Lubrication Theory for Micropolar Fluids

1971 ◽  
Vol 38 (3) ◽  
pp. 646-650 ◽  
Author(s):  
S. J. Allen ◽  
K. A. Kline
Keyword(s):  
Flow Field ◽  
Differential Equations ◽  
Boundary Conditions ◽  
Two Dimensional ◽  
Slider Bearing ◽  
Governing Equations ◽  
Micropolar Fluids ◽  
Linear Ordinary Differential Equations ◽  
Two Dimensional Flow ◽  
Order Of Magnitude

The equations governing the flow of a fluid with rigid, spherical substructure are summarized. A two-dimensional flow field is considered and applied to the geometry of a slider bearing. Order-of-magnitude arguments are used which reduce the governing equations to a system of coupled, linear, ordinary differential equations. The equations are solved subject to appropriate boundary conditions and the effects of substructure discussed with the help of a specific numerical example.

scholarly journals Influence of a Standing Wave Flow-Field on the Dynamics of a Spray Diffusion Flame

Fluids ◽  
2021 ◽  
Vol 6 (1) ◽  
pp. 27
Author(s):  
J. Barry Greenberg ◽  
David Katoshevski
Keyword(s):  
Liquid Phase ◽  
Flow Field ◽  
Standing Wave ◽  
Diffusion Flame ◽  
Stokes Number ◽  
Flame Height ◽  
Wave Flow ◽  
Two Dimensional ◽  
Governing Equations ◽  
First Time

A theoretical investigation of the influence of a standing wave flow-field on the dynamics of a laminar two-dimensional spray diffusion flame is presented for the first time. The mathematical analysis permits mild slip between the droplets and their host surroundings. For the liquid phase, the use of a small Stokes number as the perturbation parameater enables a solution of the governing equations to be developed. Influence of the standing wave flow-field on droplet grouping is described by a specially constructed modification of the vaporization Damkohler number. Instantaneous flame front shapes are found via a solution for the usual Schwab–Zeldovitch parameter. Numerical results obtained from the analytical solution uncover the strong bearing that droplet grouping, induced by the standing wave flow-field, can have on flame height, shape, and type (over- or under-ventilated) and on the existence of multiple flame fronts.

scholarly journals Two-dimensional flow field distribution characteristics of flocking drainage pipes in tunnel

Open Physics ◽  
2020 ◽  
Vol 18 (1) ◽  
pp. 139-148
Author(s):  
Shiyang Liu ◽  
Xuefu Zhang ◽  
Feng Gao ◽  
Liangwen Wei ◽  
Qiang Liu ◽  
...  
Keyword(s):  
Flow Field ◽  
Field Distribution ◽  
Rapid Development ◽  
Maximum Velocity ◽  
Distribution Characteristics ◽  
Two Dimensional ◽  
Dimensional Flow ◽  
Laboratory Test Results ◽  
Transverse Distance ◽  
Two Dimensional Flow

AbstractWith the rapid development of traffic infrastructure in China, the problem of crystal plugging of tunnel drainage pipes becomes increasingly salient. In order to build a mechanism that is resilient to the crystal plugging of flocking drainage pipes, the present study used the numerical simulation to analyze the two-dimensional flow field distribution characteristics of flocking drainage pipes under different flocking spacings. Then, the results were compared with the laboratory test results. According to the results, the maximum velocity distribution in the flow field of flocking drainage pipes is closely related to the transverse distance h of the fluff, while the longitudinal distance h of the fluff causes little effect; when the transverse distance h of the fluff is less than 6.25D (D refers to the diameter of the fluff), the velocity between the adjacent transverse fluffs will be increased by more than 10%. Moreover, the velocity of the upstream and downstream fluffs will be decreased by 90% compared with that of the inlet; the crystal distribution can be more obvious in the place with larger velocity while it is less at the lower flow rate. The results can provide theoretical support for building a mechanism to deal with and remove the crystallization of flocking drainage pipes.

Flow Visualization by Means of Contactless Inductive Flow Tomography in the Presence of a Magnetic Brake

2015 ◽  
Vol 15 (1) ◽  
pp. 41-48 ◽  
Author(s):  
Matthias Ratajczak ◽  
Thomas Wondrak ◽  
Klaus Timmel ◽  
Frank Stefani ◽  
Sven Eckert
Keyword(s):  
Magnetic Field ◽  
External Magnetic Field ◽  
Magnetic Fields ◽  
Flow Field ◽  
Continuous Casting ◽  
Flow Structure ◽  
Cross Section ◽  
Two Dimensional ◽  
Slab Casting ◽  
Two Dimensional Flow

AbstractIn continuous casting DC magnetic fields perpendicular to the wide faces of the mold are used to control the flow in the mold. Especially in this case, even a rough knowledge of the flow structure in the mold would be highly desirable. The contactless inductive flow tomography (CIFT) allows to reconstruct the dominating two-dimensional flow structure in a slab casting mold by applying one external magnetic field and by measuring the flow-induced magnetic fields outside the mold. For a physical model of a mold with a cross section of 140 mm×35 mm we present preliminary measurements of the flow field in the mold in the presence of a magnetic brake. In addition, we show first reconstructions of the flow field in a mold with the cross section of 400 mm×100 mm demonstrating the upward scalability of CIFT.

Numerical Modeling of Radiative and Reactive Flow Field Around a Blunt Body at Hypersonic Regimes

2010 ◽  
Author(s):  
Morteza Rahmanpour ◽  
Reza Ebrahimi ◽  
Mehrzad Shams
Keyword(s):  
Flow Field ◽  
Differential Equations ◽  
Heat Fluxes ◽  
Transitional Flow ◽  
Navier Stokes ◽  
Implicit Time ◽  
Discrete Ordinates ◽  
Two Dimensional ◽  
Fully Implicit ◽  
Time Marching

A numerical method for calculation of strong radiation for two-dimensional reactive air flow field is developed. The governing equations are taken to be two dimensional, compressible Reynolds-average Navier-Stokes and species transport equations. Also, radiation heat flux in energy equation is evaluated using a model of discrete ordinate method. The model used S4 approximation to reduce the governing system of integro-differential equations to coupled set of partial differential equations. A multiband model is used to construct absorption coefficients. Tangent slab approximation is assumed to determine the characteristic parameters needed in the Discrete Ordinates Method. The turbulent diffusion and heat fluxes are modeled by Baldwin and Lomax method. The flow solution is obtained with a fully implicit time marching method. A thermochemical nonequilibrium formulation appropriate to hypersonic transitional flow of air is presented. The method is compared with existing experimental results and good agreement is observed.

scholarly journals Visualization Techniques of Differentially Heated Lid-Driven Square Cavity

2020 ◽  
Vol 2020 ◽  
pp. 1-7
Author(s):  
Vekamulla Narayana
Keyword(s):  
Flow Field ◽  
Boundary Conditions ◽  
Computational Cost ◽  
Field Synergy ◽  
Governing Equations ◽  
Square Cavity ◽  
Field Synergy Principle ◽  
Visualization Techniques

In the present study, an attempt is made to explore the flow field inside the differentially heated lid-driven square cavity. The governing equations along with boundary conditions are solved numerically. The simulated results (100 ≤ Re ≤ 1000 and 0.001 ≤ Ri ≤ 10) are validated with previous results in the literature. The convection differencing schemes, namely, UPWIND, QUICK, SUPERBEE, and SFCD, are discussed and are used to simulate the flow using the MPI code. It is observed that the computational cost for all the differencing schemes get reduced tremendously when the MPI code is implemented. Plots demonstrate the influences of Re and Ri in terms of the contours of the fluid streamlines, isotherms, energy streamlines, and field synergy principle.

Towed Underwater SPIV Measurement of Flow Fields Around a Surface-Piercing Cylinder With Free Surface Effects

2015 ◽  
Author(s):  
Jeonghwa Seo ◽  
Bumwoo Han ◽  
Shin Hyung Rhee
Keyword(s):  
Boundary Layer ◽  
Free Surface ◽  
Surface Wave ◽  
Flow Field ◽  
Cross Section ◽  
Surface Effects ◽  
Flow Fields ◽  
Two Dimensional ◽  
Two Dimensional Flow ◽  
Wave Induced

Effects of free surface on development of turbulent boundary layer and wake fields were investigated. By measuring flow field around a surface piercing cylinder in various advance speed conditions in a towing tank, free surface effects were identified. A towed underwater Stereoscopic Particle Image Velocimetry (SPIV) system was used to measure the flow field under free surface. The cross section of the test model was water plane shape of the Wigley hull, of which longitudinal length and width were 1.0 m and 100 mm, respectively. With sharp bow shape and slender cross section, flow separation was not expected in two-dimensional flow. Flow fields near the free-surface and in deep location that two-dimensional flow field was expected were measured and compared to identify free-surface effects. Some planes perpendicular to longitudinal direction near the model surface and behind the model were selected to track development of turbulent boundary layer. Froude numbers of the test conditions were from 0.126 to 0.40 and corresponding Reynolds numbers were from 395,000 to 1,250,000. In the lowest Froude number condition, free-surface wave was hardly observed and only free surface effects without surface wave could be identified while violent free-surface behavior due to wave-induced separation dominated the flow fields in the highest Froude number condition. From the instantaneous velocity fields, Time-mean velocity, turbulence kinetic energy, and flow structure derived by proper orthogonal decomposition (POD) were analyzed. As the free-surface effect, development of retarded wake, free-surface waves, and wave-induced separation were mainly observed.

scholarly journals On the Use of Asymptotic Solutions to Plane Ice—Water Problems

1969 ◽  
Vol 8 (53) ◽  
pp. 285-300 ◽  
Author(s):  
G. S. H. Lock
Keyword(s):  
Boundary Conditions ◽  
Asymptotic Solutions ◽  
Variable Properties ◽  
Governing Equations ◽  
Freezing And Thawing ◽  
One Dimensional ◽  
Wide Range ◽  
Order Of Magnitude ◽  
Water Problems ◽  
Ice Water

The paper considers one-dimensional freezing and thawing of ice–water systems for the conditions first examined by Stefan. An order-of-magnitude analysis applied to the governing equations and boundary conditions quantifies the error resulting from the neglect of various factors. Principal among these are density difference, initial superheat and variable properties.Asymptotic solutions for the temperature distribution and interface history are developed for a wide range of boundary conditions: prescribed temperature or heat flux, prescribed convection and prescribed radiation. Comparison with known results reveals the general adequacy of the asymptotic solutions and an estimate of the error incurred.

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