A comparison of turbulence closure models for transonic flows about airfoils

This paper reports a fine numerical simulation of environmental flow and contaminant transport in the Amazonian water system near the Anamã City, Brazil, solved by the Q3drm1.0 software, developed by the Authors, which can provide the different closures of three depth-integrated two-equation turbulence models. The purpose of this simulation is to refinedly debug and test the developed software, including the mathematical model, turbulence closure models, adopted algorithms, and the developed general-purpose computational codes as well as graphical user interfaces (GUI). The three turbulence models, provided by the developed software to close non-simplified quasi three-dimensional hydrodynamic fundamental governing equations, include the traditional depth-integrated two-equation turbulence model, the depth-integrated two-equation turbulence model, developed previously by the first Author of the paper, and the depth-integrated two-equation turbulence model, developed recently by the Authors of this paper. The numerical simulation of this paper is to solve the corresponding discretized equations with collocated variable arrangement on the non-orthogonal body-fitted coarse and fine two-levels’ grids. With the help of Q3drm1.0 software, the steady environmental flows and transport behaviours have been numerically investigated carefully; and the processes of contaminant inpouring as well as plume development, caused by the side-discharge from a tributary of the south bank (the right bank of the river), were also simulated and discussed in detail. Although the three turbulent closure models, used in this calculation, are all applicable to the natural rivers with strong mixing, the comparison of the computational results by using the different turbulence closure models shows that the turbulence model with larger turbulence parameter provides the possibility for improving the accuracy of the numerical computations of practical problems.

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On a solution of the closure problem for dry convective boundary layer turbulence and beyond

Journal of the Atmospheric Sciences ◽

10.1175/jas-d-21-0107.1 ◽

2021 ◽

Keyword(s):

Boundary Layer ◽

Convective Boundary Layer ◽

Higher Order ◽

Turbulence Closure ◽

Analytical Models ◽

Central Feature ◽

Closure Problem ◽

Convective Boundary ◽

Higher Order Moments ◽

Closure Models

Abstract We consider the closure problem of representing the higher order moments (HOMs) in terms of lower-order moments, a central feature in turbulence modelling based on the Reynolds-Averaged Navier-Stokes (RANS) approach. Our focus is on models suited for the description of asymmetric, non-local and semi-organized turbulence in the dry atmospheric convective boundary layer (CBL). We establish a multivariate probability density function (PDF) describing populations of plumes which are embedded in a sea of weaker randomly spaced eddies, and apply an assumed Delta-PDF approximation. The main content of this approach consists of capturing the bulk properties of the PDF. We solve the closure problem analytically for all relevant higher order moments (HOMs) involving velocity components and temperature and establish a hierarchy of new non-Gaussian turbulence closure models of different content and complexity ranging from analytical to semi-analytical. All HOMs in the hierarchy have a universal and simple functional form. They refine the widely used Millionshchikov closure hypothesis and generalize the famous quadratic skewness-kurtosis relationship to higher-order. We examine the performance of the new closures by comparison with measurement, LES and DNS data and derive empirical constants for semi-analytical models, which are best for practical applications. We show that the new models have a good skill in predicting the HOMs for atmospheric CBL. Our closures can be implemented in second-, third- and fourth-order RANS turbulence closure models of bi-, tri-and four-variate levels of complexity. Finally, several possible generalizations of our approach are discussed.

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