Wall Shear Flows Research Articles

Mean velocity and temperature profiles in turbulent vertical convection

In this study, mean velocity and temperature profiles for turbulent vertical convection (VC) confined in an infinite channel are investigated theoretically. The analysis starts from the governing equations of the thermal flow, with Reynolds shear stress and turbulent heat flux closed by the mixing length theory. Employing a three-sublayer description of the mean fields, the mean velocity and temperature profiles are found to be linear laws near the channel wall (viscosity-dominated sublayer), and they follow power laws close to the channel centre (turbulence-dominated sublayer). The characteristic scales of velocity, temperature and length in the present profiles arise naturally from the system normalisation, rather than from scaling analyses, thus ensuring a sound mathematical description. The derived profiles are verified fully via various literature data available in the classical regime; further, they are compared with the reported profiles, and the results indicate that the present profiles are the only ones with the ability to interpret data accurately from different sources, demonstrating much better versatility. Meanwhile, we provide analytical arguments showing that in the ultimate regime, the mean profiles in VC may remain in power laws, rather than the log laws inferred by analogy with Rayleigh–Bénard convection (RBC) systems. The power profiles recognised in this study are induced by the effect of buoyancy, which is in parallel with the mean flow in VC and contributes to the streamwise momentum transport, whereas in RBC systems, buoyancy is perpendicular to the mean flow, and does not influence the streamwise momentum transport, resulting in log profiles, being similar to the case of wall shear flows.

Real-time tracking of fibrinolysis under constant wall shear and various pulsatile flows in an in-vitro thrombolysis model.

A great need exists for the development of a more representative in-vitro model to efficiently screen novel thrombolytic therapies. We herein report the design, validation, and characterization of a highly reproducible, physiological scale, flowing clot lysis platform with real-time fibrinolysis monitoring to screen thrombolytic drugs utilizing a fluorescein isothiocyanate (FITC)-labeled clot analog. Using this Real-Time Fluorometric Flowing Fibrinolysis assay (RT-FluFF assay), a tPa-dependent degree of thrombolysis was observed both via clot mass loss as well as fluorometrically monitored release of FITC-labeled fibrin degradation products. Percent clot mass loss ranged from 33.6% to 85.9% with fluorescence release rates of 0.53 to 1.17 RFU/min in 40 and 1000 ng/mL tPa conditions, respectively. The platform is easily adapted to produce pulsatile flows. Hemodynamics of human main pulmonary artery were mimicked through matching dimensionless flow parameters calculated using clinical data. Increasing pressure amplitude range (4-40 mmHg) results in a 20% increase of fibrinolysis at 1000 ng/mL tPA. Increasing shear flow rate (205-913 s-1) significantly increases fibrinolysis and mechanical digestion. These findings suggest pulsatile level affects thrombolytic drug activities and the proposed in-vitro clot model offers a versatile testing platform for thrombolytic drug screening.

Transient energy growth of optimal streaks in parallel round jets

We present a linear optimal perturbation analysis of streamwise invariant disturbances evolving in parallel round jets. The potential for transient energy growth of perturbations with azimuthal wavenumber m≥1 is analyzed for different values of Reynolds number Re. Two families of steady (frozen) and unsteady (diffusing) base flow velocity profiles have been used, for different aspect ratios α = R/θ, where R is the jet radius and θ is the shear layer momentum thickness. Optimal initial conditions correspond to infinitesimal streamwise vortices, which evolve transiently to produce axial velocity streaks, whose spatial structure and intensity depend on base flow and perturbation parameters. Their dynamics can be characterized by a maximum optimal value of the energy gain Gopt, reached at an optimal time τopt after which the perturbations eventually decay. Optimal energy gain and time are shown to be, respectively, proportional to Re2 and Re, regardless of the frozen or diffusing nature of the base flow. Besides, it is found that the optimal gain scales like Gopt∝1/m3 for all m except m = 1. This quantitative difference for azimuthal wavenumber m = 1 is shown to be based on the nature of transient mechanisms. For m = 1 perturbations, the shift-up effect [J. I. Jiménez-González et al., “Modal and non-modal evolution of perturbations for parallel round jets,” Phys. Fluids 27, 044105-1–044105-19 (2015)] is active: an initial streamwise vorticity dipole induces a nearly uniform velocity flow in the jet core, which shifts the whole jet radially. By contrast, optimal perturbations with m≥2 are concentrated along the shear layer, in a way that resembles the classical lift-up mechanism in wall-shear flows. The m = 1 shift-up effect is more energetic than the m≥2 lift-up, but it is slower, with optimal times considerably shorter in the case of m≥2 disturbances. This suggests that these perturbations may emerge very quickly in the flow when injected as initial conditions. When the base flow diffuses, the large time scale for m = 1 disturbances allows the shear layer to spread and the jet core velocity to decrease substantially, thus lowering the values of corresponding optimal gain and time. For m≥2, results are less affected, since the shorter transient dynamics does not leave room for significant modifications of the base flow velocity profiles, and the scaling laws obtained in the frozen case are recovered. Nevertheless, base flow diffusion hinders the transient growth, as a consequence of a weaker component-wise non-normality and a smoother, radially spread structure of optimal disturbances.

Nonlinear regimes of spanwise modulated waves in plane Poiseuille flow

Wave modulation is an unavoidable ingredient of natural transition and wavepackets composed of a continuous range of frequencies and wavenumbers are considered as a good model for it. Conclusions regarding wavepacket nonlinear regimes are essentially based on comparison of the dominant mode in the modulated signal nonlinear bands with predictions of the most unstable mode in the corresponding unmodulated cases. The modulated signal bands are very broad and establishing the dominant mode is difficult. If the Reynolds number changes along the packet evolution, the bands also change to adapt to local conditions, which further hinders data interpretation and weakens the conclusions. In view of this, a study at a constant Reynolds number is proposed, the Poiseuille plane flow being chosen as the base flow. The flow choice also allowed an investigation of the phenomenon at different positions in the stability loop, an aspect that has never been addressed before. The work was numerical. Only spanwise modulation was considered and two different regimes were observed. Close to the first branch of the instability loop the packet splits into two patches. Oblique transition was the dominant nonlinear mechanism, which required spanwise interaction of packets. Elsewhere the dominant mechanism was fundamental instability (or$K$-type), which was fed by a previous nonlinear phenomenon and led to a subsequent one. The analysis involved comparison of growth rates, threshold amplitudes and amplitude scalings among other aspects, for modulated and corresponding unmodulated cases. Perfect agreement was found if appropriate variables were used, which enabled firm conclusions to be drawn about the phenomena investigated. This level of agreement was only possible because of the constant Reynolds number character of the flow, but the main conclusions are applicable to other wall shear flows.

Modal and non-modal evolution of perturbations for parallel round jets

The present work investigates the local modal and non-modal stability of round jets for varying aspect ratios α = R/θ, where R is the jet radius and θ the shear layer momentum thickness, for Reynolds numbers ranging from 10 to 10 000. The competition between axisymmetric (azimuthal wavenumber m = 0) and helical (m = 1) perturbations depending on the aspect ratio, α, is quantified at different time horizons. Three different techniques have been used, namely, a classical temporal stability analysis in order to characterize the unstable modes of the jet; an optimal excitation analysis, based on the resolution of the adjoint problem, to quantify the potential for non-modal perturbation dynamics; and finally an optimal perturbation analysis, focused on the very short time transient dynamics, to complement the adjoint-based study. Besides providing with the determination of the critical aspect ratio below which the most unstable perturbations switch from m = 0 to m = 1 depending on the Reynolds number, the study shows that perturbations can undergo a rapid transient growth. It is found that helical perturbations always experience the highest transient growth, although for large values of aspect ratio, this transient domination can be overcome by the eventual emergence of axisymmetric perturbation when more exponentially unstable. Furthermore, the adjoint mode, which excites optimally the most unstable mode of the flow, is found to coincide with the optimal perturbation even for short time horizons, and to drive the transient dynamics for finite times. Therefore, the adjoint-based analysis is found to characterize adequately the transient dynamics of jets, showing that a mechanism equivalent to the Orr one takes place for moderate to small wavelengths. However, in the long wavelength limit, a specific mechanism is found to shift the jet as a whole in a way that resembles the classical lift-up effect active in wall shear flows.

Effects of Pressure Gradients on Energy Dissipation Coefficient

In this study energy dissipation coefficient and entropy generation process in characteristic wall shear flows have been investigated. Effect of pressure gradients on energy dissipation coefficient for flows undergoing “bypass” transition from laminar to turbulent state has been studied. Reynolds-Averaged Navier-Stokes (RANS) models and Direct Numerical Simulations (DNS) are implemented to study the energy dissipation coefficient and local entropy generation in pre-transitional and transitional regions. Three of these RANS models are transitional models such as, traditional SST k-w (2eq), SST k-w (4eq) and k - kl -w and the results are compared with DNS. Four simulations have been performed for (1) zero, (2) favorable, (3) adverse and (4) strong-adverse pressure gradient cases. The numerical results show that the pressure gradient has a significant effect on energy dissipation coefficient and entropy generation.

Effects of adverse and favorable pressure gradients on entropy generation in a transitional boundary layer region under the influence of freestream turbulence

Fundamental understanding of the entropy generation process in characteristic wall shear flows is developed. For entropy generated by fluid friction, the rates are predictable for developed turbulent flows and pure laminar flows. The main concern lies in prediction for flows undergoing so-called “bypass” transition from laminar to turbulent state. In this study, the entropy generation process in the bypass transition scenario is investigated for a flat plate boundary layer under effects of adverse and favorable pressure gradients. For the case studied, transition occurs prematurely due to the presence of strong levels of freestream turbulence. Reynolds-Averaged Navier–Stokes (RANS) models and direct numerical simulations (DNS) are implemented to study the local entropy generation in pre-transitional and transitional regions. Three of these RANS models are transitional models such as, traditional SST k–ω (2eq), SST k–ω (4eq) and k–kl–ω. They are used for prediction of the onset of transition and the results are compared with DNS. All the RANS models predicted transition onset prematurely and, consequently, over predict the integral entropy generation rate and the skin friction coefficient in the transition region. Four simulations have been performed for (1) zero, (2) favorable, (3) adverse and (4) strong-adverse pressure gradient cases. The numerical results show that the pressure gradient has a significant effect on the onset of transition and entropy generation. Transition is early and abrupt for the strong adverse pressure gradient but occurs further downstream and is longer with the increasingly favorable flows. Entropy generation rate at the wall increases as the pressure gradient grows.

Nonlinear eddy diffusivity models reflecting buoyancy effect for wall-shear flows and heat transfer

The main objective of this study is to construct new nonlinear eddy diffusivity models reflecting buoyant effects in wall-bounded turbulent shear flows and heat transfer. It is now well known that the turbulent heat-fluxes, which are the key quantities for the prediction of turbulent flows with buoyancy, are not modeled accurately by employing the conventional turbulence models using eddy diffusivities. In order to appropriately predict wall-bounded turbulent flows with buoyancy, an innovative turbulence heat-transfer model with eddy diffusivities which are composed of the k– ε two-equation model for velocity field and the k θ – ε θ two-equation model for thermal field, must be constructed. Consequently, we should improve the modeled expressions for Reynolds stresses and turbulent heat-fluxes reflecting the buoyant effect in wall-bounded turbulent shear flows. The existing two-equation turbulence models were evaluated on the basis of the DNS data of channel flows with buoyancy. Using the results of evaluation, we constructed new modeled expressions for Reynolds stresses and turbulent heat-fluxes in explicit algebraic models, and reconstructed the nonlinear two-equation turbulence models for the buoyancy-affected wall-shear flows and heat transfer, including the newly proposed nonlinear eddy diffusivity for a momentum model (NLEDM) and the nonlinear eddy diffusivity for heat model (NLEDHM). The proposed nonlinear two-equation turbulence models reflecting buoyancy effect appropriately predict wall-bounded turbulent shear flows with buoyancy given by DNS.

Performance of Reynolds-averaged turbulence and scalar-flux models in complex turbulence with flow impingement

The present paper is a contribution to the ongoing search for better Reynolds-averaged turbulence and scalar-flux models. In this study, several combinations of velocity- and scalar-field models were investigated. Recently-developed algebraic NLEVMs generally provide reasonable turbulence properties for the present test cases. A quadratic extension of the GGDH model (quadratic model) was very effective in improving the prediction accuracy of the streamwise scalar flux in wall-shear flows. On the other hand, the GGDH model has shown an advantage in predicting the scalar transfer in the stagnation region. Therefore, a combined form of the GGDH and quadratic models was discussed.

STUDY ON RELATIONSHIP BETWEEN TURBULENCE STRUCTURES AND WATER SURFACE FLUCTUATIONS IN WIND-DRIVEN OPEN-CHANNEL FLOWS

The present study describes an experimental relationship between turbulence structures in water layer and the water-surface fluctuations in wind-driven open-channel flows by using both a laser Doppler Anemometer (LDA) and a wave gauge simultaneously. The purpose of this study is to make clear the characteristics of surface fluctuations on water dynamics in air-sheared open-channel flows, and to evaluate the effects of surface fluctuations on vertical momentum transport in the water layer. As the results of experiments, it is shown by spectral analysis that the velocity fluctuations near the interface in both only open-channel flow and wind-driven open-channel flow are significantly affected by the water surface in every range of frequency, and that there exists a high correlation between turbulence near the air-water interface and the surface fluctuations in a predominant frequency due to high-sheared wind flow. Moreover, it is recognized by wavelet analysis that the turbulence structures in weak wind-driven open-channel flows are governed by both wall shear and wind-induced flows.

ASM, WETモデル, 渦粘性/渦拡散モデルのアプリオリテスト : 非等温室内気流のLESデータベースを用いた乱流モデルの評価

A priori test using the LES database created by the authors(2001)is carried out in order to evaluate the Algebraic Stress Model(ASM), the WET model and the linear eddy viscosity/diffusivity model. The accuracy and relative performance of various models are carefully examined in the flow field including supply jet, wall shear and impingement. ASM and the WET model reproduce well anisotropy features of Reynolds stresses and turbulent heat fluxes. However, normal stresses of ASM in the impinging region show slight discrepancy from the LES data. It is clarified quantitatively that this discrepancy is caused by the inaccuracy of the modeling pressure-strain term and algebraic approximation for convection and diffusion term. Furthermore, it is concluded that the WET model requires the use of appropriate wall damping function in order to preciously predict wall shear flows.

Towards the development of a Reynolds-averaged algebraic turbulent scalar-flux model

Abstract In order to derive a possible direction for developing Reynolds-averaged algebraic turbulent scalar-flux models, a priori explorations are attempted by processing the LES data presently performed for channel flows under several flow-boundary conditions including shear-free boundaries. The present calibration has elucidated that the turbulent scalar-flux vectors obtainable from the simple generalized gradient-diffusion hypothesis (GGDH) hardly align with the simulation results in wall-shear flows at Pr ⩾0.71. However, the GGDH form returns a quite reasonable approximation in shear-free flow regions and/or lower Pr fluid cases. In the former flow cases, it has been found that an introduction of quadratic products of the Reynolds-stress tensor into the gradient diffusion model may improve the predictive performance.

A Multiple Time-Scale Model for Heat Transfer in Turbulent Shear Flows.

This paper reports a multiple time-scale turbulence model for a thermal field in shear flows. The model is based on the concept of the three divided thermal fluctuation spectra. The spectrum in the highest wavenumber region is modeled using an algebraic relation concerned with the molecular Prandtl number, and the remaining two other regions are modeled with four differential equations. Comparisons with the DNS data indicate that the present model works well for the predictions of thermal fields not only in wall shear flows under varions Prandtl numbers but in homogeneous shear flows with a mean thermal gradient.

Spectral-dynamic model for LES of free and wall shear flows

Abstract Using EDQNM nonlocal spectral expansions, we have developed a spectral-dynamic model for LES of turbulence, allowing to account for kinetic-energy spectra steeper than Kolmogorov at the cutoff. In the case of a temporal mixing layer forced by a weak 3D isotropic white noise, a self-similar state is reached, statistically in good agreement with laboratory experiments, except for kinetic-energy spectra which behave like k −2 at the cutoff, instead of k −5/3 . The pressure spectrum is compared with quasi-normal predictions. Concerning coherent-vortex dynamics, the helical-pairing organization already found with the aid of DNS has been recovered. When the initial forcing is quasi 2D, no self-similar state is reached. Coherent vortices consist then of quasi two-dimensional Kelvin–Helmholtz billows with hairpin vortices stretched in-between. Afterwards, the model has been applied successfully to a turbulent channel flow at h + =204 and h + =389. In the latter case, the computing time is reduced by a factor of 100 with respect to DNS. The model works also well for LES of a channel rotating about a spanwise axis. Finally, we have proposed a generalization of the spectral-dynamic model in physical space.

Present Status of Second Order Closure Turbulence Models. II. Applications

Turbulent flows, from simple to complex, are predicted using various turbulence models. Free shear flows; wall shear flows, with and without separation; and more complex flows such as flow past an axisymmetric body or flow past a three-dimensional ship hull are predicted by the Reynolds stress model, \ik-e-eddy viscosity model, low-Reynolds number model, two-layer model, and so forth. Each turbulence model applies successfully to some turbulent flows, but predicts others unsatisfactorily. It is concluded that at present, no unique turbulence model exists that can predict satisfactorily all turbulent flows. Turbulence model coefficients are a major concern to the model’s predictability. Using different model coefficients for free shear and wall shear flows, the existing turbulence model can predict satisfactorily more turbulent flows, including rough jet and separation flows. Adopting the Reynolds stress model in general improves the Reynolds stress prediction. However, the improvement on the mean flow quantities seems quite limited. Improving the modeled e equation,by either remodeling its production and destruction terms or recalibrating its model coefficients, seems to be the best way to improve the predictability of the existing turbulence models.

Development of a Gradient Diffusion Type of Heat-Flux Model with an Introduction of a Quadratic Reynolds Stress Tensor.

A new explicit algebraic gradient diffusion model for turbulent scalar (heat) flux in forced convection regimes is proposed. This model complies with the linearity and independence principles for passive scalar. For satisfying these, the model coefficients/functions do not include any turbulent scalar variable such as the temperature variance. The model thus does not require solving transport equations for turbulent quantities of the scalar field. The basic role of each model coefficient has been optimized by referring to the discussion with the LES data reported by the authors. The proposed model is applicable to a wide range of passive scalar fields by being coupled with a nonlinear κ-ε-A three equation turbulence model for dynamic fields. It has been confirmed that the model is able to capture the components of turbulent heat flux vectors in wall shear flows at least in the range of 0.025⪈Pr⪈95. Moreover, it has successfully distinguished the heat flux characteristics near shearfree boundaries.

Toward the Development of an Algebraic Turbulent Heat Flux Model with the Aid of LES Data.

In order to derive a possible direction for improvements of an algebraic heat flux model, a priori explorations were attempted by processing the LES data presently performed under various flow and heat transfer conditions including shear-free boundaries. The present calibration has elucidated that the turbulent heat flux vectors obtainable from the simple GGDH hardly align with the simulation results in wall-shear flows with a wall normal temperature gradient of fluids at Prg0.71. However, the GGDH returns a quite reasonable approximation for heat flux vectors in shear-free flow regions and/or lower Pr fluid cases. In the former flow cases, it has been found that a further introduction of a tensor expression, consisting of quadratic products of the Reynolds stress tensor, into the gradient diffusion model may improve the predictive performance.

RNG Modeling of Turbulent Heat Flux and Its Application to Wall Shear Flows.

In a previous paper[Phys.Fluids 9(1997)], we proposed an improved renormalization group(RNG)theory based on conditional iterative-averaging for turbulent flow with mean shear to derive an eddy-viscosity type turbulence model. In the present paper, we have applied this iterative-averaging RNG theory to the governing equation for a thermal field, and derived a thermal eddy diffusivity representation relevant to the turbulent heat flux. Furthermore, we have also obtained the RNG-based equation for the turbulent Prandtl number Prt, with a hogh Reynolds-number limit as Prt=0.79. The present RNG-based model is applied to the calculations of wall turbulent heat transfer. Agreement with the experiment and the direct simulation data is generally very satisfactory.

Multiple time-scale turbulence model for wall and homogeneous shear flows based on direct numerical simulations

The k-ϵ model is widely used and has proved effective in predicting wall shear layer turbulence. These models, however, perform poorly in prediction of homogeneous shear flows. Such inconsistency is not caused by crudeness of the eddy-viscosity approximation, but by inappropriate estimation of the relevant time-scale of turbulence. Thus, to settle this problem, we propose a low-Reynolds number-type “multiple time-scale” turbulence model on the basis of recent direct numerical simulations (DNS) of turbulence. Making a proposed model that is applicable to prediction of near-wall turbulent flows without the controversial wall functions and on reproducing the wall-limiting behavior of turbulence quantities is the emphasis. The proposed model has been tested in wall shear flows with and without a pressure gradient. We also tested the present model in homogeneous flows with and without mean strain. Assessments based on the latest DNS data and measurements indicate that the present model works well, regardless of the flow regimes.

On Reynolds-stress expressions and near-wall scaling parameters for predicting wall and homogeneous turbulent shear flows

Abstract In this paper, a new type of two-equation turbulence model that incorporates some essential characteristics of second-order closure models is proposed. The present model belongs to a nonlinear k−ϵ model taking into account low-Reynolds-number effects originating from the physical requirements, and is applicable to complex turbulent flows with separation and reattachment. The model successfully predicts both wall-turbulent and homogeneous shear flows, the latter of which has been very difficult to simulate with existing two-equation turbulence models. Channel flows with injection and suction at wall surfaces and separated and reattaching flows downstream of a backward-facing step are also calculated. Comparisons of the computational results with the measurements and the direct numerical simulation data indicate that the present model is effective in calculating complex turbulent flows of technological interest. Furthermore, the parameters for scaling the near-wall region in the low-Reynolds-number model functions are re-evaluated, yielding some insights into the near-wall scaling parameters for application to complex turbulent flows.