Theoretical Investigation on Inflow Between Two Rotating Disks

2017 ◽  
Vol 139 (11) ◽  
Author(s):  
Achhaibar Singh
Keyword(s):  
Reynolds Number ◽  
Radial Velocity ◽  
Tangential Velocity ◽  
Tangential Direction ◽  
Speed Ratio ◽  
Rotating Disks ◽  
Practical Applications ◽  
Parabolic Profile ◽  
Pressure Decrease ◽  
Radial Convection

Mathematical relations are obtained for velocities and pressure distribution for a fluid entering the peripheral clearance of a pair of rotating concentric disks that converges and discharges through an opening at the center. Both, the flows in the gap of corotating disks and in the gap of contrarotating disks can be predicted using the present analytical solutions. The prediction of instability of radial velocity for corotating disks at the speed ratio of unity is very important for practical applications. The radial velocity profile is similar to a parabolic profile exactly at speed ratio of unity. The profile drastically changes with the small difference of ±1% in the disks’ rotation. The radial convection was observed in the tangential velocity at a low radius. Centrifugal force caused by disk rotation highly influences the flow resulting in backflow on the disks. The pressure consists of friction losses and convective inertia. Therefore, the pressure decrease is high for increased speed ratio, throughflow Reynolds number, and rotational Reynolds number. The pressure decrease for the flow between contrarotating disks is lesser than that for the flow between corotating disks due to decreased viscous losses in the tangential direction. This study provides valuable guidance for the design of devices where disks are rotated independently by highlighting the instabilities in the radial velocity at the speed ratio of unity.

An Asymptotic Solution for Laminar Flow of an Incompressible Fluid Between Rotating Disks

1968 ◽  
Vol 35 (1) ◽  
pp. 155-159 ◽  
Author(s):  
L. Matsch ◽  
W. Rice
Keyword(s):  
Reynolds Number ◽  
Laminar Flow ◽  
Radial Velocity ◽  
Velocity Component ◽  
Tangential Velocity ◽  
Outer Radius ◽  
Creeping Flow ◽  
Arbitrary Distribution ◽  
Rotating Disks ◽  
Inner Radius

Laminar flow is considered between parallel rotating disks having a circular exhaust hole at an inner radius and supplied with fluid at the outer radius with pressure higher than the available sink pressure. The problem statement for asymptotic (fully developed) flow is formulated. A procedure for perturbing a creeping flow solution and an iteration scheme are developed to produce a solution for higher Reynolds numbers. The solution depends on two parameters, a Reynolds number and a mass flow parameter, and is asymptotic in the sense that a third parameter would be necessary for a solution with an arbitrary tangential velocity component specified at the outer radius of the disks and/or an arbitrary distribution of the radial velocity component between the disks. From computations conducted by digital computer, the region having uninflected radial velocity profiles is delineated. Typical results are presented for the velocity components as functions of Reynolds number, the average radial component of velocity at the entrance, and the inner radius of the disks.

Laminar Inward Flow of an Incompressible Fluid Between Rotating Disks, With Full Peripheral Admission

1968 ◽  
Vol 35 (2) ◽  
pp. 229-237 ◽  
Author(s):  
K. E. Boyd ◽  
W. Rice
Keyword(s):  
Reynolds Number ◽  
Flow Rate ◽  
Stokes Equations ◽  
Complete Solution ◽  
Applied Pressure ◽  
Tangential Velocity ◽  
Tangential Component ◽  
Rotating Disks ◽  
Outer Periphery ◽  
Inlet Conditions

The laminar flow of an incompressible Newtonian fluid, radially inward between parallel co-rotating disks is considered. The through-flow is supported by an externally applied pressure difference between the outer periphery and a circular fluid exhaust hole at an inner radius. The fluid supplied at the outer periphery is considered with arbitrary velocity components, such that the tangential component may be greater or less than the disk peripheral velocity. A sufficiently complete problem statement is formulated from the Navier-Stokes’ equations. The problem has three parameters: a Reynolds number, a flow-rate parameter, and a peripheral tangential velocity component parameter. A numerical method of solution is detailed and typical numerical results are given illustrating the phenomena that occur in the inlet region for various inlet conditions. It is shown that the solution becomes the asymptotic solution given by previous investigators at interior radii following the inlet. Correspondence between the complete solution given herein and the earlier asymptotic solutions is established as dependent on corresponding values of Reynolds number and flow rate only. The results are discussed from the point of view of application of the solution in the development of multiple-disk turbines.

Entropy generation and heat transfer analysis for ferrofluid flow between two rotating disks with variable conductivity

2021 ◽  
pp. 095440622199118
Author(s):  
Anupam Bhandari
Keyword(s):  
Heat Transfer ◽  
Reynolds Number ◽  
Differential Equations ◽  
Entropy Generation ◽  
Heat Transfer Analysis ◽  
Entropy Generation Rate ◽  
Geometrical Parameters ◽  
Rotating Disks ◽  
Coupled Differential Equations ◽  
Lower Disk

Present model analyze the flow and heat transfer of water-based carbon nanotubes (CNTs) [Formula: see text] ferrofluid flow between two radially stretchable rotating disks in the presence of a uniform magnetic field. A study for entropy generation analysis is carried out to measure the irreversibility of the system. Using similarity transformation, the governing equations in the model are transformed into a set of nonlinear coupled differential equations in non-dimensional form. The nonlinear coupled differential equations are solved numerically through the finite element method. Variable viscosity, variable thermal conductivity, thermal radiation, and volume concentration have a crucial role in heat transfer enhancement. The results for the entropy generation rate, velocity distributions, and temperature distribution are graphically presented in the presence of physical and geometrical parameters of the flow. Increasing the values of ferromagnetic interaction number, Reynolds number, and temperature-dependent viscosity enhances the skin friction coefficients on the surface and wall of the lower disk. The local heat transfer rate near the lower disk is reduced in the presence of Harman number, Reynolds number, and Prandtl number. The ferrohydrodynamic flow between two rotating disks might be useful to optimize the use of hybrid nanofluid for liquid seals in rotating machinery.

scholarly journals Kinematics of Disk Stars in the Solar Neighbourhood

1998 ◽  
Vol 11 (1) ◽  
pp. 574-574
Author(s):  
A.E. Gómez ◽  
S. Grenier ◽  
S. Udry ◽  
M. Haywood ◽  
V. Sabas ◽  
...  
Keyword(s):  
Dispersion Relation ◽  
Radial Velocity ◽  
Velocity Dispersion ◽  
Tangential Velocity ◽  
Thin Disk ◽  
The Other ◽  
Proper Motions ◽  
Velocity Data ◽  
Kinematic Data ◽  
Radial Velocity Data

Using Hipparcos parallaxes and proper motions together with radial velocity data and individual ages estimated from isochones, the velocity ellipsoid has been determined as a function of age. On the basis of the available kinematic data two different samples were considered: a first one (7789 stars) for which only tangential velocities were calculated and a second one containing 3104 stars with available U, V and W velocity components and total velocities ≤ 65 km.s-1. The main conclusions are: -Mixing is not complete at about 0.8-1 Gyr. -The shape of the velocity ellipsoid changes with time getting rounder from σu/σv/σ-w = 1/0.63/0.42 ± 0.04 at about 1 Gyr to1/0.7/0.62 ±0.04 at 4-5 Gyr. -The age-velocity-dispersion relation (from the sample with kinematical selection) rises to a maximum, thereafter remaining roughly constant; there is no dynamically significant evolution of the disk after about 4-5 Gyr. -Among the stars with solar metallicities and log(age) > 9.8 two groups are identified: one has typical thin disk characteristics, the other is older than 10 Gyr and lags the LSR at about 40 km.s-1 . -The variation of the tangential velocity with age(without selection on the tangential velocity) shows a discontinuity at about 10 Gyr, which may be attributed to stars typically of the thick disk populations for ages > 10 Gyr.

An example of steady laminar flow at large Reynolds number

1960 ◽  
Vol 9 (4) ◽  
pp. 593-602 ◽  
Author(s):  
Iam Proudman
Keyword(s):  
Boundary Layer ◽  
Reynolds Number ◽  
Boundary Layers ◽  
Tangential Velocity ◽  
Fluid Flows ◽  
The Other ◽  
Large Reynolds Number ◽  
Rotational Flows ◽  
Flow Domain ◽  
Source Of Information

The purpose of this note is to describe a particular class of steady fluid flows, for which the techniques of classical hydrodynamics and boundary-layer theory determine uniquely the asymptotic flow for large Reynolds number for each of a continuously varied set of boundary conditions. The flows involve viscous layers in the interior of the flow domain, as well as boundary layers, and the investigation is unusual in that the position and structure of all the viscous layers are determined uniquely. The note is intended to be an illustration of the principles that lead to this determination, not a source of information of practical value.The flows take place in a two-dimensional channel with porous walls through which fluid is uniformly injected or extracted. When fluid is extracted through both walls there are boundary layers on both walls and the flow outside these layers is irrotational. When fluid is extracted through one wall and injected through the other, there is a boundary layer only on the former wall and the inviscid rotational flow outside this layer satisfies the no-slip condition on the other wall. When fluid is injected through both walls there are no boundary layers, but there is a viscous layer in the interior of the channel, across which the second derivative of the tangential velocity is discontinous, and the position of this layer is determined by the requirement that the inviscid rotational flows on either side of it must satisfy the no-slip conditions on the walls.

Application of IVAP-Based Observation Operator in Radar Radial Velocity Assimilation: The Case of Typhoon Fitow

2017 ◽  
Vol 145 (10) ◽  
pp. 4187-4203 ◽  
Author(s):  
Feng Chen ◽  
Xudong Liang ◽  
Hao Ma
Keyword(s):  
Spatial Distribution ◽  
Radial Velocity ◽  
Doppler Radar ◽  
Tangential Velocity ◽  
Distribution Characteristics ◽  
Observation Operator ◽  
Spatial Distribution Characteristics ◽  
Tangential Wind ◽  
Analysis System ◽  
Background Fields

An improved Doppler radar radial velocity assimilation observation operator is proposed based on the integrating velocity–azimuth process (IVAP) method. This improved operator can ingest both radial wind and its spatial distribution characteristics to deduce the two components of the mean wind within a given area. With this operator, the system can be used to assimilate information from tangential wind and radial wind. On the other hand, because the improved observation operator is defined within a given area, which can be uniformly chosen in both the observation and analysis coordinate systems, it has a thinning function. The traditional observation operator and the improved observation operator, along with their corresponding data processing modules, were implemented in the community Gridpoint Statistical Interpolation analysis system (GSI) to demonstrate the superiority of the improved operator. The results of single analysis unit experiments revealed that the two operators are comparable when the analysis unit is small. When the analysis unit becomes larger, the analysis results of the improved operator are better than those of the traditional operator because the former can ingest more wind information than the latter. The results of a typhoon case study indicated that both operators effectively ingested radial wind information and produced more reasonable typhoon structures than those in the background fields. The tangential velocity relative to the radar was retrieved by the improved operator through ingesting tangential wind information from the spatial distribution characteristics of radial wind. Because of the improved vortex intensity and structure, obvious improvements were seen in both track and intensity predictions when the improved operator was used.

Performance Estimation of Axial Flow Turbines

1970 ◽  
Vol 185 (1) ◽  
pp. 407-424 ◽  
Author(s):  
H. R. M. Craig ◽  
H. J. A. Cox
Keyword(s):  
Reynolds Number ◽  
Aspect Ratio ◽  
Gas Turbines ◽  
Three Dimensional ◽  
Axial Flow ◽  
Performance Estimation ◽  
Speed Ratio ◽  
Test Results ◽  
Wide Range ◽  
Relevant Variables

A comprehensive method of estimating the performance of axial flow steam and gas turbines is presented, based on analysis of linear cascade tests on blading, on a number of turbine test results, and on air tests of model casings. The validity of the use of such data is briefly considered. Data are presented to allow performance estimation of actual machines over a wide range of Reynolds number, Mach number, aspect ratio and other relevant variables. The use of the method in connection with three-dimensional methods of flow estimation is considered, and data presented showing encouraging agreement between estimates and available test results. Finally ‘carpets’ are presented showing the trends in efficiencies that are attainable in turbines designed over a wide range of loading, axial velocity/blade speed ratio, Reynolds number and aspect ratio.

Pressure, Frictional Resistance, and Flow Characteristics of the Partially Wetted Rotating Disk

1968 ◽  
Vol 90 (2) ◽  
pp. 395-404 ◽  
Author(s):  
H. N. Ketola ◽  
J. M. McGrew
Keyword(s):  
Experimental Data ◽  
Reynolds Number ◽  
Pressure Gradient ◽  
Flow Characteristics ◽  
Frictional Resistance ◽  
Rotating Disk ◽  
Practical Applications ◽  
Stationary Wall ◽  
Spacing Ratio ◽  
Analytical Expressions

A theory of the partially wetted rotating disk is described and experimental data presented which verify the application of this theory in practical applications. Four different flow regimes may be identified according to the value of the disk Reynolds number and the spacing ratio between the disk and stationary wall. The analytical expressions for prediction of the pressure gradient developed and the frictional resistance are uniquely determined by the disk Reynolds number, spacing ratio, and the degree of wetting of the disk.

The Numerical Simulation of Turbulent Flow in Semi-Closed Rotor-Stator Cavity

2016 ◽  
Author(s):  
Guohu Luo ◽  
Shengde Wang ◽  
Hong Shen ◽  
Zhenqiang Yao
Keyword(s):  
Reynolds Number ◽  
Turbulent Flow ◽  
Boundary Layers ◽  
Pressure Difference ◽  
Tangential Velocity ◽  
Reynolds Stress Model ◽  
Mean Flow ◽  
Closed Cavity ◽  
Turbulent Field ◽  
Effects Of Rotation

The present work numerically considered the turbulent flow in a semi-closed rotor-stator cavity with a superimposed throughflow based on Reynolds Stress Model (RSM). The mean flow structure and turbulent field in the semi-closed cavity (SC) were identified by comparison with the flow in open cavity (OC) and closed cavity (CC). Then the effects of rotation Reynolds number, ranging from 1 × 106 to 4 × 106, on the flow in SC were investigated. The superimposed flow noticeably decreases the tangential velocity, resulting that the pressure difference between central hub and periphery in SC is greater than the OC but less than the CC. The flow in SC belongs to Stewartson type in the region between inlet and outlet, but to Bachelor type between outlet and periphery. Around the outlets, the flow is greatly affected, especially for turbulent field, where the turbulence intensities maintain at higher levels outside the two boundary layers. With the increase of Reynolds number, the tangential velocity goes up, resulted the attenuation of jet impinging effects, the shrinking of affected zones by outlets and the enlargement of pressure difference. Moreover, with the Bödewadt layer moving toward the central hub, the turbulence intensities increase inside two boundary layers but decrease outside them. Consequently, the flow is transited to Stewartson and then Batchelor type.

scholarly journals A Numerical Study of Chemical Reaction in a Nanofluid Flow Due to Rotating Disk in the Presence of Magnetic Field

2021 ◽  
Author(s):  
Muhammad Ramzan ◽  
Poom Kumam ◽  
Kottakkaran Sooppy Nisar ◽  
Ilyas Khan ◽  
Wasim Jamshed
Keyword(s):  
Differential Equation ◽  
Radial Velocity ◽  
Chemical Reaction ◽  
Axial Velocity ◽  
Numerical Study ◽  
Tangential Velocity ◽  
Rotating Disk ◽  
Partial Differential ◽  
Suction Parameter ◽  
Matlab Programming

Abstract In this paper, a numerical study of MHD steady flow due to the rotating disk with chemical reaction was explored. Effect of different parameters such as Schmidt number, chemical reaction parameter, Prandtl number, Suction parameter, heat absorption/generation parameter, Nano-particle concentration, Reynold number, Magnetic parameter, skin friction, shear stress, temperature distribution, Nusselt number, mass transfer rate, radial velocity, axial velocity, and tangential velocity was analyzed and discussed. For the simplification of non-linear partial differential equations (PDEs) into the nonlinear ordinary differential equation (ODEs), the method of Similarity transformation was employed, and the resulting partial differential equation was solved by using finite difference method through MATLAB programming. This work's remarkable finding is that with the expansion of nanoparticle concentration radial velocity, tangential velocity and temperature of the fluid was enhanced but reverse reaction for axial velocity. Furthermore, the present results are found to be in excellent agreement with previously published work.

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