Notes on Thin Wing Theory at Low Supersonic Speeds

1959 ◽  
Vol 10 (3) ◽  
pp. 247-265
Author(s):  
G. J. Hancock
Keyword(s):  
Numerical Method ◽  
Linear Theory ◽  
Design Problem ◽  
Velocity Potential ◽  
Numerical Techniques ◽  
Integral Relationship ◽  
Thin Wing ◽  
Leading Edges

On the basis of the linearised theory, the integral relationship for the incidence distribution in terms of the velocity potential is established for wings with subsonic leading edges. Some analytical problems are analysed. A simple general numerical method is given for this design problem which compares favourably with exact linear theories. In Part II, to be published, a further numerical method is developed, for calculating the loading onanyspecified thin wing with subsonic leading edges, which again agrees favourably with exact linear theory. Both of these numerical techniques can be easily accommodated on desk calculating machines.

A Scheme for Numerical Representation of Graph Structures in Engineering Design

2013 ◽  
Vol 136 (1) ◽  
Author(s):  
David F. Wyatt ◽  
David C. Wynn ◽  
P. John Clarkson
Keyword(s):  
Engineering Design ◽  
Design Problem ◽  
Structure Design ◽  
Numerical Representation ◽  
Graph Structure ◽  
Numerical Techniques ◽  
Mathematical Properties ◽  
Conversion Algorithm ◽  
Graph Structures ◽  
Improve Access

Graph structures are fundamental in many aspects of design. This paper discusses a way to improve access to design spaces of graph structures, by converting graph structures into numerical values and vice versa. Mathematical properties of such conversions are described, and those that are desirable are identified. A candidate conversion algorithm, Indexed Stacked Blocks, is proposed. Its use and benefits are illustrated through an example graph-structure design problem. The example demonstrates that such conversions allow design spaces of graph structures to be visualized, sampled, and evaluated. In principle, they also allow other powerful numerical techniques to be applied to the design of graph-structure-based systems.

Errata: "Numerical Method for Hypersonic Internal Flow over Blunt Leading Edges and Two Blunt Bodies"

AIAA Journal ◽  
1973 ◽  
Vol 11 (2) ◽  
pp. 0256a-0256a
Author(s):  
NORBERT D'SOUZA ◽  
SANNU MOLDER ◽  
GINO MORETTI
Keyword(s):  
Numerical Method ◽  
Internal Flow ◽  
Blunt Bodies ◽  
Leading Edges

The Lift of Twisted and Cambered Wings in Supersonic Flow

1955 ◽  
Vol 6 (2) ◽  
pp. 149-163 ◽  
Author(s):  
G. N. Lance
Keyword(s):  
Integral Equation ◽  
Velocity Potential ◽  
Free Stream ◽  
Delta Wing ◽  
Complete Solution ◽  
Symmetric Potential ◽  
Leading Edges ◽  
Limiting Case ◽  
The Given ◽  
Stream Direction

SummaryA generalised conical flow theory is used to deduce an integral equation relating the velocity potential on a delta wing (with subsonic leading edges) to the given downwash distribution over the wing. The complete solution of this integral equation is derived. This complete solution is composed of two parts, one being symmetric and the other anti-symmetric with respect to the span wise co-ordinate; each part represents a velocity potential. For example, if y is the spanwise co-ordinate and x is measured in the free stream direction, then a downwash of the form w= - α11 Ux|y| is symmetric and will give rise to a symmetric potential, whereas w= - α11 Ux|y| sgn y is anti-symmetric and gives rise to an anti-symmetric potential. The velocity potentials of such flows are given in the form of Tables for all downwashes up to and including homogenous cubics in the spanwise and streamwise co-ordinates. Table III gives similar formulae in the limiting case when the leading edges become transonic; these are compared with results given elsewhere and serve as a check on the results of Tables I and II.

Early development of spherical blast from a particular charge

1955 ◽  
Vol 227 (1169) ◽  
pp. 258-270 ◽  
Keyword(s):  
Shock Wave ◽  
Numerical Method ◽  
Method Of Characteristics ◽  
Equations Of Motion ◽  
Rapid Decline ◽  
Spherical Shock Wave ◽  
Numerical Techniques ◽  
Complete Field ◽  
Observed Behaviour ◽  
Spherical Shock

The growth of spherical blast from a particular charge, the initial behaviour of which was analyzed in Berry & Holt (1954), is determined by numerical integration of equations of motion along characteristics. The complete field of disturbance and motion of boundaries are calculated during the early stages of development. It is found that, after a very brief outward movement, the second blast wave turns to move towards the centre of the explosion; this is in agreement with observed behaviour. The results, most of which are presented graphically, reveal a very rapid decline in pressure along both shocks, initially, and emphasize the dominating influence of the singularity at the origin of blast on the subsequent course of the disturbance. In the course of the work several new numerical techniques involved in the application of the method of characteristics are developed. Particular attention is drawn (§ 5) to the process of fitting a spherical shock wave between two non-uniform sectors of flow. The numerical method as a whole is quite general and, in later papers, application to spherical charges of other types will be described.

A Hybrid Numerical Method For Modeling Microwave Sintering Experiments

1996 ◽  
Vol 430 ◽  
Author(s):  
C. V. Hile ◽  
G. A. Kriegsmann
Keyword(s):  
Numerical Method ◽  
Electromagnetic Fields ◽  
Matrix Theory ◽  
Electromagnetic Interaction ◽  
Microwave Sintering ◽  
Single Mode ◽  
Numerical Techniques ◽  
Low Loss ◽  
Hybrid Numerical Method ◽  
Computer Resources

AbstractWe describe a hybrid numerical method for modeling the electromagnetic interaction of a low-loss material in a single-mode waveguide applicator. The method we propose utilizes a combination of asymptotic and numerical techniques. The interaction between the applicator and the electromagnetic fields is described using scattering matrix theory and the interaction between the electromagnetic fields and the ceramic is determined numerically. Several simulations are presented to show the accuracy and simplicity of this method along with the relatively small amount of computer resources it requires.

Numerical Method for Hypersonic Internal Flow over Blunt Leading Edges and Two Blunt Bodies

AIAA Journal ◽  
1972 ◽  
Vol 10 (5) ◽  
pp. 617-622 ◽  
Author(s):  
NORBERT D'SOUZA ◽  
SANNU MOLDER ◽  
GINO MORETTI
Keyword(s):  
Numerical Method ◽  
Internal Flow ◽  
Blunt Bodies ◽  
Leading Edges

ROTATIONAL TRANSFORMATION METHOD AND SOME NUMERICAL TECHNIQUES FOR COMPUTING MICROSTRUCTURES

1998 ◽  
Vol 08 (06) ◽  
pp. 985-1002 ◽  
Author(s):  
ZHIPING LI
Keyword(s):  
Numerical Method ◽  
Numerical Solutions ◽  
Boundary Effect ◽  
Transformation Method ◽  
Numerical Results ◽  
Numerical Techniques ◽  
Crystallization Method ◽  
Rotational Transformation

A rotational transformation method and an incremental crystallization method are developed to overcome some of the difficulties involved in the computation of microstructures. The numerical method based on these techniques has proved to be convergent. To increase further the accuracy of the computation, a technique is applied to remove the boundary effect of the numerical solutions. Numerical results for a double well problem are given to show the efficiency of the techniques.

scholarly journals A Numerical Procedure of Three-Dimensional Design Problem in Turbomachinery

1991 ◽  
Author(s):  
J. Z. Xu ◽  
C. W. Gu
Keyword(s):  
Mach Number ◽  
Boundary Conditions ◽  
Velocity Distribution ◽  
Numerical Method ◽  
Design Problem ◽  
Present Method ◽  
Three Dimensional ◽  
Numerical Procedure ◽  
Function Formulation ◽  
Mach Number Distribution

A numerical method for solving the three–dimensional aerothermodynamic design problem with some type of the Mach number distributions on the blade surfaces is presented. In the usual aerothermodynamic design of a turbomachinery the three–dimensional coordinates of the blade is attained through the stacking of the cascade profiles and may not ensure the desired velocity distribution. To avoid this problem the present method will give new coordinates of the blade according to the required Mach number distribution. The method is based on the pseudostream function formulation and the treatment of the boundary conditions in the design problem is given. The numerical results show that the method is simple and useful in design.

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