scholarly journals Nusselt Numbers for Poiseuille Flow Over Isoflux Parallel Ridges for Arbitrary Meniscus Curvature

2018 ◽  
Vol 140 (8) ◽  
Author(s):  
Simon Game ◽  
Marc Hodes ◽  
Toby Kirk ◽  
Demetrios T. Papageorgiou
Keyword(s):  
Poiseuille Flow ◽  
Channel Height ◽  
Geometrical Parameters ◽  
Asymptotic Results ◽  
Nusselt Numbers ◽  
Large Channel ◽  
Dual Series Equations ◽  
Collocation Spectral Method ◽  
Pitch Ratio ◽  
Oriented Parallel

We numerically compute Nusselt numbers for laminar, hydrodynamically, and thermally fully developed Poiseuille flow of liquid in the Cassie state through a parallel plate-geometry microchannel symmetrically textured by a periodic array of isoflux ridges oriented parallel to the flow. Our computations are performed using an efficient, multiple domain, Chebyshev collocation (spectral) method. The Nusselt numbers are a function of the solid fraction of the ridges, channel height to ridge pitch ratio, and protrusion angle of menisci. Significantly, our results span the entire range of these geometrical parameters. We quantify the accuracy of two asymptotic results for Nusselt numbers corresponding to small meniscus curvature, by direct comparison against the present results. The first comparison is with the exact solution of the dual series equations resulting from a small boundary perturbation (Kirk et al., 2017, “Nusselt Numbers for Poiseuille Flow Over Isoflux Parallel Ridges Accounting for Meniscus Curvature,” J. Fluid Mech., 811, pp. 315–349). The second comparison is with the asymptotic limit of this solution for large channel height to ridge pitch ratio.

scholarly journals Nusselt numbers for Poiseuille flow over isoflux parallel ridges accounting for meniscus curvature

2016 ◽  
Vol 811 ◽  
pp. 315-349 ◽  
Author(s):  
Toby L. Kirk ◽  
Marc Hodes ◽  
Demetrios T. Papageorgiou
Keyword(s):  
Nusselt Number ◽  
Poiseuille Flow ◽  
Numerical Solutions ◽  
Surface Deformation ◽  
Slip Length ◽  
Constant Heat Flux ◽  
Flux Boundary Condition ◽  
Nusselt Numbers ◽  
Dual Series Equations ◽  
Hydrodynamic Slip

We investigate forced convection in a parallel-plate-geometry microchannel with superhydrophobic walls consisting of a periodic array of ridges aligned parallel to the direction of a Poiseuille flow. In the dewetted (Cassie) state, the liquid contacts the channel walls only at the tips of the ridges, where we apply a constant-heat-flux boundary condition. The subsequent hydrodynamic and thermal problems within the liquid are then analysed accounting for curvature of the liquid–gas interface (meniscus) using boundary perturbation, assuming a small deflection from flat. The effects of this surface deformation on both the effective hydrodynamic slip length and the Nusselt number are computed analytically in the form of eigenfunction expansions, reducing the problem to a set of dual series equations for the expansion coefficients which must, in general, be solved numerically. The Nusselt number quantifies the convective heat transfer, the results for which are completely captured in a single figure, presented as a function of channel geometry at each order in the perturbation. Asymptotic solutions for channel heights large compared with the ridge period are compared with numerical solutions of the dual series equations. The asymptotic slip length expressions are shown to consist of only two terms, with all other terms exponentially small. As a result, these expressions are accurate even for heights as low as half the ridge period, and hence are useful for engineering applications.

scholarly journals Optimal Design of A 12-Slot/10-Pole Six-Phase SPM Machine with Different Winding Layouts for Integrated On-Board EV Battery Charging

Energies ◽  
2021 ◽  
Vol 14 (7) ◽  
pp. 1848
Author(s):  
Ahmed Hemeida ◽  
Mohamed Y. Metwly ◽  
Ayman S. Abdel-Khalik ◽  
Shehab Ahmed
Keyword(s):  
Optimal Design ◽  
Torque Ripple ◽  
Geometrical Parameters ◽  
Battery Chargers ◽  
Core Losses ◽  
Charging Mode ◽  
Slot Opening ◽  
Pitch Ratio ◽  
Fractional Slot Concentrated Winding ◽  
Electric Machine Design

The transition to electric vehicles (EVs) has received global support as initiatives and legislation are introduced in support of a zero-emissions future envisaged for transportation. Integrated on-board battery chargers (OBCs), which exploit the EV drivetrain elements into the charging process, are considered an elegant solution to achieve this widespread adoption of EVs. Surface-mounted permanent-magnet (SPM) machines have emerged as plausible candidates for EV traction due to their nonsalient characteristics and ease of manufacturing. From an electric machine design perspective, parasitic torque ripple and core losses need to be minimized in integrated OBCs during both propulsion and charging modes. The optimal design of EV propulsion motors has been extensively presented in the literature; however, the performance of the optimal traction machine under the charging mode of operation for integrated OBCs has not received much attention in the literature thus far. This paper investigates the optimal design of a six-phase SPM machine employed in an integrated OBC with two possible winding layouts, namely, dual three-phase or asymmetrical six-phase winding arrangements. First, the sizing equation and optimized geometrical parameters of a six-phase 12-slot/10-pole fractional slot concentrated winding (FSCW)-based SPM machine are introduced. Then, variations in the output average torque, parasitic torque ripple, and parasitic core losses with the slot opening width and the PM width-to-pole pitch ratio are further investigated for the two proposed winding layouts under various operation modes. Eventually, the optimally designed machine is simulated using analytical magnetic equivalent circuit (MEC) models. The obtained results are validated using 2D finite element (FE) analysis.

Local Heat Transfer and Flow Structure on and Above a Dimpled Surface in a Channel

2000 ◽  
Author(s):  
G. I. Mahmood ◽  
M. L. Hill ◽  
D. L. Nelson ◽  
P. M. Ligrani ◽  
H.-K. Moon ◽  
...  
Keyword(s):  
Heat Transfer ◽  
Surface Temperature ◽  
Local Heat Transfer ◽  
Streamwise Velocity ◽  
Test Surface ◽  
Channel Height ◽  
Stagnation Temperature ◽  
Vortex Pairs ◽  
Nusselt Numbers ◽  
Flow Visualizations

Experimental results, measured on and above a dimpled test surface placed on one wall of a channel, are given for Reynolds numbers from 1,250 to 61,500 and ratios of air inlet stagnation temperature to surface temperature ranging from 0.68 to 0.94. These include flow visualizations, surveys of time-averaged total pressure and streamwise velocity, and spatially-resolved local Nusselt numbers, which are measured using infrared thermography, used in conjunction with energy balances, thermocouples, and in situ calibration procedures. The ratio of channel height to dimple print diameter is 0.5. Flow visualizations show vortical fluid and vortex pairs shed from the dimples, including a large upwash region and packets of fluid emanating from the central regions of each dimple, as well as vortex pairs and vortical fluid which form near dimple diagonals. These vortex structures augment local Nusselt numbers near the downstream rims of each dimple, both slightly within each depression, and especially on the flat surface just downstream of each dimple. Such augmentations are spread over larger surface areas and become more pronounced as the ratio of inlet stagnation temperature to local surface temperature decreases. As a result, local and spatially-averaged heat transfer augmentations become larger as this temperature ratio decreases. This is due to the actions of vortical fluid in advecting cool fluid from the central parts of the channel to regions close to the hotter dimpled surface.

A two-dimensional-three-component model for spanwise rotating plane Poiseuille flow

2019 ◽  
Vol 880 ◽  
pp. 478-496 ◽  
Author(s):  
Shengqi Zhang ◽  
Zhenhua Xia ◽  
Yipeng Shi ◽  
Shiyi Chen
Keyword(s):  
Reynolds Number ◽  
Poiseuille Flow ◽  
Reynolds Shear Stress ◽  
Streamwise Velocity ◽  
Channel Height ◽  
Neutral Stability ◽  
Two Dimensional ◽  
Plane Poiseuille Flow ◽  
Rotation Numbers ◽  
3C Model

Spanwise rotating plane Poiseuille flow (RPPF) is one of the canonical flow problems to study the effect of system rotation on wall-bounded shear flows and has been studied a lot in the past. In the present work, a two-dimensional-three-component (2D/3C) model for RPPF is introduced and it is shown that the present model is equivalent to a thermal convection problem with unit Prandtl number. For low Reynolds number cases, the model can be used to study the stability behaviour of the roll cells. It is found that the neutral stability curves, critical eigensolutions and critical streamfunctions of RPPF at different rotation numbers ($Ro$) almost collapse with the help of a rescaling with a newly defined Rayleigh number $Ra$ and channel height $H$. Analytic expressions for the critical Reynolds number and critical wavenumber at different $Ro$ can be obtained. For a turbulent state with high Reynolds number, the 2D/3C model for RPPF is self-sustained even without extra excitations. Simulation results also show that the profiles of mean streamwise velocity and Reynolds shear stress from the 2D/3C model share the same linear laws as the fully three-dimensional cases, although differences on the intercepts can be observed. The contours of streamwise velocity fluctuations behave like plumes in the linear law region. We also provide an explanation to the linear mean velocity profiles observed at high rotation numbers.

Nusselt Numbers and Flow Structure on and Above a Shallow Dimpled Surface Within a Channel Including Effects of Inlet Turbulence Intensity Level

2004 ◽  
Vol 127 (2) ◽  
pp. 321-330 ◽  
Author(s):  
P. M. Ligrani ◽  
N. K. Burgess ◽  
S. Y. Won
Keyword(s):  
Nusselt Number ◽  
Flow Structure ◽  
Turbulence Intensity ◽  
Local Nusselt Number ◽  
Channel Height ◽  
Intensity Level ◽  
Stagnation Temperature ◽  
Channel Inlet ◽  
Local Flow ◽  
Nusselt Numbers

Experimental results from a channel with shallow dimples placed on one wall are given for Reynolds numbers based on channel height from 3,700 to 20,000, levels of longitudinal turbulence intensity from 3% to 11% (at the entrance of the channel test section), and a ratio of air inlet stagnation temperature to surface temperature of approximately 0.94. The ratio of dimple depth to dimple print diameter δ∕D is 0.1, and the ratio of channel height to dimple print diameter H∕D is 1.00. The data presented include friction factors, local Nusselt numbers, spatially averaged Nusselt numbers, a number of time-averaged flow structural characteristics, flow visualization results, and spectra of longitudinal velocity fluctuations which, at a Reynolds number of 20,000, show a primary vortex shedding frequency of 8.0Hz and a dimple edge vortex pair oscillation frequency of approximately 6.5Hz. The local flow structure shows some qualitative similarity to characteristics measured with deeper dimples (δ∕D of 0.2 and 0.3), with smaller quantitative changes from the dimples as δ∕D decreases. A similar conclusion is reached regarding qualitative and quantitative variations of local Nusselt number ratio data, which show that the highest local values are present within the downstream portions of dimples, as well as near dimple spanwise and downstream edges. Local and spatially averaged Nusselt number ratios sometimes change by small amounts as the channel inlet turbulence intensity level is altered, whereas friction factor ratios increase somewhat at the channel inlet turbulence intensity level increases. These changes to local Nusselt number data (with changing turbulence intensity level) are present at the same locations where the vortex pairs appear to originate, where they have the greatest influences on local flow and heat transfer behavior.

Fluid Flow and Heat Transfer Around Two Circular Cylinders in Side-by-Side Arrangement

2004 ◽  
Author(s):  
Minter Cheng
Keyword(s):  
Nusselt Number ◽  
Flow Velocity ◽  
Incompressible Flows ◽  
Temperature Fields ◽  
Circular Cylinders ◽  
Rapid Reduction ◽  
Nusselt Numbers ◽  
Gap Flow ◽  
Pitch Ratio ◽  
The Mean

Incompressible flows passing through two circular cylinders in side-by-side arrangement are investigated numerically. The calculations are carried out with pitch ratios from 1.1 to 2.0 at Reynolds number of 1000. The flow and temperature fields, flow interference, and the local and the mean Nusselt numbers are studied in this research. It is observed that for the pitch ratios in the range of 2.0 and 1.5, the emerging jet between cylinders deflects and one wide and one narrow wakes behind the cylinders are formed. The gap flow velocity increases as the pitch ratio decreases and consequently increases the mean Nusselt number of the cylinders. As the pitch ratio decreases and is less than 1.5, the jet deflection is more severe and the gap flow velocity starts to decrease slowly, which results in reducing the mean Nusselt number of the cylinders. Due to the rapid reduction of the narrow wake size, the mean Nusselt number of the cylinder with narrow wake shows an uprising tendency for the decreasing pitch ratio less than 1.2.

Flow and Heat Transfer Characteristics in Rectangular Channels With Staggered Transverse Ribs on Two Opposite Walls

2007 ◽  
Vol 129 (12) ◽  
pp. 1732-1736 ◽  
Author(s):  
Rong Fung Huang ◽  
Shyy Woei Chang ◽  
Kun-Hung Chen
Keyword(s):  
Heat Transfer ◽  
Flow Field ◽  
Turbulence Intensity ◽  
Flow Characteristics ◽  
Channel Height ◽  
Primary Concern ◽  
Height Ratio ◽  
Nusselt Numbers ◽  
Characteristic Flow ◽  
Rectangular Channels

The flow characteristics and the heat transfer properties of the rectangular channels with staggered transverse ribs on two opposite walls are experimentally studied. The rib height to channel height ratio ranges from 0.15 to 0.61 (rib height to channel hydraulic diameter ratio from 0.09 to 0.38). The pitch to rib height ratio covers from 2.5 to 26. The aspect ratio of the rectangular channel is 4. The flow characteristics are studied in a water channel, while the heat transfer experiments are performed in a wind tunnel. Particle image velocimetry (PIV) is employed to obtain the quantitative flow field characteristics. Fine-wire thermocouples imbedded near the inner surface of the bottom channel wall are used to measure the temperature distributions of the wall and to calculate the local and average Nusselt numbers. Using the PIV measured streamline patterns, various characteristic flow modes, thru flow, oscillating flow, and cell flow, are identified in different regimes of the domain of the rib height to channel height ratio and pitch to rib height ratio. The vorticity, turbulence intensity, and wall shear stress of the cell flow are found to be particularly larger than those of other characteristic flow modes. The measured local and average Nusselt numbers of the cell flow are also particularly higher than those of other characteristic flow modes. The distinctive flow properties are responsible for the drastic increase of the heat transfer due to the enhancement of the momentum, heat, and mass exchanges within the flow field induced by the large values of the vorticity and turbulence intensity. Although the thru flow mode is conventionally used in the ribbed channel for industrial application, the cell flow could become the choice if the heat transfer rate, instead of the pressure loss, is the primary concern.

Effects of Dimple Depth on Nusselt Numbers and Friction Factors for Internal Cooling in a Channel

2004 ◽  
Author(s):  
N. K. Burgess ◽  
P. M. Ligrani
Keyword(s):  
Reynolds Number ◽  
Nusselt Number ◽  
Local Nusselt Number ◽  
Reynolds Numbers ◽  
Secondary Flows ◽  
Channel Height ◽  
Stagnation Temperature ◽  
Nusselt Numbers ◽  
Number Ratio ◽  
Friction Factors

Experimental results, measured on dimpled test surfaces placed on one wall of different channels, are given for a ratio of air inlet stagnation temperature to surface temperature of approximately 0.94, and Reynolds numbers based on channel height from 9,940 to 74,800. The data presented include friction factors, local Nusselt numbers, spatially-averaged Nusselt numbers, and globally-averaged Nusselt numbers. The ratios of dimple depth to dimple print diameter δ/D are 0.1, 0.2, and 0.3 to provide information on the influences of dimple depth. The ratio of channel height to dimple print diameter is 1.00. At all Reynolds numbers considered, local and spatially-resolved Nusselt number augmentations increase as dimple depth increases (and all other experimental and geometric parameters are held approximately constant). These are attributed to: (i) increases in the strengths and intensity of vortices and associated secondary flows ejected from the dimples, as well as (ii) increases in the magnitudes of three-dimensional turbulence production and turbulence transport. The effects of these phenomena are especially apparent in local Nusselt number ratio distributions measured just inside of the dimples, and just downstream of the downstream edges of the dimples. Data are also presented to illustrate the effects of Reynolds number, and streamwise development for δ/D = 0.1 dimples. Significant local Nusselt number ratio variations are observed at different streamwise locations, whereas variations with Reynolds number are mostly apparent on flat surfaces just downstream of individual dimples.

Variable Property and Temperature Ratio Effects on Nusselt Numbers in a Rectangular Channel With 45 Deg Angled Rib Turbulators

2003 ◽  
Vol 125 (5) ◽  
pp. 769-778 ◽  
Author(s):  
G. I. Mahmood ◽  
P. M. Ligrani ◽  
K. Chen
Keyword(s):  
Flow Direction ◽  
Rectangular Channel ◽  
Channel Height ◽  
Global Changes ◽  
Stagnation Temperature ◽  
Temperature Ratio ◽  
Height Range ◽  
Nusselt Numbers ◽  
Friction Factors ◽  
Rib Turbulators

Measured local and spatially-averaged Nusselt numbers and friction factors (all time-averaged) are presented which show the effects of temperature ratio and variable properties in a rectangular channel with rib turbulators, and an aspect ratio of 4. The ratio of air inlet stagnation temperature to local surface temperature Toi/Tw varies from 0.66 to 0.95, and Reynolds numbers based on channel height range from 10,000 to 83,700. The square cross-section ribs are placed on two opposite surfaces, and are oriented at angles of +45 deg and −45 deg, respectively, with respect to the bulk flow direction. The ratio of rib height to channel hydraulic diameter is 0.078, the rib pitch-to-height ratio is 10, and the ribs block 25 percent of the channel cross-sectional area. Ratios of globally-averaged rib Nusselt numbers to baseline, constant property Nusselt numbers, Nu̿/Nuo,cp, increase from 2.69 to 3.10 as the temperature ratio Toi/Tw decreases from 0.95 to 0.66 (provided Reynolds number ReH is approximately constant). Friction factor ratios f/fo,cp then decrease as Toi/Tw decreases over this same range of values. In each case, a correlation equation is given which matches the measured global variations. Such global changes are a result of local Nusselt number ratio increases with temperature ratio, which are especially pronounced on the flat surfaces just upstream and just downstream of individual ribs. Thermal performance parameters are also given, which are somewhat lower in the ribbed channel than in channels with dimples and/or protrusions mostly because of higher rib form drag and friction factors.

Streamwise Flow and Heat Transfer Distributions for Jet Array Impingement With Crossflow

1981 ◽  
Author(s):  
L. W. Florschuetz ◽  
C. R. Truman ◽  
D. E. Metzger
Keyword(s):  
Heat Transfer ◽  
Flow Distribution ◽  
Reynolds Numbers ◽  
Geometric Parameters ◽  
Channel Height ◽  
Transfer Coefficients ◽  
Heat Transfer Coefficients ◽  
Nusselt Numbers ◽  
Flow And Heat Transfer ◽  
Circular Jets

Two-dimensional arrays of circular jets of air impinging on a heat transfer surface parallel to the jet orifice plate are considered. The air, after inpingement, is constrained to exit in a single direction along the channel formed by the surface and the jet plate. The downstream jets are subjected to a crossflow originating from the upstream jets. Experimental and theoretical results obtained for streamwise distributions of jet and crossflow velocities are presented and compared. Measured Nusselt numbers resolved to one streamwise hole spacing are correlated with individual spanwise row jet Reynolds numbers and crossflow-to-jet velocity ratios. Correlations are presented for both inline and staggered hole patterns including effects of geometric parameters: streamwise hole spacing, spanwise hole spacing, and channel height, normalized by hole diameter. The physical mechanisms influencing heat transfer coefficients as a function of flow distribution and geometric parameters are also discussed.

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