Turbulence Closure Models for Computational Fluid Dynamics

Durbin, Paul A.

doi:10.1002/0470091355.ecm061

Cited by 7 publications

(8 citation statements)

References 46 publications

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“…We can model the turbulent Reynolds stress in terms of the large‐scale flow with the aid of the Reynolds‐averaged Navier‐Stokes (RANS) equations. Following the RANS k ‐ ϵ model (Durbin, 2004), for a homogeneous and stationary turbulent flow in water, we can parameterize the local turbulent Reynolds stress

\overset{u_{i}^{'} u_{j}^{'}}{true}

by a turbulent eddy viscosity ν T acting on the large‐scale flow gradients S ij as (Durbin, 2004)

- \overset{u_{i}^{'} u_{j}^{'}}{true} + \frac{2}{3} \overset{u_{k}^{'} u_{k}^{'}}{true} δ i j \equiv 2 ν_{T} S_{i j}

. The mean flow strain tensor S ij is given by

S_{i j} \equiv \frac{1}{2} ((), \frac{\partial u_{i}}{\partial x_{j}} + \frac{\partial u_{j}}{\partial x_{i}}) .

…”

Section: Theoretical Considerationsmentioning

confidence: 99%

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On the Nature of the Turbulent Energy Dissipation Beneath Nonbreaking Waves

Bogucki

Haus

Barzegar

et al. 2020

Geophysical Research Letters

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Here we have determined the nature of turbulent flow associated with oceanic nonbreaking waves, which are on average much more prevalent than breaking waves in most wind conditions. We found this flow to be characterized by a low turbulence microscale Reynolds number of 30 < Re < 100. We observed that the turbulent kinetic energy dissipation rate associated with nonbreaking waves , ranged to 3 • 10 −4 W/kg for a wave amplitude 50 cm. The , under nonbreaking waves, was consistent with = 2 T (S i) 2 ; S ij is the large-scale (energy-containing scales) wave-induced mean flow stress tensor. The turbulent Reynolds stress associated with nonbreaking waves was consistent with experimental data when parameterized by an amplitude independent constant turbulent eddy viscosity, 10 times larger than the molecular value. Given that nonbreaking waves typically cover a much larger fraction of the ocean surface (90-100%) than breaking waves, this result shows that their contribution to wave dissipation can be significant. Plain Language Summary Considering that surface waves cover most of the ocean, the precise determination of the rate at which surface waves dissipate energy is necessary to properly quantify climate, weather, or ocean dynamic processes at the air-sea interface and within the upper layer of the ocean. The upper-ocean mixing intensity is often related to breaking surface waves, while the turbulence generated by nonbreaking surface waves is poorly understood and thus not well represented. Our laboratory experiments used microstructure and optical measurements to observe micro velocity shears and temperature fluctuations associated with passing nonbreaking solitary surface waves. Here we report measurements of the energy dissipation associated with these nonbreaking surface waves. We present an analytical approach to quantify the nonbreaking wave turbulence strength from large-scale (energy-containing) flow measurements. The analysis by Teixeira and Belcher (2002) demonstrated that the main mechanism responsible for NBSW turbulence is associated with Stokes drift tilting the small-scale vortex structures, followed by their RESEARCH LETTER

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\overset{u_{i}^{'} u_{j}^{'}}{true}

by a turbulent eddy viscosity ν T acting on the large‐scale flow gradients S ij as (Durbin, 2004)

- \overset{u_{i}^{'} u_{j}^{'}}{true} + \frac{2}{3} \overset{u_{k}^{'} u_{k}^{'}}{true} δ i j \equiv 2 ν_{T} S_{i j}

. The mean flow strain tensor S ij is given by

S_{i j} \equiv \frac{1}{2} ((), \frac{\partial u_{i}}{\partial x_{j}} + \frac{\partial u_{j}}{\partial x_{i}}) .

…”

Section: Theoretical Considerationsmentioning

confidence: 99%

“…With turbulent production P defined as

P \equiv - \overset{u_{i}^{'} u_{j}^{'}}{true} S_{i j}

, then after replacing the Reynolds stress

\overset{u_{i}^{'} u_{j}^{'}}{true}

by its ν T parameterization, we obtain a simple estimate of turbulent dissipation in terms of large‐scale flow gradients as (Durbin, 2004)

ϵ \approx P = 2 ν_{T} {((), S_{i j})}^{2} .

…”

Section: Theoretical Considerationsmentioning

confidence: 99%

On the Nature of the Turbulent Energy Dissipation Beneath Nonbreaking Waves

Bogucki

Haus

Barzegar

et al. 2020

Geophysical Research Letters

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“…Chorin's projection method Chorin (1968) is used for the pressure treatment and a preconditioned BiCGStab solver van der Vorst (1992) is used to solve for the pressure. Turbulence modelling is carried out based on Durbin's modification Durbin (2004) of the two equation k-ω model proposed by Wilcox Wilcox (1994). Eddy viscosity, ν t , is bounded to avoid unphysical overproduction of turbulence in strained flow as shown by DurbinDurbin (2009).…”

Section: Numerical Modelmentioning

confidence: 99%

Study of Water Impact and Entry of a Free Falling Wedge Using CFD Simulations

Kamath

Bihs

Arnsten

2016

Volume 2: CFD and VIV

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Many offshore constructions and operations involve water impact problems such as water slamming onto a structure or free fall of objects with subsequent water entry and emergence. Wave slamming on semi-submersibles, vertical members of jacket structures, crane operation of a diving bell and dropping of free fall lifeboats are some notable examples. The slamming and water entry problems lead to large instantaneous impact pressures on the structure, accompanied with complex free surface deformations. These need to be studied in detail in order to obtain a better understanding of the fluid physics involved and develop safe and economical design. In the special case of free-fall lifeboats, model testing can be expensive and time consuming. Here, numerical modelling can make useful contributions to the design process. The slamming of a free falling body into water involves several complex hydrodynamic features after its free-fall such as water entry, submergence into water and resurfacing. The water entry and submergence lead to formation of water jets and air cavities in the water resulting in large impact forces on the object. In order to evaluate the forces and hydrodynamics involved, the numerical model should be able to account for the complex free surface features, the instantaneous pressure changes around the lifeboat and accurately evaluate the loads on the lifeboat. As a step towards simulating free-fall lifeboats, water entry of a free-falling wedge into water is studied in this paper using a CFD model. The vertical velocity of the wedge during the process of free fall and water impact are calculated for different cases and the free surface deformations are captured in detail. Numerical results are compared with experimental data and a good agreement is seen. The open-source CFD model REEF3D is used in this study. The model solves the Reynolds-Averaged Navier-Stokes equations to evaluate the fluid flow. The convective terms are discretized using a 5th-order conservative finite difference WENO scheme. Time discretization is carried out using a 3rd-order Runge-Kutta scheme. Pressure discretization is carried out using Chorins projection method. The Poisson pressure equation is solved using a pre-conditioned BiCGStab algorithm. A sharp representation of the free surface is obtained using the level set method. The falling wedge is represented using the level set paradigm as well, avoiding the need for re-meshing during the simulation. Turbulence modeling is carried out using the k-ω model. Computational performance of the numerical model is improved by parallel processing using the MPI library.

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“…especially Ross and Vosper (2005) and Sogachev et al (2012). Durbin (2004) and Hanjali'c and Kenjereš (2008) provide recent reviews of the strengths and limitations of these models. Interestingly in the light of our discussion of simple canopy flows, Katul et al (2004) found that K-theory models with prescribed mixing lengths in the canopy performed as well as k − ε models in simple canopy flows.…”

Section: Eddy Diffusivities In Complex Canopy Flowsmentioning

confidence: 99%

First‐order turbulence closure for modelling complex canopy flows

Finnigan

Harman

Ross

et al. 2015

Quart J Royal Meteoro Soc

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Simple first‐order closure remains an attractive way of formulating equations for complex canopy flows when the aim is to find analytic or simple numerical solutions to illustrate fundamental physical processes. Nevertheless, the limitations of such closures must be understood if the resulting models are to illuminate rather than mislead. We propose five conditions that first‐order closures must satisfy, then test two widely used closures against them. The first is the eddy diffusivity based on a mixing length. We discuss the origins of this approach, its use in simple canopy flows and extensions to more complex flows. We find that it satisfies most of the conditions and, because the reasons for its failures are well understood, it is a reliable methodology. The second is the velocity‐squared closure that relates shear stress to the square of mean velocity. Again we discuss the origins of this closure and show that it is based on incorrect physical principles and fails to satisfy any of the five conditions in complex canopy flows; consequently its use can lead to actively misleading conclusions.

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Turbulence Closure Models for Computational Fluid Dynamics

Cited by 7 publications

References 46 publications

On the Nature of the Turbulent Energy Dissipation Beneath Nonbreaking Waves

On the Nature of the Turbulent Energy Dissipation Beneath Nonbreaking Waves

Study of Water Impact and Entry of a Free Falling Wedge Using CFD Simulations

First‐order turbulence closure for modelling complex canopy flows

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