A multigrid method for viscous flows for all Mach numbers and all grid aspect ratios

2000 ◽  
Author(s):  
Jan Vierendeels ◽  
Kris Riemslagh ◽  
Erik Dick
Keyword(s):  
Multigrid Method ◽  
Viscous Flows ◽  
Aspect Ratios ◽  
Mach Numbers

scholarly journals A Preconditioned Method for Rotating Flows at Arbitrary Mach Number

2011 ◽  
Vol 2011 ◽  
pp. 1-17 ◽  
Author(s):  
Chunhua Sheng
Keyword(s):  
Mach Number ◽  
Current Method ◽  
Viscous Flows ◽  
Original Method ◽  
Superior Performance ◽  
Governing Equations ◽  
Free Stream Mach Number ◽  
Rotating Frames ◽  
Mach Numbers ◽  
Diffusive Fluxes

An improved preconditioning is proposed for viscous flow computations in rotating and nonrotating frames at arbitrary Mach numbers. The key to the current method is the use of both free stream Mach number and rotating Mach number to construct a preconditioning matrix, which is applied to the compressible governing equations written in terms of primitive variables. A Fourier analysis is conducted that reveals the efficacy of the modified preconditioning. Numerical approximations for the convective and diffusive fluxes are detailed based on the preconditioned system of equations. A set of boundary conditions using characteristic variables are described for internal and external flow computations. Numerical validations are performed on four realistic viscous flows in both fixed and rotating frames. The results indicated that the modified preconditioning has a superior performance compared to the original method to predict flows from extremely low to supersonic Mach numbers.

Parallel Computation of Unsteady Incompressible Viscous Flows Using an Unstructured Multigrid Method

2002 ◽  
Author(s):  
Yong Zhao ◽  
Chin Hoe Tai
Keyword(s):  
Unsteady Flow ◽  
Message Passing ◽  
Message Passing Interface ◽  
Multigrid Method ◽  
Numerical Solutions ◽  
Viscous Flows ◽  
Finite Volume Scheme ◽  
Decomposition Approach ◽  
Incompressible Viscous Flows ◽  
Multigrid Solvers

The development and validation of a parallel unstructured non-nested multigrid method for simulation of unsteady incompressible viscous flow is presented. The Navier-Stokes solver is based on the artificial compressibility method (ACM) [10] and a higher-order characteristics-based finite-volume scheme [8] on unstructured multigrids. Unsteady flow is calculated with an implicit dual time stepping scheme. The parallelization of the solver is achieved by a multigrid domain decomposition approach (MG-DD), using the Single Program Multiple Data (SPMD) programming paradigm and Message-Passing Interface (MPI) for communication of data. The parallel codes using single grids and multigrids are used to simulate steady and unsteady incompressible viscous flows over a circular cylinder for validation and performance evaluation purposes. Speedups and parallel efficiencies obtained by both the parallel single-grid and multigrid solvers are reasonably good for both test cases, using up to 32 processors on the SGI Origin 2000. A maximum speedup of 12 could be achieved on 16 processors for the unsteady flow. The parallel results obtained agree well with those of serial solvers and with numerical solutions obtained by other researchers, as well as experimental measurements.

Numerical Investigation of Heat Transfer and Pressure Drop Characteristics for Different Hole Geometries of a Turbine Casing Impingement Cooling System

2011 ◽  
Author(s):  
F. Ben Ahmed ◽  
R. Tucholke ◽  
B. Weigand ◽  
K. Meier
Keyword(s):  
Heat Transfer ◽  
Pressure Drop ◽  
Cooling System ◽  
Ambient Air ◽  
Impinging Jets ◽  
Nozzle Geometry ◽  
Impingement Cooling ◽  
Pressure Losses ◽  
Aspect Ratios ◽  
Mach Numbers

A representative part of an active clearance control system for a low pressure turbine has been numerically investigated. The setup consisted of a cylindrical plenum with 20 inline arranged impinging jets at the bottom side discharging on a flat plate. The study focused on the influence of the nozzle geometry on the flow as well as heat transfer characteristics at the impingement plate and the discharge pressure drop. CFD (Computational Fluid Dynamics) simulations were performed for a constant Reynolds number ReD = 7,500 and different mean jet Mach numbers up to 0.7. Different length-to-diameter ratios of the jet holes (L/D) and various hole shapes (cylindrical, elliptic, convergent and divergent conical) were investigated to evaluate the performance of the impingement cooling configurations. The predictions showed a significant influence of the length-to-diameter ratio of the orifice bores on the heat transfer and the pressure losses. For L/D = 2 no suction of the ambient air in the nozzles was observed. In comparison to the configuration with L/D = 0.25 an improvement of the discharge coefficient of 9% for Ma = 0.7 and 20% for Ma = 0.17 was achieved. However, the highest heat transfer was observed for the smallest L/D-ratio of 0.25. The shape variation showed that only the elliptic jet holes with a ratio of AR = 0.5 enhanced the overall heat transfer and simultaneously reduced the pressure losses because of discharging onto the target plate. This result was found to be valid for all investigated jet Mach numbers. Additionally, for both elliptic jet aspect ratios of 0.5 and 2 the axis-switchover phenomenon of the flow was observed.

Straight Channel Diffuser Performance at High Inlet Mach Numbers

1969 ◽  
Vol 91 (3) ◽  
pp. 397-412 ◽  
Author(s):  
P. W. Runstadler ◽  
R. C. Dean
Keyword(s):  
Mach Number ◽  
Aspect Ratio ◽  
Pressure Recovery ◽  
Straight Channel ◽  
Single Plane ◽  
Aspect Ratios ◽  
Straight Wall ◽  
Throat Width ◽  
Mach Numbers

Measurements have been made of the pressure recovery of straight wall, single plane divergence diffusers with inlet Mach numbers between 0.2 and choking (0.2 ≤ Mt < 1.0). In contrast to the widely held assertion in the literature, there is no “critical” inlet subsonic Mach number above which pressure recovery decreases drastically. Two aspect ratios, AS = 0.25 and 1.0, have been studied for a range of length-to-throat-width ratios L/W1 and divergence angles 2θ around the regions of peak recovery. Diffuser performance maps are given showing pressure recovery Cp as a function of diffuser geometry for fixed values of throat Mach number Mt, throat blockage B, and aspect ratio AS. Significant changes in the location and magnitude of pressure recovery do occur with variations in Mt, B, and AS. The importance to the designer of a knowledge of how diffuser performance depends upon geometric and diffuser inlet parameters is discussed.

A Multigrid Method for the Solution of Ion Transport Using the Poisson Nernst Planck Equations

2007 ◽  
Author(s):  
Sanjay R. Mathur ◽  
Jayathi Y. Murthy
Keyword(s):  
Ion Transport ◽  
Multigrid Method ◽  
Convergence Rates ◽  
Relaxation Method ◽  
Governing Equations ◽  
Linear System Of Equations ◽  
Aspect Ratios ◽  
Synthetic Ion Channels ◽  
Poor Convergence ◽  
Volume Method

Recently there has been much interest in simulating ion transport in biological and synthetic ion channels using the Poisson-Nernst-Planck (PNP) equations. However, many published methods exhibit poor convergence rates, particularly at high driving voltages, and for long-aspect ratio channels. The paper addresses the development of a fast and efficient coupled multigrid method for the solution of the PNP equations. An unstructured cell-centered finite volume method is used to discretize the governing equations. An iterative procedure, based on a Newton-Raphson linearization accounting for the non-linear coupling between the Poisson and charge transport equations, is employed. The resulting linear system of equations is solved using an algebraic multigrid method, with coarse level systems being created by agglomerating finer-level equations based on the largest coefficients of the Poisson equation. A block Gauss-Seidel update is used as the relaxation method. The method is shown to perform well for ion transport in a synthetic channel for aspect ratios ranging from 16.67 to 1667 for a range of operating parameters.

Compressible Microchannel Flow

2010 ◽  
Author(s):  
Gholamreza Mirshekari ◽  
Martin Brouillette
Keyword(s):  
Gas Flow ◽  
Accurate Determination ◽  
Glass Tube ◽  
Controlled Environment ◽  
Aspect Ratios ◽  
Small Flow ◽  
Mach Numbers ◽  
High Mach ◽  
Isothermal Gas

We present experiments on the isothermal gas flow at relatively high Mach numbers in microfabricated channels of small aspect ratios. The microchannels were fabricated by deep etching on silicon wafers, bonded to a Pyrex wafer to cover and seal them; the microchannels were 10 microns deep with a variety of widths. The accurate determination of the small flow rates was performed by measuring the displacement of a bead of mercury in a precision bore glass tube in a controlled environment. The experiment setup has been specially designed to account for inlet and outlet loss. The inferred friction coefficient at different values of Knudsen, Reynolds and Mach numbers shows that the flow inside the microchannel follows the classical laminar behavior over the range of experiments.

A Note on the Supersonic Panel Flutter of Oblique Clamped Plates

1964 ◽  
Vol 68 (640) ◽  
pp. 270-271 ◽  
Author(s):  
A. Kornecki
Keyword(s):  
Present Note ◽  
Panel Flutter ◽  
Rectangular Plates ◽  
Two Dimensional ◽  
Aerodynamic Loading ◽  
Aspect Ratios ◽  
Flutter Boundary ◽  
Mode Solution ◽  
Mach Numbers ◽  
High Mach

Summary and IntroductionRecently, the effect of sweepback on the boundaries of supersonic panel flutter was studied in Ref. (1), (2) and (3), all of them dealing with rectangular plates.The present note considers the problem of panel flutter boundary of plates in the shape of a parallelogram with all edges clamped.It is assumed that Ackeret's theory of linearised two-dimensional supersonic aerodynamic loading gives an adequate approximation to the air forces for high Mach numbers.The criterion of instability is the coalescence of frequencies.A four-mode solution was obtained by means of Galerkin's method using first two streamwise and spanwise deflection modes. The results are represented in the form of diagrams for different aspect ratios(a/b)and sweep angles(ϕ).

Sign in / Sign up

Export Citation Format

Share Document