Solution in one-dimensional approximation of the variational problem of constructing a maximum-thrust nozzle for gas-particle flow

1972 ◽  
Vol 3 (4) ◽  
pp. 34-40 ◽  
Author(s):  
A. N. Kraiko ◽  
V. K. Starkov ◽  
L. E. Sternin
Keyword(s):  
Variational Problem ◽  
Particle Flow ◽  
One Dimensional ◽  
Dimensional Approximation ◽  
Maximum Thrust

A Stefan problem in a Bridgman crystal grower

1995 ◽  
Vol 6 (3) ◽  
pp. 191-199
Author(s):  
P. den Decker ◽  
R. van der Hout ◽  
C. J. Van Duijn ◽  
L. A. Peletier
Keyword(s):  
Critical Speed ◽  
Internal Heat ◽  
Mushy Region ◽  
Dimensional Model ◽  
Real Situation ◽  
One Dimensional ◽  
Dimensional Approximation ◽  
The One ◽  
Strong Curvature ◽  
Bridgman Crystal Grower

We discuss a one-dimensional model for a Bridgman crystal grower, where the removal of heat is described by an internal heat sink. A consequence is the apparent existence of mushy regions for relatively large velocities of the cooling machine; these mushy regions are an artefact of the one-dimensional approximation. We show that for some types of cooling profiles there exists a critical speed for the existence of mushy regions, whereas for different cooling profiles no such critical speed exists. The presence of a mushy region may indicate a strong curvature of the liquid/solid interface in the real situation.

scholarly journals Quasi-two-dimensional approximation for numerical simulation of flows in engine ducts

2019 ◽  
Author(s):  
V. Vlasenko ◽  
A. Shiryaeva
Keyword(s):  
High Speed ◽  
Fuel Injection ◽  
Three Dimensional ◽  
Preliminary Design ◽  
Two Dimensional ◽  
Combustion Chambers ◽  
New Approach ◽  
One Dimensional ◽  
Dimensional Approximation ◽  
3D Flows

New quasi-two-dimensional (2.5D) approach to description of three-dimensional (3D) flows in ducts is proposed. It generalizes quasi-one-dimensional (quasi-1D, 1.5D) theories. Calculations are performed in the (x; y) plane, but variable width of duct in the z direction is taken into account. Derivation of 2.5D approximation equations is given. Tests for verification of 2.5D calculations are proposed. Parametrical 2.5D calculations of flow with hydrogen combustion in an elliptical combustor of a high-speed aircraft, investigated within HEXAFLY-INT international project, are described. Optimal scheme of fuel injection is found and explained. For one regime, 2.5D and 3D calculations are compared. The new approach is recommended for use during preliminary design of combustion chambers.

Numerical and Analytical Estimation of Parameters of Pulsed Energy Sources Which Do Not Lead to Locking of Supersonic Flow in Channels of Variable Section

2013 ◽  
Vol 8 (4) ◽  
pp. 103-109
Author(s):  
Vladimir Zamuraev ◽  
Anna Kalinina
Keyword(s):  
Energy Supply ◽  
Variable Cross Section ◽  
Pulsed Power ◽  
Variable Cross ◽  
Estimation Of Parameters ◽  
One Dimensional ◽  
Dimensional Approximation ◽  
Variable Section ◽  
Analytical Estimation ◽  
Full Power

In this paper the pulse energy supply into the channel of variable cross section was studied. The approximate formulas were obtained for the value of the input energy, corresponding to the maximal distance which the shock wave from a pulsed power source reached upstream, as well as full power, energy supply period corresponding to the conditions of closing the channel. The applicability of the analytical relationships is confirmed by numerical calculations based on the Euler equations in a quasi one-dimensional approximation

scholarly journals ON A LATTICE GENERALISATION OF THE LOGARITHM AND A DEFORMATION OF THE DEDEKIND ETA FUNCTION

2020 ◽  
Vol 102 (1) ◽  
pp. 118-125
Author(s):  
LAURENT BÉTERMIN
Keyword(s):  
Variational Problem ◽  
Theta Function ◽  
Dedekind Eta Function ◽  
Dimensional Lattice ◽  
One Dimensional ◽  
Natural Logarithm ◽  
Two Parameters

We consider a deformation $E_{L,\unicode[STIX]{x1D6EC}}^{(m)}(it)$ of the Dedekind eta function depending on two $d$-dimensional simple lattices $(L,\unicode[STIX]{x1D6EC})$ and two parameters $(m,t)\in (0,\infty )$, initially proposed by Terry Gannon. We show that the minimisers of the lattice theta function are the maximisers of $E_{L,\unicode[STIX]{x1D6EC}}^{(m)}(it)$ in the space of lattices with fixed density. The proof is based on the study of a lattice generalisation of the logarithm, called the lattice logarithm, also defined by Terry Gannon. We also prove that the natural logarithm is characterised by a variational problem over a class of one-dimensional lattice logarithms.

Kinetic calculation of a turbulent flame in the one-dimensional approximation

1980 ◽  
Vol 16 (4) ◽  
pp. 365-369
Author(s):  
V. Ya. Basevich ◽  
V. P. Volodin ◽  
S. M. Kogarko ◽  
N. I. Peregudov
Keyword(s):  
Turbulent Flame ◽  
Kinetic Calculation ◽  
One Dimensional ◽  
Dimensional Approximation ◽  
The One
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