Irrotational Subsonic Flow of an Ideal Gas in Two-Dimensional Ducts-Optimal Ducts and Ducts with Plane Sonic Exits

AIAA Journal ◽  
1974 ◽  
Vol 12 (5) ◽  
pp. 608-614 ◽  
Author(s):  
M. J. COHEN ◽  
H. PORTNOY
Keyword(s):  
Subsonic Flow ◽  
Ideal Gas ◽  
Two Dimensional

Compressible Subsonic Flow in Two-dimensional Channels

1955 ◽  
Vol 6 (3) ◽  
pp. 205-220 ◽  
Author(s):  
L. C. Woods
Keyword(s):  
Conformal Mapping ◽  
Direct Problem ◽  
Subsonic Flow ◽  
Ideal Gas ◽  
Inviscid Fluid ◽  
Two Dimensional ◽  
Step Functions ◽  
Curved Walls ◽  
Special Case ◽  
The Ideal

SummaryEquations for the calculation of the subsonic flow of an inviscid fluid through given two-dimensional channels (the “ direct” problem), and for the design (the “ indirect” problem) of such channels are derived. The method is based on conformal mapping, and in the special case of channels with walls made from a number of straight sections, or with wall pressure prescribed as step-functions, yields the same results as the well-known Schwarz-Christoffel mapping theorem technique. However, it is more general than this latter method, since it is capable of dealing with curved walls or continuously varying wall pressures. The compressibility of the fluid is allowed for only approximately, the ideal gas being replaced by a Kàrmàn-Tsien tangent gas.In Part II the theory is applied to various problems of aeronautical interest, perhaps the most important of which is to the setting of “ streamlined ” walls about a symmetrical aerofoil placed in the centre of the channel.

A Numerical Study of Unsteady Natural Convection in a Rectangular Enclosure: The Effect of Compressibility

2004 ◽  
Author(s):  
K. M. Akyuzlu ◽  
Y. Pavri ◽  
A. Antoniou
Keyword(s):  
Mathematical Model ◽  
Stokes Equations ◽  
Numerical Study ◽  
Vertical Wall ◽  
Ideal Gas ◽  
Working Fluid ◽  
Two Dimensional ◽  
Algebraic Equations ◽  
Rectangular Enclosure ◽  
Circulation Patterns

A two-dimensional, mathematical model is adopted to investigate the development of buoyancy driven circulation patterns and temperature contours inside a rectangular enclosure filled with a compressible fluid (Pr=1.0). One of the vertical walls of the enclosure is kept at a higher temperature then the opposing vertical wall. The top and the bottom of the enclosure are assumed insulated. The physics based mathematical model for this problem consists of conservation of mass, momentum (two-dimensional Navier-Stokes equations) and energy equations for the enclosed fluid subjected to appropriate boundary conditions. The working fluid is assumed to be compressible through a simple ideal gas relation. The governing equations are discretized using second order accurate central differencing for spatial derivatives and first order forward finite differencing for time derivatives where the computation domain is represented by a uniform orthogonal mesh. The resulting nonlinear equations are then linearized using Newton’s linearization method. The set of algebraic equations that result from this process are then put into a matrix form and solved using a Coupled Modified Strongly Implicit Procedure (CMSIP) for the unknowns (primitive variables) of the problem. A numerical experiment is carried out for a benchmark case (driven cavity flow) to verify the accuracy of the proposed solution procedure. Numerical experiments are then carried out using the proposed compressible flow model to simulate the development of the buoyancy driven circulation patterns for Rayleigh numbers between 103 and 105. Finally, an attempt is made to determine the effect of compressibility of the working fluid by comparing the results of the proposed model to that of models that use incompressible flow assumptions together with Boussinesq approximation.

Grid-Free Vortex Methods for Natural Convection in Two-Dimensional Domains

2012 ◽  
Author(s):  
Issam Lakkis
Keyword(s):  
Natural Convection ◽  
Nonlinear Diffusion ◽  
Reacting Flows ◽  
Ideal Gas ◽  
Two Dimensional ◽  
Vortex Methods ◽  
Free Vortex ◽  
Low Mach Number ◽  
Buoyancy Driven Flows ◽  
Vorticity Generation

Vortex methods for simulating natural convection of an ideal gas in unbounded two-dimensional domains are presented. In particular, the redistribution method for diffusion is extended to enable simulation of nonlinear diffusion of an ideal gas in isobaric conditions encountered in unbounded low-Mach number flows. We also address the problem of handling source terms in grid-free vortex methods and propose a fast, accurate, and physically motivated method for solving the associated inverse problems. Examples include generation of baroclinic vorticity in non-reacting buoyancy driven flows, and in addition, generation of internal energy and species in buoyant reacting flows. Accuracy and speed of the proposed algorithms for nonlinear diffusion and vorticity generation are investigated separately. Simulations of natural convection of a “thermal patch” for Grashof number ranging from to 1562.5 to 25000 are presented.

Two-Dimensional Numerical Analysis of Gas Diffusion-Induced Cassie to Wenzel State Transition

2021 ◽  
Author(s):  
Michael D. Mayer ◽  
Jonah Kadoko ◽  
Marc Hodes
Keyword(s):  
State Transition ◽  
Concentration Field ◽  
Gas Diffusion ◽  
Ideal Gas ◽  
Two Dimensional ◽  
Structured Surfaces ◽  
Wenzel State ◽  
Transient Diffusion ◽  
Collocation Spectral Method ◽  
Quiescent Liquid

Abstract We develop a two-dimensional model for the transient diffusion of gas from the cavities in ridge-type structured surfaces to a quiescent liquid suspended above them in the Cassie state to predict the location of the liquid vapor-interface (meniscus) as a function of time. The transient diffusion equation is numerically solved by a Chebyshev collocation (spectral) method coupled to the Young-Laplace equation and the ideal gas law. We capture the effects of variable meniscus curvature and, subsequently, when applicable, movement of triple contact lines. Results are presented for the evolution of the dissolved gas concentration field in the liquid and, when applicable, the time it takes for a meniscus to depin and that for longevity, i.e., the onset of the Cassie to Wenzel state transition. Two configurations are examined; viz., one where an impermeable membrane pressurizes the liquid above the ridges and one where hydrostatic pressure is considered and the top of the liquid is exposed to non-condensable gas.

Estimates for critical Mach number under isoperimetric constraints

1995 ◽  
Vol 6 (5) ◽  
pp. 385-398 ◽  
Author(s):  
F. G. Avkhadiev ◽  
A. M. Elizarov ◽  
D. A. Fokin
Keyword(s):  
Mach Number ◽  
Subsonic Flow ◽  
Chaplygin Gas ◽  
Ideal Gas ◽  
Open Problems ◽  
Inverse Boundary ◽  
Critical Mach Number ◽  
Lindelöf Principle ◽  
Isoperimetric Constraints ◽  
Upper Estimate

The problem of maximization of the critical Mach number in a subsonic flow of an ideal gas is considered. The Chaplygin gas approximation and the integral representation of the solution of the inverse boundary-value problem of aerohydrodynamics are used to reduce the problem to a special minimax one. The exact solution of the latter is obtained on the basis of the Lindelöf principle. An upper estimate for the critical Mach number is obtained. The results are generalized for the case of airfoil cascades. Some open problems are described.

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