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Showing papers on "K-epsilon turbulence model published in 2007"


Journal ArticleDOI
TL;DR: In this paper, an LES-type variational multiscale theory of turbulence is presented, which derives completely from the incompressible Navier-Stokes equations and does not employ any ad hoc devices such as eddy viscosities.

967 citations


Journal ArticleDOI
TL;DR: Pipe flow is a prominent example among the shear flows that undergo transition to turbulence without mediation by a linear instability of the laminar profile as discussed by the authors, which can consistently be explained on the assumption that the turbulent state corresponds to a chaotic saddle in state space.
Abstract: Pipe flow is a prominent example among the shear flows that undergo transition to turbulence without mediation by a linear instability of the laminar profile. Experiments on pipe flow, as well as plane Couette and plane Poiseuille flow, show that triggering turbulence depends sensitively on initial conditions, that between the laminar and the turbulent states there exists no intermediate state with simple spatial or temporal characteristics, and that turbulence is not persistent, i.e., it can decay again, if the observation time is long enough. All these features can consistently be explained on the assumption that the turbulent state corresponds to a chaotic saddle in state space. The goal of this review is to explain this concept, summarize the numerical and experimental evidence for pipe flow, and outline the consequences for related flows.

548 citations


Journal ArticleDOI
TL;DR: In this article, a series of numerical simulations were conducted to study the transport and deposition of nano- and micro-particles in a turbulent duct flow using different turbulence models, and the importance of turbulence model, boundary conditions, and turbulence fluctuation particularly near wall on particle transport, deposition, and particle trajectory analysis were performed with the in-house PARTICLE (object-oriented C++) code, as well as with FLUENTTM code with and the use of user's defined subroutines.

324 citations


Journal ArticleDOI
TL;DR: In this article, a total of 21 planar fractal grids pertaining to three different fractal families have been used in two different wind tunnels to generate turbulence The resulting turbulent flows have been studied using hot wire anemometry.
Abstract: A total of 21 planar fractal grids pertaining to three different fractal families have been used in two different wind tunnels to generate turbulence The resulting turbulent flows have been studied using hot wire anemometry Irrespective of fractal family, the fractal-generated turbulent flows and their homogeneity, isotropy, and decay properties are strongly dependent on the fractal dimension Df≤2 of the grid, its effective mesh size Meff (which we introduce and define) and its ratio tr of largest to smallest bar thicknesses, tr=tmax∕tmin With relatively small blockage ratios, as low as σ=25%, the fractal grids generate turbulent flows with higher turbulence intensities and Reynolds numbers than can be achieved with higher blockage ratio classical grids in similar wind tunnels and wind speeds U The scalings and decay of the turbulence intensity u′∕U in the x direction along the tunnel’s center line are as follows (in terms of the normalized pressure drop CΔP and with similar results for v′∕U and w′∕U)

304 citations


Journal ArticleDOI
TL;DR: A review of recently developed turbulence models adapted to the gridless smoothed particle hydrodynamics (SPH) method is presented in this paper, from the simplistic point of view of a one-equation model involving mixing length to more sophisticated (and thus realistic) models like explicit algebraic Reynolds stress models (EARSM) or large eddy simulation (LES).
Abstract: The gridless smoothed particle hydrodynamics (SPH) method is now commonly used in computational fluid dynamics (CFD) and appears to be promising in predicting complex free-surface flows. However, increasing flow complexity requires appropriate approaches for taking account of turbulent effects, whereas some authors are still working without any turbulence closure in SPH. A review of recently developed turbulence models adapted to the SPH method is presented herein, from the simplistic point of view of a one-equation model involving mixing length to more sophisticated (and thus realistic) models like explicit algebraic Reynolds stress models (EARSM) or large eddy simulation (LES). Each proposed model is tested and validated on the basis of schematic cases for which laboratory data, theoretical or numerical solutions are available in the general field of turbulent free-surface incompressible flows (e.g. open-channel flow and schematic dam break). They give satisfactory results, even though some progress should be made in the future in terms of free-surface influence and wall conditions. Recommendations are given to SPH users to apply this method to the modelling of complex free-surface turbulent flows. Copyright © 2006 John Wiley & Sons, Ltd.

260 citations


Journal ArticleDOI
TL;DR: A growing body of experimental and observational data indicates that turbulence survives for Ri ≫ 1 as discussed by the authors, supported by a new spectral theory of turbulence that accounts for strong anisotropy and waves.

245 citations


Journal ArticleDOI
TL;DR: The repulsive force term of the social force model is extended and the empirical features characterizing crowd turbulence, such as the structure function and the probability density function of velocity increments, are reproduced well and well compatible with an analysis of video data during the annual Muslim pilgrimage.
Abstract: A recent study [D. Helbing, A. Johansson, and H. Z. Al-Abideen, Phys. Rev. E 75, 046109 (2007)] has revealed a "turbulent" state of pedestrian flows, which is characterized by sudden displacements and causes the falling and trampling of people. However, turbulent crowd motion is not reproduced well by current many-particle models due to their insufficient representation of the local interactions in areas of extreme densities. In this contribution, we extend the repulsive force term of the social force model to reproduce crowd turbulence. We perform numerical simulations of pedestrians moving through a bottleneck area with this model. The transitions from laminar to stop-and-go and turbulent flows are observed. The empirical features characterizing crowd turbulence, such as the structure function and the probability density function of velocity increments, are reproduced well; i.e., they are well compatible with an analysis of video data during the annual Muslim pilgrimage.

193 citations


Journal ArticleDOI
TL;DR: The rough-wall boundary layer is characterized by packets of hairpin vortices which induce low-speed regions with regular span-wise spacing as mentioned in this paper, and the same types of structure are observed for the rough- and smooth-wall flows.
Abstract: Turbulence measurements for rough-wall boundary layers are presented and compared to those for a smooth wall. The rough-wall experiments were made on a woven mesh surface at Reynolds numbers approximately equal to those for the smooth wall. Fully rough conditions were achieved. The present work focuses on turbulence structure, as documented through spectra of the fluctuating velocity components, swirl strength, and two-point auto- and cross-correlations of the fluctuating velocity and swirl. The present results are in good agreement, both qualitatively and quantitatively, with the turbulence structure for smooth-wall boundary layers documented in the literature. The boundary layer is characterized by packets of hairpin vortices which induce low-speed regions with regular spanwise spacing. The same types of structure are observed for the rough- and smooth-wall flows. When the measured quantities are normalized using outer variables, some differences are observed, but quantitative similarity, in large part, holds. The present results support and help to explain the previously documented outer-region similarity in turbulence statistics between smooth- and rough-wall boundary layers.

183 citations


Journal ArticleDOI
TL;DR: In this paper, the effects of initial conditions on grid turbulence are investigated for low to moderate Reynolds numbers, and the results show that these effects are primarily related to deviations between the turbulence produced in the wind tunnel and true decaying homogenous isotropic turbulence (HIT).
Abstract: The effects of initial conditions on grid turbulence are investigated for low to moderate Reynolds numbers. Four grid geometries are used to yield variations in initial conditions and a secondary contraction is introduced to improve the isotropy of the turbulence. The hot-wire measurements, believed to be the most detailed to date for this flow, indicate that initial conditions have a persistent impact on the large-scale organization of the flow over the length of the tunnel. The power-law coefficients, determined via an improved method, also depend on the initial conditions. For example, the power-law exponent m is affected by the various levels of large-scale organization and anisotropy generated by the different grids and the shape of the energy spectrum at low wavenumbers. However, the results show that these effects are primarily related to deviations between the turbulence produced in the wind tunnel and true decaying homogenous isotropic turbulence (HIT). Indeed, when isotropy is improved and the intensity of the large-scale periodicity, which is primarily associated with round-rod grids, is decreased, the importance of initial conditions on both the character of the turbulence and m is diminished. However, even in the case where the turbulence is nearly perfectly isotropic, m is not equal to -1, nor does it show an asymptotic trend in x towards this value, as suggested by recent analysis. Furthermore, the evolution of the second- and third-order velocity structure functions satisfies equilibrium similarity only approximately.

177 citations


Journal ArticleDOI
TL;DR: In this article, the authors proposed a new turbulence closure model based on the budget equations for the key second moments: turbulent kinetic and potential energies: TKE and TPE (comprising the turbulent total energy: TTE = TKE + TPE) and vertical turbulent fluxes of momentum and buoyancy (proportional to potential temperature).
Abstract: We propose a new turbulence closure model based on the budget equations for the key second moments: turbulent kinetic and potential energies: TKE and TPE (comprising the turbulent total energy: TTE = TKE + TPE) and vertical turbulent fluxes of momentum and buoyancy (proportional to potential temperature). Besides the concept of TTE, we take into account the non-gradient correction to the traditional buoyancy flux formulation. The proposed model permits the existence of turbulence at any gradient Richardson number, Ri. Instead of the critical value of Richardson number separating—as is usually assumed— the turbulent and the laminar regimes, the suggested model reveals a transitional interval, 0.1 1. Predictions from this model are con- sistent with available data from atmospheric and laboratory experiments, direct numerical simulation and large-eddy simulation.

172 citations


Journal ArticleDOI
TL;DR: The objective of this study is to numerically investigate the effects of transition and turbulence on highly localized particle deposition in a respiratory double bifurcation model in order to quantitatively validate CFD results.

Journal ArticleDOI
TL;DR: The probability density functions of the turbulent wave height are found to be asymmetric and thus non-Gaussian and the scaling of those spectra with the mean energy flux is found in disagreement with weak turbulence theory for both regimes.
Abstract: We report the observation of the crossover between gravity and capillary wave turbulence on the surface of mercury. The probability density functions of the turbulent wave height are found to be asymmetric and thus non-Gaussian. The surface wave height displays power-law spectra in both regimes. In the capillary region, the exponent is in fair agreement with weak turbulence theory. In the gravity region, it depends on the forcing parameters. This can be related to the finite size of the container. In addition, the scaling of those spectra with the mean energy flux is found in disagreement with weak turbulence theory for both regimes.

Journal ArticleDOI
TL;DR: In this paper, a Reynolds-averaged Navier-Stokes equations (RANS) model with the renormalization group (RNG) k-e turbulence model was developed for reactive pollutant dispersion in an urban street canyon with a street aspect ratio of one.

Journal ArticleDOI
TL;DR: In this paper, the scaling law of supersonic turbulence implies a momentum cascade analogous to the energy cascade in Kolmogorov turbulence, and the model is generalized to account for a diversity of outflow strengths and for outflow collimation.
Abstract: Protostellar outflows crisscross the regions of star cluster formation, stirring turbulence and altering the evolution of the forming cluster. We model the stirring of turbulent motions by protostellar outflows, building on an observation that the scaling law of supersonic turbulence implies a momentum cascade analogous to the energy cascade in Kolmogorov turbulence. We then generalize this model to account for a diversity of outflow strengths and for outflow collimation, both of which enhance turbulence. For a single value of its coupling coefficient, the model is consistent with turbulence simulations by Li & Nakamura and, plausibly, with observations of the NGC 1333 cluster-forming region. Outflow-driven turbulence is strong enough to stall collapse in cluster-forming regions for several crossing times, relieving the mismatch between star formation and turbulent decay rates. The predicted line width-size scaling implies radial density indices between -1 and -2 for regions supported by outflow-driven turbulence, with a tendency for steeper profiles in regions that are more massive or have higher column densities.

Journal ArticleDOI
TL;DR: In this article, the Hasegawa-Wakatani equations, coupling plasma density, and electrostatic potential through an approximation to the physics of parallel electron motions, are a simple model that describes resistive drift wave turbulence.
Abstract: The Hasegawa-Wakatani equations, coupling plasma density, and electrostatic potential through an approximation to the physics of parallel electron motions, are a simple model that describes resistive drift wave turbulence. Numerical analyses of bifurcation phenomena in the model are presented, that provide new insights into the interactions between turbulence and zonal flows in the tokamak plasma edge region. The simulation results show a regime where, after an initial transient, drift wave turbulence is suppressed through zonal flow generation. As a parameter controlling the strength of the turbulence is tuned, this zonal-flow-dominated state is rapidly destroyed and a turbulence-dominated state re-emerges. The transition is explained in terms of the Kelvin-Helmholtz stability of zonal flows. This is the first observation of an upshift of turbulence onset in the resistive drift wave system, which is analogous to the well-known Dimits shift in turbulence driven by ion temperature gradients.

Journal ArticleDOI
TL;DR: In this article, a non-equilibrium homogeneous buoyantly driven problem is proposed as a unit problem for variable density turbulence to study the transition to turbulence and the generation of turbulence by the conversion of potential to kinetic energy.
Abstract: Buoyancy-generated motions in an unstably stratified medium composed of two incompressible miscible fluids with different densities, as occurs in the variable-density Rayleigh–Taylor instability, are examined using direct numerical simulations. The non-equilibrium homogeneous buoyantly driven problem is proposed as a unit problem for variable density turbulence to study: (i) the nature of variable density turbulence, (ii) the transition to turbulence and the generation of turbulence by the conversion of potential to kinetic energy; (iii) the role of non-Boussinesq effects; and (iv) a parameterization of the initial conditions by a static Reynolds number. Simulations are performed for Atwood numbers up to 0.5 with root mean square density up to 50% of the mean density and Schmidt numbers, 0.1 ≤ Sc ≤ 2. The benchmark problem has been designed to have the largest mass flux possible and is, in this configuration, the maximally unstable non-equilibrium flow possible. It is found that the mass flux, owing to its central role in the conversion of potential to kinetic energy, is probably the single most important dynamical quantity to predict in lower-dimensional models. Other primary findings include the evolution of the mean pressure gradient: during the non-Boussinesq portions of the flow, the evolution of the mean pressure gradient is non-hydrostatic (as opposed to a Boussinesq fluid) and is set by the evolution of the specific volume pressure gradient correlation. To obtain the numerical solution, a new pressure projection algorithm which treats the pressure step exactly, useful for simulations of non-solenoidal velocity flows, has been constructed.

Journal ArticleDOI
TL;DR: In this article, the authors investigated the effect of particle-fluid interaction on air-solid pipe flow and showed that the relative reduction of air pressure strain is larger than the reduction of turbulent production and dissipation, and pressure strain may therefore be a cause of the reduction in other quantities.
Abstract: Turbulence characteristics of vertical air-solid pipe flow are investigated in this paper. Direct numerical simulations of the gas phase have been performed, while the solid particles have been simulated by a Lagrangian approach, including particle collisions. The modelling of wall roughness is shown to be important to obtain agreement with experimental data. Reynolds stresses and Reynolds stress budgets are given for both phases and for a wide range of solid-air mass load ratios (mass loads), varying from 0.11 to 30. Air turbulence intensities, Reynolds shear stress, and turbulence production reduce with increasing mass load. The mean air profile does not alter for low mass loads. In this regime, a simple theory predicts that the reduction of air turbulent production relative to unladen turbulent production is approximately equal to the mass load ratio. The insight that the solids Reynolds shear stress can be significant, even for low mass loads, is essential for this explanation. It is shown that at least two mechanisms cause the turbulence reduction. In addition to the classically recognized mechanism of dissipation of turbulent fluctuations by particles, there is another suppressing mechanism in inhomogeneous flows: the non-uniform relative velocity of the phases, created because particles slip at the wall, collide, and slowly react with the continuous phase. Investigation of the air turbulent kinetic energy equation demonstrates that the relative reduction of air pressure strain is larger than the reduction of turbulent production and dissipation, and pressure strain may therefore be a cause of the reduction of the other quantities. The fluctuational dissipation induced by the drag forces from particles is small compared to the other terms, but not negligible. For intermediate and high mass loads the air turbulence remains low. The relatively small turbulence intensities are not generated by the standard turbulent mechanisms any more, but directly caused by the particle motions. The particle-fluid interaction term in the turbulent kinetic energy equation is no longer dissipative, but productive instead. On increasing the mass load, the radial and azimuthal fluctuations of the particles grow. The corresponding reduction of solids anisotropy is an effect of the inter-particle collisions, which act as a solids pressure strain term. For intermediate and high mass loads, fluctuational drag force and particle collisions appear to be the relevant dissipation mechanisms in the solids fluctuational energy equation. In contrast to the air turbulent production, the solids 'turbulent' production term has the same level for low and high mass loads, while it attains a clear local minimum between. With increasing mass load, large-scale coherent turbulent fluid structures weaken, and eventually disappear. Simultaneously, the fluid fluctuations at relatively small length scales are enhanced by the motion of the particles. The highest particle concentration occurs near the wall for low mass loads, but on increasing the mass load, the concentration profile becomes uniform, while for the highest mass load particles accumulate in the centre of the pipe. Two-point correlation functions indicate that the addition of a small number of small solid particles to a clean pipe flow increases the streamwise length scale of the turbulence.

Journal ArticleDOI
TL;DR: In this article, numerical simulations are performed over an idealized urban area, modelled as regular rows of large rectangular obstacles, to estimate the impacts of buildings on air pollution dispersion.
Abstract: In order to estimate the impacts of buildings on air pollution dispersion, numerical simulations are performed over an idealized urban area, modelled as regular rows of large rectangular obstacles. The simulations are evaluated with the results of the Mock Urban Setting Test (MUST), which is a near full-scale experiment conducted in Utah’s West Desert area: it consists of releases of a neutral gas in a field of regularly spaced shipping containers. The numerical simulations are performed with the model Mercure_Saturne, which is a three-dimensional computational fluid dynamics code adapted to atmospheric flow and dispersion simulations. It resolves complex geometries and uses, in this study, a k–∈ closure for the turbulence model. Sensitivity studies focus on how to prescribe the inflow conditions for turbulent kinetic energy. Furthermore, different sets of coefficients available in the literature for the k–∈ closure model are tested. Twenty MUST trials with different meteorological conditions are simulated and detailed analyses are performed for both the dynamical variables and average concentration. Our results show overall good agreement according to statistical comparison parameters, with a fraction of predictions for average concentration within a factor of two of observations of 67.1%. The set of simulations offers several inflow wind directions and allows us to emphasize the impact of elongated buildings, which create a deflection of the plume centerline relative to the upstream wind direction.

Journal ArticleDOI
TL;DR: In this article, it was shown by direct numerical simulation that the preferential concentration of small heavy particles in homogeneous isotropic developed turbulence has a self-similar multi-scale nature when the particle relaxation time is within the inertial time scales of the turbulence.
Abstract: It is shown by direct numerical simulation that the preferential concentration of small heavy particles in homogeneous isotropic developed turbulence has a self-similar multi-scale nature when the particle relaxation time is within the inertial time scales of the turbulence. This is shown by the pair correlation function of the particle distribution extending over the entire inertial range, and the probability density function of the volumes of particle voids taking a power-law form. This self-similar multi-scale nature of particle clustering cannot be explained only by the centrifugal effect of the smallest-scale (i.e. the Kolmogorov scale) eddies, but also by the effect of co-existing self-similar multi-scale coherent eddies in the turbulence at high Reynolds numbers. This explanation implies that the preferential concentration of particles takes place even when the relaxation time of particles is much larger than the Kolmogorov time, provided it is smaller than the longest time scale of the turbulence, since even the largest-scale eddies bring about particle clustering.

Journal ArticleDOI
TL;DR: In this paper, a simulation of turbulent flow in a straight square duct was performed in order to determine the minimal requirements for self-sustaining turbulence, and it was found that turbulence can be maintained for values of the bulk Reynolds number above approximately 1100, corresponding to a friction-velocity-based Reynolds number of 80.
Abstract: A direct numerical simulation of turbulent flow in a straight square duct was performed in order to determine the minimal requirements for self-sustaining turbulence. It was found that turbulence can be maintained for values of the bulk Reynolds number above approximately 1100, corresponding to a friction-velocity-based Reynolds number of 80. The minimum value for the streamwise period of the computational domain is around 190 wall units, roughly independently of the Reynolds number. We present a characterization of the flow state at marginal Reynolds numbers which substantially differs from the fully turbulent one: the marginal state exhibits a four-vortex secondary flow structure alternating in time whereas the fully turbulent one presents the usual eight-vortex pattern. It is shown that in the regime of marginal Reynolds numbers buffer-layer coherent structures play a crucial role in the appearance of secondary flow of Prandtl's second kind.

Journal ArticleDOI
TL;DR: Depth averaged models are widely used in engineering practice in order to model environmental flows in river and coastal regions, as well as shallow flows in hydraulic structures as mentioned in this paper, where the most important and widely used depth averaged turbulence models are reviewed and discussed.
Abstract: Depth averaged models are widely used in engineering practice in order to model environmental flows in river and coastal regions, as well as shallow flows in hydraulic structures This paper deals with depth averaged turbulence modelling The most important and widely used depth averaged turbulence models are reviewed and discussed, and a depth averaged algebraic stress model is presented A finite volume model for solving the depth averaged shallow water equations coupled with several turbulence models is described with special attention to the modelling of wet-dry fronts In order to asses the performance of the model, several flows are modelled and the numerical results are compared with experimental data

Journal ArticleDOI
TL;DR: A finite element implementation of the standard κ-e turbulence model, including Chien's Low-Reynolds number modification is presented, with special emphasis on the numerical treatment of wall boundary conditions.
Abstract: A finite element implementation of the standard κ-e turbulence model, including Chien's Low-Reynolds number modification is presented. Special emphasis is laid on the numerical treatment of wall boundary conditions. In particular, logarithmic wall functions are used to derive Neumann boundary conditions for the standard κ-e model. The resulting solutions are superior to those obtained using wall functions implemented as Dirichlet boundary conditions and comparable to simulation results produced by a Low-Reynolds number κ-e model. Two representative benchmark problems (channel flow and backward facing step) are used to compare the performance of different algorithms in 3D and to investigate the influence of the near-wall treatment.

Journal ArticleDOI
TL;DR: In this article, the authors performed computational fluid dynamics (CFD) calculations of impinging jets with 13 widely spread Reynolds-averaged Navier-Stokes (RANS) turbulence models using commercial CFD software, and the only model able to predict correctly the laminar-turbulent transition occurring at small nozzle-to-plate distance was the SST k−−-ω model (transitional flow option).
Abstract: Computational fluid dynamics (CFD) calculations of impinging jets have been performed with 13 widely spread Reynolds-averaged Navier-Stokes (RANS) turbulence models using commercial CFD software. It was the aim of these calculation to assess how heat transfer and flow structure can be predicted at different Reynolds numbers and different nozzle-to-plate distances. The only model able to predict correctly the laminar–turbulent transition occurring at small nozzle-to-plate distance was the SST k − ω model (“transitional flow option”). Most of the other models can only satisfactorily predict heat transfer in the turbulent wall jet region. When the SST k − ω model with transitional flow option is applied for calculation of pulsating jets, the tendencies are predicted correctly.

Journal ArticleDOI
TL;DR: In this paper, a 3D and two-dimensional depth-averaged large-eddy simulations (LES) are presented for three different shallowwater flows involving large-scale horizontal structures: a mixing layer, the flow around a circular cylinder and the flow in a groyne field.
Abstract: Three-dimensional (3D) and two-dimensional (2D) depth-averaged (DA) large-eddy simulations (LES) are presented for three different shallow-water flows involving large-scale horizontal structures: a mixing layer, the flow around a circular cylinder, and the flow in a groyne field. The results are compared with each other and also with experiments. In the 3D-LES, most of the energy-containing turbulent motions, including the larger subdepth-scale motions, are resolved, while in the 2D-DA-LES the effect of the 3D subdepth-scale turbulence is represented by a quadratic bottom-friction model and a simple eddy-viscosity model. In the case of the mixing layer, an additional stochastic backscatter model is necessary to account for the energy transfer from the subdepth-scale turbulence to the 2D structures in order to generate the latter. The 3D-LES results are generally in good agreement with the experiments, including the evolution of the horizontal structures. The much more economic 2D-DA-LES are somewhat less realistic in detail but also produce results that are generally of sufficient accuracy for practical purposes.

Journal ArticleDOI
TL;DR: In this article, the development of a fully three-dimensional finite volume morphodynamic model for simulating fluid and sediment transport in curved open channels with rigid walls is described, where the Reynolds-averaged Navier-Stokes equations are solved numerically, without reliance on the assumption of hydrostatic pressure distribution, in a curvilinear nonorthogonal coordinate system.
Abstract: The development of a fully three-dimensional finite volume morphodynamic model, for simulating fluid and sediment transport in curved open channels with rigid walls, is described. For flow field simulation, the Reynolds-averaged Navier–Stokes equations are solved numerically, without reliance on the assumption of hydrostatic pressure distribution, in a curvilinear nonorthogonal coordinate system. Turbulence closure is provided by either a low-Reynolds number k−ω turbulence model or the standard k−e turbulence model, both of which apply a Boussinesq eddy viscosity. The sediment concentration distribution is obtained using the convection-diffusion equation and the sediment continuity equation is applied to calculate channel bed evolution, based on consideration of both bed load and suspended sediment load. The governing equations are solved in a collocated grid system. Experimental data obtained from a laboratory study of flow in an S-shaped channel are utilized to check the accuracy of the model’s hydrodyn...

Journal ArticleDOI
TL;DR: In this article, the implications of superfluid turbulence for neutron star physics were analyzed and the Gorter-Mellink form for mutual friction was derived for a straight vortex array to account for self-induced flow which arises when the vortices are curved.
Abstract: We analyse the implications of superfluid turbulence for neutron star physics. We begin by extending our previous results for the mutual friction force for a straight vortex array to account for the self-induced flow which arises when the vortices are curved. We then discuss Vinen's phenomenological model for isotropic turbulence, and derive the associated (Gorter–Mellink) form for the mutual friction. We compare this derivation to a more recent analysis of Schwarz, which sheds light on various involved issues. Having discussed isotropic turbulence, we argue that this case is unlikely to be relevant for neutron stars. Instead, we expect a rotating neutron star to exhibit polarized turbulence, where relative flow drives the turbulence and rotation counteracts it. Based on recent results for superfluid helium, we construct a phenomenological model that should have the key features of such a polarized turbulent system.

Journal ArticleDOI
TL;DR: In this article, the basic scales of motion and computational requirements for low frequency fluid drift turbulence are summarized in tutorial fashion, with emphasis on the tokamak edge region, and a trans-collisional gyrofluid model to treat cases with comparable ion and electron temperature.
Abstract: The basic scales of motion and computational requirements for low frequency fluid drift turbulence are summarized in tutorial fashion, with emphasis on the tokamak edge region. Parameters are given by experimental observations, but the computations are otherwise done from first principles. Edge turbulence is fundamentally electromagnetic and nonlinear, not treatable by standard linear or secondary instability analysis. Energetic character is determined by diagnosis of the terms in the energy theorem within the fully developed saturated phase. The spectra of the fluctuations and transport always extend to below the ion gyroradius scale. Direct coupling of pressure fluctuations and E-cross-B eddies through the parallel current is always active. Edge turbulence derives its character from steep gradients, with a parallel/perp scale ratio larger than 100, rather than from collisional effects. Collisionality is neither absent nor strongly dominant for electrons, but very weak for ions. Fluctuations in the axisymmetric component, including the Pfirsch–Schluter currents, are dynamically integrated into the turbulence. Time scales are one to two orders of magnitude shorter than the ion collision time, hence significant delays occur in the response of heat fluxes and viscosity to temperature gradients and flows. Hence the need for a trans-collisional gyrofluid model to treat cases with comparable ion and electron temperature. Two orders of magnitude in spatial scales and three in time scales are typically involved.

Journal ArticleDOI
TL;DR: In this paper, a review of existing basic turbulence modeling approaches reveals the need for the development of unified turbulence models which can be used continuously as filter density function or probability density function (PDF) methods, large eddy simulation (LES) or Reynolds-averaged Navier-Stokes (RANS) methods.
Abstract: A review of existing basic turbulence modeling approaches reveals the need for the development of unified turbulence models which can be used continuously as filter density function (FDF) or probability density function (PDF) methods, large eddy simulation (LES) or Reynolds-averaged Navier–Stokes (RANS) methods. It is then shown that such unified stochastic and deterministic turbulence models can be constructed by explaining the dependence of the characteristic time scale of velocity fluctuations on the scale considered. The unified stochastic model obtained generalizes usually applied FDF and PDF models. The unified deterministic turbulence model that is implied by the stochastic model recovers and extends well-known linear and nonlinear LES and RANS models for the subgrid-scale and Reynolds stress tensor.

Journal ArticleDOI
TL;DR: In this paper, the effect of small particles on decaying grid-generated turbulence is studied experimentally using a two-camera system, instantaneous fluid-phase and particlephase measurements can be obtained simultaneously.
Abstract: The effect of small particles on decaying grid-generated turbulence is studied experimentally. Using a two-camera system, instantaneous fluid-phase and particlephase measurements can be obtained simultaneously. The data obtained with this system are used to study the decay behaviour of the turbulent flow. The role of particle size, particle density and volume load is studied in a number of different cases. These cases are chosen so that the individual role of these parameters can systematically be evaluated. Addition of particles to the flow has significant effects on the decaying turbulence: first, the onset of the turbulent decay appears to shift upstream; second, the flow becomes anisotropic as it develops downstream. The latter is observed as an increase in integral length scale in the vertical direction. The rate at which the flow becomes anisotropic can be predicted using a new parameter: the product of the non-dimensional number density and the Stokes number (referred to as the ‘Stokes load’). This parameter, combining the relevant fluid and particle characteristics, is a measure for the energy redistribution leading to anisotropy. In addition to redistributing energy, the particles also produce turbulence. However, this only becomes evident when the grid-generated turbulence has decayed sufficiently, relatively far downstream of the grid. The turbulence production by particles can also account for the observed decrease in slope of the power spectrum, which leads to a ‘cross-over’ effect. The production of turbulence by the particles can be predicted using a model for the momentum deficit of the particle wakes. The validity of this approach is confirmed using conditional sampling of the fluid velocity field around the particles.

Journal ArticleDOI
TL;DR: In this paper, a manufactured solution (MS) resembling a two-dimensional, steady, wall-bounded, incompressible, turbulent flow for RANS codes verification is presented.
Abstract: This paper presents a manufactured solution (MS), resembling a two-dimensional, steady, wall-bounded, incompressible, turbulent flow for RANS codes verification. The specified flow field satisfies mass conservation, but requires additional source terms in the momentum equations. To also allow verification of the correct implementation of the turbulence models transport equations, the proposed MS exhibits most features of a true near-wall turbulent flow. The model is suited for testing six eddy-viscosity turbulence models: the one-equation models of Spalart and Allmaras and Menter; the standard two-equation k-e model and the low-Reynolds version proposed by Chien; the TNT and BSL versions of the k-ω model.