A turbulent plane offset jet with small offset ratio

 Mean velocities and turbulence characteristics of a turbulent plane offset jet with a small offset ratio of 2.125 have been studied using laser Doppler anemometry (LDA). Static pressure measurements highlight the importance of side plates in enhancing two-dimensionality of the jet. The spatial distributions of turbulence intensities and Reynolds shear stress show a high turbulence recirculating flow region close to the nozzle plate between the jet and the offset plate. The LDA results have been used to examine the capability of three different turbulence models (i.e. k–ɛ, RNG and Reynolds stress) in predicting the velocity field of this jet. While all three models are able to predict qualitatively the recirculation, converging and reattachment regions observed experimentally, the standard k–ɛ turbulence model predicts a reattachment length that best agrees with the experimentally determined value. Received: 11 September 1996/Accepted: 30 May 1997     

Development and characterization of a variable turbulence generation system

Experimental turbulent combustion studies require systems that can simulate the turbulence intensities [u′/U ₀ ~ 20–30% (Koutmos and McGuirk in Exp Fluids 7(5):344–354, 1989)] and operating conditions of real systems. Furthermore, it is important to have systems where turbulence intensity can be varied independently of mean flow velocity, as quantities such as turbulent flame speed and turbulent flame brush thickness exhibit complex and not yet fully understood dependencies upon both U ₀ and u′. Finally, high pressure operation in a highly pre-heated environment requires systems that can be sealed, withstand high gas temperatures, and have remotely variable turbulence intensity that does not require system shut down and disassembly. This paper describes the development and characterization of a variable turbulence generation system for turbulent combustion studies. The system is capable of a wide range of turbulence intensities (10–30%) and turbulent Reynolds numbers (140–2,200) over a range of flow velocities. An important aspect of this system is the ability to vary the turbulence intensity remotely, without changing the mean flow velocity. This system is similar to the turbulence generators described by Videto and Santavicca (Combust Sci Technol 76(1):159–164, 1991) and Coppola and Gomez (Exp Therm Fluid Sci 33(7):1037–1048, 2009), where variable blockage ratio slots are located upstream of a contoured nozzle. Vortical structures from the slots impinge on the walls of the contoured nozzle to produce fine-scale turbulence. The flow field was characterized for two nozzle diameters using three-component Laser Doppler velocimetry (LDV) and hotwire anemometry for mean flow velocities from 4 to 50 m/s. This paper describes the key design features of the system, as well as the variation of mean and RMS velocity, integral length scales, and spectra with nozzle diameter, flow velocity, and turbulence generator blockage ratio.     

Turbulent flow simulation of liquid jet emanating from pressure-swirl atomizer

The performances of three linear eddy viscosity models (LEVM) and one algebraic Reynolds stress model (ARSM) for the simulation of turbulent flow inside and outside pressure-swirl atomizer are evaluated by comparing the interface position with available experimental data and by comparing the turbulence intensity profiles at the atomizer exit. It is found that the turbulence models investigated exhibit zonal behaviors, i.e. none of the models investigated performs well throughout the entire flow field. The turbulence intensity has a significant influence on the global characteristics of the flow field. The turbulence models with better predictions of the turbulence intensity, such as Gatski-Speziale’s ARSM model, can yield better predictions of the global characteristics of the flow field, e.g. the reattachment lengths for the backward-facing step flow and the sudden expansion pipe flow, or the discharge coefficient, film thickness and the liquid sheet outer surface position for the atomizer flows. The standard k–ε model predicts stronger turbulence intensity as compared to the other models and therefore yields smaller film thickness and larger liquid sheet outer surface position. In average, the ARSM model gives both quantitatively and qualitatively better results as compared to the standard k–ε model and the low Reynolds number models.     

DNS of Mixing and Reaction of Two Species in a Turbulent Channel Flow: A Validation of the Conditional Moment Closure

We consider the chemical reaction in a turbulent flow for the case that the time scale of turbulence and the time scale of the reaction are comparable. This process is complicated by the fact that the reaction takes place intermittently at those locations where the species are adequately mixed. This is known as spatial segregation. Several turbulence models have been proposed to take the effect of spatial segregation into account. Examples are the probability density function (PDF) and the conditional moment closure (CMC) models. The main advantage of these models is that they are able to parameterize the effects of turbulent mixing on the chemical reaction rate. As a price several new unknown terms appear in these models for which closure hypothesis must be supplied. Examples are the conditional dissipation 〈 χ ∣ φ 〉, the conditional diffusion 〈 κ ∇² φ ∣ u, φ 〉 and the conditional velocity 〈 u ∣ φ 〉. In the present study we investigate these unknown terms that appear in the PDF and CMC model by means of a direct numerical simulation (DNS) of a fully developed turbulent flow in a channel geometry. We present the results of two simulations in which a scalar is released from a continuous line source. In the first we consider turbulent mixing without chemical reaction and in the second we add a binary reaction. The results of our simulations agree very well with experimental data for the quantities on which information is available. Several closure hypotheses that have been proposed in the literature, are considered and validated with help of our simulation results. This revised version was published online in July 2006 with corrections to the Cover Date.     

Scalar turbulence model investigation with variable turbulent Prandtl number in heated jets and diffusion flames

Traditional turbulence models using constant turbulent Prandtl number fail to predict the experimentally observed anisotropies in the thermal eddy diffusivity and thermal turbulent intensity fields. Accurate predictions depend strongly on the turbulence model employed. Consequently, the objective of this paper is to assess the performance of turbulence model with variable turbulent Prandtl number in predicting of thermal and scalar fields quantities. The model is applied to axisymmetric turbulent round jet with variable density and in turbulent hydrogen diffusion flames using the flamelet concept. The k − ɛ turbulence model is used in conjunction with thermal field; the model involves solving supplemental scalar equations for the temperature variance and its dissipation rate. The model predictions are compared with available experimental data for the purpose of validating model. In reacting cases, velocity and scalar (including temperature and mass fractions) predictions agree relatively well in the near field of the investigated diluted hydrogen flames.     

Impact of Turbulent Flow and Mean Mixture Fraction Results on Mixing Model Behavior in Transported Scalar PDF Simulations of Turbulent Non-premixed Bluff Body Flames

Numerical simulation results are presented for three turbulent jet diffusion flames, stabilized behind a bluff body (Sydney Flames HM1-3). Interaction between turbulence and combustion is modeled with the transported joint-scalar PDF approach. The focus of the study is on the impact of the quality of simulation results in physical space on the behavior of two micro-mixing models in composition space: the Euclidean Minimum Spanning Tree (‘EMST’) model and the modified Curl coalescence dispersion (‘CD’) model. Profiles of conditional means and variances of thermo-chemical quantities, conditioned on the mixture fraction, are discussed in the recirculation region and in the neck zone behind. The impact of the flow and mixing fields in physical space on the mixing model behavior in composition space is strong for the CD model and increases as the turbulence – chemistry interaction becomes stronger. The EMST conditional profiles, on the contrary, are hardly affected.     

Experimental and numerical investigation of turbulent cross-flow in a staggered tube bundle

This paper presents the results of measurements and numerical predictions of turbulent cross-flow in a staggered tube bundle. The bundle consists of transverse and longitudinal pitch-to-diameter ratios of 3.8 and 2.1, respectively. The experiments were conducted using a particle image velocimetry technique, in a flow of water in a channel at a Reynolds number of 9300 based on the inlet velocity and the tube diameter. A commercial CFD code, ANSYS CFX V10.0, is used to predict the turbulent flow in the bundle. The steady and isothermal Reynolds–Averaged Navier–Stokes (RANS) equations were used to predict the turbulent flow using each of the following four turbulence models: a k-epsilon, a standard k-omega, a k-omega-based shear stress transport, and an epsilon-based second moment closure. The epsilon-based models used a scalable wall function and the omega-based models used a wall treatment that switches automatically between low-Reynolds and standard wall function formulations.

The experimental results revealed extremely high levels of turbulence production by the normal stresses, as well as regions of negative turbulence production. The convective transport by mean flow and turbulent diffusion were observed to be significantly higher than in classical turbulent boundary layers. As a result, turbulence production is generally not in equilibrium with its dissipation rate. In spite of these characteristics, it was observed that the Reynolds normal stresses approximated from the k-based two-equation models were in a closer agreement with experiments than values obtained from the second moment closure. The results show that none of the turbulence models was able to consistently reproduce the mean and turbulent quantities reasonably well. The omega-based models predicted the mean velocities better in the developing region while the epsilon-based models gave better results in the region where the flow is becoming spatially periodic.     

Simulation and Modelling of Turbulent Trailing-Edge Flow

Computations of turbulent trailing-edge flow have been carried out at a Reynolds number of 1000 (based on the free-stream quantities and the trailing-edge thickness) using an unsteady 3D Reynolds-Averaged Navier–Stokes (URANS) code, in which two-equation (k–ε) turbulence models with various low-Re near wall treatments were implemented. Results from a direct numerical simulation (DNS) of the same flow are available for comparison and assessment of the turbulence models used in the URANS code. Two-dimensional URANS calculations are carried out with turbulence mean properties from the DNS used at the inlet; the inflow boundary-layer thickness is 6.42 times the trailing-edge thickness, close to typical turbine blade flow applications. Many of the key flow features observed in DNS are also predicted by the modelling; the flow oscillates in a similar way to that found in bluff-body flow with a von Kármán vortex street produced downstream. The recirculation bubble predicted by unsteady RANS has a similar shape to DNS, but with a length only half that of the DNS. It is found that the unsteadiness plays an important role in the near wake, comparable to the modelled turbulence, but that far downstream the modelled turbulence dominates. A spectral analysis applied to the force coefficient in the wall normal direction shows that a Strouhal number based on the trailing-edge thickness is 0.23, approximately twice that observed in DNS. To assess the modelling approximations, an a priori analysis has been applied using DNS data for the key individual terms in the turbulence model equations. A possible refinement to account for pressure transport is discussed. This revised version was published online in July 2006 with corrections to the Cover Date.     

Experimental study and mathematical simulation of the characteristics of a turbulent flow in a straight circular pipe rotating about its longitudinal axis

The vorticity formed in the cross section of a turbulent flow in a straight circular pipe rotating about its longitudinal axis decreases the values of the turbulent stresses, turbulence energy, and dissipation rate along the pipe. The results of laboratory experiments and calculations by the second-order closure model of turbulent transfer are presented. On the whole, the model using a system of transport equations yields better agreement with experimental data than the models with algebraic relations for second-order moments. Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 39, No. 2, pp. 103–116, March–April, 1998.     

A numerical study of non-isothermal turbulent coaxial jets

In this work, we propose to study non isothermal air–air coaxial jets with two different approaches: parabolic and elliptic approaches. The standard k−ε model and the RSM model were applied in this study. The numerical resolution of the equations governing this flow type was carried out for: the parabolic approach, by a “home-made” CFD code based on a finite difference method, and the elliptic approach by an industrial code (FLUENT) based on a finite volume method. In forced convection mode (Fr = ∞), the two turbulence models are valid for the prediction of the mean flow. But for turbulent sizes, k−ε model gives results closer to those achieved in experiments compared to RSM Model. Concerning the limit of validity of the parabolic and elliptic approaches, we showed that for velocities ratio r lower than 1, the results of the two approaches were satisfactory. On the other hand, for r > 1, the difference between the results became increasingly significant. In mixed convection mode (Fr ≅ 20), the results obtained by the two turbulence models for the mean axial velocity were very different even in the plume region. For the temperature and the turbulent sizes the two models give satisfactory results which agree well with the correlations suggested by the experimenters for X ≥ 20. Thus, the second order model with σ _t = 0.85 is more effective for a coaxial jet study in a mixed convection mode.     

Turbulence kinetic energy budget in bubbly flows in a vertical duct

Understanding turbulence kinetic energy (TKE) budget in gas–liquid two-phase bubbly flows is indispensable to develop and improve turbulence models for the bubbly flows. In this study, a molecular tagging velocimetry based on photobleaching reaction was applied to turbulent bubbly flows with sub-millimeter bubbles in a vertical square duct to examine the applicability of the k–ε models to the bubbly flows. Effects of bubbles on TKE budget are discussed and a priori tests of the standard and low Reynolds number k–ε models are carried out to examine the applicability of these models to the bubbly flows. The conclusions obtained are as follows: (1) The photobleaching molecular tagging velocimetry is of use for validating turbulence models. (2) The bubbles increase the liquid velocity gradient in the near wall region, and therefore, enhance the production and dissipation rates of TKE. (3) The k–ε models can reasonably evaluate the production rate of TKE in the bubbly flows. (4) The modulations of diffusion due to the bubbles have different characteristics from the diffusion enhancement due to shear-induced turbulence. Hence, the k–ε models fail in evaluating the diffusion rate in the near wall region in the bubbly flows. (5) The k–ε models represent the trends of the production, dissipation, and diffusion rates of ε in the bubbly flow, although more accurate experimental data are required for quantitative validation of the ε equation.     

Modeling of vertical turbulent exchange in a stratified near-wall flow

A modified model of turbulence is proposed to describe the processes of vertical transport in inhomogeneous turbulent flows. This model includes algebraic relations for the Reynolds stresses and turbulent-exchange coefficients. Using this model, the growth of the depth of a mixed layer under the action of the wind load in neutral and stable stratified near-wall flows has been predicted. The calculation results for a stable stratified flow that were obtained using the modified and standard two-parametric models of turbulence are compared with experimental data. Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 39, No. 6, pp. 57–64, November–December, 1998.     

On a Generalized Nonlinear K–ε Model and the Use of Extended Thermodynamics in Turbulence

A resent extension of the nonlinear K–ε model is critically discussed from a basic theoretical standpoint. While it was said in the paper that this model was formulated to incorporate relaxation effects, it will be shown that the model is incapable of describing one of the most basic such turbulent flows as is obvious but is described for clarity. It will be shown in detail that this generalized nonlinear K–ε model yields erroneous results for the Reynolds stress tensor when the mean strains are set to zero in a turbulent flow – the return-to-isotropy problem which is one of the most elementary relaxational turbulent flows. It is clear that K–ε type models cannot describe relaxation effects. While their general formalism can describe relaxation effects, the nonlinear K–ε model – which the paper is centered on – cannot. The deviatoric part of the Reynolds stress tensor is predicted to be zero when it actually only gradually relaxes to zero. Since this model was formulated by using the extended thermodynamics, it too will be critically assessed. It will be argued that there is an unsubstantial physical basis for the use of extended thermodynamics in turbulence. The role of Material Frame-Indifference and the implications for future research in turbulence modeling are also discussed. Received 19 February 1998 and accepted 23 October 1998     

Heat and mass transfer study of impinging turbulent premixed flames

 Impinging jet combusting flows on granite plates are studied. A mathematical model for calculating heat release in turbulent impinging premixed flames is developed. The combustion including radiative heat transfer and local extinction effects, and flow characteristics are modeled using a finite volume computational approach. Two different eddy viscosity turbulence models, namely the standard k–ɛ and the RNG k–ɛ model with and without radiation (discrete transfer model) are assessed. The heat released predictions are compared with experimental data and the agreement is satisfactory only when both radiative heat transfer and local extinction modeling are taken into account. The results indicate that the main effect of radiation is the decrease of temperature values near the jet stagnation point and along the plate surface. Radiation increases temperature gradients and affects predicted turbulence levels independently of the closure model used. Also, the RNG k–ɛ predicts higher temperatures close the solid plate, with and without radiative heat transfer. Received on 13 November 2000 / Published online: 29 November 2001     

Velocity statistics along the stagnation line of an axi- symmetric stagnating turbulent flow

 Velocity statistics along the stagnation line of an axi-symmetric wall stagnating turbulent flow are studied experimentally. A low turbulence, uniform air flow from a nozzle type air supply with an exit diameter of 50 mm stagnates at a wall located 50 mm downstream. A flow velocity is set to 3 m/s, 10 mm downstream from the exit of the air supply. Instantaneous values of streamwise and radial velocities are measured by laser-Doppler velocimetry. The turbulence level in the air flow is changed by use of turbulence generator. When the turbulence generator is not installed in the air supply, the mean velocity profile in the streamwise direction fits well with that of a laminar viscous flow with the rms value of velocity fluctuations low near the wall. With the turbulence generator installed, a significant turbulence structure appears near the wall. When the wall is approached, the rms value of velocity fluctuations in the streamwise direction decreases monotonically while the profile of the rms value in the radial direction reaches a maximum near the wall. The increase in the rms value of velocity fluctuations in the radial direction near the wall is attributed to the bi-modal histogram of the fluctuating velocity in the radial direction. Near the wall, the instantaneous stagnation streamline fluctuates and the probability of the mean location of the stagnation point reaches a maximum not at the stagnation line but on a circle around the stagnation line, resulting in the bi-modal histogram. Turbulence statistics, the rms value of velocity fluctuation and the turbulent kinetic energy, can be normalized successfully by similarity parameters based on the strain rate and the reference turbulent kinetic energy introduced by Champion and Libby. Received: 7 April 1995/Accepted: 27 September 1996     

Two-parameter model of a turbulent flow with a dispersed-particle admixture

Using a two-point probability density function for the particle distribution over velocities and coordinates, a closed model of the particle effect on the turbulent flow characteristics is formulated. The processes of turbulent dissipation and turbulent energy transfer across the spectrum are studied. Different models of two-phase turbulence are compared. Moscow. Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No. 4, pp. 40–56, July–August, 1998. The work received financial support from INTAS (grant No. 94-4348) and the Russian Foundation for Basic Research (project No. 98-01-00-353).     

SOME VALIDATION OF STANDARD,MODIFIED AND NON-LINEAR k–ε TURBULENCE MODELS

Standard, modified and non-linear k–ε: turbulence models are validated against three axisymmetric flow problems—flow through a pipe expansion, flow through a pipe constriction and an impinging jet problem—to underpin knowledge about the solution quality obtained from two-equation turbulence models. The extended models improve the prediction of turbulence as a flow approaches a stagnation point and the non-linear model allows for the prediction of anisotropic turbulence. Significantly different values for the non-linear model coefficients are proposed in comparison with values found in the literature. Nevertheless, current turbulence models are still unable to accurately predict the spreading rate of shear layers. © 1997 by John Wiley & Sons, Ltd. Int. j. numer. methods fluids, 24: 965–986, 1997.     

Numerical study of physiological turbulent flows through series arterial stenoses

A numerical investigation on the characteristics of transitional turbulent flow over series bell‐shape stenoses for a physiological pulsatile flow is presented in the present study. The flow behaviours for the physiological pulsatile flow are studied by considering the effects of the Reynolds number, Womersley number, constriction ratio and spacing ratio of the stenoses on the pulsatile turbulent flow fields. Especially, the mutual influences between the double stenoses under different flow conditions are considered. The numerical results show that the variation of these flow parameters puts significant impacts on the flow developments in the arteries with series stenoses. The double stenoses lead to the higher peak turbulence disturbance and the greater area with comparatively high turbulence intensity distal to the stenoses in comparison with the single stenosis. The analysis shows that for the physiological pulsatile flow, the downstream stenosis usually does not have perceptible influences on the upstream flow fields. Copyright © 2004 John Wiley & Sons, Ltd.     

Numerical simulation of an axisymmetric separated and reattached flow over a longitudinal blunt circular cylinder

This article presents a numerical investigation of turbulent flow in an axisymmetric separated and reattached flow over a longitudinal blunt circular cylinder. The governing equations were discretized by the finite-volume method and SIMPLER method was applied to solve the equations on a staggered grid. The turbulent flow was numerically simulated using the standard k–ε, Abe–Kondoh–Nagano (AKN) and Shear Stress Transport (SST) turbulence models. The comparisons made between numerical results and experimental measurements showed that the SST model is superior to other models in the present calculation.Computations were performed for three different Reynolds numbers of 6000, 10 000 and 20 000 based on the cylinder diameter. To our knowledge, this study represents the first numerical investigation of the present flow configuration. The computational results were validated with the available experimental data of reattachment length, mean velocity distribution and wall static pressure coefficient in the turbulent blunt circular cylinder flows. Further, other characteristics of the flow, such as turbulent kinetic energy, pressure, streamlines, and the velocity vectors are discussed.The results show that the main characteristics of the turbulence flow in the separation region, such as reattachment length or velocity profiles, are nearly independent of the Reynolds number. The obtained results showed that a secondary separation bubble may appear in the main separation bubble near the leading edge. Furthermore, it was found that the turbulent kinetic energy has a large effect on the formation of the secondary bubble.     

Novel Implementation and Assessment of a Digital Filter Based Approach for the Generation of LES Inlet Conditions

A novel implementation of a digital filter based inlet condition generator for Large Eddy Simulation (LES) is presented. The effect of using spatially varying turbulence scales as inputs is investigated; it is found that this has impact on both accuracy and affordability, and has prompted the algorithm implementation changes described in the paper. LES of a channel flow with a periodically repeating constriction was used as a test case. The accuracy of the present simulation using a streamwise periodic boundary condition (PBC) was first established by comparison with a previously published highly resolved LES study. Post-processed statistics from the PBC simulation were then input into a Digital Filter Generator (DFG) algorithm. Three time series were created using the DFG for subsequent use as LES inlet conditions. In the first, as well as inputting the spatially varying first and second moments of the velocity field over the inlet plane from the PBC simulation, the turbulence scales input into the DFG were chosen to be spatially uniform with values specified by an area weighted average across the channel inlet height. In the second and third time-series, the turbulence scales were allowed to change in the wall normal direction, their variation again being deduced from the PBC simulation. These various time series were then used as inlet boundary conditions for LES prediction of the same flow case. Analysis of the results and comparison to the PBC predictions showed that the use of spatially varying turbulence scales increased the accuracy of the simulation in some important areas. However, the cost of generating unsteady inlet conditions using the DFG approach increased significantly with the use of spatially varying turbulence scales. Consequently, a new technique applied as part of the DFG approach is described (used as an ‘on the fly’ method), which significantly reduces the cost of generating LES inlet conditions, even when spatially non-uniform turbulent scales are used.