Weakly nonlinear acoustic and shock-wave theory of the noise of advanced high-speed turbopropellers

Abstract

An acoustic and shock-wave theory of the noise generated by advanced turbo-propellers operating at supersonic tip helical velocity and high-subsonic cruise Mach number is developed. The theory includes the thickness and loading noise of the highly swept propeller blades. When operating at their design conditions these propellers radiate extremely intense sound waves. Because of the weakly nonlinear propagation effects these high-intensity acoustic disturbances steepen up quickly to form shock waves. In the present theory advantage is taken of the fact that in the blade fixed-rotating-coordinate system the acoustic and shock-wave fields are time independent. The problem is formulated in this coordinate system as a boundary-value problem. Weakly nonlinear propagation effects are incorporated into the solution following Whitham's nonlinearization procedure (Whitham 1974). The change in the disturbance-propagation velocity due to fluid-particle motion as well as the change in the speed of sound resulting from compression and rarefaction are all taken into account. It is found that the equal-area rule of Whitham's shock-fitting method is also applicable to the present problem. This method permits easy construction of the three-dimensional shock surfaces associated with the acoustic disturbances of these high-speed turbopropellers. Numerical results of the present theory are compared with the measurements of the JETSTAr flight experiment and the United Technology Research Center low-cruise Mach number open-wind-tunnel data. Very favourable overall agreements are found. The comparisons indicate clearly that, when these supersonic turbopropellers are operated at their high subsonic design-cruise Mach number, weakly nonlinear propagation effects must be included in the theory if an accurate prediction of the waveform of the sound wave incident on the design aircraft fuselage is to be obtained. This is especially true for noise radiated in the upstream or forward directions. In the forward directions the effective propagation velocity of the acoustic disturbances is greatly reduced by the convection velocity of the ambient flow. This allows more time for the cumulative nonlinear propagation effects to exert their influence, leading to severe distortion of the waveform and the formation of shock waves.

On Physical Aeroacoustics with Some Implications for Low-Noise Aircraft Design and Airport Operations

“…The first theory of aerodynamic noise applies equally [18][19][20][21][22][23] well to the to thickness (monopole), loading (dipole) and turbulence (quadrupole) noise of aircraft propellers [24][25][26][27][28][29][30][31][32][33][34][35][36][37][38][39][40] (Section 2.1.1), helicopter rotors [41][42][43][44][45][46][47][48][49][50][51][52][53][54][55] (Section 2.1.2) and turbomachinery [56][57][58][59][60][61] requiring that the aerodynamic problem be solved first to specify the sources. The blade-vortex interaction noise (BVI) involves sound radiation by noise sources convected in a non-uniform flow, that does not match so well the assumptions of the first theory of aerodynamic sound of an unbounded medium at rest or in uniform motion with static or moving sources.…”

Discretization errors inherent in finite difference solution of propeller noise problems

“…l~6 As has been discussed in some detail in Ref. 6, the thickness and loading on the blade can be modeled by adding appropriate nonhomogeneous terms on the right-hand side of Eq. (8).…”

Advanced turboprop noise prediction based on recent theoretical results

“…A recent paper of Tam and Salikuddin [18] has been brought to the attention of the authors by one of the referees. The referee believes that "Tam and Salikuddin use the same data as the present authors and provide solid explanation for the two effects mentioned on page 17 (of the original manuscript): reduction of the positive pressure peak and widening of the negative part of the pressure pulse".…”

“…As mentioned earlier, the broadening of the negative peak, which is seen also in Tam and Salikuddin's linear results, may be due to the differences in aerodynamic or perhaps geometric input data from those of the present paper. Unfortunately, no information about the input data or corrections to the data have been included in reference [18] to check the validity of this assertion. 6.…”

“…The complexity of these equations have come from the attempt to write each term of the final integrands in explicit forms for computer coding. It should be noted that a relation similar to equation (A8) exists for line sources, and which was utilized in coding [18]: …”