一类新型激波捕捉格式的耗散性与稳定性分析

高超声速流动是高复杂性的可压缩黏性流动, 其中存在激波、剪切层、激波/激波干扰、激波/边界层干扰、旋涡与分离流动等复杂流场结构. 对其进行准确模拟需要使用低耗散、强鲁棒性的激波捕捉方法. 本文基于一类新型的通量项分裂方法, 提出了一种耗散低且鲁棒性好的激波捕捉格式K-CUSP-X. 对该格式的耗散性和激波稳定性进行了详细的理论分析, 得到了格式激波稳定的数值条件. 推论认为, 迎风格式激波稳定的充分条件为速度扰动量具有衰减性, 数值实验验证了该推论. 研究表明, 该格式与Toro提出的通量分裂格式K-CUSP-T相比, 在保证精确捕捉接触间断的同时, 又具有更好的稳定性, 在激波处不会产生“红玉”现象.     

高超声速层流绕三维压缩拐角的数值模拟

通过数值模拟研究了高超声速来流绕过压缩拐角的层流分离三维流动特性.数值方法采用三维N-S方程,结合2阶精度Roe格式以及分区结构网格有限体积法进行离散.数值模拟的空间激波结构与实验纹影结果符合较好;激波/边界层干扰区内3条纵向线上的计算压力分布与实验结果进行了对比分析,计算获得在三维楔侧面存在低压力区,与实验结果反映的规律一致,计算结果表明低压力区是由楔体侧缘尖端发起的二次涡的抽吸作用造成的.此外,在楔体后端尾流区的低压沿边界层内的亚声速区往上游传递了一定距离.      

前缘曲率对三维边界层内被激发出非定常横流模态的影响研究

三维边界层感受性问题是三维边界层层流向湍流转捩的初始阶段,是实现三维边界层转捩预测与控制的关键环节.在高湍流度的环境下,非定常横流模态的失稳是导致三维边界层流动转捩的主要原因;但是,前缘曲率对三维边界层感受性机制作用的研究也是十分重要的课题之一.因此,本文采用直接数值模拟方法研究在自由来流湍流作用下具有不同椭圆形前缘三维（后掠翼平板）边界层内被激发出非定常横流模态的感受性机制;揭示不同椭圆形前缘曲率对三维边界层内被激发出非定常横流模态的扰动波波包传播速度、传播方向、分布规律、感受性系数以及分别提取获得一组扰动波的幅值、色散关系和增长率等关键因素的影响;建立在不同椭圆形前缘曲率情况下,三维边界层内被激发出非定常横流模态的感受性问题与自由来流湍流的强度和运动方向变化之间的内在联系;详细分析了不同强度各向异性的自由来流湍流在激发三维边界层感受性机制的物理过程中起着何种作用等.通过上述研究将有益于拓展和完善流动稳定性理论,为三维边界层内层流向湍流转捩的预测与控制提供依据.     

转捩与湍流对激波边界层干扰及底部流动结构的影响

为研究转捩与湍流对激波边界层干扰及底部流动结构的影响,文章选取了二维与三维高超声速双斜面进气道模型与大钝头着陆器模型,并使用γ-Re_θ转捩模型开展数值模拟研究.研究表明,对于二维进气道模型,随着前缘钝度的增加,激波边界层干扰位置前移,分离区变大,与层流流动情况相比,有转捩流动发生时,激波边界层干扰位置后移,同时分离流动强度变弱,分离区缩小;对于三维进气道模型,其拐角附近的分离流动呈现明显的三维特征,转捩流动也存在三维流动结构,与静风洞状态相比,噪音风洞状态下,有转捩流动发生,对壁面热流影响较大,对激波系影响很小.对于着陆器模型,底部流动发生转捩,使得底部流动由不稳定非定常的流动结构变为稳定定常的流动结构,这有益于姿态控制设计.      

来流边界层效应下斜坡诱导的斜爆轰波

以超声速预混气中的斜爆轰波为研究对象,对其在来流边界层效应下的特性进行了实验研究.在马赫数为3的超声速预混风洞中,通过斜坡诱导产生了斜爆轰波.当来流的当量比较低时,预混气中产生的是化学反应锋面与激波面非耦合的激波诱导燃烧现象.此时边界层分离区中的化学反应放热将使分离区尺度显著增大,流场非定常性显著增强,激波位置剧烈振荡.当来流的当量比较高时,预混气将产生斜爆轰波.此时边界层分离区会影响到斜爆轰波起爆时的形态.在小尺度分离区下,斜爆轰波起爆时呈突跃结构(有横波);在中等尺度分离区下,流场固有的非定常性使斜爆轰波呈间歇突跃结构;在大尺度分离区下,斜爆轰波起爆则呈完全的平滑结构(无横波).     

局域能量注入对高超声速进气道流动影响研究

研究了局域能量脉冲注入条件下高超声速进气道流场的扰动情况。数值模拟采用三维雷诺平均N-S方程,分别利用ROE格式和二阶中心格式对对流通量和粘性通量进行离散处理;用高斯-赛德尔隐式格式对方程进行时间推进求解,采用k-ε两方程模型用于湍流的数值模拟。开展了高超风洞平板流场能量注入实验,获取了高速纹影图像,并对实验结果与计算结果进行比较。研究表明,能量注入产生的冲击波能与高超流动产生的斜激波发生强烈干扰,脉冲能量的引入可能引起高超声速进气道流量俘获率产生剧烈震荡,从而导致进气道流场的性能急剧下降。     

内聚锥形激波的非均匀强化与结构演变特征

以高超声速内转式进气道流动中的激波汇聚问题为背景,考虑工程实际中的来流和壁面几何条件这两个关键因素,分别提出了以来流攻角为研究参数的非轴向来流内锥流动模型,和以长/短轴比为研究参数的椭圆入口内锥流动模型.采用激波风洞实验观测和数值模拟相结合的方法,揭示了两类流动中激波的非均匀汇聚特征.结果表明:由来流攻角引起的激波初始...     

壁面局部吹吸边界层感受性的数值研究

目前理论、实验以及数值模拟主要研究自由来流中的小扰动与壁面局部粗糙相互作用激发边界层感受性问题. 但是, 针对自由来流湍流与壁面局部吹吸相互作用诱导边界层感受性的相关报道甚少. 本文采用直接数值模拟和快速傅里叶变换的方法, 数值研究了二维平板壁面具有局部吹吸的边界层感受性问题. 结果发现, 在二维边界层内能找到一组被激发产生的Tollmien-Schlichting(T-S)波波包的包络序列以及从波包中能够分离出一组稳定的、中性的和不稳定的T-S波, 证明了二维边界层内感受性现象的存在性. 经数值计算获得了T-S波波包传播的群速度; 并建立了自由来流湍流强度、壁面局部吹吸强度和长度与二维边界层感受性之间的关系, 获得了与Dietz感受性实验相类似的结论. 另外, 还发现在自由来流湍流与壁面局部吹、吸相互作用下能诱导二维边界层内产生相位相反的T-S波. 依据这一理论机理来优化设计局部吹吸装置, 不但能促使层流向湍流转捩的提前, 也可以延迟转捩过程的发生, 达到控制湍流运动的目的.     

高超声速椭圆锥边界层横流转捩特性大涡模拟

横流效应显著影响高超声速飞行器的三维边界层转捩过程, 深化对该流动机制的认识有助于提升和改善飞行器气动性能及热力学环境. 针对HIFiRE5椭圆锥绕流问题, 采用大涡模拟方法计算分析了超声速边界层横流转捩特性, 并揭示其中的流动机理. 参考HIFiRE5风洞模型试验条件, 数值模拟中椭圆锥来流入口处施加人工速度扰动以激发边界层内不稳定扰动波, 进而预测了高超声速边界层流动横流失稳、转捩过程等基本流动特征, 并基于转捩热流分布形态对比, 获得了与试验数据基本吻合的计算结果. 研究发现, 椭圆锥中心线流动汇聚形成的流向涡结构非常容易失稳, 另外在中心线及侧缘之间的中部区域存在较强的横流不稳定性, 两种机制共同作用影响边界层转捩过程. 此外, 分析了来流扰动幅值对边界层横流失稳转捩的影响, 并发现静来流条件下, 横流区域出现两组独立的定常横流涡结构, 而强噪声来流条件下, 中心线主涡和中部横流涡均发生失稳转捩, 且在椭圆锥表面形成多峰状的转捩阵面. 最后, 深入分析流场的压力脉动动力学特性, 揭示了三维边界层发生失稳转捩的非线性演化机制.      

跨音速轴流风扇转子叶顶泄漏流的数值研究

采用数值模拟方法研究了不同间隙,不同流量工况下叶顶泄漏流非定常流动特征,发现在研究的三个间隙中,只有当间隙大于或等于设计间隙时,流动才会出现非定常性.随着流量的减小,泄漏涡轨迹前移,当泄漏涡轨迹到达相邻叶片压力面时,影响压力面压力分布,打破流场静态平衡,引起叶顶流场及激波位置、强度发生非定常波动.     

前缘曲率变化对平板边界层感受性问题的影响

边界层感受性问题是层流向湍流转捩的初始阶段,是实现边界层转捩预测和控制的关键环节.目前已有的研究成果显示,在声波扰动或涡波扰动作用下前缘曲率变化对边界层感受性机制有着显著的影响.本文采用直接数值模拟方法,研究了在自由来流湍流作用下具有不同椭圆形前缘平板边界层感受性问题,揭示椭圆形前缘曲率变化对平板边界层内被激发出Tollmien-Schlichting (T-S)波波包的感受性机制以及波包向前传播群速度的影响;通过快速傅里叶分析方法从波包中提取获得了不同频率的T-S波,详细分析了前缘曲率变化对不同频率的T-S波的幅值、色散关系、增长率、相速度以及形状函数的作用;确定了前缘曲率在平板边界层内激发T-S波的感受性过程中所占据的地位.通过上述研究能够进一步认识和理解边界层感受性机制,从而丰富和完善了流动稳定性理论.     

Distributed two-dimensional boundary-layer receptivity to non-stationary vortical disturbances in the presence of surface roughness

The distributed (over the longitudinal coordinate) excitation of two-dimensional (2D) Tollmien — Schlichting (TS) waves by weak non-stationary free-stream vortices propagating along the edge of the laminar boundary layer developing over a surface with small-amplitude 2D roughness is examined. The vorticity vector of the free-stream vortices was oriented over the span of the model, i. e., did not depend on the transverse coordinate. The theoretical analysis of the excitation mechanism reported in [1] was refined to develop, around it, a procedure making it possible to experimentally determine the coefficients of distributed vortical receptivity of the flow and the coefficients of “vortex-roughness” receptivity by fitting the experimental distributions with analytical solutions. Under conditions with controllable excitation of disturbances, a detailed hot-wire study of free-stream disturbances and boundary-layer disturbances at several vortex frequencies and at several surface-roughness periods was performed, and the shape of the controllable surface roughness was measured. The point-source method was employed to experimentally examine the characteristics of linear three-dimensional (3D) stability of the flow to TS waves, necessary for determination of the coefficients of distributed receptivity. It was found that the free-stream vortices with transverse orientation of the vorticity vector excited boundary-layer TS waves via two receptivity mechanisms: (a) on the smooth surface (due to natural non-uniformity of the flow) and (b) during interaction of the vortices with the surface roughness. The developed approach was used to experimentally estimate the amplitudes and phases of the coefficients of both types of distributed vortical receptivity as dependent on problem parameters. The absolute values of both types of receptivity coefficients were found to rapidly grow in value with increasing vortex frequency. It is shown that the most efficient excitation of TS waves is observed in the situation with satisfied resonance conditions for streamwise vortex, surface-roughness, and TS-wave streamwise wavenumbers, resulting in strong deviation of the increments of the TS waves from the linear-stability increments. Under no-resonance conditions, only amplitude beats of boundary-layer disturbances were observed. This work was financialy supported by the Russian Foundation for Basic Research (Grant No. 03-01-00299).     

Receptivity to free-stream disturbance waves for hypersonic flow over a blunt cone

A high-order shock-fitting finite difference scheme is studied and used to do direction numerical simulation (DNS) of hypersonic unsteady flow over a blunt cone with fast acoustic waves in the free stream, and the receptivity problem in the blunt cone hypersonic boundary layers is studied. The results show that the acoustic waves are the strongest disturbance in the blunt cone hypersonic boundary layers. The wave modes of disturbance in the blunt cone boundary layers are first, second, and third modes which are generated and propagated downstream along the wall. The results also show that as the frequency decreases, the amplitudes of wave modes of disturbance increase, but there is a critical value. When frequency is over the critial value, the amplitudes decrease. Because of the discontinuity of curvature along the blunt cone body, the maximum amplitudes as a function of frequencies are not monotone. Supported by the National Natural Science Foundation of China (Grant Nos. 10632050 and 10502052)     

High-order non-uniform grid schemes for numerical simulation of hypersonic boundary-layer stability and transition

The direct numerical simulation of receptivity, instability and transition of hypersonic boundary layers requires high-order accurate schemes because lower-order schemes do not have an adequate accuracy level to compute the large range of time and length scales in such flow fields. The main limiting factor in the application of high-order schemes to practical boundary-layer flow problems is the numerical instability of high-order boundary closure schemes on the wall. This paper presents a family of high-order non-uniform grid finite difference schemes with stable boundary closures for the direct numerical simulation of hypersonic boundary-layer transition. By using an appropriate grid stretching, and clustering grid points near the boundary, high-order schemes with stable boundary closures can be obtained. The order of the schemes ranges from first-order at the lowest, to the global spectral collocation method at the highest. The accuracy and stability of the new high-order numerical schemes is tested by numerical simulations of the linear wave equation and two-dimensional incompressible flat plate boundary layer flows. The high-order non-uniform-grid schemes (up to the 11th-order) are subsequently applied for the simulation of the receptivity of a hypersonic boundary layer to free stream disturbances over a blunt leading edge. The steady and unsteady results show that the new high-order schemes are stable and are able to produce high accuracy for computations of the nonlinear two-dimensional Navier–Stokes equations for the wall bounded supersonic flow.     

三维边界层内诱导横流失稳模态的感受性机理

边界层感受性问题是层流向湍流转捩的初始阶段,在转捩过程中起关键性作用,尤其是三维边界层流动.因此,研究三维边界层感受性问题对进一步理解层流向湍流转捩机理以及湍流成因具有重要的理论意义.采用数值方法研究自由来流湍流与三维壁面局部粗糙相互作用下三维边界层的感受性问题,确定是否能在三维边界层内寻找一种新的横流失稳模态;确定在何种条件下三维边界层内能诱导出定常、非定常的横流失稳模态;探索自由来流湍流的强度、展向波数和法向波数以及三维壁面局部粗糙的大小和结构类型等因素在自由来流湍流与三维壁面局部粗糙作用下三维边界层内被激发出的感受性过程中有何影响,并确定何种横流失稳模态在三维边界层感受性过程中占据何种地位.对自由来流湍流与三维壁面局部粗糙作用激发三维边界层内感受性问题的深入研究,将有助于完善流动稳定性与湍流理论,为层流向湍流转捩过程的预测与控制提供合理的理论依据.     

三维边界层内定常横流涡的感受性研究

层流向湍流转捩的预测与控制一直是研究的前沿热点问题之一,其中感受性阶段是转捩过程中的初始阶段,它决定着湍流产生或形成的物理过程.但是有关三维边界层内感受性问题的数值和理论研究都比较少;实际工程问题中大部分转捩过程都是发生在三维边界层流中,所以研究三维边界层中的感受性问题显得尤为重要.本文以典型的后掠角45?无限长平板为例,数值研究了在三维壁面局部粗糙作用下的三维边界层感受性问题,探讨了三维边界层感受性问题与三维壁面局部粗糙长、宽和高之间的关系;然后,考虑在后掠平板上设计不同的三维壁面局部粗糙的分布状态、几何形状、距离后掠平板前缘的位置以及流向和展向设计多个三维壁面局部粗糙对三维边界层感受性问题有何影响;最后,讨论两两三维壁面局部粗糙中心点之间的距离以及后掠角的改变对三维边界层感受性的物理过程将会发生何种影响等.这一问题的深入研究将为三维边界层流中层流向湍流转捩过程的认识和理解提供理论依据.     

Generation of nonstationary Görtler vortices by localized surface nonuniformities. Receptivity coefficients

The mechanism of production of nonstationary Görtler vortices in a boundary layer on concave wall by surface nonuniformities (vibrations and roughness) has been experimentally examined. The nonuniformities were produced by a specially developed disturbance source. They were controlled, localized along the streamwise coordinate, and periodic over the span of the experimental model. Tests in a low-turbulence wind tunnel have proved that the disturbance source is an efficient means of experimental study of the receptivity and stability problem for boundary layers dominated by Görtler instability. The operation of the disturbance source leads to the production of small-amplitude nonstationary Görtler vortices (tenth or hundredth fractions of a per cent of the free-stream velocity) with predefined characteristics (frequency and spanwise wavelength). In our experiments, we quantitatively examined the problem of linear receptivity of boundary layer to surface nonuniformities in a broad range of frequencies for the most dangerous spanwise scales of Görtler vortices. The values of the amplitudes and phases of the receptivity coefficients were determined. The amplitudes proved to be much smaller in magnitude in comparison with the excitation of modes of hydrodynamic instabilities of other types (Tollmien-Schlichting waves and cross-flow-instability modes). It was found that, with increasing the frequency, the amplitudes of the receptivity coefficients showed a distinct growth while for high frequencies those amplitudes also exhibited a growth with the spanwise scale of perturbations, although for stationary surface roughness no effect due to this scale was observed. It was found that the dependences on frequency of the efficiency of the mechanisms of stability and receptivity showed opposing behaviors, were in competition, and could partially compensate each other, promoting, thus, the production of boundary-layer Görtler vortices in a broad range of frequencies.     

High-order shock-fitting methods for direct numerical simulation of hypersonic flow with chemical and thermal nonequilibrium

In recent years, much progress has been made in the direct numerical simulation of laminar-turbulent transition of hypersonic boundary layer flow. However, most of the efforts at the direct numerical simulation of transition previously have been focused on the idealized perfect gas flow or “cold” hypersonic flows. For practical problems in hypersonic flows, high-temperature effects of thermal and chemical nonequilibrium are important and cannot be modeled by a perfect gas model. Therefore, it is necessary to include the real gas models in the numerical simulation of hypersonic boundary layer transition in order to accurately predict flow field parameters. Currently most numerical methods for hypersonic flow with thermo-chemical nonequilibrium are based on shock-capturing approach at relatively low order of accuracy. Shock capturing schemes reduce to first-order accuracy near the shock and have been shown to produce spurious oscillations behind curved strong shocks. There is a need to develop new methods capable of simulating nonequilibrium hypersonic flow fields with uniformly high-order accuracy and avoid spurious oscillations near the shock. This paper presents a fifth-order shock-fitting method for numerical simulation of thermal and chemical nonequilibrium in hypersonic flows. The method is developed based on the state-of-the-art real gas models for thermo-chemical nonequilibrium and transport phenomena. Shock-fitting approach is used because it has the advantage of capturing the entire flow field with high-order accuracy and without any oscillations near the shock. The new method has been tested and validated for a number of test cases over a wide span of free stream conditions. The developed method is applied for the study of receptivity of free stream acoustic waves over a blunt cone for hypervelocity flow. Some preliminary results of the computations of the high order shock fitting method for the above mentioned study have also been presented.