Pressure Distributions in Porous Ducts of Arbitrary Cross Section

1973 ◽  
Vol 95 (3) ◽  
pp. 342-348 ◽  
Author(s):  
J. C. P. Huang ◽  
H. S. Yu
Keyword(s):  
Pressure Gradient ◽  
Cross Section ◽  
Cross Sections ◽  
Porous Plate ◽  
Porous Wall ◽  
Design Criterion ◽  
Arbitrary Cross Section ◽  
Solid Particles ◽  
Equivalent Diameter ◽  
Pressure Distributions

A general analytical method has been developed to approximate the pressure distribution along a porous duct of an arbitrary cross section with uniform fluid extraction or addition through the wall. Application of this method is made to a variety of cross sections including circular tubes, parallel plate channels, elliptical ducts, rectangular ducts, annular ducts, and isosceles triangular ducts. Comparisons have been made with results from existing literature on cases of the circular porous tube and the parallel porous plate channel in which exact solutions are available. A numerical solution for the case of a parallel channel consisting of an impermeable wall on one side and a porous wall on the other side is also presented. One important filter duct design criterion has been found for each of the above cases. At a critical wall Reynolds number, defined by flow velocity normal to the wall and the equivalent diameter of the duct, the pressure gradient along the filter duct approaches zero. The zero pressure gradient in a filter duct ensures uniform filtration of solid particles.

Heat Transfer in a Supersonic Parallel Diffuser

1965 ◽  
Vol 7 (1) ◽  
pp. 1-7 ◽  
Author(s):  
P. J. Baker
Keyword(s):  
Heat Transfer ◽  
Pressure Gradient ◽  
Cross Section ◽  
Static Pressure ◽  
Positive Pressure ◽  
Transfer Coefficients ◽  
Heat Transfer Coefficients ◽  
Pipe Flows ◽  
Pressure Distributions ◽  
The Mean

This paper presents the results of heat transfer measurements taken on a two-dimensional supersonic parallel diffuser. The wall static pressure distributions and the corresponding heat transfer coefficients and fluxes have been measured for a range of initial total pressures. The effects of varying the area of the diffuser cross-section for the same upstream generating nozzle have also been studied. Mach number profiles measured at sections along the diffuser show that in the presence of shock waves and a positive pressure gradient the flow is very much underdeveloped. In general, the mean level of heat transfer is found to be much greater than that predicted by conventional empirical equations for subsonic pipe flows with zero pressure gradient. Further, on comparison between normal and oblique shock diffusion the former is found to give the higher level of heat transfer.

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%.

Note on Relationships between Friction and Liquid Cross-Sections during Two-Phase Flow

1966 ◽  
Vol 8 (1) ◽  
pp. 107-109 ◽  
Author(s):  
D. Chisholm
Keyword(s):  
Pressure Gradient ◽  
Cross Section ◽  
Cross Sections ◽  
Two Phase Flow ◽  
Phase Flow ◽  
Pronounced Change ◽  
Two Phase ◽  
Horizontal Tubes ◽  
A Value ◽  
Friction Pressure

Relationships between the friction pressure gradient and the cross-section of the tube occupied by the liquid are developed for the flow of air-water mixtures in rough-walled horizontal tubes. The data indicate a pronounced change in the form of the relationships when the pressure gradient reaches a value of about 60 lb/ft2ft.

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.

Magnetohydrodynamic pipe flow Part2. High Hartmann number

1962 ◽  
Vol 13 (4) ◽  
pp. 513-518 ◽  
Author(s):  
J. A. Shercliff
Keyword(s):  
Magnetic Fields ◽  
Pressure Gradient ◽  
Cross Section ◽  
Pipe Flow ◽  
Hartmann Number ◽  
Gradient Flow ◽  
Transverse Magnetic ◽  
Arbitrary Cross Section ◽  
Conducting Liquid ◽  
Experimental Pressure

The paper presents an improved, second approximation for the laminar motion of a conducting liquid at high Hartmann number in non-conducting pipes of arbitrary cross-section under uniform transverse magnetic fields. A satisfactory comparison with the author's previously experimental pressure gradient/flow results is made for the case of a circular pipe.

Laminar Flow of an Incompressible Fluid in a Conduit With Arbitrary Cross Section, Arbitrary Time-Varying Pressure Gradient, and Arbitrary Initial Velocity

1972 ◽  
Vol 94 (1) ◽  
pp. 27-32 ◽  
Author(s):  
H. K. Hepworth ◽  
W. Rice
Keyword(s):  
Pressure Gradient ◽  
Cross Section ◽  
Initial Velocity ◽  
Solution Method ◽  
Initial Conditions ◽  
Arbitrary Cross Section ◽  
Computational Time ◽  
Time Varying ◽  
Arbitrary Time ◽  
Gram Determinant

A computer-oriented solution is given for the flow described in the title of the paper. The boundary shape is represented by specification of the coordinates of N points on the boundary; the initial velocity is represented by specification of L values of the velocity in the cross section at time zero; the arbitrary time-varying pressure gradient is implemented by use of Duhamel’s Theorem. In the solution method presented, boundary and initial conditions are satisfied in the least squares sense. The Gram determinant is used to determine eigenvalues and the Gram-Schmidt orthonormalizing procedure is used to construct a set of functions appropriate for a finite series solution. Computer programs are referenced which have been used to investigate the correctness of the solution and the accuracy obtainable with reasonable digital computational time.

Vibration of Stress-Free Hollow Cylinders of Arbitrary Cross Section

1995 ◽  
Vol 62 (3) ◽  
pp. 718-724 ◽  
Author(s):  
K. M. Liew ◽  
K. C. Hung ◽  
M. K. Lim
Keyword(s):  
Cross Section ◽  
Cross Sections ◽  
Three Dimensional ◽  
Arbitrary Cross Section ◽  
Mode Shapes ◽  
Width Ratio ◽  
Cross Sectional ◽  
Hollow Cylinders ◽  
Displacement Based ◽  
Bending Modes

A three-dimensional elasticity solution to the vibrations of stress-free hollow cylinders of arbitrary cross section is presented. The natural frequencies and deformed mode shapes of these cylinders are obtained via a three-dimensional displacement-based energy formulation. The technique is applied specifically to the parametric investigation of hollow cylinders of different cross sections and sizes. It is found that the cross-sectional property of the cylinder has significant effects on the normal mode responses, particularly, on the transverse bending modes. By varying the length-to-width ratio of these elastic cylinders, interesting results demonstrating the dependence of frequencies on the length of the cylinder have been concluded.

scholarly journals Analytical Method to Interpret Displacement in Elastic Anisotropic Soil due to a Tunnel Cavity with an Arbitrary Cross Section

2021 ◽  
Vol 2021 ◽  
pp. 1-14
Author(s):  
Qiongfang Zhang ◽  
Kang Cheng ◽  
Yadong Lou ◽  
Tangdai Xia ◽  
Panpan Guo ◽  
...  
Keyword(s):  
Cross Section ◽  
Cross Sections ◽  
Surface Displacement ◽  
Horizontal Displacement ◽  
Distribution Patterns ◽  
Mapping Method ◽  
Arbitrary Cross Section ◽  
Image Method ◽  
Variable Theory ◽  
Anisotropic Soil

Based on complex variable theory and conformal mapping method, the paper presents full plane elastic solutions around an unlined tunnel with arbitrary cross section in anisotropic soil. The solutions describe soil elastic solutions for assuming that the displacement vectors along the tunnel boundary are directed towards the center of the tunnel. Tunnels with different cross sections are used to illustrate the method and its correctness. An elliptical unlined tunnel case is discussed in detail in the paper. Using the image method, an approximate solution for predicting surface displacement and subsurface horizontal displacement around an unlined tunnel in anisotropic soil can be obtained. The results show anisotropic stiffness properties n n = E h / E v and m m = G v h / E v have a great effect on the displacement distribution patterns around an elliptical tunnel with certain shape.

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