Viscoelastic Lubrication With Phan-Thein-Tanner Fluid (PTT)

2004 ◽  
Vol 126 (2) ◽  
pp. 288-291 ◽  
Author(s):  
F. Talay Akyildiz ◽  
Hamid Bellout
Keyword(s):  
Relaxation Time ◽  
Velocity Field ◽  
Constitutive Equation ◽  
Explicit Expression ◽  
Reynolds Equation ◽  
Pressure Field ◽  
Deborah Number ◽  
Time Dependent ◽  
Newtonian Case ◽  
Generalized Reynolds Equation

We analyze the lubrication flow of a viscoelastic fluid to account for the time dependent nature of the lubricant. The material obeys the constitutive equation for Phan-Thein-Tanner fluid (PTT). An explicit expression of the velocity field is obtained. This expression shows the effect of the Deborah number (De=λU/L, λ is the relaxation time). Using this velocity field, we derive the generalized Reynolds equation for PTT fluids. This equation reduces to the Newtonian case as De→0. Finally, the effect of the Deborah number on the pressure field is explored numerically in detail and the results are documented graphically.

A Comparison of the Roughness Regimes in Hydrodynamic Lubrication

2017 ◽  
Vol 139 (5) ◽  
Author(s):  
John Fabricius ◽  
Afonso Tsandzana ◽  
Francesc Perez-Rafols ◽  
Peter Wall
Keyword(s):  
Asymptotic Behavior ◽  
Stokes Flow ◽  
High Frequency ◽  
Reynolds Equation ◽  
Pressure Field ◽  
Hydrodynamic Lubrication ◽  
Narrow Gap ◽  
Surface Textures ◽  
Lubrication Regimes ◽  
Generalized Reynolds Equation

This work relates to previous studies concerning the asymptotic behavior of Stokes flow in a narrow gap between two surfaces in relative motion. It is assumed that one of the surfaces is rough, with small roughness wavelength μ, so that the film thickness h becomes rapidly oscillating. Depending on the limit of the ratio h/μ, denoted as λ, three different lubrication regimes exist: Reynolds roughness (λ = 0), Stokes roughness (0 < λ < ∞), and high-frequency roughness (λ = ∞). In each regime, the pressure field is governed by a generalized Reynolds equation, whose coefficients (so-called flow factors) depend on λ. To investigate the accuracy and applicability of the limit regimes, we compute the Stokes flow factors for various roughness patterns by varying the parameter λ. The results show that there are realistic surface textures for which the Reynolds roughness is not accurate and the Stokes roughness must be used instead.

scholarly journals Inclusion of a time-dependent, non-local convection theory in a stellar evolution code

2006 ◽  
Vol 2 (S239) ◽  
pp. 314-316 ◽  
Author(s):  
Achim Weiss ◽  
Martin Flaskamp
Keyword(s):  
Velocity Field ◽  
Local Time ◽  
Stellar Evolution ◽  
Time Dependent ◽  
Test Cases ◽  
The Sun ◽  
Specific Test ◽  
Non Local ◽  
Convective Boundaries

AbstractThe non-local, time-dependent convection theory of Kuhfuß (1986) in both its one- and three-equation form has been implemented in the Garching stellar evolution code. We present details of the implementation and the difficulties encountered. Specific test cases have been calculated, among them a 5 M⊙ star and the Sun. These cases point out deficits of the theory. In particular, the assumption of an isotropic velocity field leads to too extensive overshooting and has to be modified at convective boundaries. Some encouraging aspects are indicated as well.

Analysis of the Motion and Deformation of a Bubble Rising in a Viscoelastic Fluid

2006 ◽  
Author(s):  
Shriram Pillapakkam ◽  
Pushpendra Singh ◽  
Denis L. Blackmore ◽  
Nadine Aubry
Keyword(s):  
Velocity Field ◽  
Newtonian Fluid ◽  
Viscoelastic Fluid ◽  
Bubble Radius ◽  
Polymer Concentration ◽  
Deborah Number ◽  
Two Phase ◽  
Bubble Volume ◽  
Recirculation Zones ◽  
Bubble Rising

A finite element code based on the level set method is developed for performing two and three dimensional direct numerical simulations (DNS) of viscoelastic two-phase flow problems. The Oldroyd-B constitutive equation is used to model the viscoelastic liquid and both transient and steady state shapes of bubbles in viscoelastic buoyancy driven flows are studied. The influence of the governing dimensionless parameters, namely the Capillary number (Ca), the Deborah Number (De) and the polymer concentration parameter c, on the deformation of the bubble is also analyzed. Our simulations demonstrate that the rise velocity oscillates before reaching a steady value. The shape of the bubble, the magnitude of velocity overshoot and the amount of damping depend mainly on the parameter c and the bubble radius. Simulations also show that there is a critical bubble volume at which there is a sharp increase in the bubble terminal velocity as the increasing bubble volume increases, similar to the behavior observed in experiments. The structure of the wake of a bubble rising in a Newtonian fluid is strikingly different from that of a bubble rising in a viscoelastic fluid. In addition to the two recirculation zones at the equator of the bubble rising in a Newtonian fluid, two more recirculation zones exist in the wake of a bubble rising in viscoelastic fluids which influence the shape of a rising bubble. Interestingly, the direction of motion of the fluid a short distance below the trailing edge of a bubble rising in a viscoelastic fluid is in the opposite direction to the direction of the motion of the bubble, thus creating a “negative wake”. In this paper, the velocity field in the wake of the bubble, the effect of the parameters on the velocity field and their influence on the shape of the bubble are also investigated.

Vortex street impinging upon an elliptical leading edge

1990 ◽  
Vol 211 ◽  
pp. 211-242 ◽  
Author(s):  
Ismet Gursul ◽  
Donald Rockwell
Keyword(s):  
Velocity Field ◽  
Flow Visualization ◽  
Pressure Field ◽  
Leading Edge ◽  
Vortex Street ◽  
Transverse Displacement ◽  
Vorticity Field ◽  
Measured Velocity ◽  
Vortical Structures ◽  
Pressure Fields

The interaction of a Kármán vortex street with an elliptical edge is investigated experimentally. Basic types of interaction, as a function of scale and transverse displacement of the incident vortex street, are revealed using flow visualization. Unsteady pressure fields induced by these interactions are measured by a phase-averaging technique and correlated with the visualized flow patterns for basic classes of interactions.For a generic vortex–edge interaction, measurements of the phase-averaged velocity field allow construction of streamlines and vorticity contours showing the details of the interaction, including distortion of the vortical structures near the edge. The pressure field is calculated from the measured velocity field and interpreted in relation to the vortical structures.Simulation of flow visualization using the measured velocity field demonstrates possible misinterpretations related to the underlying vorticity field.

Propeller Loading-Induced Velocity Field by Means of Unsteady Lifting Surface Theory

1973 ◽  
Vol 17 (03) ◽  
pp. 129-139
Author(s):  
W. R. Jacobs ◽  
S. Tsakonas
Keyword(s):  
Velocity Field ◽  
High Speed ◽  
Pressure Field ◽  
Numerical Procedure ◽  
Nonuniform Flow ◽  
Surface Theory ◽  
Loading Function ◽  
Lifting Surface ◽  
Space Function ◽  
Induced Velocity

An analysis based on the lifting surface theory has been developed for evaluation of the vibratory velocity field induced by the loading of an operating propeller in both uniform and nonuniform inflow fields. The analysis demonstrates that in the case of nonuniform flow the velocity at any field point is made up of a large number of combinations of the frequency constituents of the loading function with those of the space function (propagation or influence function). A numerical procedure has been developed adaptable to a high-speed digital computer (CDC 6600), and the existing program, which evaluates the steady and unsteady propeller loadings, the resulting hydrodynamic forces and moments, and the pressure field, has been extended to include evaluation of the velocity field as well. This program should thus become a highly versatile and useful tool for the ship researcher or designer.

scholarly journals Insight of thermally stratified Jeffrey fluid flow inside porous medium subject to chemical species and melting heat transfer

2019 ◽  
Vol 11 (9) ◽  
pp. 168781401987618
Author(s):  
Mubashar Javed ◽  
Muhammad Farooq ◽  
Aisha Anjum ◽  
Shakeel Ahmad
Keyword(s):  
Heat Transfer ◽  
Velocity Field ◽  
Thermal Stratification ◽  
Heterogeneous Reaction ◽  
Concentration Field ◽  
Chemical Species ◽  
Internal Heat ◽  
Nonlinear Problems ◽  
Deborah Number ◽  
Jeffrey Fluid

This article concentrates on two-dimensional magnetohydrodynamic stagnation flow of Jeffrey liquid on a nonlinearly stretching sheet which possesses variable thickness. Simultaneous impact of melting as well as thermal stratification is specifically investigated in this study due to their tremendous involvement in plenty of natural and industrial processes. Internal heat generation and presence of chemical species are considered to ponder at heat transfer properties. Series solution has been obtained by solving the developed nonlinear problems. Physical behavior of various controlling parameters such as velocity, thermal, and concentration fields are investigated. It has been found that temperature field decays due to higher intensity of thermal stratification parameter, but thickness of thermal boundary layer boosts up. Larger Deborah number results in incremented velocity field. For uplifted wall thickness parameter, velocity field depreciates. Concentration field declines for enhanced parameters of homogeneous as well as heterogeneous reaction. Moreover, velocity is decreasing function of porosity parameter.

scholarly journals Decomposition of the forces on a body moving in an incompressible fluid

2019 ◽  
Vol 881 ◽  
pp. 1097-1122
Author(s):  
W. R. Graham
Keyword(s):  
Velocity Field ◽  
Pressure Field ◽  
Rotational Velocity ◽  
Inviscid Flow ◽  
Added Mass ◽  
The Body ◽  
Mass Force ◽  
Natural Approach ◽  
Fluid Forces ◽  
Point Pressure

In analysing fluid forces on a moving body, a natural approach is to seek a component due to viscosity and an ‘inviscid’ remainder. It is also attractive to decompose the velocity field into irrotational and rotational parts, and apportion the force resultants accordingly. The ‘irrotational’ resultants can then be identified as classical ‘added mass’, but the remaining, ‘rotational’, resultants appear not to be consistent with the physical interpretation of the rotational velocity field (as that arising from the fluid vorticity with the body stationary). The alternative presented here splits the inviscid resultants into components that are unquestionably due to independent aspects of the problem: ‘convective’ and ‘accelerative’. The former are associated with the pressure field that would arise in an inviscid flow with (instantaneously) the same velocities as the real one, and with the body’s velocity parameters – angular and translational – unchanging. The latter correspond to the pressure generated when the body accelerates from rest in quiescent fluid with its given rates of change of angular and translational velocity. They are reminiscent of the added-mass force resultants, but are simpler, and closer to the standard rigid-body inertia formulae, than the developed expressions for added-mass force and moment. Finally, the force resultants due to viscosity also include a contribution from pressure. Its presence is necessary in order to satisfy the equations governing the pressure field, and it has previously been recognised in the context of ‘excess’ stagnation-point pressure. However, its existence does not yet seem to be widely appreciated.

Unsteady Flow of a Non-Linear Viscoelastic Fluid in Pipes

2004 ◽  
Author(s):  
Mario F. Letelier ◽  
Nicola´s Madariaga ◽  
Dennis A. Siginer
Keyword(s):  
Velocity Field ◽  
Constitutive Equation ◽  
Pressure Gradient ◽  
Perturbation Method ◽  
Viscoelastic Fluid ◽  
Material Parameter ◽  
Ptt Model ◽  
Linear Viscoelastic ◽  
Dynamic Variables ◽  
Linear Viscoelastic Fluid

Flow of a viscoelastic fluid in round pipes is analyzed for the case where the pressure gradient is oscillatory with varying amplitude. The fluid is modelled according to Phan-Thien-Tanner’s constitutive equation. The analysis is carried out by using the perturbation method in which a material parameter is considered small. Velocity field and other kinematic and dynamic variables are evaluated for a range of relevant parameters. The results are compared with the base Newtonian and linear Maxwell flows. The effect of the PTT model in these type of flows is highlighted.

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