Detached direct numerical simulations of turbulent two-phase bubbly channel flow

DNS simulations of two-phase turbulent bubbly channel flow at Re_τ = 180 (Reynolds number based on friction velocity and channel half-width) were performed using a stabilized finite element method (FEM) and a level set approach to track the air/water interfaces.     

Eigenmode decomposition of the turbulent shear layer above a square rib

1D, 2D and fully 3D structural information is extracted from a large-eddy simulation of turbulent flow over a square rib, using Proper Orthogonal Decomposition. In this paper, we focus on the shear layer separating at the leading edge and developing above and behind the top face of the flow obstacle. The two-point correlation tensor, required for the solution of the related eigenvalue problem, is provided from a large-eddy simulation for a Reynolds number of about 50 000 (based on obstacle height and incoming bulk velocity). The results indicate that the eigenmode decomposition is a very useful tool to extract organized structures even from very complex turbulent velocity fields at high Reynolds numbers. A significant amount of turbulent energy can still be captured by a relatively small number of modes.     

GPU‐accelerated direct numerical simulations of decaying compressible turbulence employing a GKM‐based solver

Gas Kinetic Method‐based flow solvers have become popular in recent years owing to their robustness in simulating high Mach number compressible flows. We evaluate the performance of the newly developed analytical gas kinetic method (AGKM) by Xuan et al. in performing direct numerical simulation of canonical compressible turbulent flow on graphical processing unit (GPU)s. We find that for a range of turbulent Mach numbers, AGKM results shows excellent agreement with high order accurate results obtained with traditional Navier–Stokes solvers in terms of key turbulence statistics. Further, AGKM is found to be more efficient as compared with the traditional gas kinetic method for GPU implementation. We present a brief overview of the optimizations performed on NVIDIA K20 GPU and show that GPU optimizations boost the speedup up‐to 40x as compared with single core CPU computations. Hence, AGKM can be used as an efficient method for performing fast and accurate direct numerical simulations of compressible turbulent flows on simple GPU‐based workstations. Copyright © 2016 John Wiley & Sons, Ltd.     

Stability of free convection in a rotating porous layer distant from the axis of rotation

The stability and onset of convection in a rotating fluid saturated porous layer subject to a centrifugal body force and placed at an offset distance from the center of rotation is investigated analytically. The marginal stability criterion is established in terms of a critical centrifugal Rayleigh number and a critical wave number for different values of the parameter representing the dimensionless offset distance from the center of rotation. At the limit of an infinite distance from the center of rotation the results are identical to the convection resulting from heating a porous layer from below subject to the gravitational body force. At the other limit, when the parameter controlling the offset distance approaches zero, the results converge to previously found solutions for the convection in a porous layer adjacent to the axis of rotation. The results provide the stability map for all positive values of the parameter controlling the offset distance from the center of rotation, hence bridging the gap between the two extreme limit cases.     

Analysis on secondary instability of shear layer based on the concept of phase synchronization

A concept of phase synchronization point is proposed, and then a model is built using this concept to explain secondary instabilities. This model has been used to determine the conditions of K- and H-type secondary instabilities, which are coincident with the conditions published in literatures. It also can be used to analyze other secondary instability phenomena. For example, the numerical results validate the analysis results in the case of 1/3rd subharmonic mode secondary instability. Furthermore, the numerical results indicate that the spanwise wave number of 3D disturbance has significant effect on the secondary instability.     

An analysis of subgrid-resolved scale interactions with use of results from direct numerical simulations

Subgrid nonlinear interaction and energy transfer are analyzed using direct numerical simulations of isotropic turbulence. Influences of cutoff wave number at different ranges of scale on the energetics and dynamics have been investigated. It is observed that subgrid-subgrid interaction dominates the turbulent dynamics when cut-off wave number locates in the energy-containing range while resolved-subgrid interaction dominates if it is in the dissipation range. By decomposing the subgrid energy transfer and nonlinear interaction into ‘forward’ and ‘backward’ groups according to the sign of triadic interaction, we find that individually each group has very large contribution, but the net of them is much smaller, implying that tremendous cancellation happens between these two groups.     

可压缩自由剪切流混合转捩大涡模拟

针对湍流气动光学效应与冲压发动机气体混合机理问题,开展了可压缩混合层流动空间模式大涡模拟和时间模式直接数值模拟研究.通过对流场(包含亚/亚混合、超/亚混合两种情况)失稳、转捩直至完全湍流的空间发展过程的研究表明,对流Mach数0.4状态下流场失稳以二维最不稳定扰动为主;非线性发展中,基频涡对并及展向涡撕裂主控流动转捩,流场发生混合转捩;转捩后脉动流场基本达到局部各向同性,此时,湍流Mach数低于0.3,流动压缩性可近似忽略.     

Flow past a cylinder: shear layer instability and drag crisis

Flow past a circular cylinder for Re=100 to 10⁷ is studied numerically by solving the unsteady incompressible two‐dimensional Navier–Stokes equations via a stabilized finite element formulation. It is well known that beyond Re ～ 200 the flow develops significant three‐dimensional features. Therefore, two‐dimensional computations are expected to fall well short of predicting the flow accurately at high Re. It is fairly well accepted that the shear layer instability is primarily a two‐dimensional phenomenon. The frequency of the shear layer vortices, from the present computations, agree quite well with the Re^0.67 variation observed by other researchers from experimental measurements. The main objective of this paper is to investigate a possible relationship between the drag crisis (sudden loss of drag at Re ～ 2 × 10⁵) and the instability of the separated shear layer. As Re is increased the transition point of shear layer, beyond which it is unstable, moves upstream. At the critical Reynolds number the transition point is located very close to the point of flow separation. As a result, the shear layer eddies cause mixing of the flow in the boundary layer. This energizes the boundary layer and leads to its reattachment. The delay in flow separation is associated with narrowing of wake, increase in Reynolds shear stress near the shoulder of the cylinder and a significant reduction in the drag and base suction coefficients. The spatial and temporal power spectra for the kinetic energy of the Re=10⁶ flow are computed. As in two‐dimensional isotropic turbulence, E(k) varies as k^?5/3 for wavenumbers higher than energy injection scale and as k^?3 for lower wavenumbers. The present computations suggest that the shear layer vortices play a major role in the transition of boundary layer from laminar to turbulent state. Copyright © 2004 John Wiley & Sons, Ltd.     

Direct numerical simulation of low Reynolds number flows in an open‐channel with sidewalls

A direct numerical simulation of low Reynolds number turbulent flows in an open‐channel with sidewalls is presented. Mean flow and turbulence structures are described and compared with both simulated and measured data available from the literature. The simulation results show that secondary flows are generated near the walls and free surface. In particular, at the upper corner of the channel, a small vortex called inner secondary flows is simulated. The results show that the inner secondary flows, counter‐rotating to outer secondary flows away from the sidewall, increase the shear velocity near the free surface. The secondary flows observed in turbulent open‐channel flows are related to the production of Reynolds shear stress. A quadrant analysis shows that sweeps and ejections are dominant in the regions where secondary flows rush in toward the wall and eject from the wall, respectively. A conditional quadrant analysis also reveals that the production of Reynolds shear stress and the secondary flow patterns are determined by the directional tendency of the dominant coherent structures. Copyright © 2009 John Wiley & Sons, Ltd.     

土石混合体直剪离散元数值试验研究

工程中普遍存在的土石混合体以其复杂的工程地质力学性质越来越受研究者的关注。由于"块石"的存在使得土石混合体在细观层次上呈现明显的结构性特征,这种结构性将影响甚至控制着其变形破坏机制及宏观力学特征。本文借助三维颗粒离散元分析软件YADE分别从含石量、试样尺寸、强度特性等角度对土石混合体的力学性质开展了一系列的数值直剪试验研究工作,并取得了一些有意义的研究成果:在含石量及粒度组成相同的情况下土石混合体的宏观抗剪强度及剪胀性随着试样尺寸的增加而呈现降低趋势,而在相同试样尺寸下将随着含石量的增加而增加;内部块石的存在影响着其细观应力状态,从而影响其宏观力学特性。     

Finite‐difference 4th‐order compact scheme for the direct numerical simulation of instabilities of shear layers

An algorithm based on the 4th‐order finite‐difference compact scheme is developed and applied in the direct numerical simulations of instabilities of channel flow. The algorithm is illustrated in the context of stream function formulation that leads to field equation involving 4th‐order spatial derivatives. The finite‐difference discretization in the wall‐normal direction uses five arbitrarily spaced points. The discretization coefficients are determined numerically, providing a large degree of flexibility for grid selection. The Fourier expansions are used in the streamwise direction. A hybrid Runge–Kutta/Crank–Nicholson low‐storage scheme is applied for the time discretization. Accuracy tests demonstrate that the algorithm does deliver the 4th‐order accuracy. The algorithm has been used to simulate the natural instability processes in channel flow as well as processes occurring when the flow is spatially modulated using wall transpiration. Extensions to three‐dimensional situations are suggested. Copyright © 2005 John Wiley & Sons, Ltd.     

Averaging methods for numerical simulations of flows through heterogeneous porous media

Many natural rock systems contain small patches of different permeability which affect the flow of fluids through them. As these heterogeneities become smaller and more numerous, they become harder to model numerically. We consider how to reduce the computational effort required in simulations by incorporating their effects in the boundary conditions at the edges of each grid block. This is in contrast with current methods which involve often arbitrary changes in the fluid properties. The method is restricted to the case of widely-spaced patches, which simplifies interaction effects. The system then reduces to an array of dipoles, and two averaging methods are proposed for finite grid blocks. Several infinite systems, including vertical and horizontal bands, are also considered as further approximations. There is a great wealth of existing results from different fields which lead to identical mathematical problems and which can be used in these cases. Finally, we consider how to use these techniques when the precise configuration of the grid block is not known, but only its statistical properties. This can lead to results which are very different from the deterministic case.     

Direct numerical simulation of disturbances generated by periodic suction-blowing in a hypersonic boundary layer

A numerical algorithm and code are developed and applied to direct numerical simulation (DNS) of unsteady two-dimensional flow fields relevant to stability of the hypersonic boundary layer. An implicit second-order finite-volume technique is used for solving the compressible Navier–Stokes equations. Numerical simulation of disturbances generated by a periodic suction-blowing on a flat plate is performed at free-stream Mach number 6. For small forcing amplitudes, the second-mode growth rates predicted by DNS agree well with the growth rates resulted from the linear stability theory (LST) including nonparallel effects. This shows that numerical method allows for simulation of unstable processes despite its dissipative features. Calculations at large forcing amplitudes illustrate nonlinear dynamics of the disturbance flow field. DNS predicts a nonlinear saturation of fundamental harmonic and rapid growth of higher harmonics. These results are consistent with the experimental data of Stetson and Kimmel obtained on a sharp cone at the free-stream Mach number 8.     

Direct numerical simulation of the laminar-turbulent transition in a thick spherical layer

The results of a numerical study of the laminar-turbulent transition in unsteady isothermal three-dimensional flows of viscous incompressible fluid in a thick spherical layer between counter-rotating spherical boundaries are presented. The calculations are performed for the governing parameters corresponding to the experimental data [1, 2]. The numerical investigations include both solving the complete system of Navier-Stokes equations and analyzing the linear stability of steady-state axisymmetric flows with respect to three-dimensional disturbances. A stochastic flow regime is calculated for the first time. The limits of existence of different flow regimes and the hysteresis regions are found. The spatial flow patterns and frequency characteristics are obtained, which makes it possible to extend and refine the existing experimental data.     

Numerical simulation of stabilization of the boundary layer on a surface with a porous coating in a supersonic separated flow

Stability of a supersonic (M _∞ = 5.373) boundary layer with local separation in a compression corner with a passive porous coating partly absorbing flow perturbations is considered by solving two-dimensional Navier-Stokes equations numerically. The second mode of disturbances of a supersonic boundary layer is demonstrated to be the most important one behind the boundary-layer reattachment point. The possibility of effective stabilization of these disturbances behind the reattachment point with the use of porous coatings is confirmed. __________ Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 48, No. 2, pp. 39–47, March–April, 2007.     

Large scale numerical simulations for multi-phase fluid dynamics with moving interfaces

This short communication presents our recent studies to implement numerical simulations for multi-phase flows on top-ranked supercomputer systems with distributed memory architecture. The numerical model is designed so as to make full use of the capacity of the hardware. Satisfactory scalability in terms of both the parallel speed-up rate and the size of the problem has been obtained on two high rank systems with massively parallel processors, the Earth Simulator (Earth simulator research center, Yokohama Kanagawa, Japan) and the TSUBAME (Tokyo Institute of Technology, Tokyo, Japan) supercomputers.     

Evolution of a wall-attached buoyant plume in confined boxes: Direct numerical simulations,entrainment coefficient and an integral model

The evolution of a wall-attached plume in a confined box is studied here with the aid of three dimensional direct numerical simulations (DNS). The plume originates from a local line heat source of length, L, placed at the bottom left corner of the box. The Reynolds number of the wall plume, based on box height and buoyant velocity scale, is ${\mathit{Re}}_H=14530$ and boxes of two different aspect ratios (ratio of box width to height) for a particular value of L are simulated. We observe that the plume develops along the vertical sidewall while remaining attached to it before spreading across the top wall to form a buoyant fluid layer and eventually moving downwards and filling the whole box. The original filling box model of Baines and Turner (1969) is modified to incorporate the wall shear stress, and the results from the DNS are compared against the new model. In modelling plumes, we find that the entrainment coefficient ($\alpha$) for wall-attached plumes is reduced to approximately half of that in the free plume, and the main reason is a diminished contribution of turbulence production to $\alpha$ resulting from a restricted ability of the large-scale eddies to transport momentum. Also, unlike the free plume where away from the source inertial forces balances buoyancy forces, here in our simulations of wall-attached plumes this balance is marginally off, likely due to wall friction. A reasonable agreement is observed between our model and DNS data for the volume and momentum fluxes in the quiescent uniform environment and also for the time-dependent buoyancy profile calculated far away from the plume.     

A marker‐and‐cell approach to free surface 2‐D multiphase flows

This work describes a methodology to simulate free surface incompressible multiphase flows. This novel methodology allows the simulation of multiphase flows with an arbitrary number of phases, each of them having different densities and viscosities. Surface and interfacial tension effects are also included. The numerical technique is based on the GENSMAC front‐tracking method. The velocity field is computed using a finite‐difference discretization of a modification of the Navier–Stokes equations. These equations together with the continuity equation are solved for the two‐dimensional multiphase flows, with different densities and viscosities in the different phases. The governing equations are solved on a regular Eulerian grid, and a Lagrangian mesh is employed to track free surfaces and interfaces. The method is validated by comparing numerical with analytic results for a number of simple problems; it was also employed to simulate complex problems for which no analytic solutions are available. The method presented in this paper has been shown to be robust and computationally efficient. Copyright © 2012 John Wiley & Sons, Ltd.     

An experimental study of a turbulent shear layer at a clean and contaminated free-surface

An experimental study was performed to measure the flow properties of a vertically-orientated shear layer in the vicinity of a free-surface. The effect of surface contamination on the near surface flow field was also determined. Digital Particle Image Velocimetry was used to measure instantaneous and averaged velocity, vorticity, and Reynolds stresses. Results show that the presence of surfactants can cause directional shifts of the shear layer, as well as an overall damping of the turbulence in the vicinity of the free-surface, except in the vicinity of a Reynolds ridge where an increase in Reynolds stress was observed.     

Numerical simulation of receptivity of a hypersonic boundary layer to acoustic disturbances

Direct numerical simulations of the evolution of disturbances in a viscous shock layer on a flat plate are performed for a free-stream Mach number M _∞ = 21 and Reynolds number Re _L = 1.44 · 10⁵. Unsteady Navier-Stokes equations are solved by a high-order shock-capturing scheme. Processes of receptivity and instability development in a shock layer excited by external acoustic waves are considered. Direct numerical simulations are demonstrated to agree well with results obtained by the locally parallel linear stability theory (with allowance for the shock-wave effect) and with experimental measurements in a hypersonic wind tunnel. Mechanisms of conversion of external disturbances to instability waves in a hypersonic shock layer are discussed. __________ Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 48, No. 3, pp. 84–91, May–June, 2007.