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.

Flow in the Hydrodynamic Entrance Region of Ducts of Arbitrary Cross Section

1969 ◽  
Vol 91 (3) ◽  
pp. 345-354 ◽  
Author(s):  
David P. Fleming ◽  
E. M. Sparrow
Keyword(s):  
Experimental Data ◽  
Velocity Field ◽  
Pressure Drop ◽  
Cross Section ◽  
Cross Sections ◽  
Solution Method ◽  
Arbitrary Cross Section ◽  
Entrance Region ◽  
General Method ◽  
Good Agreement

A general method of analysis is presented for determining the developing velocity field and pressure drop for laminar flow in the entrance region of ducts having arbitrary cross sections. Application of the solution method is made to rectangular ducts and to triangular ducts. Available experimental data are compared with the analytical results and good agreement is found to prevail. Development characteristics for six ducts are brought together and compared, and various trends are identified.

Hydrodynamic Entrance Lengths for Ducts of Arbitrary Cross Section

1967 ◽  
Vol 89 (4) ◽  
pp. 847-850 ◽  
Author(s):  
S. T. McComas
Keyword(s):  
Velocity Profile ◽  
Detailed Analysis ◽  
Cross Section ◽  
Analytical Method ◽  
Arbitrary Cross Section ◽  
Numerical Results ◽  
Entrance Length ◽  
Flow Development

A general analytical method is presented for determination of the hydrodynamic entrance length of ducts of arbitrary cross section. Only knowledge of the fully developed velocity profile is required in order to determine this length in comparison to other approaches which require a detailed analysis of the flow development. This method is applied to circular, elliptical, annular, rectangular, and triangular ducts with numerical results presented.

Analytical and Experimental Characterization of Flow in Slowly-Varying Cross-Section Microchannels

2010 ◽  
Author(s):  
M. Akbari ◽  
M. Bahrami ◽  
D. Sinton
Keyword(s):  
Pressure Drop ◽  
Cross Section ◽  
Cross Sections ◽  
Rectangular Cross Section ◽  
Arbitrary Cross Section ◽  
Geometrical Parameters ◽  
Elliptical Cross ◽  
Proposed Model ◽  
Hyperbolic Contraction ◽  
Asymmetric Microchannel

This paper outlines a novel approximate solution for determining the pressure drop of laminar, single-phase flow in slowly-varying microchannels of arbitrary cross-section. The proposed analysis is general and applicable to symmetric and asymmetric microchannel cross-sections, as examples compact relationships are reported for elliptical and rectangular shapes for three common wall profiles of linear, sinusoidal and hyperbolic. An experimental setup is designed and pressure drop measurements are conducted to validate the proposed model for streamwised periodic microchannels with rectangular cross-section and linear wall with a range of channel geometrical parameters such as aspect ratio and channel slope. The model is also compared against the numerical and experimental data of hyperbolic contraction with rectangular cross-section collected by others. It is observed that although the proposed model is based on the solution of the elliptical cross-section, it can accurately predict the pressure drop in microchannels of rectangular cross-section.

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.

Laminar Incompressible Flow in the Entrance Region of Ducts of Arbitrary Cross Section

1971 ◽  
Vol 93 (1) ◽  
pp. 113-117 ◽  
Author(s):  
James A. Miller
Keyword(s):  
Cross Section ◽  
Cross Sections ◽  
Stokes Equations ◽  
Numerical Technique ◽  
Arbitrary Cross Section ◽  
Entrance Region ◽  
Navier Stokes ◽  
Initial Value ◽  
Navier Stokes Equations ◽  
Friction Factors

A combination of the numerical technique of Chorin for the solution of the Navier-Stokes equations and a transformation of the initial value problem to a boundary value problem is shown to allow calculation of the laminar hydrodynamic entrance region of ducts of arbitrary cross section. Numerical examples consisting of the solution for ducts of square and triangular cross sections are presented along with the associated friction factors.

Numerical Simulating Open-Channel Flows with Regular and Irregular Cross-Section Shapes Based on Finite Volume Godunov-Type Scheme

2020 ◽  
pp. 2050047
Author(s):  
Xiaokang Xin ◽  
Fengpeng Bai ◽  
Kefeng Li
Keyword(s):  
Finite Volume ◽  
Cross Section ◽  
Cross Sections ◽  
Open Channel ◽  
Arbitrary Cross Section ◽  
Second Order ◽  
Cross Sectional ◽  
Shallow Flows ◽  
Natural Streams ◽  
Saint Venant Equations

A numerical model based on the Saint-Venant equations (one-dimensional shallow water equations) is proposed to simulate shallow flows in an open channel with regular and irregular cross-section shapes. The Saint-Venant equations are solved by the finite-volume method based on Godunov-type framework with a modified Harten, Lax, and van Leer (HLL) approximate Riemann solver. Cross-sectional area is replaced by water surface level as one of primitive variables. Two numerical integral algorithms, compound trapezoidal and Gauss–Legendre integrations, are used to compute the hydrostatic pressure thrust term for natural streams with arbitrary and irregular cross-sections. The Monotonic Upstream-Centered Scheme for Conservation Laws (MUSCL) and second-order Runge–Kutta methods is adopted to achieve second-order accuracy in space and time, respectively. The performance of the resulting scheme is evaluated by application in rectangular channels, trapezoidal channels, and a natural mountain river. The results are compared with analytical solutions and experimental or measured data. It is demonstrated that the numerical scheme can simulate shallow flows with arbitrary cross-section shapes in practical conditions.

Estimation of Nusselt Number in Microchannels of Arbitrary Cross-Section With Constant Axial Heat Flux

2008 ◽  
Author(s):  
Ehsan Sadeghi ◽  
Majid Bahrami ◽  
Ned Djilali
Keyword(s):  
Heat Flux ◽  
Nusselt Number ◽  
Cross Section ◽  
Cross Sections ◽  
Numerical Solutions ◽  
Arbitrary Cross Section ◽  
Geometrical Parameters ◽  
Thermal Systems ◽  
Cross Sectional ◽  
Axial Heat

In many practical instances such as basic design, parametric study, and optimization analysis of thermal systems, it is often very convenient to have closed form relations to obtain the trends and a reasonable estimate of the Nusselt number. However, finding exact solutions for many practical singly-connected cross-sections, such as trapezoidal microchannels, is complex. In the present study, the square root of cross-sectional area is proposed as the characteristic length scale for Nusselt number. Using analytical solutions of rectangular, elliptical, and triangular ducts, a compact model for estimation of Nusselt number of fully-developed, laminar flow in microchannels of arbitrary cross-sections with “H1” boundary condition (constant axial wall heat flux with constant peripheral wall temperature) is developed. The proposed model is only a function of geometrical parameters of the cross-section, i.e., area, perimeter, and polar moment of inertia. The present model is verified against analytical and numerical solutions for a wide variety of cross-sections with a maximum difference on the order of 9%.

Analysis of shear lag in cylindrical tubes of arbitrary cross section

1983 ◽  
Vol 389 (1797) ◽  
pp. 259-277
Keyword(s):  
Cross Section ◽  
Cross Sections ◽  
Bending Moment ◽  
General Purpose ◽  
Simple Eigenvalue ◽  
Arbitrary Cross Section ◽  
Longitudinal Distribution ◽  
Shear Lag ◽  
Cylindrical Tubes ◽  
Polynomial Distribution

A very general analysis is given of the phenomenon of shear lag in thin-walled cylindrical tubes, with single-cell cross sections of arbitrary shape, containing any number of concentrated longitudinal booms that carry direct stress only, and subjected to any longitudinal distribution of bending moment and torque. Two equations relating the distributions of direct and shearing stresses on the cross section are derived for the most general case where the tube is non-uniform because of an arbitrary longitudinal variation of wall thicknesses and boom areas. These equa­tions, which are remarkably simple in view of their generality, incor­porate all the requirements of equilibrium and compatibility and provide corrections to the stresses, curvature and twist calculated from the engineers’ theory of bending and torsion. They also govern the distri­bution of stresses arising from the application of self-equilibrating systems of tractions to the end cross sections. Exact solutions are ob­tained for the case of a uniform, but otherwise arbitrary, cross section under any polynomial distribution of bending moment and torque, and it is shown how conditions at the end cross sections can be satisfied with the aid of solutions of a simple eigenvalue problem. The equations are in a particularly ideal form for incorporating into a general purpose com­puter program for the automatic numerical solution of any problem of this type.

scholarly journals A study by a double-refraction method of the development of turbulence in a long circular tube

1947 ◽  
Vol 192 (1028) ◽  
pp. 32-44 ◽  
Keyword(s):  
Reynolds Number ◽  
Weak Solution ◽  
Laminar Flow ◽  
Cross Section ◽  
Cross Sections ◽  
Circular Tube ◽  
Glass Tube ◽  
The Other ◽  
Double Refraction ◽  
Refraction Method

A streaming double-refraction method was employed to examine the flow in a long glass tube of a very weak solution of benzopurpurin in water. Two kinds of turbulent entry were used: with one, laminar flow at a Reynolds number of about 1900 was observed at cross-sections more than 120 diameters from the entry; with the other the corresponding distance was 90 diameters. The nature of the breakdown of laminar flow at a cross-section was found to depend upon the kind of entry and upon the distance of the cross-section from the inlet. The development of complete turbulence at various cross-sections was also investigated.

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