Turbulent Flow in a Tube With Wall Suction

1971 ◽  
Vol 93 (2) ◽  
pp. 242-244 ◽  
Author(s):  
L. Merkine ◽  
A. Solan ◽  
Y. Winograd
Keyword(s):  
Turbulent Flow ◽  
Damping Factor ◽  
Tube Flow ◽  
Turbulence Level ◽  
Mixing Length ◽  
Excellent Correlation ◽  
Extended Form ◽  
Wall Suction ◽  
Method Of Solution

The effect of wall suction on turbulent flow in a tube is analyzed, using a mixing-length model with an extended form of van Driest’s damping factor. It is shown that an empirical damping factor similar to that proposed by Kays, Moffat, and Thielbahr, when incorporated in a method of solution developed by Kinney and Sparrow, predicts that the turbulence level in tube flow decreases with suction, and yields excellent correlation with the experiments of Weissberg and Berman.

Experimental Study of Turbulent Flow in a Tube With Wall Suction

1974 ◽  
Vol 96 (3) ◽  
pp. 338-342 ◽  
Author(s):  
A. Brosh ◽  
Y. Winograd
Keyword(s):  
Reynolds Number ◽  
Turbulent Flow ◽  
Turbulent Velocity ◽  
Turbulence Level ◽  
Mixing Length ◽  
Local Flow ◽  
Wall Suction ◽  
Velocity Fluctuations ◽  
Flow Equilibrium ◽  
Continuous Suction

The effect of wall suction on the turbulent flow of air in a porous tube has been studied. Measurements of the radial distribution of the turbulent velocity fluctuations were obtained over a range of Reynolds numbers from 104 to 2 × 105. Various suction rates were employed, for both local suction over a short length of tube and continuous suction over various lengths. The results obtained for local suction (step reduction in Reynolds number) show that approximately 40 dia are required for the turbulent velocity fluctuations to reach flow equilibrium at the lower downstream value of the Reynolds number. The results for the case of continuous suction show that after a short suction length, there is an apparent increase in the turbulence level compared with that found at the same Reynolds number with no suction. This appears to be due to the greater turbulence level which exists at the higher (presuction) Reynolds number. Longer suction lengths, above 40 dia, always result in a decrease in the turbulence level compared with turbulent flow with no suction at the same Reynolds number. The present results suggest that simple mixing-length models, incorporating local flow parameters, may be inadequate to describe the turbulent momentum transport in a tube with surface suction. Certainly, the existing mixing-length models should be re-examined in the light of this new experimental data.

scholarly journals E–ε Model of Spray-Laden Near-Sea Atmospheric Layer in High Wind Conditions

2014 ◽  
Vol 44 (2) ◽  
pp. 742-763 ◽  
Author(s):  
Yevgenii Rastigejev ◽  
Sergey A. Suslov
Keyword(s):  
Turbulent Flow ◽  
Drag Coefficient ◽  
Turbulent Mixing ◽  
Numerical Solutions ◽  
Turbulent Energy ◽  
Wave Crest ◽  
Mixing Length ◽  
High Wind ◽  
Close Proximity ◽  
Ocean Spray

Abstract In-depth understanding and accurate modeling of the interaction between ocean spray and a turbulent flow under high wind conditions is essential for improving the intensity forecasts of hurricanes and severe storms. Here, the authors consider the E–ε closure for a turbulent flow model that accounts for the effects of the variation of turbulent energy and turbulent mixing length caused by spray stratification. The obtained analytical and numerical solutions show significant differences between the current E–ε model and the lower-order turbulent kinetic energy (TKE) model considered previously. It is shown that the reduction of turbulent energy and mixing length above the wave crest level, where the spray droplets are generated, that is not accounted for by the TKE model results in a significant suppression of turbulent mixing in this near-wave layer. In turn, suppression of turbulence causes an acceleration of flow and a reduction of the drag coefficient that is qualitatively consistent with field observations if spray is fine (even if its concentration is low) or if droplets are large but their concentration is sufficiently high. In the latter case, spray inertia may become important. This effect is subsequently examined. It is shown that spray inertia leads to the reduction of wind velocity in the close proximity of the wave surface relative to the reference logarithmic profile. However, at higher altitudes the suppression of flow turbulence by the spray still results in the wind acceleration and the reduction of the local drag coefficient.

scholarly journals A Case Study of Clear-Air Turbulence at Upper Levels

2021 ◽  
Author(s):  
Léo Rogel ◽  
Didier Ricard ◽  
Eric Bazile ◽  
Irina Sandu
Keyword(s):  
Turbulent Flow ◽  
Partial Information ◽  
Weather Prediction ◽  
Turbulent Fluxes ◽  
Small Scale ◽  
Mixing Length ◽  
Vertical Resolution ◽  
Stable Conditions ◽  
Study Results

<p>Because of the technical difficulties of achieving measurements at high altitudes, it is not clear how well turbulent phenomena are represented in the upper levels of current Numerical Weather Prediction (NWP) operational models.<br>Indeed, turbulence in strongly stable conditions near the tropopause is known to be particularly difficult to correctly parameterize. The constraining buoyancy forces on the vertical lead to anisotropic turbulence, potentially inhibiting turbulent production in NWP models.<br>Partial information for high altitude turbulence events is nonetheless available in the form of in-situ measurements from aircrafts. However, it only allows for qualitative comparisons with model outputs.<br>This study focuses on a turbulent episode induced by a winter upper-level jet above east Belgium on January 27, 2018, for which in-situ EDR (Eddy Dissipation Rate) reports indicate moderate-or-greater turbulence levels. Numerical simulations are performed with the Météo-France operational model AROME, and with the mesoscale research model MesoNH (Laero/CNRM), at the same horizontal grid resolution (1.3km). These two models also use the eddy-diffusivity turbulence scheme of Cuxart et al (2000), a 1.5 order closure scheme based on a prognostic Turbulent Kinetic Energy (TKE) evolution equation, with a diagnostic computation of the mixing length.<br>TKE budgets, as well as stability indices and gradient-based quantities (Richardson number, vertical wind shear) are computed from the model outputs, and qualitative comparison with in-situ data is presented. Time evolution of the turbulent event over Belgium is well captured by both models, agreeing with EDR data.<br>Several sensitivity tests on the vertical resolution, on the mixing length formulation and on the parameters of the TKE equation are then performed. Most notably, the use of an increased vertical resolution near the tropopause greatly enhances the turbulent fluxes in both operational and research models. Secondly, comparison of various expressions of the mixing length shows that the Bougeault and Lacarrere (1989) formulation produces the higher amount of subgrid TKE and turbulent mixing. A decreased turbulent dissipation parameter also significantly increases the amount of subgrid TKE. On the contrary, the use of a 3D turbulence scheme appears to have very limited impacts on the turbulent flow at this kilometer-scale horizontal resolution.<br>On a second part of this study, results from ongoing Large Eddy Simulations (LES) will be presented. These simulations aim at representing small-scale features of the turbulent flow. They will be used as a reference for the computation of turbulent fluxes at kilometer-scale resolution using a coarse-graining method, allowing for a comparison with the parameterized fluxes from the turbulence scheme. In particular, the dissipation term of the TKE equation will be examined. These results are expected to give insight on the leading turbulent mechanisms for which the current turbulence parameterization can be improved in stable conditions.</p>

Roughness Influence on Turbulent Flow Through Annular Seals

1994 ◽  
Vol 116 (2) ◽  
pp. 321-328 ◽  
Author(s):  
Victor Lucas ◽  
Sterian Danaila ◽  
Olivier Bonneau ◽  
Jean Freˆne
Keyword(s):  
Surface Roughness ◽  
Shear Stress ◽  
Wall Shear Stress ◽  
Turbulent Flow ◽  
Dynamic Characteristics ◽  
Reynolds Equation ◽  
Mixing Length ◽  
Local Shear ◽  
Wall Shear ◽  
Local Shear Stress

This paper deals with an analysis of turbulent flow in annular seals with rough surfaces. In this approach, our objectives are to develop a model of turbulence including surface roughness and to quantify the influence of surface roughness on turbulent flow. In this paper, in order to simplify the analysis, the inertial effects are neglected. These effects will be taken into account in a subsequent work. Consequently, this study is based on the solution of Reynolds equation. Turbulent flow is solved using Prandtl’s turbulent model with Van Driest’s mixing length expression. In Van Driest’s model, the mixing length depends on wall shear stress. However there are many numerical problems in evaluating this wall shear stress. Therefore, the goal of this work has been to use the local shear stress in the Van Driest’s model. This derived from the work of Elrod and Ng concerning Reichardt’s mixing length. The mixing length expression is then modified to introduce roughness effects. Then, the momentum equations are solved to evaluate the circumferential and axial velocity distributions as well as the turbulent viscosity μ1 (Boussinesq’s hypothesis) within the film. The coefficients of turbulence kx and kz, occurring in the generalized Reynolds’ equation, are then calculated as functions of the flow parameters. Reynolds’ equation is solved by using a finite centered difference method. Dynamic characteristics are calculated by exciting the system numerically, with displacement and velocity perturbations. The model of Van Driest using local shear stress and function of roughness has been compared (for smooth seals) to the Elrod and Ng theory. Some numerical results of the static and dynamic characteristics of a rough seal (with the same roughness on the rotor as on the stator) are presented. These results show the influence of roughness on the dynamic behavior of the shaft.

A mixing length model for turbulent flow in constant cross section ducts

1977 ◽  
Vol 10 (2) ◽  
pp. 125-129 ◽  
Author(s):  
R. P. Hornby ◽  
J. Mistry ◽  
H. Barrow
Keyword(s):  
Turbulent Flow ◽  
Cross Section ◽  
Constant Cross Section ◽  
Mixing Length

scholarly journals STUDY OF THE BEHAVIOURS OF SINGLE-PHASE TURBULENT FLOW AT LOW TO MODERATE REYNOLDS NUMBERS THROUGH A VERTICAL PIPE. PART I: 2D COUNTERS ANALYSIS

2020 ◽  
pp. 108-122
Author(s):  
Akeel M. Ali Morad ◽  
Rafi M. Qasim ◽  
Amjed Ahmed Ali
Keyword(s):  
Reynolds Number ◽  
Laminar Flow ◽  
Turbulent Flow ◽  
Single Phase ◽  
Static Pressure ◽  
Fluid Velocity ◽  
Mixing Length ◽  
Shearing Force ◽  
Vertical Pipe ◽  
Moderate Reynolds Number

This study presents a model to investigate the behavior of the single-phase turbulent flow at low to moderate Reynolds number of water through the vertical pipe through (2D) contour analysis. The model constructed based on governing equations of an incompressible Reynolds Average Navier-Stokes (RANS) model with (k-ε) method to observe the parametric determinations such as velocity profile, static pressure profile, turbulent kinetic energy consumption, and turbulence shear wall flows. The water is used with three velocities values obtained of (0.087, 0.105, and 0.123 m/s) to represent turbulent flow under low to moderate Reynolds number of the pipe geometry of (1 m) length with a (50.8 mm) inner diameter. The water motion behavior inside the pipe shows by using [COMSOL Multiphysics 5.4 and FLUENT 16.1] Software. It is concluded that the single-phase laminar flow of a low velocity, but obtained a higher shearing force; while the turbulent flow of higher fluid velocity but obtained the rate of dissipation of shearing force is lower than that for laminar flow. The entrance mixing length is affected directly with pattern of fluid flow. At any increasing in fluid velocity, the entrance mixing length is increase too, due to of fluid kinetic viscosity changes. The results presented the trends of parametric determinations variation through the (2D) counters analysis of the numerical model. When fluid velocity increased, the shearing force affected directly on the layer near-wall pipe. This leads to static pressure decreases with an increase in fluid velocities. While the momentum changed could be played interaction rules between the fluid layers near the wall pipe with inner pipe wall. Finally, the agreement between present results with the previous study of [1] is satisfied with the trend

scholarly journals Closed Form Solution of Plane-Parallel Turbulent Flow Along an Unbounded Plane Surface

2021 ◽  
Author(s):  
Bohua Sun
Keyword(s):  
Energy Dissipation ◽  
Turbulent Flow ◽  
Closed Form ◽  
Scaling Law ◽  
Closed Form Solution ◽  
Form Solution ◽  
Analytic Description ◽  
Mixing Length ◽  
Mean Velocity ◽  
Mixing Length Theory

In this letter, a century-old problem is studied; namely, to find a unified analytic description of the non-uniform distribution of mean velocity across the entire domain of turbulent flow for all Reynolds numbers within the framework of the Prandtl mixing length theory. Considering the Prandtl mixing length model, a closed form solution of the mean velocity profile of plane turbulent flow is obtained. The profiles of several useful quantities are given, such as turbulent viscosity, Reynolds turbulent stress, Kolmogorov's scaling law, and energy dissipation density. It is shown that the energy dissipation density at the surface is finite, whereas Landau's energy dissipation density is infinite. The closed form solution reveals that the universality of the turbulent velocity logarithmic profile no longer holds, but the von K\'arm\'an constant is still universal. The closed form solution is validated by both direct numerical simulation and experiments. The studies confirm that the van Driest mixing length theory is suitable for smooth walls, and the Prandtl mixing length theory is suitable for rough walls. Furthermore, a new formulation of the resistance coefficient of turbulent flow in pipes is given in implicit form.

An Alternative Approach for Teaching Turbulent Flow

2007 ◽  
Author(s):  
Ahmad Fakheri
Keyword(s):  
Turbulent Flow ◽  
Pipe Flow ◽  
Numerical Solutions ◽  
Experimental Results ◽  
Mixing Length ◽  
Law Of The Wall ◽  
Alternative Approach ◽  
Logarithmic Law ◽  
Basic Concepts ◽  
Moody Diagram

Teaching of turbulence in undergraduate and early graduate level fluid mechanics and heat transfer courses is a difficult undertaking. The approach taken in typical texts requires the students to accept a number of basic concepts without much quantitative justifications. This paper presents an alternative approach, one in which most of the salient features of the turbulent flow are derived by using numerical solutions and experimental results, as opposed to simply having them presented. In this approach, Prandtl’s mixing length model is used to obtain the velocity distribution for fully developed pipe flow. By comparing the numerical calculations with the experimental results, students determine the value of κ that best fits the experimental data on their own. In addition, deficiency of the mixing length in the transition region is shown. It is also shown that other models like Van Driest’s do a better job. The Logarithmic Law of the wall as well as 7th power law are also proven. The different models are used to determine the friction factor for pipe flow and the results are compared with the values obtained from the Moody diagram.

An Expression of Reynolds Stresses in Turbulent Lubrication Theory

1992 ◽  
Vol 114 (1) ◽  
pp. 57-60 ◽  
Author(s):  
A. K. Tieu ◽  
P. B. Kosasih
Keyword(s):  
Reynolds Number ◽  
Shear Stress ◽  
Turbulent Flow ◽  
Low Reynolds Number ◽  
Stress Gradient ◽  
Lubrication Theory ◽  
Mixing Length ◽  
Reynolds Stresses ◽  
Shear Stress Gradient ◽  
Low Reynolds

This paper proposes an alternative model of Reynolds stresses for turbulent lubrication theory. The approach relies on Prandtl’s mixing length theory which is based on a modified Van Driest mixing formula [1]. However, unlike the previous theories [2, 3] the proposed equation is capable of accounting for the effect of shear stress gradient on the mixing length. Thus it is well suited to turbulent flow analysis in bearings where the presence of shear stress gradient due to the effect of pressure gradient should be considered. A series of velocity measurements in thin channels in the low Reynolds number turbulent flow range are analysed using the theory. The data analysis shows a strong effect of shear stress gradient on the viscous sublayer in the low Reynolds number regime. As a result, a new model of mixing length applicable to the turbulent lubrication analysis in thin film at low or high Reynolds numbers or under low or high shear stress gradient is presented.

scholarly journals Experimental Study on Aerodynamic Characteristics of a Gurney Flap on a Wind Turbine Airfoil under High Turbulent Flow Condition

2020 ◽  
Vol 10 (20) ◽  
pp. 7258 ◽  
Author(s):  
Junwei Yang ◽  
Hua Yang ◽  
Weijun Zhu ◽  
Nailu Li ◽  
Yiping Yuan
Keyword(s):  
Wind Tunnel ◽  
Turbulent Flow ◽  
Lift Coefficient ◽  
Leading Edge ◽  
Aerodynamic Characteristics ◽  
Chord Length ◽  
Turbulence Level ◽  
Gurney Flaps ◽  
Gurney Flap ◽  
Delay Phenomenon

The objective of the current work is to experimentally investigate the effect of turbulent flow on an airfoil with a Gurney flap. The wind tunnel experiments were performed for the DTU-LN221 airfoil under different turbulence level (T.I. of 0.2%, 10.5% and 19.0%) and various flap configurations. The height of the Gurney flaps varies from 1% to 2% of the chord length; the thickness of the Gurney flaps varies from 0.25% to 0.75% of the chord length. The Gurney flap was vertical fixed on the pressure side of the airfoil at nearly 100% measured from the leading edge. By replacing the turbulence grille in the wind tunnel, measured data indicated a stall delay phenomenon while increasing the inflow turbulence level. By further changing the height and the thickness of the Gurney flap, it was found that the height of the Gurney flap is a very important parameter whereas the thickness parameter has little influence. Besides, velocity in the near wake zone was measured by hot-wire anemometry, showing the mechanisms of lift enhancement. The results demonstrate that under low turbulent inflow condition, the maximum lift coefficient of the airfoil with flaps increased by 8.47% to 13.50% (i.e., thickness of 0.75%), and the Gurney flap became less effective after stall angle. The Gurney flap with different heights increased the lift-to-drag ratio from 2.74% to 14.35% under 10.5% of turbulence intensity (i.e., thickness of 0.75%). However, under much a larger turbulence environment (19.0%), the benefit to the aerodynamic performance was negligible.

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