Bubble Force Balance Formula for Low Reynolds Number Bubbly Flows in Pipes and Channels: Comparison of Wall Force Models

2017 ◽  
Vol 16 (4) ◽  
Author(s):  
O. Marfaing ◽  
J. Laviéville
Keyword(s):  
Reynolds Number ◽  
Void Fraction ◽  
Low Reynolds Number ◽  
Laminar Flows ◽  
Force Balance ◽  
Bubbly Flows ◽  
Force Model ◽  
Wall Region ◽  
Order Of Magnitude ◽  
Low Reynolds

Abstract In recent work, we investigated analytically low Reynolds number bubbly flows in pipes. We showed that the distribution of bubbles results from a balance between lift, dispersion and wall forces, and exhibited an analytical expression for this void fraction profile. We then performed a comparison of this analytical Bubble Force Balance Formula (BFBF) with an experiment from the literature. Antal’s model was used for the wall force. The objective of the present work is to compare and assess the three main wall force models in the literature: Antal’s, Tomiyama’s and Frank’s models. We begin by deriving two new BFBF, respectively with Tomiyama’s and Frank’s forces. We can see that the choice of the model impacts the velocity with which the analytical void fraction profile goes to zero at the wall. We then compare our three analytical profiles with experimental measurements and DNS simulations of laminar flows from the literature. We restrict ourselves to the near-wall region. The choice of Antal’s wall force model yields the best agreement. The data is also used to estimate the dispersion coefficient at the wall. Interestingly, we obtain the same order of magnitude with the three wall force models.

scholarly journals Low-Reynolds-number turbulent boundary layers

1991 ◽  
Vol 230 ◽  
pp. 1-44 ◽  
Author(s):  
Lincoln P. Erm ◽  
Peter N. Joubert
Keyword(s):  
Reynolds Number ◽  
Boundary Layers ◽  
Low Reynolds Number ◽  
Turbulent Boundary Layers ◽  
Stream Velocity ◽  
Wall Region ◽  
Mean Flow ◽  
Low Reynolds ◽  
High Reynolds ◽  
Turbulent Wall

An investigation was undertaken to improve our understanding of low-Reynolds-number turbulent boundary layers flowing over a smooth flat surface in nominally zero pressure gradients. In practice, such flows generally occur in close proximity to a tripping device and, though it was known that the flows are affected by the actual low value of the Reynolds number, it was realized that they may also be affected by the type of tripping device used and variations in free-stream velocity for a given device. Consequently, the experimental programme was devised to investigate systematically the effects of each of these three factors independently. Three different types of device were chosen: a wire, distributed grit and cylindrical pins. Mean-flow, broadband-turbulence and spectral measurements were taken, mostly for values of Rθ varying between about 715 and about 2810. It was found that the mean-flow and broadband-turbulence data showed variations with Rθ, as expected. Spectra were plotted using scaling given by Perry, Henbest & Chong (1986) and were compared with their models which were developed for high-Reynolds-number flows. For the turbulent wall region, spectra showed reasonably good agreement with their model. For the fully turbulent region, spectra did show some appreciable deviations from their model, owing to low-Reynolds-number effects. Mean-flow profiles, broadband-turbulence profiles and spectra were found to be affected very little by the type of device used for Rθ ≈ 1020 and above, indicating an absence of dependence on flow history for this Rθ range. These types of measurements were also compared at both Rθ ≈ 1020 and Rθ ≈ 2175 to see if they were dependent on how Rθ was formed (i.e. the combination of velocity and momentum thickness used to determine Rθ). There were noticeable differences for Rθ ≈ 1020, but these differences were only convincing for the pins, and there was a general overall improvement in agreement for Rθ ≈ 2175.

Approximate Analytical Model for Oil Film Force of Finite Length Squeeze Film Damper Under Low Reynolds Number

2013 ◽  
Author(s):  
Yongliang Wang ◽  
Yu Gao ◽  
Jingjun Zhong ◽  
Ling Yang ◽  
Huawei Lu
Keyword(s):  
Reynolds Number ◽  
Analytical Model ◽  
Finite Length ◽  
High Speed ◽  
Low Reynolds Number ◽  
Separation Of Variables ◽  
Squeeze Film ◽  
Force Model ◽  
Oil Film ◽  
Low Reynolds

Squeeze film dampers (SFDs) are widely used in aero-engines and other high speed rotating machines as damping elements, owing to their remarkable damping effect. The oil-film force model of SFDs is the key to investigate the dynamic characteristics of the rotor-bearing systems involving SFDs. In this paper, the analytical solution of the oil film pressure of a finite length SFD is obtained by employing the separation of variables method to solve the Reynolds equation (at low Reynolds number) based upon the dynamic π boundary condition. The analytical expression of the oil film force is then derived by applying the integral method. The oil film force from the analytical model is compared with the results from other well-known methods, i.e. the long bearing approximation, the short bearing approximation and the finite difference method. The results clearly show that within a wider length-diameter ratio range, the newly proposed model can accurately predict the oil film characteristics of the SFDs at low Reynolds numbers.

Methods to Set Up and Investigate Low Reynolds Number, Fully Developed Turbulent Plane Channel Flows

1998 ◽  
Vol 120 (3) ◽  
pp. 496-503 ◽  
Author(s):  
F. Durst ◽  
M. Fischer ◽  
J. Jovanovic´ ◽  
H. Kikura
Keyword(s):  
Reynolds Number ◽  
Initial Conditions ◽  
Control Volume ◽  
Low Reynolds Number ◽  
Plane Channel ◽  
Finite Size ◽  
Wall Region ◽  
Turbulent Plane ◽  
Low Reynolds ◽  
Near Wall

The tripping of fully developed turbulent plane channel flow was studied at low Reynolds number, yielding unique flow properties independent of the initial conditions. The LDA measuring technique was used to obtain reliable mean velocities, rms values of turbulent velocity fluctuations and skewness and flatness factors over the entire cross-section with emphasis on the near-wall region. The experimental results were compared with the data obtained from direct numerical simulations available in the literature. The analysis of the data indicates the important role of the upstream conditions on the flow development. It is shown that the fully developed turbulent state at low Reynolds number can be reached only by significant tripping of the flow at the inlet of the channel. Effects related to the finite size of the LDA measuring control volume and an inaccuracy in the estimation of the wall shear stress from near-wall velocity measurements are discussed in detail since these can yield systematic discrepancies between the measured and simulated results.

Prediction of Turbulent Source Flow Between Corotating Disks With an Anisotropic Two-Equation Turbulence Model

1988 ◽  
Vol 110 (2) ◽  
pp. 187-194 ◽  
Author(s):  
S. A. Shirazi ◽  
C. R. Truman
Keyword(s):  
Reynolds Number ◽  
Kinetic Energy ◽  
Turbulent Kinetic Energy ◽  
Turbulence Model ◽  
Ad Hoc ◽  
Low Reynolds Number ◽  
Wall Region ◽  
Mixing Length ◽  
Mean Flow ◽  
Low Reynolds

An anisotropic form of a low-Reynolds-number two-equation turbulence model has been implemented in a numerical solution for incompressible turbulent flow between corotating parallel disks. Transport equations for turbulent kinetic energy and dissipation rate were solved simultaneously with the governing equations for the mean-flow variables. Comparisons with earlier mixing-length predictions and with measurements are presented. Good agreement between the present predictions and the measurements of velocity components and turbulent kinetic energy was obtained. The low-Reynolds-number two-equation model was found to model adequately the near-wall region as well as the effects of rotation and streamline divergence, which required ad hoc assumptions in the mixing-length model.

Low-Reynolds-number effects in a fully developed turbulent channel flow

1992 ◽  
Vol 236 ◽  
pp. 579-605 ◽  
Author(s):  
R. A. Antonia ◽  
M. Teitel ◽  
J. Kim ◽  
L. W. B. Browne
Keyword(s):  
Reynolds Number ◽  
Channel Flow ◽  
Low Reynolds Number ◽  
Turbulent Channel Flow ◽  
Reynolds Numbers ◽  
Wall Region ◽  
Low Reynolds Numbers ◽  
Reynolds Number Effects ◽  
Low Reynolds ◽  
Inner Region

Low-Reynolds-number effects are observed in the inner region of a fully developed turbulent channel flow, using data obtained either from experiments or by direct numerical simulations. The Reynolds-number influence is observed on the turbulence intensities and to a lesser degree on the average production and dissipation of the turbulent energy. In the near-wall region, the data confirm Wei & Willmarth's (1989) conclusion that the Reynolds stresses do not scale on wall variables. One of the reasons proposed by these authors to account for this behaviour, namely the ‘geometry’ effect or direct interaction between inner regions on opposite walls, was investigated in some detail by introducing temperature at one of the walls, both in experiment and simulation. Although the extent of penetration of thermal excursions into the opposite side of the channel can be significant at low Reynolds numbers, the contribution these excursions make to the Reynolds shear stress and the spanwise vorticity in the opposite wall region is negligible. In the inner region, spectra and co-spectra of the velocity fluctuations u and v change rapidly with the Reynolds number, the variations being mainly confined to low wavenumbers in the u spectrum. These spectra, and the corresponding variances, are discussed in the context of the active/inactive motion concept and the possibility of increased vortex stretching at the wall. A comparison is made between the channel and the boundary layer at low Reynolds numbers.

Prediction of Heat Transfer in Turbulent Channel Flow With Spanwise Rotation and Suction/Blowing Through Opposite Walls

2009 ◽  
Author(s):  
B. A. Younis ◽  
B. Weigand ◽  
A. Laqua
Keyword(s):  
Heat Transfer ◽  
Reynolds Number ◽  
Low Reynolds Number ◽  
Heat Fluxes ◽  
Function Approach ◽  
Wall Region ◽  
Turbulent Heat ◽  
Reynolds Stresses ◽  
Wall Function ◽  
Low Reynolds

This paper is concerned with the prediction of heat transfer rates in fully-developed turbulent flows in straight channels with mass transfer by suction and blowing through opposite walls, and with rotation about the spanwise axis. The predictions are based on the solution of the Reynolds-averaged forms of the governing equations using a second-order accurate finite-volume formulation. The effects of turbulence on momentum transport were accounted for by using turbulence closures based on the solution of modeled differential transport equations for the Reynolds stresses. A number of alternative models were assessed. These included a high turbulence Reynolds-number model in which the computationally-efficient ‘wall-function’ approach was used to bridge the near-wall region. As the effects of stabilizing system rotation can cause flow relaminarization, the wall-function approach becomes unreliable and integration must be carried out through the viscous sub-layer, directly to the walls. The suitability of three alternative low Reynolds-number models was assessed in these flows. Experimental data from flows in stationary channels with Reynolds numbers spanning the range of laminar, transitional and turbulent regimes were also used in this assessment. Excellent predictions of the wall skin-friction coefficient across the entire range were obtained with a low Reynolds-number model in which the effects of a rigid wall on the fluctuating pressure field in its vicinity were accounted for by a method which incorporates the gradients of the turbulence length scale and the invariants of turbulence anisotropy. For the cases of heated flows, two very different models for the turbulent heat fluxes were examined: one involved the solution of a differential transport equation for each component of the heat-flux tensor and another in which the heat fluxes were obtained from an explicit algebraic model derived from tensor representation theory. It was found that the two models yielded results that were essentially similar and in close agreement with results from recent Direct Numerical Simulations.

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