The time deuendent Navier-Stokes eauations are numerically integrated for two dimensional incompressible viscous flow in a wind-driven square cavity. Using a time-splitting method and finite differences on a staggered mesh, the momentum equations are solved by a conjugate gradient method which obviates the use of factorization. The tensor product method is incorporated for the pressure Poisson equation. The effects of increasing Reynolds numbers are studied and the developing boundary-layer is captured by using a finely clustered mesh. At Re=30,000, the flow is in a continously developing unsteady regime. Power spectrum plots indicate a rich frequency content and that the flow is in transition between laminar and turbulent states.
In this work, a computational study is presented for the investigation of gravity modulation (g-jitter) effects in thermally driven cavity flows at terrestrial and microgravity environments. The two-dimensional, time-dependent Navier-Stokes equations are numerically integrated by a time-split method using direct matrix solvers. Computations at terrestrial gravity are utilized to assess the effects of adiabatic side-wall boundary conditions as well as the full nonlinearity of the governing equations on the sinusoidally forced Benard problem studied by Gresho and Sani. The low-g calculations focus on the establishment of critical frequency ranges and consider the effects of modulation direction and randomness. The applicability of linear analysis in the excitable frequency range at low g is also discussed.
A direct numerical simulation of a fully developed, low-Reynolds-number turbulent flow in a square duct is presented. The numerical scheme employs a time-splitting method to integrate the three-dimensional, incompressible Navier-Stokes equations using spectral/high-order finite-difference discretization on a staggered mesh ; the nonlinear terms are represented by fifth-order upwind-biased finite differences. The unsteady flow field was simulated at a Reynolds number of 600 based on the mean friction velocity and the duct width, using 96 x 101 x 101 grid points. Turbulence statistics from the fully developed turbulent field are compared with existing experimental and numerical square duct data, providing good qualitative agreement. Results from the present study furnish the details of the corner effects and near-wall effects in this complex turbulent flow field; also included is a detailed description of the terms in the Reynolds-averaged streamwise momentum and vorticity equations. Mechanisms responsible for the generation of the stress-driven secondary flow are studied by quadrant analysis and by analysing the instantaneous turbulence structures. It is demonstrated that the mean secondary flow pattern, the distorted isotachs and the anisotropic Reynolds stress distribution can be explained by the preferred location of an ejection structure near the corner and the interaction between bursts from the two intersecting walls. Corner effects are also manifested in the behaviour of the pressure-strain and velocity-pressure gradient correlations.
Introduction T HE objective of this computational study is to investigate the development of nonlinear vortical structures in plane channel flow transition by the visualization of threedimensional vortex lines. It has long been recognized that transition may be viewed as a sequence of events that is triggered by two-dimensional Tollmien-Schlichting waves that become three-dimensional, leading to nonlinear wave interactions. In a recent experiment, Williams used hot film probes in a water channel boundary layer to create a data base containing three-dimensional instantaneous velocity and vorticity components documenting the evolution of the high shear layer and the formation of hairpin vortices. He then used this data base to obtain three-dimensional vortex lines. In this work, a similar technique is used to visualize the flowfield structures. In order to extract information from the computational data base, which provides the three-dimensional instantaneous velocity/vorticity field in over a quarter million grid points, vortex lines were calculated at time intervals that can be viewed sequentially. In addition, vorticity contours and velocity vector plots for the secondary flow are presented for a comparison with the findings inferred from the vortex line plots. Although flow visualization by vortex lines have been utilized in other numerical studies,' the present results effectively capture the continuous evolution of the flow, enabling the identification of various vortical structures.
An attempt is made to formulate a more accurate and physically plausible diffusion model, which will include the effects of large eddy motion on turbulent transport, by incorporating bulk convection and gradient diffusion. The two-equation model of turbulence thus obtained is used in self-similar form to calculate axisymmetric and plane two-dimensional jets.
The present numerical study establishes that, with the MacCormack and 'two-four' methods, the solution accuracy obtainable in problems involving wave propagation, shock-wave and contact discontinuities, and viscous effects, will be strongly dependent on Courant number. The application of flux correction to the MacCormack and two-four methods is noted to significantly attenuate dispersion errors; the ensuing solutions capture the discontinuities in the shock-tube problem with improved accuracy and resolution, and are free of dispersion errors for the viscous Burgers' equation.
The proper orthogonal decomposition method is used to extract empirical eigenfunctions from an incompressible turbulent flow in a square duct. The two-dimensional eigenfunctions, corresponding to the two inhomogeneous duct directions, are optimal in the energy sense. The database used to form the two-point correlation tensor is obtained from a low Reynolds number direct numerical simulation of the flow field. The symmetries inherent in the square cross section allow the formulation of the integral eigenvalue problem over one octant, producing an eigensystem of manageable size without losing any spatial scales. The extraction process reveals a gradual decrease of modal energies rather than a single dominant eigenfunction. Reconstructions of instantaneous velocity fields and Reynolds stresses indicate the efficiency, as it pertains to identifying structures and storing data, of the proper orthogonal decomposition method for this problem.
A direct numerical simulation (DNS) of spanwise-rotating turbulent channel flow was conducted for four rotation numbers: Rob=0, 0.2, 0.5, and 0.9 at a Reynolds number of 8000 based on laminar centerline mean velocity and Prandtl number 0.71. The results obtained from these DNS simulations were utilized to evaluate several turbulence closure models for momentum and heat transfer transport in rotating turbulent channel flow. Four nonlinear eddy viscosity turbulence models were tested and among these, explicit algebraic Reynolds stress models (EARSM) obtained the Reynolds stress distributions in best agreement with DNS data for rotational flows. The modeled pressure–strain functions of EARSM were shown to have strong influence on the Reynolds stress distributions near the wall. Turbulent heat flux distributions obtained from two explicit algebraic heat flux models (EAHFM) consistently displayed increasing disagreement with DNS data with increasing rotation rate.
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