Viscous Potential Research Articles

Rayleigh–Taylor instability for thin viscous gas films: Application to critical heat flux and minimum film boiling

A number of hydrodynamic models for critical heat flux and minimum film boiling rely on interfacial instability theories. Rayleigh–Taylor instability is one of the important theories, and has been usually analyzed for inviscid flows. An inviscid flow analysis is acceptable for general circumstances. However, when the gas film becomes thin to the extent of creeping flow, the viscous force is dominant over the inertia force, and thus the gas viscosity cannot be neglected. In this study, four approaches are considered for Rayleigh–Taylor instability: (1) classical inviscid flow analysis, (2) viscous potential flow analysis, (3) fully viscous flow analysis, and (4) lubrication theory. In particular, the dispersion relation including phase change is derived based on the lubrication approximation. It is shown that the most dangerous wavelength should be λd=2π[2σ/(Δρg)]1/2 instead of λd=2π[3σ/(Δρg)]1/2 for thin viscous gas film. This result is applied to the existing critical heat flux models for saturated pool boiling on horizontal surfaces. As a result, the prediction accuracy is improved at elevated pressures. In addition, the most dangerous wavelength and the most rapid growth rate for viscous thin films are shown to be applicable to the minimum heat flux condition.

A nonoverlapping heterogeneous domain decomposition method for three-dimensional gravity wave impact problems

A 3D heterogeneous flow model which combines incompressible viscous flow and potential flow both with free-surface boundaries is developed and solved numerically, using finite element method and boundary element method, respectively. The coupled model is solved based on a nonoverlapping domain decomposition method, which reduces the problem to the coupling interface. At the interface, the problem is equivalent to Bernoulli’s equation consisting of mappings from potential/velocity to velocity/pressure. These mappings enable us to design the scheme following the Dirichlet–Neumann method for nonoverlapping domain decomposition, and lead to a staggered scheme. We also discuss data transfer as well as free surface reconstruction at the interface. Errors introduced by the surface reconstruction technique are examined and discussed in detail. The errors from the first-order staggered scheme is also studied. A comparison of numerical prediction with experimental data that the proposed method performs efficiently and accurately for wave impact problems.

Kelvin-Helmholtz instability with mass transfer through porous media: Effect of irrotational viscous pressure

This paper studies the effect of the irrotational viscous pressure on Kelvin-Helmholtz instability of the plane interface of two viscous and incompressible fluids in a fully saturated porous media with mass and heat transfers across the interface. In the earlier work, the instability of the plane interface of two viscous and streaming miscible fluids through porous media was studied by assuming that the motion and the pressure are irrotational and the viscosity enters the normal stress balance. This theory is called the viscous potential flow theory. Here, we use another irrotational theory in which the discontinuities in the irrotational tangential velocity and shear stress are eliminated in the global energy balance by considering viscous contributions of the irrotational pressure. The Darcy-Brinkman model is used in the investigation and the stability criterion is formulated in terms of a critical value of the relative velocity. It is observed that the heat and mass transfer has a destabilizing effect on the stability of the system while the irrotational shearing stresses stabilize the system.

Viscous correction for the viscous potential flow analysis of Kelvin–Helmholtz instability of cylindrical flow with heat and mass transfer

We study the linear Kelvin–Helmholtz instability of the interface between two viscous and incompressible fluids, when the phases are enclosed between two horizontal cylindrical surfaces coaxial with the interface in presence of mass and heat transfer across the interface. Here we use an irrotational theory known as viscous correction for the viscous potential flow theory; in which the discontinuities in the irrotational tangential velocity and shear stress are eliminated in the global energy balance by taking viscous contributions to the irrotational pressure. Both asymmetric and axisymmetric disturbances have been studied and stability criterion is given in terms of a critical value of relative velocity. It has been shown that the irrotational viscous flow with viscous correction gives rise to exactly the same dispersion relation as obtained by the dissipation method in which the viscous effect is accounted for by evaluating viscous dissipation using the irrotational flow. It has been observed that heat and mass transfer has destabilizing effect while irrotational shearing stresses stabilize the system.

STUDY ON ELECTROHYDRODYNAMIC CAPILLARY INSTABILITY OF VISCOELASTIC FLUIDS WITH RADIAL ELECTRIC FIELD

We study the linear analysis of electrohydrodynamic capillary instability of the interface between a viscous fluid and viscoelastic fluid of Maxwell type, when the phases are enclosed between two horizontal cylindrical surfaces coaxial with the interface, and when fluids are subjected to the radial electric field. Here, we use an irrotational theory known as viscous potential flow (VPF) theory in which viscosity enters through normal stress balance but shearing stresses are assumed to be zero. A quadratic dispersion relation that accounts for the growth of axisymmetric waves is obtained and stability criterion is given in terms of a critical value of wave number as well as electric field. It is observed that the radial electric field has dual effect on the stability of the system.

Nonlinear Electrohydrodynamic Kelvin-Helmholtz Instability through Two Porous Layers with Suction / Injection : Viscous Potential Theory

The nonlinear electrohydrodynamic Kelvin-Helmholtz instability of an interface between two porous layers with heat and mass transfer is investigated. The fluid flow is considered to be through semi permeable boundaries above and below at which the fluids may either be flows in or sucked out, in a direction normal to the main streaming direction. Through the linear stability analysis, a general dispersion relation is obtained. The Ginzburg–Landau equation is obtained by employing the method of multiple scale expansion according to the nonlinear stability theorem. The stability of the system is discussed and is presented graphically. It is found that the injection of the two fluids at both boundaries has a stabilizing effect in contrast with the suction at both boundaries. The stable and unstable regions in the nonlinear case are drawn and discussed. Keywords Nonlinear Kelvin-Helmholtz instability ; Viscous potential flow; Interfacial instability; Heat transfer ; Mass transfer; Flow through porous media; Electrohydrodynamic; Multiple scale methods; Suction/Injection.

A transversely isotropic visco-hyperelastic constitutive model for soft tissues

A transversely isotropic visco-hyperelastic constitutive model is provided for soft tissues, which accounts for large deformations, high strain rates, and short-term memory effects. In the first part, a constitutive model for quasi-static deformations of soft tissues is presented, in which a soft tissue is simulated as a transversely isotropic hyperelastic material composed of a matrix and reinforcing fibers. The strain energy density function for the soft tissue is additively decomposed into two terms: a neo-Hookean function for the base matrix, and a polyconvex polynomial function of four invariants for the fibers. A comparison with existing experimental data for porcine brain tissues and bovine pericardium shows that this new model can well represent the quasi-static mechanical behavior of soft tissues. In the second part, a viscous potential is proposed to describe the rate-dependent short-term memory effects, resulting in a visco-hyperelastic constitutive model. This model is tested for a range of strain rates from 0.1 /s to 90 /s and for multiple loading scenarios based on available experimental data for porcine and human brain tissues. The model can be applied to other soft tissues by using different values of material and fitting parameters.

Nonlinear Rayleigh–Taylor instability of cylindrical flow with mass transfer through porous media

The work discusses nonlinear Rayleigh–Taylor instability of the interface between two viscous, incompressible and thermally conducting fluids in a fully saturated porous medium, when the phases are enclosed between two horizontal cylindrical surfaces coaxial with the interface, and when there is mass and heat transfer across the interface. We use viscous potential flow theory in which the flow is assumed to be irrotational and viscosity enters through normal viscous stresses at the interface. The perturbation analysis, in the light of the multiple expansions in both space and time, leads to imposing the well-known Ginzburg–Landau equation. The various stability conditions are discussed both analytically and numerically. The results are displayed in many plots showing the stability criteria in various parameter planes. It is observed that heat and mass transfer has stabilizing effect on the stability of the considered system while medium porosity destabilizes the interface. The flow through porous media is more stable than the pure flow.

Nonlinear analysis of capillary instability with mass transfer through porous media

In this paper, we investigate the nonlinear capillary instability of the interface between two viscous, incompressible and thermally conducting fluids in a fully saturated porous medium, when the phases are enclosed between two horizontal cylindrical surfaces coaxial with the interface, and when there is mass and heat transfer across the interface. We use viscous potential flow theory in which the flow is assumed to be irrotational and viscosity enters through normal viscous stresses at the interface. The perturbation analysis, in the light of the multiple expansions, leads to imposing a first-order nonlinear partial differential equation. The various stability conditions are discussed both analytically and numerically. The results are displayed in many plots showing the stability criteria in various parameter planes. It is observed that the heat and mass transfer and porous medium both stabilize the interface while porosity supports the growth of disturbance waves.

Magnetoviscous potential flow analysis of Kelvin–Helmholtz instability with heat and mass transfer

A linear analysis of the Kelvin–Helmholtz instability of interface between two viscous and magnetic fluids has been carried out where there was heat and mass transfer across the interface while the fluids have been subjected to a constant magnetic field parallel to the streaming direction. The viscous potential flow theory has been used for the investigation. A dispersion relation has been obtained and a stability criterion is given by a critical value of relative velocity as well as the critical value of magnetic field. The resulting plots show the effect of various physical parameters such as wave number, viscosity ratio, ratio of magnetic permeabilities and heat transfer coefficient. It has been observed that heat and mass transfer has a destabilizing effect whereas the horizontal magnetic field stabilizes the system.

Electrohydrodynamic Kelvin–Helmholtz instability with heat and mass transfer: Effect of perpendicular electric field

In this paper, we investigate the effect of perpendicular electric field on the linear analysis of Kelvin–Helmholtz instability of a plane interface between two viscous and dielectric fluids, when the fluids are subjected to constant normal electric field and, when there is heat and mass transfer across the interface. We use viscous correction for the viscous potential flow theory in which the discontinuities in the irrotational tangential velocity and shear stress are eliminated in the global energy balance by taking viscous contributions to the irrotational pressure. A quadratic dispersion relation that accounts for the growth of disturbance waves is obtained and stability criterion is given in terms of a critical value of relative velocity as well as applied electric field. It is observed that heat transfer and perpendicular electric field both have destabilizing effect while vapor fraction stabilizes the interface.

Study on Electrohydrodynamic Rayleigh-Taylor Instability with Heat and Mass Transfer

The linear analysis of Rayleigh-Taylor instability of the interface between two viscous and dielectric fluids in the presence of a tangential electric field has been carried out when there is heat and mass transfer across the interface. In our earlier work, the viscous potential flow analysis of Rayleigh-Taylor instability in presence of tangential electric field was studied. Here, we use another irrotational theory in which the discontinuities in the irrotational tangential velocity and shear stress are eliminated in the global energy balance. Stability criterion is given by critical value of applied electric field as well as critical wave number. Various graphs have been drawn to show the effect of various physical parameters such as electric field, heat transfer coefficient, and vapour fraction on the stability of the system. It has been observed that heat transfer and electric field both have stabilizing effect on the stability of the system.

Viscous potential flow analysis of magnetohydrodynamic Rayleigh–Taylor instability with heat and mass transfer

The effect of tangential magnetic field on the linear analysis of Rayleigh–Taylor instability of two viscous, incompressible and electrically conducting fluids is studied when there is heat and mass transfer across the interface. We use an irrotational theory known as viscous potential flow theory; in which viscosity enters through normal stress balance but shearing stresses are assumed to be zero. A quadratic dispersion relation that accounts for the growth of disturbance waves is obtained and stability criterion is given in terms of a critical value of wave number as well as applied magnetic field. We observe that heat and mass transfer and magnetic field both stabilize the interface while vapour thickness has destabilizing effect.

A heterogeneous flow model based on DD method for free surface fluid–structure interaction problems

SUMMARYAn efficient heterogeneous flow model that combines incompressible viscous flow and potential flow(PF)(both) with free‐surface boundaries for fluid–structure interaction(FSI) problems was developed and solved numerically. In the model, the near field(viscous) fluid subdomain of the FSI simulation is described by the Navier–Stokes equations(NSE), whereas the far field(inviscid) subdomain is described by PF. This method is particularly suitable for modeling a large fluid domain while avoid solving the NSE at the far field, where the inviscid flow assumption is appropriate and adopting a simplified(e.g., PF) flow description reduces computing cost. Numerically, the NSE are solved using a FEM, and the PF is solved using a BEM. Free surface tracking is achieved through a hybrid level set method for the NSE and the mixed Eulerian–Lagrangian method for the PF. The coupling is based on a non‐overlapping DD method similar to the Dirichlet–Neumann method. At the interface between the two flow model subdomains, velocity and pressure are matched to ensure continuity of the corresponding variables at the common boundary. In this framework of the heterogeneous DD method, an explicit scheme is developed and implemented. The relation between this scheme and the classical Dirichlet–Neumann method for a homogeneous problem is revealed. Numerical examples demonstrating the capability of the method to model nonlinear wave phenomena and FSI problems with flexible structures are presented. Copyright © 2013 John Wiley & Sons, Ltd.

Electrohydrodynamic capillary instability with heat and mass transfer

We study the linear analysis of capillary instability of a cylindrical interface between two viscous and dielectric fluids, when the fluids are subjected to a constant axial electric field and, when there is heat and mass transfer across the interface. We use viscous correction for the viscous potential flow theory in which the discontinuities in the irrotational tangential velocity and shear stress are eliminated in the global energy balance by taking viscous contributions to the irrotational pressure. A quadratic dispersion relation that accounts for the growth of axisymmetric waves is obtained and stability criterion is given in terms of a critical value of wave number as well as electric field. It is observed that heat transfer and electric field both have stabilizing effect while vapor fraction has destabilizing effect on the stability of the system.

Viscous Potential Flow Analysis of Kelvin–Helmholtz Instability of a Cylindrical Flow with Heat and Mass Transfer

A linear analysis of Kelvin–Helmholtz instability of a cylindrical interface has been carried out when there is heat and mass transfer across the interface, using viscous potential flow theory. Both fluids are considered as incompressible, viscous, and thermally conducting with different kinematic viscosities. Both axisymmetric as well as asymmetric disturbances are considered. Stability criterion is given by a critical value of relative velocity and stability is discussed theoretically as well as numerically. Various graphs with respect to physical parameters such as wave number, viscosity ratio, heat transfer coefficients, Reynolds number, etc., have been drawn and the effect of various parameters have been described. A comparison with the linear stability analysis of inviscid fluids (Lee [10]) has been made and it is observed that viscosity has a stabilizing effect on the stability of the system. © 2013 Wiley Periodicals, Inc. Heat Trans Asian Res, 43(6): 489–503, 2014; Published online 3 October 2013 in Wiley Online Library (wileyonlinelibrary.com/journal/htj). DOI 10.1002/htj.21092

Kelvin-Helmholtz instability for flow in porous media under the influence of oblique magnetic fields: A viscous potential flow analysis

In this paper, the Kelvin-Helmholtz instability of viscous incompressible magnetic fluid fully saturated porous media is achieved through the viscous potential theory. The flow is considered to be through semi-permeable boundaries above and below the fluids through which the fluid may either be blown in or sucked out, in a direction normal to the main streaming direction of the fluid flow. An oblique magnetic field, mass, heat transfer, and surface tension are present across the interface. Through the linear stability analysis, a general dispersion relation is derived and the natural curves are plotted. Therefore, the linear stability condition is discussed in some depth. In view of the multiple time scale technique, the Ginzburg–Landau equation, which describes the behavior of the system in the nonlinear approach, is obtained. The effects of the orientation of the magnetic fields on the stability configuration in linear, as well as nonlinear approaches, are discussed. It is found that the Darcy's coefficient for the porous layers plays a stabilizing role. The injection of the fluids at both boundaries has a stabilizing effect, in contrast with the suction at both boundaries.

Added Mass and Aeroelastic Stability of a Flexible Plate Interacting With Mean Flow in a Confined Channel

This work presents a review and theoretical study of the added-mass and aeroelastic instability exhibited by a linear elastic plate immersed in a mean flow. We first present a combined added-mass result for the model problem with a mean incompressible and compressible flow interacting with an elastic plate. Using the Euler–Bernoulli model for the plate and a 2D viscous potential flow model, a generalized closed-form expression of added-mass force has been derived for a flexible plate oscillating in fluid. A new compressibility correction factor is introduced in the incompressible added-mass force to account for the compressibility effects. We present a formulation for predicting the critical velocity for the onset of flapping instability. Our proposed new formulation considers tension effects explicitly due to viscous shear stress along the fluid-structure interface. In general, the tension effects are stabilizing in nature and become critical in problems involving low mass ratios. We further study the effects of the mass ratio and channel height on the aeroelastic instability using the linear stability analysis. It is observed that the proximity of the wall parallel to the plate affects the growth rate of the instability, however, these effects are less significant in comparison to the mass ratio or the tension effects in defining the instability. Finally, we conclude this paper with the validation of the theoretical results with experimental data presented in the literature.

Study on Electrohydrodynamic Capillary Instability with Heat and Mass Transfer

The effect of an axial electric field on the capillary instability of a cylindrical interface in the presence of heat and mass transfer has been investigated using viscous potential flow theory. In viscous potential flow, the viscous term in Navier-Stokes equation vanishes as vorticity is zero but viscosity is not zero. Viscosity enters through normal stress balance in the viscous potential flow theory and tangential stresses are not considered. A dispersion relation that accounts for the growth of axisymmetric waves is derived and stability is discussed theoretically as well as numerically. Stability criterion is given by critical value of applied electric field as well as critical wave number. Various graphs have been drawn to show the effect of various physical parameters such as electric field, heat transfer capillary number, conductivity ratio, permittivity ratio on the stability of the system. It has been observed that the axial electric field and heat and mass transfer both have stabilizing effect on the stability of the system. Keywords—Capillary instability, Viscous potential flow, Heat and mass transfer, Axial electric field.

Study on magnetohydrodynamic Kelvin-Helmholtz instability with mass transfer through porous media

We study the linear analysis of Kelvin-Helmholtz instability of the interface between two viscous and magnetic fluids in a fully saturated porous medium using viscous potential flow theory, when the fluids are subjected to a constant tangential magnetic field, and when there is heat and mass transfer across the interface. The Darcy-Brinkman model has been used for the investigation. A dispersion relation has been derived and stability is discussed theoretically as well as numerically. The stability criterion is given in terms of a critical value of relative velocity as well as the critical value of applied magnetic field. It has been observed that both tangential magnetic field and vapor fraction have stabilizing effect on the stability of the system while heat and mass transfer destabilizes the interface. Porosity stabilizes the interface while the porous medium has destabilizing effect.