Is this project an undergraduate, graduate, or faculty project?

Undergraduate

Project Type

group

Campus

Daytona Beach

Authors' Class Standing

Sharjeel Malik, Freshman Justin Della

Lead Presenter's Name

Sharjeel Malik

Lead Presenter's College

DB College of Engineering

Faculty Mentor Name

Dr. Ronald Adams

Abstract

Combustion instability in liquid rocket engines is driven by coupling acoustic pressure oscillations and unsteady heat release. To achieve specific desired outcomes, small perturbations can be made to either decay or grow, depending on system dynamics and artificial parameters. Using a linearized eigenvalue framework, where eigenvalues determine growth/decay rates and frequencies, and eigenvectors describe spatial mode shapes and couplings between pressure, velocity, and heat release, a mathematical model can be derived to describe said behavior for a cross-section of the rocket engine. The Rayleigh criterion is used to identify conditions under which energy is added to oscillations, while flame transfer functions introduce time-delay effects that lead to Helmholtz-type eigenvalue problems. Based on the Rayleigh criterion, the thermal behavior is thus modeled separately using the heat equation with internal heat generation. The solution is then decomposed into steady-state and transient components, with the transient solved via separation of variables and eigenfunction expansions. The same method and boundaries are applied to the momentum section, where momentum equations are linearized alongside continuity to relate velocity and pressure perturbations, leading to a wave equation for acoustic pressure. Two variations in the models for rectangular and cylindrical coordinates were also explored to offer sine modes and Bessel modes, respectively, to be used in different sections of the engine depending on geometry. Overall, the approach shows that eigenvalues control stability and decay, while eigenfunctions define spatial patterns, providing a unique method for analyzing thermoacoustic instability and heat transfer in rocket engine components. The primary recommendation for the use of this method of finding acoustic pressure oscillations and unsteady heat release is to be used in combination with high computational models and simulations to verify specific sections of the engine that require more in-depth analysis for precise engineering.

Did this research project receive funding support (Spark, SURF, Research Abroad, Student Internal Grants, Collaborative, Climbing, or Ignite Grants) from the Office of Undergraduate Research?

No

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Modeling Seiche Oscillations using Damped Vibration Differential Equations

Combustion instability in liquid rocket engines is driven by coupling acoustic pressure oscillations and unsteady heat release. To achieve specific desired outcomes, small perturbations can be made to either decay or grow, depending on system dynamics and artificial parameters. Using a linearized eigenvalue framework, where eigenvalues determine growth/decay rates and frequencies, and eigenvectors describe spatial mode shapes and couplings between pressure, velocity, and heat release, a mathematical model can be derived to describe said behavior for a cross-section of the rocket engine. The Rayleigh criterion is used to identify conditions under which energy is added to oscillations, while flame transfer functions introduce time-delay effects that lead to Helmholtz-type eigenvalue problems. Based on the Rayleigh criterion, the thermal behavior is thus modeled separately using the heat equation with internal heat generation. The solution is then decomposed into steady-state and transient components, with the transient solved via separation of variables and eigenfunction expansions. The same method and boundaries are applied to the momentum section, where momentum equations are linearized alongside continuity to relate velocity and pressure perturbations, leading to a wave equation for acoustic pressure. Two variations in the models for rectangular and cylindrical coordinates were also explored to offer sine modes and Bessel modes, respectively, to be used in different sections of the engine depending on geometry. Overall, the approach shows that eigenvalues control stability and decay, while eigenfunctions define spatial patterns, providing a unique method for analyzing thermoacoustic instability and heat transfer in rocket engine components. The primary recommendation for the use of this method of finding acoustic pressure oscillations and unsteady heat release is to be used in combination with high computational models and simulations to verify specific sections of the engine that require more in-depth analysis for precise engineering.

 

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