Steady Laminar Flow in a Stationary Tank With a Spinning Bottom

1975 ◽  
Vol 42 (4) ◽  
pp. 771-776 ◽  
Author(s):  
C. V. Alonso
Keyword(s):  
Stokes Equations ◽  
Tangential Velocity ◽  
Navier Stokes ◽  
Navier Stokes Equations ◽  
General Validity ◽  
Alternating Direction Implicit ◽  
Incompressible Viscous Flow ◽  
Alternating Direction ◽  
Alternating Direction Implicit Scheme ◽  
Steady Laminar

The steady incompressible viscous flow induced in a cylindrical tank by the rotation of its bottom was studied both theoretically and experimentally. The complete Navier-Stokes equations are expressed in terms of the tangential velocity, vorticity, and meridional stream function. The transformed equations are solved numerically using an alternating-direction implicit scheme and a nonuniform grid. The general validity of the numerical solution was demonstrated by the agreement between the computed and experimental results.

A Theoretical and Experimental Study of Confined Vortex Flow

1969 ◽  
Vol 36 (4) ◽  
pp. 687-692 ◽  
Author(s):  
G. J. Farris ◽  
G. J. Kidd ◽  
D. W. Lick ◽  
R. E. Textor
Keyword(s):  
Flow Field ◽  
Radial Flow ◽  
Stokes Equations ◽  
Numerical Technique ◽  
Tangential Velocity ◽  
Reynolds Numbers ◽  
Navier Stokes ◽  
Navier Stokes Equations ◽  
General Validity ◽  
Wide Range

The interaction of a vortex with a stationary surface was studied both theoretically and experimentally. The flow field examined was that produced by radially inward flow through a pair of concentric rotating porous cylinders that were perpendicular to, and in contact with, a stationary flat plane. The complete Navier-Stokes equations were solved over a range of tangential Reynolds numbers from 0–300 and a range of radial Reynolds numbers from 0 to −13, the minus sign indicating radially inward flow. In order to facilitate the solution, the original equations were recast in terms of a dimensionless stream function, vorticity, and third variable related to the tangential velocity. The general validity of the numerical technique was demonstrated by the agreement between the theoretical and experimental results. Examination of the numerical results over a wide range of parameters showed that the entire flow field is very sensitive to the amount of radial flow, especially at the transition from zero radial flow to some finite value.

scholarly journals Determining the Tangential Velocity profile of a Rotating Fluid in a Static Container using Navier–Stokes equations

2020 ◽  
Author(s):  
RAJDEEP TAH ◽  
SARBAJIT MAZUMDAR ◽  
Krishna Kant Parida
Keyword(s):  
Angular Velocity ◽  
Velocity Profile ◽  
Velocity Gradient ◽  
Stokes Equations ◽  
Tangential Velocity ◽  
Navier Stokes ◽  
Rotating Fluid ◽  
Navier Stokes Equations ◽  
Similar Principle ◽  
Tangential Velocity Profile

The shape of the liquid surface for a fluid present in a uniformly rotating cylinder is generally determined by making a Tangential velocity gradient along the radius of the rotating cylindrical container. A very similar principle can be applied if the direction of the produced velocity gradient is reversed, for which the source of rotation will be present at the central axis of the cylindrical vessel in which the liquid is present. Now if the described system is completely closed, the angular velocity will decrease as a function of time. But when the surface of the rotating fluid is kept free, then the Tangential velocity profile would be similar to that of the Taylor-Couette Flow, with a modification that; due to formation of a curvature at the surface, the Navier-Stokes law is to be modified. Now the final equation may not seem to have a proper general solution, but can be approximated to certain solvable expressions for specific cases of angular velocity.

Numerical Solution of Incompressible Unsteady Flows in Turbomachinery

2000 ◽  
Vol 123 (3) ◽  
pp. 680-685 ◽  
Author(s):  
L. He ◽  
K. Sato
Keyword(s):  
Stokes Equations ◽  
Three Dimensional ◽  
Unsteady Flows ◽  
Navier Stokes ◽  
Time Step ◽  
Navier Stokes Equations ◽  
Flow Solver ◽  
Time Stepping ◽  
Incompressible Viscous Flow ◽  
Dual Time Stepping

A three-dimensional incompressible viscous flow solver of the thin-layer Navier-Stokes equations was developed for the unsteady turbomachinery flow computations. The solution algorithm for the unsteady flows combines the dual time stepping technique with the artificial compressibility approach for solving the incompressible unsteady flow governing equations. For time accurate calculations, subiterations are introduced by marching the equations in the pseudo-time to fully recover the incompressible continuity equation at each real time step, accelerated with a multi-grid technique. Computations of test cases show satisfactory agreements with corresponding theoretical and experimental results, demonstrating the validity and applicability of the present method to unsteady incompressible turbomachinery flows.

Inward Flow Between Stationary and Rotating Disks

2014 ◽  
Vol 136 (10) ◽  
Author(s):  
Achhaibar Singh
Keyword(s):  
Laminar Flow ◽  
Flow Field ◽  
Velocity Distribution ◽  
Stokes Equations ◽  
Tangential Velocity ◽  
Rotating Disk ◽  
Reynolds Numbers ◽  
Navier Stokes ◽  
Rotating Disks ◽  
Navier Stokes Equations

The present study predicts the flow field and the pressure distribution for a laminar flow in the gap between a stationary and a rotating disk. The fluid enters through the peripheral gap between two concentric disks and converges to the center where it discharges axially through a hole in one of the disks. Closed form expressions have been derived by simplifying the Navier– Stokes equations. The expressions predict the backflow near the rotating disk due to the effect of centrifugal force. A convection effect has been observed in the tangential velocity distribution at high throughflow Reynolds numbers.

Cooling Improvement of Gas Turbine Rotary Blades

2020 ◽  
Author(s):  
Faezeh Rasimarzabadi ◽  
Ramin Kamalimoghadam ◽  
Mahmoud Najafi ◽  
MohammadReza Mohammadi ◽  
Nasrin Sahranavard Fard
Keyword(s):  
Gas Turbine ◽  
Cfd Simulation ◽  
Stokes Equations ◽  
Turbine Blades ◽  
Tangential Velocity ◽  
Navier Stokes ◽  
Rotating Shaft ◽  
Navier Stokes Equations ◽  
Calculation Results ◽  
Cooling Air

Abstract A new method is presented to improve cooling of the turbine blades by using active extraction from the compressor outlet to supply more cooling air with more energy. The cool air is extracted from the end of compressor through a set of peripheral holes to the air transferring channels on the disc edge or torque tube using the tangential velocity vector of the rotating shaft which results in increasing the amount and energy of the cooling air. In fact a forward angle of inlet holes for the channels is used to help the pressurized air overcome the air centrifugal force and to accelerate the flow going into the torque tube. To investigate the effect of new idea, both the original and proposed models are analyzed using 3D CFD simulation on a selected physical domain of a gas turbine. The compressible rotating Navier-Stokes equations are used for numerical simulation of two geometries. The governing equations, mesh treatment, boundary conditions and numerical setup are described. The calculation results are compared to those of the original turbine shaft to show the heat transfer improvement by enhancing the cooling flow rate and fluid energy.

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