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.     

Numerical simulation of turbulence suppression: Comparisons of the performance of four k-? turbulence models

The standard k-ε model and three low-Reynolds number k-ε models were used to simulate pipe flow with a ring device installed in the near-wall region. Both developing and fully developed turbulent pipe flows have been investigated. Turbulence suppression for fully developed pipe flows revealed by hot-wire measurements has been predicted with all three low-Reynolds number models, and turbulence enhancement has been predicted by the standard k-ε model. All three low-Reynolds number models have predicted similar distributions of velocities, turbulence kinetic energy, and dissipation rate. For developing pipe flows, the region of turbulence suppression predicted by the three low-Reynolds number models is much more extensive (up to 30 pipe diameters downstream of the device) than for full developed flow; whereas the standard k-ε model has only predicted turbulence enhancement.     

槽道湍流近壁结构的DPIV观测实验

采用DPIV系统(由两台CCD相机组成)对槽道湍流进行速度场时间历程的观测实验，通 过对大量测量结果的综合分析，取得了槽道湍流近壁结构的空间结构及其时间演化过程特征 的结果，可以揭示上扫下掠、湍流瞬时速度型等现象与大尺度涡演化的物理关系，解释若干 湍流大尺度结构的特征机理，还表明DPIV系统提供了一种定量观测湍流的时空结构特征的手 段.     

柔性壁面湍流边界层相干结构控制的实验研究

本文利用热膜测速技术对刚性壁面和柔性壁面湍流边界层的流向速度分量进行了实验测量,首先研究了柔性壁面对平均速度分布和湍流度分布的影响,结果表明:柔性壁面的边界层速度分布在对数律层向上有所平移,缓冲层加厚,具有一般的壁面减阻特征;而柔性壁的湍流度比刚性壁的湍流度要低,分布也更为平坦。然后综合运用自相关法和条件采样技术研究了湍流近壁区的相干结构,结果表明:刚性壁自相关曲线的第二峰值出现的时间比柔性壁的短,柔性壁的猝发频率比刚性壁的低许多。实验结果表明柔性壁面具有一定的减阻作用。     

一类平衡大气边界层边界条件研究

基于标准k-ε湍流模型,首先利用湍流粘度方程和剪切应力在整个边界层内恒定的假设,推导出一类耗散率表达式,并根据常用的湍动能入口剖面方程以及平均风速剖面方程,计算获得相应的耗散率方程;然后在输运方程中添加自定义源项,通过已经确定的平均速度方程、湍动能方程、耗散率方程计算得到相应输运方程的自定义源项表达式,并进行空风洞数值模拟,从而得到了一类满足平衡大气边界层的来流边界条件．通过将这种边界条件与由湍流平衡条件得到的边界条件进行比较,表明本方法获得的边界条件更适用．并且,本方法无需考虑修正壁面函数和修正湍流模型常数,因而计算更为简单,可为平衡大气边界层的研究提供一种新的思路．     

The development of an axisymmetric curved turbulent wall jet

An experimental study has been carried out of the low speed Coanda wall jet with both streamwise and axisymmetric curvature. A single component laser Doppler technique was used, and by taking several orientations at a given point, values of the three mean velocities and five of the six Reynolds stresses were obtained. The lateral divergence and convex streamwise curvature both enhanced the turbulence in the outer part of the jet compared with a plane two-dimensional wall jet. The inner layer exhibited a large separation of the positions of maximum velocity and zero shear stress. It was found that the streamwise mean velocity profile became established very rapidly downstream of the slot exit. The profile appeared fairly similar at later downstream positions, but the mean radial velocity and turbulence parameters showed the expected nonself preservation of the flow. Removal of the streamwise curvature resulted in a general return of the jet conditions toward those expected of a plane wall jet. The range and accuracy of the data may be used for developing turbulence models and computational techniques for this type of flow.     

Algebraic turbulence modeling in adiabatic gas–liquid annular two-phase flow

The study considers algebraic turbulence modeling in adiabatic gas–liquid annular two-phase flow. After reviewing the existing literature, two new algebraic turbulence models are proposed for both the liquid film and the droplet laden gas core of annular two-phase flow. Both turbulence models are calibrated with experimental data taken from the open literature and their performance critically assessed. Although the proposed turbulence models reproduce the key parameters of annular flow well (average liquid film thickness and pressure gradient) and the predicted velocity profiles for the core flow compare favorably with available core flow velocity measurements, a more accurate experimental database is required to further improve the models accuracy and range of applicability.     

A Hybrid RANS/LES Simulation of Turbulent Channel Flow

Hybrid models combining large eddy simulation (LES) with Reynolds-averaged Navier–Stokes (RANS) simulation are expected to be useful for wall modeling in the LES of high Reynolds number flows. Some hybrid simulations of turbulent channel flow have a common defect; the mean velocity profile has a mismatch between the RANS and LES regions due to a steep velocity gradient at the interface. This mismatch is reproduced and examined using a simple hybrid model; the Smagorinsky model is switched to a RANS model increasing the filter width. It is suggested that a rapid spatial variation in the eddy viscosity is responsible for an underestimate of the grid-scale shear stress and for the steep velocity gradient. To reduce the mean velocity mismatch a new scheme is proposed; additional filtering is introduced to define two kinds of velocity components at the interface between the two regions. The two components are used to remove inconsistency in the velocity equations due to a rapid variation in the filter width. Using the new scheme, simulations of channel flow are carried out with the simple hybrid model. It is shown that the grid-scale shear stress becomes large enough and most of the mean velocity mismatch is removed. Simulations for higher Reynolds numbers are carried out with the k–ε model and the one-equation subgrid-scale model. Although it is necessary to improve the turbulence models and the treatment of the buffer region, the new scheme is shown to be effective for reducing the mismatch and to be useful for developing better hybrid simulations. Received 5 April 2002 and accepted 8 January 2003 Published online 25 March 2003 Communicated by M.Y. Hussaini     

Experiments in Turbulent Pipe Flow with Polymer Additives at Maximum Drag Reduction

In this paper we report on (two-component) LDV experiments in a fully developed turbulent pipe flow with a drag-reducing polymer (partially hydrolyzed polyacrylamide) dissolved in water. The Reynolds number based on the mean velocity, the pipe diameter and the local viscosity at the wall is approximately 10000. We have used polymer solutions with three different concentrations which have been chosen such that maximum drag reduction occurs. The amount of drag reduction found is 60–70%. Our experimental results are compared with results obtained with water and with a very dilute solution which exhibits only a small amount of drag reduction. We have focused on the observation of turbulence statistics (mean velocities and turbulence intensities) and on the various contributions to the total shear stress. The latter consists of a turbulent, a solvent (viscous) and a polymeric part. The polymers are found to contribute significantly to the total stress. With respect to the mean velocity profile we find a thickening of the buffer layer and an increase in the slope of the logarithmic profile. With respect to the turbulence statistics we find for the streamwise velocity fluctuations an increase of the root mean square at low polymer concentration but a return to values comparable to those for water at higher concentrations. The root mean square of the normal velocity fluctuations shows a strong decrease. Also the Reynolds (turbulent) shear stress and the correlation coefficient between the stream wise and the normal components are drastically reduced over the entire pipe diameter. In all cases the Reynolds stress stays definitely non-zero at maximum drag reduction. The consequence of the drop of the Reynolds stress is a large polymer stress, which can be 60% of the total stress. The kinetic-energy balance of the mean flow shows a large transfer of energy directly to the polymers instead of the route by turbulence. The kinetic energy of the turbulence suggests a possibly negative polymeric dissipation of turbulent energy. This revised version was published online in July 2006 with corrections to the Cover Date.     

Application of compressible Reynolds-averaged governing equations to turbulent mixed convection in supercritical fluids in heated vertical tubes

Accurate estimation of thermal-hydraulic characteristics of supercritical flows has long been an attractive but elusive subject to many researchers in spite of tremendous effort devoted to the development of suitable turbulence models. One of the key reasons for the difficulty is a lack of measured turbulence data, which might have been used to formulate adequate turbulence models suitable for highly buoyant fluids. Turbulence models are typically based on the log-law, while the velocity profile in buoyant fluids substantially deviates from the log-law because of significant density variation in a turbulent boundary layer. In this paper, axisymmetric compressible Reynolds-Averaged governing equations were employed together with the property-dependent turbulent Prandtl number to reproduce experimental data representing heat transfer deterioration and consequential sudden temperature increase. The additional turbulence terms associated with turbulent mass flux appeared in the governing equations were modeled using the simple gradient diffusion hypothesis (SGDH). The proposed model successfully reproduced the experimental data. The various turbulence properties are presented and discussed.     

A novel formula to describe the velocity profile of free jet flow

Having a potential core, the velocity profile in initial zone of incompressible submerged jet flow is different from that in fully developed region. In the former researches, the two regions were studied separately, even a short part between the two regions being considered as a transition region. The velocity profile in fully developed region looked as a Gaussian distribution, which is valid when jet initial region is comparatively short. But when the size of initial zone is long enough not to be able to be neglected, especially for large-size exit, this kind of assumption is not acceptable. Based on the analysis of flow structure of jet flow, a new velocity profile formula of submerged jet flow was proposed, which unites the initial, transition, fully developed regions of jet flow via modifying Gaussian distribution with a radial adjusting coefficient. For the round jet with the medium or high range of Reynolds number, the radial adjusting coefficient is a power function of reciprocal of jet distance. And then some literature experimental data were applied in verification, and the new formula exhibited a good calculation result. This work opened that the jet flow velocity profile at any site along the flow distance can be described via a same formula.     

Large eddy simulation and a simple wall model for turbulent flow calculation by a particle method

A turbulent channel flow and the flow around a cubic obstacle are calculated by the moving particle semi‐implicit method with the subparticle‐scale turbulent model and a wall model, which is based on the zero equation RANS (Reynolds Averaged Navier‐Stokes). The wall model is useful in practical problems that often involve high Reynolds numbers and wall turbulence, because it is difficult to keep high resolution in the near‐wall region in particle simulation. A turbulent channel flow is calculated by the present method to validate our wall model. The mean velocity distribution agrees with the log‐law velocity profile near the wall. Statistical values are also the same order and tendency as experimental results with emulating viscous layer by the wall model. We also investigated the influence of numerical oscillations on turbulence analysis in using the moving particle semi‐implicit method. Finally, the turbulent flow around a cubic obstacle is calculated by the present method to demonstrate capability of calculating practical turbulent flows. Three characteristic eddies appear in front of, over, and in the back of the cube both in our calculation and the experimental result that was obtained by Martinuzzi and Tropea. Mean velocity and turbulent intensity profiles are predicted in the same order and have similar tendency as the experimental result. Copyright © 2012 John Wiley & Sons, Ltd.     

Simulation of the Effect of the Freestream Turbulence Parameters on Heat Transfer in an Unsteady Boundary Layer

A variant of the two-parameter turbulence model which makes it possible continuously to calculate a flow region with laminar, transition and turbulent regimes is proposed for investigating the flow under conditions of high freestream turbulence intensity. It is shown that the properties of the thermal transition can be theoretically described using the quasi-steady turbulence model in the case of periodic freestream velocity distribution. The numerical results are compared with theoretical and experimental data. The approach proposed is developed for determining the combined effect of the parameters of harmonic fluctuations of the external velocity and freestream turbulence on the heat transfer characteristics on a flat plate with different boundary conditions for the enthalpy.     

Investigation of Advanced Turbulence Models for the Flow in a Generic Wing-Body Junction

The predictive performance of several turbulence models, among them formulations based on non-linear stress-strain relationships and on stress-transport equations, is examined in a collaborative university-industry study directed towards a generic wing-body junction. The geometry consists of a variation of the symmetric NACA 0020 aerofoil mounted on a flat plate, with the oncoming stream aligned with the aerofoil's symmetry plane. The dominant feature of this flow is a pronounced horseshoe vortex evolving in the junction region following separation ahead of the aerofoil's leading edge. This case is one of 6 forming a broad programme of turbulence-model validation by UMIST, Loughborough University, BAE Systems, Aircraft Research Association, Rolls-Royce plc and DERA. Key aspects of this collaboration were a high level of interaction between the partners, the use of common grids and boundary conditions, and numerical verifications aimed at maximizing confidence in the validity of the computational solutions. In total, 12 turbulence models were studied by four partners. Model performance is judged by comparing solutions with experimental data for pressure fields on the plane wall and around the aerofoil; for velocity, turbulence energy, shear stress and streamwise normal stress in the upstream symmetry plane; and for velocity, turbulence energy and shear stress in cross-flow planes downstream of the aerofoil leading edge. The emphasis of the study is on the structure of the horseshoe vortex and its effects on the forward flow. The main finding of the study is that, for this particular 3D flow, second-moment closure offers predictive advantages over the other models examined, especially in terms of the far-field structure of the horse-shoe vortex, although no model achieves close agreement with the experimental data in respect of both mean flow and turbulence quantities. This revised version was published online in July 2006 with corrections to the Cover Date.     

On the connection between the aerodynamic and acoustic characteristics of coaxial jets

The results are given of experimental investigations into the distributions of the mean and pulsation velocities in the mixing region of isothermal coaxial jets with ordinary velocity profile and “inverted” velocity profile (velocity of the outer flow greater than that of the inner flow). These results are used in a comparative estimate of the noise of coaxial jets with different initial velocity profiles, and a comparison is made with the data of experimental investigations of the noise.     

Finite element computation of a turbulent flow over a two-dimensional backward-facing step

This paper is devoted to the computation of turbulent flows by a Galerkin finite element method. Effects of turbulence on the mean field are taken into account by means of a k-? turbulence model. The wall region is treated through wall laws and, more specifically, Reichardt's law. An inlet profile for ? is proposed as a numerical treatment for physically meaningless values of k and ?. Results obtained for a recirculating flow in a two-dimensional channel with a sudden expansion in width are presented and compared with experimental values.     

Toward low‐noise synthetic turbulent inflow conditions for aeroacoustic calculations

The accuracy of boundary conditions for computational aeroacoustics is a well‐known challenge, due in part to the necessity of truncating the flow domain and replacing the analytical boundary conditions at infinity with numerical boundary conditions. In particular, the inflow boundary condition involving turbulent velocity or scalar fields is likely to introduce spurious waves into the domain, therefore degrading the flow behavior and deteriorating the physical acoustic waves. In this work, a method to generate low‐noise, divergence‐free, synthetic turbulence for inflow boundary conditions is proposed. It relies on the classical view of turbulence as a superposition of random eddies convected with the mean flow. Within the proposed model, the vector potential and the requirement that the individual eddies must satisfy the linearized momentum equations about the mean flow are used. The model is tested using isolated eddies convected through the inflow boundary and an experimental benchmark data for spatially decaying isotropic turbulence. Copyright © 2013 John Wiley & Sons, Ltd.     

Finite element computation of a turbulent flow over a two-dimensional backward-facing step

The present paper is devoted to the computation of turbulent flows by a Galerkin finite element method. Effects of turbulence on the mean field are taken into account by means of a (k-ε) turbulence model. The wall region is treated through wall laws and, more specifically, Reichardt's law. An inlet profile for ε is proposed as a numerical treatment for physically meaningless values of k and ε. Results obtained for a recirculating flow in a two-dimensional channel with a sudden expansion in width are presented and compared with experimental values.     

Numerical and experimental investigation of turbulent characteristics in a drag-reducing flow with surfactant additives

Cetyltrimethyl ammonium chloride (CTAC) surfactant additives, because of their long-life characteristics, can be used as promising drag-reducers in district heating and cooling systems. In the present study we performed both numerical and experimental tests for a 75 ppm CTAC surfactant drag-reducing channel flow. A two-component PIV system was used to measure the instantaneous streamwise and wall-normal velocity components. A Giesekus constitutive equation was adopted to model the extra stress due to the surfactant additives, with the constitutive parameters being determined by well-fitting apparent shear viscosities, as measured by an Advanced Rheometric Expansion System (ARES) rheometer. In the numerical study, we connected the realistic rheological properties with the drag-reduction rate. This is different from previous numerical studies in which the model parameters were set artificially. By performing consistent comparisons between numerical and experimental results, we have obtained an insight into the mechanism of the additive-induced drag-reduction phenomena.

Our simulation showed that the addition of surfactant additives introduces several changes in turbulent flow characteristics: (1) In the viscous sublayer, the mean velocity gradient becomes gentler due to the viscoelastic forces introduced by the additives. The buffer layer becomes expanded and the slope of the velocity profile in the logarithmic layer increases. (2) The locations where the streamwise velocity fluctuation and Reynolds shear stress attain their maximum value shifted from the wall region to the bulk flow region. (3) The root-mean-square velocity fluctuations in the wall-normal direction decrease for the drag-reducing flow. (4) The Reynolds shear stress decreases dramatically and the deficit of the Reynolds shear stress is mainly compensated by the viscoelastic shear stress. (5) The turbulent production becomes much smaller and its peak-value position moves toward the bulk flow region. All of these findings agree qualitatively with experimental measurements.

Regarding flow visualization, the violent streamwise vortices in the near wall region become dramatically suppressed, indicating that the additives weaken the ejection and sweeping motion, and thereby inhibit the generation of turbulence. The reduction in turbulence is accomplished by additive-introduced viscoelastic stress. Surfactant additives have dual effects on frictional drag: (1) introduce viscoelastic shear stress, which increases frictional drag; and (2) dampen the turbulent vortical structures, decrease the turbulent shear stress, and then decrease the frictional drag. Since the second effect is greater than the first one, drag-reduction occurs.     

Implementation and Evaluation of an Embedded LES-RANS Solver

In the current work, we present the development and application of an embedded large-eddy simulation (LES) - Reynolds-averaged Navier Stokes (RANS) solver. The novelty of the present work lies in fully embedding the LES region inside a global RANS region through an explicit coupling at the arbitrary mesh interfaces, exchanging flow and turbulence quantities. In particular, a digital filter method (DFM) extracting mean flow, turbulent kinetic energy and Reynolds stress profiles from the RANS region is used to provide meaningful turbulent fluctuations to the LES region. The framework is developed in the open-source computational fluid dynamics software OpenFOAM. The embedding approach is developed and validated by simulating a spatially developing turbulent channel flow. Thereafter, flow over a surface mounted spanwise-periodic vertical fence is simulated to demonstrate the importance of the DFM and the effect of the location of the RANS-LES interface. Mean and second-order statistics are compared with direct numerical simulation (DNS) data from the literature. Results indicate that feeding synthetic turbulence at the LES interface is essential to achieve good agreement for the mean flow quantities. However, in order to obtain a good match for the Reynolds stresses, the LES interface needs to be placed sufficiently far upstream, which in the present case was six spoiler heights before the fence. Further, a realistic spoiler configuration with finite-width in the spanwise direction and inclined at 30 degrees was simulated using the embedding approach. As opposed to the vertical fence case this is a genuinely (statistically) three-dimensional case and a very good match with mean and second-order statistics was obtained with the experimental data. Finally, in order to test the present solver for high sub-sonic speed flows the flow over an open cavity was simulated. A good match with reference data is obtained for mean and turbulence profile comparisons. Tones in the pressure spectra were predicted reasonably well and an overall sound pressure level with a maximum deviation of 2.6 d B was obtained with the present solver when compared with the experimental data.