Large-Eddy Simulation of the Flow Over a Circular Cylinder at Reynolds Number 2 × 104

The flow over a circular cylinder at Reynolds number 2 × 10⁴ was predicted numerically using the technique of large-eddy simulation (LES). Both incompressible and compressible flow formulations were used. The present results obtained at a low-Mach number (M?=?0.2) revealed significant inaccuracies like spurious oscillations of the compressible flow solution. A detailed investigation of such phenomena was carried out. It was found that application of blended central-difference or linear-upwind schemes could damp artificial waves significantly. However, this type of schemes has a too dissipative nature compared to pure central-differences. The incompressible flow results were found to be consistent with the existing numerical studies as well as with the experimental data. Basic flow features and flow mechanics were found to be in good agreement with existing experimental data and consistent with previously obtained LES. Special emphasis was put on the spectral analysis. Here, the classical Fourier transform as well as the continuous wavelet transform were applied. Based on the latter, the separated shear-layer instability was precisely clarified. It was found that the Reynolds number dependency between vortex shedding and shear-layer instabilities had a power law relation with n?=?0.5.     

Large-eddy simulation of flow separation on an airfoil at a high angle of attack and Re = 105 using Cartesian grids

Incompressible flow separating from the upper surface of an airfoil at an 18° angle of attack and a Reynolds number of Re = 10⁵, based on the freestream velocity and chord length c, is studied by the means of large-eddy simulation (LES). The numerical method is based on second-order central spatial discretization on a Cartesian grid using an immersed boundary technique. The results are compared with an LES using body-fitted nonorthogonal grids and with experimental data.     

Simulation of Three-Dimensional Bluff-Body Flows Using the Vortex Particle and Boundary Element Methods

Recent contributions to the 3-D vortex method for bluff-body flows are presented. The numerical method--a vortex method combined with a boundary element method--is briefy reviewed. It is applied to direct numerical simulation (DNS) of the flow past a sphere (Re= 300, 500 and 1000). The on-going work to extend the method towards vortex-based large-eddy simulation (LES) for high Reynolds number flows is also presented. Preliminary results for the flow past a hemisphere are discussed.     

Active control of flow separation over an airfoil using synthetic jets

We perform large-eddy simulation of turbulent flow separation over an airfoil and evaluate the effectiveness of synthetic jets as a separation control technique. The flow configuration consists of flow over an NACA 0015 airfoil at Reynolds number of 896,000 based on the airfoil chord length and freestream velocity. A small slot across the entire span connected to a cavity inside the airfoil is employed to produce oscillatory synthetic jets. Detailed flow structures inside the synthetic-jet actuator and the synthetic-jet/cross-flow interaction are simulated using an unstructured-grid finite-volume large-eddy simulation solver. Simulation results are compared with the 2005 experimental data of Gilarranz et al., and qualitative and quantitative agreements are obtained for both uncontrolled and controlled cases. As in the experiment, the present large-eddy simulation confirms that synthetic-jet actuation effectively delays the onset of flow separation and causes a significant increase in the lift coefficient. Modification of the blade boundary layer due to oscillatory blowing and suction and its role in separation control is discussed.     

Effects of the jet-to-crossflow momentum ratio on a sonic jet into a supersonic crossflow

Numerical investigation of a transverse sonic jet injected into a supersonic crossflow was carried out using large-eddy simulation for a free-stream Mach number M = 1.6 and a Reynolds number Re = 1.38 × 10⁵ based on the jet diameter. Effects of the jet-to-crossflow momentum ratio on various fundamental mechanisms dictating the intricate flow phenomena, including flow structures, turbulent characters and frequency behaviors, have been studied. The complex flow structures and the relevant flow features are discussed to exhibit the evolution of shock structures, vortical structures and jet shear layers. The strength of the bow shock increases and the sizes of the barrel shock and Mach disk also increase with increasing momentum ratio. Turbulent characters are clarified to be closely related to the flow structures. The jet penetration increases with the increase of the momentum ratio. Moreover, the dominant frequencies of the flow structures are obtained using spectral analysis. The results obtained in this letter provide physical insight in understanding the mechanisms relevant to this complex flow.     

Large-eddy simulations of chevron jet flows with noise predictions

Hybrid large-eddy type simulations for chevron nozzle jet flows are performed at Mach 0.9 and Re = 1.03 × 10⁶. Without using any subgrid scale model (SGS), the numerical approach applied in the present study is essentially implicit large-eddy simulation (ILES). However, a Reynolds-averaged Navier–Stokes (RANS) solution is patched into the near wall region. This makes the overall solution strategy hybrid RANS–ILES. The disparate turbulence length scales, implied by these different modeling approaches, are matched using a Hamilton–Jacobi equation. The complex geometry features of the chevron nozzles are fully meshed. With numerical fidelity in mind, high quality, hexahedral multi-block meshes of 12.5 × 10⁶ cells are used. Despite the modest meshes, the novel RANS–ILES approach shows encouraging performance. Computed mean and second-order fluctuating quantities of the turbulent near field compare favorably with measurements. The radiated far-field sound is predicted using the Ffowcs Williams and Hawkings (FW–H) surface integral method. Encouraging agreement of the predicted far-field sound directivity and spectra with measurements is obtained.     

Laser photochromic velocimetry estimation of the vorticity and pressure field – two-dimensional flow in a curved vessel

 Laser photochromic velocimetry was successfully used to determine details of a steady two-dimensional flow field. In the plane of symmetry of a 90° curved tube at a Reynolds number of 250, the axial and radial velocity fields were measured using laser photochromic velocimetry combined with a technique involving interpolation of the photochromic data. The wall shear stress, vorticity, and pressure field were also estimated. The experimental results were compared with those from numerical simulation. The agreement was remarkably good lending validity to the interpolation method used for this flow field. Received: 29 May 1997 / Accepted: 13 November 1997     

An experimental investigation of the ELAC 1 configuration at supersonic speeds

Supersonic flight of aerospace planes is of marked interest since several flow regimes characterized by different local flow structures have to be flown through. This problem was investigated experimentally for the hypersonic research configuration ELAC 1. The aim of the study was to detect the influence of the rounded leading edge, of the thickness distribution prescribed, and of the Reynolds number, especially on the flow on the leeward side of the configuration. The experiments were carried out in the transonic wind tunnel of Aerodynamisches Institut of RWTH Aachen, at a freestream Mach number Ma _∞=2, a unit Reynolds number of Re _∞=13×10⁶, angles of attack between ?3°?α?10°, and in a wind tunnel of the Institute for Theoretical and Applied Mechanics of the Russian Academy of Sciences in Novosibirsk. The freestream Mach numbers covered in these experiments were varied between 2?Ma _∞?4, freestream Reynolds numbers per unit length between 25×10⁶?Re _∞?56×10⁶ and angles of attack between ?3°?α?10°. Flow visualization studies, measurements of surface pressure distributions and of aerodynamic forces were used to analyze the flow. The results, which will also be compared with numerical data, clearly indicate marked differences in the location of the separation and reattachment lines, and the formation of the primary, secondary and tertiary vortices, for the flow regimes investigated.     

Large-eddy Simulation of Film Cooling Flows with Variable Density Jets

The present paper investigates the impact of the velocity and density ratio on the turbulent mixing process in gas turbine blade film cooling. A cooling fluid is injected from an inclined pipe at α=30° into a turbulent boundary layer profile at a freestream Reynolds number of Re_∞ = 400,000. This jet-in-a-crossflow (JICF) problem is investigated using large-eddy simulations (LES). The governing equations comprise the Navier–Stokes equations plus additional transport equations for several species to simulate a non-reacting gas mixture. A variation of the density ratio is simulated by the heat-mass transfer analogy, i.e., gases of different density are effused into an air crossflow at a constant temperature. An efficient large-eddy simulation method for low subsonic flows based on an implicit dual time-stepping scheme combined with low Mach number preconditioning is applied. The numerical results and experimental velocity data measured using two-component particle-image velocimetry (PIV) are in excellent agreement. The results show the dynamics of the flow field in the vicinity of the jet hole, i.e., the recirculation region and the inclination of the shear layers, to be mainly determined by the velocity ratio. However, evaluating the cooling efficiency downstream of the jet hole the mass flux ratio proves to be the dominant similarity parameter, i.e., the density ratio between the fluids and the velocity ratio have to be considered.     

Large-eddy simulation of low-frequency unsteadiness in a turbulent shock-induced separation bubble

The need for better understanding of the low-frequency unsteadiness observed in shock wave/turbulent boundary layer interactions has been driving research in this area for several decades. We present here a large-eddy simulation investigation of the interaction between an impinging oblique shock and a Mach 2.3 turbulent boundary layer. Contrary to past large-eddy simulation investigations on shock/turbulent boundary layer interactions, we have used an inflow technique which does not introduce any energetically significant low frequencies into the domain, hence avoiding possible interference with the shock/boundary layer interaction system. The large-eddy simulation has been run for much longer times than previous computational studies making a Fourier analysis of the low frequency possible. The broadband and energetic low-frequency component found in the interaction is in excellent agreement with the experimental findings. Furthermore, a linear stability analysis of the mean flow was performed and a stationary unstable global mode was found. The long-run large-eddy simulation data were analyzed and a phase change in the wall pressure fluctuations was related to the global-mode structure, leading to a possible driving mechanism for the observed low-frequency motions.      

Parallel FEM LES with one-equation subgrid-scale model for incompressible flows

This article develops a parallel large-eddy simulation (LES) with a one-equation subgrid-scale (SGS) model based on the Galerkin finite element method and three-dimensional (3D) brick elements. The governing filtered Navier–Stokes equations were solved by a second-order accurate fractional-step method, which decomposed the implicit velocity–pressure coupling in incompressible flow and segregated the solution to the advection and diffusion terms. The transport equation for the SGS turbulent kinetic energy was solved to calculate the SGS processes. This FEM LES model was applied to study the turbulence of the benchmark open channel flow at a Reynolds number Re_τ = 180 (based on the friction velocity and channel height) using different model constants and grid resolutions. By comparing the turbulence statistics calculated by the current model with those obtained from direct numerical simulation (DNS) and experiments in literature, an optimum set of model constants for the current FEM LES model was established. The budgets of turbulent kinetic energy and vertical Reynolds stress were then analysed for the open channel flow. Finally, the flow structures were visualised to further reveal some important characteristics. It was demonstrated that the current model with the optimum model constants can predict well the organised structure near the wall and free surface, and can be further applied to other fundamental and engineering applications.     

A complete and irreducible dynamic SGS heat-flux modelling based on the strain rate tensor for large-eddy simulation of thermal convection

In this paper, a general family of explicit algebraic tensor diffusivity functions based on the resolved temperature gradient vector and strain rate tensor is studied and applied to the construction of new constitutive relations for modelling the subgrid-scale (SGS) heat flux (HF). Based on Noll’s formulation, dynamic linear and nonlinear tensor diffusivity models are proposed for large-eddy simulation of thermal convection. The constitutive relations for these two proposed models are complete and irreducible. These two new models include several existing dynamic SGS HF models as special cases. It is shown that in contrast to the conventional modelling approach, the proposed models embody more degrees of freedom, permit non-alignment between the SGS HF and resolved temperature gradient vectors, reflect near-wall flow physics at the subgrid scale, and therefore, allow for a more realistic geometrical representation of the SGS heat flux for large-eddy simulation of thermal convection. Numerical simulations have been performed using a benchmark test case of a combined forced and natural convective flow in a vertical channel with a Reynolds number of and a Grashof number of Gr = 9.6 × 10⁵. The results obtained using the two proposed SGS HF models are compared with reported direct numerical simulation (DNS) data as well as predictions obtained using several conventional dynamic SGS HF models.     

Nonlinear dynamics between two differentially heated vertical plates in the presence of stratification

We consider the numerical simulation of the flow between infinite, differentially heated vertical plates with positive stratification. We use a two-dimensional Boussinesq approximation, with periodic boundary conditions in the vertical direction. The relative stratification parameter ${\gamma=(\frac{1}{4}Ra S)^{1/4}}$ , where Ra is the Rayleigh number and S the adimensional stratification, is kept constant and equal to 8. The Prandtl number is 0.71. We derive a complex Ginzburg-Landau equation from the equations of motion. Coefficients are computed analytically, but we find that the domain of validity of these coefficients is small and rely on the numerical simulation to adjust the coefficients over a wider range of Rayleigh numbers. We show that the Ginzburg-Landau equation is able to accurately predict the characteristics of the periodic solution at moderate Rayleigh numbers. Above the primary bifurcation at Ra = 1.63 × 10⁵, the Ginzburg-Landau model is found to be Benjamin-Feir unstable and to be characterized by modulated traveling waves and phase-defect chaos, which is supported by evidence from the DNS. As the Rayleigh number is increased beyond Ra = 2.7 × 10⁵, nonlinearities become strong and the flow is characterized by cnoidal waves.     

Large Eddy Simulation of Turbulent Convective Cavity Flow

The large eddy simulation model with Smagorinsky subgrid-scale model was applied to two-dimensional turbulent convective cavity flow. The Reynolds number is lying from 1×10⁴ to 4×10⁵ and Archimedes number from 0 to 0.4. The simulation results were compared with the k?? model results and experimental results wherever possible. Flow results were in good agreement with experimental data across the mid-planes. Effects of Smagorinsky constant and grid resolution were investigated.     

Direct Numerical Simulation of Turbulent Flow over a Rectangular Trailing Edge

This paper describes a direct numerical simulation (DNS) study of turbulent flow over a rectangular trailing edge at a Reynolds number of 1000, based on the freestream quantities and the trailing edge thickness h; the incoming boundary layer displacement thickness δ^* is approximately equal to h. The time-dependent inflow boundary condition is provided by a separate turbulent boundary layer simulation which is in good agreement with existing computational and experimental data. The turbulent trailing edge flow simulation is carried out using a parallel multi-block code based on finite difference methods and using a multi-grid Poisson solver. The turbulent flow in the near-wake region of the trailing edge has been studied first for the effects of domain size and grid resolution. Then two simulations with a total of 256 × 512 × 64 (∼ 8.4×10⁶) and 512 × 1024 × 128 (∼ 6.7×10⁷) grid points in the computational domain are carried out to investigate the key flow features. Visualization of the instantaneous flow field is used to investigate the complex fluid dynamics taking place in the near-wake region; of particular importance is the interaction between the large-scale spanwise, or Kármán, vortices and the small-scale quasi-streamwise vortices contained within the inflow boundary layer. Comparisons of turbulence statistics including the mean flow quantities are presented, as well as the pressure distributions over the trailing edge. A spectral analysis applied to the force coefficient in the wall normal direction shows that the main shedding frequency is characterized by a Strouhal number based on h of approximately 0.118. Finally, the turbulence kinetic energy budget is analysed. Received 4 March 1999 and accepted 27 October 2000     

Experimental and high-order LES analysis of the flow in near-wall region of a square cylinder

A coupled experimental/numerical analysis of turbulent flow past a square cylinder is performed at the ERCOFTAC Reynolds number Re = U_∞D/ν = 21,400, where U_∞ is the inflow velocity and D the cylinder height. Complementary Laser Doppler Velocimetry (LDV) and high-order large-eddy simulations (LES) approaches, based on a spectral vanishing technique (SVV-LES), provide a comprehensive data base including both instantaneous data and post-processed statistics. Beyond these results, an achievement of the paper is to investigate the coherent structures developing on the sides and in the wake of the cylinder with a special focus on the flow features in the near-wall region. The flow is found to separate at the leading edge of the cylinder with the occurence of three-dimensional Kelvin-Helmholtz (KH) pairings localized in the separating shear layer. The interaction between these KH vortical structures and Von Kármán vortex shedding (VK) in the near wake is discussed based on both visualisations and frequency analysis. In particular, signatures of VK and KH vortical structures are found on velocity time samples.     

Quantifying the dynamics of flow within a permeable bed using time-resolved endoscopic particle imaging velocimetry (EPIV)

This paper presents results of an experimental study investigating the mean and temporal evolution of flow within the pore space of a packed bed overlain by a free-surface flow. Data were collected by an endoscopic PIV (EPIV) technique. EPIV allows the instantaneous velocity field within the pore space to be quantified at a high spatio-temporal resolution, thus permitting investigation of the structure of turbulent subsurface flow produced by a high Reynolds number freestream flow (Re _s in the range 9.8?×?10³?C9.7?×?10⁴). Evolution of coherent flow structures within the pore space is shown to be driven by jet flow, with the interaction of this jet with the pore flow generating distinct coherent flow structures. The effects of freestream water depth, Reynolds and Froude numbers are investigated.     

Wake flow pattern modified by small control cylinders at low Reynolds number

Passive wake control behind a circular cylinder in uniform flow is studied by numerical simulation for Re_D ranging from 80 to 300. Two small control cylinders, with diameter d/D=1/8, are placed at x/D=0.5 and y/D=±0.6. Unlike the 1990 results of Strykowski and Sreenivasan, in the present study, the vortex street behind the main cylinder still exists but the fluctuating lift and the form drag on the main cylinder reduces significantly and monotonously as the Reynolds number increases from 80 to 300. Obstruction of the control cylinders to the incoming flow deflects part of the fluid to pass through the gap between the main and control cylinders, forming two symmetric streams. These streams not only eliminate the flow separation along the rear surface of the main cylinder, they also merge toward the wake centerline to create an advancing momentum in the immediate near-wake region. These two effects significantly reduce the wake width behind the main cylinder and lead to monotonous decrease of the form drag as the Reynolds number increases. As the Reynolds number gets higher, a large amount of the downstream advancing momentum significantly delays the vortex formation farther downstream, leading to a more symmetric flow structure in the near-wake region of the main cylinder. As the Reynolds number increases from 80 to 300, both increasing symmetry of the flow structure in the near-wake and significant delay of the vortex formation are the main reasons for the fluctuating lift to decrease monotonously.     

Aerodynamic forces and three-dimensional flow structures in the mean wake of a surface-mounted finite-height square prism

Different flow models have been proposed for the flow around surface-mounted finite-height square prisms, but there is still a lack of consensus about the origin and connection of the streamwise tip vortices with the other elements of the wake. This numerical study was performed to address this gap, in addition to clarifying the relationship of the near-wake structures with the far wake and the near-wall flow, which is associated with the fluid forces. A large-eddy simulation approach was adopted to solve the flow around a surface-mounted finite-height square prism with an aspect ratio of AR = 3 and a Reynolds number Re = 500. The mean drag and normal forces and the bending moment for the prism were quantitatively compared in terms of skin-friction and pressure contributions, and related to the near-wall flow. Both three-dimensional visualizations and planar projections of the time-averaged flow field were used to identify, qualitatively, the main structures of the wake, including the horseshoe vortex, corner vortices and regions of high streamwise vorticity in the upper part of the wake. These features showed the same qualitative behavior as reported in high Reynolds number studies. It was found that some regions of high streamwise vorticity magnitude, like the tip vortices, are associated with the three-dimensional bending of the flow, and the tip vortices did not continuously extend to the free end of the prism. The three-dimensional flow analysis, which integrated different observations of the flow field around surface-mounted finite-height square prisms, also revealed that the mean near-wake structure is composed of two sections of different origin and location of dominance.