On an analytical explanation of the phenomena observed in accelerated turbulent pipe flow

2019 ◽  
Vol 881 ◽  
pp. 420-461
Author(s):  
F. Javier García García ◽  
Pablo Fariñas Alvariño
Keyword(s):  
Shear Stress ◽  
Laminar Flow ◽  
Pipe Flow ◽  
Reynolds Shear Stress ◽  
Velocity Profiles ◽  
Turbulent Pipe Flow ◽  
Intensity Parameter ◽  
Mean Velocity ◽  
The Mean ◽  
Do So

This research presents a new theory that explains analytically the behaviour of any fully developed incompressible turbulent pipe flow, steady or unsteady. We propose the name of theory of underlying laminar flow (TULF), because its main consequence is the description of any turbulent pipe flow as the sum of two components: the underlying laminar flow (ULF) and the purely turbulent component (PTC). We use the framework of the TULF to explain analytically most of the important and interesting phenomena reported in He & Jackson (J. Fluid Mech., vol. 408, 2000, pp. 1–38). To do so, we develop a simple model for the pressure gradient and Reynolds shear stress that could be applied to the linearly accelerated pipe flow described by He & Jackson (2000). The following features of the unsteady flow are explained: the deformation undergone by the mean velocity profiles during the transient, the velocity overshoot observed in the more rapid excursions, the dual deformation of mean velocity profiles when overshoots are present, the laminarisation effects described during acceleration, the rapid decrease of the Reynolds shear stress upon approaching the wall that brings forth the laminar sublayer, and some other minor effects. A new field is defined to characterise the degree of turbulence within the flow, directly calculable from the theory itself. Arguably, this new field would describe the degree of turbulence in a pipe flow more accurately than the familiar turbulence intensity parameter. Finally, a paradox is found in the deformation of the unsteady mean velocity profiles with respect to equal-Reynolds-number steady profiles, which is duly explained. The research also predicts the occurrence of mean velocity undershoots if the flow is decreased rapidly enough.

scholarly journals Global energy fluxes in turbulent channels with flow control

2018 ◽  
Vol 857 ◽  
pp. 345-373 ◽  
Author(s):  
Davide Gatti ◽  
Andrea Cimarelli ◽  
Yosuke Hasegawa ◽  
Bettina Frohnapfel ◽  
Maurizio Quadrio
Keyword(s):  
Reynolds Number ◽  
Shear Stress ◽  
Energy Dissipation ◽  
Velocity Field ◽  
Flow Control ◽  
Reynolds Shear Stress ◽  
Power Input ◽  
Energy Fluxes ◽  
Mean Velocity ◽  
The Mean

This paper addresses the integral energy fluxes in natural and controlled turbulent channel flows, where active skin-friction drag reduction techniques allow a more efficient use of the available power. We study whether the increased efficiency shows any general trend in how energy is dissipated by the mean velocity field (mean dissipation) and by the fluctuating velocity field (turbulent dissipation). Direct numerical simulations (DNS) of different control strategies are performed at constant power input (CPI), so that at statistical equilibrium, each flow (either uncontrolled or controlled by different means) has the same power input, hence the same global energy flux and, by definition, the same total energy dissipation rate. The simulations reveal that changes in mean and turbulent energy dissipation rates can be of either sign in a successfully controlled flow. A quantitative description of these changes is made possible by a new decomposition of the total dissipation, stemming from an extended Reynolds decomposition, where the mean velocity is split into a laminar component and a deviation from it. Thanks to the analytical expressions of the laminar quantities, exact relationships are derived that link the achieved flow rate increase and all energy fluxes in the flow system with two wall-normal integrals of the Reynolds shear stress and the Reynolds number. The dependence of the energy fluxes on the Reynolds number is elucidated with a simple model in which the control-dependent changes of the Reynolds shear stress are accounted for via a modification of the mean velocity profile. The physical meaning of the energy fluxes stemming from the new decomposition unveils their inter-relations and connection to flow control, so that a clear target for flow control can be identified.

Turbulent Vorticity Diffusion in the Stronger Wall Jet Managed by a Flat Plate Wing in the Outer Layer

2015 ◽  
Author(s):  
Takuma Katayama ◽  
Shinsuke Mochizuki
Keyword(s):  
Shear Stress ◽  
Flat Plate ◽  
Outer Layer ◽  
Large Scale ◽  
Reynolds Shear Stress ◽  
Three Dimensional ◽  
Quantitative Relationship ◽  
Wall Jet ◽  
Mean Velocity ◽  
The Mean

The present experiment focuses on the vorticity diffusion in a stronger wall jet managed by a three-dimensional flat plate wing in the outer layer. Measurement of the fluctuating velocities and vorticity correlation has been carried out with 4-wire vorticity probe. The turbulent vorticity diffusion due to the large scale eddies in the outer layer is quantitatively examined by using the 4-wire vorticity probe. Quantitative relationship between vortex structure and Reynolds shear stress is revealed by means of directly measured experimental evidence which explains vorticity diffusion process and influence of the manipulating wing. It is expected that the three-dimensional outer layer manipulator contributes to keep convex profile of the mean velocity, namely, suppression of the turbulent diffusion and entrainment.

The effects of expansion on the turbulence structure of compressible boundary layers

1998 ◽  
Vol 367 ◽  
pp. 67-105 ◽  
Author(s):  
STEPHEN A. ARNETTE ◽  
MO SAMIMY ◽  
GREGORY S. ELLIOTT
Keyword(s):  
Boundary Layer ◽  
Shear Stress ◽  
Reynolds Shear Stress ◽  
Energy Levels ◽  
Plate Boundary ◽  
Velocity Profiles ◽  
Turbulence Structure ◽  
Mean Velocity ◽  
Measured Velocity ◽  
Vorticity Transport

A fully developed Mach 3 turbulent boundary layer subjected to four expansion regions (centred and gradual expansions of 7° and 14°) was investigated with laser Doppler velocimetry. Measurements were acquired in the incoming flat-plate boundary layer and to s/δ≃20 downstream of the expansions. While mean velocity profiles exhibit significant progress towards recovery by the most downstream measurements, the turbulence structure remains far from equilibrium. Comparisons of computed (method of characteristics) and measured velocity profiles indicate that the post-expansion flow evolution is largely inviscid for approximately 10δ. Turbulence levels decrease across the expansion, and the reductions increase in severity as the wall is approached. Downstream of the 14° expansions, the reductions are more severe and reverse transition is indicated by sharp reductions in turbulent kinetic energy levels and a change in sign of the Reynolds shear stress. Dimensionless parameters such as anisotropy and shear stress correlation coefficient highlight the complex evolution of the post-expansion boundary layer. An examination of the compressible vorticity transport equation and estimates of the perturbation impulses attributable to streamline curvature, acceleration, and dilatation both confirm dilatation to be the primary stabilizer. However, the dilatation impulse increases only slightly for the 14° expansions, so the dramatic differences downstream of the 7° and 14° expansions indicate nonlinear boundary layer response. Differences attributable to the varied radii of surface curvature are fleeting for the 7° expansions, but persist through the spatial extent of the measurements for the 14° expansions.

Estimating the value of von Kármán’s constant in turbulent pipe flow

2014 ◽  
Vol 749 ◽  
pp. 79-98 ◽  
Author(s):  
S. C. C. Bailey ◽  
M. Vallikivi ◽  
M. Hultmark ◽  
A. J. Smits
Keyword(s):  
Pipe Flow ◽  
Turbulent Pipe Flow ◽  
Data Sets ◽  
Mean Velocity ◽  
Princeton University ◽  
Best Estimate ◽  
Data Points ◽  
Smooth Pipe ◽  
The Mean ◽  
Hot Wires

AbstractFive separate data sets on the mean velocity distributions in the Princeton University/ONR Superpipe are used to establish the best estimate for the value of von Kármán’s constant for the flow in a fully developed, hydraulically smooth pipe. The profiles were taken using Pitot tubes, conventional hot wires and nanoscale thermal anemometry probes. The value of the constant was found to vary significantly due to measurement uncertainties in the mean velocity, friction velocity and the wall distance, and the number of data points included in the analysis. The best estimate for the von Kármán constant in turbulent pipe flow is found to be $0.40 \pm 0.02$. A more precise estimate will require improved instrumentation.

scholarly journals High-resolution velocity measurement in the inner part of turbulent boundary layers over super-hydrophobic surfaces

2016 ◽  
Vol 801 ◽  
pp. 670-703 ◽  
Author(s):  
Hangjian Ling ◽  
Siddarth Srinivasan ◽  
Kevin Golovin ◽  
Gareth H. McKinley ◽  
Anish Tuteja ◽  
...  
Keyword(s):  
Boundary Layer ◽  
Shear Stress ◽  
Velocity Profile ◽  
Drag Reduction ◽  
Slip Velocity ◽  
Reynolds Shear Stress ◽  
Turbulent Boundary Layers ◽  
Mean Velocity ◽  
Roughness Elements ◽  
The Mean

Digital holographic microscopy is used for characterizing the profiles of mean velocity, viscous and Reynolds shear stresses, as well as turbulence level in the inner part of turbulent boundary layers over several super-hydrophobic surfaces (SHSs) with varying roughness/texture characteristics. The friction Reynolds numbers vary from 693 to 4496, and the normalized root mean square values of roughness $(k_{rms}^{+})$ vary from 0.43 to 3.28. The wall shear stress is estimated from the sum of the viscous and Reynolds shear stress at the top of roughness elements and the slip velocity is obtained from the mean profile at the same elevation. For flow over SHSs with $k_{rms}^{+}<1$, drag reduction and an upward shift of the mean velocity profile occur, along with a mild increase in turbulence in the inner part of the boundary layer. As the roughness increases above $k_{rms}^{+}\sim 1$, the flow over the SHSs transitions from drag reduction, where the viscous stress dominates, to drag increase where the Reynolds shear stress becomes the primary contributor. For the present maximum value of $k_{rms}^{+}=3.28$, the inner region exhibits the characteristics of a rough wall boundary layer, including elevated wall friction and turbulence as well as a downward shift in the mean velocity profile. Increasing the pressure in the test facility to a level that compresses the air layer on the SHSs and exposes the protruding roughness elements reduces the extent of drag reduction. Aligning the roughness elements in the streamwise direction increases the drag reduction. For SHSs where the roughness effect is not dominant ($k_{rms}^{+}<1$), the present measurements confirm previous theoretical predictions of the relationships between drag reduction and slip velocity, allowing for both spanwise and streamwise slip contributions.

Scaling of Favorable Pressure Gradient Turbulent Boundary Layers With Eventual Relaminarization

2005 ◽  
Author(s):  
Rau´l Bayoa´n Cal ◽  
Xia Wang ◽  
Luciano Castillo
Keyword(s):  
Boundary Layer ◽  
Pressure Gradient ◽  
Boundary Layers ◽  
Reynolds Shear Stress ◽  
Velocity Profiles ◽  
Turbulent Boundary Layers ◽  
Reynolds Stresses ◽  
Mean Velocity ◽  
Favorable Pressure Gradient ◽  
The Mean

Applying similarity analysis to the RANS equations of motion for a pressure gradient turbulent boundary layer, Castillo and George [1] obtained the scalings for the mean deficit velocity and the Reynolds stresses. Following this analysis, Castillo and George studied favorable pressure gradient (FPG) turbulent boundary layers. They were able to obtain a single curve for FPG flows when scaling the mean deficit velocity profiles. In this study, FPG turbulent boundary layers are analyzed as well as relaminarized boundary layers subjected to an even stronger FPG. It is found that the mean deficit velocity profiles diminish when scaled using the Castillo and George [1] scaling, U∞, and the Zagarola and Smits [2] scaling, U∞δ*/δ. In addition, Reynolds stress data has been analyzed and it is found that the relaminarized boundary layer data decreases drastically in all components of the Reynolds stresses. Furthermore, it will be shown that the shape of the profile for the wall-normal and Reynolds shear stress components change drastically given the relaminarized state. Therefore, the mean velocity deficit profiles as well as Reynolds stresses are found to be necessary in order to understand not only FPG flows, but also relaminarized boundary layers.

Errors Characterization of a RANS Simulation

2021 ◽  
Author(s):  
Hugo D. Pasinato ◽  
Ezequiel Arthur Krumrick
Keyword(s):  
Shear Stress ◽  
Turbulent Flows ◽  
Reynolds Shear Stress ◽  
Strain Tensor ◽  
Numerical Code ◽  
Reynolds Stresses ◽  
Mean Velocity ◽  
Rans Simulation ◽  
Eddy Viscosity Model ◽  
The Mean

Abstract This research uses data from direct numerical simulation (DNS) to characterize the different errors associated with a Reynolds-averaged Navier-Stokes (RANS) simulation. The statistics from DNS (Reynolds stresses, kinetic energy of turbulence, $\kappa$, and dissipation of turbulence, $\epsilon$), are fed into a RANS simulation with the same Reynolds number, geometry, and numerical code used for DNS. Three integral metrics error based on the mean velocity, the moduli of the mean rate-of-strain tensor, and the wall shear stress are used to characterize the errors associated with the RANS technique, with the RANS model, and with the linear eddy viscosity model (LEVM). For developed and perturbed flow, it is found that the mean velocity of the RANS simulations with the DNS statistics is almost the same as the mean velocity from DNS data. This procedure enables the study of the relative importance of the different Reynolds stresses in a particular flow. It is shown that for the bounded perturbed turbulent flows studied here, almost all the necessary effects of turbulence are contained in the Reynolds shear stress.

scholarly journals Nonlinear waves with a threefold rotational symmetry in pipe flow: influence of a strongly shear-thinning rheology

2017 ◽  
Vol 818 ◽  
pp. 595-622
Author(s):  
Emmanuel Plaut ◽  
Nicolas Roland ◽  
Chérif Nouar
Keyword(s):  
Reynolds Number ◽  
Laminar Flow ◽  
Nonlinear Waves ◽  
Pipe Flow ◽  
Rotational Symmetry ◽  
Shear Thinning ◽  
Transition To Turbulence ◽  
Mean Velocity ◽  
The Mean ◽  
The One

In order to model the transition to turbulence in pipe flow of non-Newtonian fluids, the influence of a strongly shear-thinning rheology on the travelling waves with a threefold rotational symmetry of Faisst & Eckhardt (Phys. Rev. Lett., vol. 91, 2003, 224502) and Wedin & Kerswell (J. Fluid Mech., vol. 508, 2004, pp. 333–371) is analysed. The rheological model is Carreau’s law. Besides the shear-thinning index $n_{C}$, the dimensionless characteristic time $\unicode[STIX]{x1D706}$ of the fluid is considered as the main non-Newtonian control parameter. If $\unicode[STIX]{x1D706}=0$, the fluid is Newtonian. In the relevant limit $\unicode[STIX]{x1D706}\rightarrow +\infty$, the fluid approaches a power-law behaviour. The laminar base flows are first characterized. To compute the nonlinear waves, a Petrov–Galerkin code is used, with continuation methods, starting from the Newtonian case. The axial wavenumber is optimized and the critical waves appearing at minimal values of the Reynolds number $\mathit{Re}_{w}$ based on the mean velocity and wall viscosity are characterized. As $\unicode[STIX]{x1D706}$ increases, these correspond to a constant value of the Reynolds number based on the mean velocity and viscosity. This viscosity, close to the one of the laminar flow, can be estimated analytically. Therefore the experimentally relevant critical Reynolds number $\mathit{Re}_{wc}$ can also be estimated analytically. This Reynolds number may be viewed as a lower estimate of the Reynolds number for the transition to developed turbulence. This demonstrates a quantified stabilizing effect of the shear-thinning rheology. Finally, the increase of the pressure gradient in waves, as compared to the one in the laminar flow with the same mass flux, is calculated, and a kind of ‘drag reduction effect’ is found.

Nonasymptotic behavior of developing turbulent pipe flow

1976 ◽  
Vol 54 (3) ◽  
pp. 268-278 ◽  
Author(s):  
J. K. Reichert ◽  
R. S. Azad
Keyword(s):  
Reynolds Number ◽  
Pipe Flow ◽  
Reynolds Numbers ◽  
Peak Position ◽  
Turbulent Pipe Flow ◽  
Shear Stresses ◽  
Mean Velocity ◽  
Inlet Region ◽  
The Mean ◽  
Hot Film

Detailed measurements of mean velocity U profiles, in the inlet 70 diameters of a pipe, show that the development of turbulent pipe flow is nonasymptotic. Experiments were done at seven Reynolds numbers in the range 56 000–15 3000. Contours of U and V fields are presented for two representative Reynolds numbers. A U component peak exceeding the fully developed values has been found to occur along the pipe centerline. The Reynolds number behavior of the peak position has been determined. Hot film measurements of the mean wall shear stresses in the inlet region also show a nonasymptotic development consistent with the mean velocity results.

Evolution of a moderately short turbulent boundary layer in a severe pressure gradient

1974 ◽  
Vol 64 (4) ◽  
pp. 763-774 ◽  
Author(s):  
R. G. Deissler
Keyword(s):  
Boundary Layer ◽  
Shear Stress ◽  
Turbulent Boundary Layer ◽  
Pressure Gradient ◽  
Reynolds Shear Stress ◽  
Pressure Gradients ◽  
Mean Velocity ◽  
Mass Injection ◽  
The Mean ◽  
Theoretical Results

The early and intermediate development of a highly accelerated (or decelerated) turbulent boundary layer is analysed. For sufficiently large accelerations (or pressure gradients) and for total normal strains which are not excessive, the equation for the Reynolds shear stress simplifies to give a stress that remains approximately constant as it is convected along streamlines. The theoretical results for the evolution of the mean velocity in favourable and adverse pressure gradients agree well with experiment for the cases considered. A calculation which includes mass injection at the wall is also given.

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