A Calculation Procedure for Heat, Mass and Momentum Transfer in Three-Dimensional Parabolic Flows

Abstract

A general, numerical, marching procedure is presented for the calculation of the transport processes in three-dimensional flows characterised by the presence of one coordinate in which physical influences are exerted in only one direction. Such flows give rise to parabolic differential equations and so can be called three-dimensional parabolic flows. The procedure can be regarded as a boundary-layer method, provided it is recognised that, unlike earlier published methods with this name, it takes full account of the cross-stream diffusion of momentum, etc., and of the pressure variation in the cross-stream plane. The pressure field is determined by: first calculating an intermediate velocity field based on an estimated pressure field; and then obtaining appropriate correction so as to satisfy the continuity equation. To illustrate the procedure, calculations are presented for the developing laminar flow and heat transfer in a square duct with a laterally-moving wall. NOMENCLATURE ^ > the cross-stream co-ordinates; z, J <5y, Ί distances between neighbouring grid <5z, J points (Fig. 5); Ax, size of the forward step (Fig. 4); Ay, Ί cross-stream dimensions of the control Δζ, J volume (Fig. 5); Γ, transport property in equation (3.1);

Application of a roughness‐length representation to parameterize energy loss in 3‐D numerical simulations of large rivers

“…Pressure was computed using the Semi‐Implicit Method for Pressure‐Linked Equations SIMPLE [ Patankar and Spalding , 1972] algorithm, and the second‐order upstream monotonic interpolation for scalar transport (UMIST) differencing scheme [ Lien and Leschziner , 1994b] was employed to compute convective terms. A rigid‐lid approximation was applied at the free surface, introducing an additional surface‐pressure term, but necessitating a mass correction of the surface‐adjacent cells [ Bradbrook et al , 2000].…”

Quantifying model form uncertainty in Reynolds-averaged turbulence models with Bayesian deep neural networks

“…OpenFOAM is a widely accepted CFD package that contains a vast number of solvers for incompressible, compressible and multi-phase flows along with pre-and post-processing utilities. For the baseline RANS simulations the steady-state, incompressible solver simple-Foam was used which employs the semi-implicit method for pressure linked equations (SIMPLE) algorithm [47] to solve both the momentum and pressure equations. The high-fidelity LES simulations used the pimpleFoam transient solver that combines both the PISO (Pressure Implicit with Split Operator) [48] and SIMPLE algorithms to solve the pressure and momentum equations.…”

Numerical Simulation-Based Effect Characterization and Design Optimization of a Micro Cross-Flow Turbine

“…In this section, two of the widely used solution schemes in CFD, the SIMPLE and the PISO algorithms, are tested. Both algorithms are fundamentally used to drive a pressure correction equation in the Pressure-Velocity Coupling scheme in solving the turbulent Navier-Stokes equation [27]. The fundamental difference between them is that PISO uses the velocity correction from adjacent cells while solving the continuity equation, whereas SIMPLE does not.…”