Ratio Of Turbulent Kinetic Energy Research Articles

Towards a self-consistent Boltzmann's kinetic model of fluid turbulence

A closure for the effective relaxation time of the Boltzmann–BGK kinetic equation for fluid turbulence is presented, based on a double-averaging procedure over both kinetic and turbulent fluctuations. The resulting effective relaxation time appears to agree with values obtained via a renormalisation group treatment of the Navier–Stokes equation only at low values of k/T, the ratio of turbulent kinetic energy to fluid temperature. For the kinetic treatment delivers a significantly longer effective relaxation time.

A comparative study of turbulence models for non-premixed swirl-stabilized flames

ABSTRACTThe accuracy of turbulent swirl-stabilized flame simulation strongly depends on the choice of turbulence model. In this study, four 3D unsteady turbulence closures, including large eddy simulation, scale-adaptive simulation, and two detached eddy simulation variants, along with four RANS models, including RNG k−ϵ, SST k−ω, transition SST, and RSM, are examined for moderate- and high-swirl case studies. It is observed that the scale-adaptive simulation provides the most accurate results for almost all variables and both swirl conditions in the reactive flow. Only the 3D unsteady models predict the vortex breakdown bubble and flame attachment state correctly. However, based on our error analysis, the flow and composition fields predicted by the RANS models are in acceptable agreement with the experimental fields, especially the ones of transition SST when higher swirl number cases or minor species concentration are of interest. Moreover, it is concluded that the viscosity ratio criterion is a better measure of the local LES quality than the turbulent kinetic energy ratio, and the accuracy of a hybrid simulation may be much more dependent on the ability of the model to operate close to the RANS mode where the grid resolution is not sufficient for a resolving simulation than the fraction of the resolved kinetic energy. Finally, the propriety of the base (RANS) model of a DES for the application of interest is important, such that DES with realizable k−ϵ outperforms the commonly used DES with SST k−ω model.

The properties of dilute debris flow and hyper-concentrated flow in different flow regimes in open channels

Particle Image Velocimetry (PIV) technique was used to test the analogues of hyper-concentrated flow and dilute debris flow in an open flume. Flow fields, velocity profiles and turbulent parameters were obtained under different conditions. Results show that the flow regime depends on coarse grain concentration. Slurry with high fine grain concentration but lacking of coarse grains behaves as a laminar flow. Dilute debris flows containing coarse grains are generally turbulent flows. Streamlines are parallel and velocity values are large in laminar flows. However, in turbulent flows the velocity diminishes in line with the intense mixing of liquid and eddies occurring. The velocity profiles of laminar flow accord with the parabolic distribution law. When the flow is in a transitional regime, velocity profiles deviate slightly from the parabolic law. Turbulent flow has an approximately uniform distribution of velocity and turbulent kinetic energy. The ratio of turbulent kinetic energy to the kinetic energy of time-averaged flow is the internal cause determining the flow regime: laminar flow (k/K 1). Turbulent kinetic energy firstly increases with increasing coarse grain concentration and then decreases owing to the suppression of turbulence by the high concentration of coarse grains. This variation is also influenced by coarse grain size and channel slope. The results contribute to the modeling of debris flow and hyper-concentrated flow.

RAYLEIGH-TAYLOR INSTABILITY IN A RELATIVISTIC FIREBALL ON A MOVING COMPUTATIONAL GRID

We numerically calculate the growth and saturation of the Rayleigh-Taylor instability caused by the deceleration of relativistic outflows with Lorentz factor {\Gamma} = 10, 30, and 100. The instability generates turbulence whose scale exhibits strong dependence on Lorentz factor, as only modes with angular size smaller than 1/{\Gamma} can grow. We develop a simple diagnostic to measure the kinetic energy in turbulent fluctuations, and calculate a ratio of turbulent kinetic energy to thermal energy of .03 in the region affected by the instability. Although our numerical calculation does not include magnetic fields, we argue that small scale turbulent dynamo amplifies magnetic fields to nearly this same fraction, giving a ratio of magnetic to thermal energy of ~ .01, to within a factor of two. The instability completely disrupts the contact discontinuity between the ejecta and the swept up circumburst medium. The reverse shock is stable, but is impacted by the Rayleigh-Taylor instability, which strengthens the reverse shock and pushes it away from the forward shock. The forward shock front is unaffected by the instability, but Rayleigh-Taylor fingers can penetrate of order 10% of the way into the energetic region behind the shock during the two-shock phase of the explosion. We calculate afterglow emission from the explosion and find the reverse shock emission peaks at a later time due to its reduced Lorentz factor and modified density and pressure at the shock front. These calculations are performed using a novel numerical technique that includes a moving computational grid. The moving grid is essential as it maintains contact discontinuities to high precision and can easily evolve flows with extremely large Lorentz factors.

Ionizing feedback from massive stars in massive clusters - II. Disruption of bound clusters by photoionization

We present an SPH parameter study of the dynamical effect of photoionization from O--type stars on star--forming clouds of a range of masses and sizes during the time window before supernovae explode. Our model clouds all have the same degree of turbulent support initially, the ratio of turbulent kinetic energy to gravitational potential energy being set to $E_{\rm kin}/|E_{\rm pot}|$=0.7. We allow the clouds to form stars and study the dynamical effects of the ionizing radiation from the massive stars or clusters born within them. We find that dense filamentary structures and accretion flows limit the quantities of gas that can be ionized, particularly in the higher density clusters. More importantly, the higher escape velocities in our more massive (10$^{6}$M$_{\odot}$) clouds prevent the HII regions from sweeping up and expelling significant quantities of gas, so that the most massive clouds are largely dynamically unaffected by ionizing feedback. However, feedback has a profound effect on the lower--density 10$^{4}$ and 10$^{5}$M$_{\odot}$ clouds in our study, creating vast evacuated bubbles and expelling tens of percent of the neutral gas in the 3Myr timescale before the first supernovae are expected to detonate, resulting in clouds highly porous to both photons and supernova ejecta.

Nonlinear Lagrangian equations for turbulent motion and buoyancy in inhomogeneous flows

Linear and nonlinear Lagrangian equations are derived for stochastic processes that appear as solutions of the averaged hydrodynamic equations, since their moments satisfy the budgets given by these equations. These equations include the potential temperature, so that non-neutral flows can be described. They will be compared with nonlinear and non-Markovian equations that are obtained using concepts of nonequilibrium statistical mechanics. This approach permits the description of turbulent motion and buoyancy, where memory effects and driving forces with arbitrary colored noise may occur. The equations depend on assumptions that concern the dissipation and pressure redistribution. In the approximations of Kolmogorov and Rotta for these terms, the dissipation time scale remains open, which can be determined by the calculation of the production–dissipation ratio of turbulent kinetic energy. The features of these equations are illustrated by the calculation of turbulent states in the space of invariants.

Three-component LDA measurements in a turbulent boundary layer

An experimental study of a three-dimensional, pressuredriven, attached turbulent boundary-layer flow was made at Mach 0.4. Both the mean velocities and the full Reynolds stress tensor were measured simultaneously by a three-component LDA system. Value of the resultant shear stress to turbulent kinetic energy ratio varied between 0.1 and 0.2 and did not remain constant across the boundary-layer. Slopes of the streamwise and azimuthal mixing length distributions in the wall region were around 0.4 and 1.2, respectively. Skew angle of the turbulent shear stress was larger than skew angle of the velocity gradient.

Large-scale disruptions in a current-carrying magnetofluid

A pseudo-spectral three-dimensional Strauss-equations code is used to describe internal disruptions in a strongly magnetized, electrically-conducting fluid, with and without an externally applied, axial electric field. Rigid conducting walls form a square (x, y) boundary, and periodic boundary conditions are assumed in the axial (z) direction. Typical resolution is 64 × 64 × 32 and the maximum Lundquist number is approximately 400. The dynamics are dominated by a helical current filament which wraps itself around the axis of the cylinder; parts of this filament can sometimes become strongly negative. The ratio of turbulent kinetic energy to total poloidal magnetic energy rises from very small values to values of the order of a few hundredths, and executes ‘bounces’ as a function of time in the absence of the external electric field. In the presence of the external electric field, the first bounce is by far the largest, then the plasma settles into a non-uniform quasi-steady state characterized by a poloidal fluid velocity flow. At the large scales, this flow has the shape of a pair of counter-rotating bean-shaped vortices. The subsequent development of this fluid flow depends strongly upon whether or not a viscous term is added to the equation of motion. Inclusion of viscosity tends to damp the flow and leads to pronounced subsequent bounces suggestive of sawtooth oscillations, though the first bounce remains substantially the largest. By means of a three-mode (Lorenz-like) truncation of the Strauss equations, the evolution of the largest spatial scales alone may be examined. Some time-dependent solutions of the low-order truncation system suggest qualitative agreement with fully resolved solutions of the Strauss equations, while other solutions exhibit interesting dynamical-systems behaviour which is thus far unparalleled in the fully-resolved simulation results.