High performance computation for DNS/LES

The paper is focused on high-order compact schemes for direct numerical simulation (DNS) and large eddy simulation (LES) for flow separation, transition, tip vortex, and flow control. A discussion is given for several fundamental issues such as high quality grid generation, high-order schemes for curvilinear coordinates, the CFL condition for complex geometry, and high-order weighted compact schemes for shock capturing and shock–vortex interaction. The computation examples include DNS for K-type and H-type transition, DNS for flow separation and transition around an airfoil with attack angle, control of flow separation by using pulsed jets, and LES simulation for a tip vortex behind the juncture of a wing and flat plate. The computation also shows an almost linear growth in efficiency obtained by using multiple processors.     

Assessment of high-order discretization schemes for the DNS of compressible swirling mixing layers

We report on results of highly accurate Direct Numerical Simulations (DNS) solving the Navier-Stokes equations in cylindrical coordinates. The DNS code computes a compressible swirling mixing layer at Mach number Ma = 0.8. We present two simulations differing in the spatial discretization schemes for the convective terms. On the same grid, comparisons of flow simulations using different discretization schemes for otherwise identical conditions can be performed quantitatively and improve the understanding of the effects of numerical errors and in particular numerical dissipation. (© 2008 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Characterization of the Reynolds-stress and dissipation-rate decay and anisotropy from DNS of grid-generated turbulence

Grid–generated turbulence is a classical but still controversial topic, one open issue being the spatial decay rate of turbulent energy. We study the influence of grid geometry on the Reynolds–stress and dissipation–rate tensors, including the range and exponent of their self–similar spatial decay. DNS using a validated lattice Boltzmann code at mean–flow Reynolds numbers up to 1400 are performed, comparing square grids with blockage ratios from 0.05 to 0.49. A clear picture of spatial distribution and self–similarity emerges for the statistics of interest: Axisymmetry is excellently confirmed. A consistent power law decay is found in the self–similar decay region beyond 10 grid stride lengths downstream. Its exponent of –5/3 can be obtained, for weak turbulence, from a spatial flux balance reminiscent of the constant transport through the inertial range of isotropic turbulence. In the near–grid region, on the other hand, differences in Reynolds stress components are pronounced while those between dissipation tensor components are only recognizable very close to the grid, where a strong dependence on grid porosity is found. A normalization with respect to porosity is proposed that collapses the data from all runs. (© 2008 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

A fast running numerical model based on the implementation of volume forces for prediction of pressure drop in a fin tube heat exchanger

Numerical based design of geometrical structures is common when studying systems involving heat exchangers, a central component in several fields, such as industrial, vehicle and household systems. The geometrical structure of heat exchangers is generally comprised by closely placed fins and tube bundles. The creation of a mesh grid for a geometrically compact heat exchanger will result in a dense structure, which is not feasible for personal computer usage. Hence, volume forces were created based on Direct Numerical Simulations (DNS) on a Flow Representative Volume (FRV) of a tube fin heat exchanger in an internal duct system of a heat pump tumble dryer. A relation of the volume averaged velocity and the volume averaged force was established in two different FRV models with a finite element simulation in COMSOL. This relation was subsequently used to create flow resistance coefficients based on volume averaged expressions of fluid velocity and volume forces. These flow resistance coefficients were implemented in two respective porous models, which represent the entire heat exchanger except the interior arrangements of fins and tube bundles. Hence, the computation time was reduced thanks to the absence of a dense mesh grid. Experimental results of the entire heat exchanger showed good agreement with the second porous model in terms of pressure drop and volume flow rate.     

On the benefits of ODT-based stochastic turbulence modeling

We summarize the group's progress in applying, analyzing, and improving ODT and ODT-based stochastic turbulence models like ODTLES. Compared to DNS these models span a wider range of scales while compared to RANS/LES (i) the molecular effects are retained and (ii) no assumption of scale separation is made. In this regard ODTLES has more properties of DNS than of standard LES. (© 2014 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Analysis of turbulent diffusion in the temperature variance dissipation rate equation

Results of a new direct numerical simulation (DNS) for the Rayleigh‐Bénard convection at Prandtl number Pr = 0.025 and Rayleigh number Ra = 100,000 are used to analyse the turbulent diffusion term in the transport equation for the temperature variance dissipation rate. These DNS results are also used to investigate the performance of statistical models for this turbulent diffusion term. (© 2004 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

DNS and Experiment of a Turbulent Channel Flow with StreamwiseRotation - Study of the Cross Flow Phenomena

Modelling of rotating turbulent flows is a major issue in engineering applications. Intensive research has been dedicated to rotating channel flows in spanwise direction such as by [1], [2] to name only two. In this work a turbulent channel flow rotating about the streamwise direction is presented. The theory is based on the investigations of [4] employing the symmetry theory. It was found that a cross flow in the spanwise direction is induced. A series of direct numerical simulations (DNS) at different rotation numbers is carried out to examine these effects. Further, the results of the DNS are compared to the measuremets of a corresponding experiment. (© 2005 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

基于多GPU的格子Boltzmann法对槽道湍流的直接数值模拟

采用多GPU并行的格子Boltzmann方法（lattice Boltzmann method, LBM）对充分发展的槽道湍流进行了直接数值模拟．GPU(graphic processing unit)的数据并行单指令多线程（single-instruction multiple-thread, SIMT)特征与LBM完美的并行性相匹配,使得LBM求解器在GPU上运行获得了极高的性能,亦使得大规模DNS(direct numerical simulation)在桌面级计算机上进行成为可能．采用8个GPU,网格数目达到6.7×107,全场网格尺寸Δ+=1.41．模拟3×106个时间步长,用时仅24 h．另外,直接模拟结果无论是在平均流速或湍流统计量上均与Moser等的结果吻合得很好,这也证实了二阶精度的格子Boltzmann法直接模拟湍流的能力与有效性     

Numerical and experimental investigation of the turbulent flow through a low-pressure turbine cascade in the endwall region

In the present work, direct numerical simulations (DNS) of the flow through a low-pressure linear turbine cascade T106 with parallel endwalls were conducted to investigate the effects of unsteady passing wakes of the upstream blade row on the secondary flow in the endwall region of the passage. The impact of the wakes on the secondary flow is discussed by means of the time-averaged values. Furthermore, the results of DNS are compared with experimental data. (© 2013 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

DNS Curves in a Production/Inventory Model

In this paper, we investigate the bifurcation behavior of an inventory/production model close to a Hamilton-Hopf bifurcation. We show numerically that two different types of DNS curves occur: If the initial states are far from the bifurcating limit cycle, the limit cycle can be approached along different trajectories with the same cost. For a subcritical bifurcation scenario, the hyperbolic equilibrium state and the hyperbolic limit cycle coexist for some parameter range. When both the long term states yield approximately the same cost, a second DNS curve separates their domains of attraction. At the intersection of these two DNS curves, a threefold Skiba point in the state space is found. The acronym DNS stands for Dechert, Nishimura, and Skiba (Ref. 1)     

Dispersion and deposition mechanisms of particles suspended in a turbulent plane Couette flow

Inertial particle transfer in a turbulent plane Couette flow (C flow) was studied using Direct Numerical Simulation (DNS) of the flow combined with a Lagrangian particle tracking approach for particles with Stokes numbers (St) 5, 25 and 125. The particle concentration was assumed low enough, so that the simulations were done under one-way coupling condition.     

Stochastic Modeling of Turbulent Scalar Transport at Very High Schmidt Numbers

A stochastic modeling approach, the so-called One-Dimensional Turbulence (ODT), is used to study passive scalar transport in incompressible, fully-developed, turbulent channel flows up to very high Schmidt numbers Sc = ν/Γ ∼ 10⁴ (kinematic viscosity ν, scalar diffusivity Γ). Good agreement is obtained between ODT and Direct Numerical Simulation (DNS) results with respect to the mean, the fluctuation statistics, and the dimensionless mass transfer coefficient K⁺. ODT yields the mass transfer coefficient to become independent of the Reynolds number at high Schmidt numbers, which is similar to reference laboratory measurements and DNS. The present ODT results exhibit the power law K⁺ ∝ Sc^−0.65 with a scaling exponent that is only slightly larger than in the reference laboratory measurements and DNS. The results obtained suggests that ODT can be a versatile tool for turbulent transport modeling in a wide range of physical parameters. (© 2017 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Direct numerical simulation of turbulent non-Newtonian flow using OpenFOAM

Understanding transition and turbulence in the flow of shear-thinning non-Newtonian fluids remains substantially unresolved and additional research is required to develop better computational methods for wall-bounded turbulent flows of these fluids. Previous DNS studies of shear-thinning fluids mainly use purpose-built codes and simple geometries such as pipes and channels. However in practical application, the geometry of mixing vessels, pumps and other process equipment is far more complex, and more flexible computational methods are required. In this paper a general-purpose DNS approach for shear-thinning fluids is undertaken using the OpenFOAM CFD library. DNS of turbulent Newtonian and non-Newtonian flow in a pipe flow are conducted and the accuracy and efficiency of OpenFOAM are assessed against a validated high-order spectral element-Fourier DNS code – Semtex. The results show that OpenFOAM predicts the flow of shear-thinning fluids to be a little more transitional than the predictions from Semtex, with lower radial and azimuthal turbulence intensities and higher axial intensity. Despite this, the first and second order turbulence statistics differ by at most 16%, and usually much less. An assessment of the parallel scaling of OpenFOAM indicates that OpenFOAM scales very well for the CPUs from 8 to 512, but the intranode scalability is poor for less than 8CPUs. The present work shows that OpenFOAM can be used for DNS of shear-thinning fluids in the simple case of pipe flow, and suggests that more complex flows, where flow separation is often important, are likely to be simulated with accuracies that are acceptably good for engineering application.     

Direct Numerical Simulation of Liquid Films with Large Interfacial Deformation††

Liquid films are important in many industrial applications, but also from a fundamental point of view, they are important two-phase flow systems. In this paper, we develop a sharp interface/level set method for the Direct Numerical Simulation (DNS) of liquid films with large interfacial deformations, and large density ratio between the liquid and the gas phase. We use the ghost fluid method to capture the interface motion without smoothing properties across it, and adopt a maximization scheme for the implicit treatment of the viscous term in the Navier–Stokes equations. Because liquid films have very low average depth compared to the distance between waves, several innovations are required to handle solving the equations on grid structures of high aspect ratio. Two-dimensional (2D) calculations for wavy films falling down a vertical wall are presented, and good agreement is found when numerical solutions are directly compared with the experiments of Nosoko et al. [ 1 ]. Some results are also presented for falling liquid films transitioning naturally from 2D to 3D surface wave structures demonstrating the potential of the method for 3D fully coupled two-phase liquid films simulations.     

Extending temporal simulations

Direct numerical simulations (DNS) of spatially growing turbulent shear layers may be performed as temporal simulations by solving the governing equations with some additional terms while imposing streamwise periodicity. These terms are functions of the means whose spatial growth is calculated easily and accurately from statistics of the temporal DNS. Equations for such simulations are derived.     

Numerical experiments on flow control of near wall turbulence

In this paper we demonstrate by means of direct numerical simulations (DNS) of channel flow with surface structuring or modified boundary conditions how turbulence can be controlled by influencing the anisotropy state of near wall turbulence. (© 2008 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Numerical Investigation of Sound Generation due to Laminar Flow Past Elliptic Cylinders

Numerical investigation of sound generation due to unsteady laminar flow past elliptic cylinders has been carried out using direct numerical simulation $(DNS)$ approach at a free-stream Mach number of $0.2$. Effects of aspect ratio $(0.6\le AR\le 1.0)$ and Reynolds number $(100\le Re \le 160)$ on the characteristics of radiated sound fields are analyzed. Two-dimensional compressible fluid flow equations are solved on a refined grid using high resolution dispersion relation preserving $(DRP)$ schemes. Using present $DNS$ data, equivalent noise sources as given by various acoustic analogies are evaluated. Amplitudes and frequencies associated with these noise sources are further related to characteristics of disturbance pressure fields. Disturbance pressure fields are intensified with increase in Reynolds number and aspect ratio. Thus, radiated sound power increases with increase in Reynolds number and aspect ratio. Among various cases studied here, minimum and maximum values of radiated sound power are found at $Re=120$ & $AR=0.6$ and $Re=160$ & $AR=1.0$, respectively. Directivity patterns show that the generated sound fields are dominated by the lift dipole for all cases. Next, proper orthogonal decomposition $(POD)$ technique has been implemented for decomposing disturbance pressure fields. The $POD$ modes associated with the lift and the drag dipoles have been identified. $POD$ analyses also clearly display that the radiated sound fields are dominated by the lift dipole only. Further, acoustic and hydrodynamic modes obtained using Doak's decomposition method have confirmed the patterns of radiated sound field intensities.     

Direct numerical simulation of turbulent non-Newtonian flow using a spectral element method

A spectral element—Fourier method (SEM) for Direct Numerical Simulation (DNS) of the turbulent flow of non-Newtonian fluids is described and the particular requirements for non-Newtonian rheology are discussed. The method is implemented in parallel using the MPI message passing kernel, and execution times scale somewhat less than linearly with the number of CPUs, however this is more than compensated by the improved simulation turn around times. The method is applied to the case of turbulent pipe flow, where simulation results for a shear-thinning (power law) fluid are compared to those of a yield stress (Herschel–Bulkley) fluid at the same generalised Reynolds number. It is seen that the yield stress significantly dampens turbulence intensities in the core of the flow where the quasi-laminar flow region there co-exists with a transitional wall zone. An additional simulation of the flow of blood in a channel is undertaken using a Carreau–Yasuda rheology model, and results compared to those of the one-equation Spalart-Allmaras RANS (Reynolds-Averaged Navier–Stokes) model. Agreement between the mean flow velocity profile predictions is seen to be good. Use of a DNS technique to study turbulence in non-Newtonian fluids shows great promise in understanding transition and turbulence in shear thinning, non-Newtonian flows.