Pressure Drop and Flow Development in the Entrance Region of Microchannels With Second-Order Velocity Slip Condition and the Requirement for Development Length

2020 ◽  
Vol 142 (4) ◽  
Author(s):  
Baibhab Ray ◽  
Franz Durst ◽  
Subhashis Ray
Keyword(s):  
Shear Stress ◽  
Pressure Drop ◽  
Parallel Plate ◽  
Velocity Slip ◽  
Second Order ◽  
Entrance Region ◽  
Slip Condition ◽  
Local Velocity ◽  
Flow Development ◽  
Developing Region

Abstract In this investigation, Lfd* and Δp in the entrance region of circular and parallel plate microchannels have been determined for 10−2≤Re≤104 and 10−4≤Kn≤0.2, employing the second-order velocity slip condition at the wall with C1=1 and 0≤C2≤0.5. Results indicate that although local velocity slip at the wall is always higher than that for the fully developed section, local wall shear stress for higher Kn and C2 could be lower than its fully developed value, which is also more prominent for lower Re. Therefore, depending upon the operating condition, K(x) and Kfd could assume negative values, implying that pressure gradient in the developing region could even be less than that in the fully developed section. It has been further observed that both Lfd* and Kfd are characterized by the low and the high Re asymptotes, using which extremely accurate correlations have been proposed for both geometries.

A Mathematical Model for the Laminar Entrance Region of a Newtonian Fluid in a Cylindrical Pipe

2020 ◽  
Vol 143 (3) ◽  
Author(s):  
Richard J. Gross ◽  
Nicholas G. Garafolo ◽  
Garrett R. McHugh
Keyword(s):  
Shear Stress ◽  
Pressure Drop ◽  
Laminar Flow ◽  
Wall Shear Stress ◽  
Velocity Profile ◽  
Newtonian Fluid ◽  
Axial Velocity ◽  
Entrance Region ◽  
Velocity Data ◽  
Cylindrical Pipe

Abstract This paper develops equations for velocity, pressure drop, and wall shear stress in the entrance or development region of a cylindrical pipe. The model quantifies the velocity and wall shear stress contributions to the entrance region pressure drop and illustrates how data are used to determine the numerical values of parameters needed to complete the model. It assumes a Newtonian fluid, laminar flow, steady-state, and a constant mass density fluid. The fluid axial velocity profile at the entrance region inlet is modeled by an equation that is close to a flat axial velocity and drops off to zero as the radius approaches the wall. The fluid velocity at the entrance region exit is modeled as the axial, fully developed, laminar flow parabolic velocity profile. The inlet velocity profile is multiplied by a decaying function F(x) that is unity at the entrance region inlet and decreases to zero at the entrance region exit. The exit velocity profile is multiplied by a growing function G(x) that is zero at the entrance region inlet and increases to unity at the entrance region exit. The pressure drop through the entrance region is expressed in terms of the wall viscous friction and the change in axial momentum of the fluid. Two mathematical models for F(x) and G(x) are presented. One is more advantageous when pressure drop data and a few centerline velocity data points are available, and the second is more advantageous when only velocity data are available.

The Developing Laminar Flow and Pressure Drop in the Entrance Region of Annular Ducts

1964 ◽  
Vol 86 (4) ◽  
pp. 827-833 ◽  
Author(s):  
E. M. Sparrow ◽  
S. H. Lin
Keyword(s):  
Pressure Drop ◽  
Laminar Flow ◽  
Circular Tube ◽  
Outer Radius ◽  
Radius Ratio ◽  
Entrance Region ◽  
Flow Development ◽  
Inner Radius ◽  
Wide Range ◽  
Plate Channel

A new analytical method has been applied for determining the developing laminar flow in the hydrodynamic entrance region of annular ducts. Detailed results are presented for the development of the velocity distribution and the pressure drop over a wide range of annulus radius ratios r1/r2 (r1 = inner radius of annulus, r2 = outer radius of annulus). It is found that the pressure drop and flow development in annular ducts with radius ratios substantially less than unity is quite similar to that in a parallel-plate channel (r1/r2 → 1). On the other hand, the results far an annular duct with radius ratio as small as 0.001 depart significantly from those for a circular tube (r1/r2 = 0). The hydrodynamic entrance length, measured as a multiple of the hydraulic radius, increases as the duct radius ratio decreases at a fixed Reynolds number.

Pressure Drop Due to the Entrance Region in Ducts of Arbitrary Cross Section

1964 ◽  
Vol 86 (3) ◽  
pp. 620-626 ◽  
Author(s):  
T. S. Lundgren ◽  
E. M. Sparrow ◽  
J. B. Starr
Keyword(s):  
Pressure Drop ◽  
Velocity Profile ◽  
Cross Section ◽  
Cross Sections ◽  
Circular Tube ◽  
Essential Feature ◽  
Arbitrary Cross Section ◽  
Entrance Region ◽  
Flow Development ◽  
Prior Analysis

A general analytical method has been devised for determining the pressure drop due to flow development in the entrance region of ducts of arbitrary cross section. The essential feature of the analysis is that the pressure drop can be determined without actually solving for the entrance-region velocity development. Instead, the calculation only requires a knowledge of the fully developed velocity profile. Application of the method is made to a variety of cross sections including the circular tube, elliptical ducts, rectangular ducts, isosceles triangular ducts, and annular ducts. Numerical results are presented and comparisons are made with available experiments and with prior analysis.

scholarly journals Applicability of the Cox-Merz Rule to High-Density Polyethylene Materials with Various Molecular Masses

Polymers ◽  
2021 ◽  
Vol 13 (8) ◽  
pp. 1218
Author(s):  
Raffael Rathner ◽  
Wolfgang Roland ◽  
Hanny Albrecht ◽  
Franz Ruemer ◽  
Jürgen Miethlinger
Keyword(s):  
Molecular Weight ◽  
Pressure Drop ◽  
High Molecular Weight ◽  
High Density Polyethylene ◽  
Parallel Plate ◽  
Empirical Relationship ◽  
Polymer Processing ◽  
High Density ◽  
Viscosity Data ◽  
Molecular Masses

The Cox-Merz rule is an empirical relationship that is commonly used in science and industry to determine shear viscosity on the basis of an oscillatory rheometry test. However, it does not apply to all polymer melts. Rheological data are of major importance in the design and dimensioning of polymer-processing equipment. In this work, we investigated whether the Cox-Merz rule is suitable for determining the shear-rate-dependent viscosity of several commercially available high-density polyethylene (HDPE) pipe grades with various molecular masses. We compared the results of parallel-plate oscillatory shear rheometry using the Cox-Merz empirical relation with those of high-pressure capillary and extrusion rheometry. To assess the validity of these techniques, we used the shear viscosities obtained by these methods to numerically simulate the pressure drop of a pipe head and compared the results to experimental measurements. We found that, for the HDPE grades tested, the viscosity data based on capillary pressure flow of the high molecular weight HDPE describes the pressure drop inside the pipe head significantly better than do data based on parallel-plate rheometry applying the Cox-Merz rule. For the lower molecular weight HDPE, both measurement techniques are in good accordance. Hence, we conclude that, while the Cox-Merz relationship is applicable to lower-molecular HDPE grades, it does not apply to certain HDPE grades with high molecular weight.

scholarly journals Impact of chosen force fields and applied load on thin film lubrication

Friction ◽  
2021 ◽  
Author(s):  
Thi D. Ta ◽  
Hien D. Ta ◽  
Kiet A. Tieu ◽  
Bach H. Tran
Keyword(s):  
Thin Film ◽  
Shear Stress ◽  
Surface Structure ◽  
Rheological Properties ◽  
Surface Potential ◽  
Applied Load ◽  
Velocity Slip ◽  
Thin Film Lubrication ◽  
Lubrication Performance ◽  
Film Lubrication

AbstractThe rapid development of molecular dynamics (MD) simulations, as well as classical and reactive atomic potentials, has enabled tribologists to gain new insights into lubrication performance at the fundamental level. However, the impact of adopted potentials on the rheological properties and tribological performance of hydrocarbons has not been researched adequately. This extensive study analyzed the effects of surface structure, applied load, and force field (FF) on the thin film lubrication of hexadecane. The lubricant film became more solid-like as the applied load increased. In particular, with increasing applied load, there was an increase in the velocity slip, shear viscosity, and friction. The degree of ordering structure also changed with the applied load but rather insignificantly. It was also significantly dependent on the surface structure. The chosen FFs significantly influenced the lubrication performance, rheological properties, and molecular structure. The adaptive intermolecular reactive empirical bond order (AIREBO) potential resulted in more significant liquid-like behaviors, and the smallest velocity slip, degree of ordering structure, and shear stress were compared using the optimized potential for liquid simulations of united atoms (OPLS-UAs), condensed-phase optimized molecular potential for atomic simulation studies (COMPASS), and ReaxFF. Generally, classical potentials, such as OPLS-UA and COMPASS, exhibit more solid-like behavior than reactive potentials do. Furthermore, owing to the solid-like behavior, the lubricant temperatures obtained from OPLS-UA and COMPASS were much lower than those obtained from AIREBO and ReaxFF. The increase in shear stress, as well as the decrease in velocity slip with an increase in the surface potential parameter ζ, remained conserved for all chosen FFs, thus indicating that the proposed surface potential parameter ζ for the COMPASS FF can be verified for a wide range of atomic models.

In-Vitro Wall Shear Stress Measurements for Microfluid Flows by Using Second-Order SPE Micro-PIV

2007 ◽  
Author(s):  
Han-Sheng Chuang ◽  
Steven T. Wereley
Keyword(s):  
Shear Stress ◽  
Wall Shear Stress ◽  
Measurement Errors ◽  
Pearson Correlation ◽  
Second Order ◽  
Bias Error ◽  
Central Difference ◽  
Micro Piv ◽  
Wall Shear

Conventional single pixel evaluation (SPE) significantly improves the spatial resolution of PIV measurements to the physical limit of a CCD camera based on the forward difference interrogation (FDI). This paper further enhances the computational algorithm to second-order accuracy by simply modifying the numerical scheme with the central difference interrogation (CDI). The proposed central difference scheme basically superposes the forward-time and the backward-time correlation domains, thus resulting in reduced bias error as well as rapid background noise elimination. An assessment of the CDI SPE algorithm regarding the measurement errors was achieved via numerous synthetic images subject to a four-roll mill flow. In addition, preliminary wall shear stress (WSS) measurements regarding different algorithms are also evaluated with an analytical turbulent boundary flow. CDI scheme showed a 0.32% error deviated from the analytical solution and improved the same error in FFT-based correlation correlation (FFT-CC) by 32.35%. To demonstrate the performance in practice, in-vitro measurements were implemented in a serpentine microchannel made of polydimethyl siloxane (PDMS) for both CDI SPE and spatial cross-correlation. A series of steady-state flow images at five specified regions of interest were acquired using micro-PIV system. Final comparisons of the WSS regarding the Pearson correlation coefficient, R2, between the numerical schemes and the simulations showed that an overall result was improved by CDI SPE due to the fine resolution and the enhanced accuracy.

Behavior of Thermal Effects and Velocity-Slip on Performance of Externally Pressurized Porous Incompressible Gas Thrust Bearing

1979 ◽  
Vol 46 (2) ◽  
pp. 465-468 ◽  
Author(s):  
V. K. Kapur ◽  
J. S. Yadav
Keyword(s):  
Mass Flow Rate ◽  
Mass Flow ◽  
Flow Rate ◽  
Thermal Effects ◽  
Thrust Bearing ◽  
Load Capacity ◽  
Velocity Slip ◽  
Experimental Results ◽  
Slip Condition ◽  
Static Stiffness

In the present analysis, the interactions of thermal effects and velocity slip on the performance of externally pressurized porous incompressible gas thrust bearing have been studied. Numerical results for load capacity, mass flow rate, and static stiffness have been obtained and their behavior is illustrated in figures. The results for slip as well as no-slip condition have also been compared with the experimental results of Gargiulo and Gilmour [7].

The Fluid Power Control Performance Comparison Study of Two-Type ER Valve Based on FLUENT

2012 ◽  
Vol 472-475 ◽  
pp. 1989-1994
Author(s):  
Shi Sha Zhu ◽  
Liu Tao
Keyword(s):  
Pressure Drop ◽  
Power Control ◽  
Parallel Plate ◽  
Control Volume ◽  
Flow Simulation ◽  
Control Valve ◽  
Performance Comparison ◽  
Fluid Power ◽  
Control Performance ◽  
Plate Type

The current flow and pressure drop of ER valve which is a new type power control valve could be adjusted by the electric field signal directly .In this paper, the fluid power control performance of concentric cylindrical ER valve and parallel plate-type ER valve based on ER principal is comparative studied .First power control equation has been analysed, and then flow simulation of internal flow field of ER valve has been taken based on FLUENT software. The results show that with the increasing of the strength of excitation field, the flow through the two different type of ER valve decreases, the pressure drop between import and export is even greater; and the fluid power control performance of parallel plate-type ER valve is superior to concentric cylindrical ER valve under the same control volume.

scholarly journals Effects of Second-Order Slip Flow and Variable Viscosity on Natural Convection Flow of CNTs − Fe 3 O 4 /Water Hybrid Nanofluids due to Stretching Surface

2021 ◽  
Vol 2021 ◽  
pp. 1-18
Author(s):  
Ayele Tulu ◽  
Wubshet Ibrahim
Keyword(s):  
Volume Fraction ◽  
Local Heat Transfer ◽  
Velocity Slip ◽  
Local Heat ◽  
Second Order ◽  
Hybrid Nanoparticles ◽  
Temperature Dependent ◽  
Temperature Dependent Viscosity ◽  
Hybrid Nanofluids ◽  
Dependent Viscosity

This study deals with natural convection unsteady flow of CNTs − Fe 3 O 4 /water hybrid nanofluids due to stretching surface embedded in a porous medium. Both hybrid nanoparticles of SWCNTs − Fe 3 O 4 and MWCNTs − Fe 3 O 4 are used with water as base fluid. Effects of hybrid nanoparticles volume friction, second-order velocity slip condition, and temperature-dependent viscosity are investigated. The governing problem of flow is solved numerically employing spectral quasilinearization method (SQLM). The results are presented and discussed via embedded parameters using graphs and tables. The results disclose that the thermal conductivity of CNTs − Fe 3 O 4 / H 2 O hybrid nanofluids is higher than that of CNTs − H 2 O nanofluids with higher value of hybrid nanoparticle volume fraction. Also, the results show that momentum boundary layer reduces while the thermal boundary layer gros with higher values of temperature-dependent viscosity and second-order velocity slip parameters. The skin friction coefficient improves, and the local heat transfer rate decreases with higher values of nanoparticle volume fraction, temperature-dependent viscosity, and second-order velocity slip parameters. Furthermore, more skin friction coefficients and lower local heat transfer rate are reported in the CNTs − Fe 3 O 4 / H 2 O hybrid nanofluid than in the CNTs − H 2 O nanofluid. Thus, the obtained results are promising for the application of hybrid nanofluids in the nanotechnology and biomedicine sectors.

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