NORMAL GRID RULE FOR HYPERSONIC HEAT FLUX NUMERICAL SIMULATION

采用数值求解雷诺平均Navier-Stokes 方程方法对高超声速钝双锥模型进行了计算,比较了不同法向网格尺度对热流计算的影响,并在此基础上提出了一种适于热流计算的网格准则. 研究表明:在实际外形的热流计算中,使用过密或过粗的法向网格均不利于得到准确的热流数据;采用该文提出的基于当地温度梯度的法向网格尺度准则可以在保证热流计算精度的同时实现较高的收敛速度.     

多维迎风方法在非结构/混合网格热流计算中的应用研究

非结构/混合网格具有极强的几何灵活性,在复杂外形飞行器的气动力特性数值模拟中已得到广泛应用,但目前还难以准确地预测气动热环境。本文从非结构/混合网格热流计算的三个需求出发,选取了多维迎风方法,并与其他方法进行了对比研究。以二维圆柱高超声速绕流这一Benchmark典型问题为例,对比研究了多维迎风方法和几种广泛使用的无粘通量格式(Roe格式、Van Leer格式和AUSMDV格式)对混合网格热流计算精度的影响。结果表明,多维迎风方法在热流计算精度、鲁棒性以及收敛性方面表现良好。最后,将多维迎风方法应用于常规混合网格上的圆柱和钝双锥绕流问题,均得到了较好的热流计算结果,为非结构/混合网格热流计算在复杂高超飞行器中的应用奠定了基础。     

基于混合网格多维梯度重构的热流预测方法研究

高超声速气动热环境的数值计算对算法和网格的敏感度极高. 随着高超声速飞行器外形日益复杂, 生成高质量的结构网格时间成本呈指数增加, 难以满足工程应用的需求. 非结构/混合网格因具有很强的复杂外形适应能力, 为了缩短任务周期, 有必要在非结构/混合网格上开展高精度的气动热环境数值计算方法研究. 梯度重构方法是影响非结构/混合网格热流计算精度的重要因素之一. 本文通过引入多维梯度重构方法, 发展了基于常规的非结构/混合网格的高精度热流计算方法, 对典型的高超声速Benchmark算例(二维圆柱)进行了模拟, 并与气动力计算广泛采用的Green-Gauss类方法和最小二乘类方法进行了对比. 计算结果表明, 多维梯度重构方法能有效提高非结构/混合网格热流预测精度, 其鲁棒性和收敛性更好. 最后将多维梯度重构方法应用于常规混合网格的三维圆柱和三维双椭球绕流问题, 得到了与实验值吻合较好的热流计算结果, 展现了良好的应用前景.      

基于混合网格多维梯度重构的热流预测方法研究

高超声速气动热环境的数值计算对算法和网格的敏感度极高.随着高超声速飞行器外形日益复杂,生成高质量的结构网格时间成本呈指数增加,难以满足工程应用的需求.非结构/混合网格因具有很强的复杂外形适应能力,为了缩短任务周期,有必要在非结构/混合网格上开展高精度的气动热环境数值计算方法研究.梯度重构方法是影响非结构/混合网格热流计算精度的重要因素之一.本文通过引入多维梯度重构方法,发展了基于常规的非结构/混合网格的高精度热流计算方法,对典型的高超声速Benchmark算例(二维圆柱)进行了模拟,并与气动力计算广泛采用的Green-Gauss类方法和最小二乘类方法进行了对比.计算结果表明,多维梯度重构方法能有效提高非结构/混合网格热流预测精度,其鲁棒性和收敛性更好.最后将多维梯度重构方法应用于常规混合网格的三维圆柱和三维双椭球绕流问题,得到了与实验值吻合较好的热流计算结果,展现了良好的应用前景.     

机动弹头高超声速粘性绕流数值模拟

采用空间二阶精度的交替方向隐式分解的NND格式求解完全气体假定下的非定常薄层近似NaVierStokes方程,并采用抛物化的椭圆型方程生成复杂带翼弹头的空间网格.最后给出了机动弹头在M∞=7.3,α=20°下的流场计算结果.计算结果表明本文所采用的计算网格及计算方法可以适用于高超声速复杂流场的数值模拟.     

超声速、高超声速粘性气体分离流动的数值解法

本文研究了超声速、高超声速粘性气体绕二维压缩拐角的分离流动,利用混合的差分格式(滤波格式)对N-S方程进行了计算,求得了流场物理量的分布和分离图象。为了简化计算,建立了简化的N-S方程,并求得了数值解,和已有的数值结果及实验结果比较,我们采用的差分格式是好用的,简化的N-S方程是可行的。     

高超声速压缩拐角峰值热流位置预测模型研究

旨在通过建立高超声速压缩拐角流动的再附点附近的模型理论来揭示峰值热流的产生机理以及如何可靠预测其位置.首先,分析再附点附近流动特征,提出了基于可压缩斜驻点流动模型来近似该处的局部流动.其次,近似求解了该流动模型,发现边界层厚度存在极小值的特征,从而揭示了再附点后峰值热流的产生机理,并由此得到了再附点和峰值热流点间距离的半解析半数值估算方法.最后,对此结果作了数值验证,并做了讨论.      

高超声速三维热化学非平衡流场的数值模拟

对三维高超声速热化学非平衡流场进行数值模拟,采用双温度热化学非平衡、11组元空气模型,考虑振动-离解耦合．差分格式采用沈清博士提出的“迎风型NND”格式,用熵修正方法消除了高超声速流数值模拟中的“carbuncle现象”．与LU-SGS方法结合,提高了单步计算效率和收敛性．数值模拟结果与文献结果进行了对比,并在弹道靶中进行了钢质圆球的弓形激波位置实验验证．计算结果与文献、实验的对比说明,三维热化学非平衡流计算程序可以精确地捕捉到强弓形激波,得到合理的空气动力系数．     

一种求解抛物化Navier-Stokes方程的空间推进算法

讨论了抛物化NS方程(parabolized Navier-Stokesequations, PNS)的数学性质,对比分析多种处理流向压力梯度的方法的优缺点. 以此为基础,成功地将LU-SGS隐式时间积分方法推广到PNS方程的流向空间积分上,发展了基于PNS方程的有限体积单次扫描空间推进算法(single-sweep parabolized Navier-Stokesalgorithm, SSPNS). 在该算法中,横向无黏数值通量和黏性通量分别采用混合型迎风格式和中心格式求解. 用SSPNS算法计算了4个典型流场,包括超声速平板流、15$^\circ$楔板压缩高超声速流、带攻角的高超声速锥形流和侧压式高超声速进气道流动. SSPNS计算结果与NASA UPS程序数值结果、文献提供的实验数据及理论分析结果符合得很好.对比研究表明,SSPNS 法与传统时间迭代法相比,二者计算精度相当,而SSPNS计算速度快1~2个量级,存储量至少低1个量级.关键词 抛物化NS方程;空间推进算法;LU-SGS隐式积分方法;超声速/高超声速流动      

非结构混合网格高超声速绕流与磁场干扰数值模拟

对均匀磁场干扰下的二维钝头体无粘高超声速流场进行了基于非结构混合网格的数值模拟.受磁流体力学方程组高度非线性的影响及考虑到数值模拟格式的精度,目前在此类流场的数值模拟中大多使用结构网格及有限差分方法,因而在三维复杂外形及复杂流场方面的研究受到限制.本文主要探索使用非结构网格(含混合网格)技术时的数值模拟方法.控制方程为耦合了Maxwell方程及无粘流体力学方程的磁流体力学方程组,数值离散格式采用Jameson有限体积格心格式,5步Runge-Kutta显式时间推进.计算模型为二维钝头体,初始磁场均匀分布.对不同磁感应强度影响下的高超声速流场进行了数值模拟,并与有限的资料进行了对比,得到了较符合的结果.     

An extension of Osher's Riemann solver for chemical and vibrational non-equilibrium gas flows

In this paper we study an extension of Osher's Riemann solver to mixtures of perfect gases whose equation of state is of the form encountered in hypersonic applications. As classically, one needs to compute the Riemann invariants of the system to evaluate Osher's numerical flux. For the case of interest here it is impossible in general to derive simple enough expressions which can lead to an efficient calculation of fluxes. The key point here is the definition of approximate Riemann invariants to alleviate this difficulty. Some of the properties of this new numerical flux are discussed. We give 1D and 2D applications to illustrate the robustness and capability of this new solver. We show by numerical examples that the main properties of Osher's solver are preserved; in particular, no entropy fix is needed even for hypersonic applications.     

HLLC scheme for the preconditioned pseudo-compressibility Navier–Stokes equations for incompressible viscous flows

A new HLLC (Harten-Lax-van leer contact) approximate Riemann solver with the preconditioning technique based on the pseudo-compressibility formulation for numerical simulation of the incompressible viscous flows has been proposed, which follows the HLLC Riemann solver (Harten, Lax and van Leer solver with contact resolution modified by Toro) for the compressible flow system. In the authors' previous work, the preconditioned Roe's Riemann solver is applied to the finite difference discretisation of the inviscid flux for incompressible flows. Although the Roe's Riemann solver is found to be an accurate and robust scheme in various numerical computations, the HLLC Riemann solver is more suitable for the pseudo-compressible Navier--Stokes equations, in which the inviscid flux vector is a non-homogeneous function of degree one of the flow field vector, and however the Roe's solver is restricted to the homogeneous systems. Numerical investigations have been performed in order to demonstrate the efficiency and accuracy of the present procedure in both two- and three-dimensional cases. The present results are found to be in good agreement with the exact solutions, existing numerical results and experimental data.     

Dissipation matrix and artificial heat conduction for Godunov‐type schemes of compressible fluid flows

This paper aims to reassess the Riemann solver for compressible fluid flows in Lagrangian frame from the viewpoint of modified equation approach and provides a theoretical insight into dissipation mechanism. It is observed that numerical dissipation vanishes uniformly for the Godunov‐type schemes in the sense that associated dissipation matrix has zero determinant if an exact or approximate Riemann solver is used to construct numerical fluxes in the Lagrangian frame. This fact connects to some numerical defects such as the wall‐heating phenomenon and start‐up errors. To cure these numerical defects, a traditional numerical viscosity is added, as well as the artificial heat conduction is introduced via a simple passage of the Lax–Friedrichs type discretization of internal energy. Copyright © 2016 John Wiley & Sons, Ltd.     

MFCAV近似Riemann解在新型拉氏方法中的应用

Maire等提出了一种新型的有限体积中心型拉氏方法, 该方法大大地改善了一直困扰着一般中心型拉氏方法的虚假网格变形. 然而在计算数值流和移动网格时,该方法只应用了数值黏性较大的弱波近似(weak wave approximatedmethod, WWAM) Riemann解, 而且方法的设计表明其他类型的近似Riemann解不能简单直接地应用上去. 将体平均多流管(multifluid channel on averaged volume, MFCAV)近似Riemann解视为对WWAM的修正,成功将其应用于新型方法中, 数值实验表明应用了MFCAV 的新方法是有效的. 研究为将其他更为有效的近似Riemann解应用于该新型方法中开辟了一条道路.      

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.      

HLLE++格式在高马赫数空腔流动模拟中的应用

空腔流动存在剪切层运动、涡脱落与破裂,以及激波与激波、激波与剪切层、激波与膨胀波和激波/涡/剪切层相互干扰等现象,流动非常复杂,特别是高马赫数(M>2)时,剪切层和激波更强,激波与激波干扰更严重,对数值格式的要求更高,既需要格式耗散小,对分离涡等有很高的模拟精度,又需要格式在激波附近具有较大的耗散,可以很好地捕捉激波,防止非物理解的出现。Roe和HLLC等近似Riemann解格式在高马赫数强激波处可能会出现红玉现象,而HLLE++格式大大改善了这种缺陷,在捕捉高超声速激波时避免了红玉现象的发生,同时还保持在光滑区域的低数值耗散特性。本文在结构网格下HLLE++格式的基础上,通过改进激波探测的求解,建立了基于非结构混合网格的HLLE++计算方法,通过无粘斜坡算例,验证了HLLE++格式模拟高马赫数流动的能力,并应用于高马赫数空腔流动的数值模拟,开展了网格和湍流模型影响研究,验证了方法模拟高马赫数空腔流动的可靠性和有效性。     

Comparisons and applications of numerical simulation methods for predicting aerodynamic heating around complex configurations

Numerical simulation methods of aerodynamic heating were compared by considering the inuence of numerical schemes and turbulence models,and attempting to investigate the applicability of numerical simulation methods on predicting heat flux in engineering applications. For some typical cases provided with detailed experimental data,four spatial schemes and four turbulence models were adopted to calculate surface heat flux. By analyzing and comparing,some inuencing regularities of numerical schemes and turbulence models on calculating heat flux had been acquired. It is clear that AUSM+-up scheme with rapid compressibilitymodified high Reynolds number k-ω model should be appropriate for calculating heat flux. The numerical methods selected as preference above were applied to calculate the heat flux of a 3-D complex geometry in high speed turbulent flows. The results indicated that numerical simulation can capture the complex flow phenomena and reveal the mechanism of aerodynamic heating. Especially,the numerical result of the heat flux at the stagnation point of the wedge was well in agreement with the prediction of Kemp-Riddel formula,and the surface heat flux distribution was consistent with experiment results,which implied that numerical simulation can be introduced to predict heat flux in engineering applications.     

A third-order compact nonlinear scheme for compressible flow simulations

Reynolds-averaged Navier-Stokes simulations based on second-order numerical methods are widely used by commercial codes and work as dominating tools for most industrial applications. They, however, suffer from limitations in accurate and reliable predictions of skin-friction drag and aerodynamic heating, as well as in simulations of complex flows such as large-scale separation and transition. A remedy for this is the development of high-order schemes, by which numerically induced dissipation and dispersion errors of low-order schemes can be effectively reduced. Weighted compact nonlinear schemes (WCNSs) are a family of high-resolution nonlinear shock-capturing methods. A stencil-selection procedure is introduced in the proposed work with an aim to improve the nonlinear weight of the third-order WCNS. By using the approximate dispersion relation analysis, it is demonstrated that the new scheme has reduced dissipation and dispersion errors, compared with WCNSs using two typical nonlinear weights. Improvements are also achieved by the new scheme in numerical tests such as the double Mach reflection problem and the Rayleigh-Taylor instability simulation, which are characterized by strong shock discontinuities and rich small scales, respectively. The new scheme is therefore highly favored in the simulation of flow problems involving strong discontinuities and multiscales phenomena.     

A Free-Lagrange method for unsteady compressible flow: simulation of a confined cylindrical blast wave

A Free-Lagrange numerical procedure for the simulation of two-dimensional inviscid compressible flow is described in detail. The unsteady Euler equations are solved on an unstructured Lagrangian grid based on a density-weighted Voronoi mesh. The flow solver is of the Godunov type, utilising either the HLLE (2 wave) approximate Riemann solver or the more recent HLLC (3 wave) variant, each adapted to the Lagrangian frame. Within each mesh cell, conserved properties are treated as piece-wise linear, and a slope limiter of the MUSCL type is used to give non-oscillatory behaviour with nominal second order accuracy in space. The solver is first order accurate in time. Modifications to the slope limiter to minimise grid and coordinate dependent effects are described. The performances of the HLLE and HLLC solvers are compared for two test problems; a one-dimensional shock tube and a two-dimensional blast wave confined within a rigid cylinder. The blast wave is initiated by impulsive heating of a gas column whose centreline is parallel to, and one half of the cylinder radius from, the axis of the cylinder. For the shock tube problem, both solvers predict shock and expansion waves in good agreement with theory. For the HLLE solver, contact resolution is poor, especially in the blast wave problem. The HLLC solver achieves near-exact contact capture in both problems. Received May 25, 1995 / Accepted September 11, 1995