Confined, Milliscale Unsteady Laminar Impinging Slot Jets: Effects of Slot Width on Surface Stagnation Point Nusselt Numbers

2012 ◽  
Vol 134 (4) ◽  
Author(s):  
Dae Hee Lee ◽  
Jong Ryeol Bae ◽  
Mira Ryu ◽  
Phil Ligrani
Keyword(s):  
Reynolds Number ◽  
Nusselt Number ◽  
Stagnation Point ◽  
Constant Heat Flux ◽  
Slot Width ◽  
Distance Ratio ◽  
Stagnation Region ◽  
Spatially Resolved ◽  
Nusselt Numbers ◽  
Plate Distance

The effects of slot width for confined, laminar impinging slot jets of millimeter-scale are considered, including experimental measurements of spatially resolved distributions of local Nusselt numbers measured on a constant heat flux surface. The effects of Reynolds number, nozzle-to-plate distance, and dimensional slot width on the local Nusselt number are investigated for slot nozzle width B values of 0.5 mm, 1.0 mm, and 1.5 mm. Reynolds numbers Re range from 120 to 200, nozzle-to-plate distances H/B vary from 0.75 to 12.5, and the nozzle aspect ratio y/B is 50. Observed are different stagnation point Nusselt number Nuo variations with Re, H/B, and B, where the onset of unsteadiness, and the intermittent flapping motion of the jet column are both associated with important variations to local, stagnation region Nusselt numbers Nuo, as experimental configuration and condition change. The variations of these stagnation-point Nusselt numbers associated with these two modes of unsteadiness are characterized by correlations which provide the dependence upon Reynolds number and normalized nozzle-to-plate distance ratio, H/B, for different dimensional values of B. Also presented are stagnation region Nusselt number variations, for steady, impingement jets at values of H/B less than 4.6–7.8. These are characterized by three separate regimes of behavior, each of which shows significantly different Nuo dependence upon Re, H/B, and B.

Spatially Resolved Heat Transfer and Friction Factors in a Rectangular Channel With 45-Deg Angled Crossed-Rib Turbulators

2003 ◽  
Vol 125 (3) ◽  
pp. 575-584 ◽  
Author(s):  
P. M. Ligrani ◽  
G. I. Mahmood
Keyword(s):  
Heat Transfer ◽  
Reynolds Number ◽  
Nusselt Number ◽  
Rectangular Channel ◽  
Test Surface ◽  
Spatially Resolved ◽  
Nusselt Numbers ◽  
Friction Factors ◽  
Smooth Channel ◽  
Rib Turbulators

Spatially resolved Nusselt numbers, spatially averaged Nusselt numbers, and friction factors are presented for a stationary channel with an aspect ratio of 4 and angled rib turbulators inclined at 45 deg with perpendicular orientations on two opposite surfaces. Results are given at different Reynolds numbers based on channel height from 10,000 to 83,700. The ratio of rib height to hydraulic diameter is .078, the rib pitch-to-height ratio is 10, and the blockage provided by the ribs is 25% of the channel cross-sectional area. Nusselt numbers are given both with and without three-dimensional conduction considered within the acrylic test surface. In both cases, spatially resolved local Nusselt numbers are highest on tops of the rib turbulators, with lower magnitudes on flat surfaces between the ribs, where regions of flow separation and shear layer reattachment have pronounced influences on local surface heat transfer behavior. The augmented local and spatially averaged Nusselt number ratios (rib turbulator Nusselt numbers normalized by values measured in a smooth channel) vary locally on the rib tops as Reynolds number increases. Nusselt number ratios decrease on the flat regions away from the ribs, especially at locations just downstream of the ribs, as Reynolds number increases. When adjusted to account for conduction along and within the test surface, Nusselt number ratios show different quantitative variations (with location along the test surface), compared to variations when no conduction is included. Changes include: (i) decreased local Nusselt number ratios along the central part of each rib top surface as heat transfer from the sides of each rib becomes larger, and (ii) Nusselt number ratio decreases near corners, where each rib joins the flat part of the test surface, especially on the downstream side of each rib. With no conduction along and within the test surface (and variable heat flux assumed into the air stream), globally-averaged Nusselt number ratios vary from 2.92 to 1.64 as Reynolds number increases from 10,000 to 83,700. Corresponding thermal performance parameters also decrease as Reynolds number increases over this range, with values in approximate agreement with data measured by other investigators in a square channel also with 45 deg oriented ribs.

Spatially-Resolved Heat Transfer and Flow Structure in a Rectangular Channel With 45° Angled Rib Turbulators

2002 ◽  
Author(s):  
G. I. Mahmood ◽  
P. M. Ligrani ◽  
S. Y. Won
Keyword(s):  
Heat Transfer ◽  
Reynolds Number ◽  
Nusselt Number ◽  
Flow Structure ◽  
Channel Cross Section ◽  
Cross Sectional ◽  
Spatially Resolved ◽  
Nusselt Numbers ◽  
Smooth Channel ◽  
Rib Turbulators

Spatially-resolved Nusselt numbers and flow structure are presented for a stationary channel with an aspect ratio of 4 and angled rib turbulators inclined at 45° with perpendicular orientations on two opposite surfaces. The flow structure results include time-averaged distributions of streamwise velocity and total pressure, surveyed over flow cross-sectional planes, as well as flow visualization images and friction factors. Results are given at different Reynolds numbers based on channel height from 270 to 90,000. The ratio of rib height to hydraulic diameter is .078, the rib pitch-to-height ratio is 10, and the blockage provided by the ribs is 25 percent of the channel cross-sectional area. Spatially-resolved local Nusselt numbers are highest on tops of the rib turbulators, with lower magnitudes on flat surfaces between the ribs, where regions of flow separation and shear layer re-attachment have pronounced influences on local surface heat transfer behavior. Also important are intense, highly unsteady secondary flows and vortex pairs, which increase secondary advection and turbulent transport over the entire channel cross-section. The resulting augmented local and spatially-averaged Nusselt number ratios (rib turbulator Nusselt numbers normalized by values measured in a smooth channel) generally increase on the rib tops as Reynolds number increases. Nusselt number ratios decrease on the flat regions away from the ribs, especially at locations just downstream of the ribs, as Reynolds number increases. Globally-averaged Nusselt number ratios vary from 3.36 to 2.82 as Reynolds number increases from 10,000 to 90,000. Thermal performance parameters also decrease somewhat as Reynolds number increases over this range, with values in approximate agreement with, or slightly higher than 60° continuous rib data measured by other investigators in a square channel.

Spatially Resolved Surface Heat Transfer for Parallel Rib Turbulators With 45 Deg Orientations Including Test Surface Conduction Analysis

2004 ◽  
Vol 126 (2) ◽  
pp. 193-201 ◽  
Author(s):  
S. Y. Won ◽  
N. K. Burgess ◽  
S. Peddicord ◽  
P. M. Ligrani
Keyword(s):  
Heat Transfer ◽  
Reynolds Number ◽  
Nusselt Number ◽  
Surface Heat ◽  
Test Surface ◽  
Surface Heat Transfer ◽  
Spatially Resolved ◽  
Nusselt Numbers ◽  
Rib Turbulators ◽  
Surface Conduction

Spatially resolved Nusselt numbers, spatially-averaged Nusselt numbers, and friction factors are presented for a stationary channel with an aspect ratio of 4 and angled rib turbulators inclined at 45 deg with parallel orientations on two opposite surfaces. Results are given at different Reynolds numbers based on channel height from 9000 to 76,000. The ratio of rib height to hydraulic diameter is 0.078, the rib pitch-to-height ratio is 10, and the blockage provided by the ribs is 25 percent of the channel cross-sectional area. Nusselt numbers are determined with three-dimensional conduction considered within the acrylic test surface. Test surface conduction results in important variations of surface heat flux, which give decreased local Nusselt number ratios near corners, where each rib joins the flat part of the test surface, and along the central part of each rib top surface. However, even with test surface conduction included in the analysis, spatially-resolved local Nusselt numbers are highest on tops of the rib turbulators, with lower magnitudes on flat surfaces between the ribs, where regions of flow separation and shear layer re-attachment have pronounced influences on local surface heat transfer behavior. The augmented local and spatially averaged Nusselt number ratios (rib turbulator Nusselt numbers normalized by values measured in a smooth channel) decrease on the rib tops, and on the flat regions away from the ribs, especially at locations just downstream of the ribs, as Reynolds number increases. With conduction along and within the test surface considered, globally averaged Nusselt number ratios vary from 3.53 to 1.79 as Reynolds number increases from 9000 to 76,000. Corresponding thermal performance parameters also decrease as Reynolds number increases over this range.

Internal and External Cooling of a Full Coverage Effusion Cooling Plate: Effects of Double Wall Cooling Configuration and Conditions

2017 ◽  
Author(s):  
Zhong Ren ◽  
Sneha Reddy Vanga ◽  
Nathan Rogers ◽  
Phil Ligrani ◽  
Keith Hollingsworth ◽  
...  
Keyword(s):  
Heat Transfer ◽  
Reynolds Number ◽  
Film Cooling ◽  
Reynolds Numbers ◽  
Test Plate ◽  
Blowing Ratio ◽  
Spatially Resolved ◽  
Nusselt Numbers ◽  
Streamwise Location ◽  
Effusion Hole

The present study provides new heat transfer data for both the surfaces of the full coverage effusion cooling plate within a double wall cooling test facility. To produce the cooling stream, a cold-side cross-flow supply for the effusion hole array is employed. Also utilized is a unique mainstream mesh heater, which provides transient thermal boundary conditions, after mainstream flow conditions are established. For the effusion cooled surface, presented are spatially-resolved distributions of surface adiabatic film cooling effectiveness, and surface heat transfer coefficients (measured using infrared thermography). For the coolant side, presented are spatially-resolved distributions of surface Nusselt numbers (measured using liquid crystal thermography). Of interest are the effects of streamwise development, blowing ratio, and Reynolds number. Streamwise hole spacing and spanwise hole spacing (normalized by effusion hole diameter) on the effusion plate are 15 and 4, respectively. Effusion hole diameter is 6.35 mm, effusion hole angle is 25 degrees, and effusion plate thickness is 3 hole diameters. Considered are overall effusion blowing ratios from 2.9 to 7.5, with subsonic, incompressible flow, and constant freestream velocity with streamwise development, for two different mainstream Reynolds numbers. For the hot side (mainstream) of the effusion film cooling test plate, results for two mainflow Reynolds numbers of about 145000 and 96000 show that the adiabatic cooling effectiveness is generally higher for the lower Reynolds number for a particular streamwise location and blowing ratio. The heat transfer coefficient is generally higher for the low Reynolds number flow. This is due to altered supply passage flow behavior, which causes a reduction in coolant lift-off of the film from the surface as coolant momentum, relative to mainstream momentum, decreases. For the coolant side of the effusion test plate, Nusselt numbers generally increase with blowing ratio, when compared at a particular streamwise location and mainflow Reynolds number.

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.

Study of a Cooling Feed Pipe With a Covering Plate on a Ribbed Turbine Case

2019 ◽  
Vol 141 (7) ◽  
Author(s):  
Fangyuan Liu ◽  
Junkui Mao ◽  
Chao Han ◽  
Yuanjian Liu ◽  
Xingsi Han ◽  
...  
Keyword(s):  
Heat Transfer ◽  
Reynolds Number ◽  
Nusselt Number ◽  
Experimental Tests ◽  
Impinging Jet ◽  
Nusselt Numbers ◽  
Spacing Ratio ◽  
Wall Flow ◽  
Complicated Geometry ◽  
Clearance Control

Considering the complicated geometry in an active clearance control (ACC) system, the design of an improved cooling feed pipe with a covering plate for a high pressure ribbed turbine case was investigated. Numerical calculations were analyzed to obtain the interactions between the impinging jet arrays fed by the pipe. Experimental tests were performed to explore the effect of the Reynolds number (2000–20,000) and the jet-to-surface spacing ratio (6–10) on the streamwise-averaged Nusselt numbers. Additionally, the effect of the crossflow produced by the configuration was investigated. Results showed a confined curved channel was formed by the pipe and ribbed case, which resulted in crossflow. The crossflow evolved into vortices and the streamwise-averaged Nusselt number on the high ribs was subsequently increased. Furthermore, the distribution of the heat transfer on the entire surface became more uniform compared with that of traditional impinging jet arrays. A higher Nusselt number was achieved by decreasing the jet-to-surface spacing and increasing the Reynolds number. This investigation has revealed a cooling configuration for controlling the wall flow and evening the heat transfer on the case surface, especially for the ribs.

Impingement Cooling of a Semi-Spherical Concave Surface Covered by Porous Medium with a Jet Trapping Hole

2014 ◽  
Vol 348 ◽  
pp. 162-170
Author(s):  
Pey Shey Wu ◽  
Yi Hung Lin ◽  
Yue Hua Jhuo ◽  
Hsiao Ying Chan
Keyword(s):  
Heat Transfer ◽  
Reynolds Number ◽  
Nusselt Number ◽  
Porous Material ◽  
Target Surface ◽  
Temperature Fields ◽  
Concave Surface ◽  
Far Field ◽  
Impingement Heat Transfer ◽  
Plate Distance

Impingement heat transfer between a circular jet and a semi-spherical concave surface with or without coverage of porous material is investigated experimentally and numerically. For cases with coverage of the porous material on the target plate, a trapping hole for the jet fluid is fabricated. Measured local Nusselt number distributions along a meridian are documented. The flow and temperature fields at the conditions similar to that of experiments were computed with CFD software to support the experimental results and help to explain the physics. Varying parameters include Reynolds number, nozzle-to-plate distance, relative curvature, and a target surface with or without the covered porous material. Results show that the attachment of a porous material increases Nusselt number, with more influence at the stagnation zone than the far field. Increasing Reynolds number usually increases Nusselt number unless it is too high. Although an increase in the nozzle-to-plate distance decreases stagnation Nusselt number, the influence in heat transfer is small in the far field. The trapping-hole diameter should be the same as that of the jet diameter for best heat transfer enhancement.

Crossflows From Jet Array Impingement Cooling: Effects of Hole Array Spacing, Jet-to-Target Plate Distance, and Reynolds Number

2014 ◽  
Author(s):  
Junsik Lee ◽  
Zhong Ren ◽  
Phil Ligrani ◽  
Michael D. Fox ◽  
Hee-Koo Moon
Keyword(s):  
Reynolds Number ◽  
Reynolds Numbers ◽  
Impinging Jets ◽  
Hole Array ◽  
Target Plate ◽  
Impingement Jet ◽  
Nusselt Numbers ◽  
Cooling Effects ◽  
Plate Distance ◽  
Jet Array

Data which illustrate the combined and separate effects of hole array spacing, jet-to-target plate distance, and Reynolds number on cross-flows, and the resulting heat transfer, for an impingement jet array are presented. The array of impinging jets are directed to one flat surface of a channel which is bounded on three sides. Considered are Reynolds numbers ranging from 8,000 to 50,000, jet-to-target plate distances of 1.5D, 3.0D, 5.0D, and 8.0D, and steamwise and spanwise hole spacing of 5D, 8D, and 12D, where D is the impingement hole diameter. In general, the cumulative accumulations of cross-flows, from sequential rows of jets, reduce the effectiveness of each individual jet (especially for jets at larger streamwise locations). The result is sequentially decreasing periodic Nusselt number variations with streamwise development, which generally become more significant as the Reynolds number increases, and as hole spacing decreases. In other situations, the impingement cross-flow results in locally augmented Nusselt numbers. Such variations most often occur at larger downstream locations, as jet interactions are more vigorous, and local magnitudes of mixing and turbulent transport are augmented. This occurs in channels at lower Reynolds numbers, where impingement jets are confined by smaller hole spacing, and smaller jet-to-target plate distance. The overall result is complex dependence of local, line-averaged, and spatially-averaged Nusselt numbers on hole array spacing, jet-to-target plate distance, and impingement jet Reynolds number. Of particular importance are the effects of these parameters on the coherence of the shear layers which form around the impingement jets, as well as on the Kelvin-Helmholtz instability vortices which develop within the shear interface around each impingement jet.

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.

Effect of non-uniform heating on conjugate heat transfer performance for nanofluid flow in a converging duct by a two-phase Eulerian–Lagrangian method

2021 ◽  
pp. 095440892110429
Author(s):  
Md. Faizan ◽  
Sukumar Pati ◽  
Pitamber R Randive
Keyword(s):  
Heat Transfer ◽  
Heat Flux ◽  
Reynolds Number ◽  
Nusselt Number ◽  
Volume Fraction ◽  
Constant Heat Flux ◽  
Lagrangian Model ◽  
Uniform Heating ◽  
Nanofluid Flow ◽  
Two Phase

In this paper, the effect of non-uniform heating on the conjugate thermal and hydraulic characteristics for Al2O3–water nanofluid flow through a converging duct is examined numerically. An Eulerian–Lagrangian model is employed to simulate the two-phase flow for the following range of parameters: Reynolds number (100 ≤ Re ≤ 800), nanoparticle volume fraction (0% ≤  ϕ ≤ 5%) and amplitude of the sinusoidal heat flux ( A = 0, 0.5 and 1). The results reveal a similar affinity between the applied heat flux and local Nusselt number variation qualitatively, mainly at the middle of the duct. The results also indicate that there is a considerable enhancement of Nusselt number with the increase in Reynolds number and the thermal conductivity of wall materials. In addition, increasing the particle loading contributes to an enhanced rate of heat transfer. The heat transfer rate is lower for non-uniform heating when compared with the constant heat flux and the same can be compensated by the application of volume fraction of nanoparticles

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