A LINEARISED TURBULENT PRODUCTION IN THE k-ε MODEL FOR ENGINEERING APPLICATIONS

Guimet, V.; Laurence, Dominique

doi:10.1016/b978-008044114-6/50014-4

Cited by 26 publications

(20 citation statements)

References 12 publications

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“…Figure 3 also demonstrates that the production estimated with the stability function of Canuto et al [2001] overestimated observed P Re by a factor of 3. Interestingly, is consistent with the model of Guimet and Laurence [2002], based on a turbulent production source term that is linear with respect to strain, applied to impinging flows for which the standard model is well known to overestimate the production of kinetic energy. However, we are not aware of other field measurements attesting this behavior in natural surf zones.…”

Section: Resultssupporting

confidence: 83%

Turbulent viscosity in natural surf zones

Grasso¹,

Ruessink²

2012

Geophysical Research Letters

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[1] Waves breaking in the shallow surf zone near the shoreline inject turbulence into the water column that may reach the bed to suspend sediment. Breaking-wave turbulence in the surf zone is, however, poorly understood, which is one of the reasons why many process-based coastal-evolution models predict coastal change during severe storms inadequately. Here, we use data collected in two natural surf zones to derive a new parameterization for the stability function C m that determines the magnitude of the eddy viscosity n t in two-equation turbulent-viscosity models, n t = C m k 2 /ɛ, where k is turbulent kinetic energy and ɛ is the turbulence dissipation rate. In both data sets, the ratio of turbulence production to dissipation is small (≈0.15), while vertical turbulence diffusion is significant. This differs from assumptions underlying existing C m parameterizations, which we show to severely overpredict observed C m for most conditions. Additionally, we rewrite our new C m parameterization into a formulation that accurately reproduces our Reynoldsstress based estimates of turbulence production. This formulation is linear with strain, consistent with earlier theoritical work for large strain rates. Also, it does not depend on ɛ and can, therefore, also be applied in one-equation turbulentviscosity models. We anticipate our work to improve turbulence modeling in natural surf zones and to eventually lead to more reliable predictions of coastal evolution in response to severe storms.

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Section: Resultssupporting

confidence: 83%

Turbulent viscosity in natural surf zones

Grasso¹,

Ruessink²

2012

Geophysical Research Letters

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“…However, in order to avoid any overestimation of k in case of large scalar rate-of-strain (as for instance in the case of impinging jet of breaking wave), one should keep in mind that turbulence anisotropy is always bounded by C 1/2 (see e.g. Reference [19]). Hence, we consider here a linear dependency on the rate-of-strain for large deformations, writing the production of particle a as…”

Section: Traditional Turbulent Closuresmentioning

confidence: 99%

Numerical modelling of complex turbulent free‐surface flows with the SPH method: an overview

Violeau¹,

Issa²

2006

Numerical Methods in Fluids

225

137

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SUMMARYThe gridless smoothed particle hydrodynamics (SPH) method is now commonly used in computational fluid dynamics (CFD) and appears to be promising in predicting complex free-surface flows. However, increasing flow complexity requires appropriate approaches for taking account of turbulent effects, whereas some authors are still working without any turbulence closure in SPH. A review of recently developed turbulence models adapted to the SPH method is presented herein, from the simplistic point of view of a one-equation model involving mixing length to more sophisticated (and thus realistic) models like explicit algebraic Reynolds stress models (EARSM) or large eddy simulation (LES). Each proposed model is tested and validated on the basis of schematic cases for which laboratory data, theoretical or numerical solutions are available in the general field of turbulent free-surface incompressible flows (e.g. open-channel flow and schematic dam break). They give satisfactory results, even though some progress should be made in the future in terms of free-surface influence and wall conditions. Recommendations are given to SPH users to apply this method to the modelling of complex free-surface turbulent flows.

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“…C ϵ 3 is set to 1 if

double-struckG \leq 0

and 0 otherwise.

double-struckP

is calculated according to a mixed linear‐quadratic model

double-struckP = \min ((), \sqrt{C_{μ}} kS, ν_{T} S^{2})

where

S = \sqrt{2 bold-italicS : bold-italicS}

is the scalar mean rate‐of‐strain.

double-struckG

is a buoyancy production/destruction term calculated as follows :

double-struckG = β K_{T} bold-italic \nabla T \cdot bold-italicg

g is the gravity field (of magnitude g = 9.81m 2 s −1 ),

\overset{p}{true} = p + \frac{2}{3} k

with p the pressure, β is the coefficient of thermal expansion, T is the temperature field and T 0 is the mean temperature.…”

Section: Governing Equations and Modelling Choicesmentioning

confidence: 99%

Buoyancy modelling with incompressible SPH for laminar and turbulent flows

Leroy

Violeau

Ferrand³

et al. 2015

Numerical Methods in Fluids

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International audienceThis work aims at modelling buoyant, laminar or turbulent flows, using a 2D Incompressible Smoothed Particle Hydrodynamics (ISPH) model with accurate wall boundary conditions. The buoyancy effects are modelled through the Boussinesq approximation coupled to a heat equation, which makes it possible to apply an incompressible algorithm to compute the pressure field from a Poisson equation. Based on our previous work (Leroy et al., 2014), we extend the unified semi-analytical wall boundary conditions to the present model. The latter is also combined to a Reynolds-Averaged Navier-Stokes approach to treat turbulent flows. The k − turbulence model is used, where buoyancy is modelled through an additional term in the k − equations like in mesh-based methods. We propose a unified framework to prescribe isothermal (Dirichlet) or imposed heat flux (Neumann) wall boundary conditions in ISPH. To illustrate this, a theoretical case is presented (laminar heated Poiseuille flow), where excellent agreement with the theoretical solution is obtained. Several benchmark cases are then proposed: a lock-exchange flow, two laminar and one turbulent flow in differentially heated cavities, and finally a turbulent heated Poiseuille flow. Comparisons are provided with a Finite-Volume (FV) approach using an open-source industrial code

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A LINEARISED TURBULENT PRODUCTION IN THE k-ε MODEL FOR ENGINEERING APPLICATIONS

Cited by 26 publications

References 12 publications

Turbulent viscosity in natural surf zones

Turbulent viscosity in natural surf zones

Numerical modelling of complex turbulent free‐surface flows with the SPH method: an overview

Buoyancy modelling with incompressible SPH for laminar and turbulent flows

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