Showing papers on "Incompressible flow published in 1999"

Spectral/hp Element Methods for CFD

Abstract: Introduction Fundamental concepts in one dimension Multi-dimensional expansion bases Multi-dimensional formulations Diffusion equation Advection and advection-diffusion Non-conforming elements Algorithms for incompressible flows Incompressible flow simulations:verification and validation Hyperbolic conservation laws Appendices Jacobi polynomials Gauss-Type integration Collocation differentiation Co discontinuous expansion bases Characteristic flux decomposition References Index

Incompressible flows of an ideal fluid with vorticity in borderline spaces of Besov type

Abstract: We prove a uniqueness theorem for the Euler equations for an ideal incompressible fluid under the condition that vorticity belongs to a space of Besov type. We also prove an existence theorem in dimension two.

Simulation of Industrial Processes for Control Engineers

Abstract: Introduction Fundamental Concepts of Dynamic Simulation Thermodynamics and the conservation equations Steady state incompressible flow Flow through ideal nozzles Control valve flow Steady-state compressible flow Control valve liquid flow Liquid flow through the installed control valve Gas flow through the installed control valve Accumulation of liquids and gases in process vessels Two-phase systems - boiling, condensation and distillation Chemical reactions Turbine nozzles Steam and gas turbines Steam and gas turbines - simplified model Turbo pumps and compressors Flow networks Pipeline dynamics Distributed components: heat exchangers and tubular reactors Nuclear reactors Process controllers and control valve dynamics Linearization Model Validation Appendices: Comparative size of energy terms Explicit calculation of compressible flow using approximating functions Equations for control valve flow in SI units Comparison of Fisher Universal Gas Sizing Equation, FUGSE, with the nozzle-based model for control valve gas flow Measurement of the internal energy of reaction and the enthalpy of reaction using calorimeters Approximations used in modelling turbine reaction stages in off-design conditions Fuel pin average temperature and effective heat transfer coefficient Conditions for emergence from saturation for P + I controllers with integral desaturation

Numerical investigation of the flow past a cavity

Abstract: Numerical simulations are used to investigate the resonant instabilities in the flow past an open cavity. The compressible Navier-Stokes equations are solved directly (no turbulence model) for two-dimensional cavities with laminar boundary layers upstream. The computational domain is large enough to directly resolve a portion of the radiated acoustic field. The results show a transition from a shear layer mode, for shorter cavities and lower Mach numbers, to a wake mode for longer cavities and higher Mach numbers. The shear layer mode is well characterized by Rossiter modes. The wake mode is characterized instead by a large-scale vortex shedding with Strouhal number independent of the Mach number. The vortex shedding causes the boundary layer to periodically separate upstream of the cavity. The wake mode oscillation is similar to that reported by Gharib and Roshko (J. Fluid Mech.,177, 1987) for incompressible flow with a laminar upstream boundary layer. The results suggest that laminar separation upstream of the cavity edge is the cause of the transition to wake mode.

On numerical errors and turbulence modeling in tip vortex flow prediction

Abstract: The accuracy of tip vortex flow prediction in the near-field region is investigated numerically by attempting to quantify the shortcomings of the turbulence models and the flow solver. In particular, some turbulence models can produce a ‘numerical diffusion’ that artificially smears the vortex core. Low-order finite differencing techniques of the convective and pressure terms of the Navier–Stokes equations and inadequate grid density and distribution can also produce the same adverse effect. The flow over a wing and the near-wake with the wind tunnel walls included was simulated using 2.5 million grid points. Two subset problems, one using a steady, three-dimensional analytical vortex, and the other, a vortex obtained from experiment and propagated downstream, were also devised in order to make the study of vortex preservation more tractable. The method of artificial compressibility is used to solve the steady, three-dimensional, incompressible Navier–Stokes equations. Two one-equation turbulence models (Baldwin–Barth and Spalart–Allmaras turbulence models), have been used with the production term modified to account for the stabilizing effect of the nearly solid body rotation in the vortex core. Finally, a comparison between the computed results and experiment is presented. Published in 1999 by John Wiley & Sons, Ltd.

Aeroacoustic Modelling of Low-Speed Flows

Abstract: A new numerical algorithm for acoustic noise generation is developed. The approach involves two steps comprising an incompressible flow part and an inviscid acoustic part. The acoustic part can be started at any time of the incompressible computation. The formulation can be applied both for isentropic flows and non-isentropic flows. The model is validated for the cases of an isentropic pulsating sphere and non-isentropic flows past a circular cylinder. In the latter case the computations show that the generated acoustic field in addition to the dominant Strouhal frequency, f0, contains a slightly higher frequency, f2, and a modulating lower frequency, f1=f2−f0. Numerical experiments with different interpolation schemes, boundary conditions, etc., show that the appearance of these modes is not an artifact from the numerical discretization.

Three-dimensional linear stability analysis of incompressible viscous flows using the finite element method

Abstract: The linear stability of incompressible flows is investigated on the basis of the finite element method. The two-dimensional base flows computed numerically over a range of Reynolds numbers are perturbed with three-dimensional disturbances. The three-dimensionality in the flow associated with the secondary instability is identified precisely. First, by using linear stability theory and normal mode analysis, the partial differential equations governing the evolution of perturbation are derived from the linearized Navier–Stokes equation with slight compressibility. In terms of the mixed finite element discretization, in which six-node quadratic Lagrange triangular elements with quadratic interpolation for velocities (P2) and three-node linear Lagrange triangular elements for pressure (P1) are employed, a non-singular generalized eigenproblem is formulated from these equations, whose solution gives the dispersion relation between complex growth rate and wave number. Then, the stabilities of two cases, i.e. the lid-driven cavity flow and flow past a circular cylinder, are examined. These studies determine accurately stability curves to identify the critical Reynolds number and the critical wavelength of the neutral mode by means of the Krylov subspace method and discuss the mechanism of instability. For the cavity flow, the estimated critical results are Rec=920.277±0.010 for the Reynolds number and kc=7.40±0.02 for the wave number. These results are in good agreement with the observation of Aidun et al. and are more accurate than those by the finite difference method. This instability in the cavity is associated with absolute instability [Huerre and Monkewitz, Annu. Rev. Fluid Mech., 22, 473–537 (1990)]. The Taylor–Goertler-like vortices in the cavity are verified by means of the reconstruction of three-dimensional flows. As for the flow past a circular cylinder, the primary instability result shows that the flow has only two-dimensional characteristics at the onset of the von Karman vortex street, when Re<49. The estimated critical values of primary instability are Rec=46.389±0.010 and Stc=0.126 for the Strouhal number. These values are very close to the observation data [Williamson, J. Fluid Mech., 206, 579–627 (1989)] and other stability results [Morzynski and Thiele, Z. Agnew. Math. Mech., 71, T424–T428 (1991); Jackson, J. Fluid Mech., 182, 23–45 (1987)]. This onset of vortex shedding is associated with the symmetry-breaking bifurcation at the Hopf point. Copyright © 1999 John Wiley & Sons, Ltd.

Analysis of Velocity-Flux Least-Squares Principles for the Navier--Stokes Equations: Part II

Abstract: This paper continues the development of the least-squares methodology for the solution of the incompressible Navier--Stokes equations started in Part I. Here we again use a velocity-flux first-order Navier--Stokes system, but our focus now is on a practical algorithm based on a discrete negative norm.

Tsunami generation in compressible ocean

Abstract: Most of the tsunami modelling studies have been carried out within the framework of incompressible fluid theory. Estimations we made show that this approach quite appropriately describes the stages of tsunami propagation and run-up, whereas incompressible fluid theory fails to describe the process of tsunami generation properly. Comparative studies of wave generation by piston bottom displacements in compressible and incompressible fluids have been carried out within the framework of linear potential theory. The analysis of exact analytical solutions to the problem has shown that a substantial difference exists between the behaviour of compressible and incompressible fluids under typical tsunami source conditions. It was also shown that bottom displacements of seismic origin must give rise to standing acoustic waves in the source region. As a result each tsunami should have its own “voice”, the characteristics of which depend on bottom topography, sediment features and on the time history and spatial structure of the bottom displacement. This “voice” may serve as an additional important tool for tsunami forecasting.

Methods for parallel computation of complex flow problems

Abstract: This paper is an overview of some of the methods developed by the Team for Advanced Flow Simulation and Modeling (T★AFSM) [ http://www.mems.rice.edu/TAFSM/ ] to support flow simulation and modeling in a number of “Targeted Challenges”. The “Targeted Challenges” include unsteady flows with interfaces, fluid–object and fluid–structure interactions, airdrop systems, and air circulation and contaminant dispersion. The methods developed include special numerical stabilization methods for compressible and incompressible flows, methods for moving boundaries and interfaces, advanced mesh management methods, and multi-domain computational methods. We include in this paper a number of numerical examples from the simulation of complex flow problems.

Mixed hp-FEM on anisotropic meshes II : Hanging nodes and tensor products of boundary layer meshes

Abstract: The divergence stability of mixed hp Finite Element Methods for incompressible fluid flow is analyzed. A discrete inf-sup condition is proved for a general class of meshes. The meshes may be refined anisotropically, geometrically and may contain hanging nodes on geometric patches. The inf-sup constant is shown to be independent of the aspect ratio of the anisotropic elements and the dependence on the polynomial degree is analyzed. Numerical estimates of inf-sup constants confirm the theoretical results.

Stability of plane-parallel vibrational flow in a two-layer system

Abstract: The stability of the interface separating two immiscible incompressible fluids of different densities and viscosities is considered in the case of fluids filling a cavity which performs horizontal harmonic oscillations. There exists a simple basic state which corresponds to the unperturbed interface and plane-parallel unsteady counter flows; the properties of this state are examined. A linear stability problem for the interface is formulated and solved for both (a) inviscid and (b) viscous fluids. A transformation is found which reduces the linear stability problem under the inviscid approximation to the Mathieu equation. The parametric resonant regions of instability associated with the intensification of capillary-gravity waves at the interface are examined and the results are compared to those found in the viscous case in a fully numerical investigation.

Computation of the 3-D Unsteady Flow Past Deforming Geometries

Abstract: A 3-D incompressible unsteady flow solver based on simple finite elements with adaptive remeshing and grid movement for both moving and deforming surfaces is described. We demonstrate the combination of adaptive remeshing techniques with the incompressible flow solver with the computation of flow past an eel in 2-D and a blue-fin tuna in 3-D. The flow past a swimming tuna was computed for two extreme cases of the caudal fin frequency and swimming speed. A grid refinement study was performed and a grid converged solution for the force produced by the caudal fin was obtained.

Computations of a laminar backward-facing step flow at Re = 800 with a spectral domain decomposition method

Abstract: The two-dimensional laminar incompressible flow over a backward-facing step is computed using a spectral domain decomposition approach. A minimum number of subdomains (two) is used; high resolution being achieved by increasing the order of the basis Chebyshev polynomial. Results for the case of a Reynolds number of 800 are presented and compared in detail with benchmark computations. Stable accurate steady flow solutions were obtained using substantially fewer nodes than in previously reported simulations. In addition, the problem of outflow boundary conditions was examined on a shortened domain. Because of their more global nature, spectral methods are particularly sensitive to imposed boundary conditions, which may be exploited in examining the effect of artificial (non-physical) outflow boundary conditions. Two widely used set of conditions were tested: pseudo stress-free conditions and zero normal gradient conditions. Contrary to previous results using the finite volume approach, the latter is found to yield a qualitatively erroneous yet stable flow-field. Copyright © 1999 John Wiley & Sons, Ltd.

Analysis of fluid–structure interaction by an arbitrary Lagrangian–Eulerian finite element formulation

Abstract: In this paper, the interaction fluid–rigid body is analysed by a finite element procedure that incorporates the arbitrary Lagrangian–Eulerian (ALE) method into a well-known two-step projection scheme. The flow is assumed to be two-dimensional, incompressible and viscous, with no turbulence models being included. The flow past a circular cylinder at ℛℯ=200 is first analysed, for fixed and oscillating conditions. The dependence of lock-in upon the shift between the mechanical and the Strouhal frequencies, for a given amplitude of forced vibration, is illustrated. The aerodynamic forces and the wake geometry are compared for locked-in conditions with different driving frequencies. The behaviour of a rectangular cylinder (B/D=4) at ℛℯ=500 (based on height D) is also analysed. The flutter derivatives associated with aerodynamic damping (H1* and A2* in Scanlan's notation) are evaluated by the free oscillation method for several values of reduced flow speed above the Strouhal one (namely for 3≤U*≤8). Torsional flutter was attained at U*≥5, with all the other situations showing stable characteristics. Copyright © 1999 John Wiley & Sons, Ltd.

Large-scale dynamo produced by negative magnetic eddy diffusivities

Abstract: The existence of incompressible flow producing negative magnetic eddy diffusivities is demonstrated. This provides for a dynamo mechanism, alternative to α-type effects, requiring neither the presence of mean heliciiy nor the breaking of parity invariance. In the kinematic dynamo phase, the magnetic field grows exponentially with a growth rate proportional to the square of the wavenumber. The concrete example, analyzed by means of multiscale techniques, is a parity-invariant flow of the Taylor-Green type.

Rayleigh-Benard simulation using the gas-kinetic Bhatnagar-Gross-Krook scheme in the incompressible limit

Abstract: In this paper, a gas-kinetic Bhatnagar-Gross-Krook (BGK) model is constructed for the Rayleigh-B\'enard thermal convection in the incompressible flow limit, where the flow field and temperature field are described by two coupled BGK models. Since the collision times in the corresponding BGK models can be different, the Prandtl number can be changed to any value instead of a fixed $\mathrm{Pr}=1$ in the original BGK model [P. L. Bhatnagar, E. P. Gross, and M. Krook, Phys. Rev. 94, 511 (1954)]. The two-dimensional Rayleigh-B\'enard thermal convection is studied and numerical results are compared with theoretical ones as well as other simulation results.

Compatible Spectral Approximations for the Velocity-Pressure-Stress Formulation of the Stokes Problem

Abstract: The numerical approximation of the mixed velocity-pressure-stress formulation of the Stokes problem using spectral methods is considered. In addition to the compatibility condition between the discrete velocity and pressure spaces, a second condition between the discrete velocity and stress spaces must also be satisfied in order to have a well-posed problem. The theory is developed by considering a doubly constrained minimization problem in which the viscous stress tensor is minimized subject to the constraint that the viscous forces are irrotational. The discrete problem is analyzed and error estimates are derived. A comparison between the mixed approach and the standard velocity-pressure formulation is made in terms of the condition number of the resulting systems.

Implementation and Validation of the Chien k-epsilon Turbulence Model in the Wind Navier-Stokes Code

Abstract: The two equation k-epsilon turbulence model of Chien has been implemented in the WIND Navier-Stokes flow solver. Details of the numerical solution algorithm, initialization procedure, and stability enhancements are described. Results obtained with this version of the model are compared with those from the Chien k-epsilon model in the NPARC Navier-Stokes code and from the WIND SST model for three validation cases: the incompressible flow over a smooth flat plate, the incompressible flow over a backward facing step, and the shock-induced flow separation inside a transonic diffuser. The k-epsilon model results indicate that the WIND model functions very similarly to that in NPARC, though the WIND code appears to he slightly more accurate in the treatment of the near-wall region. Comparisons of the k-epsilon model results with those from the SST model were less definitive, as each model exhibited strengths and weaknesses for each particular case.

On spurious behavior of CFD simulations

Abstract: Spurious behavior in underresolved grids and/or semi-implicit temporal discretizations for four computational fluid dynamics (CFD) simulations are studied. The numerical simulations consist of (a) a 1-D chemically relaxed non-equilibrium flow model, (b) the direct numerical simulation (DNS) of 2D incompressible flow over a backward facing step, (c) a loosely coupled approach for a 2D fluid-structure interaction, and (d) a 3D unsteady compressible flow simulation of vortex breakdown on delta wings. These examples were chosen based on their non-apparent spurious behaviors that were difficult to detect without extensive grid and/or temporal refinement studies and without some knowledge from dynamical systems theory. Studies revealed the various possible dangers of misinterpreting numerical simulation of realistic complex flows that are constrained by available computing power. In large scale computations, underresolved grids, semi-implicit procedures, loosely coupled implicit procedures, and insufficiently long-time integration in DNS are most often unavoidable. Consequently, care must be taken in both computation and in interpretation of the numerical data