scholarly journals DNS Study of the Bending Effect Due to Smoothing Mechanism

Fluids ◽  
2019 ◽  
Vol 4 (1) ◽  
pp. 31 ◽  
Author(s):  
Rixin Yu ◽  
Andrei Lipatnikov
Keyword(s):  
Reaction Zone ◽  
Isotropic Turbulence ◽  
Stokes Equations ◽  
Molecular Transport ◽  
Reaction Diffusion ◽  
Reaction Diffusion Equation ◽  
Small Scale ◽  
Constant Density ◽  
Bending Effect ◽  
Reaction Wave

Propagation of either an infinitely thin interface or a reaction wave of a nonzero thickness in forced, constant-density, statistically stationary, homogeneous, isotropic turbulence is simulated by solving unsteady 3D Navier–Stokes equations and either a level set (G) or a reaction-diffusion equation, respectively, with all other things being equal. In the case of the interface, the fully developed bulk consumption velocity normalized using the laminar-wave speed SL depends linearly on the normalized rms velocity u′/SL. In the case of the reaction wave of a nonzero thickness, dependencies of the normalized bulk consumption velocity on u′/SL show bending, with the effect being increased by a ratio of the laminar-wave thickness to the turbulence length scale. The obtained bending effect is controlled by a decrease in the rate of an increase δAF in the reaction-zone-surface area with increasing u′/SL. In its turn, the bending of the δAF(u′/SL)-curves stems from inefficiency of small-scale turbulent eddies in wrinkling the reaction-zone surface, because such small-scale wrinkles characterized by a high local curvature are smoothed out by molecular transport within the reaction wave.

The turbulent burning velocity for large-scale and small-scale turbulence

1999 ◽  
Vol 384 ◽  
pp. 107-132 ◽  
Author(s):  
N. PETERS
Keyword(s):  
Level Set ◽  
Reaction Zone ◽  
Large Scale ◽  
Burning Velocity ◽  
Small Scale ◽  
Constant Density ◽  
Flame Surface ◽  
Reaction Zones ◽  
Scale Turbulence ◽  
Turbulent Burning Velocity

The level-set approach is applied to a regime of premixed turbulent combustion where the Kolmogorov scale is smaller than the flame thickness. This regime is called the thin reaction zones regime. It is characterized by the condition that small eddies can penetrate into the preheat zone, but not into the reaction zone.By considering the iso-scalar surface of the deficient-species mass fraction Y immediately ahead of the reaction zone a field equation for the scalar quantity G(x, t) is derived, which describes the location of the thin reaction zone. It resembles the level-set equation used in the corrugated flamelet regime, but the resulting propagation velocity s*L normal to the front is a fluctuating quantity and the curvature term is multiplied by the diffusivity of the deficient species rather than the Markstein diffusivity. It is shown that in the thin reaction zones regime diffusive effects are dominant and the contribution of s*L to the solution of the level-set equation is small.In order to model turbulent premixed combustion an equation is used that contains only the leading-order terms of both regimes, the previously analysed corrugated flamelets regime and the thin reaction zones regime. That equation accounts for non-constant density but not for gas expansion effects within the flame front which are important in the corrugated flamelets regime. By splitting G into a mean and a fluctuation, equations for the Favre mean [Gtilde]and the variance [Gtilde]″2 are derived. These quantities describe the mean flame position and the turbulent flame brush thickness, respectively. The equation for [Gtilde]″2 is closed by considering two-point statistics. Scaling arguments are then used to derive a model equation for the flame surface area ratio [rhotilde]. The balance between production, kinematic restoration and dissipation in this equation leads to a quadratic equation for the turbulent burning velocity. Its solution shows the ‘bending’ behaviour of the turbulent to laminar burning velocity ratio sT/sL, plotted as a function of v′/sL. It is shown that the bending results from the transition from the corrugated amelets to the thin reaction zones regimes. This is equivalent to a transition from Damköhler's large-scale to his small-scale turbulence regime.

scholarly journals Small-scale dynamics of dense gas compressible homogeneous isotropic turbulence

2017 ◽  
Vol 825 ◽  
pp. 515-549 ◽  
Author(s):  
L. Sciacovelli ◽  
P. Cinnella ◽  
F. Grasso
Keyword(s):  
Isotropic Turbulence ◽  
Stokes Equations ◽  
Equations Of State ◽  
Vapour Phase ◽  
Small Scale ◽  
Strain Rate Tensor ◽  
Dense Gas ◽  
Homogeneous Isotropic Turbulence ◽  
Third Invariant ◽  
Strong Expansion

The present paper investigates the influence of dense gases governed by complex equations of state on the dynamics of homogeneous isotropic turbulence. In particular, we investigate how differences due to the complex thermodynamic behaviour and transport properties affect the small-scale structures, viscous dissipation and enstrophy generation. To this end, we carry out direct numerical simulations of the compressible Navier–Stokes equations supplemented by advanced dense gas constitutive models. The dense gas considered in the study is a heavy fluorocarbon (PP11) that is shown to exhibit an inversion zone (i.e. a region where the fundamental derivative of gas dynamics $\unicode[STIX]{x1D6E4}$ is negative) in its vapour phase, for pressures and temperatures of the order of magnitude of the critical ones. Simulations are carried out at various initial turbulent Mach numbers and for two different initial thermodynamic states, one immediately outside and the other inside the inversion zone. After investigating the influence of dense gas effects on the time evolution of mean turbulence properties, we focus on the statistical properties of turbulent structures. For that purpose we carry out an analysis in the plane of the second and third invariant of the deviatoric strain-rate tensor. The analysis shows a weakening of compressive structures and an enhancement of expanding ones. Strong expansion regions are found to be mostly populated by non-focal convergence structures typical of strong compression regions, in contrast with the perfect gas that is dominated by eddy-like structures. Additionally, the contribution of non-focal expanding structures to the dilatational dissipation is comparable to that of compressed structures. This is due to the occurrence of steep expansion fronts and possibly of expansion shocklets which contribute to enstrophy generation in strong expansion regions and that counterbalance enstrophy destruction by means of the eddy-like structures.

Direct numerical simulation of turbulence modulation by particles in isotropic turbulence

1998 ◽  
Vol 375 ◽  
pp. 235-263 ◽  
Author(s):  
MARC BOIVIN ◽  
OLIVIER SIMONIN ◽  
KYLE D. SQUIRES
Keyword(s):  
Numerical Simulation ◽  
Kinetic Energy ◽  
Direct Numerical Simulation ◽  
Isotropic Turbulence ◽  
Stokes Equations ◽  
Relaxation Times ◽  
Relative Increase ◽  
Fluid Particle ◽  
Small Scale ◽  
Small Particles

The modulation of isotropic turbulence by particles has been investigated using direct numerical simulation (DNS). The particular focus of the present work is on the class of dilute flows in which particle volume fractions and inter-particle collisions are negligible. Gravitational settling is also neglected and particle motion is assumed to be governed by drag with particle relaxation times ranging from the Kolmogorov scale to the Eulerian time scale of the turbulence and particle mass loadings up to 1. The velocity field was made statistically stationary by forcing the low wavenumbers of the flow. The calculations were performed using 963 collocation points and the Taylor-scale Reynolds number for the stationary flow was 62. The effect of particles on the turbulence was included in the Navier–Stokes equations using the point-force approximation in which 963 particles were used in the calculations. DNS results show that particles increasingly dissipate fluid kinetic energy with increased loading, with the reduction in kinetic energy being relatively independent of the particle relaxation time. Viscous dissipation in the fluid decreases with increased loading and is larger for particles with smaller relaxation times. Fluid energy spectra show that there is a non-uniform distortion of the turbulence with a relative increase in small-scale energy. The non-uniform distortion significantly affects the transport of the dissipation rate, with the production and destruction of dissipation exhibiting completely different behaviours. The spectrum of the fluid–particle energy exchange rate shows that the fluid drags particles at low wavenumbers while the converse is true at high wavenumbers for small particles. A spectral analysis shows that the increase of the high-wavenumber portion of the fluid energy spectrum can be attributed to transfer of the fluid–particle covariance by the fluid turbulence. This in turn explains the relative increase of small-scale energy caused by small particles observed in the present simulations as well as those of Squires & Eaton (1990) and Elghobashi & Truesdell (1993).

scholarly journals Reaction waves and non-constant diffusivities

1996 ◽  
Vol 37 (4) ◽  
pp. 458-473
Author(s):  
S. D. Watt ◽  
R. O. Weber
Keyword(s):  
Diffusion Equation ◽  
Reaction Diffusion ◽  
Reaction Diffusion Equation ◽  
Constant Diffusion ◽  
Stochastic Function ◽  
Spatial Dimensions ◽  
Constant Diffusivity ◽  
Explicit Finite Difference ◽  
Reaction Wave ◽  
Explicit Finite Difference Method

AbstractA reaction-diffusion equation with non-constant diffusivity,ut = (D(x, t)ux)x + F(u),is studied for D(x, t) a continuous function. The conditions under which the equation can be reduced to an equivalent constant diffusion equation are derived. Some exact forms for D(x, t) are given. For D(x, t) a stochastic function, an explicit finite difference method is used to numerically determine the effect of randomness in D(x, t) upon the speed of the reaction wave solution to Fisher's equation. The extension to two spatial dimensions is considered.

Small-scale energy cascade in homogeneous isotropic turbulence

2019 ◽  
Vol 4 (10) ◽  
Author(s):  
Mohamad Ibrahim Cheikh ◽  
James Chen ◽  
Mingjun Wei
Keyword(s):  
Isotropic Turbulence ◽  
Energy Cascade ◽  
Small Scale ◽  
Homogeneous Isotropic Turbulence

scholarly journals Numerical Analysis WSGD Scheme for One- and Two-Dimensional Distributed Order Fractional Reaction–Diffusion Equation with Collocation Method via Fractional B-Spline

2021 ◽  
Vol 7 (2) ◽  
Author(s):  
Mohammad Ramezani
Keyword(s):  
Diffusion Equation ◽  
Collocation Method ◽  
Reaction Diffusion ◽  
Reaction Diffusion Equation ◽  
Two Dimensional ◽  
Algebraic Equations ◽  
B Spline ◽  
Computational Work ◽  
Distributed Order ◽  
Fractional Reaction

AbstractThe main propose of this paper is presenting an efficient numerical scheme to solve WSGD scheme for one- and two-dimensional distributed order fractional reaction–diffusion equation. The proposed method is based on fractional B-spline basics in collocation method which involve Caputo-type fractional derivatives for $$0 < \alpha < 1$$ 0 < α < 1 . The most significant privilege of proposed method is efficient and quite accurate and it requires relatively less computational work. The solution of consideration problem is transmute to the solution of the linear system of algebraic equations which can be solved by a suitable numerical method. The finally, several numerical WSGD Scheme for one- and two-dimensional distributed order fractional reaction–diffusion equation.

Sign in / Sign up

Export Citation Format

Share Document