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A series of project papers is presented in computational fluid dynamics. The work was performed during the 1973-74 academic year at Old Dominion University. Each paper briefly examines a numerical method(s) that can be applied to the Navier-Stokes equations governing incompressible flow in a driven cavity. Solutions obtained with a cubic spline procedure are also included.
Parallel Plate Plastometer (PPP) is a device commonly used for measuring the viscosity of high polymers at low rates of shear in the range 10 4 to 10 9 poises. This device is being validated for use in measuring the viscosity of liquid glasses at high temperatures having similar ranges for the viscosity values. PPP instrument consists of two similar parallel plates, both in the range of 1 inch in diameter with the upper plate being movable while the lower one is kept stationary. Load is applied to the upper plate by means of a beam connected to shaft attached to the upper plate. The viscosity of the fluid is deduced from measuring the variation of the plate separation, h, as a function of time when a specified fixed load is applied on the beam. Operating plate speeds measured with the PPP is usually in the range of 10 -3 cm/s or lower. The flow field within the PPP can be simulated using the equations of motion of fluid flow for this configuration. With flow speeds in the range quoted above the flow field between the two plates is certainly incompressible and laminar. Such flows can be easily simulated using numerical modeling with computational fluid dynamics (CFD) codes. We present below the mathematical model used to simulate this flow field and also the solutions obtained for the flow using a commercially available finite element CFD code.
The effect of suspended solid particles on the performance of the compressor cascade was investigated experimentally in a specially built cascade tunnel, using quartz sand particles. The cascades were made of NACA 65(10)10 airfoils. Three cascades were tested, one accelerating cascade and two diffusing cascades. The theoretical analysis assumes inviscid and incompressible two dimensional flow. The momentum exchange between the fluid and the particle is accounted for by the interphase force terms in the fluid momentum equation. The modified fluid phase momentum equations and the continuity equation are reduced to the conventional stream function vorticity formulation. The method treats the fluid phase in the Eulerian system and the particle phase in Lagrangian system. The experimental results indicate a small increase in the blade surface static pressures, while the theoretical results indicate a small decrease. The theoretical analysis, also predicts the loss in total pressure associated with the particulate flow through the cascade.
In order to study the effect of ion wind on viscous drag, the equations of electrogasdynamics are solved numerically assuming the flow is incompressible, the electric field is steady and that the fluid velocity is negligible compared to ion drift velocity. The results obtained to date in a continuing theoretical and experimental research program are presented.
The effect of inlet starvation on the hydrodynamic lubrication of lightly loaded rigid nonconformal contacts in combined rolling and normal motion is determined through a numerical solution of the Reynolds' equation for an isoviscous, incompressible lubricant. Starvation is effected by systematically reducing the fluid inlet level. The pressures are taken to be ambient at the inlet meniscus boundary and Reynolds' boundary condition is applied for film rupture in the exit region. Results are presented for the dynamic performance of the starved contacts in combined rolling and normal motion for both normal approach and separation. During normal approach the dynamic load ratio (i.e. ratio of dynamic to steady state load capacity) increases considerably with increase in the inlet starvation. The effect of starvation on the dynamic peak pressure ratio is relatively small. Further, it has been observed that with increasing starvation, film thickness effects become significant in the dynamic behavior of the nonconformal contacts. For significantly starved contacts the dynamic load ratio increases with increase in film thickness during normal approach and a similar reduction is observed during separation. A similar effect is noted for the dynamic peak pressure ratio.
The effect of inlet starvation on the hydrodynamic lubrication of lightly loaded rigid nonconformal contacts in combined rolling and normal motion is determined through a numerical solution of the Reynolds' equation for an isoviscous, incompressible lubricant. Starvation is effected by systematically reducing the fluid inlet level. The pressures are taken to be ambient at the inlet meniscus boundary and Reynolds' boundary condition is applied for film rupture in the exit region. Results are presented for the dynamic performance of the starved contacts in combined rolling and normal motion for both normal approach and separation. During normal approach the dynamic load ratio (i.e. ratio of dynamic to steady state load capacity) increases considerably with increase in the inlet starvation. The effect of starvation on the dynamic peak pressure ratio is relatively small. Further, it has been observed that with increasing starvation, film thickness effects become significant in the dynamic behavior of the nonconformal contacts. For significantly starved contacts the dynamic load ratio increases with increase in film thickness during normal approach and a similar reduction is observed during separation. A similar effect is noted for the dynamic peak pressure ratio.
It is shown that within the framework of nearly incompressible magnetohydrodynamics, but not within that of neutral-fluid hydrodynamics, a k exp -5/3 inertial-range wave number density fluctuation spectrum is to be expected at the same times that k exp -5/3 kinetic energy and magnetic energy cascade spectra are present. A previous discrepancy between theory and observation in the local interstellar medium and solar wind is thereby resolved.
The proper specification of boundary conditions at artificial boundaries for the simulation of time-dependent fluid flows has long been a matter of controversy. A general theory of asymptotic boundary conditions for dissipative waves is applied to the design of simple, accurate conditions at downstream boundary for incompressible flows. For Reynolds numbers far enough below the critical value for linear stability, a scaling is introduced which greatly simplifies the construction of the asymptotic conditions. Numerical experiments with the nonlinear dynamics of vortical disturbances to plane Poiseuille flow are presented which illustrate the accuracy of our approach. The consequences of directly applying the scalings to the equations are also considered.
One of the main themes in fluid dynamics at present and in the future is going to be computational fluid dynamics with the primary focus on the determination of drag, flow separation, vortex flows, and unsteady flows. A computation of the flow of a viscous fluid requires an understanding and consideration of the physical aspects of the flow. This is done by identifying the flow regimes and the scales of fluid motion, and the sources of vorticity. Discussions of flow regimes deal with conditions of incompressibility, transitional and turbulent flows, Navier-Stokes and non-Navier-Stokes regimes, shock waves, and strain fields. Discussions of the scales of fluid motion consider transitional and turbulent flows, thin- and slender-shear layers, triple- and four-deck regions, viscous-inviscid interactions, shock waves, strain rates, and temporal scales. In addition, the significance and generation of vorticity are discussed. These physical aspects mainly guide computations of the flow of a viscous fluid.
With the continuing development of bigger and faster supercomputers, computational fluid dynamics (CFD) has become a useful tool for real-world engineering design and analysis. However, the number of grid points necessary to resolve realistic flow fields numerically can easily exceed the memory capacity of available computers. In addition, geometric shapes of flow fields, such as those in the Space Shuttle Main Engine (SSME) power head, may be impossible to fill with continuous grids upon which to obtain numerical solutions to the equations of fluid motion. The solution to this dilemma is simply to decompose the computational domain into subblocks of manageable size. Computer codes that are single-block by construction can be modified to handle multiple blocks, but ad-hoc changes in the FORTRAN have to be made for each geometry treated. For engineering design and analysis, what is needed is generalization so that the blocking arrangement can be specified by the user. INS3D is a computer program for the solution of steady, incompressible flow problems. It is used frequently to solve engineering problems in the CFD Branch at Marshall Space Flight Center. INS3D uses an implicit solution algorithm and the concept of artificial compressibility to provide the necessary coupling between the pressure field and the velocity field. The development of generalized multi-block capability in INS3D is described.
A steady incompressible three-dimensional (3-D) viscous flow analysis was conducted for the Space Shuttle Main Propulsion External Tank (ET)/Orbiter (ORB) propellant feed line quick separable 17-inch disconnect flapper valves for liquid oxygen (LO2) and liquid hydrogen (LH2). The main objectives of the analysis were to predict and correlate the hydrodynamic stability of the flappers and pressure drop with available water test data. Computational Fluid Dynamics (CFD) computer codes were procured at no cost from the public domain, and were modified and extended to carry out the disconnect flow analysis. The grid generator codes SVTGD3D and INGRID were obtained. NASA Ames Research Center supplied the flow solution code INS3D, and the color graphics code PLOT3D. A driver routine was developed to automate the grid generation process. Components such as pipes, elbows, and flappers can be generated with simple commands, and flapper angles can be varied easily. The flow solver INS3D code was modified to treat interior flappers, and other interfacing routines were developed, which include a turbulence model, a force/moment routine, a time-step routine, and initial and boundary conditions. In particular, an under-relaxation scheme was implemented to enhance the solution stability. Major physical assumptions and simplifications made in the analysis include the neglect of linkages, slightly reduced flapper diameter, and smooth solid surfaces. A grid size of 54 x 21 x 25 was employed for both the LO2 and LH2 units. Mixing length theory applied to turbulent shear flow in pipes formed the basis for the simple turbulence model. Results of the analysis are presented for LO2 and LH2 disconnects.
Numerical solutions to the incompressible Navier-Stokes equations are in greater demand than ever before as the field of computational fluid dynamics (CFD) increases its impact as an engineering tool. An implicit upwind-relation finite-difference scheme is developed for solving unsteady incompressible Navier-Stokes equations incorporating an artificial time derivative of the pressure to the continuity equation. The essential features observed in experiments for complicated vortical flows past three round-edged low-aspect-ratio wings at high angles of attack are reproduced both qualitatively and quantitatively.
Electric field influence on fluid oscillation modes for Korteweg-Helmholtz force density on incompressible dielectric liquid immersed in electric field
Analysis predicts decrease in fluid viscosity by comparing pressure profile of fluid/gas mixture with that of power-law fluid. Fluid is taken to be viscous, non-Newtonian, and incompressible; the gas to be ideal; the flow to be inertia-free, isothermal, and one dimensional. Analysis assists in design of flow systems for petroleum, coal, polymers, and other materials.
The primary objective of this work is to study noise propagation in acoustically lined variable area ducts with mean fluid flow. The method of study is numerical in nature and involves a body-fitted grid mapping procedure in conjunction with a factored-implicit finite difference technique. The mean fluid flow model used is two-dimensional, inviscid, irrotational, incompressible, and nonheat conducting. Fully-coupled solutions of the linearized gasdynamic equations are obtained for both positive and negative Mach numbers as well as for hard and soft wall conditions. The factored-implicit finite difference technique used did give rise to short wavelength perturbations, but these were dampened by the introduction of higher order artificial dissipation terms into the scheme. Results compared favorably with available numerical and experimental data.
In order to study the effects of ion wind on the plane Poiseuille flow in a channel and Blasius flow on a flat plate, the equations of electrogasdynamics are solved numerically under the assumptions that the flow is incompressible, that the electric field is steady, and that the fluid velocity is negligible compared to ion drift velocity. The results show that ion wind strongly affects the skin-friction distribution for these flows.
Our perception of fluid instabilities and turbulence is largely based on properties of incompressible vorticity distributions, omega, and the Biot-Savart Law of 'instantaneous' induction at distance. In high-speed shear layers it is the distribution of local angular momentum rho-omega that matters; modified interaction-induction between vortical elements is likely to take place only within relative Mach cones of influence, with acoustic time delay. This and the large mean density stratifications influence strongly instability vortex roll-ups, vortex mergings, and large-scale turbulent structures. Consequences of these observations on transition to turbulence and turbulence energetics are discussed in physical terms. Free shear layers and wall layers may require distinct M modeling.
The numerical analysis of the incompressible Navier-Stokes equations are becoming important tools in the understanding of some fluid flow problems which are encountered in research as well as in industry. With the advent of the supercomputers, more realistic problems can be studied with a wider choice of numerical algorithms. An alternative formulation is presented for viscous incompressible flows. The incompressible Navier-Stokes equations are cast in a velocity/vorticity formulation. This formulation consists of solving the Poisson equations for the velocity components and the vorticity transport equation. Two numerical algorithms for the steady two-dimensional laminar flows are presented. The first method is based on the actual partial differential equations. This uses a finite-difference approximation of the governing equations on a staggered grid. The second method uses a finite element discretization with the vorticity transport equation approximated using a Galerkin approximation and the Poisson equations are obtained using a least squares method. The equations are solved efficiently using Newton's method and a banded direct matrix solver (LINPACK). The method is extended to steady three-dimensional laminar flows and applied to a cubic driven cavity using finite difference schemes and a staggered grid arrangement on a Cartesian mesh. The equations are solved iteratively using a plane zebra relaxation scheme. Currently, a two-dimensional, unsteady algorithm is being developed using a generalized coordinate system. The equations are discretized using a finite-volume approach. This work will then be extended to three-dimensional flows.