Determination of Incompressible Flow Friction in Smooth Circular and Noncircular Passages: A Generalized Approach Including Validation of the Nearly Century Old Hydraulic Diameter Concept

1988 ◽  
Vol 110 (4) ◽  
pp. 431-440 ◽  
Author(s):  
N. T. Obot
Keyword(s):  
Reynolds Number ◽  
Friction Factor ◽  
Critical Reynolds Number ◽  
Pressure Coefficient ◽  
Hydraulic Diameter ◽  
Length Scale ◽  
The Difference ◽  
Friction Method ◽  
Reduced Data

It has been demonstrated conclusively that the widely observed differences in data for frictional pressure coefficient between circular and noncircular passages derive from the inseparably connected effects of transition and the choice of a length scale. A relatively simple approach, the critical friction method (CFM), has been developed and when applied to triangular, rectangular, and concentric annular passages, the reduced data lie with remarkable consistency on the circular tube relations. In accordance with the theory of dynamical similarity, it has also been shown that noncircular duct data can be reduced using the hydraulic diameter or any arbitrarily defined length scale. The proposed method is what is needed to reconcile such data with those for circular tubes. With the hydraulic diameter, the critical friction factor almost converges to a universal value for all passages and the correction is simply that required to account for the difference in critical Reynolds number. By contrast, with any other linear parameter, two corrections are needed to compensate for variations in critical friction factor and Reynolds number. Application of the method to roughened passages is discussed.

Analysis of the Fluid Flow in 3D Symmetric Enlarged Channel

2015 ◽  
Vol 813-814 ◽  
pp. 652-657
Author(s):  
Seranthian Ramanathan ◽  
M.R. Thansekhar ◽  
P. Rajesh Kanna ◽  
S. Shankara Narayanan
Keyword(s):  
Reynolds Number ◽  
Fluid Flow ◽  
Software Package ◽  
Critical Reynolds Number ◽  
Pressure Coefficient ◽  
Reynolds Numbers ◽  
Expansion Ratio ◽  
Sudden Expansion ◽  
3 Dimensional ◽  
Ansys Workbench

A 3-Dimensional fluid flow over the sudden expansion region of a horizontal duct for various Reynolds numbers have been studied by using the CFD Software package ANSYS Workbench Fluent v 13.0. The expansion ratio and aspect ratio for the sudden expansion are taken as 2.5 and 4 respectively. This work deals with the finding of critical Reynolds number for a fluid and also the length of re-attachments on stepped walls at various Reynolds numbers for the same fluid. The simulation is carried out in sudden expansion for Reynolds number ranging from 200 to 4000. The variations of local Nusselt number along the stepped walls of the sudden expansion are presented with the heat flux of 35 W/m2 on the stepped walls. Also, the plots of pressure coefficient (Cp) along the stepped walls for different Reynolds numbers are presented in this work.

Experimental Investigation of the Air Flow Behavior and Heat Transfer Characteristics in Microchannels With Different Channel Lengths

2017 ◽  
Vol 139 (5) ◽  
Author(s):  
Zhi Tao ◽  
Zhibing Zhu ◽  
Haiwang Li
Keyword(s):  
Heat Transfer ◽  
Reynolds Number ◽  
Friction Factor ◽  
Critical Reynolds Number ◽  
Flow Behavior ◽  
Channel Length ◽  
Heat Transfer Characteristics ◽  
Transfer Characteristics ◽  
Poiseuille Number ◽  
Channel Lengths

This paper attempts to experimentally investigate the influence of channel length on the flow behavior and heat transfer characteristics in circular microchannels. The diameters of the channels were 0.4 mm and the length of them were 5 mm, 10 mm, 15 mm, and 20 mm, respectively. All experiments were performed with air and completed with Reynolds number in the range of 300–2700. Results of the experiments show that the length of microchannels has remarkable effects on the performance of flow behavior and heat transfer characteristics. Both the friction factor and Poiseuille number drop with the increase of channel length, and the experimental values are higher than the theoretical ones. Moreover, the channel length does not influence the value of critical Reynolds number. Nusselt number decrease as the increase of channel length. Larger Nusselt numbers are obtained in shorter channels. The results also indicate that in all cases, the friction factor decreases and the Poiseuille number increases with the increase of the Reynolds number. It is also observed that the value of critical Reynolds number is between 1500 and 1700 in this paper, which is lower than the value of theoretical critical Reynolds number of 2300.

A Scaling Law for Cavitation Inception in Circular Jet Flows

2007 ◽  
Author(s):  
Brian A. Edge ◽  
Eric G. Paterson ◽  
Mario F. Trujillo
Keyword(s):  
Reynolds Number ◽  
Numerical Simulations ◽  
Scale Effects ◽  
Scaling Law ◽  
Pressure Coefficient ◽  
Cavitation Number ◽  
Scaling Relations ◽  
Length Scale ◽  
Cavitation Inception ◽  
Dynamic Head

The historical data for circular jets indicates that the incipient cavitation number increases with the diameter of the jet. This trend is not explained by the classic cavitation theory which expects incipient cavitation number to remain constant regardless of the jet diameter, flow parameters, or water quality. This paper explores the origins of cavitation scale effects and explains the correlation between the incipient cavitation number, jet diameter, and nuclei size. This is accomplished through turbulence-resolving CFD simulations of the jet flow field at three length scales and Rayleigh-Plesset bubble dynamics for three nuclei sizes. The numerical simulations show that incipient cavitation number (σi) changes significantly as the size of the jet is altered while the Reynolds number and the value of the minimum pressure coefficient are held constant. Larger nuclei bubbles (100μm) exhibit an increase in σi with jet diameter, while moderate (50μm) and small (10μm) nuclei bubble exhibit a decrease in σi as jet diameter increases. The value of σi associated with a small jet was similar for all nuclei sizes. As the jet increased in size, the disparity between the values of σi associated with each nuclei size was found to increase substantially. The equilibrium form of the Rayleigh-Plesset equation was used to derive a correction to the classic theory of cavitation inception. This correction is a function of initial nuclei size and the dynamic head of the flow. As either the nuclei properties or dynamic head of the fluid change, the magnitude of the correction term will also change. This correction to the classic cavitation theory was used to make predictions of how σi will change as length scale and Reynolds number are altered. These equilibrium predictions were found to be in good agreement with the numerical simulations of cavitation inception for large and moderate (100μm and 50μm) nuclei bubbles. Comparisons with the small (10μm) nuclei bubbles indicate that the inertial terms are quite significant for these bubbles, resulting in large discrepancies between the full numerical solution and the equilibrium predictions. In general, the equilibrium scaling relations show that as the length scale of a flow is held constant and the Reynolds number is increased, σi will converge to −CPmin. The scaling relations also show that when Reynolds number is held constant and the length scale of a flow is increased, σi will depart from −CPmin.

scholarly journals A Comparison of Data Reduction Methods for Average Friction Factor Calculation of Adiabatic Gas Flows in Microchannels

Micromachines ◽  
2019 ◽  
Vol 10 (3) ◽  
pp. 171 ◽  
Author(s):  
Danish Rehman ◽  
Gian Morini ◽  
Chungpyo Hong
Keyword(s):  
Experimental Data ◽  
Reynolds Number ◽  
Numerical Analysis ◽  
Friction Factor ◽  
Data Reduction ◽  
Hydraulic Diameter ◽  
Accurate Estimation ◽  
Gas Flows ◽  
Adiabatic Wall ◽  
Loss Coefficients

In this paper, a combined numerical and experimental approach for the estimation of the average friction factor along adiabatic microchannels with compressible gas flows is presented. Pressure-drop experiments are performed for a rectangular microchannel with a hydraulic diameter of 295 μ m by varying Reynolds number up to 17,000. In parallel, the calculation of friction factor has been repeated numerically and results are compared with the experimental work. The validated numerical model was also used to gain an insight of flow physics by varying the aspect ratio and hydraulic diameter of rectangular microchannels with respect to the channel tested experimentally. This was done with an aim of verifying the role of minor loss coefficients for the estimation of the average friction factor. To have laminar, transitional, and turbulent regimes captured, numerical analysis has been performed by varying Reynolds number from 200 to 20,000. Comparison of numerically and experimentally calculated gas flow characteristics has shown that adiabatic wall treatment (Fanno flow) results in better agreement of average friction factor values with conventional theory than the isothermal treatment of gas along the microchannel. The use of a constant value for minor loss coefficients available in the literature is not recommended for microflows as they change from one assembly to the other and their accurate estimation for compressible flows requires a coupling of numerical analysis with experimental data reduction. Results presented in this work demonstrate how an adiabatic wall treatment along the length of the channel coupled with the assumption of an isentropic flow from manifold to microchannel inlet results in a self-sustained experimental data reduction method for the accurate estimation of friction factor values even in presence of significant compressibility effects. Results also demonstrate that both the assumption of perfect expansion and consequently wrong estimation of average temperature between inlet and outlet of a microchannel can be responsible for an apparent increase in experimental average friction factor in choked flow regime.

A Heat-Mass Transfer Analogy Applied to Fully Developed Turbulent Flow in an Annulus

1971 ◽  
Vol 13 (4) ◽  
pp. 286-292 ◽  
Author(s):  
J. S. Lewis
Keyword(s):  
Heat Transfer ◽  
Mass Transfer ◽  
Reynolds Number ◽  
Velocity Profile ◽  
Friction Factor ◽  
Heat Mass Transfer ◽  
Eddy Diffusivity ◽  
Round Tube ◽  
Fully Developed Turbulent Flow ◽  
The Difference

A heat-mass transfer analogy based on the ‘universal’ velocity profile applied to an annulus is compared with analogy values based on similar but more sophisticated expressions for the eddy diffusivity and hence velocity profile. The difference between these analogy values and those of Chilton and Colburn (I)† are noted to be appreciable and to increase with increasing Reynolds number. Heat transfer predictions from mass transfer measurements using ‘universal’ velocity profile type analogies are compared with established results. Friction factor measurements were made and found to be up to 10 per cent higher than the values for flow in a round tube at the corresponding Reynolds number.

Corrections to 'Nonlinear stability of boundary layers for disturbances of various sizes'

1980 ◽  
Vol 371 (1746) ◽  
pp. 439-440 ◽  
Keyword(s):  
Reynolds Number ◽  
Friction Factor ◽  
Boundary Layers ◽  
Nonlinear Stability ◽  
Length Scale ◽  
Neutral Position ◽  
Fixed Frequency ◽  
Parallel Flows ◽  
Definition Of ◽  
The Right

Dr P . Hall has kindly pointed out an error in § 2 of the paper; namely, that (2.10a) renders X complex whenever a is complex, so that inter alia a spatial growth or decay can appear in Ein (2.9). The following alterations and reinterpretations correct for this fault and some minor misprints. Equation (2.10a) should read ‘X( = X ) = h~2X X is then real and can be identified with X throughout the paper, while the terms multiplied by a 2 in (2.11), (2.12), (2.13c), (2.34a, d),(2.35), (2.37), (2.38) should be omitted. The sentence starting two lines below (2.106) should then be replaced by ‘Here, working with a wavenumber a. close to the neutral value a l5 we will keep the reference Reynolds number Re, length scale l*, frequency and velocity U* fixed and suppose that the position x = xx -f h2x2 under investigation is close to the neutral position x = xx for the particular fixed frequency disturbance considered. So the skin friction factor A = Aj + h2X + 0(h3)(2.106') is also slightly perturbed from the neutral value A = Al5 where Ax = from just below (2.2). Notice that this treatment of the nearly neutral state differs from that usually applied to parallel flows where the Reynolds number is usually varied instead’. From (2.106') onwards Ax should replace A. A term — A^ioq ZUX+ kj) should be added to the right side of (2.13c). Equation (2.146) should give U1-*XxA 1, ?72->A1A2but f^3->A1^43+ (2.17) should have A 1 = A 1(X)E-f-c.c. and the right sides of (2.30), (2.31) should be multiplied by —Ay1, Xj1 respectively. An extra term + + should be included in the right side of (2.32) and (2.34c) should have Ax 4- In (2.37) the term — 6AA31 should be replaced by — 6(A1^431 + A2H1) and — A^bX2A 1 should be added to the right side of (2.38). X should replace X in the definition of SF2{u, v,p), just above (2.13a), in TJXx in (2.136) and in U2x + U2 U

Experimental Determination of Transition Reynolds Number for Unsteady Film Cooling

1981 ◽  
Author(s):  
F. K. Tsou ◽  
L. T. Smith ◽  
S. J. Chen
Keyword(s):  
Reynolds Number ◽  
Film Cooling ◽  
Critical Reynolds Number ◽  
Subsonic Flow ◽  
Gas Injection ◽  
Wedge Flow ◽  
Ludwieg Tube ◽  
Order Of Magnitude ◽  
Unsteady Effect

In order to investigate the unsteady effect on transition in film cooling, an 11-m long Ludwieg Tube, consisting of a test section placed between the high pressure and low pressure sections of a shock tube, has been constructed. With this device, a controlled unsteady, low subsonic flow lasting for a period of several milliseconds is obtained. The transition Reynolds Number is determined from the output of thin film heat flux transducers having a response time of a fraction of a microsecond. The results indicate that, in the case of flow without gas injection into the boundary layer, the transition Reynolds Number is one order of magnitude smaller than the critical Reynolds Number for steady wedge flow with the same pressure gradient. With injection, the transition Reynolds Number is small near the injection slot; far downstream, it increases asymptotically to the value for flow without injection.

Experimental Determination of Transition to Turbulence in a Rectangular Channel With Eddy Promoters

1994 ◽  
Vol 116 (3) ◽  
pp. 484-487 ◽  
Author(s):  
J. S. Kapat ◽  
J. Ratnathicam ◽  
B. B. Mikic´
Keyword(s):  
Reynolds Number ◽  
Critical Reynolds Number ◽  
Rectangular Channel ◽  
Transition To Turbulence ◽  
Channel Height ◽  
Laminar To Turbulent Transition ◽  
Turbulent Transition ◽  
Power Spectral ◽  
Unstable Configuration

We report on laminar-to-turbulent transition in a rectangular channel in the presence of periodically placed cylindrical eddy promoters. Transition is identified through the analysis of power spectral density (PSD) of velocity fluctuations. Placement of the eddy promoters in the channel, depending on the geometric configuration, can significantly reduce the value of Reynolds number at transition. The critical Reynolds number (based on the average velocity and the channel height) ranges from 1500 (for an unobstructed channel) to about 400 (for the most unstable configuration we have deployed). For all the configurations tested, demarcation of transition can be correlated with the expression: Reτ≡τ¯w,αv/ρH/2/ν=44˜51, where τw,αv is the spatially averaged value of mean wall shear stress and H is the channel height.

Transition Criteria for Laminar to Turbulent Flow for Yield Power Law (YPL) Fluids Based on Stability Analysis

2013 ◽  
Author(s):  
Goktug Kalayci ◽  
Evren M. Ozbayoglu ◽  
Stefan Z. Miska ◽  
Mengjiao Yu ◽  
Nicholas Takach ◽  
...  
Keyword(s):  
Reynolds Number ◽  
Stability Analysis ◽  
Pressure Drop ◽  
Laminar Flow ◽  
Friction Factor ◽  
Yield Stress ◽  
Flow Regime ◽  
Power Law ◽  
Laminar Flow Regime

It is well known that a Newtonian fluid with the presence of solid particles in suspension behaves non-Newtonian. Higher the solid content, more significant the yield stress of the fluid. Determination of the hydraulic behavior of fluids having a significant yield stress is a challenging task. For engineering purposes, pressure drop within the system, during pipeline transportation, has to be estimated carefully and accurately. Flow regime plays a vital role during hydraulic calculations. The inaccurate determination of flow regime can lead us to large errors in frictional pressure drop calculations and ultimately leads to error in designing and flow assurance point of view, since hydraulic calculations are including a friction factor term, which is a direct function of flow regime. In general, Reynolds number is the main parameter used by the industry for determining the flow regime, and the friction factor. This approach works reasonably accurate for Newtonian fluids. However, as the yield stress of the fluid increases, this conventional technique for determining the flow regime is not as accurate. Although many approaches have been introduced for estimating the flow regime for non-Newtonian fluids, there exists a lack of information and confidence of such predictions for fluids having high yield stress, such as Yield Power Law (YPL) fluids (i.e., Herchel-Bulkley). (1)τ=τy+Kγm This study presents an analytical solution for predicting the transition from laminar to non-laminar flow regime based on Ryan & Johnson’s approach using the stability analysis and equation of motion for YPL fluids. Comparing with the experimental results for YPL fluids under different flow conditions, including laminar and non-laminar flow regimes, show that presented approach gives a better estimation of the transition from laminar to non-laminar flow regime than conventional Reynolds number approach. In some cases, it is observed that although the Reynolds number is high, flow is still laminar, which is predicted accurately using the presented model. This study provides a higher accuracy in estimating the flow regime, which leads to a higher confidence in hydraulic designs and determining limitations of the system in concern.

A unified correction method for Reynolds number, size, and roughness effects on the performance of compressors

2011 ◽  
Vol 225 (7) ◽  
pp. 864-876 ◽  
Author(s):  
M V Casey ◽  
C J Robinson
Keyword(s):  
Reynolds Number ◽  
Flat Plate ◽  
Friction Factor ◽  
Critical Reynolds Number ◽  
Pressure Rise ◽  
Correction Method ◽  
Roughness Effects ◽  
Wide Range ◽  
Fluid Properties ◽  
The Individual

An equation is derived that relates the changes in turbomachinery efficiency with Reynolds number to the changes in the friction factor of an equivalent flat plate. This equation takes into account the different Reynolds number and roughness dependencies of the individual components, and can be used for whole stages and multistage machines. The new method is sufficiently general to correct for changes in Reynolds number due to changes in fluid properties or speed, changes in machine size, or changes in the surface roughness of components for all types of turbomachinery, but is calibrated here for use on axial and radial compressors. The method uses friction factor equations for a flat plate which include fully rough behaviour above an upper critical Reynolds number, a transition region depending on roughness and a region with laminar flow below the lower critical Reynolds number. The correction equation for efficiency includes a single empirical factor. Based on a simple loss analysis and a calibration with over 30 sets of experimental test data covering a wide range of machine types, a suggestion for the variation of this factor with specific speed has been made. Additional correction equations are derived for the shift in flow and the change in pressure rise with Reynolds number and these are also calibrated against the same data.

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