Hybrid LES-RANS Modeling of Complex Turbulent Flows

The paper describes a state-of-the-art hybrid LES-URANS method for the simulation of complex internal and external turbulent flows. Relying on a unified LES-URANS approach with a soft interface the methodology is designed for wall-bounded non-equilibrium flows. The unsteady Reynolds-averaged Navier-Stokes (URANS) mode within the hybrid approach is taken into account by an explicit algebraic Reynolds stress model (EARSM), which guarantees an appropriate representation of the anisotropic near-wall turbulence. All non-closed terms in the transport equation of the turbulent kinetic energy are modeled by enhanced formulations using the EARSM (production and diffusion term) and the splitting of the dissipation rate into a homogeneous and an inhomogeneous contribution. The former is expressed analytically by a Taylor series expansion of the homogeneous lateral Taylor microscale in the vicinity of the wall guaranteeing the correct asymptotic behavior. The latter is incorporated into the diffusion term. The interface location between the large-eddy simulation (LES) mode and the URANS mode is determined automatically on-the-fly based on the modeled turbulent kinetic energy and the distance to the wall. For transitional (external) flows an additional dynamic transition criterion is applied which determines the laminar and the turbulent flow regimes and is combined with the existing interface criterion. An internal flow over a periodic arrangement of hills and an external flow past a SD7003 airfoil with a laminar separation bubble are taken into account for a detailed evaluation of the method. (© 2014 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

The method of lines for the computation of incompressible viscous flows

A common approach to finding numerical solutions of the time-dependent incompressible Navier-Stokes equations is considered within the method of lines framework [1]. For the determination of viscous incompressible flows the stream-function formulation for the fourth-order equation [2, 3], an artificial compressibility method [4], and a modified velocity correction method [5] are designed. Some improved and extended results of numerical simulations obtained by the author in the previous works are presented. Test calculations have been done for various flows inside square, triangular and semicircular cavities with one moving wall, the backward-facing step, double bent channels and for the flow around an aerofoil at large angle of attack. An alternative and practical methodology for resolving the Navier-Stokes equations in arbitrarily complex geometries using Cartesian meshes is proposed. Some of complex geometrical configurations can be decomposed into a set of subdomains. The simplest approach for specifying boundary conditions near curved or irregular boundaries is to transfer all the variables from the boundaries to the nearest grid knots. (© 2009 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Simulation of the flow past a circular cylinder using an unsteady panel method

In the present work, an in-house UnSteady Double Wake Model (USDWM) is developed for simulating general flow problems behind bodies. The model is presented and used to simulate flows past a circular cylinder at subcritical, supercritical, and transcritical flows. The flow model is a two-dimensional panel method which uses the unsteady double wake technique to model flow separation and its dynamics. In the present work the separation location is obtained from experimental data and fixed in time. The highly unsteady flow field behind the cylinder is analyzed in detail. The results are compared with experiments and Unsteady Reynolds-Averaged Navier Stokes (URANS) simulations and show good agreement in terms of the vortex shedding characteristics, drag, and pressure coefficients for the different flow regimes.     

Numerical study on the fluid-structure interaction in a model aquatic canopy flow

This work presents numerical simulations and selected results of the flow over aquatic canopies, consisting of artificial flexible rectangular blades, arranged in a well-defined order. The results obtained with three different Reynolds and Cauchy numbers are compared with experimental data achieving good agreement. The considered range of Cauchy numbers represents three different types of canopies ranging from rigid up to highly flexible plants. The transient flow data and blade positions are statistically analyzed to gain deeper understanding of the complex physical processes for this kind of fluid structure interaction. For example, the correlation of role of large scale motion of the flexible blades in conjunction with coherent vortex structures of the flow is addressed. (© 2017 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Statistics of numerically generated turbulence

This paper considers numerically generated turbulence obtained by integrating the complete time-dependent three-dimensional Navier-Stokes equations. The simulated unidirectional turbulent flow, bounded by two parallel planes, is strongly inhomogeneous in the direction normal to the planes but homogeneous in the parallel directions. The resulting flow field, which is considered a numerical realization of fully developed turbulent channel flow, contains detailed information on spatial coherent flow structures as well as on the time-dependency and statistics of the three-dimensional velocity and pressure fields. Focussing here on the statistics of the numerically generated turbulence, second-moments and higher-moments are presented and compared with the most recent PTV and LDV laboratory measurements. It is concluded that direct numerical simulations are an invaluable approach to turbulence which complements field studies and laboratory investigations. Numerical experiments are now becoming a principal source of detailed and reliable information, which play a key role in the deepening of our understanding of turbulent flow phenomena.     

On Symmetric Boundary Conditions in the Context of Viscoelastic Fluid Flows

In order to reduce the numerical cost of three dimensional flow problems with geometrical symmetry, the use of symmetric boundary conditions is standard. For Newtonian fluid flow problems this approximation is usually appropriate, particularly when the Reynolds number is small. In the case of viscoelastic fluid flow simulations with stabilization techniques, such as the so-called DEVSS and/or Log-Conformation tensor methods, at high Deborah number flows this implementation is not straightforward, as in the Newtonian case. It is well known that viscoelastic models (e.g. Maxwellian models), show (purely) elastic flow instabilities when the Deborah number is increased above a critical value, even under creeping flow conditions. In this work we present numerical simulations with different stabilization techniques and different differential viscoelastic models at high Deborah number flows. As a test-case, we compare the flow in a full two-dimensional cross-slot geometry to show the asymmetrical behavior of the viscoelastic fluid flow. (© 2013 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Operator splitting for the numerical solution of free surface flow at low capillary numbers

Free surface flows are pervasive in engineering and biomedical applications. In many interesting cases—particularly when small length scales are involved—surface forces (capillarity) dominate the flow dynamics. In these cases, computing the flow together with the shape of the surfaces, requires specialized solution techniques. This article investigates the capabilities of an operator splitting/finite elements method at handling accurately incompressible viscous flow with free surfaces at low capillary numbers. The test case of flow in the downstream section of a slot coater is used for three reasons: (1) it is an established benchmark; (2) it represents an idealized, yet industrially relevant flow; (3) high-fidelity results obtained with monolithic algorithms are available in literature. The flow and free surface shape attained with the new operator splitting scheme agree very satisfactorily with the results obtained with monolithic solvers. Because of its inherent computational simplicity, the new operator splitting scheme is attractive for large-scale simulations, three-dimensional flows, and flows of complex fluids.     

Large eddy simulation and PIV experiments of air–water mixing tanks

The simulations and experiments of a turbulent bubbly flow are carried out in a cylindrical mixing vessel. Dynamics of the turbulent bubbly flow is visualized using a novel two-phase particle image velocimetry (PIV) with a combination of back lighting, digital masking and fluorescent tracer particles. Using an advanced technique, Mie’s scattering at surfaces of bubbles is totally filtered out and, henceforth, images of tracer particles and of bubbles are obtained with high quality. In parallel to the comprehensive experimental studies, numerical results are obtained from large eddy simulations (LES) of the two-phase air–water mixer. The impeller-induced flow at the blade tip radius is modeled by using sliding mesh method. The results demonstrate the existence of large structures such as tip-vortex tips, and also some finer details. In addition, the stability of the jet is found to be connected with the fluctuations of the tip vortices whose dynamics are affected by the presence of bubbles. Numerical results are used to interpret the measurement data and to guide the refinement of consistent theoretical analyses. Such information is invaluable in the development of advanced theories capable of describing bubbly flows in the presence of complex liquid flow. This detailed information is of real significance in facilitating the design and scale-up of practical stirred tanks.     

Rossby Solitary Waves in the Presence of a Critical Layer

This study considers the evolution of weakly nonlinear long Rossby waves in a horizontally sheared zonal current. We consider a stable flow so that the nonlinear time scale is long. These assumptions enable the flow to organize itself into a large‐scale coherent structure in the régime where a competition sets in between weak nonlinearity and weak dispersion. This balance is often described by a Korteweg‐de‐Vries equation. The traditional assumption of a weak amplitude breaks down when the wave speed equals the mean flow velocity at a certain latitude, due to the appearance of a singularity in the leading‐order equation, which strongly modifies the flow in a critical layer. Here, nonlinear effects are invoked to resolve this singularity, because the relevant geophysical flows have high Reynolds numbers. Viscosity is introduced in order to render the nonlinear‐critical‐layer solution unique, but the inviscid limit is eventually taken. By the method of matched asymptotic expansions, this inner flow is matched at the edges of the critical layer with the outer flow. We will show that the critical‐layer–induced flow leads to a strong rearrangement of the related streamlines and consequently of the potential‐vorticity contours, particularly in the neighborhood of the separatrices between the open and closed streamlines. The symmetry of the critical layer vis‐à‐vis the critical level is also broken. This theory is relevant for the phenomenon of Rossby wave breaking and eventual saturation into a nonlinear wave. Spatially localized solutions are described by a Korteweg‐de‐Vries equation, modified by new nonlinear terms; depending on the critical‐layer shape, this leads to depression or elevation waves. The additional terms are made necessary at a certain order of the asymptotic expansion while matching the inner flow on the dividing streamlines. The new evolution equation supports a family of solitary waves. In this paper we describe in detail the case of a depression wave, and postpone for further discussion the more complex case of an elevation wave.     

Parallel Calculation of Accurate Path Lines in Virtual Environments through Exploitation of Multi-Block CFD Data Set Topology

The use of Virtual Reality (VR) techniques for the investigation of complex flow phenomena offers distinct advantages in comparison to conventional visualization techniques. Especially for unsteady flows, VR methodology provides an intuitive approach for the exploration of simulated fluid flows. However, the visualization of Computational Fluid Dynamics (CFD) data is often too time-consuming to be carried out in real-time, and thus violates essential constraints concerning real-time interaction and visualization. To overcome this obstacle, we make use of the fact that typically a multi-block approach is employed for domain decomposition, and we use the corresponding data structures for the computation of path lines and for parallelization. In this paper, we present the synthesis of fragmented multi-block data sets and our implementation of an accurate path line integration scheme in order to speed up path line computations. We report on the results of our efforts and describe a combination of this algorithm with a highly efficient visualization approach of large amounts of particle traces, thus considerably improving interactivity when exploring large scale CFD data sets.Mathematics Subject Classifications (2000) 76Mxx, 76M27, 76M28, 65M55, 65L05, 65L06, 65D05, 65Y05, 68U05.     

Space Mapping Approach for Particle Control in Turbulent Flows

Controlling the motion of particles in turbulent flows, the paper at hand presents an efficient space–mapping approach that is based on a hierarchy of models. The approach reduces the highly complex optimization of the k-ε turbulence model for high Reynolds–number flows (fine model) to the cheaper one of the Navier–Stokes equations for smaller Reynolds–number (laminar) flows in direct numerical simulations on coarser grids (coarse model) by help of a space–map function that maps the respective coarse model control onto the desired fine model control. The numerical results are very convincing in terms of accuracy and computational effort. (© 2008 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Modeling of individual coherent structures in wall region of a turbulent boundary layer

Models for individual coherent structures in the wall region of a turbulent boundary layer are proposed. Method of numerical simulations is used to follow the evolution of the structures. It is found that the proposed model does bear many features of coherent structures found in experiments.     

Improving shock-free compressible RANS solvers for LES on unstructured meshes

Standard numerical methods used to solve the Reynolds averaged Navier–Stokes equations are known to be too dissipative to carry out large eddy simulations since the artificial dissipation they introduce to stabilize the discretization of the convection term usually interacts strongly with the subgrid scale model. A possible solution is to resort to non-dissipative central schemes. Unfortunately, these schemes are in general unstable. A way to reach stability is to select a central scheme that conserves the discrete kinetic energy. To that purpose, a family of kinetic energy conserving schemes is developed to perform simulations of compressible shock-free flows on unstructured grids. A direct numerical simulation of the flow past a sphere at a Reynolds number of 300 and a large eddy simulation at a Reynolds number of 10,000 are performed to validate the methodology.     

An Experimental/Numerical Investigation on Drag Reduction by Dimples

The paper is concerned with experimental and numerical investigations of the turbulent flow over dimpled surfaces. Shallow dimples distributed regularly over the wall of a plane channel with large aspect ratio are used to study their effect on the skin-friction drag. The resulting pressure drop in the channel was measured for smooth and dimpled walls. In addition to these investigations on internal flows, an external flow study was performed and boundary-layer profiles were measured using a Pitot-tube rake. Complementary to the measurements, direct numerical simulations for the internal flow configuration with and without dimples were carried out for two different grid resolutions and analyzed in detail. The objective was to clarify whether or not dimples cause reduction of the skin-friction drag. (© 2010 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

From single obstacles to wall roughness: some fundamental investigations based on DNS results for turbulent channel flow

Turbulent flow through a plane channel with only one smooth wall is analyzed based on DNS results for three Reynolds numbers. The opposite wall has 2D bars of size k ×  k attached with the distance to each other as the crucial parameter. When they are close together they act as a wall roughness whereas they are single obstacles in character when they are far apart. These two extreme cases show very different coherent structures in the vicinity of the wall attached bars. The categories single obstacles and wall roughness are introduced as an alternative to the often used categorization in terms of k- and d-type roughness. Visualization of the coherent structures is achieved by introducing constant local entropy generation as a parameter. Finally it is discussed whether results gained in a channel with one rough wall can be transferred to the more realistic case when both walls are rough.     

Numerical Investigations of Relaxation Phenomena in Cavitating Nozzle Flows

Numerical simulations of cavitating flows are frequently performed by applying simple law of state‐models. In this study an advanced law of state‐model on the basis of a Landau‐type approach is used that focusses on the physical treatment of relaxation phenomena. Relaxation phenomena or phase non‐equilibrium effects occur within the scope of two‐phase fluid dynamics if the time scale of the flow problem is small. This appears e.g. in the case of cavitating flow in injector nozzles of diesel engines. The aim of this study is the determination of the relaxation parameter of the advanced law of state‐model. For this reason a theoretical approach is presented as well as simulations of unsteady cavitating nozzle flows that are compared with experimental data. Concerning the calculation of 2‐D unsteady cavitating flow the evolution equation for the vapor fraction is solved by a modified Volume‐of‐Fluid algorithm.     

Mathematical modeling of shock-wave processes under gas solid boundary interaction

The results of numerical simulations are presented for planar air flows in a bounded volume of square cross section diminishing due to a uniform motion of the walls, for a flow of a propane-air mixture under sinusoidal variation of the size of the square domain, and for three-dimensional supersonic air and propane-air flows in channels of variable square cross section. Specific features of shock-wave processes that are associated with the piston effect and cumulation are established. The hypersonic analogy between planar and spatial flows is confirmed, which allows one to use two-dimensional solutions in estimating three-dimensional flows. The equations of a multicomponent ideal perfect gas and one-stage kinetics of chemical reactions are used to describe the flows. The method of numerical simulations is based on S.K. Godunov’s scheme and implemented within an original software package.     

Modeling of individual coherent structures in wall region of a turbulent boundary layer

Models for individual coherent structures in the wall region of a turbulent boundary layer are proposed. Method of numerical simulations is used to follow the evolution of the structures. It is found that the proposed model does bear many features of coherent structures found in experiments. Project supported by the National Natural Science Foundation of China (Grant No. 19732005) and National Climbing Project.     

Hydraulic Theory and Particle-Driven Gravity Currents

Hydraulic theory, as it has been applied to compositionally driven gravity flows, involves the single simplifying assumption that the pressure in the fluid is hydrostatic [1]. This assumption provides, as a consequence, a depth independent horizontal velocity field. This approach has led to a greatly increased understanding of many of the phenomena associated with these complex flows, including issues surrounding internal hydraulic jumps and energy loss [2]. Recently, investigations into flow and deposition of particles from particle-driven gravity currents have been carried out using an approach that employs the hydraulic theory that had proved so successful in the case of homogeneous flows [3]–[7]. Unfortunately, as we show here, there is a fundamental contradiction in adopting this simplifying assumption when particles drive the flow. This contradiction is essentially that one cannot have a hydrostatic pressure that arises from the presence of particles while at the same time maintaining a depth-independent horizontal velocity field, as was assumed in references [3]–[7].