Date of Award

Winter 2004

Document Type


Degree Name

Doctor of Philosophy (PhD)


Aerospace Engineering

Committee Director

Oktay Baysal

Committee Member

Ponnampalam Balakumar

Committee Member

Osama Kandil

Committee Member

Fang Hu


Screech noise exists only in imperfectly expanded jets. The exit pressure of imperfectly expanded jets does not match ambient pressure, so expansion or compression waves appear out of the nozzle and generate shock cell patterns. Screech is generated by the interaction of shock cells and instability waves. Many experiments and computations have been done to model screech noise, but it is not yet a very well known subject.

A numerical study is performed to understand screech generation mechanisms and to compare with latest experiments. A supersonic underexpanded jet of 25.4 mm diameter is modeled for cases of Mach numbers of 1.19 and 1.43 in axisymmetric two-dimensions. Then the computation is extended to three-dimensions, and Mach numbers of 1.43 again and 1.80 are solved. Full Navier-Stokes equations are solved in cylindrical coordinates, and large eddy simulation (LES) turbulence modeling is added for axisymmetric cases. For spatial discretizations, fifth order Weighted Essentially Non Oscillatory (WENO) scheme is used because it is a suitable method for capturing shocks. Time discretization is third order time total variation diminishing (TVD) scheme, which is accurate enough, and needs considerably lower storage than fourth order schemes. These methods do not require any artificial viscosity or tune up parameters.

The experimental results have predicted that the solution is in axisymmetric mode for Mach 1.19 and in helical (three-dimensional) mode for 1.43. However, our solution for Mach 1.43 has produced satisfactory results. Frequency analysis has been done by taking fast Fourier transforms of pressure history data. The experimental screech frequencies of 8400 Hz for Mach 1.19 and 5400 Hz for Mach 1.43 have been verified with computational results. Computed shock cell structure is in agreement with experiments and other computations in all cases. The screech waves emerge from the second and third shock cells, like in the experiments. The screech wavelength can be roughly estimated as 1.5 D, which is close to other computational studies. In Mach 1.80 case, barrel shock concept is observed as in the experiments. Three dimensional effects are investigated by creating an animation of planes of varying azimuth angles.

This study has been a good verification of existing experimental results. It has also made a contribution, since it is a method to calculate screech frequencies without artificial damping or other tune-up parameters. Also, the visual data obtained by the animations has been useful to see shock generation locations.