scholarly journals The influence of near-wall density and viscosity gradients on turbulence in channel flows

2016 ◽  
Vol 809 ◽  
pp. 793-820 ◽  
Author(s):  
Ashish Patel ◽  
Bendiks J. Boersma ◽  
Rene Pecnik
Keyword(s):  
Reynolds Number ◽  
Energy Transfer ◽  
Stokes Equations ◽  
Constitutive Relations ◽  
Wall Turbulence ◽  
Stress Generation ◽  
Turbulence Energy ◽  
Turbulent Structures ◽  
Wide Range ◽  
Near Wall

The influence of near-wall density and viscosity gradients on near-wall turbulence in a channel is studied by means of direct numerical simulation of the low-Mach-number approximation of the Navier–Stokes equations. Different constitutive relations for density $\unicode[STIX]{x1D70C}$ and viscosity $\unicode[STIX]{x1D707}$ as a function of temperature are used in order to mimic a wide range of fluid behaviours and to develop a generalised framework for studying turbulence modulations in variable-property flows. Instead of scaling the velocity solely based on local density, as done for the van Driest transformation, we derive an extension of the scaling that is based on gradients of the semilocal Reynolds number, defined as $Re_{\unicode[STIX]{x1D70F}}^{\star }\equiv Re_{\unicode[STIX]{x1D70F}}\sqrt{(\overline{\unicode[STIX]{x1D70C}}/\overline{\unicode[STIX]{x1D70C}}_{w})}/(\overline{\unicode[STIX]{x1D707}}/\overline{\unicode[STIX]{x1D707}}_{w})$ (the bar and subscript $w$ denote Reynolds averaging and wall value respectively, while $Re_{\unicode[STIX]{x1D70F}}$ is the friction Reynolds number based on wall values). This extension of the van Driest transformation is able to collapse velocity profiles for flows with near-wall property gradients as a function of the semilocal wall coordinate. However, flow quantities like mixing length, turbulence anisotropy and turbulent vorticity fluctuations do not show a universal scaling very close to the wall. This is attributed to turbulence modulations, which play a crucial role in the evolution of turbulent structures and turbulence energy transfer. We therefore investigate the characteristics of streamwise velocity streaks and quasistreamwise vortices and find that, similarly to turbulence statistics, the turbulent structures are also strongly governed by $Re_{\unicode[STIX]{x1D70F}}^{\star }$ profiles and that their dependence on individual density and viscosity profiles is minor. Flows with near-wall gradients in $Re_{\unicode[STIX]{x1D70F}}^{\star }$ ($\text{d}Re_{\unicode[STIX]{x1D70F}}^{\star }/\text{d}y\neq 0$) show significant changes in inclination and tilting angles of quasistreamwise vortices. These structural changes are responsible for the observed modulation of the Reynolds stress generation mechanism and the inter-component energy transfer in flows with strong near-wall $Re_{\unicode[STIX]{x1D70F}}^{\star }$ gradients.

Lid-Driven Square Cavity Flow: A Benchmark Solution with an 8192x8192 Grid

2021 ◽  
Author(s):  
Carlos Marchi ◽  
Cosmo D. Santiago ◽  
Carlos Alberto Rezende de Carvalho Junior
Keyword(s):  
Reynolds Number ◽  
Stokes Equations ◽  
Accurate Determination ◽  
Stable Solution ◽  
Reynolds Numbers ◽  
Accurate Solution ◽  
Discretization Error ◽  
Square Cavity ◽  
Solution Vector ◽  
Wide Range

Abstract The incompressible steady-state fluid flow inside a lid-driven square cavity was simulated using the mass conservation and Navier-Stokes equations. This system of equations is solved for Reynolds numbers of up to 10,000 to the accuracy of the computational machine round-off error. The computational model used was the second-order accurate finite volume method. A stable solution is obtained using the iterative multigrid methodology with 8192 × 8192 volumes, while degree-10 interpolation and Richardson extrapolation were used to reduce the discretization error. The solution vector comprised five entries of velocities, pressure, and location. For comparison purposes, 65 different variables of interest were chosen, such as velocity profile, its extremum values and location, extremum values and location of the stream function. The discretization error for each variable of interest was estimated using two types of estimators and their apparent order of accuracy. The variations of the 11 selected variables are shown across 38 Reynolds number values between 0.0001 and 10,000. In this study, we provide a more accurate determination of the Reynolds number value at which the upper secondary vortex appears. The results of this study were compared with those of several other studies in the literature. The current solution methodology was observed to produce the most accurate solution till date for a wide range of Reynolds numbers.

Interphasial energy transfer and particle dissipation in particle-laden wall turbulence

2013 ◽  
Vol 715 ◽  
pp. 32-59 ◽  
Author(s):  
Lihao Zhao ◽  
Helge I. Andersson ◽  
Jurriaan J. J. Gillissen
Keyword(s):  
Energy Transfer ◽  
Kinetic Energy ◽  
Stokes Equations ◽  
Mechanical Energy ◽  
Wall Turbulence ◽  
Spherical Particles ◽  
Velocity Versus ◽  
Wall Region ◽  
Carrier Fluid ◽  
Stokes Force

AbstractTransfer of mechanical energy between solid spherical particles and a Newtonian carrier fluid has been explored in two-way coupled direct numerical simulations of turbulent channel flow. The inertial particles have been treated as individual point particles in a Lagrangian framework and their feedback on the fluid phase has been incorporated in the Navier–Stokes equations. At sufficiently large particle response times the Reynolds shear stress and the turbulence intensities in the spanwise and wall-normal directions were attenuated whereas the velocity fluctuations were augmented in the streamwise direction. The physical mechanisms involved in the particle–fluid interactions were analysed in detail, and it was observed that the fluid transferred energy to the particles in the core region of the channel whereas the fluid received kinetic energy from the particles in the wall region. A local imbalance in the work performed by the particles on the fluid and the work exerted by the fluid on the particles was observed. This imbalance gave rise to a particle-induced energy dissipation which represents a loss of mechanical energy from the fluid–particle suspension. An independent examination of the work associated with the different directional components of the Stokes force revealed that the dominating energy transfer was associated with the streamwise component. Both the mean and fluctuating parts of the Stokes force promoted streamwise fluctuations in the near-wall region. The kinetic energy associated with the cross-sectional velocity components was damped due to work done by the particles, and the energy was dissipated rather than recovered as particle kinetic energy. Componentwise scatter plots of the instantaneous velocity versus the instantaneous slip-velocity provided further insight into the energy transfer mechanisms, and the observed modulations of the flow field could thereby be explained.

scholarly journals Wall-attached structures of velocity fluctuations in a turbulent boundary layer

2018 ◽  
Vol 856 ◽  
pp. 958-983 ◽  
Author(s):  
Jinyul Hwang ◽  
Hyung Jin Sung
Keyword(s):  
Boundary Layer ◽  
Reynolds Number ◽  
High Reynolds Number ◽  
Wall Turbulence ◽  
Velocity Fluctuations ◽  
Moderate Reynolds Number ◽  
Wide Range ◽  
Logarithmic Region ◽  
High Reynolds ◽  
Attached Eddies

Wall turbulence is a ubiquitous phenomenon in nature and engineering applications, yet predicting such turbulence is difficult due to its complexity. High-Reynolds-number turbulence arises in most practical flows, and is particularly complicated because of its wide range of scales. Although the attached-eddy hypothesis postulated by Townsend can be used to predict turbulence intensities and serves as a unified theory for the asymptotic behaviours of turbulence, the presence of coherent structures that contribute to the logarithmic behaviours has not been observed in instantaneous flow fields. Here, we demonstrate the logarithmic region of the turbulence intensity by identifying wall-attached structures of the velocity fluctuations ($u_{i}$) through the direct numerical simulation of a moderate-Reynolds-number boundary layer ($Re_{\unicode[STIX]{x1D70F}}\approx 1000$). The wall-attached structures are self-similar with respect to their heights ($l_{y}$), and in particular the population density of the streamwise component ($u$) scales inversely with $l_{y}$, reminiscent of the hierarchy of attached eddies. The turbulence intensities contained within the wall-parallel components ($u$ and $w$) exhibit the logarithmic behaviour. The tall attached structures ($l_{y}^{+}>100$) of $u$ are composed of multiple uniform momentum zones (UMZs) with long streamwise extents, whereas those of the cross-stream components ($v$ and $w$) are relatively short with a comparable width, suggesting the presence of tall vortical structures associated with multiple UMZs. The magnitude of the near-wall peak observed in the streamwise turbulent intensity increases with increasing $l_{y}$, reflecting the nested hierarchies of the attached $u$ structures. These findings suggest that the identified structures are prime candidates for Townsend’s attached-eddy hypothesis and that they can serve as cornerstones for understanding the multiscale phenomena of high-Reynolds-number boundary layers.

Direct numerical simulation of turbulence in injection-driven three-dimensional cylindrical flows

2011 ◽  
Vol 670 ◽  
pp. 176-203 ◽  
Author(s):  
JU ZHANG ◽  
THOMAS L. JACKSON
Keyword(s):  
Reynolds Number ◽  
Root Mean Square ◽  
Streamwise Velocity ◽  
Wall Turbulence ◽  
Wall Friction ◽  
Mean Square ◽  
The Mean ◽  
Wall Shear ◽  
Strong Injection ◽  
Near Wall

Incompressible turbulent flow in a periodic circular pipe with strong injection is studied as a simplified model for the core flow in a solid-propellant rocket motor and other injection-driven internal flows. The model is based on a multi-scale asymptotic approach. The intended application of the current study is erosive burning of solid propellants. Relevant analysis for easily accessible parameters for this application, such as the magnitudes, main frequencies and wavelengths associated with the near-wall shear, and the assessment of near-wall turbulence viscosity is focused on. It is found that, unlike flows with weak or no injection, the near-wall shear is dominated by the root mean square of the streamwise velocity which is a function of the Reynolds number, while the mean streamwise velocity is only weakly dependent on the Reynolds number. As a result, a new wall-friction velocity $\(u_\tau{\,=\,}\sqrt{\tau_w/\rho}\)$, based on the shear stress derived from the sum of the mean and the root mean square, i.e. $\(\tau_{w,inj} {\,=\,} \mu |{\partial (\bar{u}+u_{rms})}/{\partial r}|_w\)$, is proposed for the scaling of turbulent viscosity for turbulent flows with strong injection. We also show that the mean streamwise velocity profile has an inflection point near the injecting surface.

Fluid Flow and Lateral Fluid Dispersion in Bounded Granular Beds

2002 ◽  
Author(s):  
Azita Soleymani ◽  
Eveliina Takasuo ◽  
Piroz Zamankhan ◽  
William Polashenski
Keyword(s):  
Reynolds Number ◽  
Porous Media ◽  
Numerical Solutions ◽  
Stokes Equations ◽  
Numerical Study ◽  
Fluid Velocity ◽  
Three Dimensional ◽  
Numerical Results ◽  
Transition To Turbulence ◽  
Wide Range

Results are presented from a numerical study examining the flow of a viscous, incompressible fluid through random packing of nonoverlapping spheres at moderate Reynolds numbers (based on pore permeability and interstitial fluid velocity), spanning a wide range of flow conditions for porous media. By using a laminar model including inertial terms and assuming rough walls, numerical solutions of the Navier-Stokes equations in three-dimensional porous packed beds resulted in dimensionless pressure drops in excellent agreement with those reported in a previous study (Fand et al., 1987). This observation suggests that no transition to turbulence could occur in the range of Reynolds number studied. For flows in the Forchheimer regime, numerical results are presented of the lateral dispersivity of solute continuously injected into a three-dimensional bounded granular bed at moderate Peclet numbers. Lateral fluid dispersion coefficients are calculated by comparing the concentration profiles obtained from numerical and analytical methods. Comparing the present numerical results with data available in the literature, no evidence has been found to support the speculations by others for a transition from laminar to turbulent regimes in porous media at a critical Reynolds number.

scholarly journals An Experimental Study of Water Flow in Smooth and Rough Rectangular Micro-Channels

2004 ◽  
Author(s):  
R. Baviere ◽  
F. Ayela ◽  
S. Le Person ◽  
M. Favre-Marinet
Keyword(s):  
Reynolds Number ◽  
Water Flow ◽  
Stokes Equations ◽  
Transition To Turbulence ◽  
Friction Coefficients ◽  
Micro Channels ◽  
Wide Range ◽  
Macro Scale ◽  
Experimental Apparatus ◽  
Poiseuille Number

This paper presents experimental results concerning water flow in smooth and rough rectangular micro-channels. It is part of a work intended to test the classical fluid mechanics laws when the characteristic length scale of inner liquid flows falls below 500μm. The method consists in determining experimental friction coefficients as a function of the Reynolds number. This implies simultaneous measurements of pressure drop and flow rates in microstructures. The two experimental apparatus used in this study enabled us to explore a wide range of length scales (7μm to 300μm) and of Reynolds number (0.01 to 8,000). Classical machining technologies were used to make micro-channels of various heights down to a scale of 100μm. Smaller silicon-Pyrex micro-channels were also made by means of silicon-based micro technologies. In these structures, friction coefficients have been measured locally with Cu-Ni strain gauges. For every height tested, both smooth and rough walls were successively used. When compared to macro-scale correlation the results demonstrate that i) In the smooth case, friction is correctly predicted by the Navier-Stokes equations with the classical kinematic boundary conditions, ii) For 200μm high channels, visualizations show transition to turbulence at Reynolds number of about 3,000. The presence of roughness elements did not significantly influence this result and iii) Roughness considerably increases the friction coefficient in the laminar regime. However, the Poiseuille number remains independent of the Reynolds number.

Hot-wire spatial resolution issues in wall-bounded turbulence

2009 ◽  
Vol 635 ◽  
pp. 103-136 ◽  
Author(s):  
N. HUTCHINS ◽  
T. B. NICKELS ◽  
I. MARUSIC ◽  
M. S. CHONG
Keyword(s):  
Reynolds Number ◽  
Boundary Layers ◽  
Spatial Resolution ◽  
Reynolds Numbers ◽  
Energy Spectra ◽  
Small Scale ◽  
Wire Length ◽  
Hot Wire ◽  
Wide Range ◽  
Near Wall

Careful reassessment of new and pre-existing data shows that recorded scatter in the hot-wire-measured near-wall peak in viscous-scaled streamwise turbulence intensity is due in large part to the simultaneous competing effects of the Reynolds number and viscous-scaled wire length l+. An empirical expression is given to account for these effects. These competing factors can explain much of the disparity in existing literature, in particular explaining how previous studies have incorrectly concluded that the inner-scaled near-wall peak is independent of the Reynolds number. We also investigate the appearance of the so-called outer peak in the broadband streamwise intensity, found by some researchers to occur within the log region of high-Reynolds-number boundary layers. We show that the ‘outer peak’ is consistent with the attenuation of small scales due to large l+. For turbulent boundary layers, in the absence of spatial resolution problems, there is no outer peak up to the Reynolds numbers investigated here (Reτ = 18830). Beyond these Reynolds numbers – and for internal geometries – the existence of such peaks remains open to debate. Fully mapped energy spectra, obtained with a range of l+, are used to demonstrate this phenomenon. We also establish the basis for a ‘maximum flow frequency’, a minimum time scale that the full experimental system must be capable of resolving, in order to ensure that the energetic scales are not attenuated. It is shown that where this criterion is not met (in this instance due to insufficient anemometer/probe response), an outer peak can be reproduced in the streamwise intensity even in the absence of spatial resolution problems. It is also shown that attenuation due to wire length can erode the region of the streamwise energy spectra in which we would normally expect to see kx−1 scaling. In doing so, we are able to rationalize much of the disparity in pre-existing literature over the kx−1 region of self-similarity. Not surprisingly, the attenuated spectra also indicate that Kolmogorov-scaled spectra are subject to substantial errors due to wire spatial resolution issues. These errors persist to wavelengths far beyond those which we might otherwise assume from simple isotropic assumptions of small-scale motions. The effects of hot-wire length-to-diameter ratio (l/d) are also briefly investigated. For the moderate wire Reynolds numbers investigated here, reducing l/d from 200 to 100 has a detrimental effect on measured turbulent fluctuations at a wide range of energetic scales, affecting both the broadband intensity and the energy spectra.

Improved Form of the k-ε Model for Wall Turbulent Shear Flows

1987 ◽  
Vol 109 (2) ◽  
pp. 156-160 ◽  
Author(s):  
Y. Nagano ◽  
M. Hishida
Keyword(s):  
Reynolds Number ◽  
Turbulent Flows ◽  
Plate Boundary ◽  
Wall Turbulence ◽  
Turbulent Shear ◽  
Committee Report ◽  
Low Reynolds Number Flows ◽  
Diffuser Flow ◽  
Wide Range ◽  
Predicted Values

An improved k-ε turbulence model for predicting wall turbulence is presented. The model was developed in conjunction with an accurate calculation of near-wall and low-Reynolds-number flows to meet the requirements of the Evaluation Committee report of the 1980–1981 Stanford Conference on Complex Turbulent Flows. The proposed model was tested by application to turbulent pipe and channel flows, a flat plate boundary layer, a relaminarizing flow, and a diffuser flow. In all cases, the predicted values of turbulent quantities agreed almost completely with measurements, which many previously proposed models failed to predict correctly, over a wide range of the Reynolds number.

scholarly journals Turbulent boundary layers over permeable walls: scaling and near-wall structure

2011 ◽  
Vol 687 ◽  
pp. 141-170 ◽  
Author(s):  
C. Manes ◽  
D. Poggi ◽  
L. Ridolfi
Keyword(s):  
Turbulent Flows ◽  
Laser Doppler Anemometry ◽  
Wall Turbulence ◽  
Shear Instability ◽  
Wall Structure ◽  
Wall Region ◽  
Mean Velocity ◽  
Wide Range ◽  
Permeable Walls ◽  
Near Wall

AbstractThis paper presents an experimental study devoted to investigating the effects of permeability on wall turbulence. Velocity measurements were performed by means of laser Doppler anemometry in open channel flows over walls characterized by a wide range of permeability. Previous studies proposed that the von Kármán coefficient associated with mean velocity profiles over permeable walls is significantly lower than the standard values reported for flows over smooth and rough walls. Furthermore, it was observed that turbulent flows over permeable walls do not fully respect the widely accepted paradigm of outer-layer similarity. Our data suggest that both anomalies can be explained as an effect of poor inner–outer scale separation if the depth of shear penetration within the permeable wall is considered as the representative length scale of the inner layer. We observed that with increasing permeability, the near-wall structure progressively evolves towards a more organized state until it reaches the condition of a perturbed mixing layer where the shear instability of the inflectional mean velocity profile dictates the scale of the dominant eddies. In our experiments such shear instability eddies were detected only over the wall with the highest permeability. In contrast attached eddies were present over all the other wall conditions. On the basis of these findings, we argue that the near-wall structure of turbulent flows over permeable walls is regulated by a competing mechanism between attached and shear instability eddies. We also argue that the ratio between the shear penetration depth and the boundary layer thickness quantifies the ratio between such eddy scales and, therefore, can be used as a diagnostic parameter to assess which eddy structure dominates the near-wall region for different wall permeability and flow conditions.

Modeling Reynolds-Number Effects in Wall-Bounded Turbulent Flows

1996 ◽  
Vol 118 (2) ◽  
pp. 260-267 ◽  
Author(s):  
R. M. C. So ◽  
H. Aksoy ◽  
S. P. Yuan ◽  
T. P. Sommer
Keyword(s):  
Reynolds Number ◽  
Turbulent Flows ◽  
Reynolds Stress ◽  
Strain Tensor ◽  
Reynolds Numbers ◽  
Turbulence Statistics ◽  
Wide Range ◽  
Peak Shear Stress ◽  
Reynolds Number Effects ◽  
Near Wall

Recent experimental and direct numerical simulation data of two-dimensional, isothermal wall-bounded incompressible turbulent flows indicate that Reynolds-number effects are not only present in the outer layer but are also quite noticeable in the inner layer. The effects are most apparent when the turbulence statistics are plotted in terms of inner variables. With recent advances made in Reynolds-stress and near-wall modeling, a near-wall Reynolds-stress closure based on a recently proposed quasi-linear model for the pressure strain tensor is used to analyse wall-bounded flows over a wide range of Reynolds numbers. The Reynolds number varies from a low of 180, based on the friction velocity and pipe radius/channel half-width, to 15406, based on momentum thickness and free stream velocity. In all the flow cases examined, the model replicates the turbulence statistics, including the Reynolds-number effects observed in the inner and outer layers, quite well. Furthermore, the model reproduces the correlation proposed for the location of the peak shear stress and an appropriately defined Reynolds number, and the variations of the near-wall asymptotes with Reynolds numbers. It is conjectured that the ability of the model to replicate the asymptotic behavior of the near-wall flow is most responsible for the correct prediction of the Reynolds-number effects.

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