【作者】 刘超；

【导师】 曹伟；

【作者基本信息】 天津大学 ， 流体力学， 2018， 博士

【摘要】 高超声速飞行器设计涉及两个基本物理量:气动力和气动热,其能否获得与转捩位置能否预测准确相关。对于高马赫数来流,由于激波后气体温度升高、边界层内动能转变为热力学能而导致气体温度升高,气体热物性不再满足量热完全气体的性质,计算时需要考虑高温真实气体效应。转捩位置预测及气动力和气动热计算也需要考虑高温真实气体效应。此外,转捩位置预测还与壁面条件有关,对于长航的高超声速飞行器,等温和绝热壁面条件不再适用,根据实际飞行条件飞行器表面需要考虑采用对流换热边界条件,其中关键问题是提出合适的对流换热系数计算公式。然后,获得某一时刻下壁面温度分布,再对高超声速平板边界层进行稳定性分析和转捩预测。本文选取对流换热边界条件作为壁面条件,考虑真实气体效应,对来流马赫数分别为4.5、6、8和10的高超音速平板边界层进行稳定性分析和转捩预测。主要研究内容和结论如下。1、研究并提出了适合的高超声速平板边界层对流换热系数计算公式,分析研究了对流换热系数值的影响因素和特性。根据飞行器边界层内空气温度的上升,分别考虑空气为量热完全气体模型、比热比随温度而变化(变比热)及空气分子发生离解等真实气体效应,计算验证了高超声速平板层流边界层相似性解的存在性并以之作为标准值验证对流换热系数经验公式的精度。研究发现:对于高超声速平板边界层考虑空气离解等真实气体效应,采用埃克特提出的参考焓法计算的对流换热系数同标准值相对误差较小,如,马赫数小于15,最大相对误差小于4%。而采用常值比热的参考温度法或变比热的参考焓法分别对马赫数大于4和7,则同标准值的误差变大,对马赫数等于15,最大相对误差超过65%。此外,随着马赫数增大、流向长度或壁面温度减小,对流换热系数值将增大。2、研究了高超声速零攻角钝锥边界层对流换热系数计算公式。根据飞行器边界层内空气温度的上升,考虑高温离解的真实气体效应,利用直接数值模拟计算结果作为标准值验证对流换热系数经验公式的精度。对于零攻角钝锥边界层,包括驻点以及轴心角小于60度时的对流换热系数同标准值相对误差较小,最大相对误差不超过10%。尤其在轴心角大于60度时,若压力仍采用根据局部相似性选取的平板模型的来流压力,则对流换热系数同标准值的相对误差随轴心角急剧增大。采用本文提出的来流压力修正方法,结果表明对流换热系数同标准值的误差减小,从超过40%的相对误差减小到15%以下。因此,本文提出的考虑压力补偿的修正公式,在变比热、高温离解情形下都提高了对流换热系数经验公式的计算精度。3、研究壁面采用对流换热边界条件下,高超声速平板壁面温度计算方法,给出了不同时刻壁面温度分布及其随时间的变化规律,还研究了同一流向位置不同高度温度关系、同一高度不同流向位置温度关系。等温壁条件只适用于飞行器飞行初始阶段,而绝热壁面条件几乎不适用。由于壁面温度对转捩位置有很大的影响,因此,为更符合实际飞行情况采用对流换热边界条件是必须的。对于Bi数小于0.1的薄平板,比较了集总参数法与热平衡法计算结果,发现采用这两种方法获得的壁面温度基本一致。对于Bi数大于0.1的厚平板需要考虑平板内的法向导热,因此两种方法获得的壁面温度不再相同。所以,在计算壁面温度分布时应采用热平衡方法计算平板内的法向导热。用集总参数法或热平衡法计算某一时刻的壁面温度分布时,发现不同高度之间、不同流向位置之间,均存在定量的关系,可以给出任一时刻、任一高度和流向位置的壁面温度,减少计算时间。4、对于高超声速流,考虑变比热、高温离解,计算研究了的平板边界层基本流剖面,用LST分析稳定性及预测转捩位置。研究发现,不同的壁面条件基本流剖面、中性曲线有较大差异,尤其在靠近板前缘流向位置上的差异更为明显,而且在相同流向位置不稳定波增长率也不同。通过比较不同边界条件下的N值曲线发现,在流向位置2m的位置上,等温或绝热壁面温度条件下的最大扰动幅值与对流换热边界条件下的结果相差40%以上,而且绝热壁面温度条件下的偏差有沿流向递增的趋势。因此,可以推测对于长航高超音速流的飞行器,壁面采用等温或绝热条件预测的转捩位置与真实情况应有较大误差,而采用对流换热边界条件所预测的转捩位置可能更准确。更多还原

【Abstract】 The design of hypersonic vehicle involves two basic physical quantities: aerodynamic force and aerothermal force.Whether the physical quantities can be obtained or not depends on whether the transition position can be predicted accurately.For high Mach number,gas temperature increases due to the increase of gas temperature after shock wave and the transformation of kinetic energy into thermodynamic energy in the boundary layer.Thermal properties of gas no longer satisfy the properties of calorically perfect gas,so the real gas effect at high temperature should be taken into account in calculation.The calculation of transition location,aerodynamic force and aerothermal force also need to consider the high temperature real gas effect.In addition,the prediction of transition position is also related to wall conditions.Isothermal and adiabatic wall conditions are no longer applicable for long time flight hypersonic vehicles.According to the actual flight conditions,the boundary conditions of convective heat transfer should be considered on the aircraft surface.The key problem is to put forward an appropriate formula for calculating convective heat transfer coefficient.Then,the temperature distribution of the wall at a certain time is obtained,and then the stability analysis and the calculation transition of the boundary layer around flat plate in hypersonic are carried out.Considering the real gas effect,the boundary conditions of convective heat transfer are taken to analyze the stability and transition prediction of the hypersonic plate boundary layer with Mach numbers of 4.5,6,8 and 10,respectively.The main research contents and conclusions are as follows:1、A suitable formula for calculating the convective heat transfer coefficient in the hypersonic plate boundary layer is studied and put forward.The influencing factors and characteristics of the convective heat transfer coefficient are analyzed.Considering the real gas effects such as air as calorically perfect gas,molecular vibration excitation(specific heat is a temperature function)and air molecule dissociation,the existence of similarity solutions for hypersonic laminar boundary layer is verified,and the accuracy of empirical formulas for convective heat transfer coefficient was checked basing on the similar solution.It is found that for hypersonic plate boundary layer,considering the real gas effects such as air dissociation,the relative error between the convective heat transfer coefficient calculated by the reference enthalpy method and the standard value is small.For example,the Mach number is less than 15,and the maximum relative error is less than 4%.The convective heat transfer coefficients with constant specific heat and variable specific heat are calculated by reference temperature method or reference enthalpy method,respectively.The relative error with the standard values can not be ignored when Mach number is higher than 4 and 7,respectively.The maximum relative error is more than 65% at the Mach number 15.In addition,with the increase of Mach number,the length of flow direction or the decrease of wall temperature,the value of convective heat transfer coefficient will increase.2、The calculation formula of convective heat transfer coefficient in hypersonic blunt cone boundary layer is studied.The real gas effect is considered according to the different surface temperature of the aircraft.The accuracy of the empirical formula of convection heat transfer coefficient is studied by using the direct numerical simulation results as the standard values.For blunt cone boundary layer,the relative error between the convective heat transfer coefficient and the standard value is small when the axis angle is less than 60 degrees,including the stagnation point.When the axis angle is higher than 60 degrees,the relative error between the convective heat transfer coefficient and the standard value increases sharply with the axis angle if the inflow pressure is still selected according to the plate model.A modified formula for selecting incoming pressure is proposed in this paper.The results show that the error between the convective heat transfer coefficient and the standard value can be reduced from 40% to less than 15% by using the proposed correction of inflow pressure.The modified inflow pressure formulas presented in this paper can improve the accuracy of empirical formulas for convective heat transfer coefficients in the case of calorically perfect gas,variable specific heat and high temperature dissociation.3、The wall temperature calculation method of hypersonic flat plate under convective heat transfer boundary conditions is studied.The wall temperature distribution at different time and its variation with time are given.The temperature relationship at different heights and different flow directions is also studied.The isothermal wall condition is only applicable to the initial flight time of the vehicle,while the adiabatic wall condition is hardly applicable.Because the wall temperature has a great influence on the prediction of transition position,it is necessary to adopt convective heat transfer boundary conditions in order to meet the actual flight conditions.For thin plates with Bi number less than 0.1,the results of lumped parameter method and heat balance method are compared.It is found that the wall temperature obtained by these two methods is basically the same.For a thick plate with Bi number higher than 0.1,the normal heat conduction in the plate should be considered,so the wall temperature obtained by the two methods is different.Therefore,when calculating the wall temperature distribution,the thermal balance method should be used to calculate the normal heat conduction in the plate.When calculating the wall temperature distribution at a certain time by lumped parameter method or heat balance method,it is found that there is a quantitative relationship between different heights and different flow direction positions.The wall temperature at any time,at any height and flow direction can be given with the quantitative relationship,and the calculation time can be reduced.4、The basic flow profile,stability analysis and transition location prediction of hypersonic plate boundary layer with real gas effect are calculated and studied.It is found that the basic flow profiles and neutral curves are quite different under different wall conditions,especially in the flow direction near the leading edge of the plate,and the growth rates of unstable waves are different at the same flow direction.By comparing the N values of disturbance waves under different boundary conditions,it is found that for the maximum disturbance amplitude of 2 m in the direction of flow,the difference between the disturbance amplitude under isothermal or adiabatic wall temperature conditions and the results under convective heat transfer boundary conditions is more than 40%,and the deviation under adiabatic wall temperature conditions tends to increase along the direction of flow.Therefore,it can be inferred that the transition position predicted by isothermal or adiabatic conditions on the wall for long time flight hypersonic vehicles should be quite different from the real situation,and the transition position predicted by convective heat transfer boundary conditions may be more accurate.更多还原