Showing papers on "Navier–Stokes equations published in 1973"

Damping of Water Waves Over Porous Bed

Abstract: Based on linearized Navier-Stokes equations and Darcy’s equations, the viscous damping of small amplitude surface waves over a permeable bed is reexamined. Boundary layer approximation is employed in order to solve the velocity field and pressure field. Demanding that the net dissipation per period must be balanced by the slow decay of wave energy, the damping rate is found. The shortcomings of previous works are examined and are improved. Theory agrees fairly well with the experimental results.

A Numerical Study of Viscous Flow Past a Thin Oblate Spheroid at Low and Intermediate Reynolds Numbers

Abstract: The flow past a thin oblate spheroid falling at terminal velocity in an infinite, viscous fluid was investigated using a numerical solution of the steady-state Navier-Stokes equations of motion. The detailed streamfunction and vorticity yielded the drag, pressure distribution, and the extent of the spheroid's downstream wake. Calculations were performed for spheroids of axis ratios 0.05 and 0.2 and Reynolds numbers between 0.1 and 100. The results were compared with other numerical and analytical solutions to the Navier Stokes equations of motion for viscous flow past oblate spheroids and disks and with experimental results in the literature. Our numerical results for oblate spheroids of axis ratio 0.2 agree well with the numerical results of Masliyah and Epstein and with our own experimental results. Our results for oblate spheroids of axis ratio 0.05 agree well with the numerical computations of Michael and available experimental results on disks, but depart significantly from the numerical res...

Nonlinear problems in the physical sciences and biology : proceedings of a Battelle Summer Institute, Seattle, July 3-28, 1972

Abstract: Lyapunov methods and equations of parabolic type.- Multiple solutions of nonlinear partial differential equations.- Fading memory and functional-differential equations.- Singular perturbation by a quasilinear operator.- Remarks on branching from multiple eigenvalues.- Asymptotic analysis of a class of nonlinear integral equations.- Remarks about bifurcation and stability of quasi-periodic solutions which bifurcate from periodic solutions of the Navier Stokes equations.- Bifurcation of periodic solutions into invariant tori: The work of Ruelle and Takens.- Ergodic theory and statistical mechanics of non-equilibrium processes.- Mathematical problems in theoretical biology.- On predator-prey equations simulating an immune response.- Bifurcation theory for gradient systems.- Six lectures on the transition to instability.- Groundwater flow as a singular perturbation problem and remarks about numerical methods.- Nonlinear problems in nuclear reactor analysis.- Some non-linear problems in statistical mechanics and biology.- Stability properties and periodic behavior of controlled biochemical systems.

Finite-Element Analysis of Unsteady Incompressible Flow around an Oscillating Obstacle of Arbitrary Shape

Abstract: An analytical procedure based on Navier-Stokes equations was developed for representing unsteady flow patterns around oscillating obstacles. A variational formulation of the Helmholtz vorticity equation was discretized in finite element form and integrated numerically. At each step of the numerical integration the velocity field around the obstacle was determined from the finite element solution of Poisson's equation. The time-dependent boundary conditions around the oscillating obstacle were introduced as external constraints at each time step of the numerical integration. The obtained results for a cylinder and an airfoil were illustrated in the form of streamlines and vorticity and pressure distributions.

Finite difference methods for the steady-state navier-stokes equations

Abstract: Two iterative methods for numerically solving the incompressible 2D steady-state Navier-Stokes equation are presented. These are the Numerical Oseen (NOS) method and the Laplacian Driver (LAD) method. Unlike most methods, these are not time-dependent or even time-like in their iterations. The methods make use of recent advances in numerically solving 2D linear second-order partial differential equations with methods which are direct (i.e., non-iterative).

Remarks about bifurcation and stability of quasi-periodic solutions which bifurcate from periodic solutions of the Navier Stokes equations

Abstract: L. D. Landau (1944) and E. Hopf (1948) have conjectured that the transition to turbulence may be described as repeated branching of quasi-periodic solutions into quasi-periodic solutions with more frequencies. The simplest case is the bifurcation of periodic solutions from steady solutions. The next hardest problem is the bifurcation of quasi-periodic solutions from basic time periodic solutions of fixed frequency. This problem is treated in the lecture by a generalization of the Poincare-Lindstedt perturbation which is successful in the simplest case. It is assumed that the Floquet exponents are simple eigenvalues of the spectral problem for the basic flow.

On the numerical treatment of the Navier-Stokes equations for an incompressible fluid

Abstract: A new approach for the numerical integration of the Navier-Stokes equations is presented. It is based on the perturbation of the Poisson type equation. The system of nonlinear partial differential equations obtained is solved by means of an explicit operator. Some results are presented for the problem of steady flow in a square cavity. They are in good agreement with the calculations made by Greenspan, Fortin, Teman and Peyret, Bourcier and FranCois and Burgraff. Reynolds numbers up to 400 have been considered.

Numerical solution of the unsteady navier-stokes equations in curvilinear coordinates: The hypersonic blunt body merged layer problem

Abstract: The Navier-Stokes solution of this study agrees with the Monte Carlo result in the shock layer region within the statistical scatter of the Monte Carlo calculation. Thus, it appears that the origin of the disagreement between the thin layer Navier-Stokes solution and the molecular simulation solution in the shock layer region is in the thin layer approximations and not in the Navier-Stokes stress-strain model and Fourier heat conduction law. It should be pointed out, however, that at this transitional flow condition (Kn = 0.10) the Monte Carlo solution shows that the temperature is not in equilibrium. Thus, for this particular flow condition, the molecular simulation technique is more appropriate.

Anomalous osmosis: Solutions to the Nernst‐Planck and Navier‐Stokes equations

Abstract: The phenomenon of anomalous osmosis is studied by using the coupled Nernst‐Planck and Navier‐Stokes equations to investigate diffusion of an electrolyte through a pore of an ion‐exchange membrane Exact solutions to these equations show that a concentration gradient can produce fluid motion It is found that the velocity profiles may be significantly different from those of Poiseuille flow

Numerical Solution of Interacting Supersonic Boundary Layer Flows Including Separation Effects

Abstract: : An efficient numerical solution algorithm is presented for solving the interacting supersonic laminar boundary layer problem. The method employs a time dependent approach with the alternating direction implicit (ADI) scheme and directly accounts for the necessary downstream boundary condition. Solutions are presented for (M sub infinity) = 3 cold wall boundary layer flow over a family of expansion and compression ramps including several cases with regions of reverse flow. Good comparison is given with experimental data and Navier Stokes solutions for (M sub infinity) = 4, adiabatic wall, separated flow up a ten degree compression ramp. (Author)

Effect of inclination on laminar film condensation

Abstract: The effect of inclination on laminar film condensation over and under isothermal flat plates is investigated analytically. The complete set of Navier Stokes equations in two dimensions is considered. Analysed as a perturbation problem, the zero-order perturbation represents the boundary layer equations. First and second order perturbations are solved to bring about the leading edge effects. Corresponding velocity and temperature profiles are presented. The results show decrease in heat transfer with larger ∥inclinations∥ from the vertical. Comparison with experimental data of Gerstmann and Griffith indicates a closer agreement of the present results than the analytical results of the same authors.

Numerical Model for Mixed Region Collapse in a Stratified Fluid

Abstract: : The collapse of a homogeneous fluid mass immersed in a stably stratified fluid is studied numerically. A finite difference formulation of the Navier-Stokes equations in the primitive variables is solved in a large box several times the size of the mixed region. The formulation conserves total energy in the box in the special case where the viscosity is zero. The shape of the homogeneous region and its energy content are followed in detail. Confirming a previous speculation made from a crude analytical theory, most of the energy in the homogeneous fluid mass is shown to be transferred to the exterior fluid in one Brunt-Vaisala period. The predictions agree with available analytical models in initial and intermediate stages and with a previous tank experiment in the intermediate and late stages of collapse.

Spiral Flows in Finite Rotating Annular Tubes

Abstract: Three-dimensional, time-dependent, axisymmetric flows of an incompressible Newtonian fluid in an annular tube as well as in a circular one were analyzed numerically. The flow was produced from rest by a pressure drop between the inlet and the outlet of a finite, annular (or circular) tube which was rotating around its axis. An implicit finite-difference scheme of the Navier-Stokes equations was developed to obtain the time variations of three velocity components and of the pressure as boundary conditions vary. Entrance effects on the velocity field, the pressure, and the Bernoulli-sum were analyzed.

Drop shapes and internal flow patterns by numerical solution of the Navier-Stokes equations

Abstract: INTRODUCTION LITERATURE REVIEW TABLE OF CONTEI.TS

The Use of Optimal Coordinates in the Solution of Viscous Flow Problems

Abstract: : The idea of optimal coordinates, which was first developed by Kaplun (1954) and later extended by Legner (1971), is extended further in the present work and is used to analyze several viscous flow problems. Optimal coordinates are found for incompressible flow past wedges and cones and for supersonic compressible flow past a flat plate. (Author)

A Note on the Numerical Treatment of Navier-Stokes Equations. III

Abstract: The steady viscous incompressible fluid flow past an arbitrary symmetric cylindrical obstacle being in the middle of two parallel walls is treated, and method to find its numerical solution is given. By an application of the theory of conformal mapping, the problem is reduced to a boundary value problem of partial differential equations on a rectangular domain. Then the difference analogue of the problem on the rectangular domain can be approximately solved on a digital computer. Some results of numerical calculations are reported for the cases where the obstacle is a circular cylinder and the distance between two walls is various, the Reynolds number being 1 and 5.

Laminar Incompressible Flow Past Sharp Wedges

Abstract: : The symmetric laminar incompressible flow field past wedges with a sharp leading edge has been determined using the Navier Stokes equations written in a coordinate system that is optimal to second order. Because of a singularity that develops in the skin friction at such a sharp leading edge, the flow at this singular point is calculated from the Stokes approximation to the full equations. The free constant in the Stokes solution is determined by equating the skin friction function from the two solutions at a point, on the stagnation streamline, in the immediate vicinity of the sharp tip. Good agreement is obtained with the available results for the flow past the two limiting cases: the semi-infinite flat plate and the infinite vertical wall. (Author)

Finite difference treatment of strong shock over a sharp leading edge with navier-stokes equations

Abstract: : The report develops finite difference techniques for computing with reasonable accuracy the static pressure field downstream of a strong shock wave, based on Navier-Stokes equations. The leading edge shock over a sharp flat plate in a Mach 20 uniform stream is treated as a specific example. Various analytic models have been studied for suggesting the proper approaches to various aspects of computational difficulties, the most important of which are the oscillatory extraneous component in the computed results.

Numerical Solution of the Three-Dimensional Navier-Stokes Equations in Integro-Differential Form: Flow About a Finite Body,

Abstract: : A new method of numerical solution of the incompressible Navier-Stokes equations is applied to time-dependent flow about a rectangular slab at an angle of attack. With this formulation the solition is obtained in the entire unbounded flow field, but with actual computation required only in regions of significant vorticity. This allows considerable reduction in computer storage, since only points in regions of signficant vorticity need be stored at any particular time. The computational field thus expands in time. (Modified author abstract)

Calculation of the supersonic flow past blunt bodies using the complete and simplified Navier-Stokes equations

Abstract: THE supersonic flow of a viscous gas past a spherically blunted body is studied using the complete Navier-Stokes equations, equations containing only terms of order O(1) and O( 1 √Re ) , and equations containing only terms of order O(1). The departed shock wave, which is regarded as a surface of discontinuity, is assumed to be external boundary of the flow region. The solution is found by the build-up method using an implicit finite-difference scheme. An analysis of the results obtained and a comparison with the results of calculations using the theory of non-viscous flows and of the boundary layer enable us to establish the range of applicability of the various simplified equations used at the present time for calculating the supersonic flow of a viscous gas past blunt bodies.