scholarly journals Modeling of Laminar Flows in Rough-Wall Microchannels

2005 ◽  
Vol 128 (4) ◽  
pp. 734-741 ◽  
Author(s):  
R. Bavière ◽  
G. Gamrat ◽  
M. Favre-Marinet ◽  
S. Le Person
Keyword(s):  
Experimental Data ◽  
Reynolds Number ◽  
Numerical Modeling ◽  
Pressure Drop ◽  
Analytical Model ◽  
Analytical Approach ◽  
Laminar Flows ◽  
Numerical Results ◽  
Rough Wall ◽  
Relative Roughness

Numerical modeling and analytical approach were used to compute laminar flows in rough-wall microchannels. Both models considered the same arrangements of rectangular prism rough elements in periodical arrays. The numerical results confirmed that the flow is independent of the Reynolds number in the range 1–200. The analytical model needs only one constant for most geometrical arrangements. It compares well with the numerical results. Moreover, both models are consistent with experimental data. They show that the rough elements drag is mainly responsible for the pressure drop across the channel in the upper part of the relative roughness range.

Pore-Scaled Analytical Modelling of Permeability and Inertial Coefficient for Pressure Drop Prediction of Open-Cell Metallic Foams

2016 ◽  
Author(s):  
X. H. Yang ◽  
S. Y. Song ◽  
L. Y. Zhang ◽  
T. J. Lu
Keyword(s):  
Experimental Data ◽  
Reynolds Number ◽  
Pressure Drop ◽  
Analytical Model ◽  
Unit Cell ◽  
Manufacturing Cost ◽  
Shape Effect ◽  
Metallic Foams ◽  
Open Cell ◽  
Inertial Coefficient

Amongst various porous media, open-cell metallic foams exhibit distinctive properties: relatively low manufacturing cost, ultra-low density, moderate stiffness and strength, and high surface area-to-volume ratio. They have been, therefore, utilized in a variety of applications such as microelectronics cooling, fuel cells, and compact heat exchangers. For such applications, the knowledge of pressure drop of fluid flowing across the foam is often a key issue, enabling control of fluid flow, heat transfer enhancement, planning and designing chemical engineering processes, optimal flow analysis as well as practical designs. We present in this paper an analytical model capable of predicting the pressure drop of a Newtonian incompressible fluid flowing unidirectionally across isotropic and fully-saturated micro open-cell cellular foams within the Darcy and Forchheimer flow regimes. Analytical exploitations are conducted to determine the foam permeability and inertial coefficient. The analytical model is based on the basis of volume-averaging approach and the assumption of piece-wise plane Poiseuille flow with the modified cubic lattice with spherical node at the junction of struts. To better mimic the foam struts shape, a concave-triangular-shaped strut consisting of two nose-to-nose cones is considered and particular attentions have been paid to both analytically and numerically examine the node shape as well as struts shape effect. Built upon a generalized tortuosity model derived from the modified cubic unit cell, an analytical model of permeability on the basis of a cubic unit cell is developed, valid within a typical engineering range of porosity (ε = 0.86 ∼ 0.98) and pore size (0.254 mm ∼ 5.08 mm). With the effect of Reynolds number considered, the pore-scaled Reynolds number dependent drag coefficient expression is introduced and through this the inertial coefficient is analytically modeled on the basis of flow over bluff bodies, which is found to agree well with experimental data from various sources. The modeling procedure for pressure drop (permeability and inertial coefficient) is based on physical principles and geometrical considerations, and the model predictions agree satisfactorily with existing experimental data. Results show that by building the analytical model on the basis of a cubic unit cell to represent the topology of metallic foams, pressure drops as well as hydrodynamic conditions within both the Darcy and Forchheimer regimes in a Newtonian fluid can be analytically predicted.

Friction Factor Directly From Roughness Measurements

2001 ◽  
Author(s):  
Elling Sletfjerding ◽  
Jon Steinar Gudmundsson
Keyword(s):  
Reynolds Number ◽  
Pressure Drop ◽  
Power Spectrum ◽  
Friction Factor ◽  
High Reynolds Number ◽  
Gas Flow ◽  
Relative Roughness ◽  
High Reynolds ◽  
Friction Factor Correlation ◽  
Roughness Measurements

Abstract Pressure drop experiments on natural gas flow in 150 mm pipes at 80 to 120 bar pressure and high Reynolds number were carried out for pipes smooth to rough surfaces. The roughness was measured with an accurate stylus instrument and analyzed using fractal methods. Using a similar approach to that of Nikuradse the measured friction factor was related to the measured roughness values. Taking the value of the relative roughness and dividing it by the slope of the power spectrum of the measured roughness, a greatly improved fit with the measured friction factor was obtained. Indeed, a new friction factor correlation was obtained, but now formulated in terms of direct measurement of roughness.

A Numerical Investigation of Transonic Axial Compressor Rotor Flow Using a Low-Reynolds-Number k–ε Turbulence Model

1999 ◽  
Vol 121 (1) ◽  
pp. 44-58 ◽  
Author(s):  
T. Arima ◽  
T. Sonoda ◽  
M. Shirotori ◽  
A. Tamura ◽  
K. Kikuchi
Keyword(s):  
Experimental Data ◽  
Reynolds Number ◽  
Turbulence Model ◽  
Low Reynolds Number ◽  
Axial Compressor ◽  
Numerical Results ◽  
Speed Condition ◽  
Transonic Axial Compressor ◽  
Low Reynolds ◽  
Design Speed

We have developed a computer simulation code for three-dimensional viscous flow in turbomachinery based on the time-averaged compressible Navier–Stokes equations and a low-Reynolds-number k–ε turbulence model. It is described in detail in this paper. The code is used to compute the flow fields for two types of rotor (a transonic fan NASA Rotor 67 and a transonic axial compressor NASA rotor 37), and numerical results are compared to experimental data based on aerodynamic probe and laser anemometer measurements. In the case of Rotor 67, calculated and experimental results are compared under the design speed to validate the code. The calculated results show good agreement with the experimental data, such as the rotor performance map and the spanwise distribution of total pressure, total temperature, and flow angle downstream of the rotor. In the case of Rotor 37, detailed comparisons between the numerical results and the experimental data are made under the design speed condition to assess the overall quality of the numerical solution. Furthermore, comparisons under the part-speed condition are used to investigate a flow field without passage shock. The results are well predicted qualitatively. However, considerable quantitative discrepancies remain in predicting the flow near the tip. In order to assess the predictive capabilities of the developed code, computed flow structures are presented with the experimental data for each rotor and the cause of the discrepancies is discussed.

Parallel Flow in Ordered Fibrous Structures: An Analytical Approach

2009 ◽  
Author(s):  
A. Tamayol ◽  
M. Bahrami
Keyword(s):  
Experimental Data ◽  
Pressure Drop ◽  
Entire Range ◽  
Analytical Approach ◽  
The Other ◽  
High Porosity ◽  
Fibrous Media ◽  
Fully Developed Flow ◽  
Wide Range ◽  
Hexagonal Arrays

In this study, fully-developed flow parallel to ordered fibrous structures is investigated analytically. The considered fibrous media are made up of inline (square), staggered, and hexagonal arrays of cylinders. Starting from the general solution of Poisson’s equation, compact analytical solutions are proposed for both velocity distribution and permeability of the considered structures. In addition, independent numerical simulations are performed for the considered patterns over the entire range of porosity and the results are compared with the proposed solutions. The developed models are successfully verified through comparison with existing experimental data, collected by others, and the present numerical results over a wide range of porosity. The results show that for the ordered arrangements with high porosity, the parallel permeability is independent of the microstructure geometry; on the other hand, for lower porosities the hexagonal arrays results in lower pressure drop, as expected.

A Series Pressure Drop Representation for Flow Through Orifice Tubes

2008 ◽  
Vol 130 (5) ◽  
Author(s):  
T. A. Jankowski ◽  
E. N. Schmierer ◽  
F. C. Prenger ◽  
S. P. Ashworth
Keyword(s):  
Experimental Data ◽  
Reynolds Number ◽  
Simple Model ◽  
Pressure Drop ◽  
Diameter Ratio ◽  
Pressure Drops ◽  
In Series ◽  
Orifice Flow ◽  
Flow Through ◽  
Length To Diameter Ratio

A simple model is developed here to predict the pressure drop and discharge coefficient for incompressible flow through orifices with length-to-diameter ratio greater than zero (orifice tubes) over wide ranges of Reynolds number. The pressure drop for flow through orifice tubes is represented as two pressure drops in series; namely, a pressure drop for flow through a sharp-edged orifice in series with a pressure drop for developing flow in a straight length of tube. Both of these pressure drop terms are represented in the model using generally accepted correlations and experimental data for developing flows and sharp-edged orifice flow. We show agreement between this simple model and our numerical analysis of laminar orifice flow with length-to-diameter ratio up to 15 and for Reynolds number up to 150. Agreement is also shown between the series pressure drop representation and experimental data over wider ranges of Reynolds number. Not only is the present work useful as a design correlation for equipment relying on flow through orifice tubes but it helps to explain some of the difficulties that previous authors have encountered when comparing experimental observation and available theories.

scholarly journals A Numerical Investigation of Transonic Axial Compressor Rotor Flow Using a Low Reynolds Number k-ε Turbulence Model

1997 ◽  
Author(s):  
Toshiyuki Arima ◽  
Toyotaka Sonoda ◽  
Masatoshi Shirotori ◽  
Atsuhiro Tamura ◽  
Kazuo Kikuchi
Keyword(s):  
Experimental Data ◽  
Reynolds Number ◽  
Turbulence Model ◽  
Low Reynolds Number ◽  
Axial Compressor ◽  
Numerical Results ◽  
Speed Condition ◽  
Transonic Axial Compressor ◽  
Low Reynolds ◽  
Design Speed

We have developed a computer simulation code for three-dimensional viscous flow in turbomachinery based on the time-averaged compressible Navier-Stokes equations and a low Reynolds number k-ε turbulence model. It is described in detail in this paper. The code is used to compute the flow fields for two types of rotor (a transonic fan NASA Rotor 67 and a transonic axial compressor NASA rotor 37), and numerical results are compared to experimental data based on aerodynamic probe and laser anemometer measurements. In the case of Rotor 67, calculated and experimental results are compared under the design speed to validate the code. The calculated results show good agreement with the experimental data, such as the rotor performance map and the spanwise distribution of total pressure, total temperature, and flow angle downstream of the rotor. In the case of Rotor 37, detailed comparisons between the numerical results and the experimental data are made under the design speed condition to assess the overall quality of the numerical solution. Furthermore, comparisons under the part speed condition are used to investigate a flow field without passage shock. The results are well predicted qualitatively. However, considerable quantitative discrepancies remain in predicting the flow near the tip. In order to assess the predictive capabilities of the developed code, computed flow structures are presented with the experimental data for each rotor and the cause of the discrepancies is discussed.

scholarly journals 3D Numerical Modeling of Rigid Inclusion-Improved Soft Soils Under Monotonic and Cyclic Loading—Case of a Small-Scale Laboratory Experiment

2021 ◽  
Vol 11 (4) ◽  
pp. 1426
Author(s):  
Hung Van Pham ◽  
Daniel Dias
Keyword(s):  
Experimental Data ◽  
Numerical Modeling ◽  
Cyclic Loading ◽  
Rigid Inclusion ◽  
Research Work ◽  
Reinforced Soil ◽  
Numerical Results ◽  
Small Scale ◽  
3D Numerical Modeling ◽  
Soil Arching

This paper is based on small-scale laboratory tests (1:10) of a rigid inclusion-improved soil under normal gravity. A low area improvement ratio (2.4%) under monotonic and cyclic loading was used. 3D numerical calculations are performed to model these tests. The proposed numerical modeling is performed by the finite element method (FEM) using the ABAQUS software. A representative elementary volume model is suggested for reducing the calculation time. A hypoplastic constitutive model (HYP model) is applied for the load transfer platform (LTP). A total of three geometrical configuration cases of the experimental tests are numerically considered including a rigid slab over a mattress of 100 mm on the reinforced soil, a mattress of 100 mm on the reinforced soil, and a rigid slab over a mattress of 50 mm on the reinforced soil. The proposed numerical results are compared to the experimental data and the previous numerical results of Houda. The cyclic response of the systems is shown in terms of soil arching and settlements. The decrease in pile efficacy and the cumulative settlements are exhibited. The HYP model allows to better simulate the soil arching mechanisms inside the LTP than the CYsoil model used in the Houda’s research work. A good concordance between the proposed numerical results and the experimental data was obtained.

Characterization of Surface Roughness Effects on Laminar Flow in Microchannels by Using Fractal Cantor Structures

2009 ◽  
Author(s):  
Chengbin Zhang ◽  
Yongping Chen ◽  
Panpan Fu ◽  
Mingheng Shi
Keyword(s):  
Surface Roughness ◽  
Reynolds Number ◽  
Fractal Dimension ◽  
Pressure Drop ◽  
Laminar Flow ◽  
Flow Direction ◽  
Roughness Effects ◽  
Relative Roughness ◽  
Smooth Channel

The fractal characterization of the topography of rough surfaces by using Cantor set structures is introduced in this paper. Based on the fractal Cantor surface, a model of laminar flow in rough microchannels is developed and numerically analyzed to study the characterization of surface roughness effects on laminar flow. The effects of Reynolds number, relative roughness, and fractal dimension on laminar flow are all discussed. The results indicate that the presence of roughness leads to the form of the detachment, and eddy generation is observed at the shadow of the roughness elements. The pressure drop in the rough channel along the flow direction is no longer in a linear fashion and larger than that in the smooth channel. The fluctuation characteristic of pressure drop along the stream, which is due to the vortex formation at the wall, is found. Differing from the smooth channel, the Poiseuille number for laminar flow in rough microchannels is no longer only dependent on the cross-sectional shape of the channel, but also strongly influenced by the Reynolds number, relative roughness and fractal dimension of the surface.

Cavitation in Vortex Diodes and Its Significance in Diode Pumps

1982 ◽  
Vol 24 (4) ◽  
pp. 191-198 ◽  
Author(s):  
G. H. Priestman ◽  
J. R. Tippetts
Keyword(s):  
Experimental Data ◽  
Reynolds Number ◽  
Pressure Drop ◽  
Cavitation Number ◽  
Diode Pump ◽  
Upstream Pressure ◽  
Simple Equations ◽  
Practical Implications

Vortex diodes handling liquids are subject to the effects both of cavitation and Reynolds number. The apparent complexity of their characteristics makes design and simulation difficult. To some extent, however, this complexity is artificial and can be reduced. The effect of cavitation is most severe in the forward state. The usual characterization in terms of Thoma's cavitation number (based on pressure drop and downstream pressure) obscures a much simpler relationship using the upstream pressure explicitly. This yields simple equations which cover the cavitating regime. The non-cavitating characteristics are shown to be well predicted by established data on the operation of diffusers. Experimental data vindicating this is taken from Zobel, Syred et al, and our own experiments. Cavitation in the reverse state is not simplified but it is much less important for the diodes quoted. The practical implications of these results in diode pump applications are examined and quantified.

scholarly journals EVALUATION OF PRESSURE DROP IN FLOW OVER FIXED POROUS BED

2014 ◽  
Vol 13 (1) ◽  
pp. 42 ◽  
Author(s):  
R. B. Cruz ◽  
D. R. S. Guerra ◽  
T. L. Azevedo
Keyword(s):  
Experimental Data ◽  
Reynolds Number ◽  
Pressure Drop ◽  
Seed Weight ◽  
Strong Dependence ◽  
Fixed Bed ◽  
Experimental Studies ◽  
Porous Particles ◽  
Ergun Equation ◽  
Number Of Factors

Many studies are conducted about the dynamics of fluids in porous media, which generates a number of factors and problems are solved. In particular the phenomenon of pressure drop in flows on fixed bed, although fairly well in the form Ergun’s equation, still has certain inconsistencies with regard to the types of materials to be used in the packaging of the beds. The objective of this work is to study this phenomenon using some experiments reported in the literature to determine the pressure drop in fixed bed consisting of porous particles of açaí seed. Experimental studies were conducted to predict, and take into account the losses resulting from friction and inertia that showed strong dependence on velocity. The method of using the particular friction factor prediction as a way to replace the usual calculation and measurement of pressure drop. The analysis in the wind tunnel was made from different sizes of bed, with a decrease in arithmetic progressions corresponding to half the value of the diameter of the tube used in the test. Several bands of Reynolds number were also employed in order to be able to visualize how the phenomenon behaves on various tracks. For such a survey was necessary some parameters such as açaí seeds diameters, seed weight and volume occupied by the bed; these parameters are of vital importance in Ergun equation, because an important aspect of the phenomenon is the porosity which enters as a foundation in the theory of flow fixed bed. At the end of the study was found the divergence in big bands of the Reynolds number of the correlation between experimental data and the Ergun equation.

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