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 Fully-developed laminar flow in trapezoidal ducts with rounded corners: a numerical solution and case study

2021 ◽  
Vol ahead-of-print (ahead-of-print) ◽  
Author(s):  
Mohammed S. Ismail ◽  
Mohamed R. Berber ◽  
Ziyad A. Alrowaili ◽  
Mohamed Pourkashanian
Keyword(s):  
Fuel Cells ◽  
Pressure Drop ◽  
Laminar Flow ◽  
Accurate Estimation ◽  
Hydrogen Fuel Cells ◽  
Hydrogen Fuel ◽  
Content Type ◽  
Wide Range ◽  
Poiseuille Number ◽  
The Impact

Purpose This paper aims to numerically solve fully developed laminar flow in trapezoidal ducts with rounded corners which result following forming processes. Design/methodology/approach A two-dimensional model for a trapezoidal duct with rounded corners is developed and conservation of momentum equation is solved. The flow is assumed to be steady, fully developed, laminar, isothermal and incompressible. The key flow characteristics including the Poiseuille number and the incremental pressure drop have been computed and tabulated for a wide range of: sidewall angle (θ); the ratio of the height of the duct to its smaller base (α); and the ratio of the fillet radius of the duct to its smaller base (β). Findings The results show that Poiseuille number decreases, and all the other dimensionless numbers increase with increasing the radii of the fillets of the duct; these effects were found to amplify with decreasing duct heights or increasing sidewall angles. The maximum axial velocity was shown to increase with increasing the radii of the fillets of the duct. For normally used ducts in hydrogen fuel cells, the impact of rounded corners cannot be overlooked for very low channel heights or very high sidewall angles. Practical implications The data generated in this study are highly valuable for engineers interested in estimating pressure drops in rounded trapezoidal ducts; these ducts have been increasingly used in hydrogen fuel cells where flow channels are stamped on thin metallic sheets. Originality/value Fully developed laminar flow in trapezoidal ducts with four rounded corners has been solved for the first time, allowing for more accurate estimation of pressure drop.

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.

Development-Length Requirements for Fully Developed Laminar Flow in Concentric Annuli

2010 ◽  
Vol 132 (6) ◽  
Author(s):  
R. J. Poole
Keyword(s):  
Reynolds Number ◽  
Laminar Flow ◽  
Channel Flow ◽  
Characteristic Length ◽  
Radius Ratio ◽  
Length Scale ◽  
Development Length ◽  
Characteristic Length Scale ◽  
Annular Gap ◽  
Wide Range

In this technical brief we report the results of a systematic numerical investigation of developing laminar flow in axisymmetric concentric annuli over a wide range of radius ratio (0.01<Ri/Ro<0.8) and Reynolds number (0.001<Re<1000). When the annular gap is used as the characteristic length scale we find that for radius ratios greater than 0.5 the development length collapses to the channel-flow correlation. For lower values of radius ratio the wall curvature plays an increasingly important role and the development length remains a function of both radius ratio and Reynolds number. Finally we show that the use of an empirical modified length scale to normalize both the development length and the characteristic length scale in the Reynolds number collapses all of the data onto the channel-flow correlation regardless of the radius ratio.

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.

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