Coupled f luid-thermal investigation on non-ablative thermal protection system with spiked body and opposing jet combined conf iguration

Jie HUANG , Weixing YAO , Xinyng SHAN

a State Key Laboratory of Mechanics and Control of Mechanical Structures, Nanjing University of Aeronautics and Astronautics, Nanjing 210016, China

b Key Laboratory of Fundamental Science for National Defense-Advanced Design Technology of Flight Vehicle,Nanjing University of Aeronautics and Astronautics, Nanjing 210016, China

c System Design Institute, Hubei Aerospace Technology Academy, Wuhan 430040, China

KEYWORDS Coupled method;Non-ablative;Opposing jet;Spiked body;Thermal protection system

Abstract In this paper, a Non-Ablative Thermal Protection System (NATPS) with the spiked body and the opposing jet combined conf iguration is proposed to reduce the aerodynamic heating of the hypersonic vehicle, and the coupled f luid-thermal numerical analysis is performed to study the thermal control performance of the NATPS. The results show that the spiked body pushes the bow shock away from the protected structure and thus reduces the shock intensity and the wall heat f lux. In addition, the low temperature gas of the opposing jet separates the high temperature gas behind the shock from the nose cone of the spiked body,ensuring the non-ablative property of the spiked body.Therefore,the NATPS reduces the aerodynamic heating by the reconf iguration of the f low f ield,and the thermal control eff iciency of the system is better than the Thermal Protection System(TPS)with the single spiked body and the single opposing jet.The inf luencing factors of the NATPS are analyzed.Both increasing the length of the spiked body and reducing the total temperature of the opposing jet can improve the thermal control performance of the NATPS and the nonablative property of the spiked body. However, increasing the heat conductivity coeff icient of the spiked body can enhance benef it the non-ablative property of the spiked body, but has little inf luence on the thermal control performance of the NATPS.

1. Introduction

The nose cone of the hypersonic vehicle is subjected to aerodynamic heating during the f light1-5, so the Thermal Protection System (TPS) is necessary to ensure the internal structure within the sustainable temperature range. There are mainly two types of TPS at present.One is the passive thermal protection system which is attached to the outer surface of the structure. The most widely used passive thermal protection is the ceramic tile TPS6,7, which consists of the coating, the thermal insulation material and the strain-isolation-pad. The coating with the high emissivity can radiate a large amount of energy into the atmospheric environment, and the thermal insulation material can prevent external energy from entering into the internal structure. However, the passive thermal protection system has no inf luence on aerodynamic heating. The other one is the active thermal protection system which can change the f low f ield and reduce aerodynamic heating directly, such as the opposing jet and spiked body installed on the nose cone of the hypersonic vehicle8,9. This paper deals with the nonablative thermal protection system with the combined conf iguration of the spiked body and the opposing jet, which belongs to the category of the active thermal protection system.

The spiked body is usually used to reduce the aerodynamic heating of the hypersonic vehicle, and relevant experiments and numerical studies have been conducted since the 1950s10-12. At present, the spiked body has been applied in the engineering successfully, such as UGM-133 Trident-Ⅱ.The spiked body is a slender rod,which is installed on the nose cone of the hypersonic vehicle.It can push the bow shock away from the blunt body,reduces the shock intensity and produces a recirculation zone, so the spiked body can achieve the purpose of reducing aerodynamic heating. However, as the stagnation point, the aerodynamic heating of the spiked body is very strong, which can burn the spiked body. Therefore, the spiked body is the ablative thermal protection system and needs to be replaced frequently.In recent years,some scholars studied the heat f lux reduction mechanism of the spiked blunt body with the aerodisk installed on the front of the spiked body. Huang et al.13studied the thermal control performance of the spiked blunt body with the aerodisk,and found that the spiked blunt body with the aerodisk has better thermal control performance than the spiked blunt body without the aerodisk.Besides,increasing the diameter of the aerodisk and the length of the spiked body can improve the thermal control performance. When the slender rod (spiked body) is placed on the front edge of the aircraft in order to reduce the surrounding aerodynamic thermal environment, the apex of the spiked body will be subjected to a harsh aerodynamic/thermal environment, thus the stiffness, strength and resistance to high temperature of the spiked body needs to meet the requirements, so that the body can fully withstand the hypersonic aerodynamic force and heating. However, this topic will not be studied in this paper.

In addition to the spiked body, some scholars have begun to study the application of the opposing jet technology for reducing aerodynamic heating since the 1960s.Refs.14-16studied the inf luence of the opposing jet on the aerodynamic heating of the nose cone by experimental and numerical methods.Their study shows that the opposing jet can push the bow shock away from the wall and produce a recirculation zone.Besides, the low enthalpy gas of the opposing jet can separate the high temperature gas behind the bow shock from the wall,so the opposing jet can reduce the wall heat f lux effectively and has good thermal control performance. Refs.17-19studied thermal control performance of the blunt body with opposing jet.They found that increasing the total pressure and diameter of the opposing jet can improve the thermal control performance. During the design of opposing jet, attention should be paid to the maximum gas mass that the hypersonic vehicle can carry.

In recent years, some scholars have studied the heat f lux reduction mechanism of the combined conf iguration. For example, Huang et al.20,21studied the thermal control performance of the conf iguration combining the spiked body and the opposing jet. It is found that the combined conf iguration has better thermal control performance than a single spiked body and single opposing jet.Besides,Huang et al.22studied thermal control performance of the conf iguration combining the opposing jet and acoustic cavity. Their results show that the thermal control performance of the opposing jet combined with the acoustic cavity is better than a single opposing jet and single acoustic cavity.

The above-mentioned scholars only studied the thermal control mechanism of the spiked body and opposing jet in terms of aerodynamic heating,and there is still lack of research on thermal responses of the structure,which can directly ref lect the temperature f ield and safety of the hypersonic vehicle.Based on previous studies, a new concept of the Non-Ablative Thermal Protection System(NATPS)with the spiked body and opposing jet combinational conf iguration is proposed in this paper.

The rest of the paper is organized as follows. Section 2 introduces the conf iguration and the thermal control mechanism of the NATPS. Section 3 presents the governing equations for aerodynamic heating, structural heat transfer, and the coupled f luid-thermal strategy. Section 4 describes geometries and numerical analysis models for the different thermal protection systems. In Section 5, the coupled method is used to study the thermal control performance of the NATPS,and the NATPS is compared with the single spiked body and the single opposing jet to verify its feasibility and advantages. The effects of the length of the spiked body, total temperature of the opposing jet, and heat conductivity coeff icient of the spiked body on thermal control performance of the NATPS are also analyzed in the section. Finally, some conclusions are drawn in Section 6.

2. Concept of non-ablative thermal protection system

Fig. 1 Conf iguration of NATPS.

In this paper,a combined non-ablative thermal protection system with the spiked body and opposing jet is proposed,and the conf iguration is shown in Fig.1,D is the diameter of opposing jet, D1is the double wall thickness of spiked body, L is the length of spiked body, R1is the outer radius of circular tube and R2is the inner radius of circular tube. In the NATPS, the spiked body can push the bow shock away from the protected structure, reduce the shock intensity and produce a recirculation zone in front of the protected structure. Therefore, the spiked body can reduce the aerodynamic heating of the protected structure. The opposing jet further pushes the shock away from the wall, and the low enthalpy gas of the opposing jet can separate the high temperature gas behind the shock from the protected structure and reduce the aerodynamic heating of the protected structure.In addition,the opposing jet can also reduce the aerodynamic heating and the temperature of the spiked body to ensure the non-ablative property of the NATPS,which is not available in the structure with the single spiked body.The coupled f luid-thermal numerical method will be used to analyze the thermal control performance of the NATPS, the single spiked body and the single opposing jet to validate the feasibility and advantages of the NATPS in the following sections.

3. Coupled f luid-thermal analysis method

3.1. Governing equations

The Navier-Stokes equations in the integral form without considering the volume force and internal heat source are given by

where W is the conservative vector, Fcis the convective f lux vector,Fvis the viscous f lux vector,?V is the boundary surface of the control volume V, and d S is the surface element.

As the functions of the pressure and temperature,the values of the dynamic viscosity and thermal conductivity are usually calculated by the Sutherland formula and the kinetic molecular theory, which have important inf luence on calculation accuracy of the wall heat f lux.The kinetic molecular theory is based on the Leonard Jones's molecular collision function. In this paper, the Computational Fluid Dynamics (CFD) method is adopted for aerodynamic heating analysis. According to the Finite Volume Method (FVM), the semi-discretized equations can be written as

where Wiand Viare the conservative vector and the volume of the control element i, respectively, ΔSmis the area of the boundary surface, and NFis the number of the boundary surfaces. The spatial discretization is conducted by the NND23scheme with the Total Variation Diminishing(TVD)property,and the semi-discretized upwind NND scheme is as follows:

The balance of the structural thermal energy can be expressed by the diffusion equation:

where ρ is the density, c is the specif ic heat, T is the temperature, q=-k?T denotes the Fourier's law of the structural heat transfer, k is the heat conductivity coeff icient, and φ is the internal heat source. Using the virtual temperature principle,the Gauss integral rule and the appropriate boundary conditions, the f inite element numerical method is adopted in the structural heat transfer.

3.2. Coupling strategy

During the f light of the hypersonic vehicle, the aerodynamic heating causes rise of the structural temperature, reducing the temperature gradient between the boundary layer and the structural outer surface. According to the Fourier's law, the wall heat f lux will decrease, which shows the feedback effect of increase of the wall temperature on aerodynamic heating.Fig.2 presents the coupled effect between aerodynamic heating and structural heat transfer,and the coupling variables are the wall heat f lux and the wall temperature. In this paper, the loosely coupled f luid-thermal interaction analysis method1is used to analyze the thermal control performance of the thermal protection system, and the coupling strategy is shown in Fig.3,where Δt is the time step size,Tiand Qiare the interpolation temperature and interpolation heat f lux respectively.The aerodynamic heating is calculated by the CFD method,and the structural heat transfer is calculated by the Finite Element Method(FEM).The wall temperature(or wall heat f lux)remains the same during each step of aerodynamic heating analysis (or step of structural thermal analysis). In addition,in order to ensure the accuracy of coordination and coupled time, data transfer of the coupling variables is conducted at the specif ic time nodes.

Fig. 2 Coupled analysis model.

Fig. 3 Loosely coupled f luid-thermal method.

Fig. 4 Relationship of nodes between CFD and FEM grids.

An important problem is the data transfer of the coupling variables in the f luid-thermal interaction analysis(Fig.4).This paper adopts the interpolation method based on the control plane to solve the problem1. The basic principle of the interpolation algorithm is illustrated by the data transfer of the wall heat f lux. First, the physical space (x, y, z) is mapped into a control plane (u, v) by the coordinate transformation. Then,the CFD nodes ηi(x,y,z)near the FEM nodes ζi(x,y,z)on the coupled surface in the space(x,y,z)are searched,and the corresponding nodes ηi(u, v) and ζi(u, v) on the control plane can be obtained. The CFD node coordinates ηi(u, v) and the the corresponding wall heat f lux Qi(u, v) are substituted into the cubic function Q(u, v), and the coeff icients of the function can be obtained by the least square method.The interpolation heat f lux qi(u,v)of the FEM nodes on the control plane can be obtained by substituting the FEM node coordinates ζi(u, v)into the function Q(u, v). Finally, the interpolation heat f lux qi(x, y, z) of the FEM nodes on the coupled surface in the physical space (x, y, z) can be obtained by the inverse coordinate transformation.The data transfer of the wall temperature can be conducted in the same way.In addition,the expression for the cubic function Q(u, v) is as follows:

where aiis the constant coeff icient in function Q(u, v).

4. Geometry and numerical model

Fig. 5 Shapes and sizes of analysis models.

In this paper,the original analysis model is the wind tunnel test model of the NASA hypersonic circular tube27.In order to verify the excellent thermal control performance of the NATPS,the coupled f luid-thermal numerical analyses of the original structure, the circular tube with the single opposing jet, the spiked blunt body and the NATPS with the spiked body and the opposing jet are conducted,and the corresponding geometrical shapes and sizes of the analysis models are shown in Fig. 5. In the analysis models, the length of the spiked body and the diameter of the opposing jet are the same to ensure the reasonability of the comparative analyses. This paper assumes that the material of the circular tube is the same as that of the spiked body, and the material properties are listed in Table 1. The Mach number, the static pressure, the static temperature of the free stream,the total pressure,and the total temperature of the opposing jet are shown in Table 2. The NASA hypersonic circular tube is a two-dimensional numerical model, so the analysis model and grid are twodimensional. The two-dimensional CFD and FEM numerical analysis models are established, and the f low f ield and structural temperature f ield are simulated by the four-nodes plane element.The CFD numerical models of the spiked blunt body and NATPS are similar, as shown in Fig. 6. The difference is that the front of the spiked blunt body is the wall, while it is the pressure inlet for the NATPS. In order to ensure the grid-independency of the wall heat f lux, the grid Reynolds number Recellof the CFD models is set to 1, and the f ine gridis used. The NND spatial discretization scheme, the Menter's SST k-ω turbulent model and the dual time-stepping method are used in the aerodynamic heating analysis.This paper calculates the dynamic viscosity and thermal conductivity according to the Sutherland law. In addition, the FEM numerical analysis models of the spiked blunt body and NATPS are shown in Fig.7,and the structural temperature f ield is calculated by the ABAQUS software. The initial wall temperatures of both the CFD and FEM analysis models are 294.4 K. This paper only considers the outer aerodynamic heating. Therefore, the boundary condition of the FEM analysis is only the wall heat f lux calculated by CFD analysis,which corresponds to the f irst boundary condition in Eq. (7). Both CFD and FEM analyses are transient, with the coupled time step size being 0.0001 s,and the total analysis time being 20 s.

Table 1 Properties of structural material.

Table 2 Parameters of free stream and opposing jet.

Fig. 6 CFD numerical model of spiked blunt body and NATPS.

In order to study the inf luence of the turbulent models on aerodynamic heating, the laminar model, Spalart-Allmaras(S-A) turbulent model and Menter's SST k-ω (SST) turbulent model are used to calculate the wall heat f lux of the original circular tube.Fig.8 presents the wall heat f lux(Qw)distribution of the original circular tube.The laminar model does not consider the turbulent effect. Besides, the S-A turbulent model uses the wall function correction,so it cannot calculate the wall heat f lux accurately.The SST turbulent model does not use the wall function correction,so it can obtain the best aerodynamic heating analysis result. Section 5.2 verif ies the accuracy of the SST turbulent model.

Fig. 7 FEM numerical models.

Fig. 8 Inf luence of turbulent models.

The number of the CFD grid has great inf luence on the analysis accuracy of aerodynamic heating. Fig. 9 presents the results of grid convergence analysis of the aerodynamic heating of the spiked blunt body. The coarse, medium and f ine CFD models have 93165,119426 and 136184 grid cells,respectively.According to the results in Fig.9,the f ine grid can obtain convergent wall heat f lux,and the f ine CFD grid is adopted in this paper to analyze the aerodynamic heating in subsequent sections.

5. Results and discussion

5.1. Initial f low f ield

Fig. 9 Grid convergence analysis results of spiked blunt body.

Fig. 10 presents the streamline and the temperature distributions of the initial f low f ield for the different analysis models calculated by the CFD method. According to Fig. 10(a), a bow shock appears in front of the circular tube in the hypersonic f low, and the high temperature gas in the shock layer can cause the serious aerodynamic heating effect.In Fig.10(b),the opposing jet expands and meets the free stream to form a complicated Mach disk and pushes the bow shock away from the circular tube. In addition, the opposing jet is squeezed by the free stream and reverses,thus forming a recirculation zone in front of the circular tube.After circumventing the recirculation zone,the opposing jet f lows downstream along the wall of the circular tube to form an interface,which separates the high temperature gas from the circular tube. In Fig. 10(c), the spiked body pushes the shock away from the circular tube and transforms the bow shock into the oblique shock to reduce the shock intensity, and a recirculation zone is then formed in front of the circular tube. However, at the stagnation point,the aerodynamic heating of the spiked body is very strong,which can burn the spiked body easily, so this type of thermal protection system cannot be reused and needs to be replaced repeatedly. In Fig. 10(d), the NATPS combines the characteristics of the opposing jet and the spiked body, and a larger recirculation zone is formed in front of the circular tube.Due to the opposing jet, a smaller recirculation zone is also formed in front of the spiked body.

Fig. 10 Streamline and temperature distributions of initial f low f ield.

Fig. 11 Initial wall heat f lux distributions.

The initial wall heat f luxes of the different analysis models are shown in Fig.11.The peak heat f luxes of the original structure and the circular tube with the single opposing jet appear at the stagnation point and the middle of the circular tube respectively. However the peak heat f luxes of the spiked blunt body and NATPS appear at the front end of the spiked body. The single opposing jet, the spiked blunt body and NATPS can reduce the wall heat f lux of the circular tube, and the corresponding peak heat f luxes of the circular tube decrease by 25.46%, 16.02% and 62.31% respectively, compared with the original structure. The results indicate that the NATPS has the best thermal control performance,followed by the single opposing jet,and the single spiked blunt body has the worst thermal control performance. For the NATPS, it is the most important that the low enthalpy gas of the opposing jet separates the high temperature gas after shock from the circular tube and spiked body and reduces the wall heat f luxes of the circular tube and the spiked body, which ensures the safety of the circular tube and the non-ablative property of the spiked body.Therefore,the NATPS is a type of non-ablative thermal protection, and can solve the ablation problem of the traditional spiked blunt body. Due to different sizes of the recirculation zones in front of the circular tube, the positions of the reattachment point in the f low f ield are different for different thermal protection systems, which determine the positions of the peak heat f lux of the circular tube. In addition, the wall heat f lux of the spiked body in the NATPS is signif icantly lower than that in the spiked blunt body,and this is benef icial to the non-ablative property of the NATPS.The above analyses are conducted in terms of the aerodynamic heating,and the thermal control performance of the NATPS will be studied in terms of temperature responses of the structure by the coupled f luid-thermal numerical method in the next section.

5.2. Evolution of wall heat f lux and wall temperature

Fig.12 presents the relative wall heat f lux(Q/Q0)and wall temperature (T/T0) of the original circular tube at 2 s. The calculation results match well with the experiment results. At the stagnation point, the calculated heat f lux Q0is 661 k W/m2and the experimental result is 670 k W/m2, with the relative error being 1.34%. Besides, at the stagnation point, the calculated temperature T0is 442 K, and the experimental result is 465 K, with the relative error being 4.95%. The comparisons verify the calculation accuracy of the CFD code, FEM codes and interpolation method in this paper.

Analyses of thermal control performance are conducted with the coupled f luid-thermal numerical method. Both the CFD and FEM analyses are transient, with the coupled time step Δt being 0.001 s, and the total coupled analysis time ttotalbeing 20 s. The initial wall heat f lux in Fig. 11 is used as the initial boundary condition of the coupled analysis. Figs. 13 and 14 present the wall heat f lux and wall temperature (Tw)distributions of different analysis models at different times.The results show that for all the analysis models, as the time increases,the wall heat f lux decreases gradually,while the wall temperature rises gradually. This is because the rise of structural wall temperature causes the decrease of the temperature gradient between the boundary layer and the structural outer surface, which reduces the aerodynamic heating and wall heat f lux and shows the coupled effect between the aerodynamic heating and structural heat transfer.The traditional uncoupled method does not consider the feedback effect of rise of the wall temperature on aerodynamic heating, and the wall heat f lux remains the same during the analysis. Therefore, the uncoupled method will result in higher wall heat f lux and wall temperature during the analysis, and cannot be used to evaluate the thermal control performance of the thermal protection system accurately.In addition,the wall heat f lux and wall temperature change rapidly at the beginning,then the changing speed slows down gradually,and f inally steady-state solutions will be obtained.

Fig. 12 Relative wall heat f lux and wall temperature distributions at 2 s of original structure.

Fig. 13 Variation of wall heat f lux with time.

The structural temperature f ields at 20 s of the different analysis models are shown in Fig. 15, and the maximum temperatures of the circular tube (Tmax) and the corresponding positions (θmax) are listed in Table 3. The maximum temperature of the circular tube in the NATPS is 441.4 K, which is 35.27%, 20.53% and 25.68% lower than the maximum temperatures of the circular tube in the original structure,circular tube with single opposing jet, and circular tube with single spiked blunt body, respectively. Affected by the sizes of the recirculation zones in front of the circular tube and the positions of the reattachment points on the circular tube,the positions of the maximum temperatures of the circular tube in the different analysis models are different. According to the results,the positions in the NATPS and the spiked blunt body are close,following the position in the circular tube with single opposing jet obviously. In addition, the maximum temperatures of the spiked body in the spiked blunt body and NATPS are 1223.0 K and 534.8 K, respectively, with maximum temperature in the NATPS being signif icantly lower than that in the spiked blunt body. Therefore, the NATPS can solve the ablation problem of the spiked blunt body. Fig. 16 presents the time histories of the maximum temperature of the circular tube for the different analysis models. The results show that the structural temperature rises rapidly at the beginning, and then the changing speed slows down gradually to reach a time-independent value. According to the above analyses, the NATPS is a non-ablative thermal protection system, and the non-ablative property is achieved by the opposing jet.Besides,the thermal control performance of NATPS is better than that of the spiked blunt body and that of the circular tube with the single opposing jet, showing the potential of NATPS in engineering application.

5.3. Effect of length of spiked body

The inf luences of the length of the spiked body L on the thermal control performance of the NATPS are analyzed in this paper. Fig. 17 presents the initial wall heat f lux distributions and the wall temperature distributions of the NATPS at 20 s with different parameters of L. Fig. 18 presents the structural temperature f ields of the NATPS, the maximum temperatures of the spiked body and circular tube and the corresponding positions. When the length of spiked body L increases from 20 mm to 100 mm, the initial peak heat f luxes of the spiked body and circular tube decrease by 22.35% and 52.95%,respectively, and the peak wall temperatures of the spiked body and circular tube at 20 s decrease by 31.18% and 23.12%, respectively. The results indicate that increasing the length of the spiked body L can reduce the aerodynamic heating and improve the thermal control performance of the NATPS. The fundamental cause is that increasing the parameter L increases the distance between the shock and the circular tube and thus reduces the shock intensity,which is benef icial to the thermal control performance and non-ablative property of the NATPS. The increase of the parameter L also affects the position of the reattachment point on the circular tube, and the position of the peak heat f lux and peak wall temperature of the circular tube moves downstream with the increase of the parameter L.

Fig. 14 Variation of wall temperature with time.

Fig. 15 Temperature f ields of different numerical models at 20 s.

Table 3 Maximum temperatures and corresponding positions of circular tube at 20 s.

According to Fig. 17, the decreasing speed of the wall heat f lux and structural temperature slows down gradually with the increase of the parameter L. As the parameter L grows from 80 mm to 100 mm, the maximum temperatures of the spiked body and circular tube only decrease by 1.35% and 2.31%respectively, which indicates that increasing the parameter L has little inf luence on the thermal control performance of the NATPS when the parameter L is over 80 mm. Besides, the increase of parameter L leads to a linear increase of the mass of spiked body. Therefore, the inf luences of the increasing parameter L on both the thermal control performance and the mass of the NATPS should be considered,and we should select the appropriate length of the spiked body.

Fig.16 Variation of maximum temperature of circular tube with time.

5.4. Effect of total temperature of opposing jet

The inf luences of the total temperature of the opposing jet T0on the thermal control performance of the NATPS are analyzed in this paper. Fig. 19 presents the initial wall heat f lux distributions and the wall temperature distributions of the NATPS at 20 s with different parameter T0. Fig. 20 presents the structural temperature f ields of the NATPS,the maximum temperatures of the spiked body and circular tube and the corresponding positions.As the total temperature of the opposing jet T0increases from 400 K to 1200 K,the initial peak heat f lux of the circular tube increases by 62.62%, and the peak wall temperatures of the spiked body and circular tube at 20 s increase by 86.16% and 13.08% respectively. The maximum temperature of the spiked body almost decreases linearly with the decrease of the parameter T0, which is benef icial to the non-ablative property of the NATPS.The results indicate that decreasing the total temperature of the opposing jet T0can reduce the aerodynamic heating and improve the thermal control performance of the NATPS effectively. The fundamental cause is that decreasing the parameter T0can inject the lower temperature gas into the f low f ield and cool the wall directly.However, the change of the parameter T0has no inf luence on the position of the maximum temperature of the circular tube. In addition, when the parameter T0is 400 K, the maximum temperature of the spiked body does not appear at the front end, but at the back corner, showing that when the parameter T0drops to a certain value, the ultra-low temperature gas cools the front of the spiked body directly and moves the position of the maximum temperature of the spiked body backward.

Fig. 17 Initial heat f lux and wall temperature distributions with different parameter L.

Fig. 18 Structural temperature f ields at 20 s with different parameter L.

Fig. 19 Initial heat f lux and wall temperature distributions with different parameter T0.

Fig. 20 Structural temperature f ields at 20 s with different parameter T0.

Fig. 21 Wall temperature distributions at 20 s with different parameter k1.

5.5. Effect of heat conductivity coeff icient of spiked body

The inf luences of the heat conductivity coeff icient of the spiked body k1on the thermal control performance of the NATPS are analyzed in this paper. Fig. 21 presents the wall temperature distributions of NATPS at 20 s with different parameters k1.Fig. 22 presents the structural temperature f ields of the NATPS, the maximum temperatures of the spiked body and circular tube and the corresponding positions.As the heat conductivity coeff icient of the spiked body k1increases from 5 W/(m·K) to 65 W/(m·K), the maximum wall temperature of the spiked body at 20 s in Area A decreases by 16.63%. In addition, the wall temperature of the spiked body in Area B increases with the increase of the parameter k1, but decreases in Area C with the increase of the parameter k1.The changing speed also decreases gradually with the increase of the parameter k1.The reason for this variation trend of the wall temperature in Areas A, B and C is that the wall temperature distribution of the spiked body is very uneven when the parameter k1is small, and increasing the parameter k1will increase the thermal diffusivity of the spiked body to reduce the nonuniformity of the wall temperature of the spiked body.In addition,the parameter k1has little inf luence on the wall temperature distribution and the maximum temperature of the circular tube, and has no inf luence on the position of the maximum temperature of the circular tube. The above analysis results show that increasing the parameter k1is benef icial to the non-ablative property of the spiked body, but has little inf luence on the thermal control performance of the NATPS.

Fig. 22 Structural temperature f ields at 20 s with different parameter k1.

6. Conclusions

(1) A non-ablative thermal protection system with a spiked body and opposing jet combinational conf iguration has been proposed in this paper, and the coupled f luidthermal numerical method is used to study the thermal control performance of the system.

(2) The non-ablative thermal protection system reduces the aerodynamic heating by the reconf iguration of the f low f ield, and its thermal control performance is better than the thermal protection systems with the single spiked body and the single opposing jet.

(3) Increasing the length of the spiked body and reducing the total temperature of the opposing jet can improve the thermal control performance and benef it the nonablative property of the spiked body, while increasing the heat conductivity coeff icient of the spiked body can only benef it the non-ablative property of the spiked body, which has little inf luence on the thermal control performance.

(4) The investigations in this paper show the advantage and potential of the non-ablative thermal protection system in future engineering applications.

(5) The studies in this paper are in the stage of conceptual design. For actual application in the hypersonic vehicle,the stiffness and strength of the spiked body should be studied. Besides, the inf luences of the spiked body on f light stability,center of mass and pressure of the hypersonic vehicle should also be studied to ensure the safety and f light performance of the hypersonic vehicle.

Acknowledgement

This research was supported by the Priority Academic Program Development of Jiangsu Higher Education Institutions.