Extrapolation-to-flight of aerodynamic heating measurements and determination of in-flight radiation-equilibrium surface temperature in hypersonic/high enthalpy flow conditions

The previously demonstrated success of the reference enthalpy concept in heat transfer prediction at hypersonic flow conditions is utilized herein to propose a cost-effective methodology for extrapolation-to-flight of Stanton number measurements (or baseline computational results), and the determination of radiation-equilibrium surface temperatures that develop on actual vehicle surfaces during hypersonic/high enthalpy flight conditions. The methodology couples the (analytical) generalized reference enthalpy solution with Euler computations (providing input data along the edge of thin boundary layers) and is, therefore, significantly cheaper and more efficient than the execution of full Navier–Stokes computations that are presently incorporated, particularly so in the thermo-chemically active high enthalpy flow regime. The validity of the proposed methodology is demonstrated in a first step by means of two-dimensional test cases, whereby extrapolated data accuracy is better than 20%.

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热喷干扰气体模型对飞行器气动特性影响分析

针对不同气体模型对高超声速飞行器喷流反作用控制系统(RCS)热喷干扰流场模拟的计算效率和准确性问题, 基于喷流燃气物理化学模型, 通过数值求解含化学反应源项的三维N-S方程, 建立了飞行器RCS热喷干扰流场数值模拟方法, 分别采用化学反应流、反应冻结流、二元异质流以及空气喷流四种气体模型开展了典型外形热喷干扰流场的数值模拟, 研究了不同气体模型对热喷干扰流场结构、飞行器气动力热特性的影响, 分析了不同马赫数、飞行高度下的变化规律. 研究表明: 化学反应流模型计算精度较高, 计算与风洞试验数据的吻合程度优于其他三种简化模型; 在本文的低空条件下, 采用简化模型进行热喷干扰流场数值模拟, 会低估分离区大小, 使飞行器气动力特性预测出现偏差, 同时也会低估表面热环境, 对防热系统设计不利, 随着马赫数增加, 简化模型对气动力热特性预估的误差进一步增大, 同时不同简化模型之间的差异也进一步增大; 飞行高度较高时, 模型之间的差异减小, 此时可采用简化模型进行计算以提高计算效率. 本文的研究结果可为飞行器热喷干扰流场数值模拟及喷流反作用控制系统设计提供参考.      

On the applicability of some approximate similitude laws in hypersonic aerodynamics

The range of applicability of some similitude laws for heat transfer, friction and drag coefficients is discussed on the basis of numerical solutions of the complete viscous shock layer equations describing hypersonic flow past blunt bodies. Moscow. Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No.2, pp. 121–130, March–April, 1994.     

Approximate analytical solutions for heat fluxes in three-dimensional hypersonic flow over blunt bodies

Analytical expressions for the heat flux divided by its value at the stagnation point which depend on the geometric parameters invariant with respect to the choice of the coordinate system, as well as expressions depending on the geometry and the pressure on the surface which have a wider applicability range are obtained in the problem of three-dimensional hypersonic flow over blunt bodies at large and moderate Reynolds numbers. These formulas are derived by solving the thin viscous shock layer equations for a perfect gas using the integral method of successive approximations developed by the author. The accuracy and the range of applicability of the analytical solutions are estimated by comparing them with numerical solutions. On the basis of comparisons with numerical solutions for multicomponent chemically nonequilibrium air at altitudes from 90 to 50 km of the spacecraft reentry trajectory in the Earth’s atmosphere it is shown that the formulas obtained can be used for calculations of the heat flux on an ideal catalytic surface of bodies in hypersonic chemically reacting gas flow.     

An enthalpy‐preserving shock‐capturing term for residual distribution schemes

In this contribution, we investigate strategies to perform shock‐capturing computation of steady hypersonic flow fields by means of residual distribution schemes. The ultimate objective is the computation of flow solutions for which the correct upstream enthalpy value is recovered in the postshock region. To this end, the parallelism existing between the classical Bx scheme and the stabilized finite element techniques is exploited. The simple Lax‐Friedrichs dissipation term is leveraged to build two new residual distribution schemes. Upon testing on both inviscid and viscous steady problems, solutions obtained with one of the two schemes are shown to recover the correct upstream total enthalpy level in the postshock region. This last scheme provides also improved wall pressure and skin friction predictions; heat transfer predictions are, unfortunately, similar to those offered by the Bx scheme. A conjecture for explaining this behavior is exposed.     

Simulation of supersonic and hypersonic flows

A simple convection algorithm for simulation of time-dependent supersonic and hypersonic flows of a perfect but viscous gas is described. The algorithm is based on conservation and convection of mass, momentum and energy in a grid of rectangular cells. Examples are given for starting flow in a shock tube and oblique shocks generated by a wedge at Mach numbers up to 30·4. Good comparisons are achieved with well-known perfect gas flows.     

Nonequilibrium excitation of internal molecular degrees of freedom in the shock layer during hypersonic flight

A kinetic scheme of processes including the formation and quenching of electronically and vibrationally excited particles is proposed for the shock layer adjacent to the surface of a body flying at hypersonic speed. We present results of a numerical calculations for the stagnation point obtained under the thin viscous shock layer approximation for space shuttle flight conditions.We show that the release of atom recombination energy into the internal molecular degrees of freedom and the finite rate of relaxation reduce the calculated heat flux by 20 %.This article was processed using Springer-Verlag T_EX Shock Waves macro package 1.0 and the AMS fonts, developed by the American Mathematical Society.     

克服“高超声障''的途径”

在高超声速飞行条件下, 流入冲压发动机燃烧室并降至低速的空气温度, 随着飞行马赫数增 加升得愈来愈高. 燃料与高温空气混合燃烧释放的化学能将部分转化为解离能. 这些解离能 在长度受限的尾喷管中难以充分复合形成推力, 使冲压发动机性能随飞行马赫数增大而急剧 下降. 导致冲压发动机不适应高超声速飞行器的推进要求. 将此定名为``高超声障'. 半个 世纪以来, 广泛采用``超声速燃烧'降低流入燃烧室的空气温度来克服这种障碍. 虽已取得 不少进展, 然而关键性难点仍需继续攻克. 为了多途径促进吸气推进高超声速飞行的实现, 提出克服``高超声障'的另一种思路：保持现有冲压发动机吸气与燃烧方式, 通过催化促进 燃气解离组分在尾喷管膨胀过程中的复合, 增大冲压发动机的推力, 达到满足高超声速飞行 器的推进要求.     

高速双锥绕流中热化学与输运模型影响研究

激波与边界层之间相互作用是高超声速飞行中的常见现象,对飞行器气动性能与飞行安全至关重要.对于高焓来流,流场中通常存在复杂的物理化学现象,此时准确模拟流场中激波边界层相互作用的难度大,相关物理化学建模仍有待进一步考察和研究.本文针对最近文献中纯净空气高超声速双锥绕流实验开展数值研究,分别研究了不同热化学模型与输运模型对壁面压力与热流的影响.热力学模型包括完全气体、热力学平衡和非平衡模型,化学模型包括冻结和非平衡化学模型,输运模型包括经典的Wilke/Blottner/Eucken模型与更加复杂的Gupta/SCEBD模型,以及考虑壁面催化/非催化影响的模型.计算了6个不同算例,涵盖了低焓至高焓来流等不同工况.壁面压力与热流的数值计算结果与实验结果符合较好;对于低焓来流,计算结果主要受到分子内能分布的影响,输运模型对计算结果的影响不大;对于高焓来流,一方面计算结果受到化学反应与壁面催化的影响较大,另一方面不同输运模型对计算结果的影响也更加明显.      

Analytic investigation of friction and heat transfer in the neighborhood of a three-dimensional stagnation point at low and moderate Reynolds numbers

A study is made of hypersonic three-dimensional flow of a viscous gas past blunt bodies at low and moderate Reynolds numbers with allowance for the effects of slip and a jump of the temperature across the surface. The equations of the three-dimensional viscous shock layer are solved by an integral method of successive approximation and a finite-difference method in the neighborhood of the stagnation point. In the first approximation of the method an analytic solution to the problem is found. Analysis of the obtained solution leads to the proposal of a simple formula by means of which the calculation of the heat flux to a three-dimensional stagnation point is reduced to the calculation of the heat flux to an axisymmetric stagnation point. A formula for the relative heat flux obtained by generalizing Cheng's well-known formula [1] is given. The accuracy and range of applicability of the obtained expressions are estimated by comparing the analytic and numerical solutions. Three-dimensional problems of the theory of a supersonic viscous shock layer at small Reynolds numbers were considered earlier in [2–5] in a similar formulation but without allowance for the effects of slip.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 2, pp. 143–150, March–April, 1988.     

高超声速高焓条件下的内嵌式温敏漆测量方法

热流密度点测量结果并不能完全反映详细的热流分布特征, 尤其是针对热流梯度较大、热流分布复杂的区域, 需要热流密度场测量技术以获取全场精细的热流分布特征. 应用温敏漆测量热流密度场的方法得到了广泛应用, 但实验条件来流总温较低, 与真实飞行环境存在明显差异, 真实飞行条件下的辐射效应严重限制了温敏漆技术的应用. 针对高超声速高焓条件下缺乏热流密度场测量方法的难题, 提出了内嵌式温敏漆测量方法, 基本思想是利用温敏漆测量内壁面温度的变化历程结合热传导反问题的求解确定热流密度. 本文详细介绍了内嵌式温敏漆测量方法的测量原理、测量系统构成、数据处理方法、设计原则及该测量方法的优势. 针对高超声速风洞实验中常见的阶跃、线性和局部突变等热流密度分布进行了数值验证, 验证了内嵌式温敏漆测量方法的可行性, 并分析了风洞实验温度测量精度及噪声对测量结果的影响. 内嵌式温敏漆测量方法可用于测量高超声速真实飞行环境下细致的气动热特征, 扩展了温敏漆测量方法的应用范围, 解决了高超声速高焓条件下缺乏热流密度场测量方法的难题.      

The hypersonic Mach number independence principle in the case of viscous flow

The hypersonic Mach number independence principle of Oswatitsch is important for hypersonic vehicle design. It explains why, above a certain flight Mach number (M _∞ ≈ 4−6, depending on the body shape), some aerodynamic properties become independent of the flight Mach number. For ground test facilities this means that it is sufficient for the Mach number in the test section to be high enough, that Mach number independence exists. However, the principle was derived for calorically perfect gas and inviscid flow only. In this paper a theoretical study for blunt bodies in the case of viscous flow is presented. We provide numerical results which give insight into how attached viscous flow behaves at high Mach numbers. The flow past an axisymmetric configuration is analysed by applying a coupled Euler/second-order boundary-layer method. Wall boundaries are treated by assuming an adiabatic or radiation-adiabatic wall for laminar flow. Calorically perfect or equilibrium air is accounted for. Lift, drag, and moment coefficients, and lift-to-drag ratios are given for several combinations of flight Mach number and altitude, i.e. Reynolds number. For blunt bodies considered here, which are pressure dominated, Mach number independence occurs for the adiabatic wall, but not for the radiation-adiabatic wall assumption.     

The coefficient of regeneration of the enthalpy in a three-dimensional laminar boundary layer

Self-similar solutions of the equations of a three-dimensional laminar boundary layer are of interest from two points of view. In the first place, they can be used to construct approximate calculating methods, making it possible to analyze several variants and to consider complex flows, in which it is impossible to neglect the interaction between the boundary layer and the external flow (for example, in the region of hypersonic interaction [1–3]). In the second place, the analysis of self-similar solutions permits clarifying the effect of individual parameters on one or another characteristic of the boundary layer and representing this effect in predictable form. One of the principal characteristics of a three-dimensional boundary layer, as also of a two-dimensional, is the coefficient of regeneration of the enthalpy. The value of this coefficient is needed for determining the temperature of a thermally insulated surface, as well as for finiing the real temperature (or enthalpy) head, which determines the value of the heat flux from a heated gas to the surface of the body around which the flow takes place. The article presents the results of calculations of the coefficient of regeneration of the enthalpy for locally self-similar solutions of the equations of a three-dimensional boundary layer, forming with flow around a cylindrical thermally insulated surface at an angle. It is clarified that the dependence of the coefficient of regeneration of the enthalpy on the determining parameters is not always continuous.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 1, pp. 60–63, January–February, 1973.     

Numerical simulation of hypersonic flow around a sharp cone

A hypersonic viscous flow in the shock layer near sharp cones is considered. The profiles of density and velocity, the slopes of the shock wave, and the pressures and heat fluxes calculated on the basis of the full viscous shock layer equations are compared with available experimental and theoretical data.     

Asymptotic solutions of the two-dimensional equations for a thin viscous shock layer in a rarefied gas

Two-dimensional hypersonic rarefied gas flow around blunt bodies is investigated for the continuum to free-molecular transition regime. In [1], as a result of an asymptotic analysis, three rarefied gas flow regimes, depending on the relationship between the problem parameters, were detected and one of these regimes was investigated. In the present study, asymptotic solutions of the thin viscous shock layer equations at small Reynolds numbers are obtained for the other two flow regimes. Analytical expressions for the heat transfer, friction and pressure coefficients are obtained as functions of the incident flow parameters and the body geometry and temperature. As the Reynolds number tends to zero, the values of these coefficients approach their values in free-molecular flow. The scaling parameters of hypersonic rarefied gas flow around bodies are determined for different regimes. The asymptotic solutions are compared with the results of direct Monte Carlo simulation.     

On the influence of elevated surface temperatures on hypersonic shock wave/boundary layer interaction at a heated ramp model

Although important flow parameters as Mach number, Reynolds number and total enthalpy can be reproduced in most hypersonic experiments quite well, due to different surface temperature effects in wind tunnel and flight, scaling as well as specific flow properties of shock wave/boundary layer interactions are different. This especially holds for short-duration facilities like, e.g. shock tunnels where due to short running times the models remain more or less at ambient temperature. To overcome this shortcoming, an experimental study has been conducted using a preheatable ramp model with 15° ramp angle. This allowed us to adjust the surfaces to an arbitrary temperature just before the experiment started. Pressure and heat flux measurements clearly showed the effect of varying surface and free stream temperatures. These results are supported by schlieren pictures and infrared measurements. The comparison of the measurements with theoretical and numerical results shows a good agreement. Separation bubble scaling laws proposed by Katzer and Davis have been applied and partially confirmed using the local conditions of the boundary layer at separation.     

高焓湍流边界层壁面摩阻产生机制分析

高超飞行器在中低空以极高马赫数飞行时,飞行器表面会遇到湍流与高温非平衡效应耦合作用的新问题.这种高焓湍流边界层壁面摩阻产生机制是新型高超声速飞行器所关注的基础科学问题,厘清此产生机制可以为减阻方法的设计提供指导,具有重要的工程实用价值.本文选取高超声速飞行时楔形体头部斜激波后的高焓流动状态,开展了考虑高温非平衡效应的湍流边界层直接数值模拟研究,并设置同等边界层参数下的低焓完全气体湍流边界层流动作为对比,采用RD (Renard&Deck)分解技术研究了高焓湍流边界层摩阻的主要产生机制,对摩阻产生的主要贡献项积分函数分布进行了详细分析,研究了高温非平衡效应对摩阻产生的影响规律;采用象限分析技术,研究了摩阻分解湍动能生成项的主导流动事件.计算结果表明,高温非平衡效应会使得壁面摩阻脉动条带的流向和展向尺寸均减小.分子黏性耗散项和湍动能生成项是高焓湍流边界层摩阻生成的主要流动过程.分子黏性耗散项主要作用在近壁区,高焓流动的分布与低焓流动存在差异.象限分析表明,上抛和下扫运动是影响摩阻分解中湍动能生成项的主导事件.     

Heating enhancement caused by a transverse control jet in hypersonic flow

Experiments are reported in which the heat flux distribution near a single circular, sonic transverse jet on a flat plate exposed to a hypersonic (Mach 6.7) freestream flow was quantitatively measured using thermochromic liquid crystals. The freestream conditions were such that the boundary layer growth on the plate ahead of the jet was laminar. The results indicate that the interaction of the jet with the freestream flow created a complex flowfield with regions of separation and reattachment which caused localised enhancements to the heat flux upstream and to the side of the jet, the magnitudes of which were sensitive to both jet plenum pressure and jet gas composition. Received 28 August 1996 / Accepted 6 June 1997     

On air-chemistry reduction for hypersonic external flow applications

In external hypersonic flows, viscous and compressibility effects generate very high temperatures leading to significant chemical reactions among air constituents. Therefore, hypersonic flow computations require coupled calculations of flow and chemistry. Accurate and efficient computations of air-chemistry kinetics are of much importance for many practical applications but calculations accounting for detailed chemical kinetics can be prohibitively expensive. In this paper, we investigate the possibility of applying chemical kinetics reduction schemes for hypersonic air-chemistry. We consider two chemical kinetics sets appropriate for three different temperature ranges: 2500 K to 4500 K; 4500 K to 9000 K; and above 9000 K. By demonstrating the existence of the so-called the slow manifold in each of the chemistry sets, we show that judicious chemical kinetics reduction leading to significant computational savings is possible without much loss in accuracy.     

Heat transfer to blunt-edged swept wings at angle of attack in hypersonic flow

An approximate analytic solution is obtained for the relative heat fluxes on the lateral surface of swept wings of infinite span in a hypersonic viscous gas flow at angles of attack and yaw. The accuracy of the relations obtained is estimated on the basis of a comparison with numerical solutions. Moscow. Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No. 4, pp. 170–179, July–August, 1994.