A well posed boundary value problem in transonic gas dynamics

Sanz, Joséa M.

doi:10.1002/cpa.3160310604

Cited by 4 publications

(2 citation statements)

References 10 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…The coefficients of this linear comwination are then determined by imposing the boundary condition (14). This boundary value problem has been proved to be well posed when the system (1) is reduced to Tricomi equation, [4], that is, in the case of the transonic small disturbance equation, In the general case of the full potential equation that we are dealing with here, a low condition number for the matrix associated with the linear system In question, both when the domain 0 is a circle or an ellipse, indicates the well posedness of the problem.…”

Section: Numter Ical Solutionmentioning

confidence: 99%

Design of Supercritical Cascades with High Solidity

Sanz

1983

AIAA Journal

View full text Add to dashboard Cite

The method of complex characteristics of Garabedian and Korn has been successfully used to design shockless cascades with solidities of up to one. A new code has been developed using this method and a new hodograph transformation of the flow onto an ellipse, This new code allows the design of cascades with solidities of u p to two and larger turning angles, The equations of potential flow are solved in a complex hodographlike domain by setting a characteristic initial value problem and integrating along suitable paths. The topology that the new mapping introduces permits a simpler construction of these paths of integration.

show abstract

Section: Numter Ical Solutionmentioning

confidence: 99%

Design of Supercritical Cascades with High Solidity

Sanz

1983

AIAA Journal

View full text Add to dashboard Cite

show abstract

“…The method of complex characteristics for solving the inverse problem in the case of supercritical flows is quite efficient and mathematically elegant (Bauer et al [2], Garabedian and Korn [11], Garabedian [10], Garabedian and McFadden [12], Sanz [27]). In their method the boundary is unknown and they iterate on the boundary to generate the airfoil.…”

mentioning

confidence: 99%

An exact inverse method for subsonic flows

Daripa¹

1988

Quart. Appl. Math.

View full text Add to dashboard Cite

Abstract. A new inverse method for aerodynamic design of airfoils is presented for subcritical flows. The pressure distribution in this method can be prescribed in a natural way, i.e., as a function of arclength of the as yet unknown body. This inverse problem is shown to be mathematically equivalent to solving only one nonlinear boundary value problem subject to known Dirichlet data on the boundary. The solution to this nonlinear problem determines the airfoil, free stream Mach number Moo and the upstream flow direction 6^. The existence of a solution to a given pressure distribution is discussed. The method is easy to implement and extremely efficient. We present a series of results for which comparisons are made with the known airfoils. This method will be extended to design supercritical airfoils in the future.1. Introduction. The inverse problem in the context of aerodynamics is the determination of an airfoil that will generate a given pressure distribution. This problem has been considered important for decades because many desirable features of the flowfield, such as delay of separation and laminar-turbulent transition, can be achieved by proper prescription of the pressure distribution along the surface of the as yet unknown body (Stratford [33,34,35]). The point of separation of zero skin friction is related to the specified pressure distribution (see Stratford [33,34] and references therein) and a flow with zero skin friction throughout its region of pressure rise is expected to achieve any specified pressure rise in the shortest possible distance with least possible energy loss (Stratford [35]). In aerodynamics these flow features are highly desirable and can be realized in practice since a suitable pressure distribution can be specified to avoid the undesirable flow features and an airfoil can be generated that will have this pressure distribution along its body. This paper addresses this problem of generating an airfoil from a given pressure distribution and proposes a new and extremely efficient method of solution to this problem.

show abstract

Computational Fluid Dynamics of Airfoils and Wings

Garabedian

McFadden

1982

Transonic, Shock, and Multidimensional Flows

View full text Add to dashboard Cite

A well posed boundary value problem in transonic gas dynamics

Cited by 4 publications

References 10 publications

Design of Supercritical Cascades with High Solidity

Design of Supercritical Cascades with High Solidity

An exact inverse method for subsonic flows

Computational Fluid Dynamics of Airfoils and Wings

Contact Info

Product

Resources

About