scholarly journals Direct Numerical Simulation of the Turbulent Ekman Layer: Evaluation of Closure Models

2012 ◽  
Vol 69 (3) ◽  
pp. 1106-1117 ◽  
Author(s):  
Stuart Marlatt ◽  
Scott Waggy ◽  
Sedat Biringen
Keyword(s):  
Numerical Simulation ◽  
Boundary Layer ◽  
Reynolds Number ◽  
Direct Numerical Simulation ◽  
Eddy Diffusivity ◽  
Ekman Layer ◽  
Rotational Flow ◽  
First Order ◽  
Closure Approximations ◽  
Cubic Polynomials

Abstract A direct numerical simulation (DNS) at a Reynolds number of 1000 was performed for the neutral atmospheric boundary layer (ABL) using the Ekman layer approximation. The DNS results were used to evaluate several closure approximations that model the turbulent stresses in the Reynolds averaged momentum equations. Two first-order closure equations proposed by O’Brien and by Large, McWilliams, and Doney were tested; both models approximate the eddy diffusivity as a function of height using cubic polynomials. Of these two models, the O’Brien model, which requires data both at the surface layer and at the top of the boundary layer, proved superior. The higher-order k–ɛ model also agreed well with DNS results and more accurately represented the eddy diffusivity in this rotational flow.

scholarly journals Direct numerical simulation of a self-similar adverse pressure gradient turbulent boundary layer at the verge of separation

2017 ◽  
Vol 829 ◽  
pp. 392-419 ◽  
Author(s):  
V. Kitsios ◽  
A. Sekimoto ◽  
C. Atkinson ◽  
J. A. Sillero ◽  
G. Borrell ◽  
...  
Keyword(s):  
Numerical Simulation ◽  
Boundary Layer ◽  
Reynolds Number ◽  
Direct Numerical Simulation ◽  
Pressure Gradient ◽  
Adverse Pressure Gradient ◽  
Streamwise Velocity ◽  
Far Field ◽  
Self Similar ◽  
The Mean

The statistical properties are presented for the direct numerical simulation of a self-similar adverse pressure gradient (APG) turbulent boundary layer (TBL) at the verge of separation. The APG TBL has a momentum thickness-based Reynolds number range from $Re_{\unicode[STIX]{x1D6FF}_{2}}=570$ to 13 800, with a self-similar region from $Re_{\unicode[STIX]{x1D6FF}_{2}}=10\,000$ to 12 300. Within this domain the average non-dimensional pressure gradient parameter $\unicode[STIX]{x1D6FD}=39$, where for a unit density $\unicode[STIX]{x1D6FD}=\unicode[STIX]{x1D6FF}_{1}P_{\!e}^{\prime }/\unicode[STIX]{x1D70F}_{w}$, with $\unicode[STIX]{x1D6FF}_{1}$ the displacement thickness, $\unicode[STIX]{x1D70F}_{w}$ the mean shear stress at the wall and $P_{\!e}^{\prime }$ the far-field pressure gradient. This flow is compared with previous zero pressure gradient and mild APG TBL ($\unicode[STIX]{x1D6FD}=1$) results of similar Reynolds number. All flows are generated via the direct numerical simulation of a TBL on a flat surface with far-field boundary conditions tailored to apply the desired pressure gradient. The conditions for self-similarity, and the appropriate length and velocity scales, are derived. The mean and Reynolds stress profiles are shown to collapse when non-dimensionalised on the basis of these length and velocity scales. As the pressure gradient increases, the extent of the wake region in the mean streamwise velocity profiles increases, whilst the extent of the log-layer and viscous sublayer decreases. The Reynolds stress, production and dissipation profiles of the APG TBL cases exhibit a second outer peak, which becomes more pronounced and more spatially localised with increasing pressure gradient. This outer peak is located at the point of inflection of the mean velocity profiles, and is suggestive of the presence of a shear flow instability. The maximum streamwise velocity variance is located at a wall normal position of $\unicode[STIX]{x1D6FF}_{1}$ of spanwise wavelength of $2\unicode[STIX]{x1D6FF}_{1}$. In summary as the pressure gradient increases the flow has properties less like a zero pressure gradient TBL and more akin to a free shear layer.

Direct numerical simulation of a supersonic turbulent boundary layer at Mach 2.5

2000 ◽  
Vol 414 ◽  
pp. 1-33 ◽  
Author(s):  
STEPHEN E. GUARINI ◽  
ROBERT D. MOSER ◽  
KARIM SHARIFF ◽  
ALAN WRAY
Keyword(s):  
Numerical Simulation ◽  
Boundary Layer ◽  
Reynolds Number ◽  
Turbulent Boundary Layer ◽  
Direct Numerical Simulation ◽  
Incompressible Flow ◽  
Reynolds Shear Stress ◽  
Turbulent Heat ◽  
Adiabatic Wall ◽  
Momentum Integral

A direct numerical simulation of a supersonic turbulent boundary layer has been performed. We take advantage of a technique developed by Spalart for incompressible flow. In this technique, it is assumed that the boundary layer grows so slowly in the streamwise direction that the turbulence can be treated as approximately homogeneous in this direction. The slow growth is accounted for by a coordinate transformation and a multiple-scale analysis. The result is a modified system of equations, in which the flow is homogeneous in both the streamwise and spanwise directions, and which represents the state of the boundary layer at a given streamwise location. The equations are solved using a mixed Fourier and B-spline Galerkin method.Results are presented for a case having an adiabatic wall, a Mach number of M = 2.5, and a Reynolds number, based on momentum integral thickness and wall viscosity, of Reθ′ = 849. The Reynolds number based on momentum integral thickness and free-stream viscosity is Reθ = 1577. The results indicate that the Van Driest transformed velocity satisfies the incompressible scalings and a small logarithmic region is obtained. Both turbulence intensities and the Reynolds shear stress compare well with the incompressible simulations of Spalart when scaled by mean density. Pressure fluctuations are higher than in incompressible flow. Morkovin's prediction that streamwise velocity and temperature fluctuations should be anti-correlated, which happens to be supported by compressible experiments, does not hold in the simulation. Instead, a relationship is found between the rates of turbulent heat and momentum transfer. The turbulent kinetic energy budget is computed and compared with the budgets from Spalart's incompressible simulations.

scholarly journals Low Reynolds number k-ε modeling by using the direct numerical simulation (DNS) data

2008 ◽  
pp. 48-65
Keyword(s):  
Numerical Simulation ◽  
Boundary Layer ◽  
Reynolds Number ◽  
Direct Numerical Simulation ◽  
Boundary Layer Flow ◽  
Low Reynolds Number ◽  
Reynolds Numbers ◽  
Damping Function ◽  
Layer Flow ◽  
Near Wall

The constant C and the near-wall damping function f in the eddyviscosityrelation of the k-ε model are evaluated from direct numerical simulation (DNS) data for developed channel and boundary-layer flow, eachat two Reynolds numbers. Various existing

Direct Numerical Simulation of Turbulent Flow and Aeroacoustic Fields Around an Airfoil Using Lattice Boltzmann Method

2016 ◽  
Author(s):  
Kazuya Kusano ◽  
Kazutoyo Yamada ◽  
Masato Furukawa ◽  
Kil-Ju Moon
Keyword(s):  
Numerical Simulation ◽  
Boundary Layer ◽  
Reynolds Number ◽  
Direct Numerical Simulation ◽  
Lattice Boltzmann Method ◽  
Lattice Boltzmann ◽  
Separated Flow ◽  
Broadband Noise ◽  
Suction Surface ◽  
Boltzmann Method

The paper presents a result of the direct numerical simulation with the lattice Boltzmann method which was conducted for quantitative prediction of turbulent broadband noise. For better prediction of broadband noise with high frequency, which is generally generated in high Reynolds number flows, not only high grid resolution is required for a flow simulation to capture very small eddies of the sound source inside the turbulent boundary layer, but also the computation of acoustic field is often needed. In such case, the direct simulation of flow field and acoustic field is straightforward and effective. In this study, the direct simulation with the lattice Boltzmann method was conducted for a flow around the NACA0012 airfoil with the Reynolds number of two hundred thousand. In order to efficiently simulate this high Reynolds number flow with the LBM, the multi-scale approach was introduced in conjunction with the Building-cube method, while keeping the advantage of the LBM with the Cartesian mesh. At the condition with angle-of-attack of 9 degrees, a laminar separation bubble arises on the suction surface near the leading-edge and the suction boundary layer downstream of it is turbulent due to the separated-flow transition. As a result, turbulent broadband noise is generated from the boundary layer over the airfoil with the separated-flow transition. In the paper, as for prediction of such broadband noise, the computed frequency spectrum of far-field sound is validated to agree with the experimental result. In addition, through the detailed analyses of turbulent properties of the turbulent boundary layer on the suction surface, the validity of the present direct numerical simulation is demonstrated.

scholarly journals The Turbulent Flow over the BARC Rectangular Cylinder: A DNS Study

2021 ◽  
Author(s):  
Alessandro Chiarini ◽  
Maurizio Quadrio
Keyword(s):  
Numerical Simulation ◽  
Reynolds Number ◽  
Direct Numerical Simulation ◽  
Finite Differences ◽  
Turbulence Models ◽  
Fine Tuning ◽  
Rectangular Cylinder ◽  
Budget Equation ◽  
Complete Set ◽  
First Time

AbstractA direct numerical simulation (DNS) of the incompressible flow around a rectangular cylinder with chord-to-thickness ratio 5:1 (also known as the BARC benchmark) is presented. The work replicates the first DNS of this kind recently presented by Cimarelli et al. (J Wind Eng Ind Aerodyn 174:39–495, 2018), and intends to contribute to a solid numerical benchmark, albeit at a relatively low value of the Reynolds number. The study differentiates from previous work by using an in-house finite-differences solver instead of the finite-volumes toolbox OpenFOAM, and by employing finer spatial discretization and longer temporal average. The main features of the flow are described, and quantitative differences with the existing results are highlighted. The complete set of terms appearing in the budget equation for the components of the Reynolds stress tensor is provided for the first time. The different regions of the flow where production, redistribution and dissipation of each component take place are identified, and the anisotropic and inhomogeneous nature of the flow is discussed. Such information is valuable for the verification and fine-tuning of turbulence models in this complex separating and reattaching flow.

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