scholarly journals STUDY OF SELF-SUPERPOSABLE LIQUID IN OBLATE SPHEROIDAL SHAPE

2021 ◽  
Vol 9 (11) ◽  
pp. 683-690
Author(s):  
Rajeev Mishra ◽  
◽  
Sanjai Misra ◽  
Keyword(s):  
Fluid Dynamics ◽  
Boundary Conditions ◽  
Incompressible Fluid ◽  
Pressure Distribution ◽  
Oblate Spheroidal ◽  
Spheroidal Shape ◽  
Basic Equations ◽  
Spheroidal Coordinates

The paper studiesthe self-superposable motion of a liquid of a fluid which is incompressible in nature in oblate spheroidal shape. An incompressible fluid is defined as the fluid whose volume or density does not change with pressure. Thus, the main aim of this paper is to solve the basic equations of fluid dynamics in oblate spheroidal coordinates considering self-superposable nature of the fluid. The paper includes the study of nature of vorticity and irrotationality and has not considered the boundary conditions in theanalysis. Lastly, the paper determines the pressure distribution and the solutions contain a set of constants.

scholarly journals STUDY OF SELF-SUPERPOSABLE FLUID MOTIONS IN CONFOCAL PARABOLOIDAL DUCTS

2021 ◽  
Vol 9 (12) ◽  
pp. 725-732
Author(s):  
Rajeev Mishra
Keyword(s):  
Fluid Dynamics ◽  
Fluid Flow ◽  
Boundary Conditions ◽  
Incompressible Fluid ◽  
Pressure Distribution ◽  
Basic Equations

In this paper, studies have been made on some self-superposable motion of incompressible fluid is confocal Paraboloidal ducts. The boundary conditions have been neglected therefore the solutions contain a set of constants. Pressure distribution and the nature of vorticity are discussed. Tendency of irrotationality of the fluid flow is also determined. The aim of the paper is to introduce a method for solving the basic equations of fluid dynamics in confocal paraboloidal coordinates by using the property of self superposability.

scholarly journals GENERATING ANISOTROPIC FLUIDS FROM VACUUM ERNST EQUATIONS

2010 ◽  
Vol 19 (11) ◽  
pp. 1783-1795 ◽  
Author(s):  
STEFANO VIAGGIU
Keyword(s):  
Momentum Tensor ◽  
Energy Conditions ◽  
Coordinate Systems ◽  
Field Equations ◽  
Oblate Spheroidal ◽  
Basic Equations ◽  
Ernst Equations ◽  
Vacuum Solutions ◽  
Anisotropic Fluids ◽  
Spheroidal Coordinates

Starting with any stationary axisymmetric vacuum metric, we build anisotropic fluids. With the help of the Ernst method, the basic equations are derived together with the expression for the energy–momentum tensor and with the equation of state compatible with the field equations. The method is presented by using different coordinate systems: the cylindrical coordinates ρ, z and the oblate spheroidal ones. A class of interior solutions matching with stationary axisymmetric asymptotically flat vacuum solutions is found in oblate spheroidal coordinates. The solutions presented satisfy the three energy conditions.

scholarly journals A Simple Transient Poiseuille-Based Approach to Mimic the Womersley Function and to Model Pulsatile Blood Flow

Dynamics ◽  
2021 ◽  
Vol 1 (1) ◽  
pp. 9-17
Author(s):  
Andrea Natale Impiombato ◽  
Giorgio La Civita ◽  
Francesco Orlandi ◽  
Flavia Schwarz Franceschini Zinani ◽  
Luiz Alberto Oliveira Rocha ◽  
...  
Keyword(s):  
Fluid Dynamics ◽  
Computational Fluid Dynamics ◽  
Blood Flow ◽  
Boundary Conditions ◽  
Quadratic Function ◽  
Pulsatile Blood Flow ◽  
Flow Through ◽  
Simplified Analysis ◽  
Function Models ◽  
Flow Reversals

As it is known, the Womersley function models velocity as a function of radius and time. It has been widely used to simulate the pulsatile blood flow through circular ducts. In this context, the present study is focused on the introduction of a simple function as an approximation of the Womersley function in order to evaluate its accuracy. This approximation consists of a simple quadratic function, suitable to be implemented in most commercial and non-commercial computational fluid dynamics codes, without the aid of external mathematical libraries. The Womersley function and the new function have been implemented here as boundary conditions in OpenFOAM ESI software (v.1906). The discrepancy between the obtained results proved to be within 0.7%, which fully validates the calculation approach implemented here. This approach is valid when a simplified analysis of the system is pointed out, in which flow reversals are not contemplated.

Torsional oscillation of a homogeneous elastic spheroid

1962 ◽  
Vol 52 (3) ◽  
pp. 469-484 ◽  
Author(s):  
Tatsuo Usami ◽  
Yasuo Satô
Keyword(s):  
Fundamental Mode ◽  
Free Oscillation ◽  
Torsional Oscillation ◽  
Numerical Calculations ◽  
Higher Harmonics ◽  
Oblate Spheroidal ◽  
The Earth ◽  
Spectral Peaks ◽  
The Difference ◽  
Spheroidal Coordinates

abstract There are several causes for the observations of splitting of the spectral peaks determined from the free oscillation of the earth. In this paper, the splitting due to the ellipticity is studied assuming a homogeneous earth described by oblate spheroidal coordinates. Ellipticity causes the iTn mode to split into (n + 1) modes, while the earth's rotation causes it to split into (2n + 1) modes. 1/297.0 is adopted as the ellipticity of the earth. Numerical calculations are carried out for the fundamental mode (n = 2, 3, 4) and for the first higher harmonics (n = 1). The difference between the extreme frequencies for each value of n is 0.7% (n = 2), 0.5% (n = 3), and 0.4% (n = 4).

scholarly journals Journal Bearing: An Integrated CFD-Analytical Approach for the Estimation of the Trajectory and Equilibrium Position

2020 ◽  
Vol 10 (23) ◽  
pp. 8573
Author(s):  
Franco Concli
Keyword(s):  
Fluid Dynamics ◽  
Computational Fluid Dynamics ◽  
Pressure Distribution ◽  
Equilibrium Position ◽  
Analytical Approach ◽  
Journal Bearing ◽  
Cfd Model ◽  
Cavitation Model ◽  
Computational Fluid Dynamics Cfd ◽  
The Mathematical Model

For decades, journal bearings have been designed based on the half-Sommerfeld equations. The semi-analytical solution of the conservation equations for mass and momentum leads to the pressure distribution along the journal. However, this approach admits negative values for the pressure, phenomenon without experimental evidence. To overcome this, negative values of the pressure are artificially substituted with the vaporization pressure. This hypothesis leads to reasonable results, even if for a deeper understanding of the physics behind the lubrication and the supporting effects, cavitation should be considered and included in the mathematical model. In a previous paper, the author has already shown the capability of computational fluid dynamics to accurately reproduce the experimental evidences including the Kunz cavitation model in the calculations. The computational fluid dynamics (CFD) results were compared in terms of pressure distribution with experimental data coming from different configurations. The CFD model was coupled with an analytical approach in order to calculate the equilibrium position and the trajectory of the journal. Specifically, the approach was used to study a bearing that was designed to operate within tight tolerances and speeds up to almost 30,000 rpm for operation in a gearbox.

scholarly journals Basic Solutions of Three Dimensional Elasticity

2021 ◽  
Vol 236 ◽  
pp. 05039
Author(s):  
Wx Zhang
Keyword(s):  
Boundary Conditions ◽  
Three Dimensional ◽  
Practical Calculation ◽  
Basic Solution ◽  
Final Solution ◽  
Theoretical Derivation ◽  
Basic Solutions ◽  
Special Solutions ◽  
Basic Equations ◽  
Three Dimensional Elasticity

Elastic calculation method is an important research content of computational mechanics. The problems of elasticity include basic equations and boundary conditions. Therefore, the final solution consists of the general solutions of the basic equations and the special solutions satisfying the boundary conditions. Numerical method is often used in practical calculation, but the analytical solution is also an important subject for researchers. In this paper, the basic solution of three-dimensional elastic materials is given by theoretical derivation.

Unsteady Peristaltic Pumping in a Finite Length Tube With Permeable Wall

2010 ◽  
Vol 132 (10) ◽  
Author(s):  
Y. V. K. Ravi Kumar ◽  
S. V. H. N. Krishna Kumari.P ◽  
M. V. Ramana Murthy ◽  
S. Sreenadh
Keyword(s):  
Reynolds Number ◽  
Boundary Conditions ◽  
Incompressible Fluid ◽  
Finite Length ◽  
Pressure Profile ◽  
Peristaltic Transport ◽  
Permeable Wall ◽  
Sinusoidal Wave ◽  
Peristaltic Pumping ◽  
Wall Permeability

Peristaltic transport due to a sinusoidal wave traveling on the boundary of a tube filled with an incompressible fluid is presented. Solution is obtained under infinite wavelength and zero Reynolds number in a finite length tube which extends the study of Li and Brasseur (1993, “Non-Steady Peristaltic Transport in Finite-Length Tubes,” J. Fluid Mech., 248, pp. 129–151). Boundary conditions are changed to include wall permeability. Analysis of pressure profile is described.

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