Turbulence Modelling of A Lock-Release Oil Slick

The motion of a lock-release oil slick as an immiscible two-fluid gravity current is numerically studied by a finite dif ference algorithm based on the volume of fluid （VOF） method for the basic formulation and a rigid cover approximation for the open free surface. Detailed numerical simulation with careful model validation reveals the existence of turbulence and the adaptability of the renormalization group （RNG） k - ε model for the Reynolds-stress closure in the case of the oil slick. The time evolution and spatial distribution of the mean velocity, turbulence kinetic energy and turbulent viscosity are characterized. The mechanism for the transition from an initial gravity-inertial phase to a second gravity-vinous phase is shown to be the relaminarization effect of the initially highly turbulent slick. Compared well with known theoretical analyses and experimental observations, the turbulence modeling results in self-similar spreading laws in terms of the fact that the oil slick passes through the initial gravity-inertial phase with the front speed decreasing as t ^-1/3（where t is the time measured from lock release） and the second gravity-viscous phase with the front speed decreasing as t^-5/8.

NUMERICAL SIMULATION ON COMPRESSIBLE TURBULENCE BY SPECTRAL METHOD

The numerical and physical issues of simulations on compressible turbulence are reviewed in the present paper. An outline of the global spectral methods and the progress of recent local spectral methods are illustrated. Several typical subjects in this field are studied, including homogeneous isotropic turbulence, autoignition in premixed turbulence, interaction between flames and turbulence, and shock wave in turbulence. The results of the numerical simulations are discussed, enabling us to discover and to understand the physical phenomena which have not been solved by experiments.

Theoretical Investigation of the Vortex Shedding Noise from the Wake of Airfoil

The vortex shedding noise has been revealed as an important wing noise source on some modern commercial aircraft based on the fly-over measurements with a planar microphone array by Michel (1998). In this paper, an analytical model is presented for predicting this vortex shedding noise. The downstream wake of a 2-dimensional airfoil is assumed to be dominated by the von Karman vortex street, and the strength and the shedding frequency of the wake vortex are determined from the wake structure model. An aero-acoustic model is developed based on the Howe's unified theory of trailing edge noise and is incorporated with the wake model to predict the sound pressure level and directivity of vortex shedding noise. The predicted vortex shedding frequencies, sound pressure levels and directivities compare favorably with the measured results for 6 modern commercial aircraft.

DYADIC METHOD FOR TENSOR FUNCTIONS

In this paper,we discuss tensor functions by dyadic representation of tensor.Two different cases of scalar invariants and two different cases of tensor invari- ants are calculated.It is concluded that there are six independent scale invariants for a symmetrical tensor and an antisymmetrical tensor,and there are twelve invariants for two symmetrical tensors and an antisymmetrical tensor.And we present a new list of tensor invariants for the tensor-valued isotropic function.

A DISCUSSION ABOUT SCALE INVARIANTS FOR TENSOR FUNCTIONS

It is found that in some cases the complete and irreducible scale invariants given by Ref.[1] are not independent. There are some implicit functional relations among them. The scale invariants for two different cases are calculated. The first case is an arbitrary second order tensor. The second case includes a symmetric tensor, an antisymmetric tensor and a vector. By using the eigentensor notation it is proved that in the first case there are only six independent scale invariants rather than seven as reported in Ref.[1] and in the second case there are only nine independent scale invariants which are less than that obtained in Ref.[1].

ON SEPARATED SHEAR LAYER OF BLUNT CIRCULAR CYLINDER

Separated shear layer of blunt circular cylinder has been experimentally investigated for the Reynolds numbers (based on the diameter) ranging from 2.8 x 10(3) to 1.0 x 10(5), with emphasis on evolution of separated shear layer, its structure and distribution of Reynolds shear stress and turbulence kinetic energy. The results demonstrate that laminar separated shear layer experiences 2 similar to 3 times vortex merging before it reattaches, and turbulence separated shear layer takes 5 similar to 6 times vortex merging. In addition, relationship between dimensionless initial frequencies of K-H instability and Reynolds numbers is identified, and reasons for the decay of turbulence kinetic energy and Reynolds shear stress in reattachment region are discussed.

THE EIGENTENSORS OF AN ARBITRARY SECOND-ORDER TENSOR AND THEIR QUALITY ANALYSES

A notation of the eigentensors of an arbitrary second-order tensor had been introduced by HUANG Yong-nian (1992). By using this notation an explicit solution of homogeneous linear ordinary differential equations with constant coefficients had been given. Recently, it is found that these eigentensors are dyads. By using these dyads the tensor calculations can be simplified greatly.

PATTERN SELECTION IN A REACTION-DIFFUSION EQUATION

This paper studies the pattern selection in a spatially-periodic problem of a simplified reaction-diffusion system described by an evolutionary Duffing equation. Numerical explorations by a pseudo-spectral method reveal the dependence of the pattern formation on the initial profile as well as the parameter. Only patterns with 2 m humps are found to be meta-stable in the corresponding parameter ranges.

TOPOLOGICAL STRUCTURES OF VORTEX AND HELICITY ANALYSIS

The topological structures of the vortex filaments and vortex tubes with an exact solution of a straight spiral vortex tube are discussed. It is found that there are some confusions about the calculation of the helicity of a knotted vortex filament and some linked vortex filaments by using different methods. How to unify these methods is explained and the right results are given. (Edited author abstract) 5 Refs.

Turbulent lock release gravity current

The time evolution of a turbulent lock release gravity current, formed by a finite volume ofhomogeneous fluid released instantaneously into another fluid of slightly lower density, was studied byexperimental measurements of the density structure via elaborate digital image processing and by a nu-merical simulation of the flow and mixing using a two-equation turbulence model. The essential fact thatthe gravity current passes through an initial slumping phase in which the current head advances steadilyand a second self-similar phase in which the front velocity decreases like the negative third power of thetime after release is satisfactorily presented by the laboratory observation. An overall entrainment ratioproportional to the distance from the release point is found by the numerical simulation. The renormal-ization group (RNG) k- ε model for Reynolds-stress closure is validated to characterize the gravitycurrent with transitional and localized turbulence.