Effect of Compressibility on Velocity Profile and Friction Factor of Gaseous Laminar Flows in a Microtube

2021 ◽  
Author(s):  
Shintaro Murakami ◽  
Toyoda Kaoru ◽  
Yutaka Asako
Keyword(s):  
Reynolds Number ◽  
Mach Number ◽  
Laminar Flow ◽  
Velocity Profile ◽  
Friction Factor ◽  
Radial Direction ◽  
Flow Model ◽  
Laminar Flows ◽  
Compressibility Effect ◽  
Fanning Friction Factor

Abstract Laminar flow of nitrogen gas in a microtube was simulated numerically to obtain velocity profile and Fanning friction factor in a quasi-fully developed region. The numerical procedure based on Arbitrary-Lagrangian-Eulerian method solved two-dimensional compressible momentum and energy equations. The computations were performed for a wide range of Reynolds number in laminar flow regime with adiabatic wall condition. It was found that the velocity profile deviates from the parabola as Mach number increases, and the product of Fanning friction factor and Reynolds number is not a constant but a function of only Mach number. To explain the compressibility effect, a new theoretical flow model which gives the velocity profile of gaseous laminar flows in a microtube was proposed under the assumption of purely axial flow. The theoretical velocity profile is taking radial-direction density change into account, and coincides with the numerically obtained velocity profile. The proposed flow model also shows that the Fanning friction factor of a compressible flow in a microtube is expressed by a quadratic function of Mach number. The coefficient of the Mach squared term is 40% of the numerically obtained correlation. The compressibility effect on friction factor of gaseous laminar flows in a microtube partly results from velocity profile change which must occur to keep the mass velocity profile when density changes in radial direction. The remainder of the compressibility effect can be considered to result from actual mass transfer in the radial direction whose existence was demonstrated by the numerical results.

Local Friction Factor of Compressible Laminar or Turbulent Flow in Micro-Tubes

2011 ◽  
Author(s):  
Shintaro Murakami ◽  
Yutaka Asako
Keyword(s):  
Reynolds Number ◽  
Mach Number ◽  
Friction Factor ◽  
Turbulent Flows ◽  
Numerical Procedure ◽  
Choked Flow ◽  
Curvilinear Grid ◽  
Wide Range ◽  
Darcy Friction Factor ◽  
Fanning Friction Factor

Laminar/turbulent flows of compressible fluid in microtubes were simulated numerically to obtain the effect of compressibility on the local pipe friction factors. For gaseous flows, the effect of compressibility had not been clarified except for laminar flow whose Mach number is less than 0.45, so the present work extended this to handle higher speed flows including choked ones and turbulent flows. The numerical procedure based on arbitrary-Lagrangian-Eulerian method solves two-dimensional compressible momentum and energy equations. The Lam-Bremhorst Low-Reynolds number turbulence model was adopted to calculate eddy viscosity coefficient and turbulence energy. The physical domain of simulation with the back region downstream from the outlet of the micro-tube was used to be able to calculate the case of under-expansion flow in the tube. The orthogonal curvilinear grid was used for the computational mesh to obtain accurate results. The computations were performed for a wide range of Reynolds number and Mach number including laminar/turbulent choked flows. It was found that in laminar regimes the ratio of the Darcy friction factor to its conventional (incompressible flow’s) value is a function of Mach number and the same goes for the Fanning friction factor. On the other hand, in turbulent regimes, the ratio is still a function of Mach number for the Darcy friction factor but is equal to about unity for the Fanning friction factor. Namely, the Fanning friction factor of gaseous flow in micro-tubes coincides with Blasius formula, even when Mach number is not small and compressibility effect appears. This fact can be seen in choked flow.

scholarly journals An alternative form of the Darcy equation

2014 ◽  
Vol 18 (suppl.2) ◽  
pp. 617-619 ◽  
Author(s):  
Mohamed Awad
Keyword(s):  
Reynolds Number ◽  
Laminar Flow ◽  
Friction Factor ◽  
Poiseuille Flow ◽  
Alternative Form ◽  
Bejan Number ◽  
Left Hand ◽  
Darcy Equation ◽  
The Right ◽  
Fanning Friction Factor

This study presents an alternative form of the Darcy equation. This alternative form will be presented with the use of Bejan number (Be) in the Left Hand Side (LHS) of the equation. The main advantage in this alternative form of the Darcy equation is presenting both the Left Hand Side (LHS) and the Right Hand Side (RHS) as dimensionless quantities. For instance, this is similar to the relation of Fanning friction factor with Reynolds number for Hagen-Poiseuille flow (fully developed laminar flow in a circular pipe).

scholarly journals Heavy Oil Laminar Flow in Corrugated Ducts: A Numerical Study Using the Galerkin-Based Integral Method

Energies ◽  
2020 ◽  
Vol 13 (6) ◽  
pp. 1363
Author(s):  
Valdecir Alves dos Santos Júnior ◽  
Severino Rodrigues de Farias Neto ◽  
Antonio Gilson Barbosa de Lima ◽  
Igor Fernandes Gomes ◽  
Israel Buriti Galvão ◽  
...  
Keyword(s):  
Fluid Dynamics ◽  
Reynolds Number ◽  
Laminar Flow ◽  
Heavy Oil ◽  
Integral Method ◽  
Numerical Study ◽  
Temperature Dependent ◽  
Flow Through ◽  
Fanning Friction Factor ◽  
Cylindrical Duct

Fluid flow in pipes plays an important role in different areas of academia and industry. Due to the importance of this kind of flow, several studies have involved circular cylindrical pipes. This paper aims to study fully developed internal laminar flow through a corrugated cylindrical duct, using the Galerkin-based integral method. As an application, we present a study using heavy oil with a relative density of 0.9648 (14.6 °API) and temperature-dependent viscosities ranging from 1715 to 13000 cP. Results for different fluid dynamics parameters, such as the Fanning friction factor, Reynolds number, shear stress, and pressure gradient, are presented and analyzed based on the corrugation number established for each section and aspect ratio of the pipe.

Analytical Solution for Newtonian Laminar Flow Through the Concave and Convex Ducts

2009 ◽  
Vol 131 (9) ◽  
Author(s):  
M. Firouzi ◽  
S. H. Hashemabadi
Keyword(s):  
Reynolds Number ◽  
Steady State ◽  
Friction Factor ◽  
Cross Section ◽  
Cross Sections ◽  
Fully Developed Flow ◽  
Pipe Flows ◽  
Dimensionless Velocity ◽  
Flow Through ◽  
Fanning Friction Factor

In this paper, the motion equation for steady state, laminar, fully developed flow of Newtonian fluid through the concave and convex ducts has been solved both numerically and analytically. These cross sections can be formed due to the sedimentation of heavy components such as sand, wax, debris, and corrosion products in pipe flows. The influence of duct cross section on dimensionless velocity profile, dimensionless pressure drop, and friction factor has been reported. Finally based on the analytical solutions three new correlations have been proposed for the product of Reynolds number and Fanning friction factor (Cf Re) for these geometries.

A study of non-redirection louvre fin-and-tube heat exchangers

1998 ◽  
Vol 212 (1) ◽  
pp. 1-14 ◽  
Author(s):  
C-C Wang ◽  
Y-P Chang ◽  
K-Y Chi ◽  
Y-J Chang
Keyword(s):  
Heat Transfer ◽  
Reynolds Number ◽  
Pressure Drop ◽  
Wind Tunnel ◽  
Friction Factor ◽  
Heat Exchangers ◽  
Geometrical Parameters ◽  
Tube Size ◽  
Collar Diameter ◽  
Fanning Friction Factor

Extensive experiments on the heat transfer and pressure drop characteristics of louvre finand-tube heat exchangers were carried out. In the present study, 14 samples of non-redirection louvre fin-and-tube heat exchangers with different geometrical parameters, including the number of tube row, fin pitch and tube size, were tested in a wind tunnel. Results are presented as plots of the Fanning friction factor f and the Colburn j factor against Reynolds number based on the tube collar diameter in the range of 300–8000.

scholarly journals Численное исследование вихревых структур и теплообмена при сверхзвуковом обтекании области сопряжения затупленного тела и пластины

2020 ◽  
Vol 90 (2) ◽  
pp. 185
Author(s):  
Е.В. Колесник ◽  
Е.М. Смирнов
Keyword(s):  
Heat Transfer ◽  
Numerical Simulation ◽  
Reynolds Number ◽  
Mach Number ◽  
Laminar Flow ◽  
Numerical Data ◽  
Qualitative And Quantitative ◽  
Plate Length ◽  
Gas Dynamic ◽  
Supersonic Laminar

In the paper, the results of numerical simulation of a supersonic laminar flow past a fin-body junction are presented. The gas-dynamic and vortex structure of the flow, determined by viscous-inviscid interaction, is analyzed. Numerical data showing the qualitative and quantitative effects on the flow structure and heat transfer of the following parameters: Mach number, Reynolds number, temperature factor and plate length, are presented

The Effect of Twisted-Tape Width on Heat Transfer and Pressure Drop for Fully Developed Laminar Flow

1996 ◽  
Vol 118 (3) ◽  
pp. 584-589 ◽  
Author(s):  
W. M. Chakroun ◽  
S. F. Al-Fahed
Keyword(s):  
Heat Transfer ◽  
Reynolds Number ◽  
Pressure Drop ◽  
Laminar Flow ◽  
Friction Factor ◽  
Twisted Tape ◽  
Constant Wall Temperature ◽  
Low Reynolds Number Flows ◽  
Temperature Boundary ◽  
Series Of Experiments

A series of experiments was conducted to study the effect of twisted-tape width on the heat transfer and pressure drop with laminar flow in tubes. Data for three twisted-tape wavelengths, each with five different widths, have been collected with constant wall temperature boundary condition. Correlations for the friction factor and Nusselt number are also available. The correlations predict the experimental data to within 10 to 15 percent for the heat transfer and friction factor, respectively. The presence of the twisted tape has caused the friction factor to increase by a factor of 3 to 7 depending on Reynolds number and the twisted-tape geometry. Heat transfer results have shown an increase of 1.5 to 3 times that of plain tubes depending on the flow conditions and the twisted-tape geometry. The width shows no effect on friction factor and heat transfer in the low range of Reynolds number but has a more pronounced effect on heat transfer at the higher range of Reynolds number. It is recommended to use loose-fit tapes for low Reynolds number flows instead of tight-fit in the design of heat exchangers because they are easier to install and remove for cleaning purposes.

Laminar flow in rotating curved pipes

1996 ◽  
Vol 329 ◽  
pp. 373-388 ◽  
Author(s):  
Hiroshi Ishigaki
Keyword(s):  
Experimental Data ◽  
Laminar Flow ◽  
Friction Factor ◽  
Flow Structure ◽  
Flow Characteristics ◽  
Laminar Flows ◽  
Dean Number ◽  
Governing Parameter ◽  
Curved Pipes ◽  
Wide Range

When a curved pipe rotates about the centre of curvature, the fluid flowing in it is subjected to both Coriolis and centrifugal forces. Based on the analogy between laminar flows in stationary curved pipes and in orthogonally rotating pipes, the flow characteristics of fully developed laminar flow in rotating curved pipes are made clear and definite by similarity arguments, computational studies and using experimental data. Similarity arguments clarify that the flow characteristics in loosely coiled rotating pipes are governed by three parameters: the Dean number KLC, a body force ratio F and the Rossby number Ro. As the effect of Ro is negligible when Ro is large, computational results are presented for this case first, and then the effect of Ro is studied. Flow structure and friction factor are studied in detail. Variations of flow structure show secondary flow reversal at F ≈ −1, where the two body forces are of the same order but in opposite directions. It is also shown how the Taylor–Proudman effect dominates the flow structure when Ro is small. Computed curves of the friction factor for constant Dean number have their minimum at F ≈ −1. A composite parameter KL is introduced as a convenient governing parameter and used to correlate the characteristics. By applying KL to the analogy formula previously derived for two limiting flows, a semi-empirical formula for the friction factor is presented, which shows good agreement with the experimental data for a wide range of the parameters.

Experimental Study on Thermal-Hydraulic Performance of Single-Phase Water Flow in Narrow Rectangular Channel

2009 ◽  
Author(s):  
Mei Wang ◽  
Yan Wen ◽  
Suizheng Qiu ◽  
Guanghui Su ◽  
Weifeng Ni
Keyword(s):  
Heat Transfer ◽  
Reynolds Number ◽  
Nusselt Number ◽  
Laminar Flow ◽  
Friction Factor ◽  
Water Flow ◽  
Single Phase ◽  
Rectangular Channel ◽  
Flow Region ◽  
Phase Water

The purpose of this study is to discover the differences of pressure drop and heat transfer of single-phase water flow between conventional channels and narrow rectangular channels. Furthermore, the differences between the level and the vertical channel have been studied. The gap of the test channel is 1.8mm. Compared with conventional channels, the narrow rectangular channel showed differences in both flow and heat transfer characteristics. The critical Reynolds number of transition from laminar flow to turbulent flow is 900∼1300, which is smaller compared with conventional channels. The friction factor is larger than that of the conventional channels and the correlation of friction factor with Reynolds number was given by experimental results. From the relation graph of Nusselt number and Reynolds number, the demarcation of the laminar flow region and turbulence flow region is obvious. In laminar region, Nusselt number almost remained constant and approximately consistent with numerical simulation results. While in turbulent region, Nusselt number increased significantly with increasing Reynolds number. A new Nusselt number correlation was obtained based on Dittus-Boelter equation, and the coefficients were less about 13% than that of Dittus-Boelter equation.

Laminar, Transitional and Turbulent Friction Factors for Gas Flows in Smooth and Rough Microtubes

2008 ◽  
Author(s):  
Marco Lorenzini ◽  
Gian Luca Morini ◽  
Sandro Salvigni
Keyword(s):  
Reynolds Number ◽  
Friction Factor ◽  
Turbulent Regime ◽  
Turbulent Friction ◽  
Compressibility Effect ◽  
Flow Acceleration ◽  
Friction Factors ◽  
Macro Scale ◽  
Fully Developed Turbulent Flow ◽  
Microscale Transport

Theoretical and experimental works on microscale transport phenomena have been carried out in the past decade in the attempt to analyse possible new effects and to assess the influence of scaling on the classical correlations which are used in macro-scale heat and fluid flow, following the need to supply engineers with reliable correlations to be used in the design of micro-scale devices. These results were sometimes in mutual contrast, as is the case for the determination of the friction factor, which has been found to be lower, higher or comparable to that for macroscopic channels, depending on the researchers. In this work the compressible flow of nitrogen inside circular microchannels from 26 μm to 508 μm in diameter and with different surface roughness (<1%) is investigated for the whole range of flow conditions: laminar, transitional and turbulence. Over 5000 experimental data have been collected and analysed. The data confirmed that in the laminar regime the agreement with the conventional theory is very good in terms of friction factors both for rough and smooth microtubes. For the smaller microchannels (<100 μm) when Re is greater than 1300 the friction factor tends to deviate from the Poiseuille law because the flow acceleration due to compressibility effect gains in importance. The transitional regime was found to start no earlier than at values of the Reynolds number around 1800–2000. Both smooth and sudden changes in the flow regime have been found, as reported for conventional tubes. Fully developed turbulent flow was attained with both smooth and rough tubes, and the results for smooth tubes seem to confirm Blasius’s relation, while for rough tubes the Colebrook’s correlation is found to be only partially in agreement with the experimental friction factors. In the turbulent regime the dependence of the friction factor on the Reynolds number is less pronounced for microtubes with respect to the prediction of the Colebrook’s correlation and the friction factor tends only to depend on the microtube relative roughness.

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