Stability of One-Dimensional Steady Flows with Detonation Wave in a Channel of Variable Cross-Sectional Area

2020 ◽  
Vol 60 (4) ◽  
pp. 697-710
Author(s):  
Kh. F. Valiyev ◽  
A. N. Kraiko ◽  
N. I. Tillyayeva
Keyword(s):  
Detonation Wave ◽  
Cross Sectional Area ◽  
Variable Cross ◽  
Steady Flows ◽  
Sectional Area ◽  
Cross Sectional ◽  
One Dimensional

Numerical Simulation of One-Dimensional Hyperbolic Heat Conduction Equation in Longitudinal Fins With Different Profiles

2010 ◽  
Author(s):  
Keivan Bamdad Masouleh ◽  
Hossein Ahmadikia ◽  
Aziz Azimi
Keyword(s):  
Heat Conduction ◽  
Numerical Solutions ◽  
Discontinuity Point ◽  
Cross Sectional Area ◽  
Hyperbolic Heat Conduction ◽  
Variable Cross ◽  
Sectional Area ◽  
Cross Sectional ◽  
One Dimensional ◽  
Temperature Distributions

In this paper, the steady/unsteady heat conduction in the longitudinal fins with variable cross sectional area under the periodic thermal conditions is examined. Three different one-dimensional fins are considered and solved numerically by implicit finite difference method. In the hyperbolic equation the heat wave propagates with the finite speed hence the sharp discontinuities appear at the temperature distributions. In the explicit solution oscillations appear at discontinuity point which is greatly improved at the implicit method. In the present study temperature distributions are obtained for non-Fourier fins with different profiles. The effects of frequency of temperature oscillation, relaxation time and fin cross sectional area are studied on the temperature and location of the discontinuity of temperature. In order to validate the obtained results of the present study, these results have been compared to those of numerical solutions of the non-Fourier fin with constant cross sectional area. This comparison confirms the correctness of the current results.

DETERMINATION OF THE FUNCTION OF THE ROD’S CROSS-SECTIONAL AREA USING VIBRATION EIGENFREQUENCIES

2020 ◽  
Vol 0 (4) ◽  
pp. 19-24
Author(s):  
I.M. UTYASHEV ◽  
◽  
A.A. AITBAEVA ◽  
A.A. YULMUKHAMETOV ◽  
◽  
...  
Keyword(s):  
Cross Sectional Area ◽  
Variable Cross ◽  
Sectional Area ◽  
Longitudinal Vibrations ◽  
Cross Sectional ◽  
Method Error ◽  
Various Boundary Conditions ◽  
Elastic Fixation ◽  
Crosssectional Area

The paper presents solutions to the direct and inverse problems on longitudinal vibrations of a rod with a variable cross-sectional area. The law of variation of the cross-sectional area is modeled as an exponential function of a polynomial of degree n . The method for reconstructing this function is based on representing the fundamental system of solutions of the direct problem in the form of a Maclaurin series in the variables x and λ. Examples of solutions for various section functions and various boundary conditions are given. It is shown that to recover n unknown coefficients of a polynomial, n eigenvalues are required, and the solution is dual. An unambiguous solution was obtained only for the case of elastic fixation at one of the rod’s ends. The numerical estimation of the method error was made using input data noise. It is shown that the error in finding the variable crosssectional area is less than 1% with the error in the eigenvalues of longitudinal vibrations not exceeding 0.0001.

CFD Solution of a Two-Canopy Parachute in a Top-to-Top Formation With a Vent of Air From One of Its Canopy

2008 ◽  
Author(s):  
Mohammad J. Izadi
Keyword(s):  
Cross Sectional Area ◽  
The Body ◽  
The Other ◽  
Bluff Bodies ◽  
Variable Cross ◽  
Sectional Area ◽  
Cross Sectional ◽  
Drag Forces ◽  
Varied Form ◽  
Two Bodies

A CFD study of a 3 Dimensional flow field around two bodies (Two Canopies of a Parachutes) as two bluff bodies in an incompressible fluid (Air) is modeled here. Formations of these two bodies are top-to-top (One on the top of the other) with respect to the center of each other. One canopy with a constant cross sectional area with a vent of air at its apex, and the other with a variable cross sectional area with no vent is studied here. Vertical distances of these two bodies are varied form zero to half, equal, double and triple radius of the body with a vent on it. The flow condition is considered to be 3-D, unsteady, turbulent, and incompressible. The vertical distances between the bluff bodies, cross sectional area, and also vent ratio of bluff bodies are varied here. The drag forces with static pressures around the two bodies are calculated. From the numerical results, it can be seen that, the drag coefficient is constant on the range of zero to twenty percent of the vent ratio and it decreases for higher vent ratios for when the upper parachute is smaller than the lower one, and it increases for when the upper parachute is larger than the lower one. Both Steady and Unsteady cases gave similar results especially when the distance between the canopies is increased.

Numerical Effect of Airflow From a Lower Canopy (Bluff Body) Into an Upper Canopy in Steady and Turbulent Condition

2008 ◽  
Author(s):  
Mohammad J. Izadi
Keyword(s):  
Drag Force ◽  
Bluff Body ◽  
Cross Sectional Area ◽  
The Body ◽  
Bluff Bodies ◽  
Variable Cross ◽  
Sectional Area ◽  
Cross Sectional ◽  
Varied Form ◽  
Two Bodies

In this paper, a 3-D flow field around two bluff bodies in an incompressible fluid is modeled [1]. Formations of these two bodies are top to top (One on the top of the other) with respect to the center of each other. The lower on has a constant cross sectional area with a vent of air at its apex and the upper one has a variable cross sectional area with no vent on it. The vertical distances between the bluff bodies, the cross sectional area, and also the vent ratio of bluff bodies are varied here. Vertical distances of these two bodies are varied form zero to half, equal, double and triple the radius of the body with a vent on it (lower body). Flow condition is considered 3D, steady, turbulent, and incompressible. The drag force on each body and also the pressure around the two bodies are calculated. From the numerical results, it can be seen that, the drag force is constant over the range of zero to twenty percent of the vent ratios and for higher vent ratios when the upper bluff body is smaller than the lower one the drag force decreased, and it increased when the upper bluff body is larger than the lower one.

Similarity Solution of Freezing or Melting Processes with Variable Thermal Properties

1972 ◽  
Vol 1 (1) ◽  
pp. 51-54
Author(s):  
Sui Lin
Keyword(s):  
Temperature Field ◽  
Thermal Properties ◽  
Phase Boundary ◽  
Similarity Solution ◽  
Universal Function ◽  
Cross Sectional Area ◽  
System Of Equations ◽  
Variable Cross ◽  
Sectional Area ◽  
Cross Sectional

Freezing or melting processes, using substances with variable thermal properties, taking place in a body with variable cross-sectional area, are considered. The method of obtaining the similarity solution involves three steps, 1) transformation of the position coordinate, 2) description of the temperature field, and 3) consideration of the temperature distribution in the neighbourhood of the phase boundary. It reduces the system of equations in the neighbourhood of the phase boundary to one that is independent of the cross-sectional area. The solution of this system is a universal function and is applicable to bodies with different cross-sectional areas. A theorem for calculating the rate of propagation of the phase boundary in a body of variable cross-sectional area from that in a body of constant cross-sectional area is obtained.

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