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.

A Two-Equation Model for Heat Transport in Wall Turbulent Shear Flows

1988 ◽  
Vol 110 (3) ◽  
pp. 583-589 ◽  
Author(s):  
Y. Nagano ◽  
C. Kim
Keyword(s):  
Prandtl Number ◽  
Turbulence Modeling ◽  
Plate Boundary ◽  
Eddy Diffusivity ◽  
Equation Model ◽  
Wall Turbulence ◽  
Turbulent Heat Transfer ◽  
Turbulent Shear ◽  
Turbulent Heat ◽  
Wide Range

A new proposal for closing the energy equation is presented at the two-equation level of turbulence modeling. The eddy diffusivity concept is used in modeling. However, just as the eddy viscosity is determined from solutions of the k and ε equations, so the eddy diffusivity for heat is given as functions of temperature variance t2, and the dissipation rate of temperature fluctuations εt, together with k and ε. Thus, the proposed model does not require any questionable assumptions for the “turbulent Prandtl number.” Modeled forms of the t2 and εt equations are developed to account for the physical effects of molecular Prandtl number and near-wall turbulence. The model is tested by application to a flat-plate boundary layer, the thermal entrance region of a pipe, and the turbulent heat transfer in fluids over a wide range of the Prandtl number. Agreement with the experiment is generally very satisfactory.

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.

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.

A Velocity and Length Scale Approach to k–ε Modeling

1996 ◽  
Vol 118 (4) ◽  
pp. 857-863 ◽  
Author(s):  
O. Kwon ◽  
F. E. Ames
Keyword(s):  
Reynolds Number ◽  
Kinetic Energy ◽  
Turbulent Flows ◽  
Dissipation Rate ◽  
Eddy Viscosity ◽  
Normal Component ◽  
Transport Equations ◽  
Length Scale ◽  
Wall Region ◽  
Wide Range

This paper describes a velocity and length scale approach to low-Reynolds-number k–ε modeling, which formulates the eddy viscosity on the normal component of turbulence and a length scale. The normal component of turbulence is modeled based on the dissipation and distance from the wall and is bounded by the isotropic condition. The model accounts for the anisotropy of the dissipation and the reduced length of mixing in the near wall region. The kinetic energy and dissipation rate were computed from the k and ε transport equations of Durbin (1993). The model was tested for a wide range of turbulent flows and proved to be superior to other k–ε based models.

Direct Numerical Simulation of Homogeneous Turbulent Shear Flow Containing Bubbles

2006 ◽  
Author(s):  
T. Kawamura ◽  
T. Nakatani
Keyword(s):  
Reynolds Number ◽  
Kinetic Energy ◽  
Turbulent Kinetic Energy ◽  
Production Rate ◽  
Turbulent Flows ◽  
Reynolds Numbers ◽  
Turbulent Shear ◽  
Turbulent Shear Flow ◽  
Hypothetical Model ◽  
Turbulent Reynolds Number

Direct numerical simulations of homogeneous shear turbulent flows containing deformable bubbles were carried out for clarifying the mechanism of drag reduction by microbubbles. The results show that presence of bubbles can suppress or enhance the development of turbulence depending on condition. The dissipation rate of turbulent kinetic energy is always increased by bubbles, while the production rate can be either increased or decreased depending on the turbulent and shear Reynolds numbers. As a result, the growth rate of turbulent kinetic energy can be either increased or decreased by bubbles depending on conditions. It was shown that the production rate tends to decrease at smaller shear Reynolds number, at larger turbulent Reynolds number, and at larger Weber number. Based on the results, a hypothetical model to explain the dependency on the Reynolds numbers has been proposed.

The structure of a turbulent shear layer bounding a separation region

1987 ◽  
Vol 179 ◽  
pp. 439-468 ◽  
Author(s):  
I. P. Castro ◽  
A. Haque
Keyword(s):  
Shear Layer ◽  
Turbulent Flows ◽  
Large Scale ◽  
Turbulent Shear ◽  
Turbulence Structure ◽  
Similar Data ◽  
Reynolds Stresses ◽  
Plate Height ◽  
Separated Shear Layer ◽  
Wide Range

Detailed measurements within the separated shear layer behind a flat plate normal to an airflow are reported. A long, central splitter plate in the wake prevented vortex shedding and led to an extensive region of separated flow with mean reattachment some ten plate heights downstream. The Reynolds number based on plate height was in excess of 2 × 1044.Extensive use of pulsed-wire anemometry allowed measurements of all the Reynolds stresses throughout the flow, along with some velocity autocorrelations and integral timescale data. The latter help to substantiate the results of other workers obtained in separated flows of related geometry, particularly in the identification of a very low-frequency motion with a timescale much longer than that associated with the large eddies in the shear layer. Wall-skin-friction measurements are consistent with the few similar data previously published and indicate that the thin boundary layer developing beneath the separated region has some ‘laminar-like’ features.The Reynolds-stress measurements demonstrate that the turbulence structure of the separated shear layer differs from that of a plane mixing layer between two streams in a number of ways. In particular, the normal stresses all rise monotonically as reattachment is approached, are always considerably higher than the plane layer values and develop in quite different ways. Flow similarity is not a useful concept. A major conclusion is that any effects of stabilizing streamline curvature are weak compared with the effects of the re-entrainment at the low-velocity edge of the shear layer of turbulent fluid returned around reattachment. It is argued that the general features of the flow are likely to be similar to those that occur in a wide range of complex turbulent flows dominated by a shear layer bounding a large-scale recirculating region.

Local Friction Factor of Compressible Laminar or Turbulent Flow in Micro-Tubes

2011 ◽  
Author(s):  
Shintaro Murakami ◽  
Yutaka Asako
Keyword(s):  
Reynolds Number ◽  
Mach Number ◽  
Friction Factor ◽  
Turbulent Flows ◽  
Numerical Procedure ◽  
Choked Flow ◽  
Curvilinear Grid ◽  
Wide Range ◽  
Darcy Friction Factor ◽  
Fanning Friction Factor

Laminar/turbulent flows of compressible fluid in microtubes were simulated numerically to obtain the effect of compressibility on the local pipe friction factors. For gaseous flows, the effect of compressibility had not been clarified except for laminar flow whose Mach number is less than 0.45, so the present work extended this to handle higher speed flows including choked ones and turbulent flows. The numerical procedure based on arbitrary-Lagrangian-Eulerian method solves two-dimensional compressible momentum and energy equations. The Lam-Bremhorst Low-Reynolds number turbulence model was adopted to calculate eddy viscosity coefficient and turbulence energy. The physical domain of simulation with the back region downstream from the outlet of the micro-tube was used to be able to calculate the case of under-expansion flow in the tube. The orthogonal curvilinear grid was used for the computational mesh to obtain accurate results. The computations were performed for a wide range of Reynolds number and Mach number including laminar/turbulent choked flows. It was found that in laminar regimes the ratio of the Darcy friction factor to its conventional (incompressible flow’s) value is a function of Mach number and the same goes for the Fanning friction factor. On the other hand, in turbulent regimes, the ratio is still a function of Mach number for the Darcy friction factor but is equal to about unity for the Fanning friction factor. Namely, the Fanning friction factor of gaseous flow in micro-tubes coincides with Blasius formula, even when Mach number is not small and compressibility effect appears. This fact can be seen in choked flow.

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.

The PVC technique – a method to estimate the dissipation length scale in turbulent flows

1997 ◽  
Vol 352 ◽  
pp. 135-159 ◽  
Author(s):  
CHIH-MING HO ◽  
YITSHAK ZOHAR
Keyword(s):  
Turbulent Flows ◽  
Isotropic Turbulence ◽  
Average Length ◽  
Mixing Layer ◽  
Plate Boundary ◽  
Turbulent Shear ◽  
Length Scale ◽  
Velocity Signal ◽  
Plane Mixing Layer ◽  
Zero Crossings

A time-averaged length scale can be defined by a pair of successive turbulent-velocity derivatives, i.e. [dnu(x)/ dxn]′/ [dn+1u(x)/ dxn+1]′. The length scale associated with the zeroth- and the first-order derivatives, u′/u′x, is the Taylor microscale. In isotropic turbulence, this scale is the average length between zero crossings of the velocity signal. The average length between zero crossings of the first velocity derivative, i.e. u′x/u′xx, can be reliably obtained by using the peak-valley-counting (PVC) technique. We have found that the most probable scale, rather than the average, equals the wavelength at the peak of the dissipation spectrum in a plane mixing layer (Zohar & Ho 1996). In this study, we experimentally investigate the generality of applying the PVC technique to estimate the dissipation scale in three basic turbulent shear flows: a flat-plate boundary layer, a wake behind a two-dimensional cylinder and a plane mixing layer. We also analytically explore the quantitative relationships among this length scale and the Kolmogorov and Taylor microscales.

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