An algebraic stress model for stratified turbulent shear flows

Utilizing a simple time dependent one dimensional example as a test case this paper discusses a solution which represents the important characteristics of a bouyancy dominated shear flow by solving four partial differential equations in addition to the mean equations of motion. This suggested model solves equations for total turbulent kinetic energy, $\text{k}$, total turbulent temperature fluctuations, $\text{k}{}_{\mathrm{t}}$, eddy dissipation, ?, and thermal eddy dissipation, ?_$\text{t}$. Three separate versions of this model are discussed—an algebraic length scale version, a Prandtl-Kolmogorov eddy viscosity version, and an algebraic stress and heat flux model. The final version (requiring six partial differential equations) manages to replicate results for a much more complicated version (requiring ten partial differential equations). The advantages for two and three dimensional problems are even greater.     

Small scale localization in turbulent flows. A priori tests applied to a possible Large Eddy Simulation of compressible turbulent flows

A method for the localization of small scales in turbulent velocity fields is proposed. The method is based on the definition of a function f of the velocity and vorticity fields that reproduces a normalized form of the twisting-stretching term of the Helmholtz equation. By means of this method the equations of motion can be selectively filtered in regions that are rich in small scale motions. The method is applied through a criterion built on a statistical link between the function f and a local property of the turbulence that was derived from the analysis a homogeneous and isotropic high Reynolds number (Reλ=280) turbulence field. The localization criterion is independent of the subgrid scale model used in a possible Large Eddy Simulation carried out after the small scale localization is obtained. This extends the typology of possible applications to the analysis of experimental laboratory data. In case of compressible regimes, a second sensor that depends on the local pressure variation and divergence can be associated to the previous one in order to determine the eventual emergence of shocks. The capture of shocks is made possible by suppressing the subgrid terms where this second sensor indicates the presence of a shock.A priori tests were carried out on the turbulent channel flow, Reλ=180 and 590, to validate the localization procedure in a highly inhomogeneous flow configuration. A second set of a priori test was carried out on a turbulent time decaying jet which initiates its evolution at Mach 5 and which reproduces a few hydrodynamical properties of high Reynolds number hypersonic jets which exist in the Universe.     

Numerical simulation of turbulent reactive flows

A direct numerical simulation of a turbulent homogeneous field is used study the decay of the concentration of a scalar quantity which is advected, diffused and undergoes the effect of a sink term which models the effect of a chemical reaction. The reaction rate and the one-species formulation used herein are oriented towards the simulation of the combustion of a premixed gas in order to study various quantities useful for turbulent combustion models. Computations yield results depending on the “chemical time” under the form of various probability density functions (PDF) calculated from the realizations of the reactive scalar fields.     

A numerical investigation of turbulent flows in a spanwise rotating channel

A numerical investigation of fully developed turbulent flow in a spanwise rotating channel is performed to study turbulence characteristics subject to system rotation. The work provides insight into several salient features of the spanwise rotating turbulent channel flows, including the near-wall vortical structures, turbulence energy cascade and redistribution, and vortex stretching. The influence of system rotation on the near-wall vortical structures is investigated based on the vorticity fluctuations and their probability density functions (PDF). The properties of the Lamb vector fluctuation and the corresponding PDF are examined to reveal the effect of rotation on the turbulence energy cascade and production in the rotating channel. The budgets of Reynolds stresses and fluctuating enstrophy are analyzed to elucidate the role of the Coriolis force on turbulence energy redistribution between the streamwise and wall-normal directions and the mechanisms of vortex stretching for the generation of the vorticity fluctuations near the pressure and suction walls.     

The numerical computation of turbulent flows

The paper reviews the problem of making numerical predictions of turbulent flow. It advocates that computational economy, range of applicability and physical realism are best served at present by turbulence models in which the magnitudes of two turbulence quantities, the turbulence kinetic energy $\text{k}$ and its dissipation rate ?, are calculated from transport equations solved simultaneously with those governing the mean flow behaviour. The width of applicability of the model is demonstrated by reference to numerical computations of nine substantially different kinds of turbulent flow.     

Parameter-free symmetry-preserving regularization modeling of a turbulent differentially heated cavity

Since direct numerical simulations of buoyancy driven flows cannot be computed at high Rayleigh numbers, a dynamically less complex mathematical formulation is sought. In the quest for such a formulation, we consider regularizations (smooth approximations) of the non-linearity: the convective term is altered to reduce the production of small scales of motion by means of vortex stretching. In doing so, we propose to preserve the symmetry and conservation properties of the convective terms exactly. This requirement yielded a novel class of regularizations [Comput Fluids 2008;37:887] that restrain the convective production of smaller and smaller scales of motion in an unconditionally stable manner, meaning that the velocity cannot blow up in the energy-norm (in 2D also: enstrophy-norm). The numerical algorithm used to solve the governing equations preserves the symmetry and conservation properties too. In the present work, a criterion to determine dynamically the regularization parameter (local filter length) is proposed: it is based on the requirement that the vortex stretching must stop at the scale set by the grid. Therefore, the proposed method constitutes a parameter-free turbulence model. The resulting regularization method is tested for a 3D natural convection flow in an air-filled (Pr = 0.71) differentially heated cavity of height aspect ratio 4. Direct comparison with DNS results at Rayleigh number 6.4 × 10⁸ ? Ra ? 10¹¹ shows fairly good agreement even for very coarse grids. Finally, the robustness of the method is tested by performing simulations with Ra up to 10¹⁷. A 2/7 scaling law of Nusselt number has been obtained for the investigated range of Ra.     

Adaptive finite-volume solution of complex turbulent flows

This paper describes an automatic local grid adaptation procedure driven by an evaluation of the differential residuals of the RANS equations computed using a higher-order reconstruction operator. A suitable data structure is developed for the local mesh adaptation process to be flexible and low CPU time consuming. The whole procedure is designed in the framework of finite-volume methods on unstructured grids. To avoid the appearance of ill-conditioned near-wall cells in the vicinity of curved surfaces of bodies a global mesh deformation technique is used. The whole procedure is applied to a complex turbulent flow around a high-lift multiple element airfoil in take-off configuration using the Spalart-Allmaras turbulence model. The adaptation is controlled by as many indicators as there are equations involved in the problem. It is demonstrated that the proposed methodology performs rigorous local adaptive mesh refinement and automatically achieves grid independent results. Thus, interesting gains are obtained in terms of CPU time, memory requirement and user effort compared to single mesh computations.     

Low Reynolds number turbulent flows around a dynamically shaped airfoil

A computational investigation for flows surrounding a dynamically shaped airfoil, at a chord Reynolds number of 78,800, is conducted along with a parallel experimental effort. A piezo-actuated flap on the upper surface of a fixed airfoil is adopted for active control. The actuation frequency focused on is 500 Hz. The computational framework consists of a multi-block, moving grid technique, the eⁿ-based laminar-turbulent transition model, the two-equation turbulence closure, and a pressure-based flow solver. The moving grid technique, which handles the geometric variations in time, employs the transfinite interpolation scheme with a spring network approach. Comparing the experimental and computational results for pressure and velocity fields, implications of the detailed flap geometry, the flapping amplitude, turbulence modeling, and grid distributions on the flow structure are assessed. The effect of the flap movement on the separation location and vortex dynamics is also investigated.     

Visualization of vorticity and vortices in wall-bounded turbulent flows

This study was initiated by the scientifically interesting prospect of applying advanced visualization techniques to gain further insight into various spatio-temporal characteristics of turbulent flows. The ability to study complex kinematical and dynamical features of turbulence provides means of extracting the underlying physics of turbulent fluid motion. The objective is to analyze the use of a vorticity field line approach to study numerically generated incompressible turbulent flows. In order to study the vorticity field, we present a field line animation technique which uses a specialized particle advection and seeding strategy. Efficient analysis is achieved by decoupling the rendering stage from the preceding stages of the visualization method. This allows interactive exploration of multiple fields simultaneously, which sets the stage for a more complete analysis of the flow field. Multifield visualizations are obtained using a flexible volume rendering framework which is presented in this paper. Vorticity field lines have been employed as indicators to provide a means to identify "ejection" and "sweep" regions; two particularly important spatio-temporal events in wall-bounded turbulent flows. Their relation to the rate of turbulent kinetic energy production and viscous dissipation, respectively, have been identified.     

Simple stabilizing matrices for the computation of compressible flows in primitive variables

The key ingredient that balances stability and accuracy in stabilized formulations is the parameter of intrinsic time-scales. For multi-dimensional hyperbolic systems of equations, this parameter is a matrix and the available expressions for its computation involve the solution of an eigenvalue problem, which can be tedious or cpu time consuming. Thus, for formulations based on primitive variables including pressure, a couple of simple stabilizing matrices are presented which are easy to implement and cpu-economic. Numerical evaluations show the performance of the various choices.     

Viscous heating in nanoscale shear driven liquid flows

Three-dimensional Molecular Dynamics (MD) simulations of heat and momentum transport in liquid Argon filled shear-driven nano-channels are performed using 6–12 Lennard–Jones potential interactions. Work done by the viscous stresses heats the fluid, which is dissipated through the channel walls, maintained at isothermal conditions through a recently developed interactive thermal wall model. Shear driven nano-flows for weak wetting surfaces (ε _wf /ε ≤ 0.6) are investigated. Spatial variations in the fluid density, kinematic viscosity, shear- and energy dissipation rates are presented. Temperature profiles in the nano-channel are obtained as a function of the surface wettability, shear rate and the intermolecular stiffness of wall molecules. The energy dissipation rate is almost a constant for ε _wf /ε ≤ 0.6, which results in parabolic temperature profiles in the domain with temperature jumps due to the well known Kapitza resistance at the liquid/solid interfaces. Using the energy dissipation rates predicted by MD simulations and the continuum energy equation subjected to the temperature jump boundary conditions developed in [Kim et al. Journal of Chemical Physics, 129, 174701, 2008b], we obtain analytical solutions for the temperature profiles, which agree well with the MD results.     

Neural network-based modelling of subsonic cavity flows

A fundamental problem in the applications involved with aerodynamic flows is the difficulty in finding a suitable dynamical model containing the most significant information pertaining to the physical system. Especially in the design of feedback control systems, a representative model is a necessary tool constraining the applicable forms of control laws. This article addresses the modelling problem by the use of feedforward neural networks (NNs). Shallow cavity flows at different Mach numbers are considered, and a single NN admitting the Mach number as one of the external inputs is demonstrated to be capable of predicting the floor pressures. Simulations and real time experiments have been presented to support the learning and generalization claims introduced by NN-based models.     

Direct numerical simulation of turbulent flows in fuel rod bundles

Numerical methods for solving conservation equations using the DINUS code are presented. The DINUS code has been developed for direct numerical simulation of thermal-hydraulic phenomena in fuel rod bundles. To examine the methods, two test problems have been studied: turbulent flows between parallel plates and in a Triangular-Arrayed rod bundle.     

Spectral element modeling of sediment transport in shear flows

Climate change and accelerated sea level rise coupled with increased human activities in coastal regions have resulted in severe land loss globally. Mitigating coastal erosion requires better understanding and improved capability of modeling sediment transport. This paper presents the methodology and simulation results of a new mathematical model, Virtual Identity Particles, using a spectral/hp element method for sediment transport driven by shear flows. Assimilated the advantages of Eulerian and Lagrangian methods, this model is capable of modeling each individual grain as well as a bulk of numerous grains where frequent collisions between particles and with walls are characterized by the Speed Proportional Collisions. Besides, this model maintains an excellent balance of accuracy and efficiency through its economical considerations in the formulation, allowing modeling a large number of sediment particles. Simulation results demonstrate that this model holds promising potential for investigating sediment transport and the associated land erosion problems.     

Numerical simulation of free surface flows on a fish bypass

A computational fluid dynamics (CFD) model is developed to better understand the complex flow field inside a free surface fish bypass constructed at Rocky Reach Dam. This facility consists of two identical parallel channels, with fish screens on the side walls of each channel, and a pump station recirculating 96% of incoming flows into the forebay. The model is based on the Reynolds-averaged Navier-Stokes (RANS) equations, with a standard κ-ε turbulence model. The volume of fluid (VOF) method is used to predict free surface elevations. A proportional controller is implemented in the model to achieve a target flow rate at the pump exits. The pressure drop in the fish screens is modeled using porous media. Quantitative validation and visualization of the flow field characteristics indicate that CFD modeling may be a useful tool for fish passage design.     

Direct numerical simulation of turbulent flows with chemical reaction

Results from full turbulence simulations incorporating the effects of chemical reaction are compared with simple closure theories and used to reveal some physical insights about turbulent reacting flows. Pseudospectral methods for homogeneous turbulent flows with constant physical and thermal properties in domains as large as 64³ Fourier modes were used for these simulations. For the case of nonpremixed flows involving a two-species, second-order, irreversible chemical reaction, it is found that the scalar dissipation microscale is only a weak function of the reaction rate and that chemical reaction contributes very little to the decay of the variance of the reactant concentration. Examination of local values of the velocity and concentration fields shows that the local reaction rate is highest in regions of the greatest rates of strain and that vorticity tends to align with the reaction zone. Finally, difficulties associated with the evaluation of multipoint pdf's and with the archival of time-dependent data from the threedimensional simulations are described.Presented at the Second Nobeyama Workshop on Fluid Mechanics and Supercomputers, Nobeyama, Japan (September 1987).     

Direct numerical simulation of turbulent channel flows using a stabilized finite element method

Direct numerical simulations (DNS) of incompressible turbulent channel flows at Re_τ = 180 and 395 (i.e., Reynolds number, based on the friction velocity and channel half-width) were performed using a stabilized finite element method (FEM). These simulations have been motivated by the fact that the use of stabilized finite element methods for DNS and LES is fairly recent and thus the question of how accurately these methods capture the wide range of scales in a turbulent flow remains open. To help address this question, we present converged results of turbulent channel flows under statistical equilibrium in terms of mean velocity, mean shear stresses, root mean square velocity fluctuations, autocorrelation coefficients, one-dimensional energy spectra and balances of the transport equation for turbulent kinetic energy. These results are consistent with previously published DNS results based on a pseudo-spectral method, thereby demonstrating the accuracy of the stabilized FEM for turbulence simulations.