Near-wall turbulent characteristics along very long thin circular cylinders

Understanding the salient physics within the turbulent boundary layer of towed thin cylinders is paramount to the Navy sonar array communities. However, the required long array length to achieve wide acoustic aperture creates unique and consistent flow characteristics that suggest simplified tangential forcing expressions suitable for design purposes. One well-known fact is that the majority of the array surface experiences very thick turbulent boundary layers (TBL) and large Reynolds numbers. The resultant statistics are most commonly dependent on the inner and outer length scales. Herein, we resolve the near-wall TBL structure under those flow conditions by large-eddy simulation. The turbulent mean-flow statistics showed near-wall consistency using only inner scaling. But both inner and outer variables were found necessary to properly scale the turbulent fluctuations. An expression for the tangential wall-friction coefficient (C_t) indicates two distinct flow regimes as characterized by the near-wall turbulent flow structure. The respective parameters appear independent of the outer length scale. Thickening (or thinning) the cylinder near their common threshold (defined by a radius-based Reynolds number) transitioned the turbulent character between the two regimes.     

DNS of turbulent heat transfer in a channel flow with a high spatial resolution

Direct numerical simulations of turbulent heat transfer in a channel flow are performed to investigate the effects of Reynolds and Prandtl numbers on higher-order turbulence statistics such as a turbulent Prandtl number and the budget for the dissipation rate of the temperature variance. The Reynolds numbers based on the friction velocity and the channel half width are 180 and 395, and the molecular Prandtl numbers Pr’s 0.71–10.0. Careful attention is paid to ensure accuracy of the higher-order statistics through the use of a high spatial resolution comparable to Batchelor length scale. The wall-asymptotic value of the turbulent Prandtl number is mostly independent of Reynolds number for the current range of Pr’s. The budget for the dissipation rate of the temperature variance has been computed, and the negligible effect of a Reynolds number on the sum of all source and sink terms in near-wall region in the current computational range is found. This result is quite similar to the one in the budget for the dissipation rate of turbulent energy. In addition, a priori test for existing models is also performed to assess the Pr dependence on the individual terms and their summations in the budget.     

Transition from vortex to wall driven turbulence production in the Taylor–Couette system with a rotating inner cylinder

Axisymmetrically stable turbulent Taylor vortices between two concentric cylinders are studied with respect to the transition from vortex to wall driven turbulent production. The outer cylinder is stationary and the inner cylinder rotates. A low Reynolds number turbulence model using the k‐ω formulation, facilitates an analysis of the velocity gradients in the Taylor–Couette flow. For a fixed inner radius, three radius ratios 0.734, 0.941 and 0.985 are employed to identify the Reynolds number range at which this transition occurs. At relatively low Reynolds numbers, turbulent production is shown to be dominated by the outflowing boundary of the Taylor vortex. As the Reynolds number increases, shear driven turbulence (due to the rotating cylinder) becomes the dominating factor. For relatively small gaps turbulent flow is shown to occur at Taylor numbers lower than previously reported. Copyright © 2002 John Wiley & Sons, Ltd.     

Large eddy simulation using a dynamic mixing length subgrid‐scale model

A novel dynamic mixing length (DML) subgrid‐scale model for large eddy simulations is proposed in this work to improve the cutoff length of the Smagorinsky model. The characteristic mixing length (or the characteristic wave number) is dynamically estimated for the subgrid‐scale fluctuation of turbulence by the cutoff wave‐number, k_c, and the dissipation wave‐number, k_d. The dissipation wave number is derived from the kinetic energy spectrum equation and the dissipation spectrum equation. To prove the promise of the DML model, this model is used to simulate the lid‐driven cubical cavity with max‐velocity‐based Reynolds numbers 8850 and 12,000, the channel flows with friction‐velocity‐based Reynolds numbers 180, 395, 590, and 950, and the turbulent flow past a square cylinder at the higher Reynolds number 21,400, respectively, compared with the Smagorinsky model and Germano et al.'s dynamic Smagorinsky model. Different numerical experiments with different Reynolds numbers show that the DML model can be used in simulations of flows with a wide range of Reynolds numbers without the occurrence of singular values. The DML model can alleviate the dissipation of the Smagorinsky model without the loss of its robustness. The DML model shows some advantages over Germano et al.'s dynamic Smagorinsky model in its high stability and simplicity of calculation because the coefficient of the DML model always stays positive. The characteristic mixing length in the DML model reflects the subgrid‐scale fluctuation of turbulence in nature and thus the characteristic mixing length has a spatial and temporal distribution in turbulent flow. Copyright © 2011 John Wiley & Sons, Ltd.     

Turbulence,dynamic similarity and scale effects in high-velocity free-surface flows above a stepped chute

In high-velocity free-surface flows, air entrainment is common through the interface, and intense interactions take place between turbulent structures and entrained bubbles. Two-phase flow properties were measured herein in high-velocity open channel flows above a stepped chute. Detailed turbulence measurements were conducted in a large-size facility, and a comparative analysis was applied to test the validity of the Froude and Reynolds similarities. The results showed consistently that the Froude similitude was not satisfied using a 2:1 geometric scaling ratio. Lesser number of entrained bubbles and comparatively greater bubble sizes were observed at the smaller Reynolds numbers, as well as lower turbulence levels and larger turbulent length and time scales. The results implied that small-size models did underestimate the rate of energy dissipation and the aeration efficiency of prototype stepped spillways for similar flow conditions. Similarly a Reynolds similitude was tested. The results showed also some significant scale effects. However a number of self-similar relationships remained invariant under changes of scale and confirmed the analysis of Chanson and Carosi (Exp Fluids 42:385-401, 2007). The finding is significant because self-similarity may provide a picture general enough to be used to characterise the air–water flow field in large prototype channels.     

Direct numerical simulation of turbulent wake behind a surface-mounted square cylinder

In this research, direct numerical simulation has been performed to study the turbulent wake behind a wall-mounted square cylinder with aspect ratio 4 and Reynolds number 12 000 (based on the free-stream velocity and obstacle side length) in a developing boundary layer. Owing to the relatively high Reynolds number and high aspect ratio of the cylinder tested, the wake is wide spread behind the cylinder and exhibits complex and energetic vortex motions. The lateral and tip vortex shedding patterns at different frequencies, coherent structures downstream of the obstacle, the production rate and distribution of turbulent kinetic energy, and the instantaneous pressure distribution in the wake region have been thoroughly investigated. In order to validate the numerical results, the first- and second-order flow statistics obtained from the simulations have been carefully compared against available wind-tunnel measurement data.     

Vortex reynolds number in turbulent boundary layers

The effects of vortex Reynolds number on the statistics of turbulence in a turbulent boundary layer have been investigated. Vortex Reynolds number is defined as the ratio of circulation around the vortex structure to the fluid viscosity. The vortex structure of the outer region was modeled and a full numerical simulation was then conducted using a high-order spectral method. A unit domain of the outer region of a turbulent boundary layer was assumed to be composed of essentially three elements: a wall, a Blasius mean shear, and an elliptic vortex inclined at 45° to the flow direction. The laminar base-flow Reynolds number is roughly in the same range as that of a turbulent boundary layer based on eddy viscosity, and the vortex-core diameter based on the boundary-layer thickness is nearly the same as the maximum mixing length in a turbulent boundary layer. The computational box size, namely, 500, 150, and 250 wall units in the streamwise, surface-normal, and spanwise directions, respectively, is approximately the same as the measured quasi-periodic spacings of the near-wall turbulence-producing events in a turbulent boundary layer. The effects of vortex Reynolds number and the signs of the circulation on the moments of turbulence were examined. The signs mimic the ejection and sweep types of organized motions of a turbulent boundary layer. A vortex Reynolds number of 200 describes the turbulence moments in the outer layer reasonably well.     

Anisotropic Organised Eddy Simulation for the prediction of non-equilibrium turbulent flows around bodies

The unsteady turbulent flow around bodies at high Reynolds number is predicted by an anisotropic eddy-viscosity model in the context of the Organised Eddy Simulation (OES). A tensorial eddy-viscosity concept is developed to reinforce turbulent stress anisotropy, that is a crucial characteristic of non-equilibrium turbulence in the near-region. The theoretical aspects of the modelling are investigated by means of a phase-averaged PIV in the flow around a circular cylinder at Reynolds number 1.4×10⁵. A pronounced stress–strain misalignment is quantified in the near-wake region of the detached flow, that is well captured by a tensorial eddy-viscosity concept. This is achieved by modelling the turbulence stress anisotropy tensor by its projection onto the principal matrices of the strain-rate tensor. Additional transport equations for the projection coefficients are derived from a second-order moment closure scheme. The modification of the turbulence length scale yielded by OES is used in the Detached Eddy Simulation hybrid approach. The detached turbulent flows around a NACA0012 airfoil (2-D) and a circular cylinder (3-D) are studied at Reynolds numbers 10⁵ and 1.4×10⁵, respectively. The results compared to experimental ones emphasise the predictive capabilities of the OES approach concerning the flow physics capture for turbulent unsteady flows around bodies at high Reynolds numbers.     

A dynamic two-equation Sub Grid Scale model

In this paper we demonstrate that the transport equation of the generalised subgrid scale (SGS) turbulent stress tensor is form-invariant but not frame-indifferent under Euclidean transformations of the frame. A new closure equation between the generalized SGS turbulent stress tensor and the resolved kinematic quantities is proposed. The closure equation at the basis of the proposed model (Two-Equation Model, TEM): a) respects the principle of the turbulence frame indifference [1]; b) takes into account both the anisotropy of the turbulence velocity scales and turbulence length scales; c) removes any balance assumption between the production and dissipation of SGS turbulent kinetic energy; d) assumes scale similarity in the definition of the second-order tensor representing the turbulent velocity scales. In the proposed model: a) the closure coefficient C which appears in the constitutive equation is uniquely determined without using Germanos dynamic procedure [2]; b) the generalized SGS turbulent stress tensor is related exclusively to the generalized SGS turbulent kinetic energy (which is calculated by means of its balance equation) and the modified Leonard tensor; c) the viscous dissipation of the generalized SGS turbulent kinetic energy is calculated by solving the balance equation. The proposed model is tested for a turbulent channel flow at Reynolds numbers (based on friction velocity and channel half-width) ranging from 180 to 2340.Received: 11 February 2004, Accepted: 20 August 2004, Published online: 22 February 2005PACS: 02.60.Cb, 47.27.Eq, 47.11. + j Correspondence to: F. Gallerano     

Spatial resolution effects on the measurement of scalar variance and scalar gradient in turbulent nonpremixed jet flames

The effect of spatial averaging is important for scalar gradient measurements in turbulent nonpremixed flames, especially when the local dissipation length scale is small. Line imaging of Raman, Rayleigh and CO-LIF is used to investigate the effects of experimental resolution on the scalar variance and radial gradient in the near field of turbulent nonpremixed CH₄/H₂/N₂ jet flames at Reynolds numbers of 15,200 and 22,800 (DLR-A and B) and in piloted CH₄/air jet flames at Reynolds numbers of 13,400, 22,400 and 33,600 (Sandia flames C/D/E). The finite spatial resolution effects are studied by applying the Box filter with varying filter widths. The resulting resolution curves for both scalar variance and mean squared-gradient follow nearly the same trends as theoretical curves calculated from the model turbulence kinetic energy spectrum of Pope. The observed collapse of resolution curves of mean squared-gradient for nearly all studied cases implies the shape of the dissipation spectrum is approximately universal. Fluid transport properties are shown to have no effect on the dissipation resolution curve, which implies that the dissipation length scale inferred from the square gradient is equivalent to the length scale for the scalar dissipation rate, which includes the diffusion coefficient. With the Box filter, the required spatial resolution to resolve 98% of the mean dissipation rate is about one−two times of the dissipation cutoff length scale (analogous to the Batchelor scale in turbulent isothermal flows). The effects of resolution on the variances of mixture fraction, temperature, and the inverted Rayleigh signal are also compared. The ratio of the filtered variance to the true variance is shown to depend nearly linearly on the probe resolution. The inverted Rayleigh scattering signal can be used to study the resolution effect on temperature variance even when the Rayleigh scattering cross section is not constant. The experimental results also indicate that these laboratory scale turbulent jet flames have small effective Reynolds numbers, such that there is some direct interaction of the large (energy containing) and small (dissipative) scalar length scales, especially for the near field case at x/d = 7.5 of the piloted Sandia flames C/D/E.     

Vortex shedding and structural loading characteristics of finned cylinders

The flow development and structural loading characteristics of cylinders with equispaced circular fins were studied experimentally for a range of fin pitches with constant fin thickness and diameter. The experiments were performed for a range of Reynolds numbers, corresponding to the shear layer transition turbulent shedding regime. Time-resolved planar Particle Image Velocimetry and direct mean drag and fluctuating lift measurements are employed to relate spatio-temporal flow development to structural loading. The results show that wake development is dominated by vortex shedding for all the cases examined. However, the fin pitch ratio has a significant effect on vortex shedding characteristics. The addition of fins increases the characteristic spatial and temporal scales of the main spanwise vortices forming in the near wake. As the fin pitch is decreased to a critical value, the coalescence of boundary layers between the adjacent fins leads to a significant enlargement of the vortex formation region. A modified vortex shedding frequency scaling is proposed, based on the effective diameter, that incorporates a Reynolds number dependence associated with the lateral boundary layers developing on the fin surfaces. A detailed analysis is conducted to characterize the strength of the vortical structures forming in the near wake. The addition of the fins is shown to produce a stabilizing effect on the roll-up process, associated with a reduction in the generation of smaller scale, three-dimensional structures. The results demonstrate that the addition of fins leads to an increase in the mean drag, which is driven primarily by the associated increase in skin friction. The significant effect of the fin pitch ratio on the characteristics of the shed vortices as well as the size of the vortex formation region is shown to lead to substantial variations in the fluctuating loads.     

分区Lagrangian涡方法及瞬时起动圆柱初期流动的模拟

本文提出一种分区Lagrangian涡方法:将附着流动和分离流动分开处理,在附着区解边界层方层,只在分离区用涡方法解N-S方程。由于将尺度不同的区域分开了,求解分离区流动的涡方法中,每一时间步上物面引出的涡数在较小程度上依赖于Re数。这样,求解高Re数流动时,流场内的涡数,因而计算机内存和时间得以大大减小。用该方法计算了瞬时起动圆柱的初期流动,与实验结果比较相符很好。     

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.     

Numerical study on the turbulent mixing of planar shock-accelerated triangular heavy gases interface

The interaction of a planar shock wave with a triangle-shaped sulfur hexafluoride (\(\mathrm{SF_6}\)) cylinder surrounded by air is numerically studied using a high resolution finite volume method with minimum dispersion and controllable dissipation reconstruction. The vortex dynamics of the Richtmyer–Meshkov instability and the turbulent mixing induced by the Kelvin–Helmholtz instability are discussed. A modified reconstruction model is proposed to predict the circulation for the shock triangular gas–cylinder interaction flow. Several typical stages leading the shock-driven inhomogeneity flow to turbulent mixing transition are demonstrated. Both the decoupled length scales and the broadened inertial range of the turbulent kinetic energy spectrum in late time manifest the turbulent mixing transition for the present case. The analysis of variable-density energy transfer indicates that the flow structures with high wavenumbers inside the Kelvin–Helmholtz vortices can gain energy from the mean flow in total. Consequently, small scale flow structures are generated therein by means of nonlinear interactions. Furthermore, the occasional “pairing” between a vortex and its neighboring vortex will trigger the merging process of vortices and, finally, create a large turbulent mixing zone.     

Large-eddy simulation of counter-rotating Taylor–Couette flow: The effects of angular velocity and eccentricity

In the present work, turbulent flow in the annulus of a counter-rotating Taylor-Couette (CRTC) system is studied using large-eddy simulation. The numerical methodology employed is validated, for both the mean and second-order statistics, with the direct numerical simulation (DNS) data available in the literature, for a range of Reynolds numbers from 500 to 4000. Thereafter, turbulent flow occurring in this system at Reynolds numbers of 8000 and 16000 are studied, and the results obtained are analyzed using mean and second-order statistics, vortical structures, velocity vector plots and power energy spectra. Further, the spatio-temporal variation of azimuthal velocity, extracted near the inner cylinder, shows the existence of herringbone like patterns similar to that observed in the previous studies. The effect of eccentricity of the inner cylinder with respect to the outer cylinder is studied, on the turbulent flow in the CRTC system, for two different eccentricity ratios of 0.2 and 0.5 and for two different Reynolds numbers of 1500 and 4000. The results of the eccentric CRTC are analyzed using contours of pressure, mean and second-order statistics, velocity vectors, vortical structures, and turbulence anisotropy maps. It is observed from the eccentric CRTC simulations that the smaller-gap region seems to contain higher amplitude fluctuations and more vortical structures when compared with the larger-gap region. The mean turbulent kinetic energy contours do not change qualitatively with the Reynolds number, however, quantitatively a higher turbulent kinetic energy is observed in the higher Reynolds number case of 4000.     

Reynolds number dependence of the inertial range scaling of energy dissipation rate and enstrophy in a cylinder wake

The full energy dissipation rate and enstrophy are measured simultaneously using a probe consisting of four X-wires in the intermediate region of a cylinder wake for Taylor microscale Reynolds number in the range of 120–320. Longitudinal and transverse velocity increments are also obtained temporally using Taylor’s hypothesis. The inertial range scaling exponents indicate that the full enstrophy field has a stronger intermittency than does the full dissipation field for all the Reynolds numbers considered. The approximations of the energy dissipation rate and enstrophy based on isotropy are more intermittent than their corresponding true values. While the scaling exponents of the full energy dissipation rate remain approximately constant for different Reynolds numbers, those of the enstrophy decrease slightly and consistently with the increase of Reynolds number. It is conjectured that the scaling of the energy dissipation rate and the enstrophy may be the same when Reynolds number is extremely high, a trend that is consistent with that suggested by Nelkin (Phys Fluids 11:2202–2204, 1999; Am J Phys 68:310–318, 2000).     

Wake development in staggered short cylinder arrays within a channel

Staggered arrays of short cylinders, known as pin?Cfins, are commonly used as a heat exchange method in many applications such as cooling electronic equipment and cooling the trailing edge of gas turbine airfoils. This study investigates the near wake flow as it develops through arrays of staggered pin fins. The height-to-diameter ratio was unity while the transverse spacing was kept constant at two cylinder diameters. The streamwise spacing was varied between 3.46 and 1.73 cylinder diameters. For each geometric arrangement, experiments were conducted at Reynolds numbers of 3.0e3 and 2.0e4 based on cylinder diameter and velocity through the minimum flow area of the array. Time-resolved flowfield measurements provided insight into the dependence of row position, Reynolds number, and streamwise spacing. Decreasing streamwise spacing resulted in increased Strouhal number as the near wake length scales were confined. In the first row of the bundle, low Reynolds number flows were mainly shear-layer-driven while high Reynolds number flows were dominated by periodic vortex shedding. The level of velocity fluctuations increased for cases having stronger vortex shedding. The effect of streamwise spacing was most apparent in the reduction of velocity fluctuations in the wake when the spacing between rows was reduced from 2.60 diameters to 2.16 diameters.     

Spatial resolution and dissipation rate estimation in Taylor--Couette flow for tomographic PIV

This paper assesses the spatial resolution and accuracy of tomographic particle image velocimetry (PIV). In tomographic PIV the number of velocity vectors are of the order of the number of reconstructed particle images, and sometimes even exceeds this number when a high overlap fraction between adjacent interrogations is used. This raises the question of the actual spatial resolution of tomographic PIV in relation to the various flow scales. We use a Taylor--Couette flow of a fluid between two independently rotating cylinders and consider three flow regimes: laminar flow, Taylor vortex flow and fully turbulent flow. The laminar flow has no flow structures, and the measurement results are used to assess the measurement uncertainty and to validate the accuracy of the technique for measurements through the curved wall. In the Taylor vortex flow regime, the flow contains large-scale flow structures that are much larger than the size of the interrogation volumes and are fully resolved. The turbulent flow regime contains a range of flow scales. Measurements in the turbulent flow regime are carried out for a Reynolds number Re between 3,800 and 47,000. We use the measured torque on the cylinders to obtain an independent estimate of the energy dissipation rate and estimate of the Kolmogorov length scale. The data obtained by tomographic PIV are assessed by estimating the dissipation rate and comparing the result against the dissipation rate obtained from the measured torque. The turbulent flow data are evaluated for different sizes of the interrogation volumes and for different overlap ratios between adjacent interrogation locations. The results indicate that the turbulent flow measurements for the lowest Re could be (nearly) fully resolved. At the highest Re only a small fraction of the dissipation rate is resolved, still a reasonable estimate of the total dissipation rate could be obtained by means of using a sub-grid turbulence model. The resolution of tomographic PIV in these measurements is determined by the size of the interrogation volume. We propose a range of vector spacing for fully resolving the turbulent flow scales. It is noted that the use of a high overlap ratio, that is, 75?%, yields a substantial improvement for the estimation of the dissipation rate in comparison with data for 0 and 50?% overlap. This indicates that additional information on small-scale velocity gradients can be obtained by reducing the data spacing.     

Velocity field after wave breaking

The velocity field in breaking water waves is considered in this paper. A numerical simulation describes in detail the transition from a primary overturning and consequent rebounding jets into a bore front, where the vorticity in the coherent large‐scale eddy structures devolves into turbulence. Spatial changes in the frequency spectra of the kinetic energy and the enstrophy are associated with the production, transport and dissipation of the Reynolds stress and the various wave and turbulent mixing length scales. Mean velocity fields and the wave and kinetic energy in a surf zone are evaluated. Fourier and wavelet spectral analysis is applied to study both the surface elevation and energy changes, and the distinction that must be made between spilling and plunging breakers is clarified in this paper. Copyright © 2002 John Wiley & Sons, Ltd.     

Controlling spatio-temporal evolution of natural and excited square jets via inlet conditions

The paper presents numerical investigations of square jets in a wide range of Reynolds numbers with varying inlet turbulence characteristics. The research focuses on flow characteristics depending on inflow turbulent length/time scales and excitation frequencies in case of excited jets. It is found that the parameters of inlet turbulence affect the solutions qualitatively when the Reynolds number is sufficiently low. In these cases the impact of varying the turbulent time scale is considerably larger than changing the turbulent length scale. It was also observed that at sufficiently high Reynolds numbers the jets become quite independent of the inlet turbulence characteristics. This confirms findings of Xu et al. (Phys. Fluids, 2013) concerning weak/strong dependence of the jet evolution on inflow conditions. In case of excited jets the excitation frequencies play an important role and influence the jet behaviour most strongly at lower values of the Reynolds number. For some forcing frequencies a bifurcation occurs at sufficiently large forcing amplitudes. This phenomenon turned out to be independent of the assumed length and time scales of the turbulent fluctuations, both in terms of robustness as well as amplitude.