Infrared radiation characteristics of a hypersonic vehicle under time-varying angles of attack

Qinglin NIU , Zhihao YUAN , Biao CHEN , Shikui DONG ,*

a School of Energy Science and Engineering, Harbin Institute of Technology, Harbin 150001, China

b Key Laboratory of Aerospace Thermophysics of Ministry of Industry and Information Technology,Harbin Institute of Technology, Harbin 150001, China

c Key Laboratory of Chemical Laser, Dalian Institute of Chemical Physics, Chinese Academy of Sciences, Dalian 116024, China

KEYWORDS Angle of attack;Fluid-thermal interaction;HTV-2;Hypersonic vehicle;IR radiation;Surface temperature

Abstract Hypersonic vehicles emit strong infrared(IR)radiation signatures that can be treated as a detecting source for object identif ication and routine diagnosis.This paper is aimed at examining the intrinsic radiation characteristics of a Boost-Glide Vehicle(BGV)under the condition of various Angles of Attack (AOAs). A two-temperature model considering the thermal and chemical nonequilibrium effects is coupled with Navier-Stokes equations solved by the finite volume technique.A gas-solid conjunction heat transfer model is also added into the fluid solver to simulate the surface temperature of the vehicle. The radiative transfer equation is solved with Line of Sight (LOS)algorithm.The computational results for a Hypersonic Technology Vehicle-2(HTV-2)type vehicle show that radiances of the vehicle are strongly dependent on the surface temperature.The presence of AOA results in the signif icant difference of the surface temperature. Infrared radiation characteristics are also changed in intensity and spectral band due to the AOA.Simulations are performed with two time-varying AOAs.Transient results indicate that the variation of AOA does have a great effect on the infrared radiance and is closely related to observation angle,spectral band,angle size,angular velocity and time history.

1. Introduction

Boost-Glide Vehicles (BGVs) can glide long distances in near space with an extremely high speed.Such a vehicle is generally propelled to great speed and altitude by a large booster or released from a space orbiter, and then re-enters the atmosphere to begin a long hypersonic glide.1The prototype example for such a vehicle is Hypersonic Technology Vehicle-2(HTV-2)2in the Falcon program. It is a boost-glide vehicle with an arrow-head design and wave-rider conf iguration.During the glide phase,the highest Mach number can reach up to 20, and the range may be over 10000 km.3Due to many advantages such as high speed, long glide range, and strong maneuverability in the hypersonic regime, BGVs have attracted the attention of major research institutes and will have a broad array of applications. Generally, a BGV has a distinctive ballistic flight scheme composed of launch, pullup, reentry, glide and terminal phases, as route-A in Fig. 1.Thus,the BGV needs adjust its attitude by continuous control of AOA to meet the requirement of the predetermined trajectory in some typical cases. For instance, to increase the range and penetrating probability, BGVs often have a ‘‘hopping”trajectory,4meaning that it is necessary to achieve the skipping motion using a sequence of appropriate AOAs.5Besides, the glider must maintain a high AOA to provide enough lift in trajectory guidance problems, for example, in no-f ly zones for threat avoidance or geopolitical restriction6as route-B in Fig. 1. In addition, gliding at a fixed AOA for a long time increases the integrated heat loads,meaning that it will present material and thermal insulation challenges for the Thermal Protection System (TPS). As convention hypersonic aircraft,atmospheric gliding at high AOA may diminish the heat load integrated over the trajectory.7With a reduction in total heat load, the size of the TPS may be reduced, improving vehicle payload fraction.8Therefore, the presence of AOA with a low rate of change is an inevitable flight condition for a BGV during the glide phase.

During aircraft sliding through earth’s atmosphere, the slider encounters denser atmospheric layers as it progresses towards the surface, dissipating its kinetic energy through drag. A strong bow shock in front of the nose can heat up the gas to several thousand degrees Kelvin.9In this region,there exist complex physical and chemical processes such as dissociation, ionization, recombination, viscous interaction,etc.These main physical processes near the wake and the base flow are plotted in Fig.2.To simulate such a hypersonic flow,many effects should be taken into account in numerical models,including chemistry,nonequilibrium thermal effect,turbulence, internal energy relaxation and so on. Some special hypersonic codes have been developed for the requirements of the TPS and aerodynamics in recent decades, such as DPLA10by University of Minnesota, LAURA11by NASA Langley Research Center,and UST3D12by Russian Academy of Sciences. These codes are widely used for simulations of reentry vehicles’ flows in the continuum region. Up to now,numerical calculations of the hypersonic flows are still a complex issue and the numerical models have been constantly improving. For numerical calculations of hypersonic flows of BGVs, some works have been carried out in recent years.Liu et al.13calculated the hypersonic flows of a HTV-2 type waverider using the nonequilibrium real gas and the perfect gas.They focused on the effect of gas models on aerodynamic characteristics. Shao et al.14,15simulated the thermo-chemical nonequilibrium ablation flows of an HTV-2 type vehicle and used them to examine the electromagnetic scattering characteristics. Shi et al.16computed thermal equilibrium flows of the HTV-2 shape vehicle to use for the optimization of aerodynamic force and heating. However, few literatures research on infrared characteristics of such a BGV.

Fig. 1 Flight profiles of a HTV-2 type glider.

Fig. 2 Flow phenomena of HTV-2 type vehicle during gliding phase.

At extremely high temperatures, the internal energy of gas atoms and molecules can be excited so that the emission will be radiated from the surface of the vehicle and its surrounding flows. For infrared radiation calculations, some line-by-line radiation codes have also been developed,such as NEQAIR,17NERD,18NERAT19and SPRADIAN0720.These tools can be used to predict the radiation intensity in states of non-Local Thermal Equilibrium (non-LTE) or thermal equilibrium.Ozawa et al.18predicted the infrared spectra from the forward-looking DEBI spectrometer at an altitude of 40 km and 3.5 km/s using NERD code and NEQAIR-IR code.Levin et al.21also computed the DEBI spectrometer under the free stream conditions of 40 km and 5.1 km/s. These results indicate that the peak intensity of radiating species is weak less than 10-4W/(cm2·sr·μm) in these calculational cases. For the surface emissions, Winter et al.22pointed out that thermal radiation of the glowing heat surface follows the Planck’s law and can be computed as grey body radiation with a given emissivity. Obviously, surface emissions are dominant in the infrared spectral bands for the surface temperature above one thousand degrees Kelvin. It means that radiation calculations are strongly dependent on the surface temperatures. In practice, the hypersonic vehicles have to be restricted to f ly within a narrow flight corridor at feasible AOA bounds due to some stringent constraints, such as heat flux, structural load, angles of path and dynamic pressure.23Therefore, it is very meaningful to study the radiation characteristics, which can be used for signal detection and diagnosis tracking.Recently, radiation characteristics of hypersonic vehicles including different AOAs have been investigated, but most of the subjects are for space shuttle orbiters and reentry capsules.24-26Thus, the effects of the AOA on surface temperatures and IR irradiances for a BGV need further investigations.

It is of great importance for accurate calculations of flow field and wall temperatures, which can be used as input data for the prediction of radiance signatures. So far, it is still a challenging issue for the coupling solutions between the flow and structure in the governing equations due to the complex physical and chemical processes. Against such background,the present investigation adopts a fluid-solid coupling heat transfer method to predict the surface temperature and then explores the AOA effect on IR intrinsic radiations. An HTV-2 type vehicle is chosen as a waverider conf iguration representative of an unpowered glider. The numerical study is carried out by a hypersonic computational fluid dynamics code, and then analyses are conducted by a radiative transfer module.In this paper, a computed trajectory point at an altitude of 50 km is selected for computations. Effects of AOA on the IR radiation are investigated from two aspects: (A) in the steady state, and (B) in the transient state.

2. Computational model and methodology

2.1. Governing equations

On the assumption that the continuum approximation is still valid, the Navier-Stokes equations of thermal-chemical nonequilibrium flows in a three-dimensional system are expressed as

where U and S are the vectors of conservative variables and source terms,respectively;t is the time;Fcand Fvare the inviscid and viscous flux matrices. They are given as following expressions:

where ρ is the density of the gas mixture,p is the pressure,Y is the vector of mass fraction of species,u is the velocity vector,E and Eveare the total energy and the vibrational energy per unit mass of mixture,respectively, ˙ω is the mass production rate per unit volume for species, ˙ωveis the vibrational energy source term, τ is the stress tensor, I and J are the flux tensors, and q and h are the vectors of the heat flux and the enthalpy per unit mass of species, respectively. In these symbols, the subscript ‘‘tr” and ‘‘ve” denote the translational-rotational state and the vibrational-electronic state, respectively.

The heat flux in the gas towards the wall can be written as

In the two-temperature model, the heat flux acting on the surface from the fluid part at certain time can be expressed as

where hiand Yiare the sensible enthalpy per unit of mass and mass fraction of species i, respectively; T is the temperature;qwnis the heat flux component in direction normal to the wall;Nsis the number of the species;Diis the diffusion coefficient of species i, η is the thermal conductivity; and n is the normal derivative at the surface of the vehicle. In this equation, the translational temperature and the vibrational temperature are introduced based on the solution of the Navier-Stokes equation.

where Nrdenotes the number of the reaction;αi,jand βi,jare the stoichiometric coefficients for reactants and products for species i in the j reaction respectively; Miis the molecular weight of species i; kf,jand kb,jare the forward and backward rate coefficients for the j reaction respectively; ρiis the density of species i.

The internal or vibrational energy source term with the vibrational relaxation time has the same form with Ref.27:

For hypersonic flows with adverse pressure gradients, turbulence is molded using the Menter’s two-equation Shear Stress Transport (SST) k - ω model28in numerical calculations.This model employs a modified form of the eddy viscosity to consider the transport of Reynolds stress and two blending models. The k - ω formulation is used in the domain close to the wall while the blending k - ε model is used for the freestream.The SST model has previously been used in hypersonic flows, and its detailed expression can be seen in Ref.29.

2.2. Gas-solid coupling method

To solve a conjunction heat transfer problem, another partitioned approach is used individually to deal with the heat conduction equation, and then exchange information with the fluid solver at the coupling interface.For the solid phase being homogeneous medium, the basic governing equation of the temperature field without internal heat source can be expressed as

where Tsis the structural temperature, ρsand csare the structural density and specific heat,respectively, ηsis the structural thermal conductivity, and x, y, z are the cartesian coordinate.

An interface exists between the fluid phase and the solid structure,via which the external hypersonic aerodynamic heating interacts with the structure heat transfer inside the vehicle.For the conjunction heat transfer, the boundary conditions at the gas-solid interface thus must satisfy continuity of temperature and balance of heat flux.The heat flux conducting energy away from the surface into the body is

where ^n is the surface unit normal vector.

Under the no ablation condition, the surface energy balance is expressed as

The radiative heat flux from the surface has the following form

where ε is the emissivity of the surface, σ is the Stefan-Boltzmann constant, and Twis the surface temperature.

2.3. Chemical reaction model

For most hypersonic flow at altitudes of 40-70 km,the characteristic time of the flow field has nearly the same magnitude with the molecule vibration relaxation time and the chemical reaction time. A finite rate chemical reaction model is utilized to describe the reaction rate defined in Eq.(6).In that formula,the rate constants of both the forward reaction kf,jand the backward reaction kb,jare determined by the Arrhenius relationship:

where Af,jis the frequency factor of the forward reaction in the j reaction, Tcis the controlling temperature, nf,jis the temperature exponent of the forward reaction in the j reaction, Eais the activation energy, and Ruis the universal gas constant.

The controlling temperature Tcexpressed in Eq.(12)should count for the influences of thermal nonequilibrium on chemical reactions. A single rate-controlling temperature presented by Park30is expressed as

where a and b are the power law coefficients, and both are taken as 0.5 in this paper.

Without taking into account the surface ablation species, a kinetic model of air checked by Surzhikov,31consisting of 6 reactions and involving 7 components of partially ionized air(N2, O2, NO, N, O, NO+, e-), is selected. Thermodynamic models and transport properties are the same with the previous work32.

2.4. Numerical algorithm of CFD solver

Navier-Stokes equations are solved with a cell-centered finite volume formulation33which is used for the fluid domain computations, and an implicit scheme is employed to greatly reduce computing time. Discretization of convective fluxes has the following reconstruction method33

where the subscript ‘‘i+1” and ‘‘i-1” denote nodal point indexes in the i direction. The same form is employed in the other directions for three dimensions. The subscript ‘‘L” and‘‘R” are the left- and right-side value of the half point i+1/2. The min-mod limiter, ΨRand ΨL, borrowed from Ref.34is implemented to control the discontinuous pressure jumps at the shock front.

The forward (Δ+)and the backward (Δ-) difference operators are defined as

The treatment of convective fluxes uses the flux difference scheme, which is equivalent to the Roe approximate Riemann solver22based on a second-order upwind scheme.The convective flux at the half point is

where ΔU=UR-UL.is the Roe-average flux Jacobian matrix.,andare the matrix of the right and left eigenvectors and the diagonal matrix.The convective fluxes in the j and k directions are similar to Eq. (16).

The viscous fluxes,as a function of the gradient and conservative variables velocity and temperature, are discretized by the second-order central difference approach.35In addition,the solid phase temperature field solved by the heat flux balance method is coupled in the governing equations with the fluid-solid conjugation.The Runge-Kutta method33is utilized here for time stepping. The physical time step is set to 2×10-5s, and each time step has 20 iterations.

where n and (n+1) denote the actual and new time levels respectively; αmis the coefficient of the Runge-Kutta scheme in stage m, which can be borrowed from Ref.33;and Ωiare the residual and the i th control volume respectively,and Δtiis the physical time step.

2.5. Radiative transfer algorithm

The radiative transfer equation, determining the local spectral intensity, is expressed as36

where λ indicates the wavelength, κaλand κsλare the absorption coefficient and the scattering coefficient of the mixture respectively, Iλs（ ） and Ibλs（ ） are the local spectral intensity and the Planck blackbody radiant intensity at the s location respectively, Iλ（s ,Ω′） is the spectral scattering intensity in Ω′direction, and φλΩ′,Ω（ ） is the scattering phase function. For the no-particle flow, the scatter term can be ignored. In this case, the product of the spectral absorption coefficient and the path length, τλ= κaλs, is defined as the optical thickness.Thus, the radiative transfer equation is reduced to the following form:

The surface emission is a self-emitter radiation. The radiance per solid angle can be simply determined by this expression:

where ελis the emissivity, and c1and c2are radiation constants.

In the present work, related investigations only focus on intrinsic radiation characteristics. That is to say the radiation computation is performed only in the domain between the vehicle surface and the gas around the body without considering the atmospheric transmission and attenuation. In the flow field, only a radiating species of CO2is taken into account in the radiation transfer, and its volume fraction is 3.60×10-4in the free stream.37The physical parameters of radiation calculations are computed with a line-by-line method on the basis of HITEMP data base38.LOS propagation is used to compute the radiation transfer equation.A LOS line is divided into segments corresponding to the layers of the flow field. It is assumed that the flow field parameters are uniform in each layer. A LOS places a known travel route and keeps continuous until the line encounters wall boundaries or departs from the flow field,along which the intensity is determined by distributions and levels of temperature,pressure and species concentrations.In all,these treatments are divided into five steps:(A)emit lines from the surface shell grids to ensure a f iner allocation of LOS,(B)determine the visible surface due to the interruption of the body at a certain observation angle, (C) divide the LOS line into segments, (D) interpolate the flow field parameters using a cylinder with a radius of R to the adjacent LOS line, and (E) compute the total radiance of the LOS.Fig. 3 illustrates the process of extracting the LOS, where Liis the path of layer i.

Fig. 3 Diagrammatic sketch of LOS.

The radiative transfer equation can be solved with the LOS approach. Assume that each layered medium is isotropic and isothermal, and the radiative intensity along the LOS shown in Fig. 3 can be written as

Here, the first term on the right-hand side denotes the transmission intensity at the i-1th layer,and the second term represents the emission intensity at the i th layer. In Eq. (21), the boundary condition at the first layer is the intensity of the surface emissions, namely=Ibλ,s. Thus, the radiance along the LOS in the wavelength ranging from λ1to λ2can be given as

3. Verif ication cases

3.1. Validation of surface temperature

A UHTC(Ultra High Temperature Material)double cone was reported in Ref.39to obtain the surface temperature distribution. The forward cone with a 25° half angle is 29 mm in length,and the aft cone with a 55°half angle is 8 mm in length.Fig. 4(a) shows the geometric size of the double cone and the shape of the prop. The freestream conditions and the material properties were listed in Ref.39, but the compositions refer to Ref.40due to the insuff icient sum of the species mass fraction in Ref.39. Three domains, as shown in Fig. 4(b), are fluid for external flow, UHTC double cone and copper prop for solid respectively.

Fig. 5(a) shows a comparison of the surface temperature between computed (Cal.) and experimental (Exp.) cases along the body at 60 s. The computed results are very close to the measured data, except for some slight over-predicted values around the forward part of the hinge point between the cones.Fig.5(b)gives comparisons of time histories of surface temperatures at x1=4 mm and at x1=35 mm between computed results and measured data. The temperature profile computed at x1=4 mm is in good agreement with experimental results.The simulation results at x1=35 mm slightly over-predict the temperature rise compared to measurements.

3.2. Validation of heat flux with AOAs

The double-cone vehicle in NASA-TP-2334 report41is employed to validate the numerical model under the conditions of AOAs. The geometry of the experimental vehicle is shown in Fig. 6. The first cone has a nose radius of Rn=0.3835 m, half cone angle of φ1=12.84°, and a length of L1=6.955 m. The second cone has a half cone angle of φ2=7°,and a length of L2=12.224 m.The free stream conditions are: Mach number Ma=10.6, pressure P∞=59.92 Pa, temperature T∞=48.88 K, velocity u∞=1382 m/s. In calculations, the wall boundaries are specif ied as a non-slide condition with a constant temperature of 300 K. The heat fluxes on the surface at the AOA of α=10° and α=20° are calculated respectively. As can be seen from Fig. 7, the calculated results are in good agreement with the experimental data. In this f igure, q and q0represents the heat fluxes at any station along the surface and at the stagnation point,respectively.

Fig. 4 Geometry and computed grids of UHTC double cone.

Fig. 5 Comparison of surface temperatures between computed and experimental results.

Fig. 6 Blunt double cone geometry.

3.3. Validation of radiation transfer

In this study, the radiation sources in calculations include the emission of the surface and the radiation of gaseous species CO2. This has been mentioned in Section 2.5. In calculations of the LOS, the surface emission is the initial value, which can be computed by the Planck’s law easily.The intrinsic radiation is calculated in a conf ined domain that can cut the domain of the high-temperature flow field with a cylinder.Thus, the high- and low-temperature gas may exist in this domain.To validate the radiation transfer,two test cases with different concentrations of CO2are employed. The conditions of the two cases are listed in Table 1.Case 1 is a rom condition,which is similar with the freestream conditions. Case 2 is a high-temperature condition with 100% CO2.

Fig. 7 Comparison of computed and experimental heat fluxes along bottom central line.

Table 1 Conditions of radiation test cases for CO2.

Fig. 8 Comparison of transmissivity between computed and experimental data for CO2.

Fig.8(a) shows the comparison of predicted spectral transmissivity with reference data42in the wavelengths of 1.5-5.5 μm. Within these wavelengths, there are two distinct feature spectra of the 2.7 μm and 4.3 μm bands. It is clear that the emissivity (1-transmittance) in the 4.3 μm band is obviously higher than that in the 2.7 μm band. Fig. 8(b) shows the comparison of the spectral transmissivity between computed and experimental data43in the wave number of 1900-2400 cm-1. It can be seen that computed results in two cases match well with reference data.

4. Results and discussion

4.1. Mesh and boundary

HTV-2 is a lifting body with a sharp leading edge and sweptback expanded f lap on the trailing edge.As a BGV with a high lift to drag ratio, it was designed for 3000 s of atmospheric glide phase and allowed for substantial downrange and cross range maneuverability.Using an external tantalum in its outer shell, it has an extremely high melting point of 3290 K.44This attribute makes it valuable for applications such as a BGV,when it reaches speeds of 20 times the local speed of sound so as to withstand extremely high heat flux. An HTV-2 type geometry, shown in Fig. 9, has a 0.034 m diameter ball head,a sharp leading edge and a large back sweep, with 3.67 m in length, 2.20 m in width and 0.88 m in height, which is nearly the same size as HTV-2. During the glide phase, the glider has a ‘‘hopping” trajectory by continuous control of AOA within the range of 0-30°,and the flight conditions are selected from Refs.23,45and are given in Table 2.

Fig. 9 HTV-2 type vehicle geometry parameters.

Table 2 Freestream conditions for HTV-2 type vehicle.

Fig. 10 Grid distribution and spatial topology.

Without regard to the angle of side slip, the computational domain can be cut down to a half. The multi-block structured mesh is generated through the commercial software ICEMCFD. The domain is divided into 68 blocks and each of the blocks has the same amount of mesh in associated directions.The entire computational domain is in a half cylinder to meet a larger AOA case.According to the conf iguration of the HTV-2 type vehicle, the topology utilized to generate threedimensional structured grids is shown in Fig. 10(a). The computational grid contains two regions: one is the solid domain(as shown in Fig. 10(b)), and the other is the fluid domain(as shown in Fig. 10(c)). There is complex bow shock around the nose, so refined grids are generated by two symmetric Yshaped grid topologies (as shown in Fig. 10(d)). Additionally,the surface grid is shown in Fig.10(e),and the grid distribution in the afterbody is plotted in Fig. 10(f). The non-dimensional grid height of the first layer on the wall ngis very sensitive to the precision of the parameters for high-speed flows,especially in the shock layer and nearby the surface of the vehicle. As reported in Ref.15, the cell Reynolds number Rec= ρ∞u∞ng/μ∞is less than 2, where ρ∞, u∞and μ∞are the free stream density, velocity, and viscosity coefficient,respectively.As a compromise between accuracy and computational cost, the computed grid for the flow field consists of 4.2 million cells and ng=4×10-5m, and the number of meshes in solid domain is 0.4 million. This grid is called basic grid. To analyze the grid sensitivity during temperature and species concentration calculations, the non-dimensional grid height is reduced to half of the basic grid and the amount of the mesh is also refined by a factor of 1. A comparison of the computed parameters between the basic and refined meshes along the stagnation line is shown in Fig. 11. In this f igure,L/Rnis the dimensionless distance along the stagnation line,where L is the distance along the stagnation line and Rnis the radius of the nose. Results indicate that the current basic grid meets grid independence.

Fig. 11 Grid-independence of solution.

A uniform temperature-pressure condition was applied to far-field and inflow boundaries of the computational domain.Ambient pressure and temperature conditions are listed in Table 2. A gas-solid conjunction heat transfer boundary is imposed on the interface between the fluid and solid domains,and the interface towards the fluid side is adopted with a 0.85 emissivity. By understanding an internal insulation thermal protection system equipped on HTV-2,46an adiabatic wall boundary was specif ied at the inner shell of the solid domain.It is assumed that the carbon material is used for the structure of the vehicle.In addition,a supersonic outflow and a symmetric plane are employed.

In this paper, the LOS is parallel from the surface with a zero field of view as plotted in Fig. 3. As shown in Fig. 12,the observation angle can be described with both the zenith angle θ and the circumferential angle ψ. For example, (90°,180°) represents the observation angle in the side view, (0°,0°) in the top view, and (180°, 0°) in the upward view.

4.2.Angle of attack effects on radiation under steady conditions

In near space,the surface heat flux can be in equilibrium when the vehicle slides at a constant AOA for a long time. Such a situation may occur to achieve a ‘‘chopping” trajectory through the presence of AOA.Thus,it is meaningful to understand the variations of radiation characteristics of the HTV-2 type vehicle at different AOAs. For the sake of analysis, an invariant flight condition at an altitude of 50 km and a velocity of 5400 m/s is used for numerical calculations. Three ideal AOAs,including 0°,10°and 20°,are selected for flow field calculations in steady state.

Fig. 12 Schematic diagram of observation angles.

Fig. 13 Temperature contours in symmetric plane at α=10°.

In hypersonic flows at altitudes above 40 km, there exist obvious chemical and thermal nonequilibrium effects in the shock layer.At different AOAs,the variation of the windward side makes the aerodynamic characteristics changeable. These can affect surface temperatures,and then further affect the IR irradiances. Fig. 13 illustrates the flow field contours at α=10°. Fig. 13(a) indicates that high-temperature regions mainly occur in the shock layer and wake flows. The temperature behind the bow shock reaches up to 12000 K,and about 7000 K in wake flows due to the shock layer intersection from the upper and lower surfaces. From Fig. 13(b), it can be seen clearly that the highest vibrational temperature exists at the stagnation point that is up to 4000 K. Comparing Fig. 13(a) with Fig. 13(b), we can see that vibration temperatures are signif icantly lower than translational temperatures,namely, there exist apparent thermal nonequilibrium effects.In addition, these two contours are different in temperature distribution, especially in wakes behind the afterbody. For the other cases of α=0° and α=20°, temperatures of the flow field are similar to that for the case of α=10°.

Fig. 14 Surface temperatures at different angles of attack.

Fig. 14 shows the surface temperature contours at three AOAs. These on the left of the f igure show the upper surface temperature in the front view, and the lower surface temperature is on the right. When the AOA increases, as can be observed by comparing Fig. 14(a), (b) and (c), hightemperature area decreases on the upper surface and increases on the lower surface.In the nose of the vehicle,temperatures in the three cases are almost equal to 2200 K,which is attributed to small offset of the stagnation point on the ball head. There is a signif icant increase in temperatures near the f lange by more than 200 K with a 10° increase of the AOA. For clarity, the temperature variation along the center line of the upper and lower surfaces is given in Fig.15.In these f igures,Lvrepresents the length of the vehicle,and z is the coordinate in length direction, whose zero point is translated to the stagnation point of the nose.Compared with the case of α=0°,temperature profiles on the upper surface at α=10° and α=20° present a sharp downtrend. The temperature difference mainly exists in the region of z/Lv∈[0.15,0.9], and the maximum difference is up to 700 K. However, an increase of 10° from α=10° to α=20°does not cause such a sever change like α=0°,which is less than 200 K.In the front part of the vehicle,the region of z/Lv＜0.2 is shown in Fig. 15(a), and the temperature at α=20° is higher than that at α=10°. This phenomenon is most likely due to the heat conduction from the hightemperature lower surface and f langes as the AOA increases from α=10° to α=20°. Lower surface temperatures are shown in Fig.15(b).With the increase of the AOA,the surface temperature near the front edge increases.Comparing α=10°with α=20°,we can see that both curves are similar.The difference of the average temperature is about 300 K.

Based on the flow field parameters (pressure, temperature and composition), the intrinsic radiation of the HTV-2 type vehicle is calculated. Spectra at three AOAs are shown in Fig. 16. The integrated radiances in two bands of the Medium-Wave Infrared (MWIR) (3-5 μm) and Long-Wave Infrared (LWIR) (8-12 μm) are also plotted, which are the most interested bands in infrared detection applications. The spectra in the side view (θ=90°, ψ=0° or 180°) are shown in Fig. 16(a). The spectral intensity at α=0° is higher than that at α=10° but lower than that at α=20°.When the surface emissivity is constant,there are three factors to determine the spectral intensity: spectral bands, visible area and temperature distributions. The spectra in the top view (θ=0°,ψ=0°) are plotted in Fig. 16(b). The intensities are α=0°,α=20° and α=10° in descending order, which is associated with surface temperatures shown in Fig. 15(a). Comparing Fig. 16(a) with Fig. 16(b), the MWIR radiance shows that the intensity in the top view is about five times higher than that in the side view. In addition, the MWIR radiances are one order higher than LWIR radiances. It is indicated that these radiations have a strong spectral selectivity in infrared wavelengths.

Fig. 15 Temperatures on center line of vehicle surfaces (the stagnation point is the origin).

Fig. 16 Radiation intensities of both gas and surface in entire computational domain.

Fig. 17 Radiances in 3-5 μm band at different AOAs.

Fig.17 shows the MWIR radiances at different observation angles. Fig. 17(a) presents the radiances observed at θ=90°and ψ∈[0°,360°].As can be seen,in these three cases the strongest intensity occurs at ψ=67.5° and ψ=292.5° and the weakest is at ψ=180°.It is due to the difference of the visible area and the surface temperature at the different observation angles. With the increase of AOA, the area of the windward side increases. Furthermore, the aerodynamic heating acting on the lower surface of the vehicle will be more serious,meaning that the heat flux and the area of high-temperature regions also increase. In this case, the heat will conduct towards the wing edge, and a great difference of the surface temperature will exist. Compared with the case of α=0°, the radiation intensity at α=20° is lower in ψ∈[0°, 90°] and ψ∈[270°,360°] but higher in ψ∈[90°, 270°]. Fig. 17(b) shows the radiances observed at θ∈[0°, 360°] and ψ=0°. In θ∈[0°, 180°],the intensity at α=20° is almost equal to that at α=10°but is about half of that at α=0°.It is interesting to note that the intensity at α=10° has a profound enhancement at θ∈[180°, 360°] but is lower than that at α=20°. It is explained that these observation angles experience the windward and leeward sides of the vehicle,which are two different regions in the level and distribution of the temperature. The observation angles are in the side view at θ=0°and θ=180°.Thus,radiation intensities are the same in both cases. It is obvious that there are larger high-temperature regions in the upward view(θ=270°) than those in the top view (θ=90°) when they have an approximate equivalent observation area. Besides,compared with the 3-5 μm band, the LWIR radiances have similar regularities of distribution and the integrated intensities reduce by 40%. Thus, the corresponding f igures are not illustrated here. It is shown that the presence of AOA makes the radiance variable dependent strongly on observation angles.

4.3. Angle of attack effects on radiation under transient conditions

In this section, two time-varying AOA schemes are assumed:one is to keep the AOA change with an angular velocity of ωA=1 (°)/s from α=0° to α=30°,and the other is to have a constant angular velocity of ωA=2(°)/s for 15 s and then to maintain a constant AOA (α=30°) for 10 s. The time histories of two cases are the same for 30 s. As mentioned above,the flight altitude is 50 km.In fact,it is bound to make the altitude rise when the AOA increases in the vertical plane (as Route-A shown in Fig. 1). The purpose of the assumption is to simplify calculations and to be easy for comparison of radiation characteristics under the same free stream condition.Such AOAs may also occur within a certain altitude range during the lateral maneuver, such as to avoid no-f ly zones in Route-B shown in Fig. 1. During the boosting phase, a BGV has to be subjected to the aerodynamic heating once it falls off the fairing before entering the predetermined orbit. Flight parameters are uncertain prior to gliding at the altitude of 50 km,so it is of great difficulty to determine the initial conditions for predictions. We make use of the reasonable assumption that the vehicle has a long-time slide at α=0° so as to reach an equilibrium heat exchange on the surface. Thus,steady-state results at α=0°, as obtained in Section 4.1, are selected as the initial condition of transient calculations.

Under the conditions of the time-varying angle of attack,the time response curves of the surface temperature are useful.In the present study, two probes located at the symmetrical plane at z=0.2Lv, on the lower (Point 1) and upper (Point 2) surfaces, are selected to record the temperature history.Heat flux and temperature traces computed at the two points are shown in Fig. 18. As can be seen from Fig. 18(a), the heat flux on the surface reaches the level of 105W/m2in a short time for the two different angular velocities of the AOA.In the first 5 s, the value of the heat flux on the upper surface is negative,which denotes that the heat transfers from the surface to the fluid or solid domains.On the contrary,the positive value represents the enhancement of aerodynamic heating to the lower surface in the presence of a large AOA. For the two angular rates of AOA, the difference of the heat fluxes and temperatures on the upper surface of the vehicle is very small, while these values are very different on the lower surface. This is because the change of the AOA is very small during the time of 1-5 s so that the heat flux of the lower surface is not obvious. With the increase of the AOA, the heat flux on the windward side increases.There is no obvious influence on the upper wall due to the heat conduction inside the structure. It is clear that the growth rate of heat flux increases first, and then decreases over time. The corresponding temperature curve is given in Fig. 18(b). Temperatures at Point 1 and Point 2 on the lower surface rise rapidly and the maximum difference is about 110 K.

Fig. 18 Parameters on upper and lower surfaces with variation of time.

Fig. 19 shows radiances integrated within the 1-3 μm and 3-5 μm bands as a function of time at three observation angles.Fig.19(a),(b)and(c)plot the radiance profiles observed in the side, upward and top views, respectively. It can be seen from Fig. 19(a) that radiation intensities at ωA=2 (°)/s and ωA=1(°)/s have little change in the two bands during the initial 5 s, but after 10 s the radiances at ωA=2 (°)/s are higher than those at ωA=1(°)/s.This phenomenon can be explained by the time-dependence of heat conduction from the lower surface to the upper surface.After 10 s,compared with the case of ωA=1(°)/s,there is a larger windward and more severe aerodynamic heating at ωA=2 (°)/s, which rapidly increases temperatures on lower surfaces and f langes. The maximum difference in intensity between cases of ωA=1 (°)/s and ωA=2(°)/s is about 6.5%.It is indicated that the lower angular velocity of AOA is benef icial to reducing the radiation intensity in the side view.The radiance profiles in two spectral bands,described in Fig.19(b),show a larger rate of change of AOA, which is more conducive to decreasing the intrinsic infrared radiation in the top view. Starting from t=0 s, the decrease rate of the radiance curves at ωA=2 (°)/s increases first and then decreases. In the case of ωA=1(°)/s,the variation trend of the radiation intensity is linear approximately.Comparing the radiance at ωA=2(°)/s with that at ωA=1(°)/s, the maximum difference reaches 2.6×103W/sr in the 1-3 μm band and 1.63×103W/sr in the 3-5 μm band respectively, but both are less than 2.3%. These results show that radiation intensity variation with time are not obvious at an AOA rate of change in the top view.

In Fig. 19(a) and (b), the radiance in the 3-5 μm band is always lower than that in the 1-3 μm band in side and top views. Nevertheless, from Fig. 19(c), it is observed that the upward view radiance integrated within the wavelengths of 3-5 μm at ωA=2 (°)/s is higher than that within the wavelengths of 1-3 μm at ωA=1 (°)/s. At ωA=2 (°)/s, the radiation intensity continues to rise after t=15 s, which is attributed to the cumulative effect of heat accumulation for a long time.It makes the surface temperature rise continuously as well. In addition, the high temperature region in area and levels also increase with the increase of the AOA.The intensity in the 1-3 μm band at ωA=2(°)/s has an increase of 32.2%compared with that at ωA=2(°)/s, which shows that a low AOA rate of change can contribute to the radiance in the top view.

Radiances integrated within the wavelengths of 8-12 μm at three observation angles are plotted in Fig. 20. It can be observed that, comparing the profiles of ωA=1(°)/s and ωA=2(°)/s, the radiances are almost equal in the side and top views. However, the radiance in the upward view at ωA=2(°)/s is 12.1% higher than that at ωA=1(°)/s, but they are much less than other cases shown in Fig. 19. Results show that the AOA rate of change has little effect on the radiance in the 8-12 μm band in the side and top views.These can be explained by the following views. At two angular rates of the AOA, the high-temperature effective area is small in the side and top views. According to the Planck’s law, the peak of the radiation spectrum will move towards the short wave as the temperature increases. This makes the spectral intensity in the 8-12 μm band different. Furthermore, the heat conduction transforming the heat flux on the upwind surface to the structure needs to take a certain amount of time.

5. Conclusions

In this paper,the intrinsic radiation characteristics of an HTV-2 type vehicle with the varying AOA at the altitude of 50 km and Mach number of 16.37 are numerically examined. The computational model includes the Navier-Stokes equations of the flow field, chemical reaction kinetic model, models of physical kinetics, and radiation heat transfer models. The surface temperature is simulated by using a full Navier-Stokes equation coupled gas-solid interaction model. The radiative transfer equation is solved with the LOS algorithm. Two groups of calculational conditions are selected to examine the effect of the AOA on the infrared radiation characteristics of the BGV: (A) steady-state conditions with three AOAs of 0°, 10° and 20°, and (B) transient conditions with two AOA rates of change of ωA=1(°)/s and ωA=2(°)/s. The numerical results reveal the following:

(1) The AOA is an important factor to determine the surface temperature. Under the steady conditions, the surface temperature signif icantly increases for several hundred degrees Kelvin, especially in the regions on the lower surface and part of the front edge, with the increase of the AOA.

(2) The increase of AOA has a great influence on the infrared radiance, which strongly depends on the spectral bands and observation angles.

Further work is needed to study the infrared radiation of the multi-species gas in the high-temperature reacting flows around such a hypersonic vehicle.

Acknowledgement

This work was supported by the National Natural Science Foundation of China (No.51576054).