scholarly journals Spectral-element simulations of variable-density turbulent flow in a plane channel

2017 ◽  
Vol 159 ◽  
pp. 00041 ◽  
Author(s):  
Vladimir Ryzhenkov ◽  
Vladislav Ivashchenko ◽  
Ricardo Vinuesa ◽  
Rustam Mullyadzhanov
Keyword(s):  
Turbulent Flow ◽  
Plane Channel ◽  
Spectral Element ◽  
Variable Density

Numerical simulation of reciprocating turbulent flow in a plane channel

2009 ◽  
Vol 21 (9) ◽  
pp. 095106 ◽  
Author(s):  
Massimiliano Di Liberto ◽  
Michele Ciofalo
Keyword(s):  
Numerical Simulation ◽  
Turbulent Flow ◽  
Plane Channel

scholarly journals Incompressible variable-density turbulence in an external acceleration field

2017 ◽  
Vol 827 ◽  
pp. 506-535 ◽  
Author(s):  
Ilana Gat ◽  
Georgios Matheou ◽  
Daniel Chung ◽  
Paul E. Dimotakis
Keyword(s):  
Growth Rate ◽  
Turbulent Flow ◽  
Shear Layers ◽  
Variable Density ◽  
Fluid Composition ◽  
Turbulent Regime ◽  
Low Density ◽  
Acceleration Field ◽  
Density Ratios ◽  
Mixed Fluid

Dynamics and mixing of a variable-density turbulent flow subject to an externally imposed acceleration field in the zero-Mach-number limit are studied in a series of direct numerical simulations. The flow configuration studied consists of alternating slabs of high- and low-density fluid in a triply periodic domain. Density ratios in the range of $1.05\leqslant R\equiv \unicode[STIX]{x1D70C}_{1}/\unicode[STIX]{x1D70C}_{2}\leqslant 10$ are investigated. The flow produces temporally evolving shear layers. A perpendicular density–pressure gradient is maintained in the mean as the flow evolves, with multi-scale baroclinic torques generated in the turbulent flow that ensues. For all density ratios studied, the simulations attain Reynolds numbers at the beginning of the fully developed turbulence regime. An empirical relation for the convection velocity predicts the observed entrainment-ratio and dominant mixed-fluid composition statistics. Two mixing-layer temporal evolution regimes are identified: an initial diffusion-dominated regime with a growth rate ${\sim}t^{1/2}$ followed by a turbulence-dominated regime with a growth rate ${\sim}t^{3}$. In the turbulent regime, composition probability density functions within the shear layers exhibit a slightly tilted (‘non-marching’) hump, corresponding to the most probable mole fraction. The shear layers preferentially entrain low-density fluid by volume at all density ratios, which is reflected in the mixed-fluid composition.

Characteristics of the leading Lyapunov vector in a turbulent channel flow

2018 ◽  
Vol 849 ◽  
pp. 942-967 ◽  
Author(s):  
Nikolay Nikitin
Keyword(s):  
Turbulent Flow ◽  
Buffer Layer ◽  
Stokes Equations ◽  
Initial Conditions ◽  
Spatial Scales ◽  
Plane Channel ◽  
Base Flow ◽  
Lyapunov Vector ◽  
Perturbation Growth ◽  
Near Wall

The values of the highest Lyapunov exponent (HLE)$\unicode[STIX]{x1D706}_{1}$for turbulent flow in a plane channel at Reynolds numbers up to$Re_{\unicode[STIX]{x1D70F}}=586$are determined. The instantaneous and statistical properties of the corresponding leading Lyapunov vector (LLV) are investigated. The LLV is calculated by numerical solution of the Navier–Stokes equations linearized about the non-stationary base solution corresponding to the developed turbulent flow. The base turbulent flow is calculated in parallel with the calculation of the evolution of the perturbations. For arbitrary initial conditions, the regime of exponential growth${\sim}\exp (\unicode[STIX]{x1D706}_{1}t)$which corresponds to the approaching of the perturbation to the LLV is achieved already at$t^{+}<50$. It is found that the HLE increases with increasing Reynolds number from$\unicode[STIX]{x1D706}_{1}^{+}\approx 0.021$at$Re_{\unicode[STIX]{x1D70F}}=180$to$\unicode[STIX]{x1D706}_{1}^{+}\approx 0.026$at$Re_{\unicode[STIX]{x1D70F}}=586$. The LLV structures are concentrated mainly in a region of the buffer layer and are manifested in the form of spots of increased fluctuation intensity localized both in time and space. The root-mean-square (r.m.s.) profiles of the velocity and vorticity intensities in the LLV are qualitatively close to the corresponding profiles in the base flow with artificially removed near-wall streaks. The difference is the larger concentration of LLV perturbations in the vicinity of the buffer layer and a relatively larger (by approximately 80 %) amplitude of the vorticity pulsations. Based on the energy spectra of velocity and vorticity pulsations, the integral spatial scales of the LLV structures are determined. It is found that LLV structures are on average twice narrower and twice shorter than the corresponding structures of the base flow. The contribution of each of the terms entering into the expression for the production of the perturbation kinetic energy is determined. It is shown that the process of perturbation development is essentially dictated by the inhomogeneity of the base flow, as well as by the presence of transversal motion in it. Neglecting of these factors leads to a significant underestimation of the perturbation growth rate. The presence of near-wall streaks in the base flow, on the contrary, does not play a significant role in the development of the LLV perturbations. Artificial removal of streaks from the base flow does not change the character of the perturbation growth.

II. Determination of constitutive coefficients and illustrative examples

1989 ◽  
Vol 327 (1595) ◽  
pp. 449-475 ◽  
Keyword(s):  
Turbulent Flow ◽  
Constitutive Equations ◽  
Theoretical Calculations ◽  
Equations Of Motion ◽  
Plane Channel ◽  
General System ◽  
Turbulent Fluctuation ◽  
System Of Equations ◽  
Constitutive Response

This paper is a continuation of Part I under the same title and is concerned mainly with the determination of the constitutive response coefficients, as well as some simple illustrative examples. First, a system of simplified constitutive equations for incompressible viscous turbulent flow is obtained from the more general system of equations in Part I through a judicial choice of retaining only those terms which appear to represent major features of the turbulent flow. Even for this simplified system of equations, the identification of some of the constitutive coefficients presents a formidable task; and this is especially true in the case of those coefficients that are associated with the presence of the additional independent variables of the theory due to the manifestation of the alignment of eddies (on the microscopic scale), turbulent fluctuation and eddy density. Because of this difficulty, the present effort for identification of the various constitutive coefficients must be regarded partly as tentative, pending future availability of suitable relevant experimental data and/or pertinent numerical simulation results. Keeping this background in mind, most of the relevant coefficients in the constitutive equations are determined, or the nature of their functional forms are estimated, through consideration of‘cartoon-like’ models on the microscopic level and these results are then used in conjunction with the macroscopic equations of motion to examine a number of simple solutions. These include the possibility of a flow possessing a constant uniform velocity gradient and solutions pertaining to decay of flow anisotropy and plane turbulent channel flows. The predicted theoretical calculations are in general accord with experimental observations. In addition, for plane channel flow, plots of variation along the width of the channel for the turbulent temperature and the macroscopic velocity compare favourably with corresponding known experimental results.

Implementation and Validation of a Hybrid RANS/LES Model in the Spectral Element Solver Nek5000

2014 ◽  
Author(s):  
S. Bhushan ◽  
D. K. Walters ◽  
E. Merzari ◽  
A. Obabko
Keyword(s):  
Channel Flow ◽  
Large Scale ◽  
Nuclear Reactor ◽  
Plane Channel ◽  
Spectral Element ◽  
Small Scale ◽  
Test Case ◽  
Additional Contribution ◽  
Turbulent Structures ◽  
High Reynolds

A dynamic hybrid RANS/LES (DHRL) model has been implemented in the spectral-element solver Nek5000 to reduce computational expense for high Reynolds number applications. The model couples a k-ε URANS model and the dynamic Smagorinsky model for LES. The model is validated for plane channel flow at Reτ = 590 using DNS data, and compared with LES predictions. The model is then applied for the ANL-MAX case, which is a test case relevant to nuclear reactor cooling flow simulations. For the channel flow case, DHRL predictions were similar to LES on finer grids, but on coarser grids, the former predicted velocity profiles closer to DNS than the latter in the log-layer region. The improved prediction by the DHRL model was identified to be due to a 30% additional contribution of RANS stresses. For the ANL-MAX case, the URANS simulation predicts quasi-steady flow, with dominant large-scale turbulent structures, whereas LES predicts small-scale turbulent structures comparable with results in rapid mixing of cool and warm flow jets. DHRL simulations predict LES mode in the inlet jet region, and URANS mode elsewhere, as expected.

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