积分守恒型N-S方程通用形式及其在数值模拟中的应用

运用张量分析理论,分别给出了标量、矢量以及二阶张量等任意阶数张量的Gauss定理,并应用到积分形式流动控制方程的推导中,得到具有普遍意义的三维任意曲线坐标系上的积分守恒型N-S方程的通用形式,并采用有限体积的时间推进法对方程进行数值离散,研制了相应的CFD分析程序.作为算例,对具有复杂边界的大尺度离心叶轮内的旋转三维湍流场进行了数值模拟.与实验结果的比较表明,数值模型和解法是成功的,为复杂物理域的流动问题的数值模拟奠定了基础.     

非结构网格上的B-B单方程模型湍流计算

研究如何在非结构网格上进行Navier Stokes(N-S)方程湍流计算.采用格心有限体积方法离散N-S方程.为了适应非结构网格,计算所用的湍流模型特别选用Baldwin Barth(B-B)单方程模型.此模型由一个单一的具有源项的对流扩散方程组成.为了能在非结构网格上求解B B单方程模型,提出一显式有限体积格式,并直接对带源项的格式进行稳定性分析,得到了相应的时间步长限制条件.最后以平板、RAE 2822翼型、多段翼型绕流等数值算例验证了计算方法的有效性.     

旋翼的非定常流动及表面载荷的数值模拟

旋翼的流场呈现很强的非定常现象.目前,对旋翼定常流场的计算已经基本成熟,非定常流场的计算仍在探索之中。本文基于有限体积法的思想,利用较成熟的商用软件NUMECA/IGG生成计算所需的网格。对N-S方程进行离散,选用Baldwin-Lomax湍流模型,Dual-Time时间推进格式模拟了旋翼的非定常流场。计算的结果与文献给出的实验结果符合得较好。     

子波谱方法在三维声辐射和声散射中的应用

将边界变量用二维子波展开,获得了三维任意边界条件声辐射和声散射的边界积分方程的子波谱方法.采用以子波为权函数的Gauss积分法计算子波谱方法的系数,获得了与传统边界元法相同的计算量,克服了普通积分法计算子波系数计算量大甚至难以收敛的缺点;采用Duffy的方法解决了子波谱方法中的奇异积分,使其能够用普通的Gauss积分法计算.算例表明:子波谱方法系数矩阵压缩率超过50%以后,计算精度仍然高于传统边界元方法.     

用谱方法数值模拟槽道内的气固两相流动

在数值模拟领域内,谱方法具有收敛快、分辨率高和精度高的优点．谱方法处理边界方便,随着数值方法的改善和计算机的发展,它在数值模拟中的作用愈加重要．这里采用谱方法数值求解三维Ｎ—Ｓ方程,用这一方法计算了直槽道内流体的流动．计算得到的层流和湍流结果与理论结果符合地较好．在此基础之上进一步模拟了几种不同槽道内的三维粘性流体层流流动,特别在弯曲槽道内的流动计算中,发展了源项处理方法,正确地反映了弯曲固壁对流体流动的影响．通过对湍流计算获得的脉动速度场的统计可以得到湍流运动的许多统计量,正确地反映了湍流运动的特征,说明可以用模拟得到的流场来代替真实的流场．进行了气固两相流动的研究,由直接模拟得到的流体瞬时速度场对固体粒子的作用进行了粒子运动的模拟计算,得到了颗粒在真实流场中运动的浓度,轨道等有用信息和运动特性,得到了令人鼓舞的结果．     

激光辐照高超声速舵面热力响应研究

建立了基于流固耦合的高超声速飞行器舵面结构在激光辐照下静气动弹性模型,流体控制方程为三维雷诺平均N-S方程,分别采用了中心格式和AUSM+up格式对粘性项和对流项进行空间离散,时间推进采用了高斯-塞德尔隐式推进方法,湍流粘性系数求解使用Menter SST模型。利用冯·卡门研究所高超风洞实验结果对模型进行了校核,预估了激光辐照对高超舵面的热力影响。结果表明,气动力/热计算模型与实验数据符合较好,能够准确模拟高超飞行器的热力参数,根据模型外推结果,激光在较低功率下加热高超飞行器舵面可能导致舵面材料弹性模量大大降低,继而发生弯曲发散而折断,高超飞行器可能因此发生气动失稳而坠毁。     

Rytov相位结构函数二次近似和硬边光阑复高斯函数展开近似的验证

以受光阑限制的高斯光束在大气湍流中传输为例,用仿真程序数值模拟方法和实验方法对用Rytov相位结构函数二次近似和复高斯函数展开法得到的解析结果(如光强分布、二阶矩束宽、桶中功率和β参数)进行了比较验证.研究表明,解析结果与数值模拟结果和实验结果基本吻合.此外,对用不同研究方法所得结果的差异给出了合理的解释.     

新型大涡数值模拟亚格子模型及应用

基于湍流大小尺度间动量输运的结构函数方程，提出了一种新的湍流大涡模型(LES)亚格子涡粘模式．新亚格子涡粘系数正比于纵向速度增量的扭率，它表征大小尺度湍流间的能量输运和耗散之比．新模式通过各向同性湍流直接数值模拟数据库的检验，并用于槽道湍流的大涡模拟计算，将所得结果与DNS结果进行了比较．     

基于小关联时间两相湍流色噪声的近似模型及数值模拟

从一般高斯型色噪声模型出发,通过泛函导数,应用小关联时间,近似计算多维色噪声,得到有效Fokker-Planck方程.将其应用到两相湍流中得到颗粒相的概率密度函数输运方程,从而得到颗粒相的二阶矩模型.将颗粒应力方程简化成代数方程,建立代数应力模型.将对流扩散方程的有限分析法运用到求解两相流模型中,对壁面两相射流进行数值模拟,并将求解结果与实验结果进行对比分析.     

微槽道气体流动的统计模拟

利用基于分子模型的统计模拟方法——信息保存方法(IP)统计模拟了实验条件下微槽道气体流动,仔细讨论了用IP方法模拟长槽道稀薄气流时遇到的问题,并给出了解决的方法,即采取守恒形式的控制方程避免质量流量计算误差积累,并利用超松弛方法使收敛过程加速.将IP计算结果与压力分布和质量流量实验数据进行了比较.     

混合通量差分格式的比较

系统研究了几种混合通量差分格式的构造方法和耗散模型,分别对低速平板绕流、二维跨音速喷管流动和高超音速钝头体无粘绕流进行了数值模拟,结合先进的EASM湍流模型对格式的粘性分辨率和激波稳定性进行了细致的比较分析.结果表明混合通量差分格式兼顾了FDS和FVS格式的优点,具有较高的间断分辨率和数值稳定性.     

Propagation properties of vectorial elliptical Gaussian beams beyond the paraxial approximation

Starting from the vectorial Rayleigh diffraction integral formula and without using the far-field approximation, a solution of the wave equation beyond the paraxial approximation is found, which represents vectorial non-paraxial elliptical Gaussian beams in free space. The far-field expressions for non-paraxial Gaussian beams and elliptical Gaussian beams can be regarded as special cases treated in this paper. Some basic propagation properties of vectorial non-paraxial elliptical Gaussian beams, including the irradiance distribution, phase term, beam widths and divergence angles are studied. Numerical results are given and illustrated.     

A new bistatic model for electromagnetic scattering from randomly rough surfaces

In this paper we propose a bistatic model for electromagnetic scattering from a Gaussian rough surface with small to moderate heights. It is based on the integral equation formulation where the spectral representations of the Green's function and its gradient are in complete forms, a general approach similar to those used in the advanced integral equation model (AIEM) and the integral equation model for second-order multiple scattering (IEM2M). Yet this new model can be regarded as an extension to these two models on two accounts: first it has made fewer and less restrictive assumptions in evaluating the complementary scattering coefficient for single scattering, and second it contains a more rigorous analysis by the inclusion of the error function related terms for the cross- and complementary scattering coefficients, which stems from the absolute phase term in the spectral representation of the Green's function. It is expected that our result for the complementary scattering coefficient is more accurate and more general, even when the effect of the error function related terms is neglected. As a result, the proposed model is expected to have wider applicability with a better accuracy. Numerical simulations are provided to demonstrate the validity of the proposed model.     

湍流两相流动有燃烧颗粒相概率密度函数输运方程理论

由有燃烧的湍流气粒两相流动的瞬态方程和统计力学概率密度函数概念出发,推导了有燃烧颗粒相的质量－动量－能量联合概率密度函数（ＰＤＦ）输运方程,并对方程中条件期望项用梯度模拟概念进行了模拟封闭。封闭后的ＰＤＦ方程可作为建立颗粒拟流体模型方程和封闭二阶矩模型的基础,也可以通过Ｍｏｎｔｅ－Ｃａｒｌｏ 法求解用以直接计算颗粒雷诺应力和湍流动能,以便和二阶 矩模型的结果相对照,改善二阶矩模型。     

常气压辉光放电等离子体对边界层流动的影响

基于Shyy提出的常气压下均匀辉光放电等离子体与空气干扰的物理模型,通过求解电位势方程得到电场分布及作用于流体上的电场力.以NACA0015翼型低速绕流为对象,通过数值求解考虑等离子体作用的流体运动控制方程,研究等离子体位置和个数控制对翼型绕流分离的影响.位于分离点上游的等离子体能够有效地抑制流动分离,而在分离区的等离子体对流动影响很弱,这一结论同实验观察一致,并给出等离子体对翼型壁面压力和气动力影响的规律.     

小波自适应方法模拟二维涡旋演化

以涡量方程为控制方程,模拟初始状态涡量分布为高斯分布三个涡旋演化过程.提出一个关联实际流动的小波系数临界值,小波系数分为临界值以上及以下部分,进而涡量可分成尺度系数项、小波系数突出项和小波系数平凡项三部分.只采用尺度系数项和小波系数突出项近似涡量,既可以节约计算量,还可以自动追踪绝大部分的拟涡能.数值结果表明,用不到10%的小波系数,可控制99%以上的拟涡能.     

A new mixed subgrid-scale model for large eddy simulation of turbulent drag-reducing flows of viscoelastic fluids

A mixed subgrid-scale(SGS) model based on coherent structures and temporal approximate deconvolution(MCT) is proposed for turbulent drag-reducing flows of viscoelastic fluids. The main idea of the MCT SGS model is to perform spatial filtering for the momentum equation and temporal filtering for the conformation tensor transport equation of turbulent flow of viscoelastic fluid, respectively. The MCT model is suitable for large eddy simulation(LES) of turbulent dragreducing flows of viscoelastic fluids in engineering applications since the model parameters can be easily obtained. The LES of forced homogeneous isotropic turbulence(FHIT) with polymer additives and turbulent channel flow with surfactant additives based on MCT SGS model shows excellent agreements with direct numerical simulation(DNS) results. Compared with the LES results using the temporal approximate deconvolution model(TADM) for FHIT with polymer additives, this mixed SGS model MCT behaves better, regarding the enhancement of calculating parameters such as the Reynolds number.For scientific and engineering research, turbulent flows at high Reynolds numbers are expected, so the MCT model can be a more suitable model for the LES of turbulent drag-reducing flows of viscoelastic fluid with polymer or surfactant additives.     

Fourier spectral and wavelet solvers for the incompressible Navier–Stokes equations with volume-penalization: Convergence of a dipole–wall collision

In this study, we use volume-penalization to mimic the presence of obstacles in a flow or a domain with no-slip boundaries. This allows in principle the use of fast Fourier spectral methods and coherent vortex simulation techniques (based on wavelet decomposition of the flow variables) to compute turbulent wall-bounded flow or flows around solid obstacles by simply adding one term in the equation. Convergence checks are reported using a recently revived, and unexpectedly difficult dipole–wall collision as a benchmark computation. Several quantities, like the vorticity isolines, truncation error, kinetic energy and enstrophy are inspected for a collision of a dipole with a no-slip wall and compared with available benchmark data obtained with a standard Chebyshev pseudospectral method. We quantify the possible deteriorating effects of the Gibbs phenomenon present in the Fourier based schemes due to continuity restrictions of the penalized Navier–Stokes equations on the wall. It is found that Gibbs oscillations have a negligible effect on the flow evolution allowing higher-order recovery of the accuracy on a Fourier basis by means of postprocessing. An advantage of coherent vortex simulations, on the other hand, is that the degrees of freedom of the flow computation can strongly be reduced. In this study, we quantify the possible reduction of degrees of freedom while keeping the accuracy. For an optimal convergence scenario the penalization parameter has to scale with the number of Fourier and wavelet modes. In addition, an implicit treatment of the Darcy drag term in the penalized Navier–Stokes equations is beneficial since this allows one to set the time step independent from the penalization parameter without additional computational or memory requirements.     

Fourier spectral and wavelet solvers for the incompressible Navier–Stokes equations with volume-penalization: Convergence of a dipole–wall collision

In this study, we use volume-penalization to mimic the presence of obstacles in a flow or a domain with no-slip boundaries. This allows in principle the use of fast Fourier spectral methods and coherent vortex simulation techniques (based on wavelet decomposition of the flow variables) to compute turbulent wall-bounded flow or flows around solid obstacles by simply adding one term in the equation. Convergence checks are reported using a recently revived, and unexpectedly difficult dipole–wall collision as a benchmark computation. Several quantities, like the vorticity isolines, truncation error, kinetic energy and enstrophy are inspected for a collision of a dipole with a no-slip wall and compared with available benchmark data obtained with a standard Chebyshev pseudospectral method. We quantify the possible deteriorating effects of the Gibbs phenomenon present in the Fourier based schemes due to continuity restrictions of the penalized Navier–Stokes equations on the wall. It is found that Gibbs oscillations have a negligible effect on the flow evolution allowing higher-order recovery of the accuracy on a Fourier basis by means of postprocessing. An advantage of coherent vortex simulations, on the other hand, is that the degrees of freedom of the flow computation can strongly be reduced. In this study, we quantify the possible reduction of degrees of freedom while keeping the accuracy. For an optimal convergence scenario the penalization parameter has to scale with the number of Fourier and wavelet modes. In addition, an implicit treatment of the Darcy drag term in the penalized Navier–Stokes equations is beneficial since this allows one to set the time step independent from the penalization parameter without additional computational or memory requirements.