Transonic Flow in Curved Channels

1967 ◽  
Vol 89 (4) ◽  
pp. 748-752 ◽  
Author(s):  
P. A. Thompson
Keyword(s):  
Transonic Flow ◽  
Approximate Calculation ◽  
Continuity Condition ◽  
Numerical Results ◽  
Two Dimensional ◽  
Curved Channels ◽  
Symmetric Channel ◽  
Analytical Results ◽  
Limiting Case

Transonic flow in a curved two-dimensional throat is considered. The approximate calculation is based on the full nonlinear inviscid equations and an integral continuity condition. Numerical results are presented in the form of curves which permit the determination of the flow in a nozzle of specified geometry. Analytical results reduce after linearization to those of Sauer for the limiting case of a symmetric channel.

Numerical Solution of Inviscid Two-Dimensional Transonic Flow Through a Cascade

1987 ◽  
Vol 109 (1) ◽  
pp. 108-113
Author(s):  
J. Forˇt ◽  
K. Kozel
Keyword(s):  
Experimental Data ◽  
Weak Solution ◽  
Numerical Solution ◽  
Transonic Flow ◽  
Numerical Procedure ◽  
Numerical Results ◽  
Two Dimensional ◽  
System Of Difference Equations ◽  
Flow Through ◽  
Turbine Cascades

The paper presents a method of numerical solution of transonic potential flow through plane cascades with subsonic inlet flow. The problem is formulated as a weak solution with combined Dirichlet’s and Neumann’s boundary conditions. The numerical procedure uses Jameson’s rotated difference scheme and the SLOR technique to solve a system of difference equations. Numerical results of transonic flow are compared with experimental data and with other numerical results for both compressor and turbine cascades near choke conditions.

scholarly journals Finger Growth and Selection in a Poisson Field

2019 ◽  
Vol 178 (3) ◽  
pp. 763-774
Author(s):  
N. R. McDonald
Keyword(s):  
Arbitrary Number ◽  
Numerical Results ◽  
Poisson’S Equation ◽  
Analogous Problem ◽  
Stat Phys ◽  
Two Dimensional ◽  
Poisson's Equation ◽  
Analytical Results ◽  
Poisson Field

AbstractSolutions are found for the growth of infinitesimally thin, two-dimensional fingers governed by Poisson’s equation in a long strip. The analytical results determine the asymptotic paths selected by the fingers which compare well with the recent numerical results of Cohen and Rothman (J Stat Phys 167:703–712, 2017) for the case of two and three fingers. The generalisation of the method to an arbitrary number of fingers is presented and further results for four finger evolution given. The relation to the analogous problem of finger growth in a Laplacian field is also discussed.

scholarly journals Onset of Convection in Two-Dimensional Porous Cavities with Open and Conducting Boundaries

2021 ◽  
Vol 136 (3) ◽  
pp. 791-812
Author(s):  
Peder A. Tyvand ◽  
Jonas Kristiansen Nøland
Keyword(s):  
Critical Rayleigh Number ◽  
Numerical Results ◽  
Temperature Perturbation ◽  
Two Dimensional ◽  
Onset Of Convection ◽  
Order Problem ◽  
Fourth Order Problem ◽  
Thermally Conducting ◽  
Perturbation Pressure ◽  
Special Case

AbstractThe onset of thermal convection in two-dimensional porous cavities heated from below is studied theoretically. An open (constant-pressure) boundary is assumed, with zero perturbation temperature (thermally conducting). The resulting eigenvalue problem is a full fourth-order problem without degeneracies. Numerical results are presented for rectangular and elliptical cavities, with the circle as a special case. The analytical solution for an upright rectangle confirms the numerical results. Streamlines penetrating the open cavities are plotted, together with the isotherms for the associated closed thermal cells. Isobars forming pressure cells are depicted for the perturbation pressure. The critical Rayleigh number is calculated as a function of geometric parameters, including the tilt angle of the rectangle and ellipse. An improved physical scaling of the Darcy–Bénard problem is suggested. Its significance is indicated by the ratio of maximal vertical velocity to maximal temperature perturbation.

scholarly journals Geometrical four-point functions in the two-dimensional critical Q-state Potts model: the interchiral conformal bootstrap

2020 ◽  
Vol 2020 (12) ◽  
Author(s):  
Yifei He ◽  
Jesper Lykke Jacobsen ◽  
Hubert Saleur
Keyword(s):  
Potts Model ◽  
Correlation Functions ◽  
Liouville Theory ◽  
Analytical Determination ◽  
Conformal Weight ◽  
Two Dimensional ◽  
Conformal Blocks ◽  
Conformal Bootstrap ◽  
Point Correlation

Abstract Based on the spectrum identified in our earlier work [1], we numerically solve the bootstrap to determine four-point correlation functions of the geometrical connectivities in the Q-state Potts model. Crucial in our approach is the existence of “interchiral conformal blocks”, which arise from the degeneracy of fields with conformal weight hr,1, with r ∈ ℕ*, and are related to the underlying presence of the “interchiral algebra” introduced in [2]. We also find evidence for the existence of “renormalized” recursions, replacing those that follow from the degeneracy of the field $$ {\Phi}_{12}^D $$ Φ 12 D in Liouville theory, and obtain the first few such recursions in closed form. This hints at the possibility of the full analytical determination of correlation functions in this model.

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