Numerical solutions of the Navier‐Stokes and energy equations for laminar incompressible flow past parabolic bodies

2000 ◽  
Vol 10 (1) ◽  
pp. 80-93 ◽  
Author(s):  
O.M. Haddad ◽  
M. Abu‐Qudais ◽  
A.M. Maqableh
Keyword(s):  
Incompressible Flow ◽  
Numerical Solutions ◽  
Navier Stokes ◽  
Flow Past ◽  
Energy Equations

Numerical Solutions of Transients in Pneumatic Networks—Transmission-Line Calculations

1968 ◽  
Vol 35 (3) ◽  
pp. 588-595 ◽  
Author(s):  
S. Tsao
Keyword(s):  
Wave Propagation ◽  
Transmission Lines ◽  
Numerical Solutions ◽  
Navier Stokes ◽  
Damping Factor ◽  
Temperature Profiles ◽  
Hypothetical Case ◽  
One Dimensional ◽  
Simplifying Assumptions ◽  
Energy Equations

Equations governing the damped wave propagation along transmission lines are obtained from the Navier-Stokes and energy equations by making certain simplifying assumptions. The flow considered is essentially one-dimensional. However, radial variations of the velocity and temperature profiles must be considered, because the damping factor is directly dependent on them. The equations are integrated by numerical methods. A hypothetical case is computed as an example.

Laminar incompressible flow past a semi-infinite flat plate

1967 ◽  
Vol 27 (4) ◽  
pp. 691-704 ◽  
Author(s):  
R. T. Davis
Keyword(s):  
Flat Plate ◽  
Incompressible Flow ◽  
Stokes Equations ◽  
Leading Edge ◽  
Navier Stokes ◽  
Local Similarity ◽  
Approximate Methods ◽  
Navier Stokes Equations ◽  
Flow Past

Laminar incompressible flow past a semi-infinite flat plate is examined by using the method of series truncation (or local similarity) on the full Navier-Stokes equations. The first and second truncations are calculated at points on the plate away from the leading edge, while only the first truncation is calculated at the leading edge. The solutions are compared with the results from other approximate methods.

Numerical Solutions of a Viscous Uniform Approach Flow Past Square and Diamond Cylinders

2002 ◽  
Author(s):  
Charles Dalton ◽  
Wu Zheng
Keyword(s):  
Stream Function ◽  
Numerical Solutions ◽  
Stokes Equations ◽  
Elliptic Partial Differential Equation ◽  
Navier Stokes ◽  
Central Difference ◽  
Uniform Approach ◽  
Flow Past ◽  
Line Force ◽  
Vorticity Transport

Numerical results are presented for a uniform approach flow past square and diamond cylinders, with and without rounded corners, at Reynolds numbers of 250 and 1000. This unsteady viscous flow problem is formulated by the 2-D Navier-Stokes equations in vorticity and stream-function form on body-fitted coordinates and solved by a finite-difference method. Second-order Adams-Bashforth and central-difference schemes are used to discretize the vorticity transport equation while a third-order upwinding scheme is incorporated to represent the nonlinear convective terms. A grid generation technique is applied to provide an efficient mesh system for the flow. The elliptic partial differential equation for stream-function and vorticity in the transformed plane is solved by the multigrid iteration method. The Strouhal number and the average in-line force coefficients agree very well with the experimental and previous numerical values. The vortex structures and the evolution of vortex shedding are illustrated by vorticity contours. Rounding the corners of the square and diamond cylinders produced a noticeable decrease on the calculated drag and lift coefficients.

A Theory of Rotating Condensation

1959 ◽  
Vol 81 (2) ◽  
pp. 113-119 ◽  
Author(s):  
E. M. Sparrow ◽  
J. L. Gregg
Keyword(s):  
Numerical Solutions ◽  
Saturated Vapor ◽  
Large Body ◽  
Rotating Disk ◽  
Disk Surface ◽  
Film Condensation ◽  
Navier Stokes ◽  
Torque Moment ◽  
Prandtl Numbers ◽  
Energy Equations

An analysis is made for film condensation on a rotating disk situated in a large body of pure saturated vapor. The centrifugal field associated with the rotation sweeps the condensate outward along the disk surface, and gravity forces need not be involved. The problem is formulated as an exact solution of the complete Navier-Stokes and energy equations. Numerical solutions are obtained for Prandtl numbers between 0.003 and 100 and for cpΔT/hfg in the range 0.0001 to 1.0. Results are given for the heat transfer, as well as for the condensate layer thickness, torque moment, and temperature and velocity profiles.

Influence of temperature dependent physical properties on liquid metal droplet impact dynamics

2021 ◽  
pp. 1-15
Author(s):  
Akash Chowdhury ◽  
Anandaroop Bhattacharya ◽  
Partha Bandyopadhyay
Keyword(s):  
Surface Tension ◽  
Numerical Solutions ◽  
Substrate Surface ◽  
Metal Droplet ◽  
Navier Stokes ◽  
Complex Flow ◽  
Liquid Metal Droplet ◽  
Aluminium Copper ◽  
Energy Equations ◽  
Surface Tension Forces

Abstract The dynamics of a metal droplet impacting on a substrate surface has been studied in the paper numerically. Numerical solutions of the Navier-Stokes and Energy equations show the evolution of the droplet as it spreads upon impact with the substrate while simultaneously undergoing solidification. The interplay of the different forces including inertia, viscous and surface tension, coupled with solidification of the molten material in layers lead to complex flow dynamics. The change in density and viscosity owing to change in temperature resulting from the cooling process, is found to influence the spreading of the droplet significantly. The model was exercised for three different materials viz. aluminium, copper and nickel to determine the final splat radius as well as spreading time. The surface tension forces as well as solidification rates were found to be the dominant factors in determining the above parameters as well as the shape of the splat during spreading. The results were found to be in good agreement with existing analytical model.

Steady incompressible flow past a row of circular cylinders

1991 ◽  
Vol 225 ◽  
pp. 655-671 ◽  
Author(s):  
Bengt Fornberg
Keyword(s):  
Reynolds Number ◽  
Incompressible Flow ◽  
Numerical Solutions ◽  
Major Change ◽  
Circular Cylinders ◽  
Two Dimensional ◽  
Single Cylinder ◽  
Flow Past

Numerical solutions are presented for steady two-dimensional incompressible flow past an infinite row of cylinders (of unit radii, with distances W between their centres). The calculations cover R [les ] 700 for 5 [les ] W [les ] ∞ and also R = 800 for 5 [les ] W [les ] 100 (where R denotes the Reynolds number based on the cylinder diameters). The recirculation regions (wake bubbles) are found to grow in length approximately linearly with R in all cases. For high values of R, a major change occurs in their character when W is increased past Wcrit ≈ 16. While they have remained slender up to this point (essentially only stretching in length in proportion to R), their centres of circulation have moved towards their ends. As W is further increased, the wake bubbles widen rapidly, beginning from the rear of the wakes. In the limit of W→∞, the present results agree with the previous ones for a single cylinder as reported by Fornberg (1985).

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