Concept of Steady Glide Reentry Trajectory and Stability of Its Regular Perturbation Solutions

2020 ◽  
pp. 125-148
Author(s):  
Wanchun Chen ◽  
Hao Zhou ◽  
Wenbin Yu ◽  
Liang Yang
Keyword(s):  
Regular Perturbation ◽  
Reentry Trajectory ◽  
Perturbation Solutions

Perturbation Solutions for Spherical Solidification of Saturated Liquids

1973 ◽  
Vol 95 (1) ◽  
pp. 42-46 ◽  
Author(s):  
R. I. Pedroso ◽  
G. A. Domoto
Keyword(s):  
Boundary Condition ◽  
Series Solution ◽  
Freezing Temperature ◽  
Perturbation Solution ◽  
Partial Sums ◽  
Regular Perturbation ◽  
Constant Wall Temperature ◽  
Temperature Boundary ◽  
Temperature Boundary Condition ◽  
Perturbation Solutions

A perturbation solution is obtained for outward and partial inward spherical solidification of a liquid initially at the freezing temperature. The constant-wall-temperature boundary condition is considered with the properties of the solidified material assumed as constants. A nonlinear transformation is applied to the sequence of partial sums in the perturbation solution to increase its range of applicability. For inward solidification it is found that the regular perturbation solution diverges for front positions close to the center. An Euler transformation and an overall energy balance are then used to obtain a modified series solution which is compared with numerical results.

Partial Spectral Expansions for Problems in Thermal Convection

1978 ◽  
Vol 100 (3) ◽  
pp. 435-441 ◽  
Author(s):  
E. J. Shaughnessy ◽  
J. Custer ◽  
R. W. Douglass
Keyword(s):  
Heat Transfer ◽  
Convective Heat Transfer ◽  
Thermal Convection ◽  
Perturbation Methods ◽  
Nonlinear Partial Differential Equations ◽  
Regular Perturbation ◽  
Spectral Expansions ◽  
Valid Evidence ◽  
Parameter Values ◽  
Perturbation Solutions

The use of spectral expansions for solving nonlinear partial differential equations is explained, and two examples drawn from convective heat transfer are presented. For both problems the results agree well with regular perturbation solutions at parameter values for which the latter remain valid. Evidence is given to indicate that the spectral solutions are valid for considerably larger parameter values than can be reached with the perturbation methods.

Perturbation solutions for highly frictional granular media

2005 ◽  
Vol 461 (2053) ◽  
pp. 21-42 ◽  
Author(s):  
Ngamta Thamwattana ◽  
James M. Hill
Keyword(s):  
Internal Friction ◽  
Granular Media ◽  
Numerical Solutions ◽  
Solution Procedure ◽  
Perturbation Series ◽  
Regular Perturbation ◽  
Approximate Analytical Solutions ◽  
Leading Term ◽  
Flow Through ◽  
Perturbation Solutions

In this paper, we deal with the materials possessing angles of internal friction ϕ for which 1 − sin ϕ is close to zero, and we use the solution for sin ϕ = 1 as the leading term in a regular perturbation series, where the correction terms are of order 1 − sin ϕ . In this way we obtain approximate analytical solutions which can be used to describe the behaviour of real granular materials. The solution procedure is illustrated with reference to quasi–static flow through wedge–shaped and conical hoppers. For these two problems, the obtained perturbation solutions are shown to be graphically indistinguishable from the numerical solutions for high angles of internal friction, and for moderately high angles of internal friction the perturbation solutions still provide excellent approximations.

Parallel Plate Flow of a Third-Grade Fluid and a Newtonian Fluid With Variable Viscosity

2016 ◽  
Vol 71 (7) ◽  
pp. 595-606
Author(s):  
Volkan Yıldız ◽  
Mehmet Pakdemirli ◽  
Yiğit Aksoy
Keyword(s):  
Newtonian Fluid ◽  
Parallel Plate ◽  
Numerical Solutions ◽  
Variable Viscosity ◽  
Third Grade ◽  
Third Grade Fluid ◽  
Regular Perturbation ◽  
Approximate Analytical Solutions ◽  
Grade Fluid ◽  
Perturbation Solutions

AbstractSteady-state parallel plate flow of a third-grade fluid and a Newtonian fluid with temperature-dependent viscosity is considered. Approximate analytical solutions are constructed using the newly developed perturbation-iteration algorithms. Two different perturbation-iteration algorithms are used. The velocity and temperature profiles obtained by the iteration algorithms are contrasted with the numerical solutions as well as with the regular perturbation solutions. It is found that the perturbation-iteration solutions converge better to the numerical solutions than the regular perturbation solutions, in particular when the validity criteria of the regular perturbation solution are not satisfied. The new analytical approach produces promising results in solving complex fluid problems.

A WEAKLY NONLINEAR INSTABILITY OF MISCIBLE DISPLACEMENTS IN A RECTILINEAR POROUS MEDIA FLOW

1994 ◽  
Vol 04 (05) ◽  
pp. 1319-1328 ◽  
Author(s):  
WILLIAM B. ZIMMERMAN
Keyword(s):  
Linear Theory ◽  
Landau Equation ◽  
Separation Of Variables ◽  
Finite Amplitude ◽  
Linear Stability Theory ◽  
Porous Media Flow ◽  
Perturbation Scheme ◽  
Viscous Effects ◽  
Regular Perturbation ◽  
Displacement Front

The linear stability theory of Tan & Homsy [1986] is extended to include the effects of weak nonlinear coupling between mass flux and viscous effects when the viscous fingers grow from a slowly diffusing, nearly flat displacement front. A regular perturbation scheme combined with a similarity-separation of variables technique leads to a Landau equation for the amplitude of the disturbance. The Landau constant has a simple pole for a given wavenumber within the linear theory cutoff wavenumber for growth. An argument is given that this pole leads to pairing of fingers while the instability remains small. Comparison of the length scale of the pole of the Landau constant with experimental measurements of finger scale shows good agreement where plausibly finite-amplitude effects might come into play, but with the linear theory otherwise.

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