Computation of internal turbulent flow with a large separated flow region

An implicit two-equation turbulence solver, KEM. in generalized co-ordinates, is used in conjunction with the three-dimensional incompressible Navier–Stokes solver, INS3D, to calculate the internal flow in a channel and a channel with a sudden 2:3 expansion. A new and consistent boundary procedure for a low Reynolds number form of the κ-ε turbulence model is chosen to integrate the equations up to the wall. The high Reynolds number form of the equations is integrated using wall functions. The latter approach yields a faster convergence to the steady-state solution than the former. For the case of channel flow, both the wall-function and wall-boundary-condition approaches yield results in good agreement with the experimental data. The back-step (sudden expansion) flow is calculated using the wall-function approach. The predictions are in reasonable agreement with the experimental data.     

PIV–LES analysis of channel flow rotating about the streamwise axis

The flow field of a channel rotating about the streamwise axis is analyzed experimentally and numerically. The current investigations were carried out at a bulk velocity based Reynolds number of Re_m = 2850 and a friction velocity based Reynolds number of Re_τ = 180, respectively. Particle-image velocimetry (PIV) measurements are compared with large-eddy simulation data to show earlier direct numerical simulation findings to generate too large a reverse flow region in the center region of the spanwise flow. The development of the mean spanwise velocity distribution and the influence of the rotation on the turbulent properties, i.e., the Reynolds stresses and the two-point correlations of the flow, are confirmed in both investigations. The rotation primarily influences those components of the Reynolds shear stresses, which contain the spanwise velocity component. The size of the correlation areas and thus the length scales of the flow generally grow in all three coordinate directions leading to longer structures. Furthermore, experimental results of the same channel flow at a significantly lower bulk Reynolds number of Re_{m, l} = 665, i.e., a laminar flow in a non-rotating channel, are introduced. The experiments show the low Reynolds number flow to become turbulent under rotation and to develop the same characteristics as the high Reynolds number flow.     

Numerical prediction of locally forced turbulent separated and reattaching flow

An unsteady numerical simulation was performed for locally forced separated and reattaching flow over a backward-facing step. The local forcing was given to the separated and reattaching flow by means of a sinusoidally oscillating jet from a separation line. A version of the k––f_μ model was employed, in which the near-wall behavior without reference to distance and the nonequilibrium effect in the recirculation region were incorporated. The Reynolds number based on the step height (H) was fixed at Re_H=33 000, and the forcing frequency was varied in the range 0St_H2. The predicted results were compared and validated with the experimental data of Chun and Chun. It was shown that the unsteady locally forced separated and reattaching flows are predicted reasonably well with the k––f_μ model. To characterize the large-scale vortex evolution due to the local forcing, numerical flow visualizations were carried out.     

High-order LES modeling of turbulent incompressible flow

This article presents the high-order algorithms that we have developed for large-eddy simulation of incompressible flows, and the results that have been obtained for the 3D turbulent wake of a cylinder at a Reynolds number of $\mathit{Re}=3900$. To cite this article: R. Pasquetti, C. R. Mecanique 333 (2005).     

Self-consistency and the use of correlated stochastic separated flow models for prediction of particle-laden flows

Computational fluid dynamics (CFD) is being used increasingly in the design and analysis of particle-laden flows. A significant challenge of this work is in correctly predicting the interaction of the fluid turbulence with the particulate phase. Typically, Lagrangian tracking is used to calculate the particle trajectories with stochastic treatments used to provide an instantaneous turbulent flow field. The stochastic calculations are based on the mean velocities and turbulence quantities calculated by the CFD solver. The current work examines the correlated stochastic separated flow (SSF) model used to synthesize the instantaneous fluid velocity field. Two functional forms of the Eulerian spatial correlation are considered: exponential, and Frenkiel with loop parameter m equal to unity. It is well known that the use of a Frenkiel function is incorrect due to the Markovian nature of the model. Nonetheless, a literature review indicates that the Frenkiel function is still being used in the CFD community. In order to illustrate the implications of this, numerical predictions are compared to Taylor's analytical result for fluid particle dispersion in homogeneous isotropic turbulence. Excellent predictions are obtained with the exponential correlation and recommendations on timestep requirements are made. In contrast, predictions from the Frenkiel model are in poor agreement with Taylor's solution. This poor agreement results from an inconsistency between the effective correlation of fluid velocities arising from the model and the original intended correlation.     

Large eddy simulation of boundary layer flow under cnoidal waves

Water waves in coastal areas are generally nonlinear, exhibiting asymmetric velocity profiles with different amplitudes of crest and trough. The behaviors of the boundary layer under asymmetric waves are of great significance for sediment transport in natural circumstances. While previous studies have mainly focused on linear or symmetric waves, asymmetric wave-induced flows remain unclear, particularly in the flow regime with high Reynolds numbers.Taking cnoidal wave as a typical example of asymmetric waves, we propose to use an infinite immersed plate oscillating cnoidally in its own plane in quiescent water to simulate asymmetric wave boundary layer. A large eddy simulation approach with Smagorinsky subgrid model is adopted to investigate the flow characteristics of the boundary layer. It is verified that the model well reproduces experimental and theoretical results. Then a series of numerical experiments are carried out to study the boundary layer beneath cnoidal waves from laminar to fully developed turbulent regimes at high Reynolds numbers, larger than ever studied before.Results of velocity profile, wall shear stress, friction coefficient, phase lead between velocity and wall shear stress, and the boundary layer thickness are obtained. The dependencies of these boundary layer properties on the asymmetric degree and Reynolds number are discussed in detail.     

Disturbed boundary layer flow with local time-dependent surface heating

Local flows in a laminar boundary layer flowing over surface heating elements are investigated. Mathematical models of disturbed flows are constructed on the basis of an asymptotic analysis and the similarity parameters are determined. The time-dependent local heating regimes ensuring control of separation and flow stability in the boundary layer are studied. The results of a numerical and analytic analysis are obtained.     

Calculation of separated flow around multi-element aerofoils using conformal mapping

A method is presented to calculate the low-speed incompressible separated flow around multi-element aerofoils. The geometries of multi-element aerofoils in the physical plane are completely arbitrary and are transformed into multiple circles in the computational plane by a conformal mapping technique. Jacob's model, which distributes sources on the separated surfaces of multi-element aerofoils to simulate the effects of separation, is adopted here. The position of the separated point and the pressure on the surfaces of multi-element aerofoils are calculated by iteratively coupling the potential flow and boundary layer. The effects of the boundary layer are simulated by modification of the boundary condition. All iterative procedures converge rapidly as a result of using the fast Fourier transform (FFT) technique.     

Evaluation of subgrid-scale models in large-eddy simulation of flow past a two-dimensional block

Large-eddy simulations of flow past a two-dimensional (2D) block were performed to evaluate four subgrid-scale (SGS) models: (i) the traditional Smagorinsky model, (ii) the Lagrangian dynamic model, (iii) the Lagrangian scale-dependent dynamic model, and (iv) the modulated gradient model. An immersed boundary method was employed to simulate the 2D block boundaries on a uniform Cartesian grid. The sensitivity of the simulation results to grid refinement was investigated by using four different grid resolutions. The velocity streamlines and the vertical profiles of the mean velocities and variances were compared with experimental results. The modulated gradient model shows the best overall agreement with the experimental results among the four SGS models. In particular, the flow recirculation, the reattachment position and the vertical profiles are accurately reproduced with a relative coarse grid resolution of (N_x × N_y × N_z=) 160 × 40 × 160 (n_x × n_z = 13 × 16 covering the block). Besides the modulated gradient model, the Lagrangian scale-dependent dynamic model is also able to give reasonable prediction of the flow statistics with some discrepancies compared with the experimental results. Relatively poor performance by the Lagrangian dynamic model and the Smagorinsky model is observed, with simulated recirculating patterns that differ from the measured ones. Analysis of the turbulence kinetic energy (TKE) budget in this flow shows evidence of a strong production of TKE in the shear layer that forms as the flow is deflected around the block.     

A filtered mass density function approach for modeling separated two-phase flows for LES II: Simulation of a droplet laden temporally developing mixing layer

A two-phase velocity-scalar filtered mass density function (TVSFMDF) formulation developed for large eddy simulation (LES) is applied to a temporally developing counter-current mixing layer seeded with water droplets. Closure models for both the dispersed and carrier phases are developed and implemented that are self-consistent with the original TVSFMDF mathematical formulation developed by Carrara and DesJardin. Several simulation cases are conducted to examine the sensitivity of both evaporating and non-evaporating droplet dispersion on various levels of subgrid scale (SGS) modeling approximation – highlighting the importance of variations in composition space in the phase-coupling terms.     

Smagorinsky constant in LES modeling of anisotropic MHD turbulence

Turbulent fluctuations in magnetohydrodynamic (MHD) flows can become strongly anisotropic or even quasi-2D under the action of an applied magnetic field. We investigate this phenomenon in the case of low magnetic Reynolds numbers. It has been found in earlier DNS and LES of homogeneous turbulence that the degree of anisotropy is predominantly determined by the value of the magnetic interaction parameter and only slightly depends on the Reynolds number, type of large-scale dynamics, and the length scale. Furthermore, it has been demonstrated that the dynamic Smagorinsky model is capable of self-adjustment to the effects of anisotropy. In this paper, we capitalize on these results and propose a simple and effective generalization of the traditional non-dynamic Smagorinsky model to the case of anisotropic MHD turbulence.      

3-D measurements of separated flow over rigid plates with spanwise periodic cambering at low Reynolds number

Measurements of the flow field around a flat plate and rigid plates with spanwise periodic cambering were performed using volumetric three-component velocimetry (V3V) at a Reynolds numbers of 28,000 at α=12° where the flow is fully separated. The Reynolds normal and shear stresses, and the streamwise, spanwise and normal components of the vorticity vector are investigated for three-dimensionality. Flow features are discussed in context of the periodic cambering and corresponding aerodynamic force measurements. The periodic cambering results in spanwise variation in the reversed-flow region, Reynolds stresses and spanwise vorticity. These spanwise variations are induced by streamwise and normal vortices of opposite directions of rotation. Moreover, measurements were carried out for the cambered plates at α=8°, where a long separation bubble exists, to further understand the behavior of the streamwise and normal vortices. These vortices become more organized and increase in strength and size at the lower angle of attack. It is also speculated that these vortices contribute to the increase in lift at and beyond the onset of stall angle of attack.     

A filtered mass density function approach for modeling separated two-phase flows for LES I: Mathematical formulation

The overall objective of this study is to develop a full velocity-scalar filtered mass density function (FMDF) formulation for large eddy simulation (LES) of a separated two-phase flow. Required in the development of the two-phase FMDF transport equation are the local instantaneous equations of motion for a two-phase flow previously derived by Kataoka. In Kataoka’s development, phase interaction terms are cast in terms of a Dirac delta distribution on the phase interface. For this reason, it is difficult to close these coupling terms in the instantaneous formulation and this difficulty is propagated into the phase-coupling terms in the FMDF transport equation. To address this point a new derivation of the local instantaneous equations for a separated two-phase flow is given. The equations are shown to be consistent with the formulation given by Kataoka, and in the development, a direct link between the conditionally surface-filtered coupling terms, arising in the FMDF formulation, and LES phase-coupling terms is established. Clarification of conditions under which conditionally filtered interphase conversion terms in the marginal FMDF transport equations may be disregarded in a separated continuum-dispersed phase flow is discussed. Modeling approaches and solutions procedures to solve the two-phase FMDF transport equation via Monte-Carlo methods are outlined.     

An immersed boundary finite difference method for LES of flow around bluff shapes

A three‐dimensional numerical model using large eddy simulation (LES) technique and incorporating the immersed boundary (IMB) concept has been developed to compute flow around bluff shapes. A fractional step finite differences method with rectilinear non‐uniform collocated grid is employed to solve the governing equations. Bluff shapes are treated in the IMB method by introducing artificial force terms into the momentum equations. Second‐order accurate interpolation schemes for all sorts of grid points adjacent to the immersed boundary have been developed to determine the velocities and pressure at these points. To enforce continuity, the methods of imposition of pressure boundary condition and addition of mass source/sink terms are tested. It has been found that imposing suitable pressure boundary condition (zero normal gradient) can effectively reproduce the correct pressure distribution and enforce mass conservation around a bluff shape. The present model has been verified and applied to simulate flow around bluff shapes: (1) a square cylinder and (2) the Tsing Ma suspension bridge deck section model. Complex flow phenomena such as flow separation and vortex shedding are reproduced and the drag coefficient, lift coefficient, and pressure coefficient are calculated and analyzed. Good agreement between the numerical results and the experimental data are obtained. The model is proven to be an efficient tool for flow simulation around bluff bodies in time varying flows. Copyright © 2004 John Wiley & Sons, Ltd.     

Grid-averaged Lagrangian LES model for multiphase turbulent flow

A grid-averaged Lagrangian (GAL) model for dispersed particle motion in multiphase turbulent flow is presented to provide a large eddy simulation (LES) model for multiphase turbulent flow in which a quite large number of particles are involved. The GAL model is based on an averaging operation for a Lagrangian-type equation of motion of a particle over a computational grid volume and a procedure of reallocation of a dispersed particle cloud with its centroid movement to each grid. The model is therefore a mixed Eulerian–Lagrangian model which can effectively reduce computational time compared with existing Lagrangian-type models, without losing the advantage of Lagrangian-type models that they can properly describe the dynamical evolution of particles. Since the GAL model adopts the grid-volume averaging operation it can easily provide an effective SGS model for LES modeling of multiphase turbulent flow. The validity of the multiphase LES model developed, which is named the GAL-LES model, is confirmed through its application to a particle plume, in which the present model is found to simulate large-eddy motion usually observed in a jet and plume, and to give good agreements with experimental data.     

Effect of a local stationary flow disturbance on separated boundary layer stability

The separated flow past a transverse barrier on a plate surface is modeled in a wind tunnel. The linear stability of the two-dimensional laminar flow in the separation zone is investigated in the presence of a stationary disturbance imposed on the flow and concentrated in a narrow spanwise region. It is experimentally shown that the local flow nonuniformity leads to a change in the flow stability features, such as the frequencies of the growing oscillations, their growth rate, and the dispersion characteristics. As a result, the transverse velocity gradients induced in the separation zone exert a strong destabilizing influence on the flow. Novosibirsk. Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No. 1, pp. 174–178, January–February, 2000. The study was carried out with the support of the INTAS Foundation under grant No, 96-2225.