Entropic lattice Boltzmann method for turbulent flow simulations: Boundary conditions

We introduce a new concept of boundary conditions for realization of the lattice Boltzmann simulations of turbulent flows. The key innovation is the use of a universal distribution function for particles, analogous to the Tamm–Mott-Smith solution for the shock wave in the classical Boltzmann kinetic equation. Turbulent channel flow simulations demonstrate that the new boundary enables accurate results even with severely under-resolved grids. Generalization to complex boundary is illustrated with an example of turbulent flow past a circular cylinder.     

High-order compact schemes for incompressible flows: A simple and efficient method with quasi-spectral accuracy

In this paper, a finite difference code for Direct and Large Eddy Simulation (DNS/LES) of incompressible flows is presented. This code is an intermediate tool between fully spectral Navier–Stokes solvers (limited to academic geometry through Fourier or Chebyshev representation) and more versatile codes based on standard numerical schemes (typically only second-order accurate). The interest of high-order schemes is discussed in terms of implementation easiness, computational efficiency and accuracy improvement considered through simplified benchmark problems and practical calculations. The equivalence rules between operations in physical and spectral spaces are efficiently used to solve the Poisson equation introduced by the projection method. It is shown that for the pressure treatment, an accurate Fourier representation can be used for more flexible boundary conditions than periodicity or free-slip. Using the concept of the modified wave number, the incompressibility can be enforced up to the machine accuracy. The benefit offered by this alternative method is found to be very satisfactory, even when a formal second-order error is introduced locally by boundary conditions that are neither periodic nor symmetric. The usefulness of high-order schemes combined with an immersed boundary method (IBM) is also demonstrated despite the second-order accuracy introduced by this wall modelling strategy. In particular, the interest of a partially staggered mesh is exhibited in this specific context. Three-dimensional calculations of transitional and turbulent channel flows emphasize the ability of present high-order schemes to reduce the computational cost for a given accuracy. The main conclusion of this paper is that finite difference schemes with quasi-spectral accuracy can be very efficient for DNS/LES of incompressible flows, while allowing flexibility for the boundary conditions and easiness in the code development. Therefore, this compromise fits particularly well for very high-resolution simulations of turbulent flows with relatively complex geometries without requiring heavy numerical developments.     

Characteristic boundary conditions for direct simulations of turbulent counterflow flames

Improved Navier–Stokes characteristic boundary conditions (NSCBC) are formulated for the direct numerical simulations (DNS) of laminar and turbulent counterflow flame configurations with a compressible flow formulation. The new boundary scheme properly accounts for multi-dimensional flow effects and provides nonreflecting inflow and outflow conditions that maintain the mean imposed velocity and pressure, while substantially eliminating spurious acoustic wave reflections. Applications to various counterflow configurations demonstrate that the proposed boundary conditions yield accurate and robust solutions over a wide range of flow and scalar variables, allowing high fidelity in detailed numerical studies of turbulent counterflow flames.     

Improvement of the pressure algorithm of the stand-alone PDF method to treat unsteady three-dimensional turbulent reacting flows

This paper deals with the particle-mesh probability density function (PDF) method. It shows how an existing but less precise pressure algorithm for the stand-alone method can be improved. The present algorithm is able to handle the general case of an unsteady three-dimensional turbulent reacting flow. The transport equation of the joint PDF of velocity and composition is solved with a particle method. Open boundary conditions are realized and for statistical reasons a simple but effective particle splitting procedure is applied.

Based on a simple configuration, the properties of the presented improved pressure algorithm are analysed. It is shown which numerical condition must be taken care of so that the algorithm is able to correct the particle positions such that the normalization condition is fulfilled as accurately as specified.

To verify the algorithm the combustion of a methane–air mixture enclosed in an open simulation volume is calculated. It is shown that the simple particle splitting algorithm works very effectively in the studied case. The behaviour of the improved pressure algorithm is examined by different calculations. To analyse the convergence of the algorithm, the particle number per cell and the grid spacing are varied. To demonstrate the accuracy, a statistically stationary inflow/outflow configuration is used and the numerical solution is compared to an analytical one. For a less symmetric test case, the previous unsteady combustion problem is simulated, including an additional mean velocity in one direction.

The presented improved pressure algorithm provides the opportunity to calculate unsteady three-dimensional turbulent reacting flows with a stand-alone method, and offers an alternative to the complex hybrid finite-volume/particle PDF method.     

Explicit algebraic Reynolds stress model for compressible flow turbulence

Algebraic Reynolds stress model (ARSM) is often employed in practical turbulent flow simulations. Most of previous works on ARSM have been carried out for incompressible flows. In the present paper, a new ARSM model is suggested for compressible flows. The model adopts a compressibility factor function involving the turbulent Mach number and the gradient Mach number. Compared to incompressible flow, explicit solution for ARSM for compressible flow can hardly be obtained due to dilatation terms. We propose approximate representations for these dilatation-related terms to obtain an explicit procedure for compressible flow turbulence. The model is applied to compressible mixing layer, supersonic flat-plate boundary and planar supersonic wake flow. It is found that the model works very well yielding results that are in good agreement with the DNS and the experimental data.     

An improved high-order scheme for DNS of low Mach number turbulent reacting flows based on stiff chemistry solver

We present an improved numerical scheme for numerical simulations of low Mach number turbulent reacting flows with detailed chemistry and transport. The method is based on a semi-implicit operator-splitting scheme with a stiff solver for integration of the chemical kinetic rates, developed by Knio et al. [O.M. Knio, H.N. Najm, P.S. Wyckoff, A semi-implicit numerical scheme for reacting flow II. Stiff, operator-split formulation, Journal of Computational Physics 154 (2) (1999) 428–467]. Using the material derivative form of continuity equation, we enhance the scheme to allow for large density ratio in the flow field. The scheme is developed for direct numerical simulation of turbulent reacting flow by employing high-order discretization for the spatial terms. The accuracy of the scheme in space and time is verified by examining the grid/time-step dependency on one-dimensional benchmark cases: a freely propagating premixed flame in an open environment and in an enclosure related to spark-ignition engines. The scheme is then examined in simulations of a two-dimensional laminar flame/vortex-pair interaction. Furthermore, we apply the scheme to direct numerical simulation of a homogeneous charge compression ignition (HCCI) process in an enclosure studied previously in the literature. Satisfactory agreement is found in terms of the overall ignition behavior, local reaction zone structures and statistical quantities. Finally, the scheme is used to study the development of intrinsic flame instabilities in a lean H₂/air premixed flame, where it is shown that the spatial and temporary accuracies of numerical schemes can have great impact on the prediction of the sensitive nonlinear evolution process of flame instability.     

Spatial filtering of wall pressure fluctuations beneath a turbulent boundary layer

Methods of experimental spatial filtering of wall pressure fluctuations beneath a turbulent boundary layer are developed with the aim of obtaining information on the wave number-frequency spectrum. The spatial filtering of the pressure field components by wave-vector filters is studied. The method of spatial filtering of pressure fluctuations by an acoustic array, i.e., a periodic structure with a finite number of elementary transducers, is analyzed. The relation between the wave number characteristic of the acoustic array and the wave number spectrum of the amplitude distribution of transducer’s local sensitivity is determined. Quantitative estimates are obtained for the sensitivity of the array to the wave number spectrum of turbulent boundary-layer pressures, which is necessary for measuring the wall pressure fluctuations in a turbulent boundary layer by wave-vector filters.     

Simple models of the characteristic functional in hydrodynamic acoustics

Simple models of the characteristic functional are considered in the context of analyzing the probabilistic characteristics of turbulent pressure fluctuations. The Gaussian model of the spatial characteristic functional of wall-pressure fluctuations is shown to be more appropriate for jet flows, while the Poisson model better describes the characteristic features (splashes) of pressure fluctuations in a turbulent boundary layer. The suggestion is made that the representation of the characteristic functional as a superposition of simple models can reduce the experimental determination of the characteristic functional and the multidimensional distribution functions to measuring only a limited number of parameters and dependences characterizing the turbulent flow under study.     

Unsteady coupling of Navier-Stokes and radiative heat transfer solvers applied to an anisothermal multicomponent turbulent channel flow

Direct numerical simulations (DNS) of an anisothermal reacting turbulent channel flow with and without radiative source terms have been performed to study the influence of the radiative heat transfer on the optically non-homogeneous boundary layer structure. A methodology for the study of the emitting/absorbing turbulent boundary layer (TBL) is presented. Details on the coupling strategy and the parallelization techniques are exposed. An analysis of the first order statistics is then carried out. It is shown that, in the studied configuration, the global structure of the thermal boundary layer is not significantly modified by radiation. However, the radiative transfer mechanism is not negligible and contributes to the heat losses at the walls. The classical law-of-the-wall for temperature can thus be improved for RANS/LES simulations taking into account the radiative contribution.     

A wave field synthesis approach to reproduction of spatially correlated sound fields

This article discusses an open-loop wave field synthesis (WFS) approach for the reproduction of spatially correlated sound fields. The main application concerns laboratory reproduction of turbulent boundary layer wall pressure on aircraft fuselages and measurement of their sound transmission loss. The problem configuration involves reconstruction of random sound pressure distributions on a planar reproduction surface using a planar array of reproduction monopoles parallel to the reproduction plane. In this paper, the WFS formulation is extended to sound fields with imposed time and spatial correlation properties (or equivalently imposed cross-spectral density in the frequency and wave number domains). Numerical examples are presented for the reproduction of a propagating plane wave, diffuse acoustic field and wall pressure in subsonic or supersonic turbulent boundary layers. The reproduction accuracy is examined in terms of the size of the source plane and reproduction plane, their separation, and the number of reproduction sources required per acoustic wavelength. While the reproduction approach cannot reconstruct sub-wavelength correlation scales of subsonic turbulent boundary layers, it effectively reconstructs correlation scales larger than the acoustic wavelength, making it appropriate for diffuse acoustic field and supersonic turbulent layers.     

湍流燃烧的新二阶矩模型

本文针对湍流燃烧中模拟包括污染物生成的详细有限反应动力学的要求，用二阶矩封闭与简化概率密度的概念相结合的方法，提出了湍流燃烧的新二阶矩模型。此模型可兼顾适用于工程问题中的合理性和经济性。     

激波与层流/湍流边界层相互作用实验研究

在超声速风洞中,分别对层流和湍流来流条件下的边界层和斜激波(激波强度足以引起流动分离)相互干扰进行了实验研究,利用纳米粒子示踪平面激光散射(NPLS)技术获得了两种条件下流场的精细结构图像;利用粒子图像测速(PIV)技术获得了两种条件下流场的速度场和涡量场;综合运用NPLS结果和PIV结果对比分析了两种流动的瞬时流动结构和时间相关性,实验结果表明:层流边界层内的分离区呈现出狭长的条状,而湍流边界层内分离区呈现出较规则的椭圆;在入射激波上游距入射点较远的位置,层流边界层外围拟序结构会诱导出一系列压缩波系,进而汇聚成空间位置不稳定的诱导激波,而湍流边界层则是在入射激波上游较近的地方直接形成较强且稳定的诱导激波;在入射激波下游,层流边界层内的膨胀区域较小且急促,膨胀后产生的再附激波很弱,而湍流边界层内的膨胀区域较大,膨胀后产生的激波较强。     

环形燃烧室火焰简及旋流器流场计算

本文采用偏微分方程法生成贴体网格,在任意曲线坐标系下数值研究两种先进燃烧室火焰筒及其旋流器三维紊流流场。由于旋流器的形状复杂,本文采用型线定点法确定网格的边界。在非交错网格系下采用SIMPLE算法和混合差分格式对离散方程进行求解。计算结果表明计算方法合理,这计算程序进一步扩展,可用来预估环形燃烧室反应流流场。     

An adaptive implicit–explicit scheme for the DNS and LES of compressible flows on unstructured grids

An adaptive implicit–explicit scheme for Direct Numerical Simulation (DNS) and Large-Eddy Simulation (LES) of compressible turbulent flows on unstructured grids is developed. The method uses a node-based finite-volume discretization with Summation-by-Parts (SBP) property, which, in conjunction with Simultaneous Approximation Terms (SAT) for imposing boundary conditions, leads to a linearly stable semi-discrete scheme. The solution is marched in time using an Implicit–Explicit Runge–Kutta (IMEX-RK) time-advancement scheme. A novel adaptive algorithm for splitting the system into implicit and explicit sets is developed. The method is validated using several canonical laminar and turbulent flows. Load balance for the new scheme is achieved by a dual-constraint, domain decomposition algorithm. The scalability and computational efficiency of the method is investigated, and memory savings compared with a fully implicit method is demonstrated. A notable reduction of computational costs compared to both fully implicit and fully explicit schemes is observed.     

A mixed-time-scale low-Reynolds-number one-equation turbulence model

In this paper, a new low-Reynolds-number (LRN) one-equation turbulence model for eddy viscosity is proposed. A mixed time scale, representing a combination of three time scales: two time scales made of strain-rate parameter S and vorticity parameter Ω and the turbulent time scale k/?, is introduced into this model. The proposed model is derived from an LRN k?? two-equation model where the mixed time scale has been proved to be very effective for predicting local flows over complex terrains. In the transport equation of the model, the mixed time scale is included in the production and the dissipation terms. The new model is evaluated in channel flows at various Reynolds numbers, boundary layer flows with or without pressure gradient and backward-facing step flows with different expansion ratios and Reynolds numbers. Then the grid convergence of the model is investigated. Finally, the model performance for different values of the weighting constant C_s in the mixed time scale is assessed. The results show that the proposed model reproduces the correct wall-limiting behaviour of turbulent quantities and performs well in the near-wall region of turbulent flows. The model could be expected to be adopted in hybrid Reynolds averaged Navier–Stokes/large eddy simulation methodology for complex wall-bounded flows at high Reynolds numbers.     

Errors when assuming locally reacting boundary condition in the estimation of the surface acoustic impedance

Numerical simulations usually require boundary conditions in terms of surface acoustic impedance. The surface acoustic impedance depends on the porous material acoustic properties (e.g., characteristic impedance and wave number) and its thickness as well as the type of wave front impinging on its surface. The locally reactive behaviour hypothesis is often assumed to simplify the choice of proper boundary conditions assigning a constant acoustic impedance value on the porous material surface at a given frequency and for each angle of sound incidence. This hypothesis is also used in measurement procedures or for the estimation of the edge effects.     

Low-dimensional models of coherent structures in turbulence

For fluid flow one has a well-accepted mathematical model: the Navier-Stokes equations. Why, then, is the problem of turbulence so intractable? One major difficulty is that the equations appear insoluble in any reasonable sense. (A direct numerical simulation certainly yields a “solution”, but it provides little understanding of the process per se.) However, three developments are beginning to bear fruit: (1) The discovery, by experimental fluid mechanicians, of coherent structures in certain fully developed turbulent flows; (2) the suggestion, by Ruelle, Takens and others, that strange attractors and other ideas from dynamical systems theory might play a role in the analysis of the governing equations, and (3) the introduction of the statistical technique of Karhunen-Loève or proper orthogonal decomposition, by Lumley in the case of turbulence. Drawing on work on modeling the dynamics of coherent structures in turbulent flows done over the past ten years, and concentrating on the near-wall region of the fully developed boundary layer, we describe how these three threads can be drawn together to weave low-dimensional models which yield new qualitative understanding. We focus on low wave number phenomena of turbulence generation, appealing to simple, conventional modeling of inertial range transport and energy dissipation.