Magnetic Field Effects On Backward-facing Step Flow of Ferrofluids

2021 ◽  
Author(s):  
Wenming Yang ◽  
Boshi Fang ◽  
Beiying Liu
Keyword(s):  
Magnetic Field ◽  
Reynolds Number ◽  
Reynolds Numbers ◽  
Magnetic Reynolds Number ◽  
Magnetic Field Effects ◽  
Backward Facing Step ◽  
Number Range ◽  
Concave Corner ◽  
Small Reynolds Numbers ◽  
Recirculation Length

Abstract Backward-facing step (BFS) flow is a benchmark case study in fluid mechanics. Its control by means of electromagnetic actuation has attracted great interest in recent years. This paper focuses on the effects of a uniform stationary magnetic field on the laminar ferrofluid BFS flows for the Reynolds number range 0.1=Re=400 and different expansion ratios. The coupled ferrohydrodynamic equations, including the microscopically derived magnetization equation, for a two-dimensional domain are solved numerically by an Open FOAM solver after validation and a test of accuracy. The application of a magnetic field causes the corner vortices in the concave corner behind the step to be retracted compared with their positions in the absence of a magnetic field. The maximum percentage of the normalized decrease in length of these eddies reaches 41.23% in our simulations. For small Reynolds numbers (<10), the flow separation points on the convex corner are lowered in the presence of a magnetic field. Furthermore, the dimensionless total pressure drop between the channel inlet and outlet decreases almost linearly with Reynolds number Re, but the drop is greater when a magnetic field is applied. On the whole, the normalized recirculation length of the corner vortex increases nonlinearly with increasing magnetic Reynolds number Rem and Brownian Péclet number Pe, but it tends to constant values in the limits Re ≪ 1 and Re ≫ 1.

Backward-Facing Step Flows for Various Expansion Ratios at Low and Moderate Reynolds Numbers

2004 ◽  
Vol 126 (3) ◽  
pp. 362-374 ◽  
Author(s):  
G. Biswas ◽  
M. Breuer ◽  
F. Durst
Keyword(s):  
Reynolds Number ◽  
Three Dimensional ◽  
Side Wall ◽  
Reynolds Numbers ◽  
Two Dimensional ◽  
Backward Facing Step ◽  
Wall Jets ◽  
Number Range ◽  
Reynolds Number Range ◽  
Concave Corner

This paper is concerned with the behavior of flows over a backward-facing step geometry for various expansion ratios H/h=1.9423, 2.5 and 3.0. A literature survey was carried out and it was found that the flow shows a strong two-dimensional behavior, on the plane of symmetry, for Reynolds numbers ReD=ρUbD/μ below approximately 400 (Ub=bulk velocity and D=hydraulic diameter). In this Reynolds number range, two-dimensional predictions were carried out to provide information on the general integral properties of backward-facing step flows, on mean velocity distributions and streamlines. Information on characteristic flow patterns is provided for a wide Reynolds number range, 10−4⩽ReD⩽800. In the limiting case of ReD→0, a sequence of Moffatt eddies of decreasing size and intensity is verified to exist in the concave corner also at ReD=1. The irreversible pressure losses are determined for various Reynolds numbers as a function of the expansion ratio. The two-dimensional simulations are known to underpredict the primary reattachment length for Reynolds numbers beyond which the actual flow is observed to be three-dimensional. The spatial evolution of jet-like flows in both the streamwise and the spanwise direction and transition to three-dimensionality were studied at a Reynolds number ReD=648. This three-dimensional analysis with the same geometry and flow conditions as reported by Armaly et al. (1983) reveals the formation of wall jets at the side wall within the separating shear layer. The wall jets formed by the spanwise component of the velocity move towards the symmetry plane of the channel. A self-similar wall-jet profile emerges at different spanwise locations starting with the vicinity of the side wall. These results complement information on backward-facing step flows that is available in the literature.

On the stability of plane flow of a conducting fluid in the presence of a coplanar magnetic field

1970 ◽  
Vol 43 (3) ◽  
pp. 591-596 ◽  
Author(s):  
C. Sozou
Keyword(s):  
Magnetic Field ◽  
Reynolds Number ◽  
Reynolds Numbers ◽  
Magnetic Reynolds Number ◽  
Conducting Fluid ◽  
Unstable Flow ◽  
Plane Flow ◽  
The Stability ◽  
Two Parameters ◽  
The Relationship

The equations governing the propagation of small perturbations to plane flow of a viscous incompressible conducting fluid are re-examined with special reference to the case when the constant unperturbed magnetic field and flow velocity are parallel. We use the relationship between two parameters in one equation and, without computations, show the following: If for a non-zero value of the Alfvén number the flow is unstable when the Reynolds and magnetic Reynolds numbers take particular finite values, then, for that value of the Alfvén number, the flow cannot be completely stabilized for all finite Reynolds numbers, when the magnetic Reynolds number is finite. Since for a finite Alfvén number one expects that unstable flow cannot be stabilized for all finite Reynolds numbers, unless the magnetic Reynolds number exceeds some value, we deduce the following: An unstable parallel flow of a finitely conducting fluid cannot be completely stabilized for all finite Reynolds numbers by a constant magnetic field, which is coplanar with the flow.

Flow induced in a cylindrical column by a uniformly rotating magnetic field

1967 ◽  
Vol 297 (1451) ◽  
pp. 558-563
Keyword(s):  
Magnetic Field ◽  
Boundary Layer ◽  
Reynolds Number ◽  
High Frequency ◽  
Fourier Transforms ◽  
Reynolds Numbers ◽  
Magnetic Reynolds Number ◽  
Rotating Magnetic Field ◽  
Cylindrical Column ◽  
Field Lines

Under laboratory conditions, the magnetic Reynolds number is quite small in a conductor, but can be made appreciable if a high frequency rotating field is applied. Moffatt investigated this problem for high magnetic Reynolds numbers and concluded that there existed a magnetic boundary layer due to spiralling of field lines. Applying Fourier transforms and solving the corrected equations, we find that at low magnetic Reynolds numbers the field lines uniformly penetrate the cylindrical column and do not exhibit any appreciable spiralling. The rotation opposes the drift due to conductivity which is evened out as one proceeds from the centre to the surface. This uniform behaviour persists for small magnetic Reynolds number inside and outside. When the magnetic Reynolds number becomes large, of the order of 100 (say), the field lines passing through the axis of the cylinder exhibit spiralling as suggested by Moffatt since the diffusion is unable to counterbalance the rotational effects.

Heat Transfer for High Aspect Ratio Rectangular Channels in a Stationary Serpentine Passage With Turbulated and Smooth Surfaces

2013 ◽  
Author(s):  
Matthew A. Smith ◽  
Randall M. Mathison ◽  
Michael G. Dunn
Keyword(s):  
Heat Transfer ◽  
Reynolds Number ◽  
Aspect Ratio ◽  
Flow Behavior ◽  
Reynolds Numbers ◽  
Hydraulic Diameter ◽  
Internal Cooling ◽  
Number Range ◽  
Aspect Ratios ◽  
Parallel Configuration

Heat transfer distributions are presented for a stationary three passage serpentine internal cooling channel for a range of engine representative Reynolds numbers. The spacing between the sidewalls of the serpentine passage is fixed and the aspect ratio (AR) is adjusted to 1:1, 1:2, and 1:6 by changing the distance between the top and bottom walls. Data are presented for aspect ratios of 1:1 and 1:6 for smooth passage walls and for aspect ratios of 1:1, 1:2, and 1:6 for passages with two surfaces turbulated. For the turbulated cases, turbulators skewed 45° to the flow are installed on the top and bottom walls. The square turbulators are arranged in an offset parallel configuration with a fixed rib pitch-to-height ratio (P/e) of 10 and a rib height-to-hydraulic diameter ratio (e/Dh) range of 0.100 to 0.058 for AR 1:1 to 1:6, respectively. The experiments span a Reynolds number range of 4,000 to 130,000 based on the passage hydraulic diameter. While this experiment utilizes a basic layout similar to previous research, it is the first to run an aspect ratio as large as 1:6, and it also pushes the Reynolds number to higher values than were previously available for the 1:2 aspect ratio. The results demonstrate that while the normalized Nusselt number for the AR 1:2 configuration changes linearly with Reynolds number up to 130,000, there is a significant change in flow behavior between Re = 25,000 and Re = 50,000 for the aspect ratio 1:6 case. This suggests that while it may be possible to interpolate between points for different flow conditions, each geometric configuration must be investigated independently. The results show the highest heat transfer and the greatest heat transfer enhancement are obtained with the AR 1:6 configuration due to greater secondary flow development for both the smooth and turbulated cases. This enhancement was particularly notable for the AR 1:6 case for Reynolds numbers at or above 50,000.

Turbulent dynamo action at low magnetic Reynolds number

1970 ◽  
Vol 41 (2) ◽  
pp. 435-452 ◽  
Author(s):  
H. K. Moffatt
Keyword(s):  
Magnetic Field ◽  
Reynolds Number ◽  
Large Scale ◽  
Isotropic Turbulence ◽  
Magnetic Energy ◽  
Magnetic Reynolds Number ◽  
Dynamo Action ◽  
Ohmic Dissipation ◽  
Magnetic Energy Density ◽  
Magnetic Diffusivity

The effect of turbulence on a magnetic field whose length-scale L is initially large compared with the scale l of the turbulence is considered. There are no external sources for the field, and in the absence of turbulence it decays by ohmic dissipation. It is assumed that the magnetic Reynolds number Rm = u0l/λ (where u0 is the root-mean-square velocity and λ the magnetic diffusivity) is small. It is shown that to lowest order in the small quantities l/L and Rm, isotropic turbulence has no effect on the large-scale field; but that turbulence that lacks reflexional symmetry is capable of amplifying Fourier components of the field on length scales of order Rm−2l and greater. In the case of turbulence whose statistical properties are invariant under rotation of the axes of reference, but not under reflexions in a point, it is shown that the magnetic energy density of a magnetic field which is initially a homogeneous random function of position with a particularly simple spectrum ultimately increases as t−½exp (α2t/2λ3) where α(= O(u02l)) is a certain linear functional of the spectrum tensor of the turbulence. An analogous result is obtained for an initially localized field.

Heat Transfer And Pressure Drop Of An Angled Discrete Turbulator At Elevated Reynolds Numbers Up To 900,000

2021 ◽  
pp. 1-29
Author(s):  
Sam Ghazi-Hesami ◽  
Dylan Wise ◽  
Keith Taylor ◽  
Peter Ireland ◽  
Étienne Robert
Keyword(s):  
Heat Transfer ◽  
Reynolds Number ◽  
Pressure Drop ◽  
Friction Factor ◽  
Rectangular Channel ◽  
Reynolds Numbers ◽  
Enhance Heat Transfer ◽  
Near Surface ◽  
Number Range ◽  
Smooth Channel

Abstract Turbulators are a promising avenue to enhance heat transfer in a wide variety of applications. An experimental and numerical investigation of heat transfer and pressure drop of a broken V (chevron) turbulator is presented at Reynolds numbers ranging from approximately 300,000 to 900,000 in a rectangular channel with an aspect ratio (width/height) of 1.29. The rib height is 3% of the channel hydraulic diameter while the rib spacing to rib height ratio is fixed at 10. Heat transfer measurements are performed on the flat surface between ribs using transient liquid crystal thermography. The experimental results reveal a significant increase of the heat transfer and friction factor of the ribbed surface compared to a smooth channel. Both parameters increase with Reynolds number, with a heat transfer enhancement ratio of up to 2.15 (relative to a smooth channel) and a friction factor ratio of up to 6.32 over the investigated Reynolds number range. Complementary CFD RANS (Reynolds-Averaged Navier-Stokes) simulations are performed with the κ-ω SST turbulence model in ANSYS Fluent® 17.1, and the numerical estimates are compared against the experimental data. The results reveal that the discrepancy between the experimentally measured area averaged Nusselt number and the numerical estimates increases from approximately 3% to 13% with increasing Reynolds number from 339,000 to 917,000. The numerical estimates indicate turbulators enhance heat transfer by interrupting the boundary layer as well as increasing near surface turbulent kinetic energy and mixing.

Fully developed MHD turbulence near critical magnetic Reynolds number

1981 ◽  
Vol 104 ◽  
pp. 419-443 ◽  
Author(s):  
J. Léorat ◽  
A. Pouquet ◽  
U. Frisch
Keyword(s):  
Reynolds Number ◽  
Kinetic Energy ◽  
Isotropic Turbulence ◽  
Magnetic Energy ◽  
Reynolds Numbers ◽  
Magnetic Reynolds Number ◽  
Mhd Equations ◽  
Liquid Sodium ◽  
Turbulent Heat ◽  
Mhd Turbulence

Liquid-sodium-cooled breeder reactors may soon be operating at magnetic Reynolds numbers RM where magnetic fields can be self-excited by a dynamo mechanism (as first suggested by Bevir 1973). Such flows have kinetic Reynolds numbers RV of the order of 107 and are therefore highly turbulent.This leads us to investigate the behaviour of MHD turbulence with high RV and low magnetic Prandtl numbers. We use the eddy-damped quasi-normal Markovian closure applied to the MHD equations. For simplicity we restrict ourselves to homogeneous and isotropic turbulence, but we do include helicity.We obtain a critical magnetic Reynolds number RMc of the order of a few tens (non-helical case) above which magnetic energy is present. RMc is practically independent of RV (in the range 40 to 106). RMc can be considerably decreased by the presence of helicity: when the overall size of the flow L is much larger than the integral scale l0, RMc can drop below unity as suggested by an α-effect argument. When L ≈ l0 the drop can still be substantial (factor of 6) when helicity is a maximum. We examine how the turbulence is modified when RM crosses RMc: presence of magnetic energy, decreased kinetic energy, steepening of kinetic-energy spectrum, etc.We make no attempt to obtain quantitative estimates for a breeder reactor, but discuss some of the possible consequences of exceeding RMc, such as decreased turbulent heat transport. More precise information may be obtained from numerical simulations and experiments (including some in the subcritical regime).

Time-Dependent Laminar Backward-Facing Step Flow in a Two-Dimensional Duct

1988 ◽  
Vol 110 (3) ◽  
pp. 289-296 ◽  
Author(s):  
F. Durst ◽  
J. C. F. Pereira
Keyword(s):  
Reynolds Number ◽  
Steady State ◽  
Separated Flow ◽  
Flow Region ◽  
Reynolds Numbers ◽  
Steady State Flow ◽  
Backward Facing Step ◽  
Step Flow ◽  
Recirculating Flow ◽  
State Flow

This paper presents results of numerical studies of the impulsively starting backward-facing step flow with the step being mounted in a plane, two-dimensional duct. Results are presented for Reynolds numbers of Re = 10; 368 and 648 and for the last two Reynolds numbers comparisons are given between experimental and numerical results obtained for the final steady state flow conditions. In the computational scheme, the convective terms in the momentum equations are approximated by a 13-point quadratic upstream weighted finite-difference scheme and a fully implicit first order forward differencing scheme is used to discretize the temporal derivatives. The computations show that for the higher Reynolds numbers, the flow starts to separate on the lower and upper corners of the step yielding two disconnected recirculating flow regions for some time after the flow has been impulsively started. As time progresses, these two separated flow regions connect up and a single recirculating flow region emerges. This separated flow region stays attached to the step, grows in size and approaches, for the time t → ∞, the dimensions measured and predicted for the separation region for steady laminar backward-facing flow. For the Reynolds number Re = 10 the separation starts at the bottom of the backward-facing step and the separation region enlarges with time until the steady state flow pattern is reached. At the channel wall opposite to the step and for Reynolds number Re = 368, a separated flow region is observed and it is shown to occur for some finite time period of the developing, impulsively started backward-facing step flow. Its dimensions change with time and reduce to zero before the steady state flow pattern is reached. For the higher Reynolds number Re = 648, the secondary separated flow region opposite to the wall is also present and it is shown to remain present for t → ∞. Two kinds of the inlet conditions were considered; the inlet mean flow was assumed to be constant in a first study and was assumed to increase with time in a second one. The predicted flow field for t → ∞ turned out to be identical for both cases. They were also identical to the flow field predicted for steady, backward-facing step flow using the same numerical grid as for the time-dependent predictions.

Empirical Estimates of Body Drag of Large Waterfowl and Raptors

1988 ◽  
Vol 135 (1) ◽  
pp. 253-264 ◽  
Author(s):  
C. J. PENNYCUICK ◽  
HOLLIDAY H. OBRECHT ◽  
MARK R. FULLER
Keyword(s):  
Reynolds Number ◽  
Reynolds Numbers ◽  
The Body ◽  
Number Range ◽  
Empirical Estimates ◽  
A Value ◽  
Body Drag ◽  
Wind Tunnel Measurements ◽  
Large Living ◽  
Performance Estimates

To whom reprint requests should be addressed. Measurements of the body frontal area of some large living waterfowl (Anatidae) and raptors (Falconiformes) were found to vary with the two-thirds power of the body mass, with no distinction between the two groups. Wind tunnel measurements on frozen bodies gave drag coefficients ranging from 0.25 to 0.39, in the Reynolds number range 145 000 to 462 000. Combining these observations with those of Prior (1984), which extended to lower Reynolds numbers, a practical rule is proposed for choosing a value of the body drag coefficient for use in performance estimates.

Friction Factor Behavior From Flat-Plate Tests of 12.15 mm Diameter Hole-Pattern Roughened Surfaces

2011 ◽  
Author(s):  
Thanesh Deva Asirvatham ◽  
Dara W. Childs ◽  
Stephen Phillips
Keyword(s):  
Reynolds Number ◽  
Flat Plate ◽  
Friction Factor ◽  
Dynamic Pressure ◽  
Reynolds Numbers ◽  
Stagnation Temperature ◽  
Flat Plates ◽  
Number Range ◽  
Current Test ◽  
Rough Plate

A flat-plate tester is used to measure the friction-factor behavior for a hole-pattern-roughened surface facing a smooth surface with compressed air as the medium. Measurements of mass flow rate, static pressure drop and stagnation temperature are carried out and used to find a combined (stator + rotor) Fanning friction factor value. In addition, dynamic pressure measurements are made at four axial locations at the bottom of individual holes of the rough plate and at facing locations in the smooth plate. The description of the test rig and instrumentation, and the procedure of testing and calculation are explained in detail in Kheireddin in 2009 and Childs et al. in 2010. Three hole-pattern flat-plates with a hole-pattern diameter of 12.15 mm were tested having depths of 0.9, 1.9, and 2.9 mm. Tests were done with clearances at 0.254, 0.381, and 0.653 mm, and inlet pressures of 56, 70 and 84 bar for a range of pressure ratios, yielding a Reynolds-number range of 100,000 to 800,000. The effects of Reynolds number, clearance, inlet pressure, and hole depth on friction factor are studied. The data are compared to friction factor values of three hole-pattern flat-plates with 3.175 mm diameter holes with hole depths of 1.9, 2.6, and 3.302 mm tested in the same rig described by Kheireddin in 2009. The test program was initiated mainly to investigate a “friction-factor jump” phenomenon cited by Ha et al. in 1992 in test results from a flat-plate tester using facing hole-pattern plates where, at elevated values of Reynolds numbers, the friction factor began to increase steadily with increasing Reynolds numbers. Friction-factor jump was not observed in any of the current test cases.

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