International Journal for Numerical Methods in Fluids

de With, G.; Holdø, A. E.; Huld, T. A.

doi: 10.1002/fld.418pmid: N/A

In the present study a dynamic grid adaptation (DGA) algorithm is utilized for predicting flow around a circular cylinder in sub‐critical flow regime at a Reynolds number of 1.4×105. The reason for adopting a DGA algorithm is the unsteadiness of the flow field which makes a conventional mesh inefficient. The concept being adopted is to concentrate mesh refinement in regions with high gradients and high turbulent viscosity, while in the region further downstream where the flow is fully developed a coarser mesh will develop and turbulence is modelled with the large eddy simulation (LES) turbulence model. The aim of the study is to present an appropriate variable for mesh refinement, which accomplishes a high rate of mesh refinement in the region with high gradients. The new variable is a product of the local mesh cell size and the rate of strain and includes two additional variables to allow control over the refinement behaviour. The results are compared with experimental data at the corresponding Reynolds number and also with numerical results obtained with conventional mesh. It is demonstrated that DGA algorithms can give results of a very high quality for a mesh that is significantly smaller than for a conventional mesh. Copyright © 2003 John Wiley & Sons, Ltd.

Aliabadi, S.; Abedi, J.; Zellars, B.

doi: 10.1002/fld.459pmid: N/A

The coupling between the equations governing the free‐surface flows, the six degrees of freedom non‐linear rigid body dynamics, the linear elasticity equations for mesh‐moving and the cables has resulted in a fluid‐structure interaction technology capable of simulating mooring forces on floating objects. The finite element solution strategy is based on a combination approach derived from fixed‐mesh and moving‐mesh techniques. Here, the free‐surface flow simulations are based on the Navier–Stokes equations written for two incompressible fluids where the impact of one fluid on the other one is extremely small. An interface function with two distinct values is used to locate the position of the free‐surface. The stabilized finite element formulations are written and integrated in an arbitrary Lagrangian–Eulerian domain. This allows us to handle the motion of the time dependent geometries. Forces and momentums exerted on the floating object by both water and hawsers are calculated and used to update the position of the floating object in time. In the mesh moving scheme, we assume that the computational domain is made of elastic materials. The linear elasticity equations are solved to obtain the displacements for each computational node. The non‐linear rigid body dynamics equations are coupled with the governing equations of fluid flow and are solved simultaneously to update the position of the floating object. The numerical examples includes a 3D simulation of water waves impacting on a moored floating box and a model boat and simulation of floating object under water constrained with a cable. Copyright © 2003 John Wiley & Sons, Ltd.

Tekasakul, P.; Loyalka, S. K.

doi: 10.1002/fld.467pmid: N/A

Rotary oscillations of several axi‐symmetric bodies in axi‐symmetric viscous flows with slip are investigated. A numerical method based on the Green's function technique is used wherein the relevant Helmholtz equation, as obtained from the unsteady Stokes equation, is converted into a surface integral equation. The technique is benchmarked against a known analytical solution, and accurate numerical results for local stress and torque on spheres and spheroids as function of the frequency parameter and the slip coefficients are obtained. It is found that in all cases, slip reduces stress and torque, and increasingly so with the increasing frequency parameter. The method discussed here can be potentially extended to the realistic case of an oscillating disk viscometer. Copyright © 2003 John Wiley & Sons, Ltd.

Gottardi, Guido; Venutelli, Maurizio

doi: 10.1002/fld.471pmid: N/A

The resolution of the Saint‐Venant equations for modelling shock phenomena in open‐channel flow by using the second‐order central schemes of Nessyahu and Tadmor (NT) and Kurganov and Tadmor (KT) is presented. The performances of the two schemes that we have extended to the non‐homogeneous case and that of the classical first‐order Lax–Friedrichs (LF) scheme in predicting dam‐break and hydraulic jumps in rectangular open channels are investigated on the basis of different numerical and physical conditions. The efficiency and robustness of the schemes are tested by comparing model results with analytical or experimental solutions. Copyright © 2003 John Wiley & Sons, Ltd.

Nilsson, H.; Davidson, L.

doi: 10.1002/fld.472pmid: N/A

This work compares CFD results with experimental results of the flow in two different kinds of water turbine runners. The runners studied are the GAMM Francis runner and the Hölleforsen Kaplan runner. The GAMM Francis runner was used as a test case in the 1989 GAMM Workshop on 3D Computation of Incompressible Internal Flows where the geometry and detailed best efficiency measurements were made available. In addition to the best efficiency measurements, four off‐design operating condition measurements are used for the comparisons in this work. The Hölleforsen Kaplan runner was used at the 1999 Turbine 99 and 2001 Turbine 99—II workshops on draft tube flow, where detailed measurements made after the runner were used as inlet boundary conditions for the draft tube computations. The measurements are used here to validate computations of the flow in the runner. The computations are made in a single runner blade passage where the inlet boundary conditions are obtained from an extrapolation of detailed measurements (GAMM) or from separate guide vane computations (Hölleforsen). The steady flow in a rotating co‐ordinate system is computed. The effects of turbulence are modelled by a low‐Reynolds number k‐ω turbulence model, which removes some of the assumptions of the commonly used wall function approach and brings the computations one step further. The computational results are compared to the measurements with respect to detailed velocity and pressure distributions at several measurement sections and several operating conditions. The computational results are also compared to coarse grid wall function computations by the TASCflow CFD code, which uses a similar methodology as the CALC‐PMB CFD code used in the present work. The comparisons show where the computational method is sufficient and where it is not sufficient.The behaviour of the computational method is similar for both kinds of water turbines, which shows that experience of computations in water turbines will ultimately give quantitatively correct results. Copyright © 2003 John Wiley & Sons, Ltd.

Eguchi, Yuzuru

doi: 10.1002/fld.482pmid: N/A

A new regularization method is proposed for the Galerkin approximation of the incompressible Navier–Stokes equations with Q1/P0 element, by newly introducing a square‐type linear form into the variational divergence‐free constraint regularized with the global pressure jump (GPJ) method. The addition of the square‐type linear form is intended to eliminate the hydrostatic pressure mode appearing in confined flows, and to make the discretized matrix positive definite and then non‐singular without the pressure pegging trick. Effects of the free parameters for the regularization on the solutions are numerically examined with a 2‐D driven cavity flow problem. Furthermore, the convergences in the conjugate gradient iteration for the solution of the pressure Poisson equation are compared among the mixed method, the GPJ method and the present method for both leaky and non‐leaky 3‐D driven cavity flows. Finally, the non‐leaky 3‐D cavity flows at different Re numbers are solved to compare with the literature data and to demonstrate the accuracy of the proposed method. Copyright © 2003 John Wiley & Sons, Ltd.