Viscous Flow Theory Research Articles

Pressure corrections for the potential flow analysis of Kelvin–Helmholtz instability with heat and mass transfer

Pressure corrections for the viscous potential flow analysis of Kelvin–Helmholtz instability at the interface of two viscous fluids have been carried out when there is heat and mass transfer across the interface. Both fluids are taken as incompressible and viscous with different kinematic viscosities. In viscous potential flow theory, viscosity enters through normal stress balance and effect of shearing stresses is completely neglected. We include the viscous pressure in the normal stress balance along with irrotational pressure and it is assumed that this viscous pressure will resolve the discontinuity of the tangential stresses at the interface for two fluids. It has been observed that heat and mass transfer has destabilizing effect on the stability of the system. A comparison between viscous potential flow (VPF) solution and viscous contribution to the pressure for potential flow (VCVPF) solution has been made and it is found that the effect of irrotational shearing stresses stabilizes the system.

Viscous potential flow analysis of capillary instability with radial electric field

A linear analysis of capillary instability with radial electric field is carried out using viscous potential flow theory. In viscous potential flow, the viscous term in the Navier-Stokes equation vanishes as vorticity is zero but viscosity is not zero. Viscosity enters through normal stress balance in viscous potential flow theory and the tangential stresses are not considered. The effect of gravity and free surface charges at the interface are neglected. A dispersion relation is derived for the case of radially imposed electric field and stability is discussed in terms of various parameters such as Ohnesorge number, permittivity ratio, etc. A condition for neutral stability is obtained and it is given in terms of critical value of electric field. It is observed that the radial electric field has dual effect on the stability of the system corresponding to the values of conductivities and permittivities of the fluids.

Analytical solution of the stochastic steady-state creep boundary value problem for a thick-walled tube

A non-linear steady-state creep stochastic boundary value problem is solved for a thick-walled tube acted upon by an internal pressure for the case of a plane strain state. It is assumed that the properties of the tube material are described by a random function of its radius. The constitutive creep relations are taken in accordance with non-linear viscous flow theory in a stochastic form. A recurrent form of the system of stochastic differential equations is obtained by expanding the radial stress in a series in powers of a small parameter, from which the components of the radial stress can be found to any degree of accuracy. The random stress field and strain rate field are analised statistically as a function of the non-linearity exponent and the degree of inhomogeneity of the material. A comparative analysis of the solutions of the stochastic steady-state creep boundary value problem for a thick-walled tube, obtained is the fourth approximation of the small parameter method and the Monte carlo method, is performed.

Flow transport in a microchannel induced by moving wall contractions: a novel micropumping mechanism

A novel micropumping mechanism based on a theoretical model that describes flow transport in a microchannel induced by moving wall contractions in the low Reynolds number flow regime is presented. The channel is assumed to have a length that is much greater than its width (\({\delta = W/L \ll 1}\)) and the upper wall is subjected to prescribed, non-peristaltic, localized moving contractions. Lubrication theory for incompressible viscous flow at low Reynolds number (Re ~ δ) is used to model the problem mathematically and to derive expressions for the velocity components, pressure gradient, wall shear stress, and net flow produced by the wall contractions. The effect of contraction parameters such as amplitude and phase lag on the time-averaged net flow over a single cycle of wall motions is studied. The results presented here are supported by passive particle tracking simulations to investigate the possibility of using this system as a pumping mechanism. The present study is motivated by collapse mechanisms observed in entomological physiological systems that use multiple contractions to transport fluid, and the emerging novel microfluidic devices that mimic these systems.

Viscous Potential Flow Analysis of Rayleigh-Taylor Instability of Cylindrical Interface

The present paper deals with the study of Rayleigh-Taylor instability at the cylindrical interface using viscous potential flow theory. In the inviscid potential flow theory, the viscous term in Navier-Stokes equation vanishes as viscosity is zero. 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 viscous potential flow theory and tangential stresses are not considered. A dispersion relation is derived and stability is discussed in terms of various parameters such as Ohnesorge number, density ratio etc. A condition for neutral stability is obtained and it is given in terms of critical value of the wave number. It is observed that the Ohnesorge number has destabilizing effect while inner fluid fraction has stabilizing effect on the stability of the system.

Pressure Corrections for the Potential Flow Analysis of Kelvin-Helmholtz Instability

The present paper deals with the study of viscous contribution to the pressure for the viscous potential flow analysis of Kelvin-Helmholtz instability of two viscous fluids. Viscosity enters through normal stress balance in the viscous potential flow theory and tangential stresses for two fluids are not continuous at the interface. Here we have considered viscous pressure in the normal stress balance along with the irrotational pressure and it is assumed that the addition of this viscous pressure will resolve the discontinuity between the tangential stresses and the tangential velocities at the interface. The viscous pressure is derived by mechanical energy equation and this pressure correction applied to compute the growth rate of Kelvin-Helmholtz instability. A dispersion relation is obtained and a stability criterion is given in the terms of critical value of relative velocity. It has been observed that the inclusion of irrotational shearing stresses stabilizes the system.

Nonlinear analysis of capillary instability with heat and mass transfer

The nonlinear capillary instability of the cylindrical interface between the vapor and liquid phases of a fluid is studied when there is heat and mass transfer across the interface, using viscous potential flow theory. The fluids are considered to be viscous and incompressible with different kinematic viscosities. Both asymmetric and axisymmetric disturbances are considered. The analysis is based on the method of multiple scale perturbation and the nonlinear stability is governed by first-order nonlinear partial differential equation. The stability conditions are obtained and discussed theoretically as well as numerically. Regions of stability and instability have been shown graphically indicating the effect of various parameters. It has been observed that the heat and mass transfer has stabilizing effect on the stability of the system in the nonlinear analysis for both axisymmetric as well as asymmetric disturbances.

Numerical simulation of viscous cavitating flow around a ship propeller

In the present study, cavitation and a ship propeller wake are reported by computed fluid dynamics based on viscous multiphase flow theory. Some recent validation results with a hybrid grid based on unsteady Navier-Stokes (N-S) and bubble dynamics equations are presented to predict velocity, pressure and vapor volume fraction in propeller wake in a uniform inflow. Numerical predictions of sheet cavitation, tip vortex cavitation and hub vortex cavitation are in agreement with the experimental data, same as numerical predictions of longitudinal and transversal evolution of the axial velocity. Blade and shaft rate frequency of propeller is well predicted by the computed results of pressure, and tip vortex is the most important to generate the pressure field within the near wake. The overall results indicate that the present approach is reliable for prediction of cavitation and propeller wake on the condition of uniform inflow.

Added Mass, Added Stiffness and Added Damping Coefficients for a Parallel Plate-Type Structure

Flow-induced vibrations of parallel plates in axial viscous flow were studied. Viscous flow theory was applied to describe the fluid-structure interaction. The fluid was supposed to be two-dimensional. The expressions of fluid velocities were created. The pressure grads were gotten with two-dimensional Navier-Stocks equations. Semi-analytical fluid pressures of a three-parallel plate-type structure were obtained. The added mass coefficients, added damping and added stiffness coefficients were determined. These analytical coefficients indicate a strong dependence on gap width.

Viscous potential flow analysis of Kelvin-Helmholtz instability of cylindrical interface

A linear analysis of Kelvin-Helmholtz instability of cylindrical interface is carried out using viscous potential flow theory. In the inviscid potential flow theory, the viscous term in Navier-Stokes equation vanishes as viscosity is zero. 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 viscous potential flow theory and tangential stresses are not considered. Both asymmetric and axisymmetric disturbances are considered. A dispersion relation has been obtained and stability criteria are given in the terms of the relative velocity. A comparison between inviscid potential flow and viscous potential flow has been made. It has been observed that Reynolds number and inner fluid fraction both have destabilizing effect on the stability of the system.

Hull gesture and resistance prediction of high-speed vessels

Since trim and sinkage are significant while vessels are advancing forward with high speed, the predicted vessel resistance based on restrained model theory or experiment may not be real resistance of vessels during voyage. It is necessary to take the influence of hull gesture into account for oredicting the resistance of high-speed ship. In the present work the resistance problem of high speed ship is treated with the viscous flow theory, and the dynamic mesh technique is adopted to coincide with variation of hull gesture of high speed vessel on voyage. The simulation of the models of S60 ship and a trimaran moving in towing tank with high speed are conducted by using the above theory and technique. The corresponding numerical results are in good agreement with the experimental data. It indicates that the resistance prediction for high speed vessels should take hull gesture into consideration and the dynamic mesh method proposed here is effective in calculating the resistance of high speed vessels.

Numerical simulation of water–heat coupled movements in seasonal frozen soil

In view of the insufficiencies of existing research into soil water and heat movements in seasonally frozen soil regions, water–heat coupled movements in seasonally frozen soil were studied by using a numerical simulation method. On the basis of viscous flow theory for liquid water in porous media and the heat balance principle, one-dimensional seasonal frozen soil water–heat coupled movements were modeled. A finite difference method was then performed to give the fully implicit finite difference form of the model. Finally the water status and the heat status of the seasonally frozen soil in the study area on November 3 2008 were simulated and tested. The results indicated that the simulated values of moisture and temperature for seasonally frozen soil had the same trends as the measured values, and the average relative errors of the soil temperature and moisture simulation were 9.67% and 9.54% respectively, which are both less than 10%. Thus, the one-dimensional seasonally frozen soil water–heat coupled movements model constructed in this paper and the numerical computation method are rational and reliable.

Characteristic analysis of unsteady viscous flow around a cavitating propeller

Based on viscous multiphase flow theory, this paper presents some recent validation results with a hybrid grid and sliding mesh solving Unsteady Navier-Stokes (N-S) and Bubble Dynamics equations as applied to prediction of pressure, velocity and vapor volume fraction in the wake in an uniform inflow. Comparable to experimental results, numerical predictions of sheet cavitation, tip vortex cavitation and hub vortex cavitation are in agreement with the corresponding experimental data, the same as numerical predictions of pressure in wake. Tip vortex cavitation is the most important to generate the pressure fluctuation within the near wake. The characteristics such as blade and shaft rate frequency of propeller pressure in wake coincide with its geometric model and parameters. With increasing distance from propeller disk, the pressure signals at blade frequency decrease. The process of attenuation becomes fast with the decreased advance coefficient and cavitation number.

Relative pressure, temperature, and gas composition sensitivity of damping-based resonant sensors

Measurement of the damping in resonant microsystems and nanosystems has been proposed for measurement of pressure, temperature, and gas composition. Because the damping will be a function of all three of these variables, estimating the sensitivity of these transducers requires modeling the effect each of these variables will have on the damping of the system. Using viscous flow theory, the relative sensitivity of damping to pressure, temperature, relative humidity, and the concentration of selected contaminants is computed. These results show that these sensors are accurate as pressure sensors across a range of conditions. Resonators are accurate as temperature sensors only if the relative humidity is known. Resonators are not accurate as humidity sensors, and are accurate as gas composition sensors only under limited conditions.

Deformation behavior and formability of a Ti–Zr–Ni–Be bulk metallic glass within supercooled liquid region

Deformation behavior of a Ti-based bulk metallic glass (BMG) has been investigated by performing a series of uniaxial compression tests at various temperatures within the supercooled liquid region (SLR). Non-Newtonian viscous flow characteristics of BMG alloys was found to change into a homogeneous Newtonian viscous flow under a proper combination of strain rate and test temperature by compression tests. These Newtonian and non-Newtonian viscous flows were analyzed by applying the Newtonian viscous flow theory and the transition state theory, respectively. A processing map could be also constructed based on a dynamic materials model to estimate the formability and the results were then compared with those of laboratory-scale extrusion tests performed under various punch jig speeds.

Experimental investigation of fluid flow and heat transfer in a single-phase liquid flow micro-heat exchanger

This work presents an experimental analysis of the hydrodynamic and thermal performance of micro-heat exchangers. Two micro-heat exchangers, characterized by microchannels of 100 × 100 and 200 × 200 μm square cross-sections, were designed for that purpose. The fluid used was deionized water and there was no phase change along the fluid circuit. The fluid pressure drop along the heat exchanger and the heat transfer were measured and corrections were made to isolate the contribution of the microchannels. The results were compared with the predictions of the classical viscous flow and heat transfer theory. The main conclusions show that the experimental results fit well with these theories. No effects of heat transfer enhancement or pressure drop increase were observed as a consequence of the small scale of the microchannels.

Quasi - 3D and Full - 3D Approaches for Numerical Simulation in Axial Flow Hydraulic Turbine

Water passes through the rows of stationary and rotating blades in the turbine space and thus the flow becomes complex. The application of computational fluid dynamics (CFD) is steadily increasing to improve design of hydraulic turbines. The numerical flow simulation in the hydraulic turbine space can either be based on potential or viscous flow theory. In both the approaches, detailed flow behavior in complete turbine space is obtained. The quasi- 3D potential flow approach is quick and simple as compared to full-3D viscous flow methods of analysis but do not take into account the friction losses, which need to be computed separately. The direct flow analysis has been carried out in an experimentally tested model of axial flow hydraulic turbine using the two approaches and the comparison of flow pattern and computed parameters in runner is made in present paper. The computed efficiencies and other performance parameters have also been compared with experimental values at some critical points for validation.Hydro Nepal: Journal of Water, Energy and Environment Issue No. 4, January, 2009 Page 42-48

Mechanisms of microhole formation on glasses by an abrasive slurry jet

Abrasive jet micromachining is considered as a promising precision processing technology for brittle materials such as silicon substrates and glasses that are increasingly used in various applications. In this paper, the mechanisms of microhole formation on brittle glasses by an abrasive slurry jet are studied based on the viscous flow and erosion theories. It is shown that the hole cross section is characterized by a “W” shape and can be classified into three zones caused, respectively, by jet direct impact, viscous flow, and turbulent flow induced erosion. An analysis of the surface morphology shows that ductile-mode erosion is dominant. The effect of process parameters on material removal is studied which shows that increasing the pressure and erosion time increases the hole depth, but has little effect on the hole diameter.

Solution of the plane stochastic creep boundary value problem

The solution of the non-linear stochastic boundary-value problem of the creep of a thin plate in a plane stress state when the elastic strains are small and can be neglected is presented. The plate material is stochastically inhomogeneous so that the stress and strain tensors are random functions of the coordinates. The constitutive creep relation, taken as in non-linear viscous flow theory, is formulated in a stochastic form. Using the perturbation method, the non-linear stochastic problem is reduced to a system of three linear partial differential equations in the fluctuations of the stress tensor and, then, changing by implementing the stress function, to a differential equation, the solution of which is represented in the form of the sum of two series. The first series is the solution far from the boundary of the plate, ignoring edge effects, and the second is the solution in the boundary layer, and its terms rapidly decay as the distance from the boundary of the plate increases. The stretching of a stochastically inhomogeneous half-plane in the direction of two mutually orthogonal axes is considered as an example. The stress concentration in the boundary of the half-plane is investigated. It is shown that the spread of the stresses in the surface layer, the width of which depends on the degree of non-linearity of the material, can be much greater than in the deep layers.

High-Temperature Deformation Behavior and Formability of a Zr-Cu-Al-Ni Bulk Metallic Glass

The deformation behavior of a monolithic Zr55Cu30Al10Ni5 (at. pct) bulk metallic glass (BMG) fabricated by suction casting has been investigated at elevated temperatures in this study. A series of compression tests has been performed in the supercooled liquid temperature region. In the homogeneous flow regime, this alloy exhibited a transition from the Newtonian to non-Newtonian flow depending upon both the strain rate and the temperature. These two flow modes were then described by applying the Newtonian viscous flow theory and the transition state theory, respectively. On the basis of a dynamic materials model (DMM), a processing map could successfully be constructed to estimate the feasible forming conditions for this BMG alloy. Imaginary laboratory-scale extrusion tests were also performed to determine solid-to-solid formability, and the results from both the finite element method (FEM)-based simulation and processing map were then compared and discussed.