Numerical investigation of flow over two sweepback wedges at M = 4 and 6

Results of numerical simulation are discussed: simulation was carried out for a configuration of two wedges with sweepback leading edges placed on a pre-compression ramp in a way that skewed surfaces of the wedges deflect the compressed flows in the opposite directions. It was demonstrated that this configuration produces a flow with irregular interaction in the plane of symmetry for shock waves produced by sweepback wedges. The shock waves formed by the skew wedges induce 3D boundary layer separations along sweepback leading edges of the wedges. Flows in the separation zones are directed toward the plane of symmetry of this configuration; they interact and produce in the central part a “swollen” zone of separation flow with a typical S-shaped profile of velocity. Simulation data was obtained for the free stream flow with Mach number M = 4 and 6 and based upon Navier—Stokes equations and k-ωSST turbulence model using FLUENT computation code. Inviscid flow described by Euler equations was considered as well.     

On the generation and maintenance of waves and turbulence in simulations of free-surface turbulence

One of the challenges in numerical simulation of wave–turbulence interaction is the precise setup and maintenance of wave and turbulence fields. In this paper, we investigate techniques for the generation and suppression of specific surface wave modes, the generation of turbulence in an inhomogeneous physical domain with a wavy boundary-fitted grid, and the generation and maintenance of waves and turbulence during the complex wave–turbulence interaction process. We apply surface pressure to generate and suppress waves. Based on the solution of linearized Cauchy–Poisson problem, we derive three pressure expressions, which lead to a δ-function method, a time-segment method, and a gradual method. Numerical experiments show that these methods generate waves as specified and eliminate spurious waves effectively. The nonlinear wave effect is accounted for with a time-relaxation method. For turbulence generation, we extend the linear forcing method to an inhomogeneous physical domain with a curvilinear computational grid. Effects of force distribution and computational grid distortion are examined. For wave–turbulence interaction, we develop an algorithm to instantaneously identify specific progressive and standing waves. To precisely control the wave amplitude in a complex turbulent flow field, we further develop an energy controlling method. Finally, a simulation example of wave–turbulence interaction is presented. Results show that turbulence has unique features in the presence of waves. Velocity fluctuations are found to be strongly dependent on the wave phase; variations of these fluctuations are explained by the pressure–strain correlation associated with the wave-induced strain field.     

Simulation of viscous flows with undulatory boundaries: Part II. Coupling with other solvers for two-fluid computations

We extend the direct numerical simulation (DNS) capability developed in [D. Yang, L. Shen, Simulation of viscous flows with undulatory boundaries: Part I. Basic solver, J. Comput. Phys. (submitted for publication) ] to the simulation of two-fluid interaction with deformable interface. Two approaches are used to couple the DNS of one fluid with the simulation of another fluid. In the first, the DNS is coupled with a potential-flow based wave solver that uses a high-order spectral (HOS) method. This coupled method is applied to simulate the interaction of turbulent wind with surface waves, including single wave train and broadband wavefield. Validation with previous theoretical and experimental studies shows the accuracy and efficiency of this coupled DNS-HOS method for capturing the essential physics of wind–wave interaction. In the second approach, both of the fluids are simulated by the DNS and are coupled by an efficient iterative scheme, in which the continuity of velocity and the balance of stress are enforced at the interface. The performance of this coupled DNS–DNS method is demonstrated and validated by several test cases including: interfacial wave between two viscous fluids, water surface wave over highly viscous mud flow with interfacial wave, and interaction of two-phase vortex pairs with a deformable interface. Comparison with existing theoretical and numerical results confirms the accuracy of this coupled DNS–DNS method. Finally, this method is applied to study the interaction of air and water turbulence. The nonlinear development of interfacial wave by the excitation of the air and water turbulence, and the wave effect on the instantaneous and statistical characteristics of the turbulence are elucidated.     

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.     

典型自由面流动问题的SPH-ALE数值模拟

应用基于黎曼解的SPH-ALE方法对两种典型自由面流动问题进行数值模拟,并提出一种一阶核函数修正压力计算方法,通过对临近边界的水粒子压力进行核积分,近似估算固壁边界压力.给出不同时刻的流场压力分布及自由液面演化过程,将计算结果与相关的试验值及数值解进行对比,分析结果表明：SPH-ALE方法较传统SPH方法在流场压力计算精度上有较大的改进,在处理强非线性自由面流动问题时能够达到较高的精度.     

Experimental characterization of the convective heat transfer in a vortex-wall interaction

The development of turbulence models and wall laws for the numerical simulation of flows in complex geometries requires a detailed experimental analysis of turbulence and of the phenomena that appear in turbulent boundary layers. There is a strong need to develop new measurement systems allowing the determination of unsteady wall heat transfer coefficients. In order to improve the knowledge of the unsteady phenomena occurring in perturbed boundary layers, a fundamental study is conducted on the interaction of a single vortex with a flat plate. An experimental methodology using a specific thermal sensor whose surface temperature is measured by an infrared thermography system is presented. It allows the characterization of the unsteady convective heat transfer coefficient whose evolution is compared with the fluctuations of the wall friction coefficient, calculated from velocity profiles measured by laser Doppler velocimetry.     

Modeling the propagation of electromagnetic waves over the surface of the human body

The results of modeling and an experimental study of electromagnetic (EM) waves in microwave range propagating along the surface of the human body have been presented. The parameters of wave propagation, such as the attenuation and phase velocity, have also been investigated. The calculation of the propagation of EM waves by the numerical method FDTD (finite difference time domain), as well as the use of the analytical model of the propagation of the EM wave along flat and curved surfaces has been fulfilled. An experimental study on a human body has been conducted. It has been shown that creeping waves are slow and exhibit a noticeable dispersion, while the surface waves are dispersionless and propagate at the speed of light in free space. A comparison of the results of numerical simulation, analytical calculation, and experimental investigations at a frequency of 2.55 GHz has been carried out.     

Numerical computation of an immiscible two-phase flow in comparison with experiment

The flow of fluids with interfaces or free surfaces is of great interest in both basic and applied research. Despite enormous efforts to develop numerical methods for solving such flow problems, no undisputed standards have emerged yet. We compare here three different approaches for the problem of a liquid film falling down along a vertical wall under the action of gravity. Due to an instability, waves form on the film surface and a nontrivial flow pattern emerges. This provides a test case for two-phase flow simulation methods under conditions of practical relevance. The methods compared are a moving boundary method and a volume of fluid method implemented in commercial software packages and a new phase field method. A set of experimental data is used as a reference for the comparison. All three methods correctly reproduce the main features of the experiment; however, none are free of quantitative deviations from the data. The text was submitted by the authors in English.     

Extensive characterisation of a high Reynolds number decelerating boundary layer using advanced optical metrology

Over the last years, the observation of large-scale structures in turbulent boundary layer flows has stimulated intense experimental and numerical investigations. Nevertheless, partly due to the lack of comprehensive experimental data at sufficiently high Reynolds number, our understanding of turbulence near walls, especially in decelerating situations, is still quite limited. The aim of the present contribution is to combine the equipment and skills of several teams to perform a detailed characterisation of a large-scale turbulent boundary layer under adverse pressure gradient. Extensive particle image velocimetry (PIV) measurements are performed, including a set-up with 16 sCMOS cameras allowing the characterisation of the boundary layer on 3.5 m, stereo PIV and high resolution near wall measurements. In this paper, detailed statistics are presented and discussed, boundary conditions are carefully characterised, making this experiment a challenging test case for numerical simulation.     

Computation of Hele-Shaw flows with free boundaries

A novel method for calculation of Hele-Shaw flows with receding free boundaries is presented. The method is applied to flows with suction from a point sink and to flow in a channel with parallel walls. In each case the unknown fluid region is mapped conformally onto the unit disc, the free boundary being mapped onto the unit circle. This mapping, which is a function of position and time, is calculated numerically at points on the unit circle using a version of the boundary integral method. The free boundary is thus found without explicit calculation of the pressure at internal points, and the computation times are much less than those for other numerical methods for this problem. Numerical results are compared with explicit analytic solutions for several test problems.     

Low-frequency surface wave propagation along plane boundaries in fluid-saturated porous media

A method of the mechanics of a fluid-saturated porous medium is used to study the propagation of harmonic surface waves along the free boundary of such a medium, along the boundary between a porous medium and a fluid, and along the boundary between two porous half-spaces. It is shown that, at low frequencies (i.e., for waves with frequencies lower than the Biot characteristic frequency), the corresponding dispersion equations in zero-order approximation are reduced to the equations for an “equivalent” elastic medium. For the wave numbers of surface waves, corrections taking into account the generation of longitudinal waves of the second kind at the boundary are calculated. Examples of numerical solutions of dispersion equations for rock are presented.     

应用GAO-YONG可压缩湍流模式数值模拟RAE2822翼型绕流

应用Gao-Yong可压缩湍流模式,数值模拟RAE2822二维翼型在两种不同来流情况下的跨音速粘性绕流问题.湍流模式的对流项用ROE格式离散,扩散项用中心差分格式离散,空间离散后的控制方程用多步Runge-Kutta显式时间推进格式求解.计算结果预测了翼型表面的压力系数的分布、平均速度剖面、激波的位置、马赫数等值线等情况.同时,对翼型表面激波与边界层相互干扰以及转捩问题进行分析计算,结果表明,Gao-Yong可压缩湍流模式结合适当的数值方法能够成功地模拟翼型跨音速粘性流动.最后,基于Gao-Yong可压缩湍流模式各项异性湍流粘性的机理,初步提出一种预测转捩起始位置的方法.     

液气共存的耗散粒子动力学模拟

传统的耗散粒子动力学方法(DPD)由于采用了纯排斥的守恒力相互作用,从而不能适应液气共存或者带有自由面流体的模拟.这里研究了DPD方法中新近提出的一种短程排斥、长程吸引相互作用,探索了这种改进势能对于DPD方法模拟液气共存的能力.模拟了这种新势能所形成的液气过渡界面,计算了过渡界面区的应力分布,发现应力分布与多体DPD方法所得结果一致.进一步对表面张力进行了研究,验证了这种势能所形成的界面满足Laplace定律,而通过理论公式与Laplace定律分别所得到的表面张力也彼此相符。     

On the use of the discontinuous Galerkin method for numerical simulation of two-dimensional compressible turbulence with shocks

In this paper, the discontinuous Galerkin (DG) method combined with localized artificial diffusivity is investigated in the context of numerical simulation of broadband compressible turbulent flows with shocks for under-resolved cases. Firstly, the spectral property of the DG method is analyzed using the approximate dispersion relation (ADR) method and compared with typical finite difference methods, which reveals quantitatively that significantly less grid points can be used with DG for comparable numerical error. Then several typical test cases relevant to problems of compressible turbulence are simulated, including one-dimensional shock/entropy wave interaction, two-dimensional decaying isotropic turbulence, and two-dimensional temporal mixing layers. Numerical results indicate that higher numerical accuracy can be achieved on the same number of degrees of freedom with DG than high order finite difference schemes. Furthermore, shocks are also well captured using the localized artificial diffusivity method. The results in this work can provide useful guidance for further applications of DG to direct and large eddy simulation of compressible turbulent flows.     

Forced solitary waves and fronts past submerged obstacles

Herein, an efficient numerical method is presented to describe the flow of a liquid in an open channel with various types of bottom configurations. The method is developed for steady two-dimensional potential free surface flows. The resulting nonlinear problem is solved numerically by boundary integral equation methods. In addition weakly nonlinear solutions are derived. New solutions which complement those of Dias and Vanden-Broeck [J. Fluid Mech. 59, 93-102 (2004)] are presented. Furthermore some solutions for channel flows past dips in the bottom are discussed.     

Freely decaying weak turbulence for sea surface gravity waves

We study the long-time evolution of deep-water ocean surface waves in order to better understand the behavior of the nonlinear interaction processes that need to be accurately predicted in numerical models of wind-generated ocean surface waves. Of particular interest are those nonlinear interactions which are predicted by weak turbulence theory to result in a wave energy spectrum of the form of [k](-2.5). We numerically implement the primitive Euler equations for surface waves and demonstrate agreement between weak turbulence theory and the numerical results.     

The effect of turbulence damping on acoustic wave propagation in tubes

The attenuation of sound due to the interaction between a low Mach number turbulent boundary layer and acoustic waves can be significant at low frequencies or in narrow tubes. In a recent publication by the present authors the acoustics of charge air coolers for passenger cars has been identified as an interesting application where turbulence attenuation can be of importance. Favourable low-frequency damping has been observed that could be used for control of the in-duct sound that is created by the engine gas exchange process. Analytical frequency-dependent models for the eddy viscosity that controls the momentum and thermal boundary layers are available but are restricted to thin acoustic boundary layers. For cases with cross-sections of a few millimetres a model based on thin acoustic boundary layers will not be applicable in the frequency range of interest.In the present paper a frequency-dependent axis-symmetric numerical model for interaction between turbulence and acoustic waves is proposed. A finite element scheme is used to formulate the time harmonic linearized convective equations for conservation of mass, momentum and energy into one coupled system of equations. The turbulence is introduced with a linear model for the eddy viscosity that is added to the shear viscosity. The proposed model is validated by comparison with experimental data from the literature.     

Reynolds stress models applied to canonical shock-turbulence interaction

Shock waves in high-speed flows can drastically alter the nature of Reynolds stresses in a turbulent flow. We study the canonical interaction of homogeneous isotropic turbulence passing through a normal shock, where the shock wave generates significant anisotropy of Reynolds stresses. Existing Reynolds stress models are applied to this canonical problem to predict the amplification of the stream-wise and transverse normal Reynolds stresses across the shock wave. In particular, the efficacy of the different models for the rapid pressure–strain correlation is evaluated by comparing the results with available direct numerical simulation (DNS) data. The model predictions are found to be grossly inaccurate, especially at high-Mach numbers. We propose physics-based improvement to the Reynolds stress-transport equation in the form of shock-unsteadiness effect and enstrophy amplification for turbulent dissipation rate . The resulting model is found to capture the essential physics of Reynolds stress amplification, and match DNS data for a range of Mach numbers. Numerical error encountered at shock waves are also analysed and the model equations are cast in conservative form to obtain physically consistent results with successive grid refinement. Finally, the proposed model for canonical shock-turbulence interaction is generalised to multi-dimensional flows with shock of arbitrary orientation.     

Sharp interface immersed-boundary/level-set method for wave–body interactions

A sharp interface Cartesian grid method for the large-eddy simulation of two-phase turbulent flows interacting with moving bodies is presented. The overall approach uses a sharp interface immersed boundary formulation and a level-set/ghost–fluid method for solid–fluid and fluid–fluid interface treatments, respectively. A four-step fractional-step method is used for velocity–pressure coupling, and a Lagrangian dynamic Smagorinsky subgrid-scale model is adopted for large-eddy simulations. A simple contact angle boundary condition treatment that conforms to the immersed boundary formulation is developed. A variety of test cases of different scales ranging from bubble dynamics, water entry and exit, landslide-generated waves, to ship hydrodynamics are performed for validation. Extensions for high Reynolds number ship flows using wall-layer models are also considered.     

Investigation of Lamb elastic waves in anisotropic multilayered composites applying the Green’s matrix

This article presents a numerical study of dispersion characteristics of some symmetric and antisymmetric composites modelled as multilayered packets of layers with arbitrary anisotropy of each layer. The authors introduce a subsidiary boundary problem of three-dimensional elasticity theory for the system of partial differential equations describing the harmonic oscillations of the composite caused by a surface load. The problem reduces to a boundary problem for ordinary differential equations by employing the Fourier transform. An algorithm of constructing the Fourier transform of the Green’s matrix of the given boundary problem is presented. The wave numbers of Lamb waves propagating in composites, their phase velocity surfaces and group wave surfaces are presented through the poles of the transform of the Green’s matrix. The authors obtain the dispersion curves for different directions and frequencies and investigate the dispersion curves and surfaces of wave numbers, phase velocities and group wave surfaces for various composites. The numerical results are then compared with the results obtained by applying other methods.