A note on transonic flow past a thin airfoil oscillating in a wind tunnel

At present no analytical model is available for predicting the unsteady aerodynamic forces acting on staggered cascade blades subjected to transonic flow. The unsteady aerodynamic models for cascades developed so far are useful in the Mach number range of 0.0-0.9 and 1.1 and above. The objective of the present analysis is to develop an efficient model for obtaining unsteady aerodynamic forces in the neighborhood of Mach number = 1.0. An incremental annulus of blade row is represented by a rectilinear two-dimensional cascade of thin flat plate airfoils. The steady flow approaching the cascade is assumed to be transonic, irrotational, and inviscid. The equations of motion are derived using linearized transonic small perturbation theory. An analytical solution is obtained by using the Wiener-Hopf procedure. Unsteady aerodynamic forces and moments acting on the blades are obtained for Mach number = 1.0. Making use of transonic similarity law, the results of the present analysis are compared with the results obtained from other linearized cascade analyses. A parametric study is conducted to find the effects of reduced frequency, stagger angle, solidity, and location of pitching axis on cascade stability. Nomenclature a n = constant, Eq. (29) A',B' -constant, Eq. (A10) A 0 = amplitude of angular displacement A!, B j = constants b = blade semichord C' (CL),C_ (a) -functions, Eq. (43) d Q -distance between leading edge of blade and reference point G + ,G_ -functions, Eq. (A7) G+,G + -functions, Eq. (42) h Q ,h m -functions, Eq. (18) h±,h -functions, Eq. (38) and (39) H Q = amplitude of vertical displacement H + (a) -function, Eq. (Al) / -V -l Im -imaginary part k -reduced frequency k { -V2/A: k 2 =k/2 K(oi,rj) -function, Eq. (23) K + (a),K_ (a) -functions, Eq. (A5) L m,n M M, P Qn S s + ss gn t = nondimensional lift = summation indices = nondimensional moment = local Mach number = pressure = pressure for nonsummation and summation terms, Eq. (36) = function, Eq. (36) = distance between adjacent blades = signum function = timê functions, Eqs. (28-33) = freestream velocity

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“…(4) by means of the following Fourier transform yields The solution to Eq. (13) is given by (14) where k { = V2/fc and k 2 = k/2.…”

Section: Upstream Solutionmentioning

confidence: 99%

“…By comparison, the progress on the development of such methods for transonic flow has been slow. Savkar 14 examined the problem of a thin airfoil oscillating in a transonic stream in a wind tunnel. This problem represents a zero staggered cascade whose members oscillate 180 deg out of phase with each other.…”

mentioning

confidence: 99%

Unsteady transonic flow over cascade blades

Surampudi

Adamczyk

1986

AIAA Journal

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A note on transonic flow past a thin airfoil oscillating in a wind tunnel

Cited by 1 publication

References 5 publications

Unsteady transonic flow over cascade blades

Unsteady transonic flow over cascade blades

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