Transient cavities near boundaries. Part 1. Rigid boundary

1986 ◽  
Vol 170 ◽  
pp. 479-497 ◽  
Author(s):  
J. R. Blake ◽  
B. B. Taib ◽  
G. Doherty
Keyword(s):  
Stagnation Point ◽  
Numerical Solutions ◽  
Relative Magnitude ◽  
Boundary Integral ◽  
Stagnation Point Flow ◽  
Boundary Integral Method ◽  
Physical Parameters ◽  
Jet Formation ◽  
Rigid Boundary ◽  
Parameter Ranges

The growth and collapse of transient vapour cavities near a rigid boundary in the presence of buoyancy forces and an incident stagnation-point flow are modelled via a boundary-integral method. Bubble shapes, particle pathlines and pressure contours are used to illustrate the results of the numerical solutions. Migration of the collapsing bubble, and subsequent jet formation, may be directed either towards or away from the rigid boundary, depending on the relative magnitude of the physical parameters. For appropriate parameter ranges in stagnation-point flow, unusual ‘hour-glass’ shaped bubbles are formed towards the end of the collapse of the bubble. It is postulated that the final collapsed state of the bubble may be two toroidal bubbles/ring vortices of opposite circulation. For buoyant vapour cavities the Kelvin impulse is used to obtain criteria which determine the direction of migration and subsequent jet formation in the collapsing bubble.

scholarly journals Hydromagnetic Stagnation-Point Flow towards a Radially Stretching Convectively Heated Disk

2013 ◽  
Vol 2013 ◽  
pp. 1-8 ◽  
Author(s):  
S. Shateyi ◽  
O. D. Makinde
Keyword(s):  
Stagnation Point ◽  
Numerical Solutions ◽  
Relaxation Method ◽  
Disk Surface ◽  
Stagnation Point Flow ◽  
Temperature Fields ◽  
Physical Parameters ◽  
Local Skin ◽  
Spectral Relaxation Method ◽  
Spectral Relaxation

The steady stagnation-point flow and heat transfer of an electrically conducted incompressible viscous fluid are extended to the case where the disk surface is convectively heated and radially stretching. The fluid is subjected to an external uniform magnetic field perpendicular to the plane of the disk. The governing momentum and energy balance equations give rise to nonlinear boundary value problem. Using a spectral relaxation method with a Chebyshev spectral collocation method, the numerical solutions are obtained over the entire range of the physical parameters. Emphasis has been laid to study the effects of viscous dissipation and Joule heating on the thermal boundary layer. Pertinent results on the effects of various thermophysical parameters on the velocity and temperature fields as well as local skin friction and local Nusselt number are discussed in detail and shown graphically and/or in tabular form.

scholarly journals Numerical Analysis of MHD Stagnation Point Flow Towards a Radially Stretching Convectively Heated Disk

2020 ◽  
Vol 14 ◽  
Keyword(s):  
Stagnation Point ◽  
Numerical Solutions ◽  
Relaxation Method ◽  
Disk Surface ◽  
Stagnation Point Flow ◽  
Temperature Fields ◽  
Physical Parameters ◽  
Local Skin ◽  
Spectral Relaxation Method ◽  
Spectral Relaxation

The steady stagnation point flow and heat transferof an electrically conducting incompressible viscous fluid isextended to the case where the disk surface is convectivelyheated and radially stretching. The fluid is subjected to anexternal uniform magnetic field perpendicular to the planeof the disk. The governing momentum and energy balanceequations give rise to non-linear boundary value problem.Using a spectral relaxation method with a Chebyshev spectralcollocation method, the numerical solutions are obtained overthe entire range of the physical parameters. Emphasis hasbeen laid to study the effects of viscous dissipation and Jouleheating on the thermal boundary layer. Pertinent results on theeffects of various thermophysical parameters on the velocityand temperature fields as well as local skin friction and localNusselt number are discussed in detail and shown graphicallyand/or in tabular form.

Numerical solutions of non-alignment stagnation-point flow and heat transfer over a stretching/shrinking surface in a nanofluid

2016 ◽  
Vol 26 (6) ◽  
pp. 1747-1767 ◽  
Author(s):  
Ioan Pop ◽  
Kohi Naganthran ◽  
Roslinda Nazar
Keyword(s):  
Heat Transfer ◽  
Differential Equations ◽  
Stagnation Point ◽  
Numerical Solutions ◽  
Dual Solutions ◽  
Stagnation Point Flow ◽  
Content Type ◽  
Boundary Layer Equations ◽  
Flow And Heat Transfer ◽  
Shrinking Surface

Purpose – The purpose of this paper is to analyse numerically the steady stagnation-point flow of a viscous and incompressible fluid over continuously non-aligned stretching or shrinking surface in its own plane in a water-based nanofluid which contains three different types of nanoparticles, namely, Cu, Al2O3 and TiO2. Design/methodology/approach – Similarity transformation is used to convert the system of boundary layer equations which are in the form of partial differential equations into a system of ordinary differential equations. The system of similarity governing equations is then reduced to a system of first-order differential equations and solved numerically using the bvp4c function in Matlab software. Findings – Unique solution exists when the surface is stretched and dual solutions exist as the surface shrunk. For the dual solutions, stability analysis has revealed that the first solution (upper branch) is stable and physically realizable, while the second solution (lower branch) is unstable. The effect of non-alignment is huge for the shrinking surface which is in contrast with the stretching surface. Practical implications – The results obtained can be used to explain the characteristics and applications of nanofluids, which are widely used as coolants, lubricants, heat exchangers and micro-channel heat sinks. This problem also applies to some situations such as materials which are manufactured by extrusion, production of glass-fibre and shrinking balloon. In this kind of circumstance, the rate of cooling and the stretching/shrinking process play an important role in moulding the final product according to preferable features. Originality/value – The present results are original and new for the study of fluid flow and heat transfer over a stretching/shrinking surface for the problem considered by Wang (2008) in a viscous fluid and extends to nanofluid by using the Tiwari and Das (2007) model.

scholarly journals Extinction Limits of Nonadiabatic, Catalyst-Assisted Flames in Stagnation-Point Flow

2001 ◽  
Author(s):  
Stephen B. Margolis ◽  
Timothy J. Gardner
Keyword(s):  
Stagnation Point ◽  
Heat Loss ◽  
Heat Production ◽  
Fuel Efficiency ◽  
Premixed Flames ◽  
Stagnation Point Flow ◽  
Pollutant Formation ◽  
Flow Geometry ◽  
Parameter Ranges

Abstract Because combustion is essentially an Arrhenius process, premixed flames generally can only exist within certain parameter ranges, or extinction limits, that correspond to a rate of heat production that is sufficient to sustain the reaction in a given flow geometry. Nonetheless, it is frequently desirable to extend these limits, often for the purpose of increasing fuel efficiency and/or reducing the rate of formation of pollutant species. Another emerging motivation is to allow combustion to be sustained in relatively small volumes, which are characterized by larger surface-to-volume ratios, that would otherwise lead to extinguishing levels of heat loss. Surface catalysts are widely used to achieve such enhancements with respect to efficiency and pollutant formation, and we wish to now consider the role catalysts might play with respect to nonadiabatic flames.

Numerical analysis of time-dependent stagnation point flow of Oldroyd-B fluid subject to modified Fourier’s law

2021 ◽  
pp. 2150187
Author(s):  
Foukeea Qasim ◽  
Tian-Chuan Sun ◽  
S. Z. Abbas ◽  
W. A. Khan ◽  
M. Y. Malik
Keyword(s):  
Differential Equation ◽  
Fluid Flow ◽  
Stagnation Point ◽  
Numerical Solutions ◽  
Fluid Velocity ◽  
Nonlinear Partial Differential Equation ◽  
Thermal Relaxation ◽  
Stagnation Point Flow ◽  
Time Dependent ◽  
Parameter Values

This paper aims to investigate the time-dependent stagnation point flow of an Oldroyd-B fluid subjected to the modified Fourier law. The flow into a vertically stretched cylinder at the stagnation point is discussed. The heat flux model of a non-Fourier is intended for the transfer of thermal energy in fluid flow. The study is carried out on the surface heating source, namely the surface temperature. The developed nonlinear partial differential equation for regulating fluid flow and heat transport is transformed via appropriate similarity variables into a nonlinear ordinary differential equation. The development and analysis of convergent series solutions were considered for velocity and temperature. Prandtl number numerical values are computed and investigated. This study’s findings are compared to the previous findings. By making use of the bvp4c Matlab method, numerical solutions are obtained. Besides, high buoyancy parameter values are found to increase the fluid velocity for the stimulating approach. By improving the thermal relaxation time parameter values, heat transfer in the fluid flow decreases. The temperature field effects are displayed graphically.

scholarly journals Microbubble dynamics in a viscous compressible liquid near a rigid boundary

2019 ◽  
Vol 84 (4) ◽  
pp. 696-711 ◽  
Author(s):  
Qianxi Wang ◽  
WenKe Liu ◽  
David M Leppinen ◽  
A D Walmsley
Keyword(s):  
Potential Flow ◽  
Stokes Equations ◽  
Bubble Surface ◽  
Compressible Liquid ◽  
Boundary Integral ◽  
Boundary Integral Method ◽  
Viscous Effects ◽  
Rigid Boundary ◽  
Viscous Potential Flow ◽  
Viscous Compressible Liquid

Abstract This paper is concerned with microbubble dynamics in a viscous compressible liquid near a rigid boundary. The compressible effects are modelled using the weakly compressible theory of Wang & Blake (2010, Non-spherical bubble dynamics in a compressible liquid. Part 1. Travelling acoustic wave. J. Fluid Mech., 730, 245–272), since the Mach number associated is small. The viscous effects are approximated using the viscous potential flow theory of Joseph & Wang (2004, The dissipation approximation and viscous potential flow. J. Fluid Mech., 505, 365–377), because the flow field is characterized as being an irrotational flow in the bulk volume but with a thin viscous boundary layer at the bubble surface. Consequently, the phenomenon is modelled using the boundary integral method, in which the compressible and viscous effects are incorporated into the model through including corresponding additional terms in the far field condition and the dynamic boundary condition at the bubble surface, respectively. The numerical results are shown in good agreement with the Keller–Miksis equation, experiments and computations based on the Navier–Stokes equations. The bubble oscillation, topological transform, jet development and penetration through the bubble and the energy of the bubble system are simulated and analysed in terms of the compressible and viscous effects.

scholarly journals Bubble dynamics in a compressible liquid in contact with a rigid boundary

2015 ◽  
Vol 5 (5) ◽  
pp. 20150048 ◽  
Author(s):  
Qianxi Wang ◽  
Wenke Liu ◽  
A. M. Zhang ◽  
Yi Sui
Keyword(s):  
Shock Waves ◽  
Thin Layer ◽  
High Speed ◽  
Bubble Radius ◽  
Time History ◽  
Bubble Surface ◽  
Boundary Integral ◽  
Boundary Integral Method ◽  
Imaging Method ◽  
Rigid Boundary

A bubble initiated near a rigid boundary may be almost in contact with the boundary because of its expansion and migration to the boundary, where a thin layer of water forms between the bubble and the boundary thereafter. This phenomenon is modelled using the weakly compressible theory coupled with the boundary integral method. The wall effects are modelled using the imaging method. The numerical instabilities caused by the near contact of the bubble surface with the boundary are handled by removing a thin layer of water between them and joining the bubble surface with its image to the boundary. Our computations correlate well with experiments for both the first and second cycles of oscillation. The time history of the energy of a bubble system follows a step function, reducing rapidly and significantly because of emission of shock waves at inception of a bubble and at the end of collapse but remaining approximately constant for the rest of the time. The bubble starts being in near contact with the boundary during the first cycle of oscillation when the dimensionless stand-off distance γ = s / R m < 1, where s is the distance of the initial bubble centre from the boundary and R m is the maximum bubble radius. This leads to (i) the direct impact of a high-speed liquid jet on the boundary once it penetrates through the bubble, (ii) the direct contact of the bubble at high temperature and high pressure with the boundary, and (iii) the direct impingement of shock waves on the boundary once emitted. These phenomena have clear potential to damage the boundary, which are believed to be part of the mechanisms of cavitation damage.

Impact of Entropy Generation on Stagnation-Point Flow of Sutterby Nanofluid: A Numerical Analysis

2016 ◽  
Vol 71 (9) ◽  
pp. 837-848 ◽  
Author(s):  
Ehtsham Azhar ◽  
Z. Iqbal ◽  
E.N. Maraj
Keyword(s):  
Boundary Layer ◽  
Differential Equations ◽  
Stagnation Point ◽  
Entropy Generation ◽  
Computational Analysis ◽  
Similarity Transformation ◽  
Nonlinear Partial Differential Equations ◽  
Stagnation Point Flow ◽  
Physical Parameters ◽  
Stretching Plate

AbstractThe present article dicusses the computational analysis of entropy generation for the stagnation-point flow of Sutterby nanofluid over a linear stretching plate. The Sutterby fluid is chosen to study the effect for three major classes of non-Newtonian fluids, i.e. pseudoplastic, Newtonian, and dilatant. The effects of pertinent physical parameters are examined under the approximation of boundary layer. The system of coupled nonlinear partial differential equations is simplified by incorporating suitable similarity transformation into a system of non-linear-coupled ordinary differential equations. Entropy generation analysis is conducted numerically, and the results are displayed through graphs and tables. Significant findings are listed in the closing remarks.

Theory and experiment on the low-Reynolds-number expansion and contraction of a bubble pinned at a submerged tube tip

1998 ◽  
Vol 356 ◽  
pp. 93-124 ◽  
Author(s):  
HARRIS WONG ◽  
DAVID RUMSCHITZKI ◽  
CHARLES MALDARELLI
Keyword(s):  
Surface Tension ◽  
Reynolds Number ◽  
Numerical Solutions ◽  
Full Range ◽  
Boundary Integral ◽  
Gas Pressure ◽  
Boundary Integral Method ◽  
Liquid Density ◽  
Gravitational Acceleration ◽  
Dynamic Surface

The expansion and contraction of a bubble pinned at a submerged tube tip and driven by constant gas flow rate Q are studied both theoretically and experimentally for Reynolds number Re[Lt ]1. Bubble shape, gas pressure, surface velocities, and extrapolated detached bubble volume are determined by a boundary integral method for various Bond (Bo=ρga2/σ) and capillary (Ca=μQ/σa2) numbers, where a is the capillary radius, ρ and μ are the liquid density and viscosity, σ is the surface tension, and g is the gravitational acceleration.Bubble expansion from a flat interface to near detachment is simulated for a full range of Ca (0.01–100) and Bo (0.01–0.5). The maximum gas pressure is found to vary almost linearly with Ca for 0.01[les ]Ca[les ]100. This correlation allows the maximum bubble pressure method for measuring dynamic surface tension to be extended to viscous liquids. Simulated detached bubble volumes approach static values for Ca[Lt ]1, and asymptote as Q3/4 for Ca[Gt ]1, in agreement with analytic predictions. In the limit Ca→0, two singular time domains are identified near the beginning and the end of bubble growth during which viscous and capillary forces become comparable.Expansion and contraction experiments were conducted using a viscous silicone oil. Digitized video images of deforming bubbles compare well with numerical solutions. It is observed that a bubble contracting at high Ca snaps off.

A BOUNDARY INTEGRAL METHOD FOR ACOUSTIC SOURCE LOCALIZATION IN A WAVEGUIDE WITH INCLUSIONS

1994 ◽  
Vol 02 (02) ◽  
pp. 133-145 ◽  
Author(s):  
YONGZHI XU ◽  
YI YAN
Keyword(s):  
Source Localization ◽  
Sound Source ◽  
Boundary Integral ◽  
Boundary Integral Method ◽  
Rigid Boundary ◽  
Matched Field Processing ◽  
Acoustic Source Localization ◽  
Continuous Waves ◽  
Hydrophone Array ◽  
Computation Load

In this paper, we continue our study on combining the matched field processing with the boundary integral equation (BIE) method of scattering theory to solve a sound source localization problem in a shallow ocean with a large inclusion which has a rigid boundary. We consider an enviroment where continuous waves (CW) are produced by a sound source, scattered by the inclusion, and then received by a hydrophone array. The symmetry of the waveguide is destroyed by the existence of the inclusion, and a proper procedure is therefore required to avoid the mismatching. We present a numerical scheme which makes use of the separation of the source and the detection array, and a BIE method. The separation greatly reduces the computation load. The BIE method preserves a certain accuracy on one hand and minimizes arithmetic operations on the other. Some numerical simulations using this scheme are presented.

Sign in / Sign up

Export Citation Format

Share Document