Numerical simulation of turbulent free surface flow with two‐equation k–ε eddy‐viscosity models

Abstract

SUMMARYThis paper presents a ÿnite di erence technique for solving incompressible turbulent free surface uid ow problems. The closure of the time-averaged Navier-Stokes equations is achieved by using the twoequation eddy-viscosity model: the high-Reynolds k-(standard) model, with a time scale proposed by Durbin; and a low-Reynolds number form of the standard k-model, similar to that proposed by Yang and Shih. In order to achieve an accurate discretization of the non-linear terms, a second=third-order upwinding technique is adopted. The computational method is validated by applying it to the at plate boundary layer problem and to impinging jet ows. The method is then applied to a turbulent planar jet ow beneath and parallel to a free surface. Computations show that the high-Reynolds k-model yields favourable predictions both of the zero-pressure-gradient turbulent boundary layer on a at plate and jet impingement ows. However, the results using the low-Reynolds number form of the k-model are somewhat unsatisfactory.

Numerical simulation of drop impact and jet buckling problems using the eXtended Pom–Pom model

“…Examples of those numerical methods are: SMAC [3], GENSMAC [34], SIMAC [4], the methods of Ushijima [41], Kim and No [19], among others. More recently, improved variants have been developed: for instance, Sousa et al [32] used the MAC method for 3D multi-fluid flows with free surfaces (and interfaces); Ferreira et al [13] presented numerical simulations of turbulent free surface flows based on MAC techniques; Mangiavacchi et al [21] implemented an effective technique for dealing with axisymmetric and planar flows when surface tension is relevant; Ferreira et al [14] adapted the MAC method to calculate confined and free surface flows at both low and high Reynolds numbers. A review on the MAC method was presented by McKee et al [22].…”

Stability of numerical schemes on staggered grids

“…Matrix F satisfies the assumptions of Theorem 2, with = = 0, a = c = 1 and b = 2. Therefore, its eigenvalues can be computed from (18) giving F i = 2+2 cos(i /(m +1)) for i = 1, . .…”

“…Many other authors have used essentially the same MAC ideas to simulate the impact drop problem [14], for second-order reconstruction of interfaces [15] and in a Lagrangian-Eulerian formulation for the simulation of three-dimensional flows in arbitrary domains [16]. More recently, Sousa et al [17] used the MAC method for three-dimensional multifluid flows with free surfaces (and interfaces), Ferreira et al [18] presented numerical simulations of turbulent free surface flows based on MAC techniques, Mangiavacchi et al [19] implemented an effective technique for dealing with axisymmetric and planar flows when surface tension is significant and Ferreira et al [20] adapted the MAC method to calculate confined and free surface fluid flows at both low and high Reynolds numbers.…”

The MAC method

“…Work in this area continues: see, for example, a recent application of the SMAC method to the j-e equations by Ferreira et al [24].…”