scholarly journals Singularities in a two-fluid medium

1983 ◽  
Vol 6 (4) ◽  
pp. 737-754 ◽  
Author(s):  
Rathindra Nath Chakrabarti ◽  
Birendranath Mandal
Keyword(s):  
Horizontal Plane ◽  
Plane Surface ◽  
Finite Depth ◽  
Point Singularity ◽  
Fluid Medium ◽  
Two Fluids ◽  
Line Singularity ◽  
Lower Fluid ◽  
Irrotational Motion ◽  
Two Fluid

We compute the irrotational motion of two fluids with a horizontal plane surface of separation, under gravity. The fluids are nonviscous and incompressible, the upper one of finite depth with a free surface; they contain a line singularity or a point singularity. We obtain the velocity potentials for each singularity located in the upper or the lower fluid; if the upper depth tends to infinity, known results are recovered.

Forced gravity waves in two-layered fluids with the upper fluid having a free surface

2003 ◽  
Vol 81 (4) ◽  
pp. 675-689 ◽  
Author(s):  
H H Sherief ◽  
M S Faltas ◽  
E I Saad
Keyword(s):  
Free Surface ◽  
Wave Motion ◽  
Harmonic Wave ◽  
Density Ratio ◽  
Finite Depth ◽  
Reflection And Transmission ◽  
Transmission Coefficients ◽  
Two Fluids ◽  
Lower Fluid ◽  
Wave Maker

The steady-gravity wave motion is considered for two immiscible layers of incompressible and nonviscous fluids in the presence of a porous wave maker immersed vertically in the two fluids, the upper fluid having a free surface and the lower fluid is of infinite depth. The boundary value problem for the velocity potentials is solved using Taylor's assumption on the wave maker. Also the scattering of a harmonic wave incident normally to the wave maker is considered and the reflection and transmission coefficients are obtained. The case when the lower fluid is of finite depth is also considered. The results are plotted for different values of porosity and different values of the density ratio. PACS Nos.: 47.35.+i, 47.55.Hd, 47.55.Mh

scholarly journals Ring source potentials in two superposed fluids separeted by an inertial surface

1988 ◽  
Vol 11 (3) ◽  
pp. 535-541
Author(s):  
B. N. Mandal ◽  
Krishna Kundu
Keyword(s):  
Time Dependent ◽  
Body Of Revolution ◽  
Fluid Medium ◽  
Two Fluids ◽  
Inertial Surface ◽  
Superposed Fluids ◽  
Two Fluid ◽  
Ring Source

The study of waves at the interface of two superposed fluids due to the presence of a vertical body of revolution requires the consideration of potentials due to horizontal ring sources submerged in one of the fluids. In this paper, the velocity potentials in the two fluids are computed due to a horizontal ring of sources of time-dependent strength submerged in either of the fluids of a two-fluid medium that are separated by an inertial surface.

scholarly journals Two-dimensional source potentials in a two-fluid medium for the modified Helmholtz's equation

1986 ◽  
Vol 9 (1) ◽  
pp. 175-184 ◽  
Author(s):  
B. N. Mandal ◽  
R. N. Chakrabarti
Keyword(s):  
Line Source ◽  
Horizontal Plane ◽  
Incompressible Fluids ◽  
Vertical Line ◽  
Two Dimensional ◽  
Laplace’S Equation ◽  
Fluid Medium ◽  
Laplace's Equation ◽  
Time Harmonic ◽  
Two Fluid

Velocity potentials describing the irrotational infinitesimal motion of two superposed inviscid and incompressible fluids under gravity with a horizontal plane of mean surface of separation, are derived due to a vertical line source present in either of the fluids, whose strength, besides being harmonic in time, varies sinusiodally along its length. The technique of deriving the potentials here is an extension of the technique used for the case of only time harmonic vertical line source. The present case is concerned with the two-dimensional modified Helmholtz's equation while the previous is concerned with the two-dimensional Laplace's equation.

scholarly journals The sputtering temperature of a cooling cylindrical rod without and with an insulated core in a two-fluid medium

1996 ◽  
Vol 38 (1) ◽  
pp. 87-100 ◽  
Author(s):  
R. K. Bera ◽  
A. Chakrabarti
Keyword(s):  
Inner Core ◽  
Finite Depth ◽  
Numerical Results ◽  
Explicit Solutions ◽  
Fluid Medium ◽  
Temperature Distributions ◽  
Infinite Extent ◽  
Special Circumstances ◽  
Two Fluid

AbstractUtilising Jones' method associated with the Wiener-Hopf technique, explicit solutions are obtained for the temperature distributions on the surface of a cylindrical rod without an insulated core as well as that inside a cylindrical rod with an insulated inner core when the rod, in either of the two cases, is allowed to enter, with a uniform speed, into two different layers of fluid with different cooling abilities. Simple expressions are derived for the values of the sputtering temperatures of the rod at the points of entry into the respective layers, assuming the upper layer of the fluid to be of finite depth and the lower of infinite extent. Both the problems are solved through a three-part Wiener-Hopf problem of special type and the numerical results under certain special circumstances are obtained and presented in tabular forms.

Cooling of a composite slab in a two-fluid medium

1991 ◽  
Vol 42 (6) ◽  
pp. 943-959 ◽  
Author(s):  
R. K. Bera ◽  
A. Chakrabarti
Keyword(s):  
Fluid Medium ◽  
Composite Slab ◽  
Two Fluid

scholarly journals Topology design of two-fluid heat exchange

2020 ◽  
Author(s):  
Hiroki Kobayashi ◽  
Kentaro Yaji ◽  
Shintaro Yamasaki ◽  
Kikuo Fujita
Keyword(s):  
Heat Transfer ◽  
Heat Exchange ◽  
Heat Transfer Rate ◽  
Design Variable ◽  
Pressure Loss ◽  
Transfer Rate ◽  
Maximum Heat ◽  
Variable Field ◽  
Two Fluids ◽  
Two Fluid

Abstract Heat exchangers are devices that typically transfer heat between two fluids. The performance of a heat exchanger such as heat transfer rate and pressure loss strongly depends on the flow regime in the heat transfer system. In this paper, we present a density-based topology optimization method for a two-fluid heat exchange system, which achieves a maximum heat transfer rate under fixed pressure loss. We propose a representation model accounting for three states, i.e., two fluids and a solid wall between the two fluids, by using a single design variable field. The key aspect of the proposed model is that mixing of the two fluids can be essentially prevented. This is because the solid constantly exists between the two fluids due to the use of the single design variable field. We demonstrate the effectiveness of the proposed method through three-dimensional numerical examples in which an optimized design is compared with a simple reference design, and the effects of design conditions (i.e., Reynolds number, Prandtl number, design domain size, and flow arrangements) are investigated.

scholarly journals Simulation of Free Surface Compressible Flows via a Two Fluid Model

2008 ◽  
Author(s):  
Fre´de´ric Dias ◽  
Denys Dutykh ◽  
Jean-Michel Ghidaglia
Keyword(s):  
Free Surface ◽  
Wave Breaking ◽  
Compressible Flows ◽  
Fluid Model ◽  
Three Dimensional ◽  
Two Fluids ◽  
Equation Of States ◽  
Two Fluid Model ◽  
Velocity Pressure ◽  
Two Fluid

The purpose of this communication is to discuss the simulation of a free surface compressible flow between two fluids, typically air and water. We use a two fluid model with the same velocity, pressure and temperature for both phases. In such a numerical model, the free surface becomes a thin three dimensional zone. The present method has at least three advantages: (i) the free-surface treatment is completely implicit; (ii) it can naturally handle wave breaking and other topological changes in the flow; (iii) one can easily vary the Equation of States (EOS) of each fluid (in principle, one can even consider tabulated EOS). Moreover, our model is unconditionally hyperbolic for reasonable EOS.

scholarly journals Global Existence and Asymptotic Behavior of Solutions for Compressible Two-Fluid Euler–Maxwell Equation

2020 ◽  
Vol 2020 ◽  
pp. 1-27
Author(s):  
Ismahan Binshati ◽  
Harumi Hattori
Keyword(s):  
Asymptotic Behavior ◽  
Fourier Transform ◽  
Global Existence ◽  
Maxwell Equations ◽  
Decay Rates ◽  
Asymptotic Behavior Of Solutions ◽  
Two Fluids ◽  
The Fourier Transform ◽  
Rates Of Decay ◽  
Two Fluid

We study the global existence and asymptotic behavior of the solutions for two-fluid compressible isentropic Euler–Maxwell equations by the Fourier transform and energy method. We discuss the case when the pressure for two fluids is not identical, and we also add friction between the two fluids. In addition, we discuss the rates of decay of Lp−Lq norms for a linear system. Moreover, we use the result for Lp−Lq estimates to prove the decay rates for the nonlinear systems.

scholarly journals On-wall and interior separation in a two-fluid boundary layer

2019 ◽  
Vol 119 (1) ◽  
pp. 1-21
Author(s):  
Sergei N. Timoshin ◽  
Pallu Thapa
Keyword(s):  
Boundary Layer ◽  
Pressure Variation ◽  
Flow Reversal ◽  
Reversed Flow ◽  
Two Fluids ◽  
Transverse Pressure ◽  
Fluid Boundary ◽  
Interior Flow ◽  
High Reynolds ◽  
Two Fluid

Abstract A two-fluid boundary layer is considered in the context of a high Reynolds number Poiseuille–Couette channel flow encountering an elongated shallow obstacle. The flow is laminar, steady and two-dimensional, with the boundary layer shown to have the pressure unknown in advance and a specified displacement (a condensed boundary layer). The focus is on the detail of the flow reversal triggered by the obstacle. The interface between the two fluids passes through the boundary layer which, in conjunction with the effects of gravity and distinct densities in the two fluids, leads to several possible topologies of the reversed flow, including a conventional on-wall separation, interior flow reversal above the interface, and several combinations of the two. The effect of upstream influence due to a transverse pressure variation under gravity is mentioned briefly.

Two-Fluid Flow Between Rotating Annular Disks

1976 ◽  
Vol 98 (2) ◽  
pp. 214-222 ◽  
Author(s):  
J. E. Zweig ◽  
H. J. Sneck
Keyword(s):  
Annular Flow ◽  
Stokes Equations ◽  
Fluid Flows ◽  
Reynolds Numbers ◽  
Navier Stokes ◽  
Navier Stokes Equations ◽  
Two Fluids ◽  
Small Clearance ◽  
Annular Disks ◽  
Two Fluid

The general hydrodynamic behavior at small clearance Reynolds numbers of two fluids of different density and viscosity occupying the finite annular space between a rotating and stationary disk is explored using a simplified version of the Navier-Stokes equations which retains only the centrifugal force portion of the inertia terms. A criterion for selecting the annular flow fields that are compatible with physical reservoirs is established and then used to determine the conditions under which two-fluid flows in the annulus might be expected for specific fluid combinations.

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