Theory Of Turbulent Flow Research Articles

Deposition of inertial particles from turbulent flow in channels at high Reynolds numbers

On the basis of the previously developed asymptotic theory of turbulent particle-laden flow with particle deposition in channels coupled with the transport model for the particle Reynolds stress, an asymptotic solution to the problem on the deposition of particles in the limit of high Reynolds numbers was obtained. The numerical calculations confirmed the presence, in the region of the transition from the diffusion-impaction regime of particle sedimentation to the inertia-moderated regime, bifurcation phenomenon of a solution found previously in earlier studies. Features of particle accumulation in the viscous sublayer are analyzed. On the basis of the numerical solution, correlations for particle deposition velocity were obtained. Boundary conditions of the wall-function type for particle concentration whose use allows widening the applicability limits of the equilibrium Eulerian models in terms of particle inertia are proposed.

A general two-phase turbulent flow model applied to the study of sediment transport in open channels

A numerical model for the general description of the sediment-laden flow is developed based on an Euler–Euler approach of the two-phase turbulent flow theory. The basic equations of the model are the Reynolds averaged equations of motion for both the fluid and the sediment phase in addition to the Reynolds averaged continuity equations for the mixture and for the sediment phase. The fluid phase and the sediment phase are coupled through their interaction forces including resistance force, inertia force, and lift force. Turbulence closure of the fluid phase is based on the conventional k– ε model while an algebraic particle turbulence model is applied to the sediment phase. The numerical method is based on the modified SIMPLE scheme. The model is applied to the computation of saturated sediment-laden flows and also the non-equilibrium transport of sediment by unidirectional flows under simple erosion and simple deposition conditions. The numerical results are well verified by the available experimental data. The vertical velocity of the sediment phase is also shown to be in very good agreement with the fall velocity of the sediment particles, which strongly support the assumption of Rouse’s diffusion theory for suspended sediment under steady state.

ICONE19-43406 THE EFFECTS OF ANNULAR FLOW ON DYNAMICS OF AP1000 REACTOR COOLANT PUMP ROTOR

The feature of AP1000 RCP rotor system is that the whole rotor system is immersed in the annular flow. The rotor in annular flow induces fluctuating fluid forces, thereby causes vibration and noise, even rotor instability. The effects of annular flow on AP1000 RCP rotor system are different from that in bearings and seals and should be considered in a new approach. Based on the turbulent bulk flow theory and perturbation analysis, the rotor-flow coupled linear dynamic model is developed to predict the dynamics of AP1000 RCP immersed rotor. During the analysis, the rotor eccentricity, stator and rotor wall friction effects are emphasized. The analytic results show the rotor eccentricity induces divergence instability and significant decrease of instability speed for system with moderate or large eccentricity; however, stator and rotor wall friction effects distinctly suppress divergence instability and increase instability speed for system with small or moderate eccentricity. Finally, we can have the conclusion that the flow-structure interaction induced by annular flow has great effects on the dynamics of AP1000 RCP immersed rotor, which should be considered in rotor dynamic analysis and design of AP1000 RCP. The method and results in the paper have theoretical significance and practical importance.

Application of statistical dynamical turbulence closures to data assimilation

We describe the development of an accurate yet computationally tractable statistical dynamical closure theory for general inhomogeneous turbulent flows, coined the quasi-diagonal direct interaction approximation closure (QDIA), and its application to problems in data assimilation. The QDIA provides prognostic equations for evolving mean fields, covariances and higher-order non-Gaussian terms, all of which are also required in the formulation of data assimilation schemes for nonlinear geophysical flows. The QDIA is a generalization of the class of direct interaction approximation theories, initially developed by Kraichnan (1959 J. Fluid Mech. 5 497) for isotropic turbulence, to fully inhomogeneous flows and has been further generalized to allow for both inhomogeneous and non-Gaussian initial conditions and long integrations. A regularization procedure or empirical vertex renormalization that ensures correct inertial range spectra is also described. The aim of this paper is to provide a coherent mathematical description of the QDIA turbulence closure and closure-based data assimilation scheme we have labeled the statistical dynamical Kalman filter. The mathematical formalism presented has been synthesized from recent works of the authors with some additional material and is presented in sufficient detail that the paper is of a pedagogical nature.

Novel developments in subgrid-scale modeling of space plasma: weakly compressible turbulence in the local interstellar medium

A survey of various subgrid-scale (SGS) models for the study of compressible magnetohydrodynamic (MHD) turbulence of space plasma is given. A large eddy simulation (LES) method for the study of compressible MHD turbulence of polytropic fluid is developed. A theory of SGS turbulent flow for the new SGS terms, appearing after the Favre-filtering procedure in the system of MHD equations, is proposed. Modeling of decaying compressible MHD turbulence under various similarity numbers is carried out and the validity of the LES method for the modeling of a polytropic is shown. Numerical studies are performed for five different SGS closures: the Smagorinsky model, the Kolmogorov model, the cross-helicity model, the scale-similarity model and the mixed model. Suggested SGS parameterizations are studied and SGS models that demonstrate the most exact results for decaying compressible MHD turbulence, under various similarity numbers, are shown. Using the advantages of the LES method, a nontrivial space plasma compressible MHD turbulence regime is studied when initially supersonic fluctuations become weakly compressible. An as yet unexplained observation is that density fluctuations in the local interstellar medium exhibit a Kolmogorov-like spectrum over an extraordinary range of scales with a spectral index close to −5/3. In spite of the compressibility and the presence of a magnetic field in the local interstellar medium, density fluctuations nevertheless admit a Kolmogorov-like power law. Supersonic flows with high large-scale Mach numbers are characterized in the interstellar medium. Nevertheless, there are subsonic fluctuations of weakly compressible components of the interstellar medium. These weakly compressible subsonic fluctuations are responsible for the emergence of a Kolmogorov-type spectrum in the interstellar turbulence which is observed from experimental data. It is shown that density fluctuations are a passive scalar in a weakly compressible MHD turbulence velocity field and demonstrate a Kolmogorov-like spectrum.

Shark-skin surfaces for fluid-drag reduction in turbulent flow: a review

The skin of fast-swimming sharks exhibits riblet structures aligned in the direction of flow that are known to reduce skin friction drag in the turbulent-flow regime. Structures have been fabricated for study and application that replicate and improve upon the natural shape of the shark-skin riblets, providing a maximum drag reduction of nearly 10 per cent. Mechanisms of fluid drag in turbulent flow and riblet-drag reduction theories from experiment and simulation are discussed. A review of riblet-performance studies is given, and optimal riblet geometries are defined. A survey of studies experimenting with riblet-topped shark-scale replicas is also given. A method for selecting optimal riblet dimensions based on fluid-flow characteristics is detailed, and current manufacturing techniques are outlined. Due to the presence of small amounts of mucus on the skin of a shark, it is expected that the localized application of hydrophobic materials will alter the flow field around the riblets in some way beneficial to the goals of increased drag reduction.

A phenomenological model for erosion of material in a horizontal slurry pipeline flow

Based on the turbulent flow theory and a single particle erosion model developed by Huang et al. (2008) [9], a comprehensive phenomenological model for erosion of material in slurry pipeline flow is developed. This model captures the effects of particle shape, particle size, slurry mean velocity, pipe diameter, fluid viscosity and the properties of target material. The model shows that the erosion rate has a power-law relation with slurry mean velocity, particle size, pipe diameter, fluid viscosity and solid concentration. The erosion rate depends strongly on the slurry mean velocity and weakly on pipe diameter and fluid viscosity. The exponent of slurry mean velocity varies in a range of 2–3.575, which is consistent with most of the experiments. The model also elucidates that the effect of particle size on erosion rate depends on the particle shape, flow condition and erosion location on the periphery of a pipe. To test the model developed, a simplified version was used to compare with the experiments conducted by Karabelas. Both of them are in good agreement.

Understanding jökulhlaups: From tale to theory

AbstractThe study of jökulhlaups has advanced from describing them qualitatively to measuring systematically on site their discharge curves and source geometry, as well as investigating conditions when particular floods were initiated. In the early days of this science, hypotheses were formulated which attempted to explain the processes responsible for unstable flood growth. The general theory of time-dependent turbulent water flow through intraglacial conduits marked a breakthrough in understanding jökulhlaup hydraulics and has since remained a classical foundation for jökulhlaup studies. This theory described flood evolution in terms of water input into the upper end of a tunnel leading from a reservoir, taking account of sensible stored lake heat and geometry. Such a tunnel expands by positive feedback, since its ice walls melt through frictional heat produced by the flowing water. While this model successfully described jökulhlaups in which the discharge hydrograph increases more or less exponentially over time, other floods were observed which are in stark contrast. In them, pressurized floodwater propagates in a turbulent subglacial water sheet which opens and expands a system of conduits, with an extremely rapid linear rise in discharge. The rushing water enlarges its subglacial pathway not only by melting the ice around it but also by lifting, deforming and fracturing it. Subsequent drainage is nourished by two different sources, with conduit growth being controlled not only by water input at the upper end of the flood path but also by further water joining in, all the way to the edge of the glacier. Moreover, the trigger for releasing meltwater from glacial lakes has been seen to be either of two conduit opening mechanisms, which also determine whether a turbulent subglacial water sheet will result or not. On the one hand, drainage may begin by expanding already existing conduits, in which case the pressure remains lower than that of the ice overburden at the dam and the conduits grow slowly. On the other hand, lake levels may rise until flotation of the ice dam, abruptly opening a sufficient gap for water to propagate as a sheet flow. In order to explain which of these two initiation mechanisms will act, further studies are required into the structure of hydrological drainage systems under ice dams and into their linkage with these two mechanisms. Although current theoretical models of jökulhlaups drainage have managed to reproduce the observed discharge patterns, inconsistencies with the observed behaviour of subglacial drainage systems along the flood path demand further exploration of the actual hydraulic and glaciodynamic processes of jökulhlaups.

The multifractal structure of satellite sea surface temperature maps can be used to obtain global maps of streamlines

Abstract. Nowadays Earth observation satellites provide information about many relevant variables of the ocean-climate system, such as temperature, moisture, aerosols, etc. However, to retrieve the velocity field, which is the most relevant dynamical variable, is still a technological challenge, specially in the case of oceans. New processing techniques, emerged from the theory of turbulent flows, have come to assist us in this task. In this paper, we show that multifractal techniques applied to new Sea Surface Temperature satellite products opens the way to build maps of ocean currents with unprecedented accuracy. With the application of singularity analysis, we show that global ocean circulation patterns can be retrieved in a daily basis. We compare these results with high-quality altimetry-derived geostrophic velocities, finding a quite good correspondence of the observed patterns both qualitatively and quantitatively; and this is done for the first time on a global basis, even for less active areas. The implications of this findings from the perspective both of theory and of operational applications are discussed.

Reynolds averaged theory of turbulent shear flows over undulating beds and formation of sand waves

Based on the Reynolds averaged Navier-Stokes (RANS) equations and the time-averaged continuity equation, a theory of turbulent shear flow over an undulating sand bed is developed addressing the instability criterion of plane sand beds in free-surface flows leading to the formation of sand waves. In the analysis, the integration of RANS equations leads to generalized Saint Venant equations, in which the time-averaged streamwise velocity is characterized by a power law obtained from turbulence closure, treating the curvilinear streamlines by the Boussinesq approximation. As a consequence, the modified pressure distribution has a departure from the traditionally linear hydrostatic pressure distribution. The instability analysis of a plane sand bed yields the curves of the Froude number versus nondimensional wave number, determining an instability zone for which at lower Froude numbers (less than 0.8), the plane bed becomes unstable with the formation of dunes; whereas at higher Froude numbers, the plane bed becomes unstable with the formation of standing waves and antidunes. For higher Froude numbers, the experimental data for antidunes lie within the unstable zone; while for lower Froude numbers, the same is found for dunes with some experimental scatter.

3D Numerical Simulation for Water Flows and Sediment Deposition in Dam Areas of the Three Gorges Project

This paper presents a three-dimensional (3D) mathematical model for suspended load transport in turbulent flows. Based on the stochastic theory of turbulent flow proposed by Dou, numerical schemes of Reynolds stresses for anisotropic turbulent flows are obtained. Instead of a logarithmic law, a specific wall function is used to describe the velocity profile close to wall boundaries. The equations for two-dimensional suspended load motion and sorting of bed material have been improved for a 3D case. Numerical results are in good agreement with the measured data of the Gezhouba Project. The present method has been employed to simulate sediment erosion and deposition in the vicinity of the Three Gorges Dam. The size distribution of the deposits and bed material, and flow and sediment concentration at different times and elevations, are predicted. The results agree well with the observations in physical experiments. Thus, a new method is established for 3D simulation of sediment motion in the vicinity of dams.

3-D Stochastic model for turbulent silt-laden flows

A 3-D stochastic model is developed for turbulent silt-laden flows in the Xiaolangdi river. Based on the stochastic theory of turbulent flows, Reynolds stresses for anisotropic turbulent flows, a pressure Poisson equation for free surface flow and a refined wall function for solid wall boundaries are obtained. In body-fitted coordinates, the finite volume method (FVM) is used to discretize the turbulent equations together with a staggered grid system, and the SIMPLEC algorithm is applied to simulate the flow over the complex geometry field. Finally, this mathematical model is applied to simulate water levels, silt concentrations and velocity distributions at the various cross-sections in this river, and all the computed results agreed well with the observed data, indicating this model and this computational schedule are reliable.

Turbulent Marginal Separation and the Turbulent Goldstein Problem

A new rational theory of incompressible turbulent boundary-layer flows having a large velocity defect is presented on basis of the Reynolds-averaged Navier-Stokes equations in the limit of infinite Reynolds number. This wake-type formulation allows for, among others, the prediction of singular solutions of the boundary-layer equations under the action of a suitably controlled adverse pressure gradient, which are associated with the onset of marginally separated flows. Increasing the pressure gradient locally then transforms the marginal-separation singularity into a weak Goldstein-type singularity occurring in the slip velocity at the base of the outer wake layer. Interestingly, this behavior is seen to be closely related to (but differing in detail from) the counterpart of laminar marginal separation, in which the skin friction replaces the surface slip velocity. Most important, adopting the concept of locally interacting boundary layers results in a closure-free and uniformly valid asymptotic description of boundary layers that exhibit small, closed reverse-flow regimes. Numerical solutions of the underlying triple-deck problem are discussed.

Extension of a fluctuating plume model of tracer dispersion to a sheared boundary layer and to a large array of obstacles

Fluctuating plume models provide a useful conceptual paradigm in the understanding of plume dispersion in a turbulent flow. In particular, these models have enabled analytical predictions of higher-order concentration moments, and the form of the one-point concentration probability density function (PDF). In this paper, we extend the traditional formalism of these models, grounded in the theory of homogeneous and isotropic turbulent flow, to two cases: namely, a simple sheared boundary layer and a large array of regular obstacles. Some very high-resolution measurements of plume dispersion in a water channel, obtained using laser-induced fluorescence (LIF) line-scan techniques are utilised. These data enable us to extract time series of plume centroid position (plume meander) and dispersion in the relative frame of reference in unprecedented detail. Consequently, experimentally extracted PDFs are able to be directly compared with various theoretical forms proposed in the literature. This includes the PDF of plume centroid motion, the PDF of concentration in the relative frame, and a variety of concentration moments in the absolute and relative frames of reference. The analysis confirms the accuracy of some previously proposed functional forms of model components used in fluctuating plume models, as well as suggesting some new forms necessary to deal with the complex boundary conditions in the spatial domain.

On the initiation of surface waves by turbulent shear flow

An analytical model is developed for the initial stage of surface wave generation at an air–water interface by a turbulent shear flow in either the air or in the water. The model treats the problem of wave growth departing from a flat interface and is relevant for small waves whose forcing is dominated by turbulent pressure fluctuations. The wave growth is predicted using the linearised and inviscid equations of motion, essentially following Phillips [Phillips, O.M., 1957. On the generation of waves by turbulent wind. J. Fluid Mech. 2, 417–445], but the pressure fluctuations that generate the waves are treated as unsteady and related to the turbulent velocity field using the rapid-distortion treatment of Durbin [Durbin, P.A., 1978. Rapid distortion theory of turbulent flows. PhD thesis, University of Cambridge]. This model, which assumes a constant mean shear rate Γ, can be viewed as the simplest representation of an oceanic or atmospheric boundary layer. For turbulent flows in the air and in the water producing pressure fluctuations of similar magnitude, the waves generated by turbulence in the water are found to be considerably steeper than those generated by turbulence in the air. For resonant waves, this is shown to be due to the shorter decorrelation time of turbulent pressure in the air (estimated as ∝ 1/ Γ), because of the higher shear rate existing in the air flow, and due to the smaller length scale of the turbulence in the water. Non-resonant waves generated by turbulence in the water, although being somewhat gentler, are still steeper than resonant waves generated by turbulence in the air. Hence, it is suggested that turbulence in the water may have a more important role than previously thought in the initiation of the surface waves that are subsequently amplified by feedback instability mechanisms.

Analytical solutions for water flow passing over a vegetal area

This study is aimed at investigating the vertical velocity profile of flow passing over a vegetal area by an analytical approach. The soil ground is considered as pervious and thus non-zero velocity at the ground surface can be estimated. The soil and vegetation layers are regarded as homogeneous and isotropic porous media. Therefore the solution of the flow can be obtained by applying the theory of turbulent flow and Biot’s theory of poroelasticity after dividing the flow field into three layers: homogenous water, vegetation and pervious soil. The velocity distribution is compared with the experimental data of [Rowiński PM, Kubrak J. A mixing-length model for predicting vertical velocity distribution on flows through emergent vegetation. J Hydrol Sci 2002;47(6):893–904] to show its validity. In addition, five dimensionless parameters denoting the variation of slope, permeability of soil, Reynolds stress, density of vegetation, and relative height of vegetation are proposed to reveal their effects on the surface water flow. The analytical solutions of flow velocity can also be simplified into simpler expressions to describe the flow passing over a non-vegetated area.

Turbulent boundary layer over a flat plate with uniform wall suction

A complete theory of turbulent boundary layer flow over a flat plate with uniform wall suction is proposed. The theory relies on an asymptotic analysis of the Reynolds equations and dimensional considerations and does not involve any special closure hypotheses. Characteristics of the turbulent boundary layer with suction are calculated for the entire range of flow parameters by using the known characteristics of a reference flow (turbulent boundary layer over an impermeable flat plate). The velocity and shear stress profiles, the distribution of skin friction along the plate, and integral flow characteristics are obtained by using only the known velocity profile in the reference flow. The normal Reynolds stresses are calculated by using analogous characteristics of the reference flow. Results are presented in terms of scaling variables.

Molecule dependent turbulent memory

The transition from turbulent to laminar regime in a pipe flow of He, N 2, CO 2 and SF 6 have been studied experimentally. Dependence of the flow on molecular specie and initial conditions has been observed. The role of initial conditions is discussed with respect to the theory of turbulent flows.

A tractable inhomogeneous closure theory for flow over mean topography

The quasi-diagonal direct interaction approximation (QDIA) is shown to be a computationally tractable closure theory for inhomogeneous two-dimensional turbulent flow over mean (single-realization) topography. In this paper numerical results for the QDIA are compared to direct numerical simulation (DNS) at moderate Reynolds number for two cases with quite different topographic and mean field amplitudes. The QDIA is found to be in excellent agreement with DNS for cases where the small-scale topographic amplitude is significant. For cases where the small-scale topography is weak, the QDIA closely reproduces the evolving mean field and large-scale energy containing transients but under represents the amplitudes of the small-scale transients in a similar way to the homogeneous DIA. We discuss the prospects of ameliorating the small-scale deficiencies using a regularization of the interaction coefficients.

3D mathematical model for suspended load transport by turbulent flows and its applications

This paper presents a 3D mathematical model for suspended load transport in turbulent flows. Based on Dou’s stochastic theory of turbulent flow, numerical schemes of Reynolds stresses for anisotropic turbulent flows were obtained. A refined wall function was employed to treat solid wall boundaries. The equations for 2D suspended load motion and sorting of bed material have been expanded into 3D cases. Numerical results are validated by the measured data of the Gezhouba Project, and proved to be in good agreement with the experimental. The present method has been employed to simulate sediment erosion and deposition in the dam area of Three Gorges Project, and for the operation of the project, siltation process and deposition pattern in the near-dam area of the reservoir, size distribution of the deposits and bed material, and flow fields and sediment concentration fields at different time and elevations are predicted. The predicted results are close to the experimental observations in physical model studies. Thus, a new method is established for 3D simulation of sediment motion in dam areas of multi-purpose water projects.