Laminar Compressible Flow Over a Stationary Disk in a Rotating Cylinder

1979 ◽  
Vol 101 (2) ◽  
pp. 173-180 ◽  
Author(s):  
M. Toren ◽  
A. Solan
Keyword(s):  
Angular Velocity ◽  
Compressible Flow ◽  
Close Agreement ◽  
Numerical Solutions ◽  
Stokes Equations ◽  
Meridional Circulation ◽  
Rotating Cylinder ◽  
Navier Stokes ◽  
Navier Stokes Equations ◽  
The Core

The laminar isothermal compressible flow in a rotating cylinder with a stationary bottom is treated both numerically and by boundary layer matching. The numerical solution of the Navier-Stokes equations is based on a modified Cheng-Allen finite difference scheme. An approximate solution is obtained by matching boundary layers to an interior core. For sufficiently low Ekman numbers, the approximate and numerical solutions are in close agreement. The compressibility is shown to increase the angular velocity in the core and to decrease the meridional circulation. When the aspect ratio of the cylinder is increased, both the angular velocity in the core and the meridional circulation increase.

Similarity solutions for viscous vortex cores

1992 ◽  
Vol 238 ◽  
pp. 487-507 ◽  
Author(s):  
Ernst W. Mayer ◽  
Kenneth G. Powell
Keyword(s):  
Numerical Solutions ◽  
Stokes Equations ◽  
Axial Flow ◽  
Similarity Solutions ◽  
Navier Stokes ◽  
Navier Stokes Equations ◽  
The Core ◽  
Axial Pressure Gradient ◽  
Self Similar ◽  
Similar Solutions

Results are presented for a class of self-similar solutions of the steady, axisymmetric Navier–Stokes equations, representing the flows in slender (quasi-cylindrical) vortices. Effects of vortex strength, axial gradients and compressibility are studied. The presence of viscosity is shown to couple the parameters describing the core growth rate and the external flow field, and numerical solutions show that the presence of an axial pressure gradient has a strong effect on the axial flow in the core. For the viscous compressible vortex, near-zero densities and pressures and low temperatures are seen on the vortex axis as the strength of the vortex increases. Compressibility is also shown to have a significant influence upon the distribution of vorticity in the vortex core.

Axisymmetric compressible flow in a rotating cylinder with axial convection

1985 ◽  
Vol 154 ◽  
pp. 121-144 ◽  
Author(s):  
Marius Ungarish ◽  
Moshe Israeli
Keyword(s):  
Compressible Flow ◽  
Numerical Solutions ◽  
Stokes Equations ◽  
Nonlinear Effects ◽  
Ideal Gas ◽  
Navier Stokes ◽  
Linear Perturbation ◽  
Linear Extensions ◽  
Navier Stokes Equations ◽  
Thermally Conducting

The steady compressible flow of an ideal gas in a rotating annulus with thermally conducting walls is considered for small Rossby number ε and Ekman number E and moderate rotational Mach numbers M. Attention is focused on nonlinear effects which show up when σ and εM2 are not small (σ = ε/HE½, H is the dimensionless height of the container). These effects are not properly predicted by the classical linear perturbation analysis, and are treated here by quasi-linear extensions.The extra work required by these extensions is only the numerical solution of one ordinary differential equation for the pressure.Numerical solutions of the full Navier–Stokes equations in the nonlinear range are presented, and the validity of the present approach is confirmed.

Autorotation of an elliptic cylinder about an axis perpendicular to the flow

1980 ◽  
Vol 99 (4) ◽  
pp. 817-840 ◽  
Author(s):  
Hans J. Lugt
Keyword(s):  
Angular Velocity ◽  
Vortex Shedding ◽  
Large Scale ◽  
Numerical Solutions ◽  
Stokes Equations ◽  
Elliptic Cylinder ◽  
Navier Stokes ◽  
Navier Stokes Equations ◽  
Flow Effects ◽  
Large Scale Flow

Autorotation of an elliptic cylinder about an axis fixed perpendicular to a parallel flow is explained in this paper by means of numerical solutions of the Navier-Stokes equations. Potential-flow theory predicts, for constant angular velocity, half a period in which a torque supports rotation and half a period in which it opposes rotation, with vanishing torque in the average. This balance is disturbed by viscous-flow effects in such a way that, for a given angular velocity, vortex shedding either damps rotation or, under certain conditions, favours rotation. The proper interplay of those conditions, which include synchronization of vortex shedding and rate of rotation, results in auto-rotation. The numerical results forRe[les ] 400 are compared with experimental data forRe= 90000 from the literature. The agreement of the force coefficients and the large-scale flow patterns is surprisingly good.

Natural Convection in Shallow Enclosures With Differentially Heated Endwalls

1988 ◽  
Vol 110 (3) ◽  
pp. 625-634 ◽  
Author(s):  
S. Paolucci ◽  
D. R. Chenoweth
Keyword(s):  
Numerical Solutions ◽  
Stokes Equations ◽  
Ideal Gas ◽  
Navier Stokes ◽  
Navier Stokes Equations ◽  
The Core ◽  
Nusselt Numbers ◽  
Aspect Ratios ◽  
Ideal Gas Law ◽  
Rayleigh Numbers

We consider a low-aspect-ratio two-dimensional rectangular cavity, differentially heated with an arbitrarily large horizontal temperature difference. Steady-state results obtained from numerical solutions of the transient Navier-Stokes equations are given for air using the ideal gas law and Sutherland law transport properties. We clarify the different flow regimes possible by using numerical results for aspect ratios 0.025 ≤ A ≤ 1 and for Rayleigh numbers (based on height) 102 ≤ Ra ≤ 109. We present Nusselt numbers, and temperature and velocity distributions, and compare them with existing data. At high Ra in the Boussinesq limit we show the existence of weak secondary and tertiary flows in the core of the cavity. In addition we present novel solutions in the non-Boussinesq regime. We find that the classical parallel flow solution, accurate in the core of the cavity in the Boussinesq limit, does not exist when variable properties are introduced. For higher Rayleigh numbers, we generalize the well-known analytical boundary layer solution of Gill. The non-Boussinesq solutions show greatly reduced static pressure levels and lower critical Rayleigh numbers.

scholarly journals Vibrations of Nonlinear Elastic Structure Excited by Compressible Flow

2021 ◽  
Vol 11 (11) ◽  
pp. 4748
Author(s):  
Monika Balázsová ◽  
Miloslav Feistauer ◽  
Jaromír Horáček ◽  
Adam Kosík
Keyword(s):  
Compressible Flow ◽  
Nonlinear Elasticity ◽  
Vocal Tract ◽  
Stokes Equations ◽  
Vocal Folds ◽  
Nonlinear Material ◽  
Navier Stokes ◽  
Arbitrary Lagrangian Eulerian ◽  
Navier Stokes Equations ◽  
Reliable Solution

This study deals with the development of an accurate, efficient and robust method for the numerical solution of the interaction of compressible flow and nonlinear dynamic elasticity. This problem requires the reliable solution of flow in time-dependent domains and the solution of deformations of elastic bodies formed by several materials with complicated geometry depending on time. In this paper, the fluid–structure interaction (FSI) problem is solved numerically by the space-time discontinuous Galerkin method (STDGM). In the case of compressible flow, we use the compressible Navier–Stokes equations formulated by the arbitrary Lagrangian–Eulerian (ALE) method. The elasticity problem uses the non-stationary formulation of the dynamic system using the St. Venant–Kirchhoff and neo-Hookean models. The STDGM for the nonlinear elasticity is tested on the Hron–Turek benchmark. The main novelty of the study is the numerical simulation of the nonlinear vocal fold vibrations excited by the compressible airflow coming from the trachea to the simplified model of the vocal tract. The computations show that the nonlinear elasticity model of the vocal folds is needed in order to obtain substantially higher accuracy of the computed vocal folds deformation than for the linear elasticity model. Moreover, the numerical simulations showed that the differences between the two considered nonlinear material models are very small.

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.

NUMERICAL SOLUTIONS OF 2D AND 3D SLAMMING PROBLEMS

2021 ◽  
Vol 153 (A2) ◽  
Author(s):  
Q Yang ◽  
W Qiu
Keyword(s):  
Free Surface ◽  
Numerical Solutions ◽  
Stokes Equations ◽  
Type Equation ◽  
The Body ◽  
Navier Stokes ◽  
Time Step ◽  
Navier Stokes Equations ◽  
Highly Nonlinear ◽  
2D And 3D

Slamming forces on 2D and 3D bodies have been computed based on a CIP method. The highly nonlinear water entry problem governed by the Navier-Stokes equations was solved by a CIP based finite difference method on a fixed Cartesian grid. In the computation, a compact upwind scheme was employed for the advection calculations and a pressure-based algorithm was applied to treat the multiple phases. The free surface and the body boundaries were captured using density functions. For the pressure calculation, a Poisson-type equation was solved at each time step by the conjugate gradient iterative method. Validation studies were carried out for 2D wedges with various deadrise angles ranging from 0 to 60 degrees at constant vertical velocity. In the cases of wedges with small deadrise angles, the compressibility of air between the bottom of the wedge and the free surface was modelled. Studies were also extended to 3D bodies, such as a sphere, a cylinder and a catamaran, entering calm water. Computed pressures, free surface elevations and hydrodynamic forces were compared with experimental data and the numerical solutions by other methods.

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.

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