scholarly journals Conformal Invariance of Characteristic Lines in a Class of Hydrodynamic Models

Symmetry ◽  
2020 ◽  
Vol 12 (9) ◽  
pp. 1482
Author(s):  
Marta Wacławczyk ◽  
Vladimir N. Grebenev ◽  
Martin Oberlack
Keyword(s):  
Conformal Invariance ◽  
Large Scale ◽  
Conformal Group ◽  
Navier Stokes ◽  
Hydrodynamic Models ◽  
Navier Stokes Equation ◽  
Molecular Diffusivity ◽  
Characteristic Lines ◽  
The One ◽  
Zero Viscosity

This paper addresses the problem of the existence of conformal invariance in a class of hydrodynamic models. For this we analyse an underlying transport equation for the one-point probability density function, subject to zero-scalar constraint. We account for the presence of non-zero viscosity and large-scale friction. It is shown analytically, that zero-scalar characteristics of this equation are invariant under conformal transformations in the presence of large-scale friction. However, the non-zero molecular diffusivity breaks the conformal group (CG). This connects our study with previous observations where CG invariance of zero-vorticity isolines of the 2D Navier–Stokes equation was analysed numerically and confirmed only for large scales in the inverse energy cascade. In this paper, an example of CG is analysed and possible interpretations of the analytical results are discussed.

Coriolis force influence on the AKA effect

2021 ◽  
Author(s):  
Peter Rutkevich ◽  
Georgy Golitsyn ◽  
Anatoly Tur
Keyword(s):  
Steady State ◽  
Stokes Equation ◽  
Nonlinear Equations ◽  
Coriolis Force ◽  
Large Scale ◽  
Fluid Velocity ◽  
Navier Stokes ◽  
Basic Solution ◽  
Navier Stokes Equation ◽  
Alpha Effect

<p>Large-scale instability in incompressible fluid driven by the so called Anisotropic Kinetic Alpha (AKA) effect satisfying the incompressible Navier-Stokes equation with Coriolis force is considered. The external force is periodic; this allows applying an unusual for turbulence calculations mathematical method developed by Frisch et al [1]. The method provides the orders for nonlinear equations and obtaining large scale equations from the corresponding secular relations that appear at different orders of expansions. This method allows obtaining not only corrections to the basic solutions of the linear problem but also provides the large-scale solution of the nonlinear equations with the amplitude exceeding that of the basic solution. The fluid velocity is obtained by numerical integration of the large-scale equations. The solution without the Coriolis force leads to constant velocities at the steady-state, which agrees with the full solution of the Navier-Stokes equation reported previously. The time-invariant solution contains three families of solutions, however, only one of these families contains stable solutions. The final values of the steady-state fluid velocity are determined by the initial conditions. After account of the Coriolis force the solutions become periodic in time and the family of solutions collapses to a unique solution. On the other hand, even with the Coriolis force the fluid motion remains two-dimensional in space and depends on a single spatial variable. The latter fact limits the scope of the AKA method to applications with pronounced 2D nature. In application to 3D models the method must be used with caution.</p><p>[1] U. Frisch, Z.S. She and P. L. Sulem, “Large-Scale Flow Driven by the Anisotropic Kinetic Alpha Effect,” Physica D, Vol. 28, No. 3, 1987, pp. 382-392.</p>

Pumping Speed Measurement of the Rotary Vane Vacuum Pump by Using Numerical and Experimental Approaches

2014 ◽  
Author(s):  
M. Nadeem Azam ◽  
M. Umar ◽  
M. Maqsood ◽  
Imran Akhtar ◽  
Imran Aziz
Keyword(s):  
Internal Flow ◽  
Vacuum Pump ◽  
Assessment System ◽  
Navier Stokes ◽  
Vane Pump ◽  
Navier Stokes Equation ◽  
Time Shape ◽  
Experimental Approaches ◽  
Computational Fluid Dynamics Cfd ◽  
The One

Pumping speed is the main performance parameter of a vacuum pump. In the present work, pumping speed for a three-vane rotary vacuum pump is quantified using both experimental and numerical approaches. The numerical methodology assumes continuum flow (Knudsen number < 0.1), thus allowing the use of Navier Stokes equation. Commercial computational fluid dynamics (CFD) solver i.e. Fluent, is used to discretize the governing equations. Moving / dynamic mesh technique is used for the internal flow volumes of the pump to reproduce the change-in-time shape. Complete process starting from the CAD modeling to CFD simulations is discussed in detail. The adopted approaches are generic and can be used to find the pumping speed of any other rotary vane vacuum pump. The vane pump is also tested using an assessment system, which is constructed according to DIN28432 standard. Results of experimentally measured pumping speed are in good agreement with the one computed numerically.

scholarly journals Simple parametrization methods for generating Adomian polynomials

2016 ◽  
Vol 10 (1) ◽  
pp. 168-185 ◽  
Author(s):  
K.K. Kataria ◽  
P. Vellaisamy
Keyword(s):  
Explicit Expression ◽  
Stokes Equation ◽  
Navier Stokes ◽  
Navier Stokes Equation ◽  
Nonlinear Operators ◽  
Adomian Polynomials ◽  
The One

In this paper, we discuss two simple parametrization methods for calculating Adomian polynomials for several nonlinear operators, which utilize the orthogonality of functions einx, where n is an integer. Some important properties of Adomian polynomials are also discussed and illustrated with examples. These methods require minimum computation, are easy to implement, and are extended to multivariable case also. Examples of different forms of nonlinearity, which includes the one involved in the Navier Stokes equation, is considered. Explicit expression for the n-th order Adomian polynomials are obtained in most of the examples.

The Local Analytic Numerical Method for the Double Vortex Combustor Flow

1985 ◽  
Author(s):  
J. He ◽  
B. Q. Zhang
Keyword(s):  
Reynolds Number ◽  
Analytic Solutions ◽  
Navier Stokes ◽  
Hyperbolic Function ◽  
Navier Stokes Equation ◽  
One Dimensional ◽  
New Type ◽  
High Reynolds ◽  
The One ◽  
Coarse Grids

A new hyperbolic function discretization equation for two dimensional Navier-Stokes equation in the stream function vorticity from is derived. The basic idea of this method is to integrat the total flux of the general variable ϕ in the differential equations, then incorporate the local analytic solutions in hyperbolic function for the one-dimensional linearized transport equation. The hyperbolic discretization (HD) scheme can more accurately represent the conservation and transport properties of the governing equation. The method is tested in a range of Reynolds number (Re=100~2000) using the viscous incompressible flow in a square cavity. It is proved that the HD scheme is stable for moderately high Reynolds number and accurate even for coarse grids. After some proper extension, the method is applied to predict the flow field in a new type combustor with air blast double-vortex and obtained some useful results.

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