Near-wall modelling in computations of turbulent flows on unstructured grids

The questions related to the formulation and numerical realization of boundary conditions on a wall at the computation of turbulent flows on unstructured grids are considered. A technique is proposed for realization of weak boundary conditions assuming a non-zero value of the tangent velocity on the wall at a discretization of the Reynolds-averaged Navier — Stokes equations by the control volume method. The capabilities of the developed approach are demonstrated by the example of computing the flow in the inter-blade channel of a low-velocity compressor. The influence of the near-wall grid step on the accuracy of computations, in particular, the pressure distribution near the profile trailing edge is shown, and the solution grid dependence is investigated when using the method of near-wall functions and weak boundary conditions.     

Computation of the normal injection of a hydrogen jet into a supersonic air flow

The interaction of a planar supersonic air flow with the hydrogen jet injected perpendicularly across the slot from the duct walls is studied numerically. An algorithm is constructed for solving the Favre-averaged Navier — Stokes equations for the flow of a thermally perfect multicomponent gas based on the ENO scheme. The influence of the jet Mach number and the ratio of the jet and flow pressures on the shockwave structure of the flow and the jet penetration depth is shown.     

Slip Boundary Conditions for the Compressible Navier–Stokes Equations

The slip boundary conditions for the compressible Navier–Stokes equations are derived systematically from the Boltzmann equation on the basis of the Chapman–Enskog solution of the Boltzmann equation and the analysis of the Knudsen layer adjacent to the boundary. The resulting formulas of the slip boundary conditions are summarized with explicit values of the slip coefficients for hard-sphere molecules as well as the Bhatnagar–Gross–Krook model. These formulas, which can be applied to specific problems immediately, help to prevent the use of often used slip boundary conditions that are either incorrect or without theoretical basis.     

A hybrid CFD/characteristics method for fast characterization of hypersonic blunt forebody/inlet flow

A hybrid CFD/characteristic method(CCM) was proposed for fast design and evaluation of hypersonic inlet flow with nose bluntness, which targets the combined advantages of CFD and method of characteristics. Both the accuracy and efficiency of the developed CCM were verified reliably, and it was well demonstrated for the external surfaces design of a hypersonic forebody/inlet with nose bluntness. With the help of CCM method, effects of nose bluntness on forebody shock shapes and the flowfield qualities which dominate inlet performance were examined and analyzed on the two-dimensional and axisymmetric configurations. The results showed that blunt effects of a wedge forebody are more substantial than that of related cone cases. For a conical forebody with a properly blunted nose, a recovery of the shock front back to that of corresponding sharp nose is exhibited, accompanied with a gradually fading out of entropy layer effects. Consequently a simplification is thought to be reasonable for an axisymmetric inlet with a proper compression angle, and a blunt nose of limited radius can be idealized as a sharp nose, as the spillage and flow variations at the entrance are negligible, even though the nose scale increases to 10% cowl lip radius. Whereas for two-dimensional inlets, the blunt effects are substantial since not only the inlet capturing/starting capabilities, but also the flow uniformities are obviously degraded.     

Investigation of separation properties of turbulent boundary layer at its sequential interaction with shocks of different strengths

The results are presented for numerical modelling of two-dimensional flows with large pressure gradients in a wide range of freestream parameters (M = 2−4, Re ₁ = 5−30·10⁶ 1/m) and the intensities of perturbing factors. Computations were performed with the use of averaged unsteady Navier — Stokes equations of a viscous heat-conducting gas. The structure of a turbulent boundary layer at its passage through a single shock and a system of shocks of different strengths, which lie at a fixed distance from one another, was investigated numerically. In the case of the boundary layer passage through a system of shocks, the influence of the first interaction on the structure and separation properties of the boundary layer behind the second shock was investigated. The presence of a preliminary shock was shown to improve the boundary layer capability to withstand separation ahead of the secondary interaction region.     

Absorbing boundary conditions for nonlinear Euler and Navier–Stokes equations based on the perfectly matched layer technique

Absorbing boundary conditions for the nonlinear Euler and Navier–Stokes equations in three space dimensions are presented based on the perfectly matched layer (PML) technique. The derivation of equations follows a three-step method recently developed for the PML of linearized Euler equations. To increase the efficiency of the PML, a pseudo mean flow is introduced in the formulation of absorption equations. The proposed PML equations will absorb exponentially the difference between the nonlinear fluctuation and the prescribed pseudo mean flow. With the nonlinearity in flux vectors, the proposed nonlinear absorbing equations are not formally perfectly matched to the governing equations as their linear counter-parts are. However, numerical examples show satisfactory results. Furthermore, the nonlinear PML reduces automatically to the linear PML upon linearization about the pseudo mean flow. The validity and efficiency of proposed equations as absorbing boundary conditions for nonlinear Euler and Navier–Stokes equations are demonstrated by numerical examples.     

Modelling of methanol-to-hydrogen steam reforming with a heat flux distributed along a microchannel

The flow of reacting mixture of methanol and steam in a 2D microslot was studied numerically at activation of the reactions on the channel wall. This modelling was carried out in the framework of Navier — Stokes equations for a laminar flow of multicomponent compressible gas. Correlations between thermal, diffusion, and physical-chemical processes were studied under the conditions of intense endothermic reaction and external heat supply distributed along the channel. It is shown that not only the amount of heat supplied to the reaction zone is essential, but also the mode of heat supply along the channel length is important, which allows optimization of the compact reactor for hydrogen production.     

考虑熵层效应的扫掠激波/湍流边界层干扰特性研究

为了探究熵层对扫掠激波/湍流边界层干扰特性的影响规律,采用仿真方法对尖鳍/钝板物理模型进行研究。结果表明：扫掠激波上游的熵层厚度随着平板前缘钝化半径的增大而增加,同时边界层厚度也随着熵层厚度的增加而增加。熵层的引入并不改变扫掠激波/湍流边界层干扰固有的准锥形相似特性,也不会改变拟锥原点(virtual conical origin, VCO)的位置,仅会改变干扰形成的上游影响线和分离线的角度。扫掠激波/湍流边界层干扰形成的锥形主旋涡和角涡的尺度随着熵层厚度的增加而增大。上游熵层的引入增大了下游扫掠激波/湍流边界层干扰区的总压损失,但扫掠激波/湍流边界层干扰自身造成的相对总压损失并不受上游熵层的影响。     

Aerodynamic design of a supersonic three-dimensional inlet

The results of designing and numerical gas-dynamic modeling a supersonic three-dimensional inlet of a new type are considered. A ramp of external compression of this inlet is the V-shaped body forming an initial plane oblique shock wave and a subsequent isentropic compression wave. The inlet incorporates an entrance section of internal compression, where also a plane oblique shock wave and a subsequent isentropic compression wave are formed by a cowl. The designed three-dimensional inlet has small inclination angles of compression surfaces, which ensures its low wave drag. According to the estimates of inlet efficiency in terms of the compression ratio and the total pressure recovery factor, it is close to the optimal two-dimensional shocked inlet of external compression considered by Oswatisch as well as Petrov and Ukhov. The flow in the inlet was computed with the use of the Euler and Navier — Stokes codes provided by the commercial package “FLUENT”. The flow in the inlet throat in the design regime computed under the inviscid flow approximation is uniform. The most substantial effect of the flow viscosity in this regime manifests itself in the interaction of the shock wave from the cowl with the boundary layer on the V-shaped compression body in the inlet internal duct. According to computed data, the boundary layer separation does not occur in this case; however, due to viscosity effects, reflected shock waves are formed here which results in significant deviations of flow structure as compared to the computed inviscid flow.     

Numerical simulation of the evolution of unstable disturbances of various modes and initial stages of the laminar-turbulent transition in the boundary layer at the freestream Mach number М = 6

Direct numerical simulations of linear and nonlinear stages of the evolution of unstable disturbances of various modes and initial stages of the laminar-turbulent transition in the boundary layer on a flat plate at the freestream Mach number M = 6 are performed on the basis of full unsteady Navier–Stokes equations for a compressible gas. A considerable effect of three-dimensional unstable disturbances on initiation of the laminar-turbulent transition is demonstrated.     

Stationary Flow Past a Semi-Infinite Flat Plate: Analytical and Numerical Evidence for a Symmetry-Breaking Solution

We consider the question of the existence of stationary solutions for the Navier Stokes equations describing the flow of a incompressible fluid past a semi-infinite flat plate at zero incidence angle. By using ideas from the theory of dynamical systems we analyze the vorticity equation for this problem and show that a symmetry-breaking term fits naturally into the downstream asymptotic expansion of a solution. Finally, in order to check that our asymptotic expressions can be completed to a symmetry-breaking solution of the Navier–Stokes equations we solve the problem numerically by using our asymptotic results to prescribe artificial boundary conditions for a sequence of truncated domains. The results of these numerical computations a clearly compatible with the existence of such a solution. Mathematics Subject Classification (2000). 76D05, 76D25, 76M10, 41A60, 35Q35 Supported in part by the Fonds National Suisse.     

Numerical investigation of heat and mass transfer in the reactor of a plasma-chemical plant purposed for polychlorinated biphenyls treatment

Gas-dynamic and thermal characteristics of the gas flow in the flow part of a small-scale plasmachemical reactor for trichlorbiphenyl decomposition were calculated numerically. The investigations were performed with no regard to the chemical interaction of the components: in the calculations, the treated substance was replaced by a simulator (water steam), water steam was also used as an oxidant. Mathematical model of the flow is based on the complete system of Navier — Stokes equations in the context of axisymmetric task statement, with due regard to the gas flow swirling. The calculation results enabled us to choose the optimum geometrical parameters of the reactor design.     

考虑转动能的一维/二维Boltzmann-Rykov模型方程数值算法

研究考虑转动能的Boltzmann-Rykov模型方程,基于转动自由度对气体分子速度分布函数矩积分,引入约化速度分布函数,应用离散速度坐标法与数值积分技术,将气体运动论模型方程化为在离散速度坐标点处关于三个约化速度分布函数的联立方程组.应用拓展计算流体力学有限差分方法,数值计算考虑转动自由度的双原子气体一维、二维Boltzmann模型方程,得到高、低Knudsen数一维激波管内流动和二维竖直平板绕流问题的流场,分析验证考虑转动能的Boltzmann-Rykov模型方程全流域统一算法求解一维/二维气体流动问题的可靠性.结果表明,气体稀薄程度与分子内自由度对流场具有较大影响,且Knudsen数较高的稀薄气体流动呈现严重的非平衡流动特点.     

Nonlinear vibration of viscoelastic embedded-DWCNTs integrated with piezoelectric layers-conveying viscous fluid considering surface effects

This article studies the nonlinear vibration of viscoelastic embedded nano-sandwich structures containing of a double walled carbon nanotube (DWCNT) integrated with two piezoelectric Zinc oxide (ZnO) layers. DWCNT and ZnO layers are subjected to magnetic and electric fields, respectively. This system is conveying viscous fluid and the related force is calculated by modified Navier–Stokes relation considering slip boundary condition and Knudsen number. Visco–Pasternak model with three parameters of the Winkler modulus, shear modulus, and damp coefficient is used for simulation of viscoelastic medium. The nano-structure is simulated as an orthotropic Timoshenko beam (TB) and the effects of small scale, structural damping and surface stress are considered based on Eringen's, Kelvin-voigt and Gurtin–Murdoch theories. Energy method and Hamilton's principle are employed to derive motion equations which are then solved using differential quadrature method (DQM). The detailed parametric study is conducted, focusing on the combined effects of small scale effect, fluid velocity, thickness of piezoelectric layer, boundary condition, surface effects, van der Waals (vdW) force on the frequency and critical velocity of nano-structure. Results indicate that the frequency and critical velocity increases with assume of surface effects.     

Asymptotic Analysis of a Slightly Rarefied Gas with Nonlocal Boundary Conditions

In this paper nonlocal boundary conditions for the Navier–Stokes equations are derived, starting from the Boltzmann equation in the limit for the Knudsen number being vanishingly small. In the same spirit of (Lombardo et al. in J. Stat. Phys. 130:69–82, 2008) where a nonlocal Poisson scattering kernel was introduced, a gaussian scattering kernel which models nonlocal interactions between the gas molecules and the wall boundary is proposed. It is proved to satisfy the global mass conservation and a generalized reciprocity relation. The asymptotic expansion of the boundary-value problem for the Boltzmann equation, provides, in the continuum limit, the Navier–Stokes equations associated with a class of nonlocal boundary conditions of the type used in turbulence modeling.     

有变高度圆柱干扰的平板表面流谱拓扑结构

采用分区方法和Roe三阶流通量差分分裂格式数值求解雷诺平均N-S方程,湍流附加粘性系数由修正的Baldwin-Lomax模型计算,数值模拟了高超声速绕变高度圆柱流动,进而根据拓扑学理论给出了有变高度圆柱干扰的平板表面流谱拓扑结构,并结合对称截面流谱进行了简要的分析与探讨,指出了需要进一步深入研究的问题。     

The slip boundary condition in the dynamics of solid particles immersed in Stokesian flows

This paper reviews the classical theories of the dynamics of solid particles in a viscous flow via traditional Navier–Stokes/Stokes equations with slip or nonslip boundary conditions, and also studies a corresponding dynamical equation. The emphasis of this paper is on the explicit expressions of the slip effect at the solid-fluid boundary in the dynamics of solid particles in Stokesian fluids.     

Simulations of whistling and the whistling potentiality of an in-duct orifice with linear aeroacoustics

This paper demonstrates a linear aeroacoustic simulation methodology to predict the whistling of an orifice plate in a flow duct. The methodology is based on a linearized Navier–Stokes solver in the frequency domain with the mean flow field taken from a Reynolds-Averaged Navier–Stokes (RANS) solution. The whistling potentiality is investigated via an acoustic energy balance for the in-duct element and good agreement with experimental data is shown. A Nyquist stability criterion based on the simulation data was applied to predict whistling of the orifice when placed in a finite sized duct and experiments were carried out to validate the predictions. The results indicate that although whistling is a nonlinear phenomena caused by an acoustic-flow instability feed-back loop, the linearized Navier–Stokes equations can be used to predict both whistling potentiality and a duct system's ability to whistle or not.     

Investigation of temperature fields in supersonic flow behind a backward-facing step

The results of numerical modelling and experimental investigations of high-enthalpy turbulent flows in the neighborhood of 90-degree backward-facing steps at the Mach numbers M_∞ = 2–4 are presented. The experiments were conducted in the hot-shot wind tunnel IT-302M of ITAM SB RAS. The computations were carried out on the basis of the full Favres-averaged Navier — Stokes equations augmented by the Wilcox turbulence model. The temperature factor influence on the flow structure in the separated zone and temperature distributions was investigated numerically for different Mach numbers. The wall temperature is shown to affect significantly the quantity and sizes of recirculation vortices as well as the temperature distribution in the zone of flow separation and reattachment. The computational results are compared with experimental data on the pressure distribution on the model surface and the wave structure of the flow.     

Non-Local Scattering Kernel and the Hydrodynamic Limit

In this paper we study the interaction of a fluid with a wall in the framework of the kinetic theory. We consider the possibility that the fluid molecules can penetrate the wall to be reflected by the inner layers of the wall. This results in a scattering kernel which is a non-local generalization of the classical Maxwell scattering kernel. The proposed scattering kernel satisfies a global mass conservation law and a generalized reciprocity relation. We study the hydrodynamic limit performing a Knudsen layer analysis, and derive a new class of (weakly) nonlocal boundary conditions to be imposed to the Navier–Stokes equations.