Numerical simulation of thermo‐solutal‐capillary migration of a dissolving drop in a cavity

In the present paper the thermo‐solutal‐capillary migration of a dissolving liquid drop, composed by a binary mixture having a miscibility gap, injected in a closed cavity with differentially heated end walls, is studied. The main goal of the analysis is to clarify if and how the drop migration is affected by the dissolution process. The numerical code is based on a finite volume formulation. A level‐set technique is used for describing the dynamics of the interface separating the different phases. A thermodynamic constraint fixes the concentration jump between the interface sides. This jump, together with that of the concentration normal derivatives, in turn defines the entity of the dissolution cross‐flow through the interface and the interface velocity relative to the fluid. Since the jump singularity of normal derivatives cannot be easily mollified, while retaining the necessary accuracy, a scheme for the species equation is elaborated that allows sharp jumps and has subcell resolution. Steady migration speeds are determined after the start‐up phase for different radii and temperature differences. The results will be used for the preparation of a sounding rocket space experiment. Copyright © 2003 John Wiley & Sons, Ltd.     

High‐order upwind compact scheme and simulation of turbulent premixed V‐flame

A high‐order accurate upwind compact difference scheme with an optimal control coefficient is developed to track the flame front of a premixed V‐flame. In multi‐dimensional problems, dispersion effect appears in the form of anisotropy. By means of Fourier analysis of the operators, anisotropic effects of the upwind compact difference schemes are analysed. Based on a level set algorithm with the effect of exothermicity and baroclinicity, the flame front is tracked. The high‐order accurate upwind compact scheme is employed to approximate the level set equation. In order to suppress numerical oscillations, the group velocity control technique is used and the upwind compact difference scheme is combined with the random vortex method to simulate the turbulent premixed V‐flame. Distributions of velocities and flame brush thickness are obtained by this technique and found to be comparable with experimental measurement. Copyright © 2005 John Wiley & Sons, Ltd.     

High‐order ILU preconditioners for CFD problems

This paper tests a number of incomplete lower–upper (ILU)‐type preconditioners for solving indefinite linear systems, which arise from complex applications such as computational fluid dynamics (CFD). Both point and block preconditioners are considered. The paper focuses on ILU factorization that can be computed with high accuracy by allowing liberal amounts of fill‐in. A number of strategies for enhancing the stability of the factorizations are examined. Copyright © 2000 John Wiley & Sons, Ltd.     

Reduced order state‐space models from the pulse responses of a linearized CFD scheme

This paper describes a method for obtaining a time continuous reduced order model (ROM) from a system of time continuous linear differential equations. These equations are first put into a time discrete form using a finite difference approximation. The unit sample responses of the discrete system are calculated for each system input and these provide the Markov parameters of the system. An eigenvalue realization algorithm (ERA) is used to construct a discrete ROM. This ROM is then used to obtain a continuous ROM of the original continuous system. The focus of this paper is on the application of this method to the calculation of unsteady flows using the linearized Euler equations on moving meshes for aerofoils undergoing heave or linearized pitch motions. Applying a standard cell‐centre spatial discretization and taking account of mesh movement a continuous system of differential equations is obtained which are continuous in time. These are put into discrete time form using an implicit finite difference approximation. Results are presented demonstrating the efficiency of the system reduction method for this system. Copyright © 2003 John Wiley & Sons, Ltd.     

Effect of thermo‐solutal stratification on recirculation flow patterns in a backward‐facing step channel flow

This paper presents results on the combined effect of thermo‐solutal buoyancy forces on the recirculatory flow behavior in a horizontal channel with backward‐facing step and the ensuing impact on heat and mass transfer phenomena. The governing equations for double diffusive mixed convection are represented in velocity–vorticity form of momentum equations, velocity Poisson equations, energy and concentration equations. Galerkin's finite‐element method has been employed to solve the governing equations. Recirculatory flow fields with heat and mass transfer are simulated for opposing and aiding thermo‐solutal buoyancy forces by assuming suitable boundary conditions for energy and concentration equations. The effect of Richardson number (0.1?Ri?10) and buoyancy ratio (?10?N?10) on the recirculation bubble and Nusselt and Sherwood numbers are studied in detail. For Richardson number greater than unity, distinct variations in the gradients of Nusselt number and Sherwood number with buoyancy ratio are observed for flow regimes with opposing and aiding buoyancy forces. Copyright © 2009 John Wiley & Sons, Ltd.     

CFD simulation of two‐ and three‐dimensional free‐surface flow

The paper describes the implementation of moving‐mesh and free‐surface capabilities within a 3‐d finite‐volume Reynolds‐averaged‐Navier–Stokes solver, using surface‐conforming multi‐block structured meshes. The free‐surface kinematic condition can be applied in two ways: enforcing zero net mass flux or solving the kinematic equation by a finite‐difference method. The free surface is best defined by intermediate control points rather than the mesh vertices. Application of the dynamic boundary condition to the piezometric pressure at these points provides a hydrostatic restoring force which helps to eliminate any unnatural free‐surface undulations. The implementation of time‐marching methods on moving grids are described in some detail and it is shown that a second‐order scheme must be applied in both scalar‐transport and free‐surface equations if flows driven by free‐surface height variations are to be computed without significant wave attenuation using a modest number of time steps. Computations of five flows of theoretical and practical interest—forced motion in a pump, linear waves in a tank, quasi‐1d flow over a ramp, solitary wave interaction with a submerged obstacle and 3‐d flow about a surface‐penetrating cylinder—are described to illustrate the capabilities of our code and methods. Copyright © 2003 John Wiley & Sons, Ltd.     

Direct simulation of two‐dimensional turbulent flow over a surface‐mounted obstacle

Two‐dimensional turbulent flow over a surface‐mounted obstacle is studied as a numerical experiment that takes place in a wind tunnel. The transient Navier–Stokes equations are solved directly with Galerkin finite elements. The Reynolds number defined with respect to the height of the wind tunnel is 12 518. Instantaneous streamline patterns are shown that give a complete picture of the flow phenomena. Energy and enstrophy spectra yield the dual cascade of two‐dimensional turbulence and the ?1 power law decay of enstrophy. Mean values of velocities and root mean square fluctuations are compared with the available experimental results. Other statistical characteristics of turbulence such as Eulerian autocorrelation coefficients, longitudinal and lateral coefficients are also computed. Finally, oscillation diagrams of computed velocity fluctuations yield the chaotic behaviour of turbulence. Copyright © 2007 John Wiley & Sons, Ltd.     

Numerical simulation and experimental validation of heat transfer within rotating flows for three‐dimensional non‐axisymmetric,turbulent conditions

A control volume type numerical methodology for the analysis of steady three‐dimensional rotating flows with heat transfer, in both laminar and turbulent conditions, is implemented and experimentally tested. Non‐axisymmetric momentum and heat transfer phenomena are allowed for. Turbulent transport is alternatively represented through three existing versions of the k–ε model that were adjusted to take into account the turbulence anisotropy promoted by rotation, streamline curvature and thermal buoyancy. Their relative performance is evaluated by comparison of calculated local and global heat balances with those obtained through measurements in a laboratory device. A modified version of the Lam and Bremhorst, low Reynolds number model is seen to give the best results. A preliminary analysis focused on the flow structure and the transfer of heat is reported. Copyright © 2002 John Wiley & Sons, Ltd.     

Critical evaluation of CFD codes for interfacial simulation of bubble‐train flow in a narrow channel

Computational fluid dynamics (CFD) codes that are able to describe in detail the dynamic evolution of the deformable interface in gas–liquid or liquid–liquid flows may be a valuable tool to explore the potential of multi‐fluid flow in narrow channels for process intensification. In the present paper, a computational exercise for co‐current bubble‐train flow in a square vertical mini‐channel is performed to investigate the performance of well‐known CFD codes for this type of flows. The computations are based on the volume‐of‐fluid method (VOF) where the transport equation for the liquid volumetric fraction is solved either by the methods involving a geometrical reconstruction of the interface or by the methods that use higher‐order difference schemes instead. The codes contributing to the present code‐to‐code comparison are an in‐house code and the commercial CFD packages CFX, FLUENT and STAR‐CD. Results are presented for two basic cases. In the first one, the flow is driven by buoyancy only, while in the second case the flow is additionally forced by an external pressure gradient. The results of the code‐to‐code comparison show that only the VOF method with interface reconstruction leads to physically sound and consistent results, whereas the use of difference schemes for the volume fraction equation shows some deficiencies. Copyright © 2007 John Wiley & Sons, Ltd.     

Large‐eddy simulation with complex 2‐D geometries using a parallel finite‐element/spectral algorithm

A parallel stabilized finite‐element/spectral formulation is presented for incompressible large‐eddy simulation with complex 2‐D geometries. A unique discretization scheme is developed consisting of a streamline‐upwind Petrov–Galerkin/Pressure‐Stabilized Petrov–Galerkin (SUPG/PSPG) finite‐element discretization in the 2‐D plane with a collocated spectral/pseudospectral discretization in the out‐of‐plane direction. This formulation provides an efficient approach for solving 3‐D flows over arbitrary 2‐D geometries. Utilizing this discretization and through explicit temporal treatment of the non‐linear terms, the system of equations for each Fourier mode is decoupled within each time step. A novel parallelization approach is then taken, where the computational work is partitioned in Fourier space. A validation of the algorithm is presented via comparison of results for flow past a circular cylinder with published values for Re=195, 300, and 3900. Copyright © 2003 John Wiley & Sons, Ltd.     

Large eddy simulation of turbulent incompressible flows by a three‐level finite element method

The variational multiscale method provides a methodical framework for large eddy simulation of turbulent flows. In this work, a particular implementation in the form of a three‐level finite element method separating large resolved, small resolved, and unresolved scales is proposed. Residual‐free bubbles are used for the numerical approximation of the small‐scale momentum equation. A stabilizing term is added, in order to take into account the effect of the small‐scale continuity equation. This implementation guarantees the stability of the method without further provisions and offers substantial computational savings on the small‐scale level. Furthermore, it is accounted for the unresolved scales by a specific dynamic modelling procedure. The method is tested for two different turbulent flow situations. Copyright © 2005 John Wiley & Sons, Ltd.     

Numerical simulation of flow‐induced noise using LES/SAS and Lighthill's acoustic analogy

We present a finite element (FE) formulation of Lighthill's acoustic analogy for the hybrid computation of noise generated by turbulent flows. In the present approach, the flow field is computed using large eddy simulation and scale adaptive simulation turbulence models. The acoustic propagation is obtained by solving the variational formulation of Lighthill's acoustic analogy with the FE method. In order to preserve the acoustic energy, we compute the inhomogeneous part of Lighthill's wave equation by applying the FE formulation on the fine flow grid. The resulting acoustic nodal loads are then conservatively interpolated to the coarser acoustic grid. Subsequently, the radiated acoustic field can be solved in both time and frequency domains. In the latter case, an enhanced perfectly matched layer technique is employed, allowing one to truncate the computational domain in the acoustic near field, without compromising the numerical solution. Our hybrid approach is validated by comparing the numerical results of the acoustic field induced by a corotating vortex pair with the corresponding analytical solution. To demonstrate the applicability of our scheme, we present full 3D numerical results for the computed acoustic field generated by the turbulent flow around square cylinder geometries. The sound pressure levels obtained compare well with measured values. Copyright © 2009 John Wiley & Sons, Ltd.     

Level‐set based numerical simulation of a migrating and dissolving liquid drop in a cylindrical cavity

In the present paper the dissolution of a binary liquid drop having a miscibility gap and migrating due to thermo‐solutal capillary convection in a cylindrical cavity is studied numerically. The interest in studying this problem is twofold. From a side, in the absence of gravity, capillary migration is one of the main physical mechanisms to set into motion dispersed liquid phases and from the other side, phase equilibria of multi‐component liquid systems, ubiquitous in applications, often exhibit a miscibility gap. The drop capillary migration is due to an imposed temperature gradient between the cavity top and bottom walls. The drop dissolution is due to the fact that initial composition and volume values, and thermal boundary conditions are only compatible with a final single phase equilibrium state. In order to study the drop migration along the cavity and the coupling with dissolution, a previously developed planar two‐dimensional code is extended to treat axis‐symmetric geometries. The code is based on a finite volume formulation. A level‐set technique is used for describing the dynamics of the interface separating the different phases and for mollifying the interface discontinuities between them. The level‐set related tools of redistancing and off‐interface extension are used to enhance code resolution in the critical interface region. Migration speeds and volume variations are determined for different drop radii. Copyright © 2004 John Wiley & Sons, Ltd.     

A simple sliding‐mesh interface procedure and its application to the CFD simulation of a tidal‐stream turbine

An effective way of using computational fluid dynamics (CFD) to simulate flow about a rotating device—for example, a wind or marine turbine—is to embed a rotating region of cells inside a larger, stationary domain, with a sliding interface between. This paper describes a simple but effective method for implementing this as an internal Dirichlet boundary condition, with interfacial values obtained by interpolation from halo nodes. The method is tested in two finite‐volume codes: one using block‐structured meshes and the other unstructured meshes. Validation is performed for flow around simple, isolated, rotating shapes (cylinder, sphere and cube), comparing, where possible, with experiment and the alternative CFD approach of fixed grid with moving walls. Flow variables are shown to vary smoothly across the sliding interface. Simulations of a tidal‐stream turbine, including both rotor and support, are then performed and compared with towing‐tank experiments. Comparison between CFD and experiment is made for thrust and power coefficients as a function of tip‐speed ratio (TSR) using Reynolds‐averaged Navier–Stokes turbulence models and large‐eddy simulation (LES). Performance of most models is good near the optimal TSR, but simulations underestimate mean thrust and power coefficients in off‐design conditions, with the standard k– ? turbulence model performing noticeably worse than shear stress transport k– ω and Reynolds‐stress‐transport closures. LES gave good predictions of mean load coefficients and vital information about wake structures but at substantial computational cost. Grid‐sensitivity studies suggest that Reynolds‐averaged Navier–Stokes models give acceptable predictions of mean power and thrust coefficients on a single device using a mesh of about 4 million cells. Copyright © 2013 John Wiley & Sons, Ltd.     

Numerical simulation of particle‐laden flows by the residual‐based variational multiscale method

We present a finite element residual‐based variational multiscale formulation applied to the numerical simulation of particle‐laden flows. We employ a Eulerian–Eulerian framework to describe the flows in which the mathematical model results from the incompressible Navier–Stokes equation combined with an advection–diffusion transport equation. Special boundary conditions at the bottom are introduced to take into account sediments deposition. Computational experiments are organized in two examples. The first example deals with the well‐known gravity current benchmark, the lock‐exchange configuration. The second also employs for the current initiation the lock configuration, but the sediment particles are endowed with a deposition velocity and are allowed to leave the domain in the moment they reach the bottom. This is intended to mimic, partially, as the bed morphology is not allowed to change, the deposition process, in which sediment deposits are no longer carried by the flow. The spatial pattern of the deposition and its correlation with flow structures are the main focus of this analysis. Numerical experiments have shown that the present formulation captures most of the relevant turbulent flow features with reasonable accuracy, when compared with highly resolved numerical simulations and experimental data. Copyright © 2013 John Wiley & Sons, Ltd.     

Developing a hybrid flux function suitable for hypersonic flow simulation with high‐order methods

In this paper, we develop a new hybrid Euler flux function based on Roe's flux difference scheme, which is free from shock instability and still preserves the accuracy and efficiency of Roe's flux scheme. For computational cost, only 5% extra CPU time is required compared with Roe's FDS. In hypersonic flow simulation with high‐order methods, the hybrid flux function would automatically switch to the Rusanov flux function near shock waves to improve the robustness, and in smooth regions, Roe's FDS would be recovered so that the advantages of high‐order methods can be maintained. Multidimensional dissipation is introduced to eliminate the adverse effects caused by flux function switching and further enhance the robustness of shock‐capturing, especially when the shock waves are not aligned with grids. A series of tests shows that this new hybrid flux function with a high‐order weighted compact nonlinear scheme is not only robust for shock‐capturing but also accurate for hypersonic heat transfer prediction. Copyright © 2015 John Wiley & Sons, Ltd.     

管内均相湍流燃烧加速的数值模拟

通过均相流体模型、湍流k 模型和EBU(EddyBreak Up) Arrhenius燃烧模型 ,选用Simple格式对管中戊烷和空气的燃烧实例进行了数值求解。其结果反映了燃烧导致的爆炸过程中管内流场各参数的变化规律 ,揭示了管内燃烧、流动、湍流之间的正反馈耦合关系 ,并与实验结果和相关数值结果基本相符。     

Large eddy simulation of turbulent shallow water flows using multi‐relaxation‐time lattice Boltzmann model

In this paper, the standard Smagorinsky's algorithm is embedded into the multiple relaxation time (MRT) lattice Boltzmann model (LBM) for large eddy simulation (LES) of turbulent shallow water flows (MRT‐LABSWE^TM). The model is based on the two‐dimensional nonlinear shallow water equations, giving the depth‐averaged features. It is verified by applying the model in three typical cases in engineering with turbulence: (i) the flow around a square cylinder, (ii) plane cavity flow, and (iii) flows in a junction of 90°. The results obtained by the MRT‐LABSWE^TM are compared with BGK‐LABSWE^TM results and experimental data. The objectives of this study are to validate the MRT‐LABSWE^TM in a turbulence simulation and perform a comparative analysis between the results of BGK‐LABSWE^TM and MRT‐LABSWE^TM. Copyright © 2012 John Wiley & Sons, Ltd.