New Method for Obtaining Emission Coefficients from Emitted Spectral Intensities Part II—Asymmetrical Sources*

Application of Holographic Interferometry to Density Field Determination in Transonic Corner Flow

“…The integral inversion procedure utilized in this investigation was first reported by C. D. Maldonado, et al [5,6]. It was used subsequently by R. D. Matulka [3] and R. C. Jagota [7] to determine the density variation in an asymmetric free jet and about a cone at angle of attack in supersonic flow, respectively.…”

“…It was used subsequently by R. D. Matulka [3] and R. C. Jagota [7] to determine the density variation in an asymmetric free jet and about a cone at angle of attack in supersonic flow, respectively. The procedure involves the representation of the function f (x, y, z ) of Equation (6) in a complete set of orthogonal functions, with the expansion coefficients evaluated by use of the orthogonality condition between the functions f and g of Equation (6). The set of functions used is orthogonal over the entire (x, y) plane for every z and remains an orthoc gonal set under a rotation of the coordinate system.…”

“…In operator form, Equation (6) can be represented as g( I >y'» z c ) = TTf(x, y ,z c ) (9) and f is evaluated by inversely transforming the equation to obtain f(x,y,z c ) =T~g ( § .y'.z c ) (10) This inversion is achieved by utilizing a pair of orthogonal polynomials …”

“…In the determination of the density field around a free jet in the supersonic regime, Matulka [3,4] expressed the fringe data in a series of orthogonal polynomials and transformed them to polynomials representing density using an inversion technique reported in [5,6]. The method was extended by Jagota [7,8] to the determination of the threedimensional density field around a ten-degree half angle cone in a supersonic wind tunnel.…”

“…Utilizing the transform relation of Equation (11), Equation (6) -^v'Z OU-y (13) Equation (13) is subject to the orthogonality condition -TT -CD >/? oL mtlknn+Z.t (14) where <S is the Kronecker delta function.…”