The Shear-Driven Fluid Motion Using Oscillating Boundaries

2012 ◽  
Vol 134 (5) ◽  
Author(s):  
Md. Shakhawath Hossain ◽  
Nihad E. Daidzic
Keyword(s):  
Newtonian Fluid ◽  
Stokes Equations ◽  
Fluid Motion ◽  
Wall Slip ◽  
Shear Thinning ◽  
Infinite Domain ◽  
Diffusion Type ◽  
Flow Rates ◽  
Finite Differences Method ◽  
Fluid Rheology

A classical Stokes’ second problem has been known for a long time and represents one of the few exact solutions of nonlinear Navier-Stokes equations. However, oscillatory flow in a semi-infinite domain of Newtonian fluid under harmonic boundary excitation only leads to fluid wind-milling back and forth in close wall vicinity. In this study, we are presenting the mathematical model and the numerical simulations of the Newtonian fluid and the shear-thinning non-Newtonian blood-mimicking fluid flow. Positive flow rates were obtained by periodic yet nonharmonic oscillatory motion of one or two infinite boundary flat walls. The oscillatory flows in semi-infinite or finite 2D geometry with sawtooth or periodic rectified-sine boundary conditions are presented. Rheological human blood models used were: Power-Law, Sisko, Carreau, and Herschel-Bulkley. A one-dimensional time-dependent nonlinear coupled conservative diffusion-type boundary layer equations for mass, linear momentum, and energy were solved using the finite-differences method with finite-volume discretization. It was possible to test the accuracy of the in-house developed computational programs with the few isothermal flow analytical solutions and with the celebrated classical Stokes’ first and second problems. Positive flow rates were achieved in various configurations and in absence of the adverse pressure gradients. Body forces, such as gravity, were neglected. The calculations utilizing in-phase sawtooth and rectified-sine wall excitations resulted in respectable net flow which stabilizes and becomes quasi-steady, starting from rest, after three to ten periods depending on the fluid rheology. It was assumed that rapid return stroke of the wall actuator resulted in total wall slip while forward wall motion existed with no-slip boundary condition. Shear “driving” and “driven” fluid regions were identified. The shear-thinning fluid rheology delivered many interesting results, such as pluglike flow. Constructive interference of diffusive penetration layers from multiple flat surfaces could be used as practical pumping mechanism in micro-scales.

scholarly journals An active particle in a complex fluid

2017 ◽  
Vol 823 ◽  
pp. 675-688 ◽  
Author(s):  
Charu Datt ◽  
Giovanniantonio Natale ◽  
Savvas G. Hatzikiriakos ◽  
Gwynn J. Elfring
Keyword(s):  
Newtonian Fluid ◽  
Slip Velocity ◽  
Shear Thinning ◽  
Reciprocal Theorem ◽  
Janus Particle ◽  
Active Particles ◽  
Complex Fluid ◽  
The Reciprocal Theorem ◽  
Fluid Rheology ◽  
Shear Thinning Fluid

In this work, we study active particles with prescribed surface velocities in non-Newtonian fluids. We employ the reciprocal theorem to obtain the velocity of an active spherical particle with an arbitrary axisymmetric slip velocity in an otherwise quiescent second-order fluid. We then determine how the motion of a diffusiophoretic Janus particle is affected by complex fluid rheology, namely viscoelasticity and shear-thinning viscosity, compared to a Newtonian fluid, assuming a fixed slip velocity. We find that a Janus particle may go faster or slower in a viscoelastic fluid, but is always slower in a shear-thinning fluid as compared to a Newtonian fluid.

scholarly journals Transient Pressure-Driven Electroosmotic Flow through Elliptic Cross-Sectional Microchannels with Various Eccentricities

Computation ◽  
2021 ◽  
Vol 9 (3) ◽  
pp. 27
Author(s):  
Nattakarn Numpanviwat ◽  
Pearanat Chuchard
Keyword(s):  
Laplace Transform ◽  
Electroosmotic Flow ◽  
Stokes Equations ◽  
Navier Stokes ◽  
Mathieu Functions ◽  
Navier Stokes Equations ◽  
Flow Rates ◽  
Elliptic Cross ◽  
Flow Through ◽  
Relative Errors

The semi-analytical solution for transient electroosmotic flow through elliptic cylindrical microchannels is derived from the Navier-Stokes equations using the Laplace transform. The electroosmotic force expressed by the linearized Poisson-Boltzmann equation is considered the external force in the Navier-Stokes equations. The velocity field solution is obtained in the form of the Mathieu and modified Mathieu functions and it is capable of describing the flow behavior in the system when the boundary condition is either constant or varied. The fluid velocity is calculated numerically using the inverse Laplace transform in order to describe the transient behavior. Moreover, the flow rates and the relative errors on the flow rates are presented to investigate the effect of eccentricity of the elliptic cross-section. The investigation shows that, when the area of the channel cross-sections is fixed, the relative errors are less than 1% if the eccentricity is not greater than 0.5. As a result, an elliptic channel with the eccentricity not greater than 0.5 can be assumed to be circular when the solution is written in the form of trigonometric functions in order to avoid the difficulty in computing the Mathieu and modified Mathieu functions.

Numerical Integration of the Navier-Stokes Equations for a Disk Rotating in a Housing

1985 ◽  
Vol 40 (8) ◽  
pp. 789-799 ◽  
Author(s):  
A. F. Borghesani
Keyword(s):  
Boundary Layer ◽  
Cylindrical Cavity ◽  
Boundary Layer Thickness ◽  
Stokes Equations ◽  
Fluid Motion ◽  
Rotating Disk ◽  
Infinite Medium ◽  
Navier Stokes ◽  
Navier Stokes Equations ◽  
Viscous Torque

The Navier-Stokes equations for the fluid motion induced by a disk rotating inside a cylindrical cavity have been integrated for several values of the boundary layer thickness d. The equivalence of such a device to a rotating disk immersed in an infinite medium has been shown in the limit as d → 0. From that solution and taking into account edge effect corrections an equation for the viscous torque acting on the disk has been derived, which depends only on d. Moreover, these results justify the use of a rotating disk to perform accurate viscosity measurements.

Effect of Tip Clearance on Suction Performance at Different Flow Rates in a Mixed Flow Pump

2014 ◽  
Author(s):  
Yo Han Jung ◽  
Young Uk Min ◽  
Jin Young Kim
Keyword(s):  
Performance Test ◽  
Stokes Equations ◽  
Flow Characteristics ◽  
Tip Clearance ◽  
Low Flow ◽  
Tip Leakage Flow ◽  
Mixed Flow ◽  
Flow Rates ◽  
Suction Performance ◽  
Flow Pump

This paper presents a numerical investigation of the effect of tip clearance on the suction performance and flow characteristics at different flow rates in a vertical mixed-flow pump. Numerical analyses were carried out by solving three-dimensional Reynolds-averaged Navier-Stokes equations. Steady computations were performed for three different tip clearances under noncavitating and cavitating conditions at design and off-design conditions. The pump performance test was performed for the mixed-flow pump and numerical results were validated by comparing the experimental data for a system characterized by the original tip clearance. It was shown that for large tip clearance, the head breakdown occurred earlier at the design and high flow rates. However, the head breakdown was quite delayed at low flow rate. This resulted from the cavitation structure caused by the tip leakage flow at different flow rates.

Numerical Solutions of the Viscous Flow Equations for a Class of Closed Flows

1965 ◽  
Vol 69 (658) ◽  
pp. 714-718 ◽  
Author(s):  
Ronald D. Mills
Keyword(s):  
Moving Boundary ◽  
Numerical Solutions ◽  
Stokes Equations ◽  
Fluid Motion ◽  
Navier Stokes ◽  
Steady Flows ◽  
Flow Equations ◽  
Steady Streaming ◽  
Difference Formula ◽  
Surface Passing

The Navier-Stokes equations are solved iteratively on a small digital computer for the class of flows generated within a rectangular “cavity” by a surface passing over its open end. Solutions are presented for depth/breadth ratios ƛ=0.5 (shallow), 10 (square), 20 (deep) and Reynolds number 100. Flow photographs ore obtained which largely confirm the predicted flows. The theoretical velocity profiles and pressure distributions through the centre of the vortex in the square cavity are calculated.In an appendix an improved finite difference formula is given for the vorticity generated at a moving boundary.Since Thorn began his pioneering work some thirty-five years ago the number of numerical solutions which have been obtained for the equations of incompressible viscous fluid motion remains small (see bibliographies of Thom and Apelt, Fromm). The known solutions are principally for steady streaming flows, although two methods have now been used with success for non-steady flows (Payne jets and Fromm flow past obstacles). By contrast this paper is concerned with the class of closed flows generated in a rectangular region of varying depth/breadth ratio by a surface passing over an open end. This problem has been considered for a number of reasons.

Heat Transfer and Entropy Generation Characteristics of a Non-Newtonian Fluid Squeezed and Extruded Between Two Parallel Plates

2016 ◽  
Vol 139 (2) ◽  
Author(s):  
P Kaushik ◽  
Pranab Kumar Mondal ◽  
Sukumar Pati ◽  
Suman Chakraborty
Keyword(s):  
Heat Transfer ◽  
Newtonian Fluid ◽  
Entropy Generation ◽  
Bejan Number ◽  
Engineering Systems ◽  
Power Law Model ◽  
Parallel Plates ◽  
Unsteady Heat Transfer ◽  
Thermodynamic Performance ◽  
Fluid Rheology

This study investigates the unsteady heat transfer and entropy generation characteristics of a non-Newtonian fluid, squeezed and extruded between two parallel plates. In an effort to capture the underlying thermo-hydrodynamics, the power-law model is used here to describe the constitutive behavior of the non-Newtonian fluid. The results obtained from the present analysis reveal the intricate interplay between the fluid rheology and the squeezing dynamics, toward altering the Nusselt number and Bejan number characteristics. Findings from this study may be utilized to design optimal process parameters for enhanced thermodynamic performance of engineering systems handling complex fluids undergoing simultaneous extrusion and squeezing.

Pulsatile Waterhammer Subject to Laminar Friction

1972 ◽  
Vol 94 (2) ◽  
pp. 467-472 ◽  
Author(s):  
D. A. P. Jayasinghe ◽  
H. J. Leutheusser
Keyword(s):  
Stokes Equations ◽  
Fluid Motion ◽  
Present Theory ◽  
Navier Stokes ◽  
Navier Stokes Equations ◽  
One Dimensional ◽  
Arbitrary Velocity ◽  
Velocity Input ◽  
Special Case ◽  
Signalling Problem

This paper deals with elastic waves which may be generated in a fluid by the sudden movement of a flow boundary. In particular, an analysis of the classical piston, or signalling problem is presented for the special case of arbitrary velocity input into a stationary fluid contained in a circular, semi-infinite waveguide. The decay of the pulse, as well as the resulting flow development in the inlet region of the pipe are analyzed by means of an asymptotic expansion of the suitably nondimensionalized Navier-Stokes equations for a compressible, nonheat-conducting Newtonian fluid. The results differ significantly from those of the more conventional one-dimensional approach based on the so-called telegrapher’s equation of mathematical physics. The present theory realistically predicts the growth of a boundary layer both in time and position and, hence, it appears to represent the transient fluid motion in a manner which is physically more appealing.

scholarly journals Self-Consistent Cathode–Plasma Coupling and Role of the Fluid Flow Approach in Torch Modeling

2021 ◽  
Author(s):  
Margarita Baeva ◽  
Tao Zhu ◽  
Thorben Kewitz ◽  
Holger Testrich ◽  
Rüdiger Foest
Keyword(s):  
Mach Number ◽  
Gas Flow ◽  
Stokes Equations ◽  
Cathode Plasma ◽  
Plasma Parameters ◽  
Plasma Properties ◽  
Flow Rates ◽  
High Mach Number ◽  
Self Consistent ◽  
High Mach

AbstractA two-dimensional and stationary magnetohydrodynamic model of a plasma spray torch operated with argon is developed to predict the plasma properties in a steady operating mode. The model couples a submodel of a refractory cathode and its non-equilibrium boundary layer to a submodel of the plasma in local thermodynamic equilibrium in a self-consistent manner. The Navier–Stokes equations for a laminar and compressible flow are solved in terms of low and high Mach number numerical approaches. The results show that the Mach number can reach values close to one. Simulations are performed for electric currents of 600 A and 800 A, and gas flow rates of 40, 60, and 80 NLPM. The plasma parameters obtained by the two approaches differ, and the differences become more pronounced for higher currents and gas flow rates. The arc voltage, the electric power, and the thermal efficiency from both the low and high Mach number models of the plasma agree well with experimental findings for a current of 600 A and a flow rate of 40 NLPM. For higher currents and gas flow rates, the results of the low and high Mach number models gradually differ and underline the greater appropriateness of the high Mach number model.

An investigation on the instability of a flexible liquid-filled rotor

2019 ◽  
Vol 234 (2) ◽  
pp. 165-172
Author(s):  
Guangding Wang ◽  
Huiqun Yuan ◽  
Hongyun Sun
Keyword(s):  
Stokes Equations ◽  
Fluid Motion ◽  
Coupling Model ◽  
Frequency Equation ◽  
Rotor System ◽  
System Stability ◽  
Navier Stokes ◽  
Navier Stokes Equations ◽  
Continuity Equations ◽  
The Stability

In this paper, the stability of a flexible rotor partially filled with liquid is investigated. On the basis of the Navier-Stokes equations for the incompressible flow, a two-dimensional analytical model is developed for fluid motion. Applying the perturbation method, the linearized Navier-Stokes and continuity equations of fluid particles are obtained. Using the boundary conditions of fluid motion, the fluid forces exerted on the rotor are calculated. According to the established fluid-structure coupling model of the rotor system, the whirling frequency equation, which is applied to determine the stability of the system, is derived. The analysis results of the system stability are compared with the theoretical ones reported in the previous study. Good agreement is shown between the results of the present analysis and the literature results. The influences of the main parameters on the dynamic stability of the rotor system are discussed.

scholarly journals Numerical Solution of Non-Newtonian Fluid Flow Due to Rotatory Rigid Disk

Symmetry ◽  
2019 ◽  
Vol 11 (5) ◽  
pp. 699 ◽  
Author(s):  
Khalil Ur Rehman ◽  
M. Y. Malik ◽  
Waqar A Khan ◽  
Ilyas Khan ◽  
S. O. Alharbi
Keyword(s):  
Brownian Motion ◽  
Newtonian Fluid ◽  
Fluid Model ◽  
Rotating Disk ◽  
Casson Fluid ◽  
Infinite Domain ◽  
Nanoparticles Concentration ◽  
Navier’S Slip ◽  
Local Sherwood Number

In this article, the non-Newtonian fluid model named Casson fluid is considered. The semi-infinite domain of disk is fitted out with magnetized Casson liquid. The role of both thermophoresis and Brownian motion is inspected by considering nanosized particles in a Casson liquid spaced above the rotating disk. The magnetized flow field is framed with Navier’s slip assumption. The Von Karman scheme is adopted to transform flow narrating equations in terms of reduced system. For better depiction a self-coded computational algorithm is executed rather than to move-on with build-in array. Numerical observations via magnetic, Lewis numbers, Casson, slip, Brownian motion, and thermophoresis parameters subject to radial, tangential velocities, temperature, and nanoparticles concentration are reported. The validation of numerical method being used is given through comparison with existing work. Comparative values of local Nusselt number and local Sherwood number are provided for involved flow controlling parameters.

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