scholarly journals Magnetohydrodynamic Three-Dimensional Couette Flow of a Maxwell Fluid with Periodic Injection/Suction

2017 ◽  
Vol 2017 ◽  
pp. 1-19 ◽  
Author(s):  
Y. Ali ◽  
M. A. Rana ◽  
M. Shoaib
Keyword(s):  
Skin Friction ◽  
Couette Flow ◽  
Hartmann Number ◽  
Flow Direction ◽  
Three Dimensional ◽  
Maxwell Fluid ◽  
Approximate Solutions ◽  
Deborah Number ◽  
Main Flow ◽  
Main Flow Direction

A mathematical model for magnetohydrodynamic (MHD) three-dimensional Couette flow of an incompressible Maxwell fluid is developed and analyzed theoretically. The application of transverse sinusoidal injection at the lower stationary plate and its equivalent removal by suction through the uniformly moving upper plate lead to three-dimensional flow. Approximate solutions for velocity field, pressure, and skin friction are obtained. The effects of flow parameters such as Hartmann number, Reynolds number, suction/injection parameter, and the Deborah number on velocity components, skin friction factors along main flow direction and transverse direction, and pressure through parallel porous plates are discussed graphically. It is noted that Hartmann number provides a mechanism to control the skin friction component along the main flow direction.

scholarly journals Three-Dimensional Couette Flow of a Second-Grade Fluid Along Periodic Injection/Suction

Coatings ◽  
2019 ◽  
Vol 9 (9) ◽  
pp. 553 ◽  
Author(s):  
Muhammad Afzal Rana ◽  
Yasar Ali ◽  
Babar Ahmad ◽  
Muhammad Touseef Afzal Rana
Keyword(s):  
Transverse Direction ◽  
Flow Direction ◽  
Three Dimensional ◽  
Analytic Solutions ◽  
Main Flow ◽  
Second Grade ◽  
Second Grade Fluid ◽  
Suction Velocity ◽  
Grade Fluid ◽  
Main Flow Direction

This work explores the three-dimensional laminar flow of an incompressible second-grade fluid between two parallel infinite plates. The assumed suction velocity comprises a basic steady dispersal with a superimposed weak transversally fluctuating distribution. Because of variation of suction velocity in transverse direction on the wall, the problem turns out to be three-dimensional. Analytic solutions for velocity field, pressure and skin friction are presented and effects of dimensionless parameters emerging in the model are discussed. It is observed that the non-Newtonian parameter plays dynamic part to rheostat the velocity component along main flow direction.

Some Remarks on the Behaviour of Surface Source Distributions near the Edge of a Body

1973 ◽  
Vol 24 (1) ◽  
pp. 25-33
Author(s):  
J W Craggs ◽  
K W Mangler ◽  
M Zamir
Keyword(s):  
Flow Direction ◽  
Three Dimensional ◽  
Cross Flow ◽  
Symmetric Case ◽  
The Body ◽  
Dimensional Problem ◽  
Surface Source ◽  
Asymmetric Case ◽  
Main Flow Direction ◽  
Flow Plane

SummaryWhen the incompressible potential flow past a three-dimensional body is represented by source distributions on the body surface, these source distributions have singularities near an edge or corner, for example á trailing edge of a wing or the (unfaired) intersection of a body and a wing. The nature of these singularities is discussed. When assuming slow variations of the geometry in the main flow direction we can consider a two-dimensional problem in the cross-flow plane. Here the tangential velocities and source distributions are proportional to certain powers of the distance from the corner. For example at a convex right-angled corner these powers are − ⅓ in the asymmetric case (the bisector is a potential line) and ⅓ in the symmetric case (the bisector is a streamline) for both sources and tangential velocities. At a concave right-angled corner the corresponding values for the source distributions are ⅓ (asymmetric case) and − ⅓ (symmetric case) whereas they are 1 and 3 respectively for the tangential velocities.

Large Eddy Simulation of the 7-7-7 Shaped Film Cooling Hole at Axial and Compound Angle Orientations

2020 ◽  
Author(s):  
Kevin Tracy ◽  
Stephen P. Lynch
Keyword(s):  
Large Eddy Simulation ◽  
Film Cooling ◽  
Flow Direction ◽  
Main Flow ◽  
Blowing Ratio ◽  
Eddy Simulation ◽  
Large Eddy ◽  
Cooling Hole ◽  
Main Flow Direction ◽  
Compound Angle

Abstract Shaped film cooling holes are used extensively for film cooling in gas turbines due to their superior performance in keeping coolant attached to the surface, relative to cylindrical holes. However, fewer studies have examined the impact of the orientation of the shaped hole axis relative to the main flow direction, known as a compound angle. A compound angle can occur intentionally due to manufacturing, or unintentionally due to changes in the main flow direction at off-design conditions. In either case, the compound angle causes the film cooling jet to roll up into a strong streamwise vortex that changes the lateral distribution of coolant, relative to the pair of vortices that develop from an axially oriented film cooling hole. In this study, Large Eddy Simulation (LES) using the Wall-Adapting Local Eddy Viscosity (WALE) model was performed on the publicly available 7-7-7 shaped film cooling hole, at two orientations (0°, 30°) and two blowing ratios (M = 1, 3). Laterally-averaged film effectiveness was largely unchanged by a compound angle at a blowing ratio of 1, but improved at a blowing ratio of 3. For both blowing ratios, the lateral distribution of film was more uniform with the addition of a 30° compound angle. Both wall normal and lateral turbulent convective heat transfer was increased by the addition of a compound angle at both blowing ratios.

Numerical simulations of three-dimensional plunging breaking waves: generation and evolution of aerated vortex filaments

2015 ◽  
Vol 767 ◽  
pp. 364-393 ◽  
Author(s):  
P. Lubin ◽  
S. Glockner
Keyword(s):  
Stokes Equations ◽  
Early Stage ◽  
Flow Direction ◽  
Three Dimensional ◽  
Air Entrainment ◽  
Breaking Waves ◽  
Navier Stokes ◽  
Vortex Filaments ◽  
Navier Stokes Equations ◽  
Main Flow Direction

AbstractThe scope of this work is to present and discuss the results obtained from simulating three-dimensional plunging breaking waves by solving the Navier–Stokes equations, in air and water. Recent progress in computational capabilities has allowed us to run fine three-dimensional simulations, giving us the opportunity to study for the first time fine vortex filaments generated during the early stage of the wave breaking phenomenon. To date, no experimental observations have been made in laboratories, and these structures have only been visualised in rare documentary footage (e.g. BBC 2009 South Pacific. Available on YouTube, 7BOhDaJH0m4). These fine coherent structures are three-dimensional streamwise vortical tubes, like vortex filaments, connecting the splash-up and the main tube of air, elongated in the main flow direction. The first part of the paper is devoted to the presentation of the model and numerical methods. The air entrainment occurring when waves break is then carefully described. Thanks to the high resolution of the grid, these fine elongated structures are simulated and explained.

Influence of Chord Length and Inlet Boundary Layer on the Secondary Losses of Turbine Blades

2011 ◽  
Vol 134 (1) ◽  
Author(s):  
Helmut Sauer ◽  
Robin Schmidt ◽  
Konrad Vogeler
Keyword(s):  
Boundary Layer ◽  
Layer Thickness ◽  
Boundary Layer Thickness ◽  
Flow Direction ◽  
Velocity Ratio ◽  
Main Flow ◽  
Chord Length ◽  
Displacement Thickness ◽  
Wide Range ◽  
Main Flow Direction

In this paper, results concerning the influence of chord length and inlet boundary layer thickness on the endwall loss of a linear turbine cascade are discussed. The investigations were performed in a low speed cascade tunnel using the turbine profile T40. The turning of 90 deg and 70 deg, the velocity ratio in the cascade from 1.0 to 3.5 as well as the chord length of 100 mm, 200 mm, and 300 mm were specified. In a measurement distance of one chord behind the cascade in main flow direction, an approximate proportionality of endwall loss and chord was observed in a wide range of velocity ratios. At small measurement distances (e.g., s2/l=0.4), this proportionality does not exist. If a part of the flow path within the cascade is approximately incorporated, a proportionality to the chord at small measurement distances can be obtained, too. Then, the magnitude of the endwall loss mainly depends on the distance in main flow direction. At velocity ratios near 1.0, the influence of the chord decreases rapidly, while at a velocity ratio of 1.0, the endwall loss is independent of the chord. By varying the inlet boundary layer thickness, no correlation of displacement thickness and endwall loss was achieved. A calculation method according to the modified integral equation by van Driest delivers the wall shear stress. Its influence on the endwall loss was analyzed.

Experimental and Numerical Investigation of the Unsteady Leakage Flow Through the Rotor Tip Labyrinth of a 1.5-Stage Axial Turbine

2005 ◽  
Author(s):  
K. Wolter ◽  
A. Giboni ◽  
P. Peters ◽  
J. R. Menter ◽  
H. Pfost
Keyword(s):  
Flow Field ◽  
Flow Direction ◽  
Three Dimensional ◽  
Calculated Data ◽  
Leading Edge ◽  
Numerical Data ◽  
Potential Effect ◽  
Main Flow ◽  
Leakage Flow ◽  
Axial Turbine

This paper presents the results of unsteady probe measurements and numerical flow calculations in a 1.5-stage low speed axial turbine with a straight labyrinth seal on a rotor shroud. The unsteady development of the leakage flow in the three cavities is described and analysed in detail. For the investigation of the leakage flow detailed time-accurate measurements of the three-dimensional flow field were carried out in five measurement planes from casing to the rotor shroud over more than one pitch. These measurements were carried out with a miniature pneumatic five-hole probe and miniature triple hot-wire probes. Both probes have a spherical head for better adjustment in flow direction. The high resolution of 330 measurement points in each of the five measurement planes represents the flow field in great detail. The unsteady experimental data was compared with the results of the unsteady numerical simulation of the turbine flow, calculated by the 3D-Navier-Stokes Solver CFX-TASCflow. The calculated data correspond well with the experimental results and allow a detailed analysis of the flow in the cavities of the labyrinth. As demonstrated in this paper the investigations show that the leakage flow at the inlet ant outlet of the labyrinth is strongly influenced by the different positions of the rotor to the stator. The unsteady experimental and numerical data indicates intensive effects of the leakage flow caused and influenced by the trailing edge of the first stator and the potential effect of the rotor leading edge. An intensive vortex develops depending on the rotor position in the first cavity. This vortex is also influenced by a small corner vortex above the axial inlet gap of the labyrinth. After the fins this unsteady influence of the leakage flow decreases and below the jet a large vortex moves in circumferential direction. The intensity of this circulation vortex is reduced at the end of the last cavity due to the interaction with the main flow and the flow direction out of the labyrinth. Therefore the unsteady behaviour of the leakage flow grows up, which is also caused by its uneven entry into the main flow.

The meandering behaviour of large-scale structures in turbulent boundary layers

2019 ◽  
Vol 865 ◽  
Author(s):  
Kevin Kevin ◽  
Jason Monty ◽  
Nicholas Hutchins
Keyword(s):  
Boundary Layers ◽  
Large Scale ◽  
Flow Direction ◽  
Main Flow ◽  
Turbulent Structures ◽  
Velocity Fluctuations ◽  
Large Scale Structures ◽  
Main Flow Direction ◽  
Scale Structures ◽  
Spanwise Velocity

This paper quantifies the instantaneous form of large-scale turbulent structures in canonical smooth-wall boundary layers, demonstrating that they adhere to a form that is consistent with the self-sustaining streak instability model suggested by Flores & Jiménez (Phys. Fluids, vol. 22, 2010, 071704) and Hwang & Cossu (Phys. Fluids, vol. 23, 2011, 061702). Our motivation for this study stems from previous observations of large-scale streaks that have been spatially locked in position within spanwise-heterogeneous boundary layers. Here, using similar tools, we demonstrate that the randomly occurring large-scale structures in canonical layers show similar behaviour. Statistically, we show that the signature of large-scale coherent structures exhibits increasing meandering behaviour with distance from the wall. At the upper edge of the boundary layer, where these structures are severely misaligned from the main-flow direction, the induced velocities associated with the strongly yawed vortex packets/clusters yield a significant spanwise-velocity component leading to an apparent oblique coherence of spanwise-velocity fluctuations. This pronounced meandering behaviour also gives rise to a dominant streamwise periodicity at a wavelength of approximately $6\unicode[STIX]{x1D6FF}$. We further statistically show that the quasi-streamwise roll-modes formed adjacent to these very large wavy motions are often one-sided (spanwise asymmetric), in stark contrast to the counter-rotating form suggested by conventional conditionally averaged representations. To summarise, we sketch a representative picture of the typical large-scale structures based on the evidence gathered in this study.

Experimental Flow Structure Analysis in Plates With 90° Chevron Geometry by a Particle Visualization Technique

2007 ◽  
Author(s):  
Jose M. Luna ◽  
Ricardo Romero-Mendez ◽  
Abel Hernandez-Guerrero ◽  
Jose C. Rubio-Arana
Keyword(s):  
Flow Direction ◽  
Main Flow ◽  
Flow Structures ◽  
Visualization Technique ◽  
Corrugated Surfaces ◽  
Wide Range ◽  
Main Flow Direction ◽  
Corrugated Plates ◽  
Visualization Experiments ◽  
Particle Visualization

The flow structures in the cavities of parallel cross-corrugated surfaces, also called chevron geometry, are investigated in this work using an experimental visualization method. An angle of 45° between the corrugations and the main flow direction has been considered. Reviews show that a considerable amount of investigations, mainly experimental, of heat transfer and pressure drop for cross-corrugated plates has been performed, whereas for the flow field in the cavities has only been investigated numerically. The flow visualization experiments are performed inside a water tunnel using a wide range of the hydraulic diameter-based Reynolds number.

Detached Eddy Simulation of Turbulent Flow and Heat Transfer in a Ribbed Duct

2005 ◽  
Vol 127 (5) ◽  
pp. 888-896 ◽  
Author(s):  
Aroon K. Viswanathan ◽  
Danesh K. Tafti
Keyword(s):  
Heat Transfer ◽  
Turbulent Flow ◽  
Flow Direction ◽  
Main Flow ◽  
Detached Eddy Simulation ◽  
Heat Transfer Characteristics ◽  
Eddy Simulation ◽  
Flow And Heat Transfer ◽  
Main Flow Direction ◽  
Key Features

Detached Eddy Simulation (DES) of a hydrodynamic and thermally developed turbulent flow is presented for a stationary duct with square ribs aligned normal to the main flow direction. The rib height to channel hydraulic diameter (e∕Dh) is 0.1, the rib pitch to rib height (P∕e) is 10 and the calculations have been carried out for a bulk Reynolds number of 20,000. DES calculations are carried out on a 963 grid, a 643 grid, and a 483 grid to study the effect of grid resolution. Based on the agreement with earlier LES computations, the 643 grid is observed to be suitable for the DES computation. DES and RANS calculations carried out on the 643 grid are compared to LES calculations on 963∕1283 grids and experimental measurements. The flow and heat transfer characteristics for the DES cases compare well with the LES results and the experiments. The average friction and the augmentation ratios are consistent with experimental results, predicting values within 10% of the measured quantities, at a cost lower than the LES calculations. RANS fails to capture some key features of the flow.

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