, especially in solving complicated flow and local thermal issues. Aerojet introduced platelet devices into the aerospace field and manufactured various platelet applications, such as a platelet transpiration cooled combustion chamber [31] and a platelet transpiration nose-tip [32]. Fig. 2 shows the combinational opposing jet and platelet transpiration cooling nose-tip structure. As shown in Fig. 2(a), various platelets are precisely stacked together in an alternating pattern depending on their radial groove configuration to form the nosetip with a radius denoted as R n . Another special platelet without grooves is placed on top of the nose-tip, and the nozzle exit of the opposing jet is located at the center of the platelet. The radius of the nozzle exit is denoted as R opp . As shown in Fig. 2(b), the hole space in the center of the platelet is used for coolant channel, and the pipe in the middle of the central channel is used for the opposing jet. As shown in Fig. 2(c), each platelet has N radial grooves as narrow sectors, and the width of the outlet and the thickness of the plate are denoted as W s and L s , respectively. The adjacent platelets are disposed in a staggered manner, and the cross-bedded angle is denoted as θ . Every M platelet forms a permutation period. W s and θ are calculated as follows:
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termined the process of the flow-field transform from the SPM to LPM had been a core study. How to promote the heat flux reduction of opposing jet is another hot study [16]. Eyi et al. [17] developed a reliable and efficient design optimization method for hypersonic vehicles that produces minimum drag, subject to the constraints on heat transfer, temperature and pressure. Li et al. [18] amended the injection orifice shape, and investigated the influence of multiple injection shapes. The study showed that the pentacle shape enhanced the heat flux reduction of opposing jet. The single jet orifice was replaced by an array of forward-facing micro-jets in Sciram and Barzegar’ instructive idea [19,20]. The performance of an array of spaced distribution micro-jets was much better than the traditional single jet. The dispersive momentum flux could make it easier to cover the whole blunt surface. Surely, the intensity of opposing jet was a key factor which determined the capacity of TPS. Many factors, such as a stronger pressure, a larger injection orifice, a higher jet Mach number, and lighter gas with smaller molecular weight, could strengthen the intensity of the opposing jet [21]. At the same time, all of the corresponding factors could promote the cooling performance. Tamada and Aso [22] combined these factors into a parameter that is the momentum ratio, which stands for the intensity of opposing jet. It could help to predict the flow field and heat flux performance of opposing jet. Rong’s job of R pa had similar results with Tamada. It showed that the same shock wave position and similar total heat load can be obtained with the same R pa [23]. The flow field of the opposing jet in hypersonic flow can be described as follows. Seen in Fig. 1, a bow shock is pushed away from the blunt surface with the interaction of introduced jet stream and incoming free-stream. As a result, a recirculation region appears around the jet protrusion. The free-stream flows along the free shear layer and bypasses the recirculation region, then, causes a recompressed shock on the outer margin of the recirculation region boundary. For the aerodynamic heating, the stagnation zone as well as its’ surrounding region is covered by the cooling injection gas. The crucial aerodynamic heating is quarantined by the injection gas or recirculation flow. On the contrary, the surface called reattachment region which is stricken by the recompressed shock wave suffers an excessive heating. Though the recompressed shock is much weaker than the bow shock wave without jets, and the reattachment temperature is also lower than the stagnation temperature without jets, the heat flux introduced by the recompressed shock can produce undesirable effect in hypersonic flying condition. Geng’s research [24] indicated that a hot-spot may occur on the shoulder of the axi-symmetrical sphere cone because of the influenced of recompressed shock, with the local heat-transfer is much higher than that without injection. The hot-spot weakens
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and even die away if the jet-to-freestream total pressure ratio is enhanced sufficient. On the basis of the research, the strengthened jet intensity can eliminate the hot-spot on the shoulder of the sphere body, however, it results in incremental jet mass flux. The strengthened jet intensity enhances the whole thermal protection capacity but a high-efficient local thermal protection technique is in requirement of eliminating hot-spot. A simplex opposing jet can’t conquer this problem, therefore, several novel combinatorial strategies between the opposing jet and other means have been put forward including the combination of opposing jet and forward-facing cavity [25], the combination of opposing jet and an aerospike [26], the combination of opposing jet and an aerodisk [27], the combination of opposing jet and energy deposition [28]. These combinatorial configurations are conductive to eliminate the hot-spot at the shoulder of the blunt body and economize the jet mass flux. Based on the constructive idea above, an array of micro jets which has been used on the mixing of fuel in the cavity flame holder of the scramjet are introduced to ameliorate the local thermal protection capacity of opposing jet blunt body [29]. In this paper, a combinational opposing jet and platelet transpiration cooling nose-tip is designed for hypersonic vehicles [30]. On the working flying condition, the opposing jet can protect the stagnation zone from the grievous aerodynamic heating while the micro-jets from platelet structures can cool the local high heat flux region apart from the stagnation zone. The purpose of this paper is to investigate the cooling efficiency of the combinational opposing jet and platelet transpiration cooling nose-tip in hypersonic flow and demonstrate that the combinational none-tip can strengthen the thermal protection capacity.
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Fig. 3. Simplified structures.
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C 1 is related to the radius of the nose-tip and the transpiration injection design methods. L o is the distance from the upper surface of the platelet to the stagnation point. 3. Physical model and numerical approach
55 57 58 59 60 61 62 63 64 65 66
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Table 1 Parameters of the combinational structures.
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Fig. 2. Structures of combinatorial opposing jet and platelet transpiration thermal protection system.
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3.1. Physical model
The combinational opposing jet and platelet transpiration model delineated in Fig. 2 is simplified to facilitate the numerical simulation for determining the influence of transpiration on the flow-field and heat transfer. The simplified model is shown in Fig. 3. The number of pores for transpiration is reduced, whereas the size of pores is magnified. The structure of the nose-tip is a spherical model with a radius of 25 mm. Table 1 lists the other structure parameters. The transpiration pores are processed in four representative locations by
96 97
Parameter
Value
Rn R opp M N
25 mm 2 mm 2 12 15◦ 0.33
θ C1
98 99 100 101 102 103 104 105 106
Table 2 Parameters of the platelets.
107
Platelet
L s (mm)
L o (mm)
A B C D
0.3 0.45 0.6 0.7
1.5 3 6 9
108 109 110 111 112 113 114
stacking the programming platelets in a predetermined sequence. Table 2 presents the thicknesses and locations of the platelets. The first transpiration pore, called Tran A, is located on the recirculation region. The second transpiration pore, called Tran B, is located on the upstream of the reattachment point and the downstream of the recirculation region. Trans C and D, representing the third and fourth transpiration pores, respectively, are located on the upstream margin of the reattachment point and the downstream of the reattachment point, respectively. Trans A–D correspond to platelets A–D (Fig. 3).
115 116 117 118 119 120 121 122 123 124 125 126
3.2. Numerical method
127 128
The 3D Reynolds-averaged Navier–Stokes (RANS) equations are employed as governing equations to simulate the flow-field and heat transfer of the combinational sphere nose-tip. The essential equations are briefly introduced as follows:
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(1) Equation of mass conservation:
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∂ ∂ρ + (ρ u i ) = 0 ∂t ∂ xi
69
(3)
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(2) Equation of momentum conservation:
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∂ ∂ ∂ ∂T (ρ E ) + u i (ρ E + p ) = − k + u j τi j ∂t ∂ xi ∂ xi ∂ xi
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τi j = μ
27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48
∂u j ∂ ui + ∂xj ∂ xi
E =e+
1 2
3
xl
u 2i
(7)
where
Γk = μ +
56 57 58 59 60 61
μt =
(11)
μt is the turbulent viscosity and is evaluated by
64 65 66
ρk 1 ω max[ α1∗ , Ωa Fω2 ] 1
(12)
Ω is the strain rate magnitude, and the coefficient α ∗ causes a low Reynolds number correction for turbulent viscosity. σk and σω are the turbulent Prandtl numbers for k and ω , respectively. They are evaluated by
62 63
(9)
(10)
54 55
(8)
σk = σω =
79 80 81 82
Fig. 4. Grids and boundary condition of the local model.
Table 3 Boundary conditions.
(6)
δi j
where k and ω stand for the turbulence kinetic energy and specific dissipation rate in compressible turbulent flow, respectively. G k and G ω denote the generation of turbulence kinetic energy due to mean velocity gradients and the generation of ω respectively. Y k and Y ω represent the dissipation of k and ω due to turbulence, respectively. D ω indicates the cross-diffusion term. S k and S ω are the user-defined source terms. Γk and Γω denote the effective diffusivity of k and ω , respectively, which are defined as follows:
53
51
ul
∂ ∂ ∂k Γk + G K − Y K + Sk (ρ ku i ) = ∂ xi ∂xj ∂xj ∂ ∂ ∂ω Γω + Gω − Yω + Dω + Sω (ρωu i ) = ∂ xi ∂xj ∂xj
52
50
2
− μ
The turbulence equations are described by the Menter’s k–ω shear stress transport (SST) model with compressible correction, which has been employed in published works on opposing jet configurations in hypersonic flow and transverse injection of the micro jet [33,34]. The turbulent equations are presented as follows [35]:
μt σk μt Γω = μ + σω
49
78
Free stream
air Ma∞ = 6 P 0,∞ = 4.02 MPa T 0,∞ = 1815 K
where μ denotes the dynamic viscosity coefficient and δi j stands for the Kronecker delta function. Besides, E represent the total energy which is defined as
25 26
77
(5)
Herein, ρ is the density, p is the static pressure, u i , u j represent the components’ velocity and k stands for the thermal conductivity coefficient. τi j is the shear stress tensor and is obtained by the following equation:
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(3) Equation of energy conversation
83 84 85
Opposing jet
Transpiration
air Ma j = 1 PR = 0.1 T 0, j = 300 K
air mtran = 0.01mjet T 0,Tran = 295 K
σk,1 = 1.176,
σk,2 = 1.0,
σω,1 = 1.168,
a1 = 0.31
1 F 1 /σk,1 + (1 − F 1 )/σk,2 1 F 1 /σω,1 + (1 − F 1 )/σω,2
(13) (14)
87 88 89 90 92 93 94 95 96 97 98
σω,1 = 2.0,
99
(15)
100 101
The equations presented above are solved with a density-based (coupled) double precision solver. And the second spatially accurate upwind scheme (SOU) with the advection upstream splitting method (AUSM) flux vector splitting is adopted. The Courant– Friedrichs–Levy number is set to 0.25 initially to ensure a stable convergence flow and then increased gradually to 4 to quicken convergence speed. Finally, the governing equations are solved in The ANSYS Fluent 16.0 working in a Dell workstation at Science and technology on Scramjet Laboratory which can provide a parallel computing environment for flow solutions.
102 103 104 105 106 107 108 109 110 111 112
3.3. Boundary conditions
113 114
Fig. 4 and Table 3 show the boundary conditions. The numerical simulations of the combinational opposing jet and platelet transpiration model contain three kinds of inlet boundaries including a far-field boundary condition to describe the free-stream, a pressure inlet boundary condition on the opposing jet, and a mass-flow boundary condition on the transpiration pores. The operation gas for three inlet boundaries is air, which is assumed to be thermally and calorically perfect gas. The free-stream condition is obtained in accordance with the flying condition at a height of 25 km with the total pressure and total temperature of 4.02 MPa and 1815 K, respectively. Correspondingly, the flying Mach number is 6. The Mach number of the opposing jet is 1, and its total temperature is 300 K. Its pressure is related to the jet-to-freestream total pressure ratio PR, which is helpful in describing the relationship between opposing jet and free stream. PR is defined as follows:
PR =
86
91
F 1 and F 2 are the blending functions, they determine which turbulence model, the original k–ω model or the standard k–ε model, is chosen in different location of flow-field. In addition, their values are related to the distance from the wall. Other parameters with their values are listed as follows:
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∂ τi j ∂ ∂p ∂ (ρ u i ) + (ρ u i u j ) = − + ∂t ∂xj ∂ xi ∂xj
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(16)
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Table 4 Grid system conditions.
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Grid 1 Grid 2 Grid 3
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Num. of grid
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Fig. 6. Comparisons of y + for different grids.
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Table 5 Freestream and jet conditions of experiment.
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Opposing jet
Wall
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Ma∞ = 3.98 P 0,∞ = 1.37 MPa T 0,∞ = 397 K
Ma j = 1 PR = 0, 0.4, 0.6, 0.8 T 0, j = 300 K
T = 295 K
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Fig. 5. Comparisons of wall St for different grids.
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31 32 33 34 35 36 37 38 39 40 41
where p 0, j and p 0,∞ refer to the total pressure of the jet and free stream, respectively. The PR is set to be 0.1 in this condition for guaranteeing the stable short jet penetration mode (SPM) of the flow around the combinational model. The mass-flow rate of the transpiration is approximately 0.01mjet . mjet stands for the mass flux of the opposing jet. The surface of the blunt is prescribed as non-slip for velocity, zero normal gradient of pressure and as isothermal at a temperature of 295 K. The flow is hypersonic at the outlet. Thus, the physical information of the outlet is extrapolated from the internal flow-field. Rotational periodic boundary is adopted to reduce the computer resource of the simplified model.
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4. Code validation
44 45
4.1. Grid independence
46 48 49 50 51 52 53 54 55 56 57 58 59 60 61
In this work, 1/12 model is analyzed because of flow symmetry. Fig. 4 shows the divided grid system that adopts the commercial software ICEM 16.0. The space is filled with hexahedron elements that are efficient in obtaining meshes. Proper grid organization is a pivotal factor to obtain accurate and receivable results. Accurate predictions of the heat transfer near the surface require a strict grid arrangement. Hence, the mesh used must be evaluated to eliminate errors introduced by meshes. Three meshes, namely Grids 1–3, are utilized to perform the grid independency analysis with a stretching factor of 1.05. Table 4 shows the grid information. The opposing orifice, transpiration pore, the bow shock wave region and wall boundary layer are arranged with detailed cells. Fig. 5 shows the comparison of the wall Stanton number (St), which is defined as follows:
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St =
64 65 66
where q w represents the wall heat flux, T aw stands for the adiabatic wall temperature, and T w stands for the wall temperature. ρ∞ , u ∞ , T ∞ , and Ma∞ denote the essential free-stream parameters respectively. c p ∞ indicates the specific heat, P r w represents the Prandtl number, and γ represents the ratio of specific heats. The comparisons of St in Fig. 5 show that St distributions exhibit good agreement in Grids 2 and 3, whereas the distributions are higher than those in Grid 1. Fig. 6 shows the variations in y + along the body surface. y + should be less than 1 in accordance with the SST k–ω model to ensure a credible prediction. Hence, Grid 2 is considered in the subsequent simulation because its y + is kept below 1 and its St reaches convergence.
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T aw
qw
( T aw − T w )ρ∞ c p ∞ u ∞
√ (γ − 1) 2 = T ∞ 1 + 3 pr w Ma∞ 2
(17) (18)
4.2. Validation of numerical models
93 94 95 96 97 98 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113
The numerical methods are validated against the available experimental data by using Hayashi’s test [12]. The model structures and boundary conditions are the same as those in Hayashi’s work. The freestream and jet condition are given in Table 5. The cases with PR = 0.4, 0.6, 0.8 can guarantee the stable jet-freestream interactive flow-field. Besides, the case with PR = 0 means a simple blunt-body flow-field without opposing jet. In Fig. 7, the comparisons between the predicted results and experimental data are presented. At each PR, predicted results exhibit the reasonable variation trend to that obtained in the experiment. The predicted St is slightly lower than that of experimental data with PR = 0. For the cases with PR = 0.4, 0.6, 0.8, the predicted St achieves good coincidence with the experimental data except several individual points. The errors may be related to counting error, experimental measurement and assumption of simulation models. Generally, the comparisons of heat transfer distributions exhibits good qualitative coincidence between the predicted results and experimental data, thereby confirming that the numerical methods are credible to predict the surface heat transfer in opposing jet flow.
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Fig. 7. Comparisons between predicted results and experimental data.
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5. Results and discussions 5.1. Feature of the flow-field
26 27 28 29 30
The flow structure around the combinational opposing jet and platelet transpiration nose-tip is discussed, and the stream-lines of Surfaces A and B are illustrated in Figs. 8 and 9, respectively. Surface A is the section that crosses Tran A, Tran C, and the opposing
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Fig. 8. The stream-lines distributions of Surface A.
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orifice, whereas Surface B is the section that crosses Tran B, Tran D, and the opposing orifice. In this case, the flow-field around nose-tip is caused by the interaction of free-stream, opposing jet, and transpiration gas. Figs. 8(a) and 9(a) show the whole stream-lines of Surfaces A and B, respectively. As shown in the figures, the flow-field is composed of a bow shock wave, a reattach shock wave, a Mack disk, a recirculation region, and a contact surface. The feature of the flow-field and the location of the characteristic structures are in accordance with that without transpiration, and the influence of the transpiration gas is not obvious in the whole flow-fields because of its low intensity. The local stream-lines at the transpiration pores are illustrated below. The transpiration gas is injected into the external flow-field along the radial direction of the platelet. However, the transpiration gas cannot penetrate into the far flow-field because its intensity is less powerful than that of the opposing jet. The transpiration gas can only adheres to the wall surface because it is squeezed by the recirculation or reattachment flow. As a result, the transpiration film emerges along the outer flow. Transpiration film cooling is an active thermal protection means that can isolate serious aerodynamic heating. Fig. 8(b) depicts the local stream-lines of Tran A, which is located on the recirculation region. The transpiration gas from Tran A flows into stagnation of the nose-tip with the force of the recirculation flow. Fig. 9(b) shows the local stream-lines of Tran B. A large proportion of gas interacts with the reattachment flow and then flows downstream along the wall surface. The rest of the gas is affected by the recirculation flow and flows into the stagnation regions, such as Tran A. Figs. 8(c) and 9(c) show the lo-
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Fig. 9. The stream-lines distributions of Surface B.
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Fig. 10. Influence of Tran A on wall St distributions.
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26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60
5.2. Cooling effect of transpiration pore The transpiration gases of Tran A–D exhibit unique flow characteristics which leads to different cooling effect. In this section, the cooling effect of each transpiration injection is analyzed. To eliminate the interference of adjacent pores, only a group of pores in same platelet are permitted to inject gas, and other transpiration pores are dealt with wall surface. Figs. 10–13 show the influence of Trans A–D on St distributions. The transpiration gas of Tran A, which is influenced by recirculation flow, can only cool the inner side (the side near the stagnation point) of the pores. Fig. 10 shows that St reduced in the outer side of the pore, but the cooling gas of Tran A has no effect on the reattachment point where the peak flux occurs. The transpiration gas of Tran B can strengthen the cooling effect in its downstream region. As shown in Fig. 11, the cooling effect gradually weakens as θ increases. The influence of Tran B on the reattachment point nearly disappears. Thus, the peak flux decreases by around 1.1%. Tran C, where the transpiration gas covers the reattachment point, can improve the extremely aerodynamic heating environment on the reattachment point, and the peak flux declines by 8.6%. The transpiration gas of Tran D considerably influences the downstream region, but it does not affect the cooling of the reattachment point. Consequently, the peak flux has slight changes compared with that in the arrangement without transpiration. Overall, the transpiration pore, such as Tran C located on the upstream margin of reattachment point, is an optimum position to strengthen the cooling capacity of the local high heat flux region.
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82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97
100 101 102 103 104 105
Fig. 12. Influence of Tran C on wall St distributions.
106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125
Fig. 13. Influence of Tran D on wall St distributions.
126 127
5.3. Cooling effect of the combinational nose-tip
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cal stream-lines of Trans C and D, respectively. Both of them are influenced by the reattachment flow and flow downstream. The reattachment flow clings to the solid surface and forms a stable boundary layer without the influence of transpiration gas. In the flow-field of combinational nose-tip, the reattachment flow bypasses the transpiration pore in front of the pore and then reattaches away from the pore. The transpiration gas insulates the reattachment flow with high temperature and strengthens the thermal protection capacity.
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Fig. 11. Influence of Tran B on wall St distributions.
79
A large amount of tiny pores may interact to ensure that the transpiration gas can cover the whole reattachment region in the real manufacture of nose-tip. However, this arrangement results in
enormous workload. In this section, the structures of the combinational opposing jet and platelet transpiration are improved. Fig. 14 shows the optimized simplified structure. The transpiration pores are mainly arranged in the reattachment region to enhance the local cooling effect because of its high efficiency in reducing
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Table 6 Parameters of the combinational structures.
23
Parameter
Value
24
Rn R opp M N
25 mm 2 mm 2 12 15◦ 0.33 0.25 mm
25 26 27
θ
28
C1 Ls
29
Fig. 16. Temperature distributions with combination nose-tip.
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Fig. 15. Temperature distributions without transpiration.
the peak heat flux. The tiny transpiration pores are replaced with narrow gaps such as Trans E and F, as shown in the figure. The distance from the upper surface of the first platelet to the stagnation point is 2.7 mm. Table 6 lists the other structure parameters. The flow-field and heat transfer of the improved combinational nose-tip are numerically simulated, PR is 0.1, and the total mass flow rate of the transpiration gas is 0.075 mjet . Other boundary conditions are present in Table 3. Fig. 15 shows the temperature distributions without transpiration, and Fig. 16 shows the temperature distributions with the combinational nose-tip. The whole flow-field and temperature dis-
79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105 106 107 108 109 110 111 112
Fig. 17. Temperature distributions without transpiration on local region A.
tributions of the combinational nose-tip show no obvious difference from that without transpiration. The intensity of the transpiration gas is too weak to affect the whole flow-field and local flowfield around the gaps. Fig. 18 shows the local temperature around the transpiration gaps, and Fig. 17 shows that without transpiration. As shown in Fig. 17, a thin smooth boundary layer adheres to the body surface on the force of reattachment flow. Different from Fig. 17, the transpiration gases hit against the reattachment flow and destroy the boundary layer in Fig. 18. An embossment forms and covers the gaps with the interaction of the transpiration gas and reattachment flow. The temperature gradient in this region decreases. The embossment fades away due to the feeble intensity of transpiration gas with the distance increasing away from the gap, and the temperature gradient increases gradually until the next gap. Then, a new embossment is produced, and a new circulation begins. Fig. 19 shows the comparison of St contour between the nosetip without transpiration and combinational nose-tip. The heat flux
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between two gaps. However, the heat flux exhibits an obvious reduction with transpiration contrary to that without transpiration. Fig. 20 shows the St comparisons between nose-tip without transpiration and combinational nose-tip. Surface A is the section that crosses Tran E and the opposing orifice, whereas Surface B is the section that crosses Tran F and the opposing orifice. The peak St of Surface A decreases by 10.46%, whereas it declines by 12.15% in Surface B compared with that without transpiration. At the same time, the mass flux of total cool gas only increases by 7.5%. Overall, the combinational nose-tip strengthens the cooling effect of the reattachment region without leading to an identical addition of cool gas. Moreover, the simplified model for the simulation differs from the real structures of the combinational nosetip. The number of transpiration pores is decreased, and the size of pores is enlarged. These factors adversely affect the cooling efficiency. This study shows that the simplified model can promote the cooling efficiency compared with that of without transpiration.
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6. Conclusion
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Fig. 18. Temperature distributions with combination nose-tip on local region B.
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without transpiration distributes annularly, whereas it is disturbed by the transpiration gas in the combinational nose-tip. All transpiration gaps are arranged outside of the recirculation region and cannot be affected by the recirculation flows. The transpiration gases flow into the downstream of the gaps and mainly cool the reattachment region. In the inner part of the first loop of gaps, the heat flux distributes annularly. The same condition is observed in that of without transpiration. In the outer part of the first loop of gaps, the transpiration gas destroys the temperature boundary layer, thereby reducing the temperature gradient and the heat flux. Then, the temperature boundary recovers gradually with the influence of the outer attached flow. As a result, the temperature gradient increases and the heat flux rises again. Finally, a sharp decreasing trend of heat flux is observed owing to the effect of the low enthalpy transpiration gas from the next gap. The heat flux increases first and then declines with the increase in the distance
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In this work, a combinational opposing jet and platelet transpiration nose-tip is introduced for hypersonic vehicles to enhance the cooling effect. Moreover, a numerical study on heat flux reduction in hypersonic flow with the combinational nose-tip is conducted. On this basis, the flow-field and heat transfer are obtained. The major works are summarized as follows. The transpiration gas flow adheres to the body surface with the force of the outer flows (recirculation or reattachment flow) and forms the transpiration cooling film. The cooling capacity of the pores varies with different pore locations. The transpiration pore, which is located on the upstream margin of the reattachment point, exerts the optimum cooling effect on the local peak heat flux region. The heat flux exhibits an obvious reduction with transpiration contrary to that of without transpiration. The peak heat flux decreases by more than 12%, whereas the mass flux of total cool gas increases by 7.5% only. The simplified model for simulation reduces the number of pores and enlarges the size of pores compared with real combinational nose-tip. These factors lead to adverse cooling efficiency.
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Fig. 19. Comparisons of St contour between nose-tip without transpiration and combination nose-tips.
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Fig. 20. Comparisons of St between nose-tip without transpiration and combination nose-tips.
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This study shows that the simplified model with a limited number of pores can promote the cooling efficiency compared with that without transpiration.
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Conflict of interest statement
29 30 31
The authors declare there is not conflict of interest regarding the publication of this paper.
32 33
Acknowledgements
34 36 37 38 39 40
The authors would like to express their thanks for the support from the National Natural Science Foundation of China (No. 11802340) and the National Science Foundation of Jiangsu Province, China (BK20130084). Also, the authors thank the anonymous reviewers for some very critical and constructive recommendations on this paper.
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[1] J.A. Fay, Riddell, Theory of stagnation point heat transfer in dissociated air, J. Aeronaut. Sci. 25 (2) (1958) 73–85. [2] Y. Qiang, W. Xie, Z. Peng, New concepts and trends in development of thermal protection design and analysis technology, Acta Aeronaut. Astronaut. Sin. 36 (9) (2015) 2981–2991 (in Chinese). [3] D. Glass, Physical challenges and limitations confronting the use of UHTCs on hypersonic vehicles, in: 17th AIAA International Space Planes and Hypersonic Systems and Technologies Conference, AIAA 2011-2304. [4] Y. Liu, Z. Jiang, Concept of non-ablative thermal protection system for hypersonic vehicles, AIAA J. 51 (3) (2013) 584–590. [5] M.B. Gerdroodbary, S.M. Hosseinalipour, Numerical simulation of hypersonic flow over highly blunted cones with spike, Acta Astronaut. 67 (2010) 180–193. [6] M. Ou, Y. Li, W. Huang, Detailed parametric investigations on drag and heat flux reduction induced by a combinational spike and opposing jet concept in hypersonic flows, Int. J. Heat Mass Transf. 126 (2018) 10–31. [7] X.D. Li, Z.M. Hu, Z.L. Jiang, Numerical investigation on the thermal protection mechanism for blunt body with forward-facing cavity, Sci. China, Technol. Sci. 59 (7) (2016) 1120–1129. [8] K.M. Hanquist, K. Hara, I.D. Boyd, Detailed modeling of electron emission for transpiration cooling of hypersonic vehicles, J. Appl. Phys. 121 (2017) 053302.
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