Purely accelerating and decelerating flows within two flat disks
TL;DR: In this paper, the power series solutions of the steady, laminar, radial flows either purely accelerating, or purely decelerating, that develop in the gap formed by two flat disks are compared with previously reported approximate solutions or the experimental data for the pressure obtained by others.
Abstract: This paper deals with the power series solutions of the steady, laminar, radial flows either purely accelerating, or purely decelerating, that develop in the gap formed by two flat disks. The results include velocity profiles and static pressure distributions. These are compared with previously reported approximate solutions or the experimental data for the pressure obtained by others. The development of the two types of flows is shown to be entirely different except for λ (parameter that combines the non-dimensional radial distance and Reynolds number) close to zero where both behave as Poiseuille's flows between two infinite plates. For the inflow, the radial velocity flattens near the mid-plane diffusing towards the walls as the parameter λ increases. In contrast to the inflow, the magnitude of the maximum velocity of the outflow is shown to increase with λ, indicating that most of the fluid motion is taking place near the central channel region. For the outflow, two critical values of λ are used to indicate notable flow field transformations. The first marks the point where the pressure difference changes sign, while the second denotes when the derivative of the velocity (in the axial direction) on the wall becomes zero. Beyond the second value, purely decelerating flow cannot exist. The sign change of the pressure is attributed to the interaction between the inertia, viscous, and pressure forces.
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TL;DR: Investigations that provide a critical wall shear stress of 3 Pa for the standardised EHEDG cleaning test method are presented and it is shown that the empirical solution gives a good prediction even in the real RFC from a radius of 15 mm and outwards.
Abstract: In order to simulate the results of practical cleaning tests on closed processing equipment, based on wall shear stress predicted by computational fluid dynamics, a critical wall shear stress is required for that particular cleaning method. This work presents investigations that provide a critical wall shear stress of 3 Pa for the standardised EHEDG cleaning test method. The cleaning tests were performed on a test disc placed in a radial flowcell assay. Turbulent flow conditions were generated and the corresponding wall shear stresses were predicted from CFD simulations. Combining wall shear stress predictions from a simulation using the low Re k-e and one using the two-layer model of Norris and Reynolds were found to produce reliable predictions compared to empirical solutions for the ideal flow case. The comparison of wall shear stress curves predicted for the real RFC with the empirical solution showed that the empirical solution gives a good prediction even in the real RFC from a radius of 15 mm and outwards.
43 citations
TL;DR: In this article, the authors studied the flow driven by a rapidly expanding and collapsing cavitation bubble in a narrow cylindrical gap with the volume of fluid method and found that an adverse pressure gradient leads to boundary layer separation and flow reversal, causing large shear stress near the boundaries.
Abstract: The flow driven by a rapidly expanding and collapsing cavitation bubble in a narrow cylindrical gap is studied with the volume of fluid method. The simulations reveal a developing plug flow during the early expansion followed by flow reversal at later stages. An adverse pressure gradient leads to boundary layer separation and flow reversal, causing large shear stress near the boundaries. Analytical solution to a planar pulsating flow shows qualitative agreement with the CFD results. The shear stress close to boundaries has implications to deformable objects located near the bubble: experiments reveal that thin, flat biological cells entrained in the boundary layer become stretched, while cells with a larger cross-section are mainly transported with the flow.
10 citations
TL;DR: In this article, the authors considered sink and source flows developed in cones with small apex angles and in narrow gaps formed by two concentric cones and derived exact analytical solutions to these flows.
Abstract: This paper deals with sink and source flows developed in cones with small apex angles and in narrow gaps formed by two concentric cones. Numerical and approximate analytical solutions to these flows are presented. An exact solution for the creeping flow in conical gaps in terms of Legendre polynomials is derived. The analytical solutions to the flow in cones, includes the linearized inertia terms in the momentum equations, and are given using Gauss' hypergeometric series. For low Reynolds numbers, both converging and diverging flows are shown to coincide and are similar to Poiseuille's flow. However, when inertia effects are included, these are found to be radically different. For a sink flow, the radial velocity flattens in the neighborhood of the mid-angle and, as Re increases, the plateau expands out towards the conical walls, tending to the inviscid flat profile throughout the entire flow field. Contrary to the accelerating flow, the maximum velocity of the decelerating flow is shown to increase with Re. As a first critical Reynolds number is approached, the shear stress reduces to zero on the cone walls or, for a conical gap, on the outer cone walls. A further increase in Re above this first critical value, is found to produce a flow reversal either near the wall or, for the case of a conical gap, in the proximity of the outer cone. Thus, when Re exceeds this second value, purely decelerating flow cannot exist. The results for accelerating (sink) flow indicate that the approximate analytic solution is an excellent representation of this flow, whereas, for decelerating (source) flows particularly near separation, the results indicate that the numerical approach is needed to properly capture all flow features.
8 citations
Cites background from "Purely accelerating and deceleratin..."
...The general flow phenomenon is qualitatively similar to Jeffrey [1] fluid motion between two inclined planes, the radial flow in two parallel disks investigated by Zitouni and Vatistas [ 2 ], and the flow within two concentric spheres reported recently by Vatistas and Ghaly [3]....
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TL;DR: The present observations reveal distinct flow structure between two parallel discs and provide insights for understanding of radial flow structure.
Abstract: In the present work a confined, submerged, laminar water jet is issued axially from a short, circular nozzle and fed radially outward through the clearance of two parallel circular discs. The disc assembly was fully submerged into the water-filled tank. Water has been used as the experimental fluid and flow diagnosis has been performed using 2D particle image velocimetry (PIV) technique. Effect of inlet flow rates, disc radius and clearance between the two parallel discs have been investigated to understand the characteristics of submerged radial flow. It is observed that the flow field consists of several interesting features like toroidal recirculation, annular separation bubble around the inlet corner and flow reattachment, which are strongly influenced by the clearance between the two parallel discs and the flow rate. The present observations reveal distinct flow structure between two parallel discs and provide insights for understanding of radial flow structure. The numerical results simulated from PIV experiments are also included in the form of vector plots and from it a close consistency between the two results is clearly visible.
6 citations
TL;DR: In this article, a numerical steady state turbulence model for buoyant incompressible fluids exploiting the variation of the duct cross-section was developed, and the corresponding friction factor and Nusselt number correlations were suggested for intermediate range of Reynolds numbers.
6 citations
Cites methods from "Purely accelerating and deceleratin..."
...Additionally, the power series approach was employed to solve the same problem (Zitouni and Vatistas, 1997)....
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References
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TL;DR: In this article, a combined experimental and theoretical analysis of radial flow, without swirl, between parallel discs using air at incompressible speeds is presented, with emphasis on the pressure distribution sufficiently far downstream of the channel inlet for the entry conditions to be unimportant.
Abstract: An understanding of radial flow between confined boundaries is of practical importance in the design of radial diffusers and air bearings. This study presents a combined experimental and theoretical analysis of radial flow, without swirl, between parallel discs using air at incompressible speeds. Emphasis is placed on the pressure distribution sufficiently far downstream of the channel inlet for the entry conditions to be unimportant. However, a study is also made of the main features of the flow near the inlet, particularly within the annular separation bubble. It is shown, for both turbulent and laminar flow, that a similarity solution is possible only in special cases where certain terms in the equations of motion can be neglected. Approximate solutions are obtained for the turbulent and the laminar radial pressure distributions using an integral momentum method. Both theories agree well with experiment. The critical Reynolds number for reverse transition is found to be approximately the same as that for flow in twodimensional channels and circular pipes. With the flow separating at the channel inlet, it is established that both a suitably chosen, minimum pressure coefficient of the separation bubble and the reattachment distance are functions only of the channel width for a given inlet pipe diameter and are independent of Reynolds number and the diameter of the discs.
113 citations
"Purely accelerating and deceleratin..." refers background or methods in this paper
...A satisfactory solution for the pressure was obtained by Savage [9], in the range of Moller's [6] experiments, by perturbing the parabolic velocity for the outflow case in terms of the downstream coordinate....
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...Among those are Woolard [4], Livesey [5], Moiler [6], Boyack and Rice [7], and Kwok and Lee[8]....
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...The pressure distribution for an outflow, along with the observations of Moiler [6] are given in Fig....
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...O Exper imen t s of Hayes and Tucker [11], [] Exper imen t s of Moller [6], - - p resent theory, and ....
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...Typical AII values for outflow 2 Presen t Savage [9] Moller [6] Vatistas [13] 0....
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71 citations
TL;DR: In this paper, a method for including the inertia effects by solving the equation of motion approximately, in its integral form, is demonstrated with reference to the particular problem of radial flow between parallel plates.
64 citations
"Purely accelerating and deceleratin..." refers background in this paper
...Among those are Woolard [4], Livesey [5], Moiler [6], Boyack and Rice [7], and Kwok and Lee[8]....
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Abstract: Laterally converging flow occurs between two parallel surfaces with an exit hole formed in one. The present study examines the flow at a distance from the exit as a means of investigating an accelerating radial internal flow induced by the lateral convergence and satisfying the boundary-layer approximations. The measurements range from laminar to turbulent conditions, including the intermediate stage referred to by some investigators as laminarizing or laminarescent. The acceleration parameter K v = (ν/ V 2 ) dV / dr ranges from 2·6 × 10 −8 to 2·2 × 10 ×4 and the local Reynolds number varies from 210 to 6·8 × 10 4 for the data reported; the relation between the Reynolds number and the acceleration parameter was varied by adjusting the convergence angle or the plate spacing. For the main experiment the accelerating region is 86 plate spacings in length. Comparison with numerical predictions for laminar and turbulent flow leads to identification of flow regimes in terms of popular acceleration parameters K v , K p = (ν/ρ u 3 * ) dp / dr and K τ = (ν/ρ u 3 * ) (∂τ/∂ z ) w . Results demonstrate that a potentially turbulent entry flow subjected to accleration due to lateral convergence shows features common to laminarization in accelerating turbulent boundary layers in other geometries. Application of the function A + ( K p ) for a modified van Driest wall-region model is examined briefly for the intermediate regime.
54 citations
TL;DR: In this article, the authors investigate radial flow between parallel circular disks with a steady influx and conclude that the separation and reattachment of shear layers in the radial flow through parallel disks are unsteady phenomena and the sequence of nucleation, growth, migration and decay of the vortices is self-sustained.
Abstract: The flow-visualization methods of dye injection, hydrogen-bubble generation and paraffin mist are employed to investigate radial flow between parallel circular disks with a steady influx. Three distinct flow patterns are observed in the range of Re between 1.5 and 50. (1) Steady flow without boundary-layer separation and re-attachment, for Re < Rec. (2) A self-controlled flow oscillation which decays further downstream, in the range of Rec [les ] Re < Ret. (3) A self-sustained flow fluctuation which develops into a laminar-turbulent transition with a reverse transition further downstream, when Re [ges ] Ret. Rec and Ret are the critical and transition Reynolds number, respectively.The oscillating flows are caused by a vortex street consisting of vortices (i.e. separating annular bubbles) that separate periodically and alternately from both disks. Finite-difference solutions of the unsteady vorticity transport equation broadly agree with certain experimental observations. The study concludes that the separation and reattachment of shear layers in the radial flow through parallel disks are unsteady phenomena and the sequence of nucleation, growth, migration and decay of the vortices is self-sustained.
31 citations
"Purely accelerating and deceleratin..." refers background in this paper
...Three distinct outflow manifestations have been observed by Mochizuki and Yang [ 2 ]: (a) steady laminar flows without boundary layer separation, at low inlet Reynolds numbers, (b) a decaying self controlled oscillatory flow that is characterized by near the wall nucleation, growth, migration and decay of alternating vortices, for intermediate inlet Reynolds numbers, and (c) self-sustained fluctuating flows evolving into laminar-turbulent ......
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