scholarly journals A Pressure-Correction Scheme for Rotational Navier-Stokes Equations and Its Application to Rotating Turbulent Flows

2011 ◽  
Vol 9 (3) ◽  
pp. 740-755 ◽  
Author(s):  
Dinesh A. Shetty ◽  
Jie Shen ◽  
Abhilash J. Chandy ◽  
Steven H. Frankel
Keyword(s):  
Boundary Conditions ◽  
Turbulent Flows ◽  
Incompressible Flows ◽  
Stokes Equations ◽  
Navier Stokes ◽  
Navier Stokes Equations ◽  
Pressure Correction ◽  
Correction Scheme ◽  
Diagonalization Method ◽  
Pseudo Spectral

AbstractThe rotational incremental pressure-correction (RIPC) scheme, described in Timmermans et al. [Int. J. Numer. Methods. Fluids., 22 (1996)] and Shen et al. [Math. Comput., 73 (2003)] for non-rotational Navier-Stokes equations, is extended to rotating incompressible flows. The method is implemented in the context of a pseudo Fourier-spectral code and applied to several rotating laminar and turbulent flows. The performance of the scheme and the computational results are compared to the so-called diagonalization method (DM) developed by Morinishi et al. [Int. J. Heat. Fluid. Flow., 22 (2001)]. The RIPC predictions are in excellent agreement with the DM predictions, while being simpler to implement and computationally more efficient. The RIPC scheme is not in anyway limited to implementation in a pseudo-spectral code or periodic boundary conditions, and can be used in complex geometries and with other suitable boundary conditions.

Multigrid Computation of Incompressible Flows Using Two-Equation Turbulence Models: Part II—Applications

1997 ◽  
Vol 119 (4) ◽  
pp. 900-905 ◽  
Author(s):  
X. Zheng ◽  
C. Liao ◽  
C. Liu ◽  
C. H. Sung ◽  
T. T. Huang
Keyword(s):  
Turbulent Flows ◽  
Incompressible Flows ◽  
Stokes Equations ◽  
Three Dimensional ◽  
Turbulence Models ◽  
Navier Stokes ◽  
Navier Stokes Equations ◽  
Time Stepping ◽  
Grid Algorithm ◽  
High Reynolds

In this paper, computational results are presented for three-dimensional high-Reynolds number turbulent flows over a simplified submarine model. The simulation is based on the solution of Reynolds-Averaged Navier-Stokes equations and two-equation turbulence models by using a preconditioned time-stepping approach. A multiblock method, in which the block loop is placed in the inner cycle of a multi-grid algorithm, is used to obtain versatility and efficiency. It was found that the calculated body drag, lift, side force coefficients and moments at various angles of attack or angles of drift are in excellent agreement with experimental data. Fast convergence has been achieved for all the cases with large angles of attack and with modest drift angles.

ISOGEOMETRIC DIVERGENCE-CONFORMING B-SPLINES FOR THE STEADY NAVIER–STOKES EQUATIONS

2013 ◽  
Vol 23 (08) ◽  
pp. 1421-1478 ◽  
Author(s):  
JOHN A. EVANS ◽  
THOMAS J. R. HUGHES
Keyword(s):  
Boundary Conditions ◽  
Numerical Experiments ◽  
Incompressible Flows ◽  
Stokes Equations ◽  
A Priori ◽  
Navier Stokes ◽  
Slip Boundary Conditions ◽  
Navier Stokes Equations ◽  
Discrete Velocity ◽  
Slip Boundary

We develop divergence-conforming B-spline discretizations for the numerical solution of the steady Navier–Stokes equations. These discretizations are motivated by the recent theory of isogeometric discrete differential forms and may be interpreted as smooth generalizations of Raviart–Thomas elements. They are (at least) patchwise C0 and can be directly utilized in the Galerkin solution of steady Navier–Stokes flow for single-patch configurations. When applied to incompressible flows, these discretizations produce pointwise divergence-free velocity fields and hence exactly satisfy mass conservation. Consequently, discrete variational formulations employing the new discretization scheme are automatically momentum-conservative and energy-stable. In the presence of no-slip boundary conditions and multi-patch geometries, the discontinuous Galerkin framework is invoked to enforce tangential continuity without upsetting the conservation or stability properties of the method across patch boundaries. Furthermore, as no-slip boundary conditions are enforced weakly, the method automatically defaults to a compatible discretization of Euler flow in the limit of vanishing viscosity. The proposed discretizations are extended to general mapped geometries using divergence-preserving transformations. For sufficiently regular single-patch solutions subject to a smallness condition, we prove a priori error estimates which are optimal for the discrete velocity field and suboptimal, by one order, for the discrete pressure field. We present a comprehensive suite of numerical experiments which indicate optimal convergence rates for both the discrete velocity and pressure fields for general configurations, suggesting that our a priori estimates may be conservative. These numerical experiments also suggest our discretization methodology is robust with respect to Reynolds number and more accurate than classical numerical methods for the steady Navier–Stokes equations.

Fluid-Inertia Effects in Radial Flow Between Oscillating, Rotating Parallel Disks

1981 ◽  
Vol 103 (1) ◽  
pp. 144-149
Author(s):  
D. K. Warinner ◽  
J. T. Pearson
Keyword(s):  
Turbulent Flows ◽  
Radial Flow ◽  
Incompressible Flows ◽  
Stokes Equations ◽  
Navier Stokes ◽  
Fluid Inertia ◽  
Rotating Disks ◽  
Spiral Flow ◽  
Navier Stokes Equations ◽  
Inertia Effects

An order-of-magnitude analysis is applied to the Navier-Stokes equations and the continuity equation for isothermal, radial fluid flow between oscillating and rotating disks. This analysis investigates the four basic cases of 1) steady, radial flow, 2) unsteady, radial flow, 3) steady, spiral flow, and 4) unsteady, spiral flow. It is shown that certain values of particular dimensionless parameters for general cases will reduce the Navier-Stokes equations to simplified forms and thus render them amenable to closed-form solutions for, say, the pressure distribution between oscillating, rotating disks. The analysis holds for laminar and turbulent flows and compressible and incompressible flows. The conditions that must be satisfied for one to reasonably neglect 1) rotation, 2) unsteady terms, and 3) convective terms are set forth. One result shown is that only rarely could one reasonably neglect the radial convective acceleration while retaining the radial local acceleration.

Reynolds-Averaged Navier–Stokes Equations for Turbulence Modeling

2009 ◽  
Vol 62 (4) ◽  
Author(s):  
Giancarlo Alfonsi
Keyword(s):  
Turbulent Flows ◽  
Incompressible Flows ◽  
Stokes Equations ◽  
Nonlinear Models ◽  
Turbulence Models ◽  
Equation Model ◽  
Navier Stokes ◽  
Navier Stokes Equations ◽  
Linear And Nonlinear ◽  
Reynolds Averaged Navier Stokes

The approach of Reynolds-averaged Navier–Stokes equations (RANS) for the modeling of turbulent flows is reviewed. The subject is mainly considered in the limit of incompressible flows with constant properties. After the introduction of the concept of Reynolds decomposition and averaging, different classes of RANS turbulence models are presented, and, in particular, zero-equation models, one-equation models (besides a half-equation model), two-equation models (with reference to the tensor representation used for a model, both linear and nonlinear models are considered), stress-equation models (with reference to the pressure-strain correlation, both linear and nonlinear models are considered) and algebraic-stress models. For each of the abovementioned class of models, the most widely-used modeling techniques and closures are reported. The unsteady RANS approach is also discussed and a section is devoted to hybrid RANS/large methods.

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