SEMI-ANALYTIC FIRST-ORDER SOLUTION FOR OPTIMAL LOW-THRUST TRAJECTORIES AROUND MOON

2021 ◽  
Author(s):  
Sandro da Silva Fernandes ◽  
Luiz Arthur Gagg Filho
Keyword(s):  
Low Thrust ◽  
First Order ◽  
Order Solution

Radiant Heat Transfer From Isothermal Dispersions With Isotropic Scattering

1967 ◽  
Vol 89 (4) ◽  
pp. 300-308 ◽  
Author(s):  
R. H. Edwards ◽  
R. P. Bobco
Keyword(s):  
Heat Transfer ◽  
Approximate Solutions ◽  
Radiant Heat ◽  
Second Order ◽  
Isotropic Scattering ◽  
Radiant Heat Transfer ◽  
Approximate Methods ◽  
First Order ◽  
Order Solution ◽  
Radiant Transfer

Two approximate methods are presented for making radiant heat-transfer computations from gray, isothermal dispersions which absorb, emit, and scatter isotropically. The integrodifferential equation of radiant transfer is solved using moment techniques to obtain a first-order solution. A second-order solution is found by iteration. The approximate solutions are compared to exact solutions found in the literature of astrophysics for the case of a plane-parallel geometry. The exact and approximate solutions are both expressed in terms of directional and hemispherical emissivities at a boundary. The comparison for a slab, which is neither optically thin nor thick (τ = 1), indicates that the second-order solution is accurate to within 10 percent for both directional and hemispherical properties. These results suggest that relatively simple techniques may be used to make design computations for more complex geometries and boundary conditions.

scholarly journals Aanalytical Solution for Motion Around Radiated Varying Mass Body

2019 ◽  
Vol 16 ◽  
pp. 8407-8419
Author(s):  
Marwa Abdullah Bin Humaidan ◽  
M. I. El-Saftawy ◽  
H. M. Asiri
Keyword(s):  
Time Series ◽  
Radiation Pressure ◽  
Pressure Effect ◽  
Hamiltonian Function ◽  
Perturbation Techniques ◽  
First Order ◽  
D Operator ◽  
Order Solution ◽  
Delaunay Variables ◽  
Varying Mass

In this work we will add the radiation pressure effect of varying mass body to the model of varying mass Hamiltonian function, including Periastron effect. The problem was formulated in terms of Delaunay variables. The solution of the problem was constructed based on Delava – Hansilmair perturbation techniques. Finally we find the first order solution for the problem as time series by calculating the desired order for the D operator and variables.

scholarly journals Lie transforms and motion of a charged particle in a periodic magnetic field

1984 ◽  
Vol 7 (1) ◽  
pp. 159-169
Author(s):  
Sikha Bhattacharyya ◽  
R. K. Roy Choudhury
Keyword(s):  
Magnetic Field ◽  
Charged Particle ◽  
Averaging Method ◽  
Second Order ◽  
Lie Series ◽  
Periodic Magnetic Field ◽  
First Order ◽  
Order Solution ◽  
Lie Transforms ◽  
Spatially Periodic

We use the Lie series averaging method to obtain a complete second order solution for motion of a charged particle in a spatially periodic magnetic field. A comparison is made with the first order solution obtained previously by Coffey.

Higher-Order Solutions for Unsteady Hypersonic and Supersonic Flow

1974 ◽  
Vol 25 (1) ◽  
pp. 59-68 ◽  
Author(s):  
W H Hui ◽  
J Hamilton
Keyword(s):  
Shock Wave ◽  
Mach Number ◽  
Supersonic Flow ◽  
Power Series ◽  
Unsteady Flow ◽  
The Body ◽  
Wedge Flow ◽  
First Order ◽  
Order Solution ◽  
Method Of Solution

SummaryThe problem of unsteady hypersonic and supersonic flow with attached shock wave past wedge-like bodies is studied, using as a basis the assumption that the unsteady flow is a small perturbation from a steady uniform wedge flow. It is formulated in the most general case and applicable for any motion or deformation of the body. A method of solution to the perturbation equations is given by expanding the flow quantities in power series in M−2, M being the Mach number of the steady wedge flow. It is shown how solutions of successive orders in the series may be calculated. In particular, the second-order solution is given and shown to give improvements uniformly over the first-order solution.

scholarly journals Breakdown of similarity solutions: a perturbation approach for front propagation during foam-improved oil recovery

2021 ◽  
Vol 477 (2245) ◽  
pp. 20200691
Author(s):  
Carlos Torres-Ulloa ◽  
Paul Grassia
Keyword(s):  
Oil Recovery ◽  
Similarity Solutions ◽  
Second Order ◽  
Perturbation Approach ◽  
Improved Oil Recovery ◽  
First Order ◽  
Order Solution ◽  
Concave Corner ◽  
Spatio Temporal ◽  
Material Points

The pressure-driven growth model has been employed to study a propagating foam front in the foam-improved oil recovery process. A first-order solution of the model proves the existence of a concave corner on the front, which initially migrates downwards at a well defined speed that differs from the speed of front material points. At later times, however, it remains unclear how the concave corner moves and interacts with points on the front either side of it, specifically whether material points are extracted from the corner or consumed by it. To address these questions, a second-order solution is proposed, perturbing the aforementioned first-order solution. However, the perturbation is challenging to develop, owing to the nature of the first-order solution, which is a similarity solution that exhibits strong spatio-temporal non-uniformities. The second-order solution indicates that the corner’s vertical velocity component decreases as the front migrates and that points initially extracted from the front are subsequently consumed by it. Overall, the perturbation approach developed herein demonstrates how early-time similarity solutions exhibiting strong spatio-temporal non-uniformities break down as time proceeds.

A Theoretical Analysis of Laminar Forced Flow and Heat Transfer About a Rotating Cone

1965 ◽  
Vol 87 (2) ◽  
pp. 184-190 ◽  
Author(s):  
C. L. Tien ◽  
I. J. Tsuji
Keyword(s):  
Heat Transfer ◽  
Cone Angle ◽  
Forced Flow ◽  
Zeroth Order ◽  
Wedge Flow ◽  
First Order ◽  
Order Solution ◽  
Flow And Heat Transfer ◽  
Rotating Cone ◽  
Fast Rotating

The present paper presents analytically a method of attack on the problem of laminar forced flow and heat transfer about a rotating cone. The nonsimilar nature of the general problem requires that separate consideration be given to a slow rotating cone and a fast rotating cone, depending on the relative magnitude of the rotating speed with respect to the free-stream velocity. The Mangler transformation first reduces the problem of a slow rotating cone to one of wedge flow with a transverse velocity component. The problem is then solved by a perturbation scheme which uses the solution of wedge flow as the zeroth-order solution. The case of a fast rotating cone is solved by a series-expansion scheme which gives successive corrections to the zeroth-order solution, i.e. the solution of a rotating disk in a quiescent fluid. The zeroth-order and first-order equations for both cases are given in the present work, together with the numerical results for the special case of a cone of about 107-deg cone angle. The first-order results in both cases are shown for the drag and torque coefficients, and the local Nusselt number. Higher-order results can be obtained according to the present analysis. The effect of cone angle on the flow and heat-transfer characteristics is indicated by the comparison between the results of the 107-deg cone and those of the disk, i.e., the 180-deg cone.

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