Equilibrium Position of a Buoyant Drop in Couette and Poiseuille Flows at Finite Reynolds Numbers

2012 ◽  
Vol 29 (1) ◽  
pp. 53-58 ◽  
Author(s):  
M. Bayareh ◽  
S. Mortazavi
Keyword(s):  
Reynolds Number ◽  
Equilibrium Position ◽  
Stokes Equations ◽  
Flow Direction ◽  
Rotational Velocity ◽  
Density Ratio ◽  
Reynolds Numbers ◽  
Initial Position ◽  
Couette And Poiseuille Flows ◽  
Poiseuille Flows

AbstractThe equilibrium position of a deformable drop in Couette and Poiseuille flows is investigated numerically by solving the full Navier-Stokes equations using a finite difference/front tracking method. The objective of this work is to study the motion of a non-neutrally buoyant drop in Couette and Poiseuille flows with different density ratios at finite Reynolds numbers. Couette flow: The equilibrium position of the lighter drops is higher than the heavier drops at each particle Reynolds number. Also, the equilibrium position height increases with increasing the Reynolds number at a fixed density ratio. At this equilibrium distance from the wall, the migration velocity is zero, while the velocity of the drop in the flow direction and rotational velocity of the drop is finite. It is observed that the equilibrium position is independent of the initial position of the drops and depends on the density ratio and the shear Reynolds number. Poiseuille flow: When the drop is slightly buoyant, it moves to an equilibrium position between the wall and the centerline. The equilibrium position is close to the centerline if the drop lags the fluid but close to the wall if the drop leads the fluid. As the Reynolds number increases, the equilibrium position of lighter drops moves slightly closer to the wall and the equilibrium position of heavier drops moves towards the centerline.

Numerical Study of Droplet Behavior in Straight and L-Shaped Channels

2007 ◽  
Author(s):  
Chang-Wei Kang ◽  
Jinsong Hua ◽  
Jing Lou
Keyword(s):  
Reynolds Number ◽  
Equilibrium Position ◽  
Numerical Study ◽  
Density Ratio ◽  
Three Dimensional ◽  
Initial Position ◽  
Straight Channel ◽  
Front Tracking Method ◽  
Droplet Behavior ◽  
Two Parameters

Numerical simulations using three-dimensional front tracking method are conducted to study the effects of droplet properties on the transient motion, rotation and deformation of a droplet during its transit in straight and L-shaped rectangular channels. The properties under investigation for straight channel are the density ratio, viscosity ratio, Reynolds number, Weber number and droplet initial position. The latter two parameters are chosen for the study of L-shaped channel. The results show that in the straight channel, despite the droplet initial positions, the droplet with the same properties ends up at the same equilibrium position. However, when the Reynolds number increases, the droplet is heavier or less viscous or droplet becomes more deformable, the droplet equilibrium position is much closer to the wall. Also, heavier or less viscous droplet exhibits higher rotational speed, which is believed to enhance oscillatory motion. As for the L-shaped channel, it is found that the droplet deformability can help to avoid the droplet from impacting upon the channel wall.

scholarly journals Canonical wall-bounded flows: how do they differ?

2015 ◽  
Vol 774 ◽  
pp. 1-4 ◽  
Author(s):  
Alexander J. Smits
Keyword(s):  
Reynolds Number ◽  
Strong Support ◽  
Reynolds Numbers ◽  
Direct Numerical Simulations ◽  
Stress Distributions ◽  
Number Range ◽  
Parallel Component ◽  
New Information ◽  
Couette And Poiseuille Flows ◽  
Poiseuille Flows

Orlandi et al. (J. Fluid Mech., vol. 770, 2015, pp. 424–441) present direct numerical simulations over a very wide Reynolds number range for plane Couette and Poiseuille flows. The results reveal new information on the abrupt nature of transition in these flows, and the comparisons between Couette and Poiseuille flows help to provide a clearer picture of Reynolds number trends, especially with regard to inner/outer layer interactions. The stress distributions give strong support to Townsend’s attached eddy hypothesis, particularly for the wall-parallel component where there has been little experimental data available. The results pose some intriguing questions regarding the reconciliation of the present results with data at higher Reynolds numbers in different canonical flows.

scholarly journals Finite-amplitude steady waves in plane viscous shear flows

1985 ◽  
Vol 160 ◽  
pp. 281-295 ◽  
Author(s):  
F. A. Milinazzo ◽  
P. G. Saffman
Keyword(s):  
Boundary Layer ◽  
Reynolds Number ◽  
Stokes Equations ◽  
Reynolds Numbers ◽  
Finite Amplitude ◽  
Linear Instability ◽  
Navier Stokes ◽  
Unidirectional Flow ◽  
Viscous Shear ◽  
Finite Amplitude Waves

Computations of two-dimensional solutions of the Navier–Stokes equations are carried out for finite-amplitude waves on steady unidirectional flow. Several cases are considered. The numerical method employs pseudospectral techniques in the streamwise direction and finite differences on a stretched grid in the transverse direction, with matching to asymptotic solutions when unbounded. Earlier results for Poiseuille flow in a channel are re-obtained, except that attention is drawn to the dependence of the minimum Reynolds number on the physical constraint of constant flux or constant pressure gradient. Attempts to calculate waves in Couette flow by continuation in the velocity of a channel wall fail. The asymptotic suction boundary layer is shown to possess finite-amplitude waves at Reynolds numbers orders of magnitude less than the critical Reynolds number for linear instability. Waves in the Blasius boundary layer and unsteady Rayleigh profile are calculated by employing the artifice of adding a body force to cancel the spatial or temporal growth. The results are verified by comparison with perturbation analysis in the vicinity of the linear-instability critical Reynolds numbers.

Lid-Driven Square Cavity Flow: A Benchmark Solution with an 8192x8192 Grid

2021 ◽  
Author(s):  
Carlos Marchi ◽  
Cosmo D. Santiago ◽  
Carlos Alberto Rezende de Carvalho Junior
Keyword(s):  
Reynolds Number ◽  
Stokes Equations ◽  
Accurate Determination ◽  
Stable Solution ◽  
Reynolds Numbers ◽  
Accurate Solution ◽  
Discretization Error ◽  
Square Cavity ◽  
Solution Vector ◽  
Wide Range

Abstract The incompressible steady-state fluid flow inside a lid-driven square cavity was simulated using the mass conservation and Navier-Stokes equations. This system of equations is solved for Reynolds numbers of up to 10,000 to the accuracy of the computational machine round-off error. The computational model used was the second-order accurate finite volume method. A stable solution is obtained using the iterative multigrid methodology with 8192 × 8192 volumes, while degree-10 interpolation and Richardson extrapolation were used to reduce the discretization error. The solution vector comprised five entries of velocities, pressure, and location. For comparison purposes, 65 different variables of interest were chosen, such as velocity profile, its extremum values and location, extremum values and location of the stream function. The discretization error for each variable of interest was estimated using two types of estimators and their apparent order of accuracy. The variations of the 11 selected variables are shown across 38 Reynolds number values between 0.0001 and 10,000. In this study, we provide a more accurate determination of the Reynolds number value at which the upper secondary vortex appears. The results of this study were compared with those of several other studies in the literature. The current solution methodology was observed to produce the most accurate solution till date for a wide range of Reynolds numbers.

scholarly journals Nonlinear amplification in hydrodynamic turbulence

2021 ◽  
Vol 930 ◽  
Author(s):  
Kartik P. Iyer ◽  
Katepalli R. Sreenivasan ◽  
P.K. Yeung
Keyword(s):  
Reynolds Number ◽  
Isotropic Turbulence ◽  
Stokes Equations ◽  
Three Dimensional ◽  
Reynolds Numbers ◽  
Navier Stokes ◽  
Navier Stokes Equations ◽  
Developed Turbulence ◽  
Advection Term ◽  
Nonlinear Amplification

Using direct numerical simulations performed on periodic cubes of various sizes, the largest being $8192^3$ , we examine the nonlinear advection term in the Navier–Stokes equations generating fully developed turbulence. We find significant dissipation even in flow regions where nonlinearity is locally absent. With increasing Reynolds number, the Navier–Stokes dynamics amplifies the nonlinearity in a global sense. This nonlinear amplification with increasing Reynolds number renders the vortex stretching mechanism more intermittent, with the global suppression of nonlinearity, reported previously, restricted to low Reynolds numbers. In regions where vortex stretching is absent, the angle and the ratio between the convective vorticity and solenoidal advection in three-dimensional isotropic turbulence are statistically similar to those in the two-dimensional case, despite the fundamental differences between them.

Jet-to-Plate Distance Effect on Heat Transfer From a Flat Plate to an Impinging Jet at Various Reynolds Numbers

2012 ◽  
Author(s):  
Patricia Streufert ◽  
Terry X. Yan ◽  
Mahdi G. Baygloo
Keyword(s):  
Heat Transfer ◽  
Experimental Data ◽  
Reynolds Number ◽  
Flat Plate ◽  
Numerical Solutions ◽  
Stokes Equations ◽  
Local Heat Transfer ◽  
Reynolds Numbers ◽  
Air Jet ◽  
Plate Distance

Local turbulent convective heat transfer from a flat plate to a circular impinging air jet is numerically investigated. The jet-to-plate distance (L/D) effect on local heat transfer is the main focus of this study. The eddy viscosity V2F turbulence model is used with a nonuniform structured mesh. Reynolds-Averaged Navier-Stokes equations (RANS) and the energy equation are solved for axisymmetric, three-dimensional flow. The numerical solutions obtained are compared with published experimental data. Four jet-to-plate distances, (L/D = 2, 4, 6 and 10) and seven Reynolds numbers (Re = 7,000, 15,000, 23,000, 50,000, 70,000, 100,000 and 120,000) were parametrically studied. Local and average heat transfer results are analyzed and correlated with Reynolds number and the jet-to-plate distance. Results show that the numerical solutions matched experimental data best at low jet-to-plate distances and lower Reynolds numbers, decreasing in ability to accurately predict the heat transfer as jet-to-plate distance and Reynolds number was increased.

scholarly journals Entrance Effects on Diffused Film-Cooling Holes

1998 ◽  
Author(s):  
A. Kohli ◽  
K. A. Thole
Keyword(s):  
Reynolds Number ◽  
Film Cooling ◽  
Gas Turbines ◽  
High Performance ◽  
Computational Study ◽  
Density Ratio ◽  
Reynolds Numbers ◽  
Supply Channel ◽  
Cooling Hole ◽  
Film Cooling Holes

Film-cooling is a widely used method of prolonging blade life in high performance gas turbines and is implemented by injecting cold air through discrete holes on the blade surface. Most experimental research on film-cooling has been performed using round holes supplied by a stagnant plenum. This can be quite different from the actual turbine blade conditions in that a crossflow may be present whereby the internal channel Reynolds number could be as high as 90,000. This computational study uses a film-cooling hole that is inclined at 35° with respect to the mainstream and is diffused at the hole exit by 15°. An engine representative jet-to-mainstream density ratio of two was simulated. The test matrix consisted of fourteen different cases that were simulated for the two different blowing ratios in which the following effects were investigated: a) the effect of the orientation of the coolant supply channel relative to the cooling hole, b) the effect of the channel Reynolds number, and c) the effect of the metering length of the cooling hole. Results showed that the orientation of the coolant supply had a large effect whereby the worst orientation, in terms of a reduced adiabatic effectiveness, was predicted when the channel supplying the cooling hole was perpendicular to the mainstream. For this particular orientation, higher laterally averaged effectiveness occurred at lower channel Reynolds numbers and with the hole having a short metering length.

Prediction of Reynolds Number Effects on Low-Pressure Turbines Using a High-Order ILES Method

2019 ◽  
Author(s):  
Marc Bolinches-Gisbert ◽  
David Cadrecha Robles ◽  
Roque Corral ◽  
Fernando Gisbert
Keyword(s):  
Boundary Layer ◽  
Reynolds Number ◽  
Fourth Order ◽  
Stokes Equations ◽  
Reynolds Numbers ◽  
Low Pressure ◽  
High Order ◽  
Experimental Results ◽  
Numerical Code ◽  
Design System

Abstract A comprehensive comparison between Implicit Large Eddy Simulations (ILES) and experimental results of a modern highlift low-pressure turbine airfoil has been carried out for an array of Reynolds numbers (Re). Experimental data were obtained in a low-speed linear cascade at the Polithecnic University of Madrid using hot-wire anemometry and LDV. The numerical code is fourth order accurate, both in time and space. The spatial discretization of the compressible Navier-Stokes equations is based on a high-order Flux Reconstruction approach while a fourth order Runge-Kutta method is used to march in time the simulations. The losses, pressure coefficient distributions, and boundary layer and wake velocity profiles have been compared for an array of realistic Reynolds numbers. Moreover, boundary layer and wake velocity fluctuations are compared for the first time with experimental results. It is concluded that the accuracy of the numerical results is comparable to that of the experiments, especially for integral quantities such as the losses or exit angle. Turbulent fluctuations in the suction side boundary layer and the wakes are well predicted also. The elapsed time of the is about 140 hours on 40 Graphics Processor Units. The numerical tool is integrated within an industrial design system and reuses pre- and post-processing tools previously developed for another kind of applications. The trend of the losses with the Reynolds number has a sub-critical regime, where the losses scale with Re−1, and a supercrital regime, where the losses scale with Re−1/2. This trend can be seen both, in the simulations and the experiments.

Unsteady flow past a rotating circular cylinder at Reynolds numbers 103 and 104

1990 ◽  
Vol 220 ◽  
pp. 459-484 ◽  
Author(s):  
H. M. Badr ◽  
M. Coutanceau ◽  
S. C. R. Dennis ◽  
C. Ménard
Keyword(s):  
Reynolds Number ◽  
Circular Cylinder ◽  
Unsteady Flow ◽  
Rotation Rate ◽  
Stokes Equations ◽  
Reynolds Numbers ◽  
Navier Stokes ◽  
Navier Stokes Equations ◽  
Number Range ◽  
Flow Past

The unsteady flow past a circular cylinder which starts translating and rotating impulsively from rest in a viscous fluid is investigated both theoretically and experimentally in the Reynolds number range 103 [les ] R [les ] 104 and for rotational to translational surface speed ratios between 0.5 and 3. The theoretical study is based on numerical solutions of the two-dimensional unsteady Navier–Stokes equations while the experimental investigation is based on visualization of the flow using very fine suspended particles. The object of the study is to examine the effect of increase of rotation on the flow structure. There is excellent agreement between the numerical and experimental results for all speed ratios considered, except in the case of the highest rotation rate. Here three-dimensional effects become more pronounced in the experiments and the laminar flow breaks down, while the calculated flow starts to approach a steady state. For lower rotation rates a periodic structure of vortex evolution and shedding develops in the calculations which is repeated exactly as time advances. Another feature of the calculations is the discrepancy in the lift and drag forces at high Reynolds numbers resulting from solving the boundary-layer limit of the equations of motion rather than the full Navier–Stokes equations. Typical results are given for selected values of the Reynolds number and rotation rate.

Analytical and numerical studies of the structure of steady separated flows

1966 ◽  
Vol 24 (1) ◽  
pp. 113-151 ◽  
Author(s):  
Odus R. Burggraf
Keyword(s):  
Reynolds Number ◽  
Numerical Solutions ◽  
Stokes Equations ◽  
Low Reynolds Number ◽  
Reynolds Numbers ◽  
Total Power ◽  
Large Reynolds Number ◽  
Boundary Velocity ◽  
Displacement Thickness ◽  
Low Reynolds

The viscous structure of a separated eddy is investigated for two cases of simplified geometry. In § 1, an analytical solution, based on a linearized model, is obtained for an eddy bounded by a circular streamline. This solution reveals the flow development from a completely viscous eddy at low Reynolds number to an inviscid rotational core at high Reynolds number, in the manner envisaged by Batchelor. Quantitatively, the solution shows that a significant inviscid core exists for a Reynolds number greater than 100. At low Reynolds number the vortex centre shifts in the direction of the boundary velocity until the inviscid core develops; at large Reynolds number, the inviscid vortex core is symmetric about the centre of the circle, except for the effect of the boundary-layer displacement-thickness. Special results are obtained for velocity profiles, skin-friction distribution, and total power dissipation in the eddy. In addition, results of the method of inner and outer expansions are compared with the complete solution, indicating that expansions of this type give valid results for separated eddies at Reynolds numbers greater than about 25 to 50. The validity of the linear analysis as a description of separated eddies is confirmed to a surprising degree by numerical solutions of the full Navier–Stokes equations for an eddy in a square cavity driven by a moving boundary at the top. These solutions were carried out by a relaxation procedure on a high-speed digital computer, and are described in § 2. Results are presented for Reynolds numbers from 0 to 400 in the form of contour plots of stream function, vorticity, and total pressure. At the higher values of Reynolds number, an inviscid core develops, but secondary eddies are present in the bottom corners of the square at all Reynolds numbers. Solutions of the energy equation were obtained also, and isotherms and wall heat-flux distributions are presented graphically.

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