Measurement of the turbulent kinetic energy budget of a planar wake flow in pressure gradients

Turbulent kinetic energy (TKE) budget measurements were conducted for a symmetric turbulent planar wake flow subjected to constant zero, favorable, and adverse pressure gradients. The purpose of this study is to clarify the flow physics issues underlying the demonstrated influence of pressure gradient on wake development, and provide experimental support for turbulence modeling. To ensure the reliability of these notoriously difficult measurements, the experimental procedure was carefully designed on the basis of an uncertainty analysis. Three different approaches were applied for the estimate of the dissipation term. An approach for the determination of the pressure diffusion term together with correction of the bias error associated with the dissipation estimate is proposed and validated with the DNS results of Moser et al (J Fluid Mech (1998) 367:255–289). This paper presents the results of the turbulent kinetic energy budget measurement and discusses their implications for the development of strained turbulent wakes.An erratum to this article can be found at     

Detailed experimental study of a highly compressible supersonic turbulent plane mixing layer and comparison with most recent DNS results: “Towards an accurate description of compressibility effects in supersonic free shear flows”

A compressible supersonic mixing layer at convective Mach number (Mc) equal to 1 has been studied experimentally in a dual stream supersonic/subsonic wind-tunnel. Laser Doppler Velocimetry (L.D.V.) measurements were performed making possible a full estimation of the mean and turbulent 3D velocity fields in the mixing layer. The Reynolds stress tensor was described. In particular, some anisotropy coefficients were obtained. It appears that the structure of the Reynolds tensor is almost not affected by compressibility at least up to Mc = 1.The turbulent kinetic energy budget was also experimentally estimated. Reynolds analogies assumptions were used to obtain density/velocity correlations in order to build the turbulent kinetic energy budget from LDV measurements. Results have been compared to other experimental and numerical results. Compressibility effects on the turbulent kinetic energy budget have been detected and commented. A study about thermodynamics flow properties was also performed using most recent DNS results experimentally validated by the present data. A non-dimensional number is then introduced in order to quantify the real effect of pressure fluctuations on the thermodynamics quantities fluctuations.     

Experimental study of an impinging jet with different swirl rates

A stereo PIV technique using advanced pre- and post-processing algorithms is implemented for the experimental study of the local structure of turbulent swirling impinging jets. The main emphasis of the present work is the analysis of the influence of swirl rate on the flow structure. During measurements, the Reynolds number was 8900, the nozzle-to-plate distance was equal to three nozzle diameters and the swirl rate was varied from 0 to 1.0. For the studied flows, spatial distributions of the mean velocity and statistical moments (including triple moments) of turbulent pulsations were measured.

The influence of the PIV finite spatial resolution on the measured dissipation rate and velocity moments was analyzed and compared with theoretical predictions. For this purpose, a special series of 2D PIV measurements was carried out with vector spacing up to several Kolmogorov lengthscales.

All terms of the axial mean momentum and the turbulent kinetic energy budget equations were obtained for the cross-section located one nozzle diameter from the impinging plate. For the TKE budget, the dissipation term was directly calculated from the instantaneous velocity fields, thereby allowing the pressure diffusion term to be found as a residual one. It was found that the magnitude of pressure diffusion decreased with the growth of the swirl rate. In general, the studied swirling impinging jets had a greater spread rate and a more rapid decay in absolute velocity when compared to the non-swirling jet.     

Direct numerical simulation of compressible turbulent flows

This paper reviews the authors＇ recent studies on compressible turbulence by using direct numerical simulation （DNS）,including DNS of isotropic（decaying） turbulence, turbulent mixing-layer,turbulent boundary-layer and shock/boundary-layer interaction.Turbulence statistics, compressibility effects,turbulent kinetic energy budget and coherent structures are studied based on the DNS data.The mechanism of sound source in turbulent flows is also analyzed. It shows that DNS is a powerful tool for the mechanistic study of compressible turbulence.     

Effect of bubbles on turbulent kinetic energy transport in downward flow measured by time-resolved PTV

A time-resolved particle tracking velocimetry (PTV) system and a shape projection imaging system were used to investigate the turbulence modifications by bubbles in a downward bubbly flow. Two bubble sizes and three mean void fractions were tested at a Reynolds number of about 20,000. The strong modifications in the mean velocity, turbulent kinetic energy (TKE) budget, and velocity spectra are observed in the central region of the pipe that has a high local void fraction. In particular, kinetic energy production decreased, whereas the TKE dissipation rate increased. This suggests that the transfer of energy due to bubbles has a very large effect on the TKE budget. Moreover, velocity spectra reveal that the presence of bubbles modifies the length scales of turbulent eddies, which contain, transfer, and dissipate energy.     

A three-velocity-component laser-Doppler velocimeter for measurements inside the linear compressor cascade

A 24′′ (610 mm) access laser-Doppler velocimeter (LDV) system was developed to make simultaneous three-velocity-component measurements in a low speed linear cascade wind tunnel with moving wall simulation. The probe has a 610 mm access length and achieves a measurement spatial resolution of 100 μm by using off-axis optical heads. With the relatively large access length, the LDV probe allows for measurements from the side of a wind tunnel instead of through the tunnel floor, while the high spatial resolution allows for quality near-wall measurements. The probe has been tested in a zero-pressure gradient 2D turbulent boundary layer and the test results agree well with the experimental data measured with different LDV systems and hot-wire anemometery for the boundary layer flows. The energy spectral density was estimated using a slot correlation, and Von Kármán’s model for the energy-spectrum function was used to analyze the measured spectral data to estimate the turbulent kinetic energy dissipation rate, which compares favorably with the measured production values in the log-layer region of the turbulent boundary layer. Measurements are presented for the moving endwall boundary layer at the inlet of the linear compressor cascade facility to validate the capability of this LDV for tip leakage flow measurements. These results indicate that the moving endwall reduces velocity gradients in the near-wall region and results in less production of Reynolds stresses and turbulent kinetic energy compared to the stationary endwall case.     

Three-dimensional particle-tracking velocimetry measurement of turbulence statistics and energy budget in a backward-facing step flow

Using a three-dimensional (3-D) particle-tracking velocimeter, detailed turbulent flow measurements were made in a plane channel with a one-sided 50% abrupt expansion, which acted as a backward-facing step. The turbulent channel flow reached a fully developed state well upstream of the step. The Reynolds number based on the upstream centerline velocity and the step height H was 5540. With the mean reattachment point located at 6.51H downstream of the step, the measurement region ranged from −2H upstream to 12H downstream of the step. Various turbulent statistics and the energy budget were calculated from numerous instantaneous vector distributions. As in previous experimental investigations, the Reynolds normal and shear stresses had maximum values upstream of the reattachment. The stress anisotropy tensor revealed a peculiar phenomenon near the reattachment wall, wherein the spanwise normal stress was the largest among the three normal stresses. The triple velocity correlations indicated large values in the separating shear layer, and hence the turbulent diffusion was a major term in the energy budget. Comparison was made between the present results and those of the direct numerical simulation (DNS) of Le et al. (1993), and it was found that the mean and fluctuating velocities, the Reynolds shear stress, and the turbulent energy budget were in excellent agreement, although there was a considerable difference in the inflow conditions.     

Experimental investigation of helicity in turbulent swirling jet using dual-plane dye laser PIV technique

This paper reports a new method of generating two light sheets using a dye laser system and the use of this dual-plane dye laser system to analyse average helicity and energy dissipation in a turbulent swirling flow. The dual-plane PIV system that was used in this study consisted of three cameras and a single frequency Nd:YAG laser, which was used to generate two parallel light sheet planes with differing wavelengths(colour). The method of generating two different light sheet wavelengths using a single laser source is an innovative and new technique. Stereoscopic PIV measurements were obtained in one plane with the use of two CCD cameras, and standard PIV measurements were obtained in the other plane with the use of one CCD camera. The light scattered by the particles on two different light sheets were separated using appropriate optical filters. The measurements obtained were used to estimate the components of the velocity gradient tensor. The tensor components were then used to determine the average vorticity components and helicity quantities of the fluid that was investigated. To determine the average turbulent kinetic energy dissipation, the continuity equation was used to infer the out-of-plane gradient of the out-of-plane velocity. From the analysis of the results, it was found that regions with high helicity were correlated with regions of high turbulent kinetic energy dissipation.     

Direct numerical simulation of turbulent heat transfer in a wall-normal rotating channel flow

Investigations into the characteristics of turbulent heat transfer and coherent flow structures in a plane-channel subjected to wall-normal system rotation are conducted using direct numerical simulation (DNS). In order to investigate the influence of system rotation on the temperature field, a wide range of rotation numbers are tested, with the flow pattern transitioning from being fully turbulent to being quasilaminar, and eventually, fully laminar. In response to the Coriolis force, secondary flows appear as large vortical structures, which interact intensely with the wall shear layers and have a significant impact on the distribution of turbulence kinetic energy (TKE), turbulence scalar energy (TSE), temperature statistics, and turbulent heat fluxes. The characteristic length scales of turbulence structures responsible for the transport of TSE are the largest at the quasilaminar state, which demands a very large computational domain in order to capture the two-dimensional spectra of temperature fluctuations. The effects of the Coriolis force on the turbulent transport processes of the temperature variance and turbulent heat fluxes are thoroughly examined in terms of their respective budget balances.     

Explicit algebraic Reynolds stress model for shock-dominated flows

Shock waves drastically alter the nature of Reynolds stresses in a turbulent flow, and conventional turbulence models cannot reproduce this effect. In the present study, we employ explicit algebraic Reynolds stress model (EARSM) to predict the Reynolds stress anisotropy generated by a shockwave. The model by Wallin and Johansson (2000) is used as the baseline model. It is found to over-predict the post-shock Reynolds stresses in canonical shock turbulence interaction. The budget of the transport equation of Reynolds stresses computed using linear interaction analysis shows that the unsteady shock distortion mechanism and the pressure–velocity correlations are important. We propose improvement to the baseline model using linear interaction analysis results and redistribute the turbulent kinetic energy between the principle Reynolds stresses. The new model matches DNS data for the amplification of Reynolds stresses across the shock and their post-shock evolution, for a range of Mach numbers. It is applied to oblique shock/boundary-layer interaction at Mach 5. Significant improvements are observed in predicting surface pressure and skin friction coefficient, with respect to experimental measurements.     

Review of Experimental Data on Incompressible Turbulent Round Jets

This article reviews measurements for the canonical flow: incompressible turbulent round jets issuing into a large, ideally infinite, quiescent domain. The available far-field data on mean velocity, momentum-flux conservation, Reynolds stresses and triple fluctuation correlations are presented. The budget equations for turbulent kinetic energy and for the individual Reynolds stresses are shown, including different formulations for dissipation and pressure-velocity correlations. Evidence of the persistence of source conditions in the self-preserving far field is observed in several cases. This article analyses and compares several data sets, obtained at different levels of detail, against analytical constraints, discusses limitations and provides insights aided by reference to recent numerical work. It is hoped that this will prove useful in guiding future experiments and numerical test cases, where complete details of the jet configuration are required for validation and comparison.     

Numerical Study of a Turbulent Flow Compressed by a Weak Shock Wave

Abstract

Modification of a two-dimensional isotropic trbulent flow by passage of a weak shock wave was numerically studied by the explicit spectral collocation method with the fourier series in the ranges of M₁ = 0.14?0.21 and M_s = 1.06?1.14. The density 1 trbulent kinetic energy increased by 10 to 19 % and density fluctuation increased by 14 to 50 % in proportion to the shock wave mach number. The amplification of turbulent kinetic energy did not change by increase of the turbulent Mach number, while that of density fluctuation decreased from1.35 to 1.15%. The argumentation of turbulent kinetic energy appeared at moderate and high wave numbers of energy spectra and resulted in a reduction of the integral scale by3.33 to 5.4%. Modifications mechanisms of turbulent kinetic energy, density fluctuation and vorticity were verified by the transport equations It was shown that the decreased amplification of the density fluctuation In the increased trbulent Mach number attributed to the unchanged production terms and the negative dilatation correlation behind the shock wave.the vorticity-dilatation term was responsible for more than 80 % of the total vorticity production at the shock front.     

Turbulent kinetic energy balance in a LEBU modified turbulent boundary layer

An experimental study of the turbulent kinetic energy balance is performed in a LEBU manipulated turbulent boundary layer. The estimation of almost all the terms of the k-equation is obtained by hot wire anemometry. Near the manipulating device, strong alterations are observed, when compared with the natural conditions. The wake of the manipulator imposes two distinct zones. The lower part is characterized by negligible production compensated by diffusion, while, in the outer part, a large excess of production is balanced by diffusion and dissipation. The excess of dissipation rapidly vanishes downstream. The relaxation process is slower for production and diffusion.A version of this paper was presented at the 11th Symposium on Turbulence, University of Missouri-Rolla, Oct. 17–19, 1988     

Development of inflow turbulence in microscale urban atmospheric environment

The sensitivity of turbulence-development to inflow turbulent statistics is investigated in microscale urban atmospheric environment flows. Large-eddy simulations(LESs) are carried out, in which the inflow error is brought in by transforming a fully developed turbulent field according to the Reynolds stress or energy spectra. A theoretical analysis is performed by neglecting the diffusion term in the budget equations of the turbulent kinetic energy. The results show that,(i) the error caused by the Reynolds stress decays until the fully developed level is achieved, and(ii) the error caused by the characteristic length scale increases immediately and then decreases. The streamwise changing rate of the inflow error weakens when the vertical coordinate increases. Further testing of the effects of the inflow inner-and outer-layer data shows that, the inflow innerlayer data dominate the near field, and the inflow outer-layer data dominate the far field.     

Turbulent structure during transition to self-similarity in a round jet

 The developing turbulent region of a round jet was investigated using an improved implementation of digital particle image velocimetry (DPIV). The two-dimensional flow field in planes normal and parallel to the axial velocity was measured at locations between 15 and 30 diameters downstream, for two Reynolds numbers of 5500 and 16,000. The study consisted of instantaneous snapshots of the velocity and vorticity fields as well as measurements of velocity correlations up to third order. In this regime, the Reynolds number had a significant effect on both the instantaneous flow structure and the profiles of mean velocity across the jet. Coherent streamwise structures were present in the jet core for the lower Reynolds number. Additional structures whose evolution was governed by time scales two orders of magnitude larger than the convective scale inside the jet were observed in the entrainment field. The velocity correlations provided further support for the validity of DPIV turbulence measurements. The data was consistent with the equations of motion and momentum was conserved. DPIV measurements of turbulent kinetic energy components agreed with the hot-wire measurements of previous studies. Received: 27 November 1996/Accepted: 14 July 1997     

Numerical modeling of a two-dimensional vertical turbulent two-phase jet

The results of numerically modeling two-dimensional two-phase flow of the “gas-solid particles” type in a vertical turbulent jet are presented for three cases of its configuration, namely, descending, ascending, and without account of gravity. Both flow phases are modeled on the basis of the Navier-Stokes equations averaged within the framework of the Reynolds approximation and closed by an extended k-? turbulence model. The averaged two-phase flow parameters (particle and gas velocities, particle concentration, turbulent kinetic energy, and its dissipation) are described using the model of mutually-penetrating continua. The model developed allows for both the direct effect of turbulence on the motion of disperse-phase particles and the inverse effect of the particles on turbulence leading to either an increase or a decrease in the turbulent kinetic energy of the gas. The model takes account for gravity, viscous drag, and the Saffman lift. The system of equations is solved using a difference method. The calculated results are in good agreement with the corresponding experimental data which confirms the effect of solid particles on the mean and turbulent characteristics of gas jets.     

Numerical investigation of the turbulent energy budget in the wake of freely oscillating elastically mounted cylinder at low reduced velocities

We present a numerical study of the turbulent kinetic energy budget in the wake of cylinders undergoing Vortex-Induced Vibration (VIV). We show three-dimensional Large Eddy Simulations (LES) of an elastically mounted circular cylinder in the synchronization regime at Reynolds number of Re=8000. The Immersed Boundary Method (IBM) is used to account for the presence of the cylinder. The flow field in the wake is decomposed using the triple decomposition splitting the flow variables in mean, coherent and stochastic components. The energy transfer between these scales of motions are then studied and the results of the free oscillation are compared to those of a forced oscillation. The turbulent kinetic energy budget shows that the maximum amplitude of VIV is defined by the ability of the mean flow to feed energy to the coherent structures in the wake. At amplitudes above this maximum amplitude, the energy of the coherent structures needs to be fed additionally by small scale, stochastic energy in form of backscatter to sustain its motion. Furthermore, we demonstrate that the maximum amplitude of the VIV is defined by the integral length scale of the turbulence in the wake.     

Simultaneous Measurement of Velocity and Fluctuating Pressure in a Turbulent Wing-tip Vortex Using Triple Hot-film Sensor and Miniature Total Pressure Probe

We have developed a probe-system for simultaneous measurement of three velocity components and pressure in turbulent flows. A miniature total pressure probe is placed adjacent to the sensors of a triple hot-film probe in order to achieve the spatial resolution which is equivalent to that of the triple hot-film probe itself. The instantaneous static pressure is calculated from measured velocity and total pressure by means of a newly developed processing method based on the Bernoulli equation for unsteady flows. The measurements were undertaken in a turbulent wing-tip vortex flow. The look-up table method is employed for the calibration of the hot-film probe so accurate velocity data could be obtained over a wide range of the flow-attack angles. It is also demonstrated that the present probe-system is capable of measuring fluctuations in both velocity and pressure in the 20?C650 Hz frequency range. The distribution of the fluctuating pressure obtained by this indirect method is in good agreement with the results from direct measurements of static pressure, demonstrating the promising performance of the present method. Furthermore, an improvement in the ability to make measurements of the velocity?Cpressure correlation across the wing-tip vortex is achieved. This improvement is possible because the effects of lateral velocity components are properly taken into account in the present formulation. The investigation regarding the transport equation budget for turbulent kinetic energy shows an anomalous structure of turbulence in this flow, mainly due to the meandering of the vortex, and the measurement of pressure diffusion is found to play an important role in the characterization of this kind of flow.     

Modeling of bubble coalescence and break-up considering turbulent suppression phenomena in bubbly two-phase flow

New mechanistic bubble coalescence and break-up models considering turbulent suppression phenomena, which can possibly occur in the high liquid velocity condition of turbulent bubbly two-phase flow, are presented. The energy exchange mechanism between a turbulent eddy and interfacial structure was taken into account in the efficiency terms. Numerical simulations of turbulent bubbly flow were conducted in a CFD code to evaluate the newly developed models, in comparison with other advanced models coupled with a bubble-induced turbulent effect for one-group interfacial area transport equation. Local measurements of the bubble characteristics on the bubble size evolution along a vertical pipe flow were performed at KAERI-VAWL test facility using the five-sensor conductivity probe method to provide database for models validation. Results from the calculation clearly show the improvements of the newly developed models.     

Analysis and Modeling of the Turbulent Diffusion of Turbulent Kinetic Energy in Natural Convection

Buoyant flows often contain regions with unstable and stable thermal stratification from which counter gradient turbulent fluxes are resulting, e.g. fluxes of heat or of any turbulence quantity. Basing on investigations in meteorology an improvement in the standard gradient-diffusion model for turbulent diffusion of turbulent kinetic energy is discussed. The two closure terms of the turbulent diffusion, the velocity-fluctuation triple correlation and the velocity-pressure fluctuation correlation, are investigated based on Direct Numerical Simulation (DNS) data for an internally heated fluid layer and for Rayleigh–Bénard convection. As a result it is decided to extend the standard gradient-diffusion model for the turbulent energy diffusion by modeling its closure terms separately. Coupling of two models leads to an extended RANS model for the turbulent energy diffusion. The involved closure term, the turbulent diffusion of heat flux, is studied based on its transport equation. This results in a buoyancy-extended version of the Daly and Harlow model. The models for all closure terms and for the turbulent energy diffusion are validated with the help of DNS data for internally heated fluid layers with Prandtl number Pr = 7 and for Rayleigh–Bénard convection with Pr = 0.71. It is found that the buoyancy-extended diffusion model which involves also a transport equation for the variance of the vertical velocity fluctuation gives improved turbulent energy diffusion data for the combined case with local stable and unstable stratification and that it allows for the required counter gradient energy flux.