Review: Adapting Scalar Turbulence Closure Models for Rotation and Curvature

Scalar, eddy viscosity models are widely used for predicting engineering turbulent flows. System rotation, or streamline curvature, can enhance or reduce the intensity of turbulence. Methods to incorporate the effects of rotation and streamline curvature consist of introducing parametric variation of model coefficients, such that either the growth rate of turbulent energy is altered; or such that the equilibrium solution bifurcates from healthy to decaying solution branches. For general use, parameters must be developed in coordinate invariant forms. Effects of rotation and of curvature can be unified by introducing the convective derivative of the rate of strain eigenvectors as their measure.

JEFFREY FLUID MODEL FOR BLOOD FLOW THROUGH A TAPERED ARTERY WITH A STENOSIS

In this article, we have studied a non-Newtonian fluid model for blood flow through a tapered artery with a stenosis by assuming blood as Jeffrey fluid. The main purpose of our study was to follow the idea of Mekheimer and El Kot (2008), for Jeffrey fluid model, mean to study Jeffrey fluid model for blood flow through a tapered artery with a stenosis, Jeffrey fluid model is a non-Newtonian fluid model in which we consider convective derivative instead of time derivative. It is capable of describing the phenomena of relaxation and retardation time. The Jeffrey fluid has two parameters, the relaxation time λ1 and retardation time [Formula: see text]. Perturbation method is used to solve the resulting equations. The effects of non-Newtonian nature of blood on velocity profile, wall shear stress, shearing stress at the stenosis throat, and impedance of the artery are discussed. The results for Newtonian fluid are obtained as special case from this model.

Solution of the Parallel sheaR Layer Green's Function Using Conservation Equations

A parallel shear flow representation of a jet is a standard way to solve for the wave propagation terms in jet noise modeling using the acoustic analogy. In this paper we show by introducing a new primary Green's function variable, proportional to the convective derivative of the pressure-like Green's function, the wave propagation equations reduce to an exact conservation form that does not include any derivatives of the mean flow. We analyze this Green's function variable numerically and show its utility when the mean flow is defined by a CFD solution and known only at a discrete set of points.

Resolving Turbulent Wakes

Resolving the turbulent statistics of bluff-body wakes is a challenging task. Frequently, the streamwise grid point spacing approaching the vortex exit boundary is sacrificed to gain near full resolution of the turbulent scales neighboring the body surface. This choice favors the solution strategies of direct numerical and large-eddy simulations (DNS and LES) that house spectral-like resolving characteristics with inherent dissipation. Herein, two differencing stencils are tested for approximating four forms of the convective derivative in the DNS and LES formulations for incompressible flows. The wake spectral characteristics and conventional parameters are computed for Reynolds numbers Re=200 (laminar wake) and Re=3900. These tests demonstrated reliable stability and spectral-like accuracy of compact fifth-order upwinding for the advective derivative and fourth-order cell-centered Pade´ (with fourth-order upwinding interpolation) for the Arakawa form of the convective derivative. Specifically, observations of the DNS computations suggest that best results of the wake properties are acquired when the inertial subrange of the spectral energy is fully resolved at the grid-scale level. The LES solutions degraded dramatically only when the fifth-order upwind stencil resolved the spanwise periodic turbulence. Although the dynamic subgrid-scale model showed strong participation on the instantaneous level, its spectral contributions were negligible regardless of the chosen grid-scale scheme.

Resolving Turbulent Wakes

Accurate resolution of turbulent wakes is a formidable task. Herein, we challenge this task by testing several compact schemes for approximating the convective derivative of the direct numerical and large-eddy simulation (DNS and LES) methodologies. The stencils house the needed resolution efficiency and numerical stability characteristics to properly resolve turbulent wakes while concurrently maintaining convergent solutions. Turbulent wakes of the circular cylinder are computed for Re = 1260 and 3900 with the results verified by the experimental evidence.

Unsteady vortical and entropic distortions of potential flows round arbitrary obstacles

This paper is concerned with small amplitude vortical and entropic unsteady motions imposed on steady potential flows. Its main purpose is to show that, even in this unsteady compressible and vortical flow, the perturbations in pressure p’ and velocity u can be written as p’ = ρ0D0ϕ/Dt and u = ϕ + u(I) respectively, where D0/Dt is the convective derivative relative to the mean potential flow, u(I) is a known function of the imposed upstream disturbance and ϕ is a solution to the linear inhomogeneous wave equation \[ \frac{D_0}{Dt}\bigg(\frac{1}{c^2_0}\frac{D_0\phi}{Dt}\bigg)-\frac{1}{\rho_0}\nabla\cdot(\rho_0\nabla\phi)=\frac{1}{\rho_0}\nabla\cdot\rho_0{\bf u}^{(I)} \] with a dipole source term ρ0−1 [xdtri ]ρ0u(I) whose strength ρ0u(I) is a known function of the imposed upstream distortion field. (Here c0 and ρ0 denote the speed of sound and density of the background potential flow.) This equation is used to extend Hunt's (1973) generalization of the ‘rapid-distortion’ theory of turbulence developed by Batchelor & Proudman (1954) and Ribner & Tucker (1953). These theories predict changes occurring in weakly turbulent flows that are distorted (by solid obstacles and other external influences) in a time short relative to the Lagrangian integral scale.The theory is applied to the unsteady supersonic flow around a corner and a closed-form analytical solution is obtained. Detailed calculations are carried out to show how the expansion at the corner affects a turbulent incident stream.