Spin-Up From Rest of a Two-Layer Liquid in a Cylinder

1994 ◽  
Vol 116 (4) ◽  
pp. 808-814 ◽  
Author(s):  
Kwan Yeop Kim ◽  
Jae Min Hyun
Keyword(s):  
Analytical Model ◽  
Numerical Solutions ◽  
Stokes Equations ◽  
Numerical Study ◽  
Bottom Layer ◽  
Meridional Flow ◽  
Individual Layer ◽  
Ekman Number ◽  
Radial Profiles ◽  
The Individual

A numerical and analytical study is made of spin-up from rest of a two-layer liquid in a rapidly rotating cylinder. The overall system Ekman number is small. The density of the top layer is smaller than that of the bottom layer (ρ1/ρ2<1.0), but the ratio of the individual layer kinematic viscosities is arbitrary (v1/v2<1.0 or v1/v2>1.0). The highlights of the analytical model, which is based on amended formulations of the Wedemeyer-Gerber-Homicz flow configurations, are briefly recapitulated. Comprehensive numerical solutions are secured to the time-dependent Navier–Stokes equations. The numerical solutions are validated by comparing the maximum interface displacements with the available experimental data as well as the analytical model predictions. Descriptions are made of the prominent characteristics of the interface shape for the two regimes of v1/v2<1.0 and v1/v2 > 1.0. Details of the azimuthal and meridional flow structures are illustrated by exploiting the numerical solutions. The computed meridional flows are compatible with the basic assumptions embedded in the development of the analytical model. Sequential plots of the radial profiles of azimuthal velocities are presented. These show that the global spin-up process is substantially accomplished over (En−1/2Ω−1), where En denotes the value of the smaller Ekman number of the two layers. The numerical study gives credence to the reliability and accuracy of the simplified analytical model.

Numerical Simulations of Flows Inside a Partially Filled Centrifuge

2003 ◽  
Vol 125 (6) ◽  
pp. 1033-1042 ◽  
Author(s):  
Fang Yan ◽  
Bakhtier Farouk
Keyword(s):  
Flow Field ◽  
Numerical Solutions ◽  
Stokes Equations ◽  
Complex Geometry ◽  
Numerical Study ◽  
Navier Stokes ◽  
Multiphase Model ◽  
Rotating Circular Cylinder ◽  
Radial Profiles ◽  
Liquid Flows

A numerical study was conducted to predict the dynamics of gas/liquid flows in a partially filled cylinder undergoing moderate to rapid rotation. Two specific problems were considered: spinup from rest of a partially filled circular container and the steady flow field in a partially filled rotating circular cylinder with an overrotating lid. Numerical solutions of the time-dependent axisymmetric Navier-Stokes equations were obtained by using a homogeneous multiphase model. The evolution of the free surface along with the flow fields in both the gas and liquid phases are predicted. The computed results were compared with available experimental data. Details of flow field structures are examined by studying the numerical solutions. Radial profiles of axial and azimuthal velocities for both the liquid and gas phases are also presented. The model developed can be used for analyzing flows and mixing problems in complex-geometry centrifuges.

A numerical study of the interaction between unsteay free-stream disturbances and localized variations in surface geometry

1989 ◽  
Vol 209 ◽  
pp. 285-308 ◽  
Author(s):  
R. J. Bodonyi ◽  
W. J. C. Welch ◽  
P. W. Duck ◽  
M. Tadjfar
Keyword(s):  
Numerical Solutions ◽  
Free Stream ◽  
Stokes Equations ◽  
Numerical Study ◽  
Navier Stokes ◽  
Surface Geometry ◽  
Navier Stokes Equations ◽  
S Waves ◽  
Tollmien Schlichting

A numerical study of the generation of Tollmien-Schlichting (T–S) waves due to the interaction between a small free-stream disturbance and a small localized variation of the surface geometry has been carried out using both finite–difference and spectral methods. The nonlinear steady flow is of the viscous–inviscid interactive type while the unsteady disturbed flow is assumed to be governed by the Navier–Stokes equations linearized about this flow. Numerical solutions illustrate the growth or decay of the T–S waves generated by the interaction between the free-stream disturbance and the surface distortion, depending on the value of the scaled Strouhal number. An important result of this receptivity problem is the numerical determination of the amplitude of the T–S waves.

Fluid Flow and Lateral Fluid Dispersion in Bounded Granular Beds

2002 ◽  
Author(s):  
Azita Soleymani ◽  
Eveliina Takasuo ◽  
Piroz Zamankhan ◽  
William Polashenski
Keyword(s):  
Reynolds Number ◽  
Porous Media ◽  
Numerical Solutions ◽  
Stokes Equations ◽  
Numerical Study ◽  
Fluid Velocity ◽  
Three Dimensional ◽  
Numerical Results ◽  
Transition To Turbulence ◽  
Wide Range

Results are presented from a numerical study examining the flow of a viscous, incompressible fluid through random packing of nonoverlapping spheres at moderate Reynolds numbers (based on pore permeability and interstitial fluid velocity), spanning a wide range of flow conditions for porous media. By using a laminar model including inertial terms and assuming rough walls, numerical solutions of the Navier-Stokes equations in three-dimensional porous packed beds resulted in dimensionless pressure drops in excellent agreement with those reported in a previous study (Fand et al., 1987). This observation suggests that no transition to turbulence could occur in the range of Reynolds number studied. For flows in the Forchheimer regime, numerical results are presented of the lateral dispersivity of solute continuously injected into a three-dimensional bounded granular bed at moderate Peclet numbers. Lateral fluid dispersion coefficients are calculated by comparing the concentration profiles obtained from numerical and analytical methods. Comparing the present numerical results with data available in the literature, no evidence has been found to support the speculations by others for a transition from laminar to turbulent regimes in porous media at a critical Reynolds number.

Axisymmetric Inertial Oscillations in Transient Rotating Flows in a Cylinder

1997 ◽  
Vol 119 (2) ◽  
pp. 390-396
Author(s):  
Jae Won Kim ◽  
Jae Min Hyun
Keyword(s):  
Large Time ◽  
Numerical Solutions ◽  
Stokes Equations ◽  
Numerical Study ◽  
Experimental Studies ◽  
Numerical Results ◽  
Navier Stokes ◽  
Inertial Oscillations ◽  
Time Duration ◽  
Navier Stokes Equations

A numerical study is made of axisymmetric inertial oscillations in a fluid-filled cylinder. The entire cylinder undergoes a spin-up process from rest with an impulsively started rotation rate Ω(t) = Ω0 + εω cos(ωt). Numerical solutions are obtained to the axisymmetric, time-dependent Navier-Stokes equations. Identification of the inertial oscillations is made by inspecting the evolution of the pressure difference between two pre-set points on the central axis, Cp. In the limit of large time, the inertial frequency thus determined is in close agreement with the results of the classical inviscid theory for solid-body rotation. As in previous experimental studies, the t* − (Ω0/ω) plots are constructed for inertial oscillations, where t* indicates the time duration until the maximum Cp is detected. These detailed numerical results are in broad agreement with the prior experimental data. Flow intensifications under the resonance conditions are illustrated based on the numerical results. Depictions are made of the increase in the amplitude of oscillating part of the total angular momentum under the resonance conditions. Also, the patterns of t* − (Ω0/ω) curves are displayed for different inertial frequency modes.

scholarly journals Leakage Effects in the Rotor Tip-Clearance Region of a Multistage Axial Compressor: Part 1 — Innovative Experiments

1998 ◽  
Author(s):  
P. C. Ivey ◽  
M. Swoboda
Keyword(s):  
Numerical Solutions ◽  
Stokes Equations ◽  
Numerical Study ◽  
Measurement Techniques ◽  
Axial Compressor ◽  
Tip Clearance ◽  
Navier Stokes ◽  
Navier Stokes Equations ◽  
Tip Clearance Flow ◽  
Clearance Flow

This paper describes work conducted as part of an experimental and numerical study of leakage effects by numerous Research and Industrial partners. For clarity it is presented in two parts. Part 1 presents measurements of tip-clearance flow for a 3rd stage rotor embedded in a four stage low-speed research compressor. The measurements are innovative and comprise measurements in the rotor relative frame of reference and 3D Laser time-of-flight Anemometry. Both techniques are relevant for improved understanding of multistage compressor flow dynamics and consequently, validated multistage CFD simulations. In part 2 of this paper (see Politis et al 1997b) it is shown that downstream of the rotor passage the location and size of a tip-clearance vortex, identified from both independent measurement techniques in Part 1, is in good agreement with 3D solutions of the Navier-Stokes equations modelling this compressor. These 3D numerical solutions reveal the tip-clearance flow structure using a multiblock grid technique.

Self-induced flow in a rotating tube

1991 ◽  
Vol 230 ◽  
pp. 505-524 ◽  
Author(s):  
S. Gilham ◽  
P. C. Ivey ◽  
J. M. Owen ◽  
J. R. Pincombe
Keyword(s):  
Boundary Layer ◽  
Numerical Solutions ◽  
Stokes Equations ◽  
Laser Doppler Anemometry ◽  
Glass Tube ◽  
The Self ◽  
Navier Stokes ◽  
Ekman Number ◽  
Induced Flow ◽  
Short Tube

When a tube, sealed at one end and open to a quiescent environment at the other, is rotated about its axis, fluid flows from the open end along the axis towards the sealed end and returns in an annular boundary layer on the cylindrical wall. This paper describes the first known study to be made of this self-induced flow. Numerical solutions of the Navier–Stokes equations are shown to be in mainly good agreement with experimental results obtained using flow visualization and laser–Doppler anemometry in a rotating glass tube.The self-induced flow in the tube can be described in terms of the length-to-radius ratio, G, and the Ekman number, E. However, for large values of G (G [ges ] 20), the flow outside the boundary layer on the endwall of the tube can be characterized by a single, modified, Ekman number, E*, where E* = GE. Although most of the fluid entering the open end of the tube is entrained into the annular (Stewartson-type) boundary layer, for small values of E* (E* < 0.2) some flow reaches the sealed end. For this so-called 'short-tube case’, the flow in the boundary layer on the endwall is shown to be similar to that associated with a disk rotating in a quiescent environment: the free disk. The self-induced flow for the short-tube case is believed to be responsible for the ’ hot-poker effect’ used, on some jet engines, to provide ice protection for the nose bullet.

Natural convection in an enclosure having a vertical sidewall with time-varying temperature

1996 ◽  
Vol 329 ◽  
pp. 65-88 ◽  
Author(s):  
Ho Sang Kwak ◽  
Jae Min Hyun
Keyword(s):  
Heat Transfer ◽  
Natural Convection ◽  
Numerical Solutions ◽  
Stokes Equations ◽  
Numerical Study ◽  
Temperature Fields ◽  
Navier Stokes ◽  
Time Varying ◽  
Vertical Sidewall ◽  
Boussinesq Fluid

A numerical study is performed for time-varying natural convection of an incompressible Boussinesq fluid in a sidewall-heated square cavity. The temperature at the cold sidewall Tc is constant, but at the hot sidewall a time-varying temperature condition is prescribed, $ T_H = \overline{T_H} + \Delta T^{\prime} \sin ft $. Comprehensive numerical solutions are found for the time-dependent Navier–Stokes equations. The numerical results are analysed in detail to show the existence of resonance, which is characterized by maximal amplification of the fluctuations of heat transfer in the interior. Plots of the dependence of the amplification of heat transfer fluctuations on the non-dimensional forcing frequency ω are presented. The failure of Kazmierczak & Chinoda (1992) to identify resonance is shown to be attributable to the limitations of the parameter values they used. The present results illustrate that resonance becomes more distinctive for large Ra and Pr ∼ 0(1). The physical mechanism of resonance is delineated by examining the evolution of oscillating components of flow and temperature fields. Specific comparisons are conducted for the resonance frequency ωr between the present results and several other previous predictions based on the scaling arguments.

A Numerical Study of the Influence of Disc Geometry on the Flow and Heat Transfer in a Rotating Cavity

1990 ◽  
Author(s):  
B. L. Lapworth ◽  
J. W. Chew
Keyword(s):  
Heat Transfer ◽  
Numerical Solutions ◽  
Stokes Equations ◽  
Numerical Study ◽  
Navier Stokes ◽  
Navier Stokes Equations ◽  
Model Calculations ◽  
Flow And Heat Transfer ◽  
Rotating Cavity ◽  
Radial Outflow

Numerical solutions of the Reynolds-averaged Navier-Stokes equations have been used to model the influence of cobs and a bolt cover on the flow and heat transfer in a rotating cavity with an imposed radial outflow of air. Axisymmetric turbulent flow is assumed using a mixing length turbulence model. Calculations for the non-plane discs are compared with plane disc calculations and also with the available experimental data. The calculated flow structures show good agreement with the experimentally observed trends. For the cobbed and plane discs, Nusselt numbers are calculated for a combination of flow rates and rotational speeds; these show some discrepancies with the experiments, although the calculations exhibit the more consistent trend. Further calculations indicate that differences in thermal boundary conditions have a greater influence on Nusselt number than differences in disc geometry. The influence of the bolt cover on the heat transfer has also been modelled, although comparative measurements are not available.

Oscillatory flow states in an enclosed cylinder with a rotating endwall

1999 ◽  
Vol 389 ◽  
pp. 101-118 ◽  
Author(s):  
J. L. STEVENS ◽  
J. M. LOPEZ ◽  
B. J. CANTWELL
Keyword(s):  
Oscillatory Flow ◽  
Numerical Solutions ◽  
Stokes Equations ◽  
Numerical Study ◽  
Modulation Frequency ◽  
Reynolds Numbers ◽  
Navier Stokes ◽  
Multiple Time ◽  
Navier Stokes Equations ◽  
Flow States

A combined experimental and numerical investigation is presented of the multiple oscillatory states that exist in the flows produced in a completely filled, enclosed, circular cylinder driven by the constant rotation of one of its endwalls. The flow in a cylinder of height to radius ratio 2.5 is interrogated experimentally using flow visualization and digitized images to extract quantitative temporal information. Numerical solutions of the axisymmetric Navier–Stokes equations are used to study the same flow over a range of Reynolds numbers where the flow is observed to remain axisymmetric. Three oscillatory states have been identified, two of them are periodic and the third is quasi-periodic with a modulation frequency much smaller than the base frequency. The range of Reynolds numbers for which the quasi-periodic flow exists brackets the switch between the two periodic states. The results from the combined experimental and numerical study agree both qualitatively and quantitatively, providing unambiguous evidence of the existence and robustness of these multiple time-dependent states.

The motion generated by a rising particle in a rotating fluid – numerical solutions. Part 1. A short container

2000 ◽  
Vol 413 ◽  
pp. 111-148 ◽  
Author(s):  
E. MINKOV ◽  
M. UNGARISH ◽  
M. ISRAELI
Keyword(s):  
Numerical Solutions ◽  
Stokes Equations ◽  
Time Development ◽  
Navier Stokes ◽  
Quasi Steady State ◽  
Rotating Fluid ◽  
Axial Motion ◽  
Good Qualitative Agreement ◽  
Navier Stokes Equations ◽  
Ekman Number

Numerical finite-difference results of the full axisymmetric incompressible Navier–Stokes equations are presented for the problem of the slow axial motion of a disk particle in an incompressible, rotating fluid in a cylindrical container. The governing parameters are the Ekman number, E, the Rossby number, Ro, and the dimensionless height of the container, H (with respect to the diameter of the particle). The study concerns small values of E, Ro, and HE−1/2 and compares the numerical results with predictions of previous analytical (mostly approximate) studies. Special attention is focused on the drag force. First, developed (quasi-steady state) cases are considered. Excellent agreement with the exact linear (Ro = 0) solution of Ungarish & Vedensky (1995) is obtained when the computational Ro = 10−4. The effects of the nonlinear momentum advection terms are analysed and shown to be proportional to RoE−1/2. Next, the time-development for both (a) impulsive start and (b) start under a constant axial force are considered, and good qualitative agreement with previous analytical results (including the appearance of oscillations in case (b)) is indicated.

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