Comparison of Analytical and CAA Solution(s): Unsteady Response of a Rectilinear Swept Cascade to an Incident Gust

This problem is aimed at testing the ability of computational aeroacoustic methods to calculate the acoustic pressure field generated as a result of the interaction of a convected harmonic gust with a rectilinear cascade of swept flat plates. All relevant geometric information is the same as the unsteady response of an isolated finite span swept airfoil to an incident gust problem with the exception of the sweep angle alpha, which is now taken to be a variable. Assume a cascade stagger angle of zero (with the x-axis aligned with the chord) and a gap-to-chord ratio of h/c = 1. The mean flow Mach number M(sub 0), gust frequency omega, gust amplitude A, and chordwise wavenumber k(sub x) are the same. But for the cascade problem take k(sub y) = pi and k(sub z) = 0. The appropriate physical scales are also the same, as is the governing equation and boundary conditions. Naturally, the impermeability condition now applies to the entire cascade. For this problem, determine the amplitude of upstream-radiated rms acoustic pressure as a function of the sweep angle at the specified frequency. Specifically, show the variations of rms acoustic pressure amplitude at the upstream location (-5c, 0, l/2) for sweep angle alpha in the range (0.0 deg, 30.0 deg). Use sweep angle increments no larger than 2.5 deg. Express the results in dB using the rms pressure value for alpha = 0.0 deg as the reference level. The appropriate FORTRAN output statement should read "WRITE(IUNIT,*) alpha, 20-log10 (p(sub rms)(alpha)/p(sub rms)(0))".