Showing papers on "Incompressible flow published in 1986"

Fundamentals of Aerodynamics

Abstract: TABLE OF CONTENTS Preface to the Fifth Edition Part 1: Fundamental Principles 1. Aerodynamics: Some Introductory Thoughts 2. Aerodynamics: Some Fundamental Principles and Equations Part 2: Inviscid, Incompressible Flow 3. Fundamentals of Inviscid, Incompressible Flow 4. Incompressible Flow Over Airfoils 5. Incompressible Flow Over Finite Wings 6. Three-Dimensional Incompressible Flow Part 3: Inviscid, Compressible Flow 7. Compressible Flow: Some Preliminary Aspects 8. Normal Shock Waves and Related Topics 9. Oblique Shock and Expansion Waves 10. Compressible Flow Through Nozzles, Diffusers and Wind Tunnels 11. Subsonic Compressible Flow Over Airfoils: Linear Theory 12. Linearized Supersonic Flow 13. Introduction to Numerical Techniques for Nonlinear Supersonic Flow 14. Elements of Hypersonic Flow Part 4: Viscous Flow 15. Introduction to the Fundamental Principles and Equations of Viscous Flow 16. A Special Case: Couette Flow 17. Introduction to Boundary Layers 18. Laminar Boundary Layers 19. Turbulent Boundary Layers 20. Navier-Stokes Solutions: Some Examples Appendix A: Isentropic Flow Properties Appendix B: Normal Shock Properties Appendix C: Prandtl-Meyer Function and Mach Angle Appendix D: Standard Atmosphere Bibliography Index

Statistical theory for compressible turbulent shear flows, with the application to subgrid modeling

Abstract: A statistical theory for compressible turbulent shear flows subject to buoyancy effects is developed. Important correlation functions in compressible shear flows are calculated with the aid of a multiscale direct‐interaction approximation. They are expressed in the gradient‐diffusion form similar to the eddy‐viscosity representation for the Reynolds stress in incompressible flows. The results obtained are applicable to subgrid modeling, and a Smagorinsky‐type model in compressible flows is constructed.

Universal short-wave instability of two-dimensional eddies in an inviscid fluid.

Abstract: It is shown that a broad class of two-dimensional vortices occurring in the flow of an incompressible, inviscid fluid are unstable to three-dimensional perturbations. At short wavelengths along the vortex axis the growth rate becomes independent of wavelength, and the eigenmode becomes concentrated near the center of the vortex.

The compressible Euler equations in a bounded domain: existence of solutions and the incompressible limit

Abstract: A short-time existence theorem is proven for the Euler equations for nonisentropic compressible fluid flow in a bounded domain, and solutions with low Mach number and almost incompressible initial data are shown to be close to corresponding solutions of the equations for incompressible flow.

Magnetostatic equilibria and analogous Euler flows of arbitrarily complex topology. Part 2. Stability considerations

Abstract: 0 The stability (i) of fully three-dimensional magnetostatic equilibria of arbitrarily complex topology, and (ii) of the analogous steady solutions of the Euler equations of incompressible inviscid flow, are investigated through construction of the second variations S2M and S2K of the magnetic energy and kinetic energy with respect to a virtual displacement field q(x) about the equilibrium configuration. The expressions for S2M and S2K differ because in case (i) the magnetic lines of force are frozen in the fluid as it undergoes displacement, whereas in case (ii) the vortex lines are frozen, so that the analogy between magnetic field and velocity field on which the existence of steady flows is based does not extend to the perturbed states. It is shown that the stability condition S2M > 0 for all q(x) for the magnetostatic case can be converted to a form that does not involve the arbitrary displacement q(x), whereas the condition S2K > 0 for all q for the stability of the analogous Euler flow cannot in general be so transformed. Nevertheless it is shown that, if S2M and S2K are evaluated for the same basic equilibrium field, then quite generally S2M+S2K > 0 (all non-trivial q). A number of special cases are treated in detail. In particular, it is shown that the space-periodic Beltrami field BE = (B, cosaz+B, sinuy, B, cosax+ B, sinuz, B, cosay+ B, sinux) is stable (i.e. S2M > 0 for all q) and that the medium responds in an elastic manner to perturbations on a scale large compared with a-l. By contrast, it is shown that S2K is indefinite in sign for the analogous Euler flow, and it is argued that the flow is unstable to certain large-scale helical perturbations having the same sign of helicity as the unperturbed flow. It is conjectured that all topologically non-trivial Euler flows are similarly unstable. 0

A three-dimensional incompressible Navier-Stokes flow solver using primitive variables

Abstract: An implicit, finite difference computer code has been developed to solve the incompressible Navier-Stokes equations in a three-dimensional curvilinear coordinate system. The pressure field solution is based on the pseudocompressibility approach in which a time derivative pressure term is introduced into the mass conservation equation. The solution procedure employs an implicit, approximate factorization scheme. The Reynolds Stresses, which are uncoupled from the implicit scheme, are lagged by one time step to facilitate implementing various levels of the turbulence model. Test problems for external and internal flows are computer and the results are compared with existing experimental data. The application of this technique for general three-dimensional problems is then demonstrated.

Numerical investigation of incompressible flow in grooved channels. Part 1. Stability and self-sustained oscillations

Abstract: Incompressible moderate-Reynolds-number flow in periodically grooved channels is investigated by direct numerical simulation using the spectral element method. For Reynolds numbers less than a critical value Rc the flow is found to approach a stable steady state, comprising an ‘outer’ channel flow, a shear layer at the groove lip, and a weak re-circulating vortex in the groove proper. The linear stability of this flow is then analysed, and it is found that the least stable modes closely resemble Tollmien–Schlichting channel waves, forced by Kelvin–Helmholtz shear-layer instability at the cavity edge. A theory for frequency prediction based on the Orr–Sommerfeld dispersion relation is presented, and verified by variation of the geometric parameters of the problem. The accuracy of the theory, and the fact that it predicts many qualitative features of low-speed groove experiments, suggests that the frequency-selection process in these flows is largely governed by the outer, more stable flow (here a channel), in contrast to most current theories based solely on shear-layer considerations. The instability of the linear mode for R > Rc is shown to result in self-sustained flow oscillations (at frequencies only slightly shifted from the originating linear modes), which again resemble (finite-amplitude) Tollmien-Schlichting modes driven by an unstable groove vortex sheet. Analysis of the amplitude dependence of the oscillations on degree of criticality reveals the transition to oscillatory flow to be a regular Hopf bifurcation.

An exact solution of the Navier-Stokes equation which describes non-orthogonal stagnation-point flow in two dimensions

Abstract: A similarity solution is found which describes the flow impinging on a flat wall at an arbitrary angle of incidence. The technique is similar to a method used by Jeffery (1915) and discussed more recently by Peregrine (1981).

Numerical investigation of incompressible flow in grooved channels. Part 2. Resonance and oscillatory heat-transfer enhancement

Abstract: Modulatory heat-transfer enhancement in grooved channels is investigated by direct numerical simulation of the Navier–Stokes and energy equations using the spectral element method. It is shown that oscillatory perturbation of the flow at the frequency of the least-stable mode of the linearized system results in subcritical resonant excitation and associated transport enhancement as the critical Reynolds number of the flow is approached. The Tollmien–Schlichting frequency theory that was presented in Part 1 of this paper is shown to accurately predict the optimal frequency for transport augmentation for small values of the modulatory amplitude, and the effect of the excited travelling-wave channel modes on the resulting temperature distribution is described. The importance of (non-trivial) geometry in the forced response of a flow is discussed, and grooved-channel flow is compared to (straight-channel) plane Poiseuille flow, for which no resonance excitation occurs owing to a zero projection of the forcing inhomogeneity on the dangerous modes of the system. For the particular grooved-channel geometry investigated, resonant oscillatory forcing at modulatory amplitudes as small as 20% of the mean flow results in a doubling of transport as measured by a time, space-averaged Nusselt number.

Conservation laws of mixed type describing three-phase flow in porous media

Abstract: In this paper we examine the mathematical structure of a model for three-phase, incompressible flow in a porous medium. We show that, in the absence of diffusive forces, the system of conservation laws describing the flow is not necessarily hyperbolic. We present an example in which there is an elliptic region in saturation space for reasonable relative permeability data. A linearized analysis shows that in nonhyperbolic regions solutions grow exponentially. However, the nonhyperbolic region, if present, will be of limited extent which inherently limits the exponential growth. To examine these nonlinear effects we resort to fine grid numerical experiments with a suitably dissipative numerical method. These experiments indicate that the solutions of Riemann problems remain well behaved in spite of the presence of a linearly unstable elliptic region in saturation space. In particular, when initial states are outside the elliptic region the Riemann problem solution appears to stay outside the region. Further...

The Segregated Approach to Predicting Viscous Compressible Fluid Flows

Abstract: The SIMPLE method of Patankar and Spalding and its variants such as SIMPLER, SIMPLEC and SIMPLEX are segregated methods for solving the discrete algebraic equations representing the equations of motion for an incompressible fluid flow. The present paper presents the extension of these methods to the solution of compressible fluid flows within the context of a generalized segregated approach. To provide a framework for better understanding the segregated approach to solving viscous compressible fluid flows an interpretation of the role of pressure in the numerical method is presented. With this interpretation it becomes evident that the linearization of the equation for mass conservation and the approach used to solve the linearized algebraic equations representing the equations of motion are important in determining the performance of the numerical method. The relative performance of the various segregated methods are compared for several subsonic and supersonic compressible fluid flows.Copyright © 1986 by ASME

Rayleigh–Taylor stability for a normal shock wave–density discontinuity interaction

Abstract: The solution for the perturbation growth of a shock wave striking a density discontinuity at a material interface is developed. The Laplace transformation of the perturbation results in an equation which has a simple solution for weak shock waves. The solution for strong shock waves may be given by a power series. It is assumed that the equation of state is that of an ideal gas. The four independent parameters of the solution are the ratio of specific heat for each material, the density ratio at the interface, and the incoming shock strength. Properties of the solution which are investigated include the asymptotic behavior at large times of the perturbation velocity at the interface, the vorticity near the interface, and the rate of decay of the solution at large distances from the interface. The last is much weaker than the exponential decay in an incompressible fluid. The asymptotic solution near the interface, in addition to a constant term, consists of a number of slowly decaying discrete frequencies. The number is roughly proportional to the logarithm of the density ratio at the surface for strong shocks, and decreases with shock strength. For weak shocks the solution is compared with results for an incompressible fluid. Only interface perturbation velocities which tend to zero at large times lead to a limited deformation of the interface. It is found that these are possible only for density ratios less than about 1.5.

Ablative stabilization in the incompressible Rayleigh--Taylor instability

Abstract: Ablative Rayleigh–Taylor instabilities are analyzed in terms of an incompressible fluid model. A generalized surface wave dispersion relation can be derived for arbitrary step‐profiles with ablative mass and heat flow. A systematic overview on different regimes of ablative stabilization and growth reduction is given. Convective stabilization by the incoming and outcoming flows are found included as upper and lower limits on the instability growth. Applications for self‐consistent steady‐state conditions are discussed and a comparison is made with previous numerical work.

Viscous starting jets

Abstract: The transient motion which is produced when a viscous incompressible fluid is forced from an initial state of rest is studied. The equations for unsteady particle paths, written in terms of similarity variables, are analyzed as a quasi-autonomous system with the Reynolds number treated as a parameter. By finding and classifying critical points in the system's phase portrait, the flow structure is examined. It is shown that: (1) bifurcations in the phase portrait occur at specific values of the Reynolds number of the flow in question, and (2) the exact solutions of the Stokes equations for the low-Reynolds-number limit contain two critical Reynolds numbers and three distinct states of motion which culminate in the onset of a vortex roll-up.

Lagrangian finite element method for the analysis of two‐dimensional sloshing problems

Abstract: A new version of a numerical algorithm for the Lagrangian treatment of incompressible fluid flows with free surfaces is developed The novel features of the present method are the adoptions of the Lagrangian finite element method and the velocity correction technique The use of the velocity correction approach makes the computational scheme extremely simple in algorithmic structure Hence, the present method is particularly attractive for large-scale problems The techniques discussed here are applied to some two-dimensional sloshing problems, which may indicate the versatility and effectiveness of the present method

The first instability in spherical Taylor-Couette flow

Abstract: In this paper continuation methods are applied to the axisymmetric Navier-Stokes equations in order to investigate how the stability of spherical Couette flow depends on the gap size σ. We find that the flow loses its stability due to symmetry-breaking bifurcations and exhibits a transition with hysteresis into a flow with one pair of Taylor vortices if the gap size is sufficiently small, i.e. if σ ≤σ_B. In wider gaps, i.e. for σ_B σ_F. The numbers σ_B and σ_F are computed by calculating the instability region of the spherical Couette flow and the region of existence of the flow with one pair of Taylor vortices.

Thermocapillary free boundaries in crystal growth

Abstract: In this paper a two-dimensional free boundary arising from the steady thermo-capillary flow in a viscous incompressible fluid is studied numerically. The problem is considered in the context of the open-boat crystal-growth technique. The motion of the fluid is governed by the Navier-Stokes equations coupled with the heat equation. The problem is solved numerically by a finite-element-method discretization. Three iterative methods are introduced for the computation of the free boundary. The non-dimensional form of the problem gives rise to the following characteristic parameters: Reynolds, Grashof, Prandtl, Marangoni, Bond, Ohnesorge, Biot numbers. The influence of these parameters on the flow field, the temperature distribution and the shape of the free boundary is studied.

Prediction of Incompressible Flow in Labyrinth Seals

Abstract: A new approach was developed and tested for alleviating the substantial convergence difficulty which results from implementation of the QUICK differencing scheme into a TEACH-type computer code. It is relatively simple, and the resulting CPU time and number of numerical iterations required to obtain a solution compare favorably with a previously recommended method. This approach has been employed in developing a computer code for calculating the pressure drop for a specified incompressible flow leakage rate in a labyrinth seal. The numerical model is widely applicable and does not require an estimate of the kinetic energy carry-over coefficient for example, whose value is often uncertain. Good agreement with measurements is demonstrated for both straight-through and stepped labyrinths. These new detailed results are examined, and several suggestions are offered for the advancement of simple analytical leakage as well as rotordynamic stability models.

Squire’s theorem for two stratified fluids

Abstract: It is demonstrated that only two‐dimensional perturbations need be considered in determining the marginal stability boundary in the parameter space for the incompressible, parallel flow of two stratified, homogeneous, immiscible fluids, with constant interfacial tension, bounded by two (possibly moving) parallel plates.

Numerical-perturbation technique for stability of flat-plate boundary layers with suction

Abstract: A numerical-perturbation scheme is proposed for determining the stability of flows over plates with suction through a finite number of porous suction strips. The basic flow is calculated as the sum of the Blasius flow and closed-form linearized triple-deck solutions of the flow due to the strips. A perturbation technique is used to determine the increment a(ij) in the complex wavenumber at a given location x(j) due to the presence of a strip centered at x(i). The end result is a set of influence coefficients that can be used to determine the growth rates and amplification factors for any suction levels without repeating the calculations. The numerical-perturbation results are verified by comparison with interacting boundary layers for the case of six strips and the experimental data of Reynolds and Saric for single- and multiple-strip configurations. The influence coefficient form of the solution suggests a scheme for optimizing the strip configuration. The results show that one should concentrate the suction near branch I of the neutral stability curve, a conclusion verified by the experiments.

Magnetohydrodynamic channel flow study

Abstract: A finite‐difference study of a steady, incompressible, viscous, magnetohydrodynamic (MHD) channel flow which has direct application to dc electromagnetic pumps is presented. The study involves the numerical solution of the coupled Navier–Stokes and Maxwell equations at low magnetic Reynolds numbers. It is shown that the axial velocity profiles have a characteristic M shape as the fluid approaches and passes the electrode. The electric potential varies almost linearly from the channel centerline to the channel wall. The current shows a steep gradient near the electrodes. Comparison between the finite‐difference solution and a quasi‐one‐dimensional approach are presented. The two‐dimensional numerical calculations predict a larger pressure rise, a smaller net current, and a smaller pump efficiency than the quasi‐one‐dimensional model.