Jorge Bailon-Cuba

Theoretical evaluation of the Reynolds shear stress and flow parameters in transitionally rough turbulent boundary Layers

The theory by W.K. George and L. Castillo (Zero-pressure gradient turbulent boundary layers, Appl. Mech. Rev. 50 (1997), pp. 689–729) is extended for rough surfaces and numerically implemented on zero pressure gradient turbulent boundary layers. The method is based on the similarity transformations of the Navier–Stokes equations. From these equations, a composite profile for the Reynolds shear stress-⟨ uv⟩ is obtained over the entire boundary layer. The solution is in good agreement with the experiments in the inner and outer regions, for hydraulically smooth (k+ < 5) and transitionally rough surfaces up to roughness parameter of k+ ≈ 55. Beyond this limit, the accuracy of the solutions decreases with k+, especially in the inner region of the mean velocity. However, the accuracy always increases with the Reynolds number, Re_θ. In addition, the eddy viscosity ⟨ ν_T⟩/ν and flow parameters, including the x-dependence, have also been computed and tested with experimental data. Furthermore, the friction power law for smooth/rough surfaces has been used for all calculations and comparisons with direct methods and velocity-based methods are shown to be in good agreement with the theory.

Low-dimensional model of turbulent Rayleigh-Bénard convection in a Cartesian cell with square domain

A low-dimensional model (LDM) for turbulent Rayleigh-Benard convection in a Cartesian cell with square domain, based on the Galerkin projection of the Boussinesq equations onto a finite set of empirical eigenfunctions, is presented. The empirical eigenfunctions are obtained from a joint proper orthogonal decomposition (POD) of the velocity and temperature fields using the snapshot method on the basis of direct numerical simulation (DNS). The resulting LDM is a quadratic inhomogeneous system of coupled ordinary differential equations which we use to describe the long-time temporal evolution of the large-scale mode amplitudes for a Rayleigh number of 105 and a Prandtl number of 0.7. The truncation to a finite number of degrees of freedom, which does not exceed a number of 310 for the present, requires the additional implementation of an eddy viscosity-diffusivity to capture the missing dissipation of the small-scale modes. The magnitude of this additional dissipation mechanism is determined by taking statis...

Inner and Outer Scalings in Rough Surface Turbulent Boundary Layers

The incompressible, zero-pressure-gradient turbulent boundary layer is investigated in light of the effect of the Reynolds number and surface roughness. The experimental data from various researchers has been collected and analyzed in order to study the effect of the roughness on the inner and outer flow. The scalings of George and Castillo (GC) (1997) for the mean velocity profiles and Reynolds stresses are used for the analysis and compared with the results of the classical scalings. Moreover, the true asymptotic profile (self-preserving) solution for the velocity deficit profiles is found when the profiles are normalized by the Zagarola/Smits (1998) scaling, U∞δ /δ. This scaling successfully removes the effects of the Reynolds number, the upstream conditions, and the roughness from the outer flow. Similarly, the classical scaling, uτ , tends to remove the effects from the outer flow but not in the inner region. However, it will be shown that as the roughness parameter, k, increases beyond k ≈ 28 or less, the Reynolds stresses and velocity profiles are influenced in the outer flow by roughness. This limit corresponds to the lower limit of the outer region of a boundary layer, thus the outer flow is affected by roughness beyond this limit. However, for the inner layer, the Reynolds stresses are sensitive to values of the roughness parameter, k ≈ 0.4 while the velocity profiles are affected for values of about k ≈ 17.

Large Eddy Simulations and Direct Numerical Simulations using Equilibrium Similarity Methods for Turbulent Boundary Layers

Bohr et al. [1] carried out Direct Numerical Simulations (DNS) and Large Eddy Simulations (LES) on a at plate turbulent boundary layer, considering an ino w condition for mean velocity and its uctuations on nonperiodic domains. The solution was rescaled from an internal downstream position using similarity tools in order to nd the velocity and temporal scalings. The downstream position was chosen such that the uctuations between this position and the ino w were decorrelated. The scaling laws based on the theory by George and Castillo, 1997 (GC-97) for at plate turbulent boundary layer were used and compared to the rescaling proposed by Lund, Wu and Squires [12]. Two simulations were performed for Reynolds number of R 1700 at the inlet. In the rst one, the scaling used was based on the classical theory of turbulent boundary layers while the second was based on the proposed scaling via similarity of the Navier-Stokes equations. However, they were not able to perform DNS at R > 2000. In this investigation we seek to carry out DNS for R 2500 and zero pressure gradient, by using the multiscale approach proposed by Bohr et al. and GC-97.

Inflow Generation Technique for Large Eddy Simulation using Equilibrium Similarity Analysis

When using Large Eddy Simulation (LES) on domains that are non-periodic in the streamwise direction, the inflow condition for velocity is specified by using a RANS solution for the mean quantities at the inflow. But as LES resolves large eddies, the solved velocity is instantaneous, thus the mean velocity imposed at the inflow boundary condition needs to be completed by also specifying the fluctuations. The solution can be rescaled from an internal downstream position using self-similarity of the turbulent boundary layer flows. The downstream position is chosen such that the fluctuations between this recycling position and the inflow are decorrelated. In this work, the scaling for the fluctuations are derived using the equilibrium similarity analysis based on the theory by George and Castillo (1997). Two large eddy simulations of turbulent flat plate boundary layers at zero pressure gradient are performed. In the first one, the scaling used is based on the classical theory of turbulent boundary layers. In the second the proposed scaling is used. Their solutions are compared to experimental data for zero pressure gradient of turbulent flat plate boundary layer. Both LES solutions give good agreement with experimental data and the equilibrium similarity analysis theory.