Turbulent kinetic energy balance in the wake of a self-propelled body

An experimental study of the turbulent wake of a self-propelled body in a wind tunnel is reported. A significant difference is formed between the turbulent kinetic energy balance in a wake with drag and in the wake of a self-propelled body: the production term is very small in comparison with the other terms of the turbulent kinetic energy balance, and this result seems to be typical of self-propulsion. The axial evolution of the wake radius and turbulent kinetic energy profiles are described. Sufficiently far downstream from the body, a self-similar profile is found. Particular attention is devoted to the turbulent kinetic energy balance; all the terms in the energy balance are evaluated experimentally.List of Symbols D diameter of the body - L axial length scale - l radial length scale - R radius of the body - r radial coordinate - r ^* radius of the wake - U mean axial velocity scale - Û defect velocity - U _e freestream velocity - u fluctuating velocity scale - x axial coordinate - dissipation rate - = r/r ^* radial relative direction - azimuthal coordinate - kinematic viscosity - density     

Performance assessment of a non-linear eddy-viscosity turbulence model applied to the anisotropic wake flow of a low-pressure turbine blade

The wake flow produced by a low-pressure turbine blade is modeled using a non-linear eddy-viscosity turbulence model. The theoretical benefit of using a non-linear eddy-viscosity model is strongly related to the capability of resolving highly anisotropic flows in contrast to the linear turbulence models, which are unable to correctly predict anisotropy. The main aim of the present work is to practically assess the performance of the model, by examining its ability to capture the anisotropic behavior of the wake-flow, mainly focusing on the measured velocity and Reynolds-stress distributions and to provide accurate results for the turbulent kinetic energy balance terms. Additionally, the contribution of each term of its non-linear constitutive expression for the Reynolds stresses is also investigated, in order to examine their direct effect on the modeling of the wake flow. The assessment is based on the experimental measurements that have been carried-out by the same group in Thessaloniki, Sideridis et al. (2011). The computational results show that the non-linear eddy viscosity model is capable to predict, with a good accuracy, all the flow and turbulence parameters while it is easy to program it in a computer code thus meeting the expectations of its originators.     

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     

Three-component velocity field measurements of propeller wake using a stereoscopic PIV technique

A stereoscopic PIV (Particle Image Velocimetry) technique was used to measure the three-dimensional flow structure of the turbulent wake behind a marine propeller with five blades. The out-of-plane velocity component was determined using two CCD cameras with an angular displacement configuration. Four hundred instantaneous velocity fields were measured for each of four different blade phases, and ensemble averaged in order to find the spatial evolution of the propeller wake in the region from the trailing edge up to one propeller diameter (D) downstream. The influence of propeller loading conditions on the wake structure was also investigated by measuring the velocity fields at three advance ratios (J=0.59, 0.72 and 0.88). The phase-averaged velocity fields revealed that a viscous wake formed by the boundary layers developed along the blade surfaces. Tip vortices were generated periodically and the slipstream contracted in the near-wake region. The out-of-plane velocity component and strain rate had large values at the locations of the tip and trailing vortices. As the flow moved downstream, the turbulence intensity, the strength of the tip vortices, and the magnitude of the out-of-plane velocity component at trailing vortices all decreased due to effects such as viscous dissipation, turbulence diffusion, and blade-to-blade interaction.     

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.     

Diffusion flame analysis of twin plane jets via a kinetic theory approach

Diffusion flame solutions of twin plane jets based on a turbulent kinetic theory due to Chung and a Green function method by Hong are presented. The chemical reaction between fuel and oxidizer is assumed to be one-step, one-direction and infinitely fast. The solutions are obtained by direct integration over a constructed probability density function in velocity space. The probability density functions of reactants in transverse velocity space, species mass fraction distributions, turbulent transport of momentum and heat, temperature distributions and flame structure are also considered in this paper. The diffusion flame phenomena of the twin plane jets show that the interaction between the two jets is a dominant factor.     

Preliminary report on the energy balance for nonlinear oscillations

In this paper, a reliable technique for calculating angular frequencies of nonlinear oscillators is developed. The new algorithm offers a promising approach by constructing a Hamiltonian for the nonlinear oscillator. Some illustrative examples are given.     

Two-equation turbulence models for prediction of heat transfer on a transonic turbine blade

Two versions of the two-equation k–ω model and a shear stress transport (SST) model are used in a three-dimensional, multi-block, Navier–Stokes code to compare the detailed heat transfer measurements on a transonic turbine blade. It is found that the SST model resolves the passage vortex better on the suction side of the blade, thus yielding a better comparison with the experimental data than either of the k–ω models. However, the comparison is still deficient on the suction side of the blade. Use of the SST model does require the computation of distance from a wall, which for a multi-block grid, such as in the present case, can be complicated. However, a relatively easy fix for this problem was devised. Also addressed are issues such as (1) computation of the production term in the turbulence equations for aerodynamic applications, and (2) the relation between the computational and experimental values for the turbulence length scale, and its influence on the passage vortex on the suction side of the turbine blade.     

Separation-induced boundary layer transition: Modeling with a non-linear eddy-viscosity model coupled with the laminar kinetic energy equation

We present an effort to model the separation-induced transition on a flat plate with a semi-circular leading edge, using a cubic non-linear eddy-viscosity model combined with the laminar kinetic energy. A non-linear model, compared to a linear one, has the advantage to resolve the anisotropic behavior of the Reynolds-stresses in the near-wall region and it provides a more accurate expression for the generation of turbulence in the transport equation of the turbulence kinetic energy. Although in its original formulation the model is not able to accurately predict the separation-induced transition, the inclusion of the laminar kinetic energy increases its accuracy. The adoption of the laminar kinetic energy by the non-linear model is presented in detail, together with some additional modifications required for the adaption of the laminar kinetic energy into the basic concepts of the non-linear eddy-viscosity model. The computational results using the proposed combined model are shown together with the ones obtained using an isotropic linear eddy-viscosity model, which adopts also the laminar kinetic energy concept and in comparison with the existing experimental data.     

Experimental investigation on the wake interference among wind turbines sited in atmospheric boundary layer winds

We examined experimentally the effects of incom-ing surface wind on the turbine wake and the wake interfer-ence among upstream and downstream wind turbines sited in atmospheric boundary layer (ABL) winds. The experi-ment was conducted in a large-scale ABL wind tunnel with scaled wind turbine models mounted in different incom-ing surface winds simulating the ABL winds over typical offshore/onshore wind farms. Power outputs and dynamic loadings acting on the turbine models and the wake flow char-acteristics behind the turbine models were quantified. The results revealed that the incoming surface winds significantly affect the turbine wake characteristics and wake interference between the upstream and downstream turbines. The velocity deficits in the turbine wakes recover faster in the incoming surface winds with relatively high turbulence levels. Varia-tions of the power outputs and dynamic wind loadings acting on the downstream turbines sited in the wakes of upstream turbines are correlated well with the turbine wakes charac-teristics. At the same downstream locations, the downstream turbines have higher power outputs and experience greater static and fatigue loadings in the inflow with relatively high turbulence level, suggesting a smaller effect of wake inter-ference for the turbines sited in onshore wind farms.     

Prediction of wake in a curved duct

Experimental data on the development of an aerofoil wake in a curved stream are compared with calculations based on the k-ε model of turbulence with standard constants and with the model constant C_μ dependent on the local curvature. The mean velocity profile is asymmetric, the half-width of the wake is more on the inner side of the curved duct than on the outer side, and the turbulent shear stress decreases rapidly on the outer side. The standard k-ε model is able to satisfactorily reproduce this behaviour. Making C_μ dependent on the local radius improves the agreement on the inner side but slightly worsens it on the outer side.     

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.     

First instabilities in the wake past a circular cylinder. Comparison of transient regimes with landau's model

Velocity measurements were carried out in the flow past a circular cylinder at Reynolds number ranging from 30 to 180 to study the genesis and the evolution of the first instabilities in the wake. Since the occurrence of aeroelastic coupling between flow and cylinder has been cause of debate about the results obtained in recent experiments on the subject, a great deal of care has been taken to avoid that coupling. We focused our attention on two points: the onset of the first instability and the transition from the low-speed to the high-speed oscillation mode. With regard to the second topic we can confirm the existence of a discontinuity in the relation between St and Re at Re90 even in the absence of any aeroelastic coupling. However, no band enlargements in the velocity spectrum, indicating the appearance of highly disorganized motion, were observed for Re varying through that discontinuity interval. To investigate the onset of the first periodic oscillation we performed measurements with a slowly varying Reynolds number by means of very small positive or negative accelerations. Our results indicate that in the neighborhood of the onset of the first oscillation the amplitude of the transient velocity fluctuations does not obey the so-called Landau model.

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Sommario Al fine di studiare la genesi e l'evoluzione delle prime instabilitá nelle scie si sono eseguite delle misure della velocitá nel flusso a valle di un cilindro circolare variando il numero di Reynolds tra 30 e 180. Poiché esiste, per questo tipo di esperimento, la possibilitá di ritrovarsi in una situazione di accoppiamento aeroelastico tra il cilindro ed il flusso, situazione tale da inficiarne l'attendibilitá e che é stata causa di dispute scientifiche sull'interpretazione dei risultati ottenuti nei piú recenti esperimenti sul soggetto, si é accuratamnete progettato l'esperimento in modo da escludere qualisiasi condizione suscettibile di innescare un tale accoppiamento. Si é concentrata l'attenzione su due punti principali: l'insorgere della prima instabilitá e la transizione tra il low-speed ed il high-speed oscillation mode. Per quel che concerne il secondo punto noi possiamo confermare l'esistenza di una discontinuitá nella relazione St=f(Re) quando il Re 90 anche in assenza di qualsiasi accoppiamneto aeroelastico. Inoltre, al variare del Re attraverso questa discontinuitá, non si é osservato nessun allargamento di banda nello spettro delle velocitá che potesse indicare l'apparire di un moto altamente disorganizzato. Per studiare la genesi della prima oscillazione periodica si sono eseguite delle misure al lento variare del Re per mezzo di piccolissime accelerazioni, sia positive che negative, impartite al campo di moto. I risultati ottenuti indicano che nelle vicinanze dell' insorgere della prima oscillazione l'ampiezza delle fluttuazioni transienti non obbedisce al modello di Landau.

     

Effects of camberwise varying tip injection on loss and wake characteristics of a low pressure turbine blade

This paper presents the results of an experimental study that investigates the effects of camberwise varying tip injection on the total pressure loss and wake flow characteristics downstream of a row of Low Pressure Turbine (LPT) blades. This injection technique involves spanwise jets at the tip that are issued from a series of holes distributed along the camber line. The injection from each hole is individually and separately controlled using a computer driven solenoid valve and therefore the flow injection geometrical pattern at the tip can be adjusted to any desired variation. Three different injection cases are investigated including triangular, reversed triangular and uniform injection patterns. Here, triangular and reversed triangular cases refer to discrete blowing from the blade tip in which the blowing velocity increases (triangular) or decreases (reverse triangular) linearly from the leading to trailing edge along the camber. For uniform injection, the injection velocity is kept constant for all injection holes. The total mass injection from the tip is kept the same for all injection cases. The experiments are conducted in a continuous-flow wind tunnel with a linear cascade test section and measurements involve Kiel probe traverses 0.5 axial chords downstream of the blades covering a region between 85% and 100% span as well as two-dimensional Particle Image Velocimetry (PIV) measurements on 50%, 85% and 95% spanwise planes. For all injection cases, results show that tip injection reduces the total pressure loss levels in general. Highest measured overall loss reduction occurs in the case of reversed-triangular injection. The least effective waveform is observed to be triangular injection. There is significant reduction in the extent of the low momentum zone of the leakage vortex with injection. This effect is much less pronounced for the passage vortex. On the other hand, complex flow patterns are observed within the passage vortex, especially in the case of reversed-triangular injection, such as a possible embedded vortical structure along the passage vortex core, which creates double peaks in the velocity and turbulent kinetic energy fields.     

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     

Wake impacts on aerodynamic and aeroelastic behaviors of a horizontal axis wind turbine blade for sheared and turbulent flow conditions

The magnitude and temporal variations of wind speed considerably influence aerodynamic and structural responses of MW-sized horizontal axis wind turbines. Thus, this paper investigates the variations in airloads and blade behavior of a wind turbine blade resulting from operations in sheared and turbulent flow conditions. First, in order to validate the present methods, comparisons of aerodynamic results were made among the blade element momentum method, free-wake method, and numerical results from the previous studies. Then, the validated methods were applied to a national renewable energy laboratory 5 MW reference wind turbine model for fluid–structure interaction analyses. From the numerical simulations, it can be clearly seen that unfavorable airloads and blade deformations occur due to the sheared and turbulent flow conditions. In addition, it is clear that wake impacts are not as substantial at those of high wind speeds; however, the effects obviously affect the aerodynamic and structural behaviors of the blade at lower wind speeds. Therefore, it is concluded that the numerical results markedly indicate the demand for accurate assessment of wake dynamics for accurate estimations of the aerodynamic and structural responses for sheared and turbulent flow environments.