Date of Award


Degree Type


Degree Name

Master of Science in Mechanical Engineering (MSME)


Mechanical Engineering

Committee Chair

Douglas E. Adams

Committee Co-Chair

Farshid Sadeghi

Committee Member 1

Jeff Rhoads


Combustion instability has plagued the rocket industry since its beginnings. It is characterized by sustained pressure oscillations in the combustion chamber due to the coupling of natural pressure fluctuations with unsteady heat release. Typically, combustion instabilities are identified and mitigated during ground testing. Occasionally combustion instabilities do not present themselves until after a system is fielded and may only occur in a flight environment. While ground tests are heavily instrumented, operational flight data may not contain any direct measurement of the combustion forcing function. Post-event efforts to characterize anomalous combustion instabilities with existing instrumentation have had little success.

Accelerometers, which are native to a rocket's guidance system and payload monitoring, capture spectral signatures of shock and vibration flight events including combustion instability. The relationship between forced response and the pressure forcing function can be understood through modal analysis. Recent advances in operational modal analysis (OMA) have allowed the modal parameters of launch vehicles to be tracked through typical flight events such as launch and stage separation. In this thesis, the reaches of OMA were extended to unstable combustion.

High frequency pressure and structural response data were obtained using the continuously variable resonance combustor (CVRC) at Purdue University. The CVRC is a single element liquid rocket engine with the unique ability to tune the length of the oxidizer post for different stability conditions. Although the CVRC is a fixed test article, changing internal pressures and wall temperatures caused non-stationary structural dynamics throughout the test sequence which presented similar challenges to actual flight data.

Investigation of the high frequency pressure measurements revealed that the combustion forcing function violates standard OMA assumptions. State of the art OMA techniques that relax standard force assumptions and allow for harmonic excitations were investigated. An algorithm was developed to automatically estimate the non- stationary modal parameters throughout the test sequence with a sliding time window. A modified least squares complex exponential method was used to estimate modal parameters in the presence of harmonic excitation. Structural modes and harmonic forcing were successfully tracked throughout the test sequence.

The combustion forcing function was characterized by frequency and acoustic mode shape. The forcing frequencies were identified by interpreting the spectral kurtosis and singular value decomposition of structural responses. A linear acoustic model was developed to characterize the distribution of the combustion forcing function by the chamber acoustic modes. The estimated forcing frequencies had a maximum error of 1.2%. Predicted and measured acoustic mode-shapes showed excellent agreement with modal assurance criterion values ranging from 0.7 to 1.0.