Search

A two-dimensional body that moves suddenly in a viscous fluid can instantly generate vortices at its sharp edges. Recent work using inviscid flow theory, based on the Birkhoff–Rott equation and the Kutta condition, predicts that the 'starting vortices' generated by the sharp and straight edges of a body – i.e. the vortices formed immediately after motion begins – can be one of three distinct self-similar types. We explore the existence of these starting vortices for a flat plate and two symmetric Joukowski aerofoils immersed in a viscous fluid, using high-fidelity direct numerical simulations (DNS) of the Navier–Stokes equations. A lattice Green's function method is employed and simulations are performed for chord Reynolds numbers ranging from 5040 to 45 255. Vortices generated at the leading and trailing edges of the flat plate show agreement with the derived inviscid theory, for which a detailed assessment is reported. Agreement is also observed for the two symmetric Joukowski aerofoils, demonstrating the utility of the inviscid theory for arbitrary bodies. While this inviscid theory predicts an abrupt transition between the starting-vortex types, DNS shows a smooth transition. This behaviour occurs for all Reynolds numbers and is related to finite-time effects – there is a maximal time for which the (self-similar) starting vortices exist. We confirm the inviscid prediction that the leading-edge starting vortex of a flat plate can be suppressed dynamically. This has implications for the performance of low-speed aircraft such as model aeroplanes, micro air vehicles and unmanned air vehicles. [ABSTRACT FROM AUTHOR]

A study shows that the vortex pair created by shock-induced separation is a strong feature of leeward flow, in the case of inviscid hypersonic flow over a delta wing. Separation happens at inboard of leading edge for viscous flow. Leeward surface local heating occurs due to separation and resulting vortex formations. The study is done using kinetic theory and a Navier-Stokes solver with a parallel supercomputer.

Presents a class of subgrid stress models for large-eddy simulation, based on the idea of structure-based Reynolds-stress closure. Derivation of an equation which relates the subgrid stress to the structure orientation and the subgrid kinetic energy, together with an assumed Kolmogorov energy spectrum for the subgrid vortices.

Calculates the velocity structure functions for vortex models of isotropic turbulence. Integral operator used to define an isotropic two-point field from a volume-orientation average for a specific solution of the Navier-Stokes equations; Explicit formulas from the application of positive integer powers of the longitudinal velocity difference.

Examines numerically the issue of convergence for initial-value solutions and similarity solutions of the compressible Euler equations in two dimensions in the presence of vortex sheets. Normal shock wave; Inclined density discontinuity in the presence of a solid boundary; Nonconvergence of the initial-value calculation at fixed time.

Calculates pressure spectra at large wave numbers for Lundgren-Townsend vortex models of the fine scales of homogeneous turbulence. Contribution to the shell-summed spectrum produced by the interaction between the axisymmetric and nonaxisymmetric components of the velocity field; Numerical estimates of the dimensionless prefactors for the component.

Presents a numerical study of the stability of the axisymmetric Burgers vortex solution of the Navier-Stokes equations to two-dimensional perturbations.

A model for the flux of a passive scalar by the subgrid motions in the large-eddy simulation of turbulent flow is proposed within the framework of the stretched-vortex subgrid stress model. The model is based on an analytical solution for the winding of a scalar field by an elemental subgrid vortex. This gives a tensor gradient-diffusion expression for the local flux of the scalar with subgrid turbulent diffusivity which depends upon the subgrid energy, the local cell size, and the vortex orientation in space. The scalar-flux subgrid model is tested by comparison of the results of 32[sup 3] large-eddy simulation of passive-scalar transport by forced isotropic turbulence in the presence of a mean scalar gradient, with the direct-numerical simulation results of Overholt and Pope [Phys. Fluids 8, 2128 (1996)]. The present large-eddy simulation results predict that at large Taylor-Reynolds numbers, the ratio of the scalar variance to the squared product of the scalar gradient with the dissipation length of the turbulence, is asymptotic to a nearly constant value c[sup ′2]/(α[sub 1] L[sub ε])[sup 2]approx. 0.36. © 2000 American Institute of Physics. [ABSTRACT FROM AUTHOR]

A physical-space version of the stretched-vortex subgrid-stress model is presented and applied to large-eddy simulations of incompressible flows. This version estimates the subgrid-kinetic energy required for evaluation of the subgrid-stress tensor using local second-order structure-function information of the resolved velocity field at separations of order the local cell size. A relation between the structure function and the energy spectrum is derived using the kinematic assumptions of the stretched-vortex model for locally homogeneous anisotropic turbulence. Results of large-eddy simulations using this model are compared to experimental and direct numerical simulation data. Comparisons are shown for the decay of kinetic energy and energy spectra of decaying isotropic turbulence and for mean velocities, root-mean-square velocity fluctuations and turbulence-kinetic energy balances of channel flow at three different Reynolds numbers. © 2000 American Institute of Physics. [ABSTRACT FROM AUTHOR]