scholarly journals Prediction and Measurement of Pressure Drop of Water Flowing in a Rectangular Microchannel

2013 ◽  
Vol 3 (2) ◽  
Author(s):  
M. Mirmanto
Keyword(s):  
Experimental Data ◽  
Reynolds Number ◽  
Pressure Drop ◽  
Reynolds Numbers ◽  
Hydraulic Diameter ◽  
Inlet Temperature ◽  
Mean Velocity ◽  
Rectangular Microchannel ◽  
The Mean ◽  
Poiseuille Number

This paper presents experimental results of pressure drop measurement and prediction of water flowing through a copper rectangular microchannel with a hydraulic diameter of 437 µm. The aim of this work is to identify discrepancies between experimental data and macrochannel theory. An inlet temperature of 60oC was kept constant at the channel entrance and the experiments were performed with Reynolds numbers (based on the mean velocity and hydraulic diameter) ranging up to 4500.  The results show that the pressure drop prediction agrees with the theory. However, the trend of Poiseuille number with the Reynolds number was not constant for laminar flow. This could be due to the entrance effect. Moreover, the friction factor theory could predict the experimental data for turbulent flow. Thus, in this experiment, the theory for flow in macro passages is still applicable.

scholarly journals Model-based scaling of the streamwise energy density in high-Reynolds-number turbulent channels

2013 ◽  
Vol 734 ◽  
pp. 275-316 ◽  
Author(s):  
Rashad Moarref ◽  
Ati S. Sharma ◽  
Joel A. Tropp ◽  
Beverley J. McKeon
Keyword(s):  
Reynolds Number ◽  
Stokes Equations ◽  
Reynolds Numbers ◽  
Low Rank ◽  
Navier Stokes ◽  
Mean Velocity ◽  
Navier Stokes Equations ◽  
Self Similar ◽  
The Mean ◽  
High Reynolds

AbstractWe study the Reynolds-number scaling and the geometric self-similarity of a gain-based, low-rank approximation to turbulent channel flows, determined by the resolvent formulation of McKeon & Sharma (J. Fluid Mech., vol. 658, 2010, pp. 336–382), in order to obtain a description of the streamwise turbulence intensity from direct consideration of the Navier–Stokes equations. Under this formulation, the velocity field is decomposed into propagating waves (with single streamwise and spanwise wavelengths and wave speed) whose wall-normal shapes are determined from the principal singular function of the corresponding resolvent operator. Using the accepted scalings of the mean velocity in wall-bounded turbulent flows, we establish that the resolvent operator admits three classes of wave parameters that induce universal behaviour with Reynolds number in the low-rank model, and which are consistent with scalings proposed throughout the wall turbulence literature. In addition, it is shown that a necessary condition for geometrically self-similar resolvent modes is the presence of a logarithmic turbulent mean velocity. Under the practical assumption that the mean velocity consists of a logarithmic region, we identify the scalings that constitute hierarchies of self-similar modes that are parameterized by the critical wall-normal location where the speed of the mode equals the local turbulent mean velocity. For the rank-1 model subject to broadband forcing, the integrated streamwise energy density takes a universal form which is consistent with the dominant near-wall turbulent motions. When the shape of the forcing is optimized to enforce matching with results from direct numerical simulations at low turbulent Reynolds numbers, further similarity appears. Representation of these weight functions using similarity laws enables prediction of the Reynolds number and wall-normal variations of the streamwise energy intensity at high Reynolds numbers (${Re}_{\tau } \approx 1{0}^{3} {\unicode{x2013}} 1{0}^{10} $). Results from this low-rank model of the Navier–Stokes equations compare favourably with experimental results in the literature.

Effect of Upstream Flow Processes on Hydrodynamic Development in a Duct

1977 ◽  
Vol 99 (3) ◽  
pp. 556-560 ◽  
Author(s):  
E. M. Sparrow ◽  
C. E. Anderson
Keyword(s):  
Reynolds Number ◽  
Reynolds Numbers ◽  
Center Line ◽  
Viscous Effects ◽  
Mean Velocity ◽  
Inertia Effects ◽  
Reynolds Number Flow ◽  
Compact Size ◽  
Number Flow ◽  
The Mean

Consideration is given to the developing laminar flow in a parallel plate channel, with the fluid being drawn from a large upstream space. The flow fields upstream and downstream of the channel inlet were solved simultaneously. A finite-difference technique was employed which was facilitated by a coordinate transformation that telescoped the broadly extended flow domain into a more compact size. For the solutions, the Reynolds number was assigned values from 1 to 1000, covering the range from viscous-dominated flows to those where both viscous and inertia effects are relevant. Streamline maps indicate that whereas a low Reynolds number flow glides smoothly into the channel, a high Reynolds number flow has to turn sharply to enter the channel, with the result that the sharply turning fluid tends to overshoot at first and then readjust. A significant amount of upstream predevelopment occurs at low and intermediate Reynolds numbers. Thus, for example, at Re = 1 and 100, the center-line velocities at inlet are, respectively, 1.37 and 1.13 times the mean velocity (the fully developed center-line velocity is 1.5 times the mean). The upstream pressure drop, measured in terms of the velocity head, is substantially increased by viscous effects at low and intermediate Reynolds numbers.

Structure of Turbulent Flows Over Forward Facing Steps With Adverse Pressure Gradient

2016 ◽  
Vol 138 (11) ◽  
Author(s):  
Hassan Iftekhar ◽  
Martin Agelin-Chaab
Keyword(s):  
Reynolds Number ◽  
Pressure Gradient ◽  
Turbulent Flows ◽  
Large Scale ◽  
Adverse Pressure Gradient ◽  
Reynolds Numbers ◽  
Step Height ◽  
Reattachment Length ◽  
Mean Velocity ◽  
The Mean

This paper reports an experimental study on the effects of adverse pressure gradient (APG) and Reynolds number on turbulent flows over a forward facing step (FFS) by employing three APGs and three Reynolds numbers. A particle image velocimetry (PIV) technique was used to conduct velocity measurements at several locations downstream, and the flow statistics up to 68 step heights are reported. The step height was maintained at 6 mm, and the Reynolds numbers based on the step height and freestream mean velocity were 1600, 3200, and 4800. The mean reattachment length increases with the increase in Reynolds number without the APG whereas the mean reattachment length remains constant for increasing APG. The proper orthogonal decomposition (POD) results confirmed that higher Reynolds numbers caused the large-scale structures to be more defined and organized close to the step surface.

Nonasymptotic behavior of developing turbulent pipe flow

1976 ◽  
Vol 54 (3) ◽  
pp. 268-278 ◽  
Author(s):  
J. K. Reichert ◽  
R. S. Azad
Keyword(s):  
Reynolds Number ◽  
Pipe Flow ◽  
Reynolds Numbers ◽  
Peak Position ◽  
Turbulent Pipe Flow ◽  
Shear Stresses ◽  
Mean Velocity ◽  
Inlet Region ◽  
The Mean ◽  
Hot Film

Detailed measurements of mean velocity U profiles, in the inlet 70 diameters of a pipe, show that the development of turbulent pipe flow is nonasymptotic. Experiments were done at seven Reynolds numbers in the range 56 000–15 3000. Contours of U and V fields are presented for two representative Reynolds numbers. A U component peak exceeding the fully developed values has been found to occur along the pipe centerline. The Reynolds number behavior of the peak position has been determined. Hot film measurements of the mean wall shear stresses in the inlet region also show a nonasymptotic development consistent with the mean velocity results.

scholarly journals Fluid motion between parallel planes. Dynamical stability

1946 ◽  
Vol 186 (1006) ◽  
pp. 391-409 ◽  
Keyword(s):  
Reynolds Number ◽  
Critical Reynolds Number ◽  
Fluid Motion ◽  
Reynolds Numbers ◽  
Small Disturbance ◽  
Mean Velocity ◽  
High Reynolds Numbers ◽  
The Mean ◽  
Parabolic Flow ◽  
High Reynolds

If U is the velocity of the mean motion the following main results are obtained: 1. The region where U = c , c being the wave velocity, is the source where vibrations are generated; i.e. the slowly varying vibrations give rise to large rapidly varying vibrations in passing through the critical point. 2. Curved profiles admit a periodic motion at sufficiently high Reynolds numbers. 3. Parabolic flow is unstable at high Reynolds numbers; i.e. an infinitely small disturbance is sufficient to break up such flow. The critical Reynolds number is equal to R = U 0 h/v =6700, and the corresponding wavelength is about three times the width of the channel ( U 0 is the mean velocity at the axis, and h is the half-width of the channel).

The intermediate wake of a body of revolution at high Reynolds numbers

2010 ◽  
Vol 659 ◽  
pp. 516-539 ◽  
Author(s):  
JUAN M. JIMÉNEZ ◽  
M. HULTMARK ◽  
A. J. SMITS
Keyword(s):  
Reynolds Number ◽  
Reynolds Numbers ◽  
Stress Distributions ◽  
Body Of Revolution ◽  
Self Similarity ◽  
Mean Velocity ◽  
High Reynolds Numbers ◽  
Order Of Magnitude ◽  
The Mean ◽  
High Reynolds

Results are presented on the flow field downstream of a body of revolution for Reynolds numbers based on a model length ranging from 1.1 × 106 to 67 × 106. The maximum Reynolds number is more than an order of magnitude larger than that obtained in previous laboratory wake studies. Measurements are taken in the intermediate wake at locations 3, 6, 9, 12 and 15 diameters downstream from the stern in the midline plane. The model is based on an idealized submarine shape (DARPA SUBOFF), and it is mounted in a wind tunnel on a support shaped like a semi-infinite sail. The mean velocity distributions on the side opposite the support demonstrate self-similarity at all locations and Reynolds numbers, whereas the mean velocity distribution on the side of the support displays significant effects of the support wake. None of the Reynolds stress distributions of the flow attain self-similarity, and for all except the lowest Reynolds number, the support introduces a significant asymmetry into the wake which results in a decrease in the radial and streamwise turbulence intensities on the support side. The distributions continue to evolve with downstream position and Reynolds number, although a slow approach to the expected asymptotic behaviour is observed with increasing distance downstream.

Behavior of Separation Bubble and Reattached Boundary Layer Around a Circular Leading Edge

1994 ◽  
Author(s):  
B. K. Hazarika ◽  
C. Hirsch
Keyword(s):  
Boundary Layer ◽  
Reynolds Number ◽  
Separation Bubble ◽  
Low Frequency ◽  
Leading Edge ◽  
Reynolds Numbers ◽  
Mean Velocity ◽  
Low Frequency Oscillations ◽  
Lower Reynolds Number ◽  
The Mean

The flow around a circular leading edge airfoil is investigated in an incompressible, low turbulence freestream. Hot-wire measurements are performed through the separation bubble, the reattachment and the recovery region till development of the fully turbulent boundary layer. The results of the experiments in the range of Reynolds numbers 1.7×103 to 11.8×103 are analysed and presented in this paper. A separation bubble is present near the leading edge at all Reynolds numbers. At the lowest Reynolds number investigated, the transition is preceded by strong low frequency oscillations. The correlation given by Mayle for prediction of transition of short separation bubbles is successful at the lower Reynolds number cases. The length of the separation bubble reduces considerably with increasing Reynolds number in the range investigated. The turbulence in the reattached flow persists even when the Reynolds number based on momentum thickness of the reattached boundary layer is small. The recovery length of the reattached layer is relatively short and the mean velocity profile follows logarithmic law within a short distance downstream of the reattachment point and the friction coefficient conforms to Prandtl-Schlichting skin-friction formula for a smooth flat plate at zero incidence.

An experimental study of reverse transition in two-dimensional channel flow

1968 ◽  
Vol 31 (3) ◽  
pp. 609-623 ◽  
Author(s):  
M. A. Badri Narayanan
Keyword(s):  
Reynolds Number ◽  
Reynolds Numbers ◽  
Wave Number ◽  
Two Dimensional ◽  
Mean Velocity ◽  
Lateral Direction ◽  
Reverse Transition ◽  
Lissajous Figures ◽  
The Mean ◽  
Prime 2

An experimental investigation on reverse transition from turbulent to laminar flow in a two-dimensional channel was carried out. The reverse transition occurred when Reynolds number of an initially turbulent flow was reduced below a certain value by widening the duct in the lateral direction. The experiments were conducted at Reynolds numbers of 625, 865, 980 and 1250 based on half the height of the channel and the average of the mean velocity. At all these Reynolds numbers the initially turbulent mean velocity profiles tend to become parabolic. The longitudinal and vertical velocity fluctuations ($\overline{u^{\prime 2}}$and$\overline{v^{\prime 2}}$) averaged over the height of the channel decrease exponentially with distance downstream, but$\overline{u^{\prime}v^{\prime}} $tends to become zero at a reasonably well-defined point. During reverse transition$\overline{u^{\prime}}\overline{v^{\prime}}/\sqrt{\overline{u^{\prime 2}}}\sqrt{\overline{v^{\prime 2}}}$also decreases as the flow moves downstream and Lissajous figures taken withu’ andv’ signals confirm this trend. There is approximate similarly between$\overline{u^{\prime 2}} $profiles if the value of$\overline{u^{\prime 2}_{\max}} $and the distance from the wall at which it occurs are taken as the reference scales. The spectrum of$\overline{u^{\prime 2}} $is almost similar at all stations and the non-dimensional spectrum is exponential in wave-number. All the turbulent quantities, when plotted in appropriate co-ordinates, indicate that there is a definite critical Reynolds number of 1400±50 for reverse transition.

Computational Fluid Dynamics Based Investigation of the Performance of Hybrid Heat Sinks

2021 ◽  
Author(s):  
Anas Alkhazaleh ◽  
Mohamed Younes El-Saghir Selim ◽  
Fadi Alnaimat ◽  
Bobby Mathew
Keyword(s):  
Reynolds Number ◽  
Pressure Drop ◽  
Thermal Resistance ◽  
Reynolds Numbers ◽  
Hydraulic Diameter ◽  
Heat Sinks ◽  
Geometrical Parameters ◽  
Microchannel Heat Sink ◽  
Liquid Cooling ◽  
Pin Fins

Abstract This article discusses the mathematical modeling of a straight microchannel heat sink, embedded with pin-fins, for purposes of liquid cooling of microelectronic chips. The influence of three different geometrical parameters, pin fins’ diameter, pitch, and hydraulic diameter, on the heat sinks performance is studied. The studies are performed for Reynolds numbers varying from 250 to 2000, and the results are quantified based on thermal resistance and pressure drop. The heat sinks embedded with pin fins have better performance in terms of thermal resistance but at the same time have higher pressure drop. Studies revealed that increasing the pin fins’ diameter, pitch, and hydraulic diameter have an influence on the thermal resistance; the thermal resistance is found to be decreasing with increasing these parameters for the same Reynolds number. For the cases studied, the reduction in thermal resistance of straight microchannels embedded with pin fins varied from 18% to 60% compared with that of traditional straight microchannels for different heat sinks configurations and Reynolds number. On the other hand, the pressure drop is increasing with an increase in pin fins’ diameter and pitch, while it is found to be decreasing with increasing the hydraulic diameter.

scholarly journals A theory for the streamwise turbulent fluctuations in high Reynolds number pipe flow

2012 ◽  
Vol 707 ◽  
pp. 575-584 ◽  
Author(s):  
Marcus Hultmark
Keyword(s):  
Experimental Data ◽  
Reynolds Number ◽  
Pipe Flow ◽  
High Reynolds Number ◽  
Mean Flow ◽  
Mean Velocity ◽  
Theoretical Derivation ◽  
Turbulent Fluctuations ◽  
The Mean ◽  
High Reynolds

AbstractA new theory for the streamwise turbulent fluctuations in fully developed pipe flow is proposed. The theory extends the similarities between the mean flow and the streamwise turbulence fluctuations, as observed in experimental high Reynolds number data, to also include the theoretical derivation. Connecting the derivation of the fluctuations to that of the mean velocity at finite Reynolds number as introduced by Wosnik, Castillo & George (J. Fluid Mech., vol. 421, 2000, pp. 115–145) can explain the logarithmic behaviour as well as the coefficient of the logarithm. The slope of the logarithm, for the fluctuations, depends on the increase of the fluctuations with Reynolds number, which is shown to agree very well with the experimental data. A mesolayer, similar to that introduced by Wosnik et al., exists for the fluctuations for $300\gt {y}^{+ } \gt 800$, which coincides with the mesolayer for the mean velocities. In the mesolayer, the flow is still affected by viscosity, which shows up as a decrease in the fluctuations.

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