Numerical Modeling of Unsteady, Separated Viscous Flow

1977 ◽  
Vol 99 (4) ◽  
pp. 657-665 ◽  
Author(s):  
A. R. Giaquinta
Keyword(s):  
Numerical Solutions ◽  
Finite Difference Methods ◽  
Fluid Motion ◽  
Reynolds Numbers ◽  
Main Flow ◽  
Sudden Expansion ◽  
Spatial Diffusion ◽  
Transient Phase ◽  
Transient Solution ◽  
Steady State Condition

Numerical solutions of the equations governing the laminar flow of an incompressible fluid through a two-dimensional sudden expansion are discussed. The fluid motion is started impulsively from rest and is examined in detail during the transient phase to the steady-state condition. Solutions are obtained by two independent finite-difference methods which are discussed. The development of the flow in the zone of separation is investigated, and, during the earliest phases of motion, the generation of vorticity at the solid boundaries and its spatial diffusion is studied in the region of uniform flow. The numerical treatment of the boundary conditions is discussed. Characteristics of the transient solution for two different Reynolds numbers in the laminar range are presented. Included with the results is the temporal development of the streamline dividing the zone of separation from the main flow.

Low Reynolds number flow over a plane symmetric sudden expansion

1974 ◽  
Vol 64 (1) ◽  
pp. 111-128 ◽  
Author(s):  
F. Durst ◽  
A. Melling ◽  
J. H. Whitelaw
Keyword(s):  
Reynolds Number ◽  
Fluid Motion ◽  
Three Dimensional ◽  
Reynolds Numbers ◽  
Velocity Profiles ◽  
Sudden Expansion ◽  
Main Stream ◽  
Plane Symmetric ◽  
Dimensional Effects ◽  
Separation Zones

Flow visualization and laser-anemometry measurements are reported in the flow downstream of a plane 3: 1 symmetric expansion in a duct with an aspect ratio of 9·2: 1 downstream of the expansion. The flow was found to be markedly dependent on Reynolds number, and strongly three-dimensional even well away from the channel corners except at the lowest measurable velocities. The measurements at a Reynolds number of 56 indicated that the separation regions behind each step were of equal length. Symmetric velocity profiles existed from the expansion to a fully developed, parabolic profile far downstream, although there were substantial three-dimensional effects in the vicinity of the separation regions. The velocity profiles were in good agreement with those obtained by solving the two-dimensional momentum equation. At a Reynolds number of 114, the two separation regions were of different lengths, leading to asymmetric velocity profiles; three dimensional effects were much more pronounced. At a Reynolds number of 252, a third separation zone was found on one wall, downstream of the smaller of the two separation zones adjacent to the steps. As at the lower Reynolds numbers, the flow was very stable. At higher Reynolds numbers the flow became less stable and periodicity became increasingly important in the main stream; this was accompanied by a highly disturbed fluid motion in the separation zones, as the flow tended towards turbulence.

New Algorithm for the Lid-driven Cavity Flow Problem with Boussinesq-Stokes Suspension

2018 ◽  
pp. 462-472 ◽  
Keyword(s):  
Numerical Solutions ◽  
Suspended Particle ◽  
Finite Difference Methods ◽  
Reynolds Numbers ◽  
Driven Cavity ◽  
Time Stepping ◽  
Differential Transform ◽  
High Reynolds ◽  
Newtonian Liquids ◽  
Limiting Case

In the present investigation, a streamfunction-vorticity form for Boussinesq-Stokes liquids (with suspended particles) is suitably used to examine the problem of 2-D unsteady incompressible flow in a square cavity with moving top and bottom wall. A new algorithm is used for this form in order to compute the numerical solutions for high Reynolds numbers up to Re=2500. This algorithm is conducted as a combination of the multi-time-stepping temporal differential transform and the spatial finite difference methods. Convergence of the time-series solution is ensured by multi-time-stepping method. The classical benchmark results of the Newtonian liquid are recovered as a limiting case and the decelerating influence of the suspended particle on the Newtonian liquids’ flow field is clearly elaborated.

Laminar Flow of a Nonlinear Viscoplastic Fluid Through an Axisymmetric Sudden Expansion

1999 ◽  
Vol 121 (2) ◽  
pp. 488-495 ◽  
Author(s):  
Khaled J. Hammad ◽  
M. Volkan O¨tu¨gen ◽  
George C. Vradis ◽  
Engin B. Arik
Keyword(s):  
Laminar Flow ◽  
Numerical Solutions ◽  
Computational Study ◽  
Reynolds Numbers ◽  
Experimental Results ◽  
Viscoplastic Fluid ◽  
Sudden Expansion ◽  
Test Fluid ◽  
Flow Zone ◽  
Recirculating Flow

A combined experimental and computational study was carried out to investigate the laminar flow of a nonlinear viscoplastic fluid through an axisymmetric sudden expansion. The yield-stress, power-law index, and the consistency index of the yield shear-thinning test fluid were 0.733 Pa, 0.68, and 0.33 Pa · s0.68, respectively, resulting in a Hedstrom number of 1.65. The Reynolds number ranged between 1.8 and 58.7. In addition, the flow of a Newtonian fluid through the same expansion was also studied to form a baseline for comparison. Velocity vectors were obtained on the vertical center plane using a digital particle image velocimeter (PIV). From these measurements. two-dimensional distributions of axial and radial velocity as well as the stream function were calculated covering the separated, reattached and redeveloping flow regions. These results were compared to finite difference numerical solutions of the governing continuity and fully-elliptic momentum equations. The calculations were found to be in good agreement with the experimental results. Both computational and experimental results indicate the existence of two distinct flow regimes. For low Reynolds numbers, a region of nonmoving fluid is observed immediately downstream of the step and no separated flow zone exists. For the higher Reynolds numbers, a recirculating flow zone forms downstream of the expansion step, which is followed by a zone of stagnant fluid adjacent to pipe wall characterizing reattachment.

Experimental and Numerical Modeling of Viscous Fluid Flow in Bifurcated Long Pipes for Oil Transport

2020 ◽  
Author(s):  
Victorita Radulescu
Keyword(s):  
Numerical Modeling ◽  
Fluid Flow ◽  
Numerical Solutions ◽  
Fluid Motion ◽  
Reynolds Numbers ◽  
Navier Stokes ◽  
Local Pressure ◽  
Pressure Losses ◽  
Main Pipe ◽  
Experimental And Numerical Modeling

Abstract The present paper presents some experimental and numerical modeling of the Newtonian and viscoelastic flows in bifurcated configurations of pipes, for stationary and non-permanent regimes. The main purpose of this study is to select an optimal design of the pipes ramifications, for minimizing the local pressure losses and to improve the efficiency of fluid transportation. The method is based on the transformation of the flow field obtained with particle image visualization technique, for different Reynolds numbers. Based on experimental results will be established optimum geometry of the ramifications. The results will be used as the boundary conditions for numerical modeling. The experimental measurements were performed into a closed circuit of pipes, with different diameters, consisting of a centrifugal pump supplied by a tank, sensors for estimating the pressure losses and devices for measuring the flow rate. It is detailed presented in a dedicated paragraph. The main pipe is connected to a transparent bifurcation with branches at different angles from the main pipe axis. The measurements illustrate that the flow has different aspects, depending on the bifurcation’s angle. The numerical simulations are performed with Fluent CFD based on the volume numerical method, to obtain the Navier-Stokes solutions for the Newtonian model in the laminar or turbulent flow conditions. A pre-processor has been used to create the geometry of the bifurcation and to generate the mesh. The 3D-flow domain contains 944390 volumes, tetrahedral hybrid. It was obtained the numerical solutions of the fluid flow in branching pipes for the Reynolds numbers from 1000 up to 40000. The governing equations were assumed from the k-ε model for turbulence flow, the equation of continuity, equation of fluid motion, and the transport equation. Finally, some conclusions and references are presented.

Laminar Flow of a Herschel-Bulkley Fluid Over an Axisymmetric Sudden Expansion

2001 ◽  
Vol 123 (3) ◽  
pp. 588-594 ◽  
Author(s):  
Khaled J. Hammad ◽  
George C. Vradis ◽  
M. Volkan O¨tu¨gen
Keyword(s):  
Laminar Flow ◽  
Flow Regime ◽  
Power Law ◽  
Numerical Solutions ◽  
Flow Region ◽  
Reynolds Numbers ◽  
Sudden Expansion ◽  
High Yield ◽  
Recirculating Flow ◽  
Power Law Index

The steady flow of non-Newtonian Herschel-Bulkley fluids over a one-to-two axisymmetric sudden expansion was studied numerically. Finite difference numerical solutions of the governing continuity and fully-elliptic momentum equations were obtained within the laminar flow regime for a range of Reynolds numbers, yield numbers, and power-law index values. The Reynolds number, based on the upstream pipe diameter and bulk velocity, was varied between 50 and 200, while the yield number was varied between 0 and 2. The power-law index values mapped the 0.6–1.2 range, allowing for the investigation of both shear-thinning and shear-thickening effects. Two distinct flow regimes are identified. One is associated with a combination of low yield numbers, high Reynolds numbers, and high power-law indexes, and exhibits a recirculating flow region at the step corner which is similar to that seen in Newtonian flows. The other flow regime, however, is characterized by a dead-zone behind the step corner, and is obtained for a combination of high yield numbers, low Reynolds numbers, and low power-law indexes. The yield number appears to be the dominant parameter affecting the shape and extent of the corner flow region as well as flow redevelopment further downstream. In general, the influence of the power-law index on the flow structure is stronger when the yield number is small. A flow character that is an exception to this general trend is the recirculating corner vortex intensity which decreases substantially with decreasing power-law index values for all investigated yield numbers.

Experimental Study on Racetrack-Shaped Holes Impingement Cooling With Bump Type Roughening Element

2012 ◽  
Author(s):  
Chiyuki Nakamata ◽  
Yoji Okita ◽  
Takashi Yamane ◽  
Yoshitaka Fukuyama ◽  
Toyoaki Yoshida
Keyword(s):  
Experimental Study ◽  
Flow Condition ◽  
Reynolds Numbers ◽  
Main Flow ◽  
The Other ◽  
Relative Location ◽  
Target Plate ◽  
Cooling Effectiveness ◽  
Impingement Cooling ◽  
Cooling Air

Cooling effectiveness of an impingement cooling with array of racetrack-shaped impingement holes is investigated. Two types of specimens are investigated. One is a plain target plate and the other is a plate roughened with bump type elements. Sensitivity of relative location of bump to impingement hole on the cooling effectiveness is also investigated. Experiments are conducted under three different mainflow Reynolds numbers ranging from 2.6×105 to 4.7×105, with four different cooling air Reynolds numbers for each main flow condition. The cooling air Reynolds numbers are in the range from 1.2×103 to 1.3×104.

scholarly journals Aboodh Transform Iterative Method for Spatial Diffusion of a Biological Population with Fractional-Order

Mathematics ◽  
2021 ◽  
Vol 9 (2) ◽  
pp. 155
Author(s):  
Gbenga O. Ojo ◽  
Nazim I. Mahmudov
Keyword(s):  
Iterative Method ◽  
Fractional Order ◽  
Population Model ◽  
Numerical Solutions ◽  
Computational Effort ◽  
Spatial Diffusion ◽  
Transform Method ◽  
Biological Population ◽  
The Laplace Transform ◽  
New Iterative Method

In this paper, a new approximate analytical method is proposed for solving the fractional biological population model, the fractional derivative is described in the Caputo sense. This method is based upon the Aboodh transform method and the new iterative method, the Aboodh transform is a modification of the Laplace transform. Illustrative cases are considered and the comparison between exact solutions and numerical solutions are considered for different values of alpha. Furthermore, the surface plots are provided in order to understand the effect of the fractional order. The advantage of this method is that it is efficient, precise, and easy to implement with less computational effort.

A Numerical and Experimental Investigation of Turbulent Heat Transport Downstream From an Abrupt Pipe Expansion

1983 ◽  
Vol 105 (4) ◽  
pp. 862-869 ◽  
Author(s):  
R. S. Amano ◽  
M. K. Jensen ◽  
P. Goel
Keyword(s):  
Heat Transfer ◽  
Numerical Solutions ◽  
Numerical Study ◽  
Separated Flow ◽  
Flow Region ◽  
Reynolds Numbers ◽  
Turbulent Heat ◽  
Transfer Coefficients ◽  
Heat Transfer Coefficients ◽  
Pipe Expansion

An experimental and numerical study is reported on heat transfer in the separated flow region created by an abrupt circular pipe expansion. Heat transfer coefficients were measured along the pipe wall downstream from an expansion for three different expansion ratios of d/D = 0.195, 0.391, and 0.586 for Reynolds numbers ranging from 104 to 1.5 × 105. The results are compared with the numerical solutions obtained with the k ∼ ε turbulence model. In this computation a new finite difference scheme is developed which shows several advantages over the ordinary hybrid scheme. The study also covers the derivation of a new wall function model. Generally good agreement between the measured and the computed results is shown.

Bifurcation Characteristics of Flows in Rectangular Sudden Expansion Channels

2005 ◽  
Author(s):  
Francine Battaglia ◽  
George Papadopoulos
Keyword(s):  
Reynolds Number ◽  
Laminar Flow ◽  
Critical Reynolds Number ◽  
Three Dimensional ◽  
Reynolds Numbers ◽  
Expansion Ratio ◽  
Sudden Expansion ◽  
Two Dimensional ◽  
Effective Expansion ◽  
Three Dimensional Simulations

The effect of three-dimensionality on low Reynolds number flows past a symmetric sudden expansion in a channel was investigated. The geometric expansion ratio of in the current study was 2:1 and the aspect ratio was 6:1. Both experimental velocity measurements and two- and three-dimensional simulations for the flow along the centerplane of the rectangular duct are presented for Reynolds numbers in the range of 150 to 600. Comparison of the two-dimensional simulations with the experiments revealed that the simulations fail to capture completely the total expansion effect on the flow, which couples both geometric and hydrodynamic effects. To properly do so requires the definition of an effective expansion ratio, which is the ratio of the downstream and upstream hydraulic diameters and is therefore a function of both the expansion and aspect ratios. When the two-dimensional geometry was consistent with the effective expansion ratio, the new results agreed well with the three-dimensional simulations and the experiments. Furthermore, in the range of Reynolds numbers investigated, the laminar flow through the expansion underwent a symmetry-breaking bifurcation. The critical Reynolds number evaluated from the experiments and the simulations was compared to other values reported in the literature. Overall, side-wall proximity was found to enhance flow stability, helping to sustain laminar flow symmetry to higher Reynolds numbers in comparison to nominally two-dimensional double-expansion geometries. Lastly, and most importantly, when the logarithm of the critical Reynolds number from all these studies was plotted against the reciprocal of the effective expansion ratio, a linear trend emerged that uniquely captured the bifurcation dynamics of all symmetric double-sided planar expansions.

Electrohydrodynamic rotation of drops at large electric Reynolds numbers

2016 ◽  
Vol 788 ◽  
Author(s):  
Ehud Yariv ◽  
Itzchak Frankel
Keyword(s):  
Electric Fields ◽  
Numerical Solutions ◽  
Fluid Velocity ◽  
Reynolds Numbers ◽  
Mirror Image ◽  
Liquid Drops ◽  
Weakly Conducting ◽  
Strong Electric Fields ◽  
Quincke Rotation ◽  
Asymmetric Solution

When subject to sufficiently strong electric fields, particles and drops suspended in a weakly conducting liquid exhibit spontaneous rotary motion. This so-called Quincke rotation is a fascinating example of nonlinear symmetry-breaking phenomena. To illuminate the rotation of liquid drops we here analyse the asymptotic limit of large electric Reynolds numbers, $\mathit{Re}\gg 1$, within the framework of a two-dimensional Taylor–Melcher electrohydrodynamic model. A non-trivial dominant balance in this singular limit results in both the fluid velocity and surface-charge density scaling as $\mathit{Re}^{-1/2}$. The flow is governed by a self-contained nonlinear boundary-value problem that does not admit a continuous fore–aft symmetric solution, thus necessitating drop rotation. Furthermore, thermodynamic arguments reveal that a fore–aft asymmetric solution exists only when charge relaxation within the suspending liquid is faster than that in the drop. The flow problem possesses both mirror-image (with respect to the direction of the external field) and flow-reversal symmetries; it is transformed into a universal one, independent of the ratios of electric conductivities and dielectric permittivities in the respective drop phase and suspending liquid phase. The rescaled angular velocity is found to depend weakly upon the viscosity ratio. The corresponding numerical solutions of the exact equations indeed collapse at large $\mathit{Re}$ upon the asymptotically calculated universal solution.

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