Vortex breakdown in turbulent pipe flows

In many technical applications turbulent flows with embedded slender vortices exist. Depending on the boundary conditions vortex breakdown can occur. The purpose of this work is to develop and implement a solution scheme for large‐eddy simulations of vortex breakdown in turbulent pipe flows. One of the main problems in this simulation is the formulation of the inflow boundary condition for a fully developed turbulent flow with an embedded vortex. For that purpose a rescaling technique is developed in which a solution at a downstream location is inserted at the inflow boundary after an appropriate rescaling. To determine rescaling laws for pipe flows with an embedded vortex, analytical velocity profiles of swirling flows are first prescribed in a laminar flow. From the spatial development of the vortex a scaling law is deduced. In a next step this procedure is to be transferred to turbulent flows.     

Randomly oscillating turbulent channel flows

The velocity response to a sinusoidally oscillating pressure gradient is obtained for turbulent flow in a two-dimensional channel. The statistical relations between a spectrum of such pressure pulsations and the resulting spectrum of velocity oscillations are then written in terms of a spectral transfer function. This function, which incorporates the dynamic solution is complicated, but is well approximated with a simple expression.

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Zusammenfassung Für turbulente Strömung in einem zweidimensionalen Kanal wird die Geschwindigkeitsverteilung, die durch einen sinusoidal oszillierenden Druckgradient verursacht ist,

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Nomenclature A, B coefficients defined by comparison of Equation (1) with the appropriate dynamical equation foru - a half width of channel, or radius of pipe - b rate of increase of withy - c defined in Equation (31) - d defined in Equation (32) - f normalized spectral density of pressure oscillations - g normalized spectral density of velocity oscillations - h turbulent viscosity parameter defined in Equation (26) - I - K _n amplitude of the individual pressure oscillations - L ₁,L ₂,L ₃,L ₄,L ₅,L ₆ functions defined by Equations (18) (19) (20) (21) (24) (25) - m defined in Equation (30) - n frequency of pressure and velocity oscillations - p pressure - p _x defined in Equation (2) - R _p autocorrelation coefficient for pressure oscillations - R _u autocorrelation coefficient for velocity oscillations - t time - u axial velocity - w variable defined after Equation (15) - x axial position coordinate - y transverse position coordinate - z variable defined after Equation (15) - eddy diffusivity for momentum - dimensionless frequency, defined in Equation (7), for laminar case - _t dimensionless frequency, defined after Equation (16), for turbulent case - function defined in Equation (13) - laminar kinematic viscosity - variable displacement in time - fluid density - spectral transfer function - variable defined after Equation (16) This study was supported in part by the R. L. Albrook Hydraulic Laboratory of the Wash. State Univ. Division of Industrial Research.     

Numerical solution of turbulent jet flows

The work deals with numerical modelling of several turbulent 3D jet flows: steady impinging jet, steady free jet in cross–flow, synthetic free jet (unsteady) and synthetic impinging jet (unsteady). The numerical method is based on artificial compressibility method with dual time extension for unsteady cases. Space discretization uses cell–centered finite volume method with third order accurate upwind approximation for convection, the time discretisations are implicit. Turbulence is modelled using two–equation eddy viscosity models and by explicit algebraic Reynolds stress model (EARSM by Wallin and Hellsten). The results of first three cases are compared with measurements. (© 2008 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Numerical calculation of turbulent corner flows

Numerical predictions are presented of the hydrodynamic characteristics of developing and fully-developed turbulent flow in a square duct. The turbulent stresses in the plane of the cross-section, gradients of which cause the familiar secondary flows, are approximated by gradients in the axial mean velocity. Two distinct approximations are investigated, one of which specifies some of the model ‘constants’ as functions of the gradient of the length scale to account for wall effects. The stresses in the axial momentum equation are calculated from an eddy viscosity deduced from the K-W model of turbulence, K being the turbulence energy and W, a measure of the time-mean-square-vorticity fluctuations. The approximation incorporating wall effects generally performs better than the other when compared with fully-developed flow-data. This same approximation also compares favourably with data for developing flow and predictions based on K-? models in the literature.     

Computation of turbulent asymmetric trailing-edge flows

Turbulent compressible flow past an asymmetric trailing edge has been computed using the generalised-coordinate time-split group finite-element method and a lagged algebraic eddy viscosity turbulence model. The test case considered is that of a flow at a nominal Mach number of 0.4 and a Reynolds number of 26.2×10⁶. Mean velocity profiles and the displacement thickness distribution are in good agreement with the experimental results. The pressure and surface shear stress indicate reasonable agreement with the experimental results, except near the shoulder on the upper surface.

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Zusammenfassung Die Methode der finiten Elemente in verallgemeinerten Koordinaten mit time-split wird benützt, um die kompressible Strömung an einer unsymmetrischen Hinterkante zu berechnen. Das Turbulenz-Modell benützt eine zeitverzögerte algebraische turbulente Zähigkeit. Der Testfall ist eine Strömung mit der nominellen Machzahl 0.4 und der Reynoldszahl 26.2×10⁶. Mittlere Geschwindigkeitsprofile und die Verteilung der Verdrängungsdicke stimmen mit den experimentellen Resultaten gut überein. Der Druck und die Wandschubspannung zeigen eine vernünftige Übereinstimmung mit den experimentellen Werten, mit Ausnahme der Umgebung der Schulter auf der Oberseite.

     

Computation of turbulent reactive flows in industrial burners

This paper presents models that are suitable for computing steady and unsteady gaseous combustion with finite rate chemistry. Reynold averaging and large eddy simulation (LES) techniques are used to model turbulence for the steady and unsteady cases, respectively. In LES, the Reynold stress terms are modelled by a linear combination of the scale-similarity and eddy dissipation models while the cross terms are of the scale-similarity type. In Reynold averaging, the conventional k–ε two-equation model is used. For the chemical reactions, a 3-step mechanism is used for methane oxidation and the extended Zeldovich and N₂O mechanism are used for NO formation. The combustion model is a hybrid model of the Arrhenius type and a modified eddy dissipation model to take into account the effects of reaction rate, flame stretch and turbulent intensity and scale. Numerical simulations of a flat pulse burner and a swirling burner are discussed.     

Direct numerical simulation of turbulent flows in eccentric pipes

A numerical algorithm was developed for solving the incompressible Navier-Stokes equations in curvilinear orthogonal coordinates. The algorithm is based on a central-difference discretization in space and on a third-order accurate semi-implicit Runge-Kutta scheme for time integration. The discrete equations inherit some properties of the original differential equations, in particular, the neutrality of the convective terms and the pressure gradient in the kinetic energy production. The method was applied to the direct numerical simulation of turbulent flows between two eccentric cylinders. Numerical computations were performed at Re = 4000 (where the Reynolds number Re was defined in terms of the mean velocity and the hydraulic diameter). It was found that two types of flow develop depending on the geometric parameters. In the flow of one type, turbulent fluctuations were observed over the entire cross section of the pipe, including the narrowest gap, where the local Reynolds number was only about 500. The flow of the other type was divided into turbulent and laminar regions (in the wide and narrow parts of the gap, respectively).     

Large eddy simulation for turbulent magnetohydrodynamic flows

We investigate the mathematical properties of a model for the simulation of large eddies in turbulent, electrically conducting, viscous, incompressible flows. We prove existence and uniqueness of solutions for the simplest (zeroth) closed MHD model (1.7), we show that its solutions converge to the solution of the MHD equations as the averaging radii converge to zero, and derive a bound on the modeling error. Furthermore, we show that the model preserves the properties of the 3D MHD equations: the kinetic energy and the magnetic helicity are conserved, while the cross helicity is approximately conserved and converges to the cross helicity of the MHD equations, and the model is proven to preserve the Alfvén waves, with the velocity converging to that of the MHD, as δ₁,δ₂ tend to zero. We perform computational tests that verify the accuracy of the method and compare the conserved quantities of the model to those of the averaged MHD.     

Complex diffusion filtering of three dimensional turbulent flows

The linear and nonlinear complex diffusion filtering methods are proposed to extract the organized coherent part as well as the random incoherent part from forced and decaying turbulent flows. An attempt to examine the robustness of the two methods in filtering the turbulent flow field without the transformation into the frequency domain is carried out. The velocity fields of the forced and decaying cases are decomposed into coherent and incoherent parts in the spatial domain. The complex diffusion process can be obtained by combining the linear diffusion equation and the free particle Schrodinger equation. The imaginary parts in the two methods serve as a robust edge-detector with increasing confidence in time. The numerical implementations of the 3D linear and nonlinear complex diffusion partial differential equations are done using the finite difference method. The flatness, skewness and spectrum of the extracted fields are also studied for each filtering method. Results show that the two filtering methods can identify the coherent fields and preserve the features of the turbulent fields. Comparisons to the wavelet and Fourier decompositions are also considered.     

Investigation of structure and non-gradient turbulent transfer in swirling flows

Turbulence structure of swirling flows is being investigated in this paper, on the basis of experimental, self conducted measurements, and theoretical and numerical results. Turbulent swirling flows are extremely inhomogeneous, three dimensional and anisotropic. The aim of this paper is to investigate significant influence of swirl onto statistical parameters and non-gradient turbulent transfer. Contemporary optical measuring techniques two component laser Doppler anemometry (LDA) and stereo particle image velocimetry (SPIV) have been applied. (© 2012 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Interaction between inner and outer layer in drag-reduced turbulent flows

Effects of wall-based skin-friction drag reduction strategies on the statistical properties of large-scale motions in moderate Reynolds number turbulent flows have been investigated by exploiting Direct Numerical Simulation of turbulent channels. To educe large scales, a new efficient parallel distributed memory algorithm has been implemented which delivers data-driven modes of increasing characteristic lengthscales: the Fast and Adaptive Bidimensional Empirical Mode Decomposition (FABEMD). The influence of wall-based skin friction reduction on large scales is studied by comparing single point statistics, such as r.m.s. fluctuations, and two-point statistics, as cross-correlation functions in controlled and uncontrolled channel flow fields at constant friction Reynolds number. The traditional way of observing large-scale footprinting at the wall, as cross-correlation of the streamwise velocity components at different wall distances, has been found to be unreliable when comparing drag-reduced flows, due to the arbitrary choice of a reference plane in the logarithmic layer. A more sound way of observing the footprinting via the correlation of the streamwise velocity with the friction velocity is addressed and shows an increase of the footprinting in drag-reduced flows. (© 2016 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Computational fluid dynamics simulation of fluid particle fragmentation in turbulent flows

A simulation methodology is presented that allows detailed studies of the breakup mechanism of fluid particles in turbulent flows. The simulations, based on large eddy and volume of fluid simulations, agree very well with high-speed measurements of the breakup dynamics with respect to deformation time and length scales, and also the resulting size of the daughter fragments. The simulations reveal the size of the turbulent vortices that contribute to the breakup and how fast the interaction and energy transfer occurs. It is concluded that the axis of the deformed particle and the vortex core axis are aligned perpendicular to each other, and that breakup sometimes occurs due to interaction with two vortices at the same time. Analysis of the energy transfer from the continuous phase turbulence to the fluid particles reveals that the deformed particle attains it maximum in interfacial energy before the breakup is finalized. Similar to transition state theory in chemistry this implies that an activation barrier exists. Consequently, by considering the dynamics of the phenomenon, more energy than required at the final stage needs to be transferred from the turbulent vortices for breakup to occur. This knowledge helps developing new, more physical sound models for the breakup phenomenon required to solve scale separation problems in computational fluid dynamics simulations.     

Velocity fields with power-law spectra for modeling turbulent flows

We consider a generalization of homogeneous and isotropic Çinlar velocity fields to capture power-law spectra. The random velocity field is non-Gaussian with a representation motivated by Lagrangian and Eulerian observations. A wide range of turbulent flows can be generated by varying the stochastic parameters of the model. The velocity field being a functional version of Poisson shot-noise is constructed as the superposition of eddies randomized through their types and arrival times. We introduce a dependence between the eddy types which are spatial parameters and the decay parameter which is temporal. As a result, long-range correlation in space and a power-law spectrum previously used with Ornstein–Uhlenbeck velocity fields are achieved. We show that a corresponding power-law form for the probability distribution of the eddy diameter is sufficient for this result. The parameters of the probability distribution are further specified in view of Kolmogorov theory of the inertial scales. In particular, ∣k∣^−5/3 scaling of the spectrum is obtained. In the diffusive limit, we show that the parameters governing the decay and the arrival rate, and the speed of rotation of an eddy increase while its diameter decreases. That is, the eddies arrive fast, decay fast, and rotate fast with a small radius for a Brownian limit.     

New explicit algebraic stress model for three-dimensional turbulent flows

An explicit algebraic turbulent-stress model is built in the framework of so-called Rodi's weak-equilibrium approximation, which, taking into account the known model representations for the pressure-strain-rate correlation and turbulence-dissipation rate, reduces the differential equations for the Reynolds-tensor components to a system of quasi-linear algebraic equations for the five independent components of the anisotropy tensor B. We propose an original method for solving this quasi-linear system. The tensor in question B is sought in the form of an expansion in a tensorial basis formed from the mean strain and rotation rate tensors which contains only five elements. The expansion's coefficients are functions of five simultaneous invariants of these tensors. (© 2016 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Existence of stationary turbulent flows with variable positive vortex intensity

We prove the existence of stationary turbulent flows with arbitrary positive vortex circulation on non-simply connected domains. Our construction yields solutions for all real values of the inverse temperature with the exception of a quantized set, for which blow-up phenomena may occur. Our results complete the analysis initiated in Ricciardi and Zecca (2016).     

A Lagrangian stochastic model for nonpassive particle diffusion in turbulent flows

In this paper, we present a Lagrangian stochastic model for heavy particle dispersion in turbulence. The model includes the equation of motion for a heavy particle and a stochastic approach to predicting the velocity of fluid elements along the heavy particle trajectory. The trajectory crossing effect of heavy particles is described by using an Ito type stochastic differential equation combined with a fractional Langevin equation. The comparison of the predicted dispersion of four heavy particles with the observations shows that the model is potentially useful but requires further development.