Numerical Analysis of Turbulent Flow in a U-Bend with Rectangular Cross Section

A numerical analysis has been performed for a three-dimensional turbulent flow developing in a 180°bent tube with straight inlet and outlet sections by three low-Reynolds-number turbulent models. The calculated results for three types of turbulent model are compared with available experimental data. The calculated results show comparatively good agreement with the experimental data of time-averaged velocity and fluctuating velocity, irrespective of the turbulent model adopted in this study. As a striking feature of the flow, it has been pointed out in the experiment of the 180°-bent tube that the cross-stream flow undergoes a second reversal in its direction of motion and is redirected toward the pipe inner radius. The three turbulent models predict well the occurrence of the cross-stream flow reversal in the bend. Moreover, these turbulent models predict well the velocity distribution near the wall in the bend. Judging from these comparisons with experimental data, turbulent flow of the bent tube is predicted well by low-Reynolds-number turbulent models and the difference among these turbulent models is negligible in the bent tube flow.

In this paper the development and a partially verification of an anisotropic modification of linear and nonlineare models of turbulence is presented. This modification departs from the observation that there are some regions of fluid domains in which the Reynolds stresses do not depend on the magnitude of the mean flow gradients. The model is based on the hypothesis that actions of fluctuating motion on mean motion are almost exclusively due to large turbulent eddies, and that the latter contain the same kinetic energy of the small eddies of mean flow. The contribution of large turbulent eddies to the Reynolds stresses is then modelled by a linear combination of an isotropic term and an anisotropic term. The latter is obtained by multiplying a quote of the turbulent kinetic energy by a normalised redistribution tensor. The performances of the model are tested calculating the Reynolds stresses in a fully developed turbulent channel flow, and simulating the separated turbulent flow over a backward-facing step, and a fully developed turbulent flow in a squared duct. The results show that the modified models improve the prediction of the normal Reynolds stresses in a bidimensional channel and of the reattachment point in a backward-facing step. On the other hand, these models do not supply any improvement of the secondary flow in a squared duct. INTRODUCTION Algebraic two-equation models of turbulence for Reynolds averaged Navier-Stokes equations are still, today, among the most widely used in the field of engineering design. The two major alternative to such models are the second-order closure models and large-eddy simulations (LES). The weak points of the first approach are high computational cost, due to the five more equations to be solved, and wall-bounded turbulent flows. On the other hand, LES requires much more computational time than second-order closure models, and improved models for the smallscale and the wall region are needed. For these reasons these two approaches have not become yet a useful engineering tool. The aim of this work is to develop an anisotropic modification for linear and nonlinear turbulence model which improves the prediction of normal Reynolds stresses, without increasing the number of differential equations to be solved. More precisely, the objective is to simulate the contribution to the anisotropy of the turbulent stresses observable in areas characterised by low mean velocity gradients. This phenomenon, which can be noted, for example, in experimental data of the turbulent channel flow in figure 5, is not actually described by standard, explicit algebraic models. The starting point of this model consists in the substitution of turbulent kinetic energy by an appropriate vectorial magnitude which provides information about the anistropy of the turbulent stresses. The quantity is identified by the field of velocity of the small eddies of mean motion. The kinetic energy of these small eddies is obtained by assuming that these t Dr, Center of Studies and Activities for Space (CISAS). Dr, Department of Mechanical Engineering. ' Professor, Department of Mechanical Engineering. Copyright © 2001 by the American Institute of Aeronautics and Astronautics, Inc. All rights reserved. 1 American Institute of Aeronautics and Astronautics (c)2001 American Institute of Aeronautics & Astronautics or Published with Permission of Author(s) and/or Author(s)' Sponsoring Organization. have the same kinetic energy content of the large turbulent eddies: the two fields of motion are said to be similar. It has been demonstrated that the field of motion of large turbulent eddies, or coherent structures^ can be obtained directly from measurements of instantaneous velocity once the quota of turbulent kinetic energy has been defined. The models obtained provides improvements in the predictions of normal Reynolds stresses present in the turbulent flow of a bidimensional channel; as for the separated turbulent flow in a backward-facing step appreciable improved results of mean flow and of normal Reynolds stresses have been attained compared to standard algebraic models. On the other side, as it will be shown in the following paragraphs, the model of the turbulent kinetic energy redistribution tensor does not supply any improvement in the case of the fully developed turbulent flow in a squared duct. ANISOTROPIC MODIFICATION OF THE REYNOLDS STRESSES Let us consider a field of turbulent motion of a viscous, homogenous and incompressible fluid; the instantaneous velocity v and the instantaneous pressure p can be set out as follows in a mean and fluctuating parts: v = v -f v' p-p + p (1) The evolution of the velocities and mean pressures can be described completely by the well-known Reynolds equations:

A numerical analysis of turbulent axisymmetric radial compressible channel flow between a nozzle and a flat plate is presented in this paper. In particular, the application of this type of flow situation in pneumatic dimensional control systems is considered. The Spalart-Allmaras one-equation turbulence model is used. The resulting highly coupled PDE system has been solved using the control volume based numerical approach where the power-law scheme was used extensively to compute the diffusive and convective fluxes of momentum. Results show that local Mach numbers can easily achieve and surpass unity for typical industrial configurations. Also, in the case of a standard industrial nozzle geometry, the presence of a toroidal recirculation zone that moves radially outward is clearly identified in most cases. Separated flow areas are of particular concern as it has been shown previously that they can cause nozzle fouling in industrial applications. It has been shown that the size of this region is dependant on feed pressure. Considerable differences between results obtained using the Spalart-Allmaras and standard k- e turbulence models have also been noticed.

The current paper presents a cold flow simulation study of a low Mach number air-air ejector with a four ring entraining diffuser that is used in a variety of applications including infrared (IR) suppression of exhaust from helicopters and fixed wing aircraft. The main objectives of this investigation were to identify key issues that must be addressed in successful CFD modelling of such devices, and recognize opportunities to improve the performance of these devices. Two-dimensional CFD simulations were carried out using commercial software, Ansys14. Studies of mesh and domain size sensitivity were made to ensure the CFD results were independent of both factors. A turbulence model independence study using k-ε, k-ω and RSM turbulence models was performed to figure out the appropriate turbulence model that produced the best agreement with the experimental data for several of ejector performance criteria. The measured flow properties in the annulus were used as input boundary conditions for the CFD simulations. However, in the comprehensive turbulence model study, the measured flow parameters at the nozzle exit were also applied as inlet boundary conditions for the CFD simulations. The measured flow velocity at the nozzle exit, at one centerline section inside the mixing tube and at the diffuser exit and the system pressure recovery were compared with the CFD predictions. The ejector pumping ratios, back pressure coefficient and diffuser gap velocities were also compared. It was found that the RANS-based CFD predictions were sensitive to the changes in the ejector domain size, mesh refinement and inlet boundary condition locations. With the annulus inlet boundary conditions, the tested turbulence models under predicted the size of the core separation downstream of the system, back pressure, pumping ratio and pressure recovery in the mixing tube and diffuser. However, the ability of the RNG turbulence model to predict the ejector performance parameters was better than that of the other turbulence models at all inlet flow conditions. Nevertheless, applying the inlet boundary conditions at the nozzle exit enhanced the capability of the RANS-based turbulence model particularly in predicting the ejector pumping ratios, pressure recovery and the size of the core separation. Finally, the acceptable agreement between the experimental data and the CFD predictions provides a valid tool to continue improving these devices using CFD techniques.

Chapter 8 - Channel Bed Resistance

Simulating drag reduction phenomenon in turbulent pipe flows

3-D numerical analysis of EHD turbulent flow and mono-disperse charged particle transport and collection in a wire-plate ESP

Oscillation of the vocal folds makes a sound source of the human voiced sound. Understanding of the oscillation mechanism, which is a complex flow-structure interaction problem in the airway, is crucial for considering clinical diagnosis of voice disorders. However, details of the oscillation mechanism are still unclear partly because, from a fluid mechanical viewpoint, the effect of oscillation of the vocal fold wall during the phonation on airflow behaviors remains elusive. In the present study, flow characteristics in a sinusoidally-oscillating constriction mimicking the vocal fold were investigated by numerical and experimental approaches. The numerical analyses focused in particular on the effect of constriction oscillation on flow separation demonstrated that the flow separation point moves continuously and periodically in a frequency-dependent manner. In the experimental study, an apparatus was newly designed, with a view to detect the oscillation-induced movement of the flow separation point, to enable detailed measurement of pressure distribution along the constriction with an interval of 2 mm that is synchronized with measurement of constriction displacement. Although movement of the separation point as seen in the numerical analyses was not detected by this limiting resolution of the apparatus, we obtained pressure-width relations that is partly contrary to the numerical results but is presumably dependent on the inlet boundary condition. These findings indicate that appropriate evaluations of separation point and inlet boundary conditions are key factors to characterize the flow in oscillating constriction, which is crucial for better understanding of the vocal fold mechanics.

CFD Simulations of Abnormal Flow in Horizontal Pipes for Offshore Hydrocarbon Transport

The accurate modelling of heat transfer to turbulent flow and the prediction of the temperature distribution in the flow remain one of the problem areas of numerical simulations. Traditional turbulence closure models, like the k–ε model, effectively only increase the viscosity of the fluid and introduce wall functions close to boundaries to obtain the correct velocity distribution. These turbulence models do not model the small‐scale mixing that occurs in turbulent flow. When solving the energy equation these small‐scale mixings dominate the heat transfer rate at the boundaries as well as the temperature distribution in the flow. This paper outlines a revised method, based on the k–ε turbulence model, that can be used to predict heat transfer in turbulent flow. A single turbulent conductivity term is introduced that can be used over the complete flow field including the boundaries. A detailed description of the mathematical model and boundary conditions used for the turbulence model are included in the paper. The effective turbulent conductivity method was evaluated in several finite difference simulations of water flowing through a smooth pipe while being heated. Simulation and verification were performed over a range of Reynolds numbers. Verification of the model is accomplished by comparing the numerically predicted centre temperature of the fluid as well as the heat flux to the fluid to measured temperatures in a similar pipe. From these results it is concluded that the revised turbulent conductivity model holds great potential to obtain accurate simulated heat transfer rates for general applications.

On different numerical inverse Laplace methods for solute transport problems

Numerical simulations based on Reynolds-averaged Navier Stokes (RANS) models are still the work-horse tool in engineering design involving turbulent flows. Two decades ago, when LES started gaining popularity thanks to the increasing availability of computational resources, it was widely expected that it would have gradually replaced RANS methods in industrial CFD for decades to come. In the past two decades, however, while LES-based methods gained widespread applications and the earlier hope did not diminish, the predicted time when LES would replace RANS has been significantly delayed. Most industrial users are probably decades away from any routine use of scale resolving simulations, not to mention the cost, time and user skill it take to run these computations. In brief, RANS solvers, particularly those based on standard eddy viscosity models (e.g k-e, k-ω, S-A and k-ω SST) are expected to remain the workhorse in the CFD of high Reynolds number flows for decades. However, predictions from RANS simulations are known to have large discrepancies in many flows of engineering relevance, including those with swirl, pressure gradients, or mean streamline curvature. It is a consensus that the dominant cause for such discrepancies is the RANS-modeled Reynolds stresses. In light of the long stagnation in traditional turbulence modeling, researchers explored machine learning as an alternative to improve RANS modeling by leveraging data from highfidelity simulations. The goal is to make use of vast amounts of turbulent flows data, machine learning techniques and current understanding of turbulence physics to develop models with better predictive capabilities in the context of RANS simulations. Recently, in a seminar work, Ling et al (2016) developed a neural network architecture capable of embedding invariance properties into the Reynolds stress tensor predicted in output. Such a network, named the tensor basis neural network (TBNN), was applied to a variety of flow fields with encouraging results compared to both classical turbulence models and neural networks that do not preserve Galilean invariance. Yet, as in most data driven turbulence modelling approaches, the TBNN was used as a post-processing tool to correct the Reynolds stress tensor field predicted by a RANS simulation run with standard closure models. This means that, theoretically, the network can be applied only to correct the Reynolds stress tensor for the same RANS model on which it has been trained since, in general, different turbulence models yield different results depending on the flow type. Moreover, there is no physisical insight that suggests a relation between the RANS velocity gradients - used as inputs of the machine learning model - and the true Reynolds stress tensor. Differently, in this work a network with a similar architecture to the Ling’s one was trained and tested on a database of high-fidelity data of eight different flows to learn a functional mapping between the inputs of Pope’s General Eddy Viscosity Model and the anisotropic part of the Reynolds stress tensor. Then the network was embedded into a CFD RANS solver as a replacement of the standard closure model - and therefore called at every solver’s iteration. Lasty, the RANS solver with embedded TBNN was be tested on a canonical flow case - turbulent channel flow - to evaluate its performances. As for the organization of this work: in Chapter 1 further details on the data driven turbulence modelling will be given, RANS models and equations will be introduced and also an introduction to Neural Networks will be presented. In Chapter 2, it will be given a detailedexplanation of the RANS CFD solver and the neural network’s implementation. In Chapter 3, the method will be tested on a turbulent channel flow case and the results will be discussed. Lastly, in Chapter 4, some meaningful conclusions will be drawn.

Numerical analysis has been performed for three-dimensional developing turbulent flow in a square duct with rib-roughened walls by using an algebraic Reynolds stress model. This squared sectioned duct with roughened wall has been applied for coolant passage employed in gas turbine blades and heat exchanger in many engineering fields. Roughened wall is composed of many ribs, which is periodically located along the flow on the bottom wall of a square duct. In the numerical calculation, periodic boundary condition has been used for this flow and an algebraic Reynolds stress model is adopted in order to predict preciously Reynolds stresses. Calculated results of mean velocity and Reynolds stresses are compared with the experimental data in order to examine the validity of the presented numerical method and an algebraic Reynolds stress model. It has been pointed out as a characteristic features from the experimental result that secondary flow of the second kind is generated near roughened wall with flowing to roughened wall. The present method could predict its phenomenon correctly and reproduce well mean velocity profile distorted by the secondary flow. Besides, calculated results of Reynolds stresses are in good agreement with the experimental results, especially, shear stress distributions, which are characterized by generating the opposite sign regions, are predicted well as a result of estimating the secondary flow pattern preciously. Since the presented turbulent model is defined as high Reynolds number model, wall function is used for setting boundary conditions of turbulent energy and dissipation. As for this wall function, calculated results suggest that the universal constant of log-law velocity which is assumed in wall function, has to be changed according to the wall condition, that is smooth or rough.

Russian papers on differential models of turbulence and numerical simulation of nonequilibrium turbulent flows of liquids, gases, and conducting media, published for the most part in this journal over the last 10–15 years, are reviewed. The turbulence models considered in this review are based on Kolmogorov's ideas, which generated a new approach to the mathematical modeling of turbulent flows consisting in the use of transport equations for the turbulence properties. The subsequent development of these models was due to the emergence of computers which made it possible to change over from a qualitative analysis in particular regions to obtaining quantitative results with the influence of viscosity, and also such effects as diffusion and convection, taken directly into account in the mathematical simulation of turbulent flows. In this review the models are selected in accordance with the following criteria. 1. Only differential models are considered, that is models in which transport equations are used for the main turbulence properties: the turbulence energy, shear stress or the turbulent viscosity and a parameter involving the integral turbulence scale. According to the number of the transport equations the models are classified as one-, two-, or three-parameter. The application of the models is restricted to flows for which the boundary layer approximation holds true. 2. The models must have been put to practical use in the analysis of particular flows, and their most efficient areas of application specified. The models must have been tested by comparison with the most reliable experimental data. The models must be highly universal, thus making it possible, without adjusting the constants entering into the model, to take into account the inlet and boundary conditions, the variations of the physical properties of the medium, and external influences. The review aims to demonstrate the potential of the turbulence models considered in relation to a wide variety of flows in boundary layers and channels, and also to draw them to the attention of users and researchers developing scientific and applied computational programs for the description and control of devices with complicated working processes in aviation and space technology, and other areas.

Turbulence modelling for wall-bounded particle-laden flow with separation