The robustness issue on multigrid schemes applied to the Navier–Stokes equations for laminar and turbulent, incompressible and compressible flows

A pressure-based finite volume procedure developed previously for incompressible flows is extended to predict the three-dimensional compressible flow within a centrifugal impeller. In this procedure, the general curvilinear coordinate system is used and the collocated grid arrangement is adopted. Mass-averaging is used to close the instantaneous Navier-Stokes equations. The covariant velocity components are used as the main variables for the momentum equations, making the pressure-velocity coupling easier. The procedure is successfully applied to predict various compressible flows from subsonic to supersonic. With the aid of the k-ɛ turbulence model, the flow details within a centrifugal impeller are obtained using the present procedure. Predicted distributions of the meridional velocity and the static pressure are reasonable. Calculated radial velocities and flow angles are favourably compared with the measurements at the exit of the impeller.

Download Full-text

NUMERICAL SIMULATION OF FREE VORTEX WITH MODIFIED NAVIER–STOKES CHARACTERISTIC BOUNDARY CONDITIONS

Modern Physics Letters B ◽

10.1142/s0217984910023554 ◽

2010 ◽

Vol 24 (13) ◽

pp. 1333-1336

Author(s):

LIN CHEN ◽

DENGBIN TANG ◽

XIN GUO

Keyword(s):

Boundary Condition ◽

Compressible Flows ◽

Diffusion Processes ◽

Stokes Equations ◽

Navier Stokes ◽

Free Vortex ◽

Navier Stokes Equations ◽

Characteristic Boundary ◽

Accurate Treatment ◽

Characteristic Boundary Condition

The convection and diffusion processes of free vortex in compressible flows are simulated by using high precision numerical method to solve for the Navier–Stokes equations. Accurate treatment of the boundary condition is extremely important for simulation of vortex flows. The developed numerical methods are well presented by combining six-order non-dissipation compact schemes with Navier–Stokes characteristic boundary condition having transverse and viscous terms, and can accurately simulate the movement of free vortex. The numerical reflecting waves at the boundaries are well controlled.

Download Full-text

Development of a Pressure-Based Coupled CFD Solver for Turbulent and Compressible Flows in Turbomachinery Applications

Volume 2B: Turbomachinery ◽

10.1115/gt2014-25967 ◽

2014 ◽

Author(s):

Luca Mangani ◽

Marwan Darwish ◽

Fadl Moukalled

Keyword(s):

Compressible Flows ◽

Stokes Equations ◽

Computational Cost ◽

Simple Algorithm ◽

Numerical Data ◽

Navier Stokes ◽

Navier Stokes Equations ◽

Analysis And Design ◽

Flow Problems ◽

Matrix Coefficients

In this paper we present a fully coupled algorithm for the resolution of compressible flows at all speed. The pressure-velocity coupling at the heart of the Navier Stokes equations is accomplished by deriving a pressure equation in similar fashion to what is done in the segregated SIMPLE algorithm except that the influence of the velocity fields is treated implicitly. In a similar way, the assembly of the momentum equations is modified to treat the pressure gradient implicitly. The resulting extended system of equations, now formed of matrix coefficients that couples the momentum and pressure equations, is solved using an algebraic multigrid solver. The performance of the coupled approach and the improved efficiency of the novel developed code was validated comparing results with experimental and numerical data available from reference literature test cases as well as with segregated solver as exemplified by the SIMPLE algorithm. Moreover the reference geometries considered in the validation process cover the typical aerodynamics applications in gas turbine analysis and design, considering Euler to turbulent flow problems and clearly indicating the substantial improvements in terms of computational cost and robustness.

Download Full-text

Prediction and physical analysis of unsteady flows around a pitching airfoil with the dynamic mesh approah

European Journal of Computational Mechanics ◽

10.13052/remn.16.451-476 ◽

2007 ◽

pp. 451-476

Author(s):

Sébastien Bourdet ◽

Marianna Braza ◽

Yannick Hoarau ◽

Rajah El Akoury ◽

Arif Ashraf ◽

...

Keyword(s):

Compressible Flows ◽

Stokes Equations ◽

Dynamic Mesh ◽

Navier Stokes ◽

Physical Analysis ◽

Navier Stokes Equations ◽

Pitching Airfoil ◽

Eddy Simulation ◽

Mesh Method ◽

High Reynolds

The fluid structure interaction due to the pitching motion of a NACA0012 aerofoil has been studied numerically at moderate and high Reynolds numbers. The dynamic mesh method has been employed in the code ICARE/IMFT solving the Navier-Stokes equations in compressible flows. At high Reynolds number, the phase-averaged Navier-Stokes equations have been solved, coupled with advanced URANS modelling in the NSMB code. The vortex dynamics and especially the stall are physically captured by the dynamic mesh method and by the URANS/Organised Eddy Simulation approach.

Download Full-text

Compressible Navier-Stokes Equations in Cylindrical Passages and General Dynamics of Surfaces—(I)-Flow Structures and (II)-Analyzing Biomembranes under Static and Dynamic Conditions

Mathematics ◽

10.3390/math7111060 ◽

2019 ◽

Vol 7 (11) ◽

pp. 1060 ◽

Cited By ~ 1

Author(s):

Terry E. Moschandreou ◽

Keith C. Afas

Keyword(s):

Compressible Flows ◽

Solid Mechanics ◽

Stokes Equations ◽

Variational Calculus ◽

Navier Stokes ◽

Navier Stokes Equations ◽

Correct Definition ◽

Dynamic Membranes ◽

Approach Zero ◽

Two Parameters

A new approach to solve the compressible Navier-Stokes equations in cylindrical co-ordinates using Geometric Algebra is proposed. This work was recently initiated by corresponding author of this current work, and in contrast due to a now complete geometrical analysis, particularly, two dimensionless parameters are now introduced whose correct definition depends on the scaling invariance of the N-S equations and the one parameter δ defines an equation in density which can be solved for in the tube, and a geometric Variational Calculus approach showing that the total energy of an existing wave vortex in the tube is made up of kinetic energy by vortex movement and internal energy produced by the friction against the wall of the tube. Density of a flowing gas or vapour varies along the length of the tube due to frictional losses along the tube implying that there is a pressure loss and a corresponding density decrease. After reducing the N-S equations to a single PDE, it is here proven that a Hunter-Saxton wave vortex exists along the wall of the tube due to a vorticity argument. The reduced problem shows finite-time blowup as the two parameters δ and α approach zero. A rearranged form for density is valid for δ approaching infinity for the case of incompressible flow proving positive for the existence of smooth solutions to the cylindrical Navier-Stokes equations. Finally we propose a CMS (Calculus of Moving Surfaces)–invariant variational calculus to analyze general dynamic surfaces of Riemannian 2-Manifolds in R 3 . Establishing fluid structures in general compressible flows and analyzing membranes in such flows for example flows with dynamic membranes immersed in fluid (vapour or gas) with vorticity as, for example, in the lungs there can prove to be a strong connection between fluid and solid mechanics.

Download Full-text

DOMAIN DECOMPOSITION APPROXIMATION TO A GENERALIZED STOKES PROBLEM BY SPECTRAL METHODS

Mathematical Models and Methods in Applied Sciences ◽

10.1142/s0218202591000253 ◽

1991 ◽

Vol 01 (04) ◽

pp. 501-515 ◽

Cited By ~ 2

Author(s):

CLAUDIO CARLENZOLI ◽

PAOLA ZANOLLI

Keyword(s):

Spectral Methods ◽

Compressible Flows ◽

Stokes Equations ◽

Stokes Problem ◽

Navier Stokes ◽

Computational Domain ◽

Navier Stokes Equations ◽

Generalized Stokes Problem ◽

Spectral Approximations ◽

Viscous Compressible Flows

We consider here the approximation of a generalized Stokes problem by spectral methods in the collocation form. This problem is of particular interest when Navier-Stokes equations for viscous compressible flows are investigated. We also analyze a coupling of a viscous model with an inviscid one; precisely, we split the computational domain in two parts and in one of them we eliminate the viscous coefficient from the Stokes equations. Such an approach can be worthwhile in the study of compressible fluids around rigid profiles with critical layers. Finally we consider some numerical results with the aim of showing the excellent accuracy of the spectral approximations, as well as the efficiency of an iterative algorithm that we propose in order to alternate viscous and inviscid numerical solvers.

Download Full-text

Numerical Simulation of the Two-Dimensional Viscous Compressible Flow in Blade Cascades Using a Solution-Adaptive Unstructured Mesh

Journal of Turbomachinery ◽

10.1115/1.2927660 ◽

1990 ◽

Vol 112 (3) ◽

pp. 311-319 ◽

Cited By ~ 6

Author(s):

G. L. D. Side´n ◽

W. N. Dawes ◽

P. J. Albra˚ten

Keyword(s):

Compressible Flows ◽

Stokes Equations ◽

Rapid Development ◽

Automatic Generation ◽

Navier Stokes ◽

Two Dimensional ◽

Navier Stokes Equations ◽

Explicit Finite Element ◽

Eddy Viscosity Model ◽

Viscous Compressible Flow

An explicit finite element procedure has been coupled with an automatic generation procedure for mesh-adaptive steady-state simulations of two-dimensional viscous compressible flows in cascades. Turbulence is modeled by a two-layer algebraic eddy viscosity model. Results show good behavior in comparison with measurements and results of a conventional H-mesh viscous flow solver. Computed loss approaches measured loss as the mesh is refined. Currently, the unstructured solver suffers in efficiency terms because the automatic mesh generator tends to produce inefficient equilateral triangles in the regions of shock waves and boundary layers where stretched elements would be more appropriate. This means that, at least for the Navier–Stokes equations, the unstructured approach is not yet competitive with conventional structured techniques. Nevertheless, this will change once the key advantages of geometric flexibility and user-independent solutions force rapid development.

Download Full-text