scholarly journals Origin of the Turbulence Structure in Wall-Bounded Flows, and Implications toward Computability

Fluids ◽  
2021 ◽  
Vol 6 (9) ◽  
pp. 333
Author(s):  
T.-W. Lee
Keyword(s):  
Turbulent Flows ◽  
Coordinate Frame ◽  
Turbulence Structure ◽  
Pressure Gradients ◽  
Boundary Layer Flows ◽  
Mean Velocity ◽  
Basic Physics ◽  
Symmetric Set ◽  
Wall Bounded Flows ◽  
Turbulence Transport

Coordinate-transformed analysis of turbulence transport is developed, which leads to a symmetric set of gradient expressions for the Reynolds stress tensor components. In this perspective, the turbulence structure in wall-bounded flows is seen to arise from an interaction of a small number of intuitive dynamical terms: transport, pressure and viscous. Main features of the turbulent flow can be theoretically prescribed in this way and reconstructed for channel and boundary layer flows, with and without pressure gradients, as validated in comparison with available direct numerical simulation data. A succinct picture of turbulence structure and its origins emerges, reflective of the basic physics of momentum and energy balance if placed in a specific moving coordinate frame. An iterative algorithm produces an approximate solution for the mean velocity, and its implications toward computability of turbulent flows is discussed.

Spanwise turbulence structure over permeable walls

2017 ◽  
Vol 822 ◽  
pp. 186-201 ◽  
Author(s):  
Kazuhiko Suga ◽  
Yuka Nakagawa ◽  
Masayuki Kaneda
Keyword(s):  
Turbulent Flows ◽  
High Speed ◽  
Solid Wall ◽  
Measurement Data ◽  
Field Measurements ◽  
Wall Turbulence ◽  
Turbulence Structure ◽  
Mean Velocity ◽  
Permeable Walls ◽  
Plane Displacement

Spanwise flow field measurements are carried out for turbulent flows in channels with permeable bottom walls by particle image velocimetry (PIV) to understand the effects of the wall permeability on turbulence structure near porous walls. The porous media used are three kinds of foamed ceramics which have the same porosities (0.8) but different permeabilities. The turbulent flow fields in spanwise planes are discussed using instantaneous and statistical measurement data. At a small permeability Reynolds number ($Re_{K}$), low-speed and high-speed streaks, which are similar to those of solid-wall turbulence, are observed near the walls while at a large $Re_{K}$ the observed structure is very different from that of the solid-wall turbulence. It is found that the obtained spanwise scales of the structure can be reasonably correlated with the wall normal distance plus the zero-plane displacement which is estimated from the mean velocity profile. With the distribution profiles of the spanwise streak spacing and integral length scales, the transitional change of the turbulence structure over permeable walls is discussed.

High-strain-rate free-surface boundary-layer flows

1983 ◽  
Vol 126 ◽  
pp. 443-461 ◽  
Author(s):  
J. R. Bertschy ◽  
R. W. Chin ◽  
F. H. Abernathy
Keyword(s):  
Boundary Layer ◽  
Turbulent Flows ◽  
Water Table ◽  
High Strain ◽  
Laser Doppler Anemometry ◽  
Streamwise Velocity ◽  
Surface Boundary ◽  
Boundary Layer Flows ◽  
Mean Velocity ◽  
Law Of The Wall

Two-dimensional boundary-layer flows of water down an inclined table were investigated in both the laminar and turbulent regimes. Mean, r.m.s. and skewness and velocity spectra were determined from streamwise velocity measurements. Two laser-Doppler anemometry methods were developed (for studying polymer-solution flows using this same water table) and compared with measurements obtained using hot-film anemometry. All three techniques obtained consistent results.An analysis based on a von Mises transformation is presented which accurately predicts the mean-velocity profile and flow development in the laminar regime. High strain rates are achieved which can be varied independently of Reynolds number, and turbulent flows are easily generated by inserting a disturbance. These turbulent flows are surprisingly similar to more commonly investigated turbulent boundarylayer flows of much greater y+ extent. Turbulent water-table flows typically extend only to y+ = 100, yet mean velocity essentially follows the law of the wall, and intensity and skewness measurements are similar to those obtained in flows much less limited in y+.

scholarly journals Asymmetrical Order in Wall-Bounded Turbulent Flows

Fluids ◽  
2021 ◽  
Vol 6 (9) ◽  
pp. 329
Author(s):  
T.-W. Lee
Keyword(s):  
Turbulent Flows ◽  
Outer Boundary ◽  
Plate Boundary ◽  
Turbulence Structure ◽  
Boundary Layer Flows ◽  
Self Similarity ◽  
Transport Dynamics ◽  
Dissipation Structure ◽  
Stress Components ◽  
Turbulent Wall

Scaling of turbulent wall-bounded flows is revealed in the gradient structures, for each of the Reynolds stress components. Within the “dissipation” structure, an asymmetrical order exists, which we can deploy to unify the scaling and transport dynamics within and across these flows. There are subtle differences in the outer boundary conditions between channel and flat-plate boundary-layer flows, which modify the turbulence structure far from the wall. The self-similarity exhibited in the gradient space and corresponding transport dynamics establish capabilities and encompassing knowledge of wall-bounded turbulent flows.

scholarly journals Variable-Order Fractional Models for Wall-Bounded Turbulent Flows

Entropy ◽  
2021 ◽  
Vol 23 (6) ◽  
pp. 782
Author(s):  
Fangying Song ◽  
George Em Karniadakis
Keyword(s):  
Fractional Derivative ◽  
Turbulent Flows ◽  
Fractional Order ◽  
Variable Order ◽  
Universal Curve ◽  
Reynolds Stresses ◽  
Continuous Change ◽  
Mean Velocity ◽  
Symmetric Variable ◽  
Fractional Models

Modeling of wall-bounded turbulent flows is still an open problem in classical physics, with relatively slow progress in the last few decades beyond the log law, which only describes the intermediate region in wall-bounded turbulence, i.e., 30–50 y+ to 0.1–0.2 R+ in a pipe of radius R. Here, we propose a fundamentally new approach based on fractional calculus to model the entire mean velocity profile from the wall to the centerline of the pipe. Specifically, we represent the Reynolds stresses with a non-local fractional derivative of variable-order that decays with the distance from the wall. Surprisingly, we find that this variable fractional order has a universal form for all Reynolds numbers and for three different flow types, i.e., channel flow, Couette flow, and pipe flow. We first use existing databases from direct numerical simulations (DNSs) to lean the variable-order function and subsequently we test it against other DNS data and experimental measurements, including the Princeton superpipe experiments. Taken together, our findings reveal the continuous change in rate of turbulent diffusion from the wall as well as the strong nonlocality of turbulent interactions that intensify away from the wall. Moreover, we propose alternative formulations, including a divergence variable fractional (two-sided) model for turbulent flows. The total shear stress is represented by a two-sided symmetric variable fractional derivative. The numerical results show that this formulation can lead to smooth fractional-order profiles in the whole domain. This new model improves the one-sided model, which is considered in the half domain (wall to centerline) only. We use a finite difference method for solving the inverse problem, but we also introduce the fractional physics-informed neural network (fPINN) for solving the inverse and forward problems much more efficiently. In addition to the aforementioned fully-developed flows, we model turbulent boundary layers and discuss how the streamwise variation affects the universal curve.

An Assessment of Three-Dimensional Turbulent Boundary Layer Prediction Methods

1973 ◽  
Vol 95 (3) ◽  
pp. 415-421 ◽  
Author(s):  
A. J. Wheeler ◽  
J. P. Johnston
Keyword(s):  
Boundary Layer ◽  
Eddy Viscosity ◽  
Three Dimensional ◽  
High Sensitivity ◽  
Boundary Layer Flows ◽  
Mean Velocity ◽  
Eddy Viscosity Model ◽  
Separating Flow ◽  
Dimensional Boundary ◽  
Stress Models

Predictions have been made for a variety of experimental three-dimensional boundary layer flows with a single finite difference method which was used with three different turbulent stress models: (i) an eddy viscosity model, (ii) the “Nash” model, and (iii) the “Bradshaw” model. For many purposes, even the simplest stress model (eddy viscosity) was adequate to predict the mean velocity field. On the other hand, the profile of shear stress direction was not correctly predicted in one case by any model tested. The high sensitivity of the predicted results to free stream pressure gradient in separating flow cases is demonstrated.

Direct numerical simulation of turbulent channel flow up to

2015 ◽  
Vol 774 ◽  
pp. 395-415 ◽  
Author(s):  
Myoungkyu Lee ◽  
Robert D. Moser
Keyword(s):  
Numerical Simulation ◽  
Reynolds Number ◽  
Direct Numerical Simulation ◽  
Turbulent Flows ◽  
Channel Flow ◽  
Turbulent Channel Flow ◽  
Streamwise Velocity ◽  
Mean Velocity ◽  
Layer Structures ◽  
High Reynolds

A direct numerical simulation of incompressible channel flow at a friction Reynolds number ($\mathit{Re}_{{\it\tau}}$) of 5186 has been performed, and the flow exhibits a number of the characteristics of high-Reynolds-number wall-bounded turbulent flows. For example, a region where the mean velocity has a logarithmic variation is observed, with von Kármán constant ${\it\kappa}=0.384\pm 0.004$. There is also a logarithmic dependence of the variance of the spanwise velocity component, though not the streamwise component. A distinct separation of scales exists between the large outer-layer structures and small inner-layer structures. At intermediate distances from the wall, the one-dimensional spectrum of the streamwise velocity fluctuation in both the streamwise and spanwise directions exhibits $k^{-1}$ dependence over a short range in wavenumber $(k)$. Further, consistent with previous experimental observations, when these spectra are multiplied by $k$ (premultiplied spectra), they have a bimodal structure with local peaks located at wavenumbers on either side of the $k^{-1}$ range.

Calculation of Developing Turbulent Flows in a Rotating Pipe

1991 ◽  
Vol 113 (1) ◽  
pp. 34-41 ◽  
Author(s):  
G. J. Yoo ◽  
R. M. C. So ◽  
B. C. Hwang
Keyword(s):  
Turbulent Flows ◽  
Reynolds Stress ◽  
Circumferential Strain ◽  
Three Dimensional ◽  
Wall Region ◽  
Boundary Layer Flows ◽  
Viscous Effects ◽  
Wide Range ◽  
Turbulence Closures ◽  
Rotating Boundary

Internal rotating boundary-layer flows are strongly influenced by large circumferential strain and the turbulence field is anisotropic. This is especially true in the entry region of a rotating pipe where the flow is three dimensional, the centrifugal force due to fluid rotation is less important, and the circumferential strain created by surface rotation has a significant effect on the turbulence field near the wall. Consequently, viscous effects cannot be neglected in the near-wall region. Several low-Reynolds-number turbulence closures are proposed for the calculation of developing rotating pipe flows. Some are two-equation closures with and without algebraic stress correction, while others are full Reynolds-stress closures. It is found that two-equation closures with and without algebraic stress correction are totally inadequate for this three-dimensional flow, while Reynolds-stress closures give results that are in good agreement with measurements over a wide range of rotation numbers.

scholarly journals Velocity transformation for compressible wall-bounded turbulent flows with and without heat transfer

2021 ◽  
Vol 118 (34) ◽  
pp. e2111144118 ◽  
Author(s):  
Kevin Patrick Griffin ◽  
Lin Fu ◽  
Parviz Moin
Keyword(s):  
Heat Transfer ◽  
Boundary Layer ◽  
Turbulent Flows ◽  
Viscous Sublayer ◽  
Mean Velocity ◽  
General Transformation ◽  
Law Of The Wall ◽  
Velocity Transformation ◽  
Logarithmic Region ◽  
Logarithmic Layer

In this work, a transformation, which maps the mean velocity profiles of compressible wall-bounded turbulent flows to the incompressible law of the wall, is proposed. Unlike existing approaches, the proposed transformation successfully collapses, without specific tuning, numerical simulation data from fully developed channel and pipe flows, and boundary layers with or without heat transfer. In all these cases, the transformation is successful across the entire inner layer of the boundary layer (including the viscous sublayer, buffer layer, and logarithmic layer), recovers the asymptotically exact near-wall behavior in the viscous sublayer, and is consistent with the near balance of turbulence production and dissipation in the logarithmic region of the boundary layer. The performance of the transformation is verified for compressible wall-bounded flows with edge Mach numbers ranging from 0 to 15 and friction Reynolds numbers ranging from 200 to 2,000. Based on physical arguments, we show that such a general transformation exists for compressible wall-bounded turbulence regardless of the wall thermal condition.

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