Second Moment Closure Modeling and DNS of Stratified Shear Layers

Buoyant shear layers encountered in many engineering and environmental applications have been studied by researchers for decades. Often, these flows have high Reynolds and Richardson numbers, which leads to significant/intractable space-time resolution requirements for DNS or LES. On the other hand, many of the important physical mechanisms, such as stress anisotropy, wake stabilization, and regime transition, inherently render eddy viscosity-based RANS modeling inappropriate. Accordingly, we pursue second-moment closure (SMC), i.e., full Reynolds stress/flux/variance modeling, for moderate Reynolds number non-stratified, and stratified shear layers for which DNS is possible. A range of sub-model complexity is pursued for the diffusion of stresses, density fluxes and variance, pressure strain and scrambling, and dissipation. These sub-models are evaluated in terms of how well they are represented by DNS in comparison to the exact Reynolds averaged terms, and how well they impact the accuracy of full RANS closure. For the non-stratified case, SMC model predicts the shear layer growth rate and Reynolds shear stress profiles accurately. Stress anisotropy and budgets are captured only qualitatively. Comparing DNS of exact and modeled terms, inconsistencies in model performance and assumptions are observed, including inaccurate prediction of individual statistics, non-negligible pressure diffusion, and dissipation anisotropy. For the stratified case, shear layer and gradient Richardson number growth rates, and stress, flux and variance decay rates, are captured with less accuracy than corresponding flow parameters in the non-stratified case. These studies lead to several recommendations for model improvement.

Vortex Trapping Cavity on Airfoil: High-Order Penalized Vortex Method Numerical Simulation and Water Tunnel Experimental Investigation

This paper presents a two-dimensional implementation of the high-order penalized vortex in cell method applied to solve the flow past an airfoil with a vortex trapping cavity operating under moderate Reynolds number. The purpose of this article is to investigate the fundamentals of the vortex trapping cavity. The first part of the paper treats with the numerical implementation of the method and high-order schemes incorporated into the algorithm. Poisson, stream-velocity, advection, and diffusion equations were solved. The derivation, finite difference formulation, Lagrangian particle remeshing procedure, and accuracy tests were shown. Flow past complex geometries was possible through the penalization method. A procedure description for preparing geometry data was included. The entire methodology was tested with flow past impulsively started cylinder for three Reynolds numbers: 550, 3000, 9500. Drag coefficient, streamlines, and vorticity contours were checked against results obtained by other authors. Afterwards, simulations and experimental results are presented for a standard airfoil and those equipped with a trapping vortex cavity. Airfoil with an optimized cavity shape was tested under three angles of attack: 3°, 6°, 9°. The Reynolds number is equal to Re = 2 × 104. Apart from performing flow analysis, drag and lift coefficients for different shapes were measured to assess the effect of vortex trapping cavity on aerodynamic performance. Flow patterns were compared against ultraviolet dye visualizations obtained from the water tunnel experiment.

The Symmetry and Stability of the Flow Separation around a Sphere at Low and Moderate Reynolds Numbers

The flow separation state reflects the symmetry and stability of flow around spheres. The three-dimensional structures of flow around a rigid sphere at moderate Reynolds number (Re) between 20 and 400 by using finite volume method with adaptive mesh refinement are presented, and the process of separation angles changing from stable to oscillating state with increasing of Re is analyzed. The results show that the flow is steady, and the separation angles are stable and axisymmetric at Re in less than 200. The flow is unsteady and time-periodic, and the flow separation becomes regular fluctuations and asymmetric at Re = 300, which leads to the nonzero value of lateral force and the phase difference between lift and lateral force. At Re = 400, the flow is unsteady, non-periodic, and asymmetric, as is the flow separation. It’s concluded that the flow separation angle increases when Re increases within a range between 40 and 200. With Re continues to increase, the flow separation state changes from stable to periodically regular until quasi-periodically irregular. The vortex structure changes from no shedding to asymmetric periodic shedding, and finally to asymmetric and intermittently periodic vortex shedding. These results have important implications for the stability of flow around spheres.

Effects of uniform injection and suction through perforated pentagonal cylinders on the flow and heat transfer

Purpose The purpose of this paper is to study the effects of uniform injection and suction through a perforated pentagonal cylinder on the flow field and heat transfer. Design/methodology/approach The finite-volume method has been used to solve the ensemble-averaged Navier-Stokes equations for incompressible flow at moderate Reynolds number (Re = 22,000) with the k-ɛ turbulence model equations. Findings A computational fluid dynamics analysis of turbulent flow past a non-regular pentagonal cylinder with three different aspect ratios aspect ratios has been carried out to investigate the effects of uniform injection/suction through the front and all surfaces of the cylinder. It is found that flow field parameters such as drag coefficient, pressure coefficient and Nusselt number are affected considerably in some cases depend on injection/suction rate (Γ) and perforated wall position. Research limitations/implications To optimize the efficiency of the injection and suction through a perforated surface, both wide-ranging and intensive further studies are required. Using various perforation ratios and injection/suction intensities are some possibilities. Practical implications Control of the vortex shedding and wake region behind bluff bodies is of vital interest in fluid dynamics. Therefore, applying uniform injection and suction from a perforated bluff body into the main flow can be used as a drag reduction mechanism, thermal protection and heat transfer enhancement. Originality/value This study provides unique insights into the active flow control method around pentagonal cylinders that can be useful for researchers in the field of fluid dynamics and aeronautics.

Density distribution in the flow past a sphere descending in a salt-stratified fluid

The density distribution around a sphere descending in a salt-stratified fluid is measured by the laser-induced fluorescence (LIF) method. The corresponding velocity distribution is measured by particle image velocimetry (PIV), and numerical simulation is also performed to supplement the observations by LIF and PIV. In steady flow, LIF observes a thin and vertically long structure which corresponds to a buoyant jet. The bell-shaped structure, which appears under strong stratification and moderate Reynolds number (Froude number $Fr \lesssim 3$ , Reynolds number $50 \lesssim Re \lesssim 500$ ), is also identified. The measured density distributions in the salinity boundary layer and in the jet agree with the numerical simulations which use the Schmidt number of the fluorescent dye ( $Sc \sim 2000$ ). The initially unsteady process of the jet formation is also investigated. Under weak stratification, the LIF shows an initial development of an axisymmetric rear vortex as observed in homogeneous fluids. However, as time proceeds and the effect of stratification becomes significant, the vortex shrinks and disappears, while the jet extends vertically upward. Under strong stratification, a thin jet develops without generating a rear vortex, since the effect of stratification becomes significant in a short time before the vortex is generated.