Nonstationary motion of a shell on the surface of a heavy fluid

2009 ◽  
Vol 50 (4) ◽  
pp. 599-606
Author(s):  
Yu. F. Orlov ◽  
A. S. Suvorov
Keyword(s):  
Heavy Fluid ◽  
Nonstationary Motion

scholarly journals An experimental investigation of convection in a fluid that exhibits phase change

1981 ◽  
Vol 102 ◽  
pp. 85-100 ◽  
Author(s):  
D. E. Fitzjarrald
Keyword(s):  
Thin Layer ◽  
Phase Change ◽  
Latent Heat ◽  
Thermal Gradient ◽  
Lower Boundary ◽  
Working Fluid ◽  
Heavy Fluid ◽  
Convective Motions ◽  
Rayleigh Benard Convection ◽  
Rayleigh Benard

Convection flows have been systematically observed in a layer of fluid between two isothermal horizontal boundaries. The working fluid was a nematic liquid crystal, which exhibits a liquid–liquid phase change at which latent heat is released and the density changed. In addition to ordinary Rayleigh–Bénard convection when either phase is present alone, there exist two distinct types of convective motions initiated by the unstable density difference. When a thin layer of heavy fluid is present near the top boundary, hexagons with downgoing centres exist with no imposed thermal gradient. When a thin layer of light fluid is brought on near the lower boundary, the hexagons have upshooting centres. In both cases, the motions are kept going once they are initiated by the instability due to release of latent heat. Relation of the results to applicable theories is discussed.

Asymptotic stability of a polar vortex perturbed by harmonic waves describing atmospheric gravity waves circulating in an equatorial plane of a spherical planet

2018 ◽  
Vol 13 (4) ◽  
pp. 36
Author(s):  
Ranis Ibragimov ◽  
Pirooz Mohazzabi ◽  
Rebecca Roembke ◽  
Justin Van Ee
Keyword(s):  
Shallow Water ◽  
Gravity Waves ◽  
Equatorial Plane ◽  
Polar Vortex ◽  
Water Model ◽  
Large Radius ◽  
Atmospheric Gravity Waves ◽  
Nonstationary Motion ◽  
Two Parameters ◽  
Atmospheric Gravity

We examine stability of the vortex that represents one particular class of exact solution of a a nonlinear shallow water model describing atmospheric gravity waves circulating in an equatorial plane of a spherical planet. The mathematical model is represented by a two-dimensional free boundary Cauchy–Poisson problem on the nonstationary motion of a perfect uid around a solid circle with a sufficiently large radius so that the gravity is directed to the center of the circle. It is shown that the model admits two functionally independent nonlinear systems of shallow water equations. Two essential parameters that control stability of the vortex for both systems are identified. The order of their importance is analyzed and it is shown that one of the systems is more resistant to small perturbations and remains stable for larger range of these two parameters.

scholarly journals A MATHEMATICAL MODEL OF NONSTATIONARY MOTION OF A VISCOELASTIC FLUID IN ROLLER BEARINGS

2019 ◽  
Vol 81 (4) ◽  
pp. 501-512
Author(s):  
I.A. Zhurba Eremeeva ◽  
D. Scerrato ◽  
C. Cardillo ◽  
A. Tran
Keyword(s):  
Mathematical Model ◽  
Viscoelastic Fluid ◽  
Viscoelastic Properties ◽  
Fluid Model ◽  
Maxwell Fluid ◽  
Initial Boundary ◽  
Deborah Number ◽  
Nonstationary Motion ◽  
Friction Forces ◽  
Roller Bearings

Nowadays, the emergence of new lubricants requires an enhancement of the rheological models and methods used for solution of corresponding initial boundary-value problems. In particular, models that take into account viscoelastic properties are of great interest. In the present paper we consider the mathematical model of nonstationary motion of a viscoelastic fluid in roller bearings. We used the Maxwell fluid model for the modeling of fluid properties. The viscoelastic properties are exhibited by many lubricants that use polymer additives. In addition, viscoelastic properties can be essential at high fluid speeds. Also, viscoelastic properties can be significant in the case of thin gaps. Maxwell's model is one of the most common models of viscoelastic materials. It combines the relative simplicity of constitutive equations with the ability to describe a stress relaxation. In addition, viscoelastic fluids also allow us to describe some effects that are missing in the case of viscous fluid. An example it is worth to mention the Weissenberg effect and a number of others. In particular, such effects can be used to increase the efficiency of the film carrier in the sliding bearings. Here we introduced characteristic assumptions on the form of the flow, allowing to significantly simplify the solution of the problem. We consider so-called self-similar solutions, which allows us to get a solution in an analytical form. As a result these assumptions, the formulae for pressure and friction forces are derived. Their dependency on time and Deborah number is analyzed. The limiting values of the flow characteristics were obtained. The latter can be used for steady state of the flow regime. Differences from the case of Newtonian fluid are discussed. It is shown that viscoelastic properties are most evident at the initial stage of flow, when the effects of non-stationarity are most important.

Forces Exerted on a Hovercraft by a Moving Pressure Distribution: Robustness of Mathematical Models

2006 ◽  
Vol 50 (01) ◽  
pp. 38-48 ◽  
Author(s):  
Gregory Zilman
Keyword(s):  
Free Surface ◽  
Mathematical Models ◽  
Pressure Distribution ◽  
Constant Pressure ◽  
Wave Resistance ◽  
Excess Pressure ◽  
Physical Parameters ◽  
Rectangular Region ◽  
Heavy Fluid ◽  
Side Force

The wave resistance, side force, and yawing moment acting on a hovercraft moving on the free surface of a heavy fluid is studied. The hovercraft is represented by a distributed excess pressure. Various types of pressure and bounding contours are considered. The sensitivity of the results to numerous uncertainties in the problem's physical parameters is investigated. It is found that constant pressure over a rectangular region moving with an angle of drift results in peculiar side force values. Several robust mathematical models of a moving hovercraft are proposed and analyzed.

Statistical characteristics of turbulent mixing in spherical and cylindrical converging Richtmyer–Meshkov instabilities

2021 ◽  
Vol 928 ◽  
Author(s):  
Xinliang Li ◽  
Yaowei Fu ◽  
Changping Yu ◽  
Li Li
Keyword(s):  
Turbulent Mixing ◽  
Initial Perturbation ◽  
Great Influence ◽  
Mixing Layers ◽  
Statistical Characteristics ◽  
Computational Domain ◽  
Heavy Fluid ◽  
Node Number ◽  
Geometric Effect ◽  
Atwood Number

In this paper, the Richtmyer–Meshkov instabilities in spherical and cylindrical converging geometries with a Mach number of approximately 1.5 are investigated by using the high resolution implicit large eddy simulation method, and the influence of the geometric effect on the turbulent mixing is investigated. The heavy fluid is sulphur hexafluoride (SF6), and the light fluid is nitrogen (N2). The shock wave converges from the heavy fluid into the light fluid. The Atwood number is 0.678. The total structured and uniform Cartesian grid node number in the main computational domain is 20483. In addition, to avoid the influence of boundary reflection, a sufficiently long sponge layer with 50 non-uniform coarse grids is added for each non-periodic boundary. Present numerical simulations have high and nonlinear initial perturbation levels, which rapidly lead to turbulent mixing in the mixing layers. Firstly, some physical-variable mean profiles, including mass fraction, Taylor Reynolds number, turbulent kinetic energy, enstrophy and helicity, are provided. Second, the mixing characteristics in the spherical and cylindrical turbulent mixing layers are investigated, such as molecular mixing fraction, efficiency Atwood number, turbulent mass-flux velocity and density self-correlation. Then, Reynolds stress and anisotropy are also investigated. Finally, the radial velocity, velocity divergence and enstrophy in the spherical and cylindrical turbulent mixing layers are studied using the method of conditional statistical analysis. Present numerical results show that the geometric effect has a great influence on the converging Richtmyer–Meshkov instability mixing layers.

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