Ph.D. Proposal
Robert “Casey” Wilson
(Advisor: Prof. Dimitri N. Mavris)
"Improvements to Liquid Rocket Engine Structural Assessment Under Uncertainty"
Monday, December 9
10:00 a.m.
Abstract
Liquid rocket engines are the work horses of the space launch industry. Most launch vehicles utilize liquid engines for both first stage and upper stage propulsion. The prolific use of these systems is attributed to their performance, operability, and reusability. A notable downside is their high complexity – many engines utilize complex combustion devices and turbomachinery to drive the engine cycle. Due to the mass constraints of launch vehicles, engine structures must be designed for minimal excess margin. Because of the steep consequence of failure, structures must also be highly reliable. Among the most challenging sub-systems for structural design is the hot section. Hot sections are located downstream of combustors and operate at extreme temperatures and pressures to maximize performance. Structural design and assessment of hot sections requires solving complex thermomechanical problems; challenges include: 1. Nonlinearity of design space 2. Complex geometry, loads, and materials and 3. Uncertainties associated with inputs.
Numerical methods such as Finite Element Analysis (FEA) are commonly used to address nonlinearities and system complexities. These simulations can be computationally expensive, requiring intensive resources. Uncertainty in structural assessment is addressed either deterministically or probabilistically. The most popular techniques are deterministic Factor of Safety (FoS) methods. FoS methods treat stochastic inputs deterministically and apply a fixed factor to outputs to account for uncertainty. Downsides of FoS methods are their subjective nature, need for subject matter expert (SME) opinion, inability to quantitatively predict reliability, and poor adaptation to changes in epistemic uncertainty. Instead, probabilistic methods are attractive as they require fewer SME decisions, allow for a reliability prediction, and are well suited to handle changes to input uncertainties. A key barrier to adoption of probabilistic methods, such as Monte Carlo or Fast Probability Integration, is their high cost due to large numbers of required simulations. To address the barrier, methods are proposed that reduce the computational costs associated with the simulation, the uncertainty quantification (UQ) framework, or both.
Surrogate modeling can be used to replace the FEA simulation with a low-expense approximation. To capture variability of the thermomechanical domain, field surrogate techniques such as Reduced Order Models (ROMs) are proposed as they allow for spatially and temporally varying outputs. ROMs can be constructed via Proper Orthogonal Decomposition where dominant field attributes are reduced to characteristic modes. By regressing training data to determine modal weights, linear back-mapping can be used generate an approximation of the FEA output field.
Recent advancements in uncertainty propagation (UP) methods are explored to reduce the number of required simulations. Stochastic Collocation Method (SCM) is a Stochastic Spectral technique for UP that has been demonstrated to be several orders of magnitude faster than Monte Carlo. SCM utilizes collocation points to regress interpolating Askey polynomials to approximate the stochastic output space.
This research will propose improvements to the structural assessment of liquid rocket engines where input uncertainty can be quantified, but propagation is challenging due to computational costs. Experiments utilizing a relevant thermomechanical problem (2D thrust chamber cooling channels) will compare methods for surrogate generation and uncertainty propagation and will ultimately support research Hypotheses. A demonstration of a high-fidelity canonical representation (3D turbine blade) will be conducted to prove scalability and address a research gap. Contributions from this research include an improved probabilistic scheme for the assessment of liquid rocket engines, an additional example of uncertainty-based design, and key insights into the deficiencies of widely used FoS methods.
Committee
- Prof. Dimitri Mavris – School of Aerospace Engineering (advisor)
- Prof. Graeme Kennedy – School of Aerospace Engineering
- Prof. Kai James – School of Aerospace Engineering
- Dr. Adam Cox – School of Aerospace Engineering
- Mr. Andres Garcia-Clark – Arbor Energy
- Dr. David Stechmann – SpaceX