Acoustic Transfer Functions Derived from Finite Element Modeling for Thermoacoustic Stability Predictions of Gas Turbine Engines Design and prediction of thermoacoustic instabilities is a major challenge in aerospace propulsion and the operation of power generating gas turbine engines. This is a complex problem in which multiple physical systems couple together. Traditionally, thermoacoustic models can be reduced to dominant physics which depend only on flame dynamics and acoustics. This is the general approach adopted in this research. The primary objective of this thesis is to describe how to obtain acoustic transfer functions using finite element modeling. These acoustic transfer functions can be coupled with flame transfer functions and other dynamics to predict the thermoacoustic stability of gas turbine engines. Results of this research effort can go beyond the prediction of instability and potentially can be used as a tool in the design stage. Consequently, through the use of these modeling tools, better gas turbine engine designs can be developed, enabling expanded operating conditions and efficiencies. This thesis presents the finite element (FE) methodology used to develop the acoustic transfer functions of the Combustion System Dynamics Laboratory (CSDL) gaseous combustor to support modeling and prediction of thermoacoustic instabilities. In this research, several different areas of the acoustic modeling were addressed to develop a representative acoustics model of the hot CSDL gaseous combustor. The first area was the development and validation of the cold acoustic finite element model. A large part of this development entailed finding simple but accurate means for representing complex geometries and boundary conditions. The cold-acoustic model of the laboratory combustor was refined and validated with the experimental data taken on the combustion rig. The second stage of the research involved incorporating the flame into the FE model and has been referred to in this thesis as hot-acoustic modeling. The hot-acoustic model also required the investigation and characterization of the flame as an acoustic source. The detailed mathematical development for the full reacting acoustic wave equation was investigated and simplified sufficiently to identify the appropriate source term for the flame. It was determined that the flame could be represented in the finite element formulation as a volumetric acceleration, provided that the flame region is small compared to acoustic wavelengths. For premixed gas turbine combustor flames, this approximation of a small flame region is generally a reasonable assumption. Both the high temperature effects and the flame as an acoustic source were implemented to obtain a final hot-acoustic FE model. This model was compared to experimental data where the heat release of the flame was measured along with the acoustic quantities of pressure and velocity. Using these measurements, the hot-acoustic FE model was validated and found to correlate with the experimental data very well. The thesis concludes with a discussion of how these techniques can be utilized in large industrial-size combustors. Insights into stability are also discussed. A conclusion is then presented with the key results from this research and some suggestions for future work. / Master of Science

Yes / An integrated Finite Element Method (FEM) model is proposed to investigate the dynamic seabed response for several specific pipeline layouts and to simulate the pipeline stability under waves loading. In the present model, the Reynolds-Averaged Navier-Stokes (RANS) equations are used to describe the wave motion in a fluid domain, while the seabed domain is described using the Biot’s poro-elastic theory. The interface between water and air is tracked by conservative Level Set method (LSM). The FEM and backward differentiation formula (BDF) are applied for spatial and temporal discretization respectively in the present model. One-way coupling is used to integrate flow and seabed models. The present model is firstly validated using several available laboratory experiments. It is then further extended to practical engineering applications, including the dynamic seabed response for the pipeline mounted on a flat seabed or inside a trench. The results show that the pipeline buried to a certain depth is better protected than that under partially buried in terms of transient liquefaction. / Energy Technology Partnership (ETP), Wood Group Kenny

Yes / This is a study of the modelling and prediction of strain recovery in a polylactide. Strain recovery near the glass transition temperature is the underlying mechanism for the shape memory in an amorphous polymer. The investigation is aimed at modelling such shape memory behaviour. A PLA-based copolymer is subjected to stress–strain, stress relaxation and strain recovery experiments at large strain at 60 C just below its glass transition temperature. The material is 13% crystalline. Using published data on the mechanical properties of the crystals, finite element modelling was used to determine the effect of the crystal phase on the overall mechanical behaviour of the material, which was found to be significant. The finite element models were also used to relate the stress–strain results to the yield stress of the amorphous phase. This yield stress was found to possess strain rate dependence consistent with an Eyring process. Stress relaxation experiments were also interpreted in terms of the Eyring process, and a two-process Eyring-based model was defined that was capable of modelling strain recovery behaviour. This was essentially a model of the amorphous phase. It was shown to be capable of useful predictions of strain recovery. / Funded by the Engineering and Physical Sciences Research Council, grant number EP/L020572/1

Yes / This is a study of the modelling and prediction of strain recovery in a polylactide. Strain recovery near the glass transition temperature is the underlying mechanism for the shape memory in an amorphous polymer. The investigation is aimed at modelling such shape memory behaviour. A PLA-based copolymer is subjected to stress-strain, stress relaxation and strain recovery experiments at large strain at 60 °C just below its glass transition temperature. The material is 13% crystalline. Using published data on the mechanical properties of the crystals, finite element modelling was used to determine the effect of the crystal phase on the overall mechanical behaviour of the material, which was found to be significant. The finite element models were also used to relate the stress-strain results to the yield stress of the amorphous phase. This yield stress was found to possess strain rate dependence consistent with an Eyring process. Stress relaxation experiments were also interpreted in terms of the Eyring process, and a two-process Eyring-based model was defined that was capable of modelling strain recovery behaviour. This was essentially a model of the amorphous phase. It was shown to be capable of useful predictions of strain recovery. / Engineering and Physical Sciences Research Council, grant number EP/L020572/1. / . Not submitted within 3 months from acceptance or publication but is a Gold paper.

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The finite element method in the form of the weak Galerkin formulation with the penalty function method was applied to several problems of axisymmetric turbulent flows including flow through a sudden pipe expansion, the stern region flow of a slender body, and flows past ducted and nonducted propellers in action. The coupled set of the Reynolds time-averaged Navier-Stokes equations and two turbulence transport equations for the turbulent kinetic energy and its rate of dissipation was solved by L/U decomposition and successive substitution with relaxation. An existing finite element code was modified with a low Reynolds number form for an appropriate treatment of wall influences on turbulence transport, which produces a better solution and provides an easier imposition of boundary conditions by solving up to wall with no slip boundary conditions. The two-equation turbulence model with the wall modification was first successfully tested by solving the turbulent flow through a sudden pipe expansion. The numerical simulation of the stern region flow of a streamlined body resulted in an excellent agreement with the measured data in terms of the mean-flow and turbulence quantities. Turbulent shear flows past a propeller at the rear end of the same slender body, modeled by an actuator disk, were successfully solved at two rotational speeds, self-propelled and 100% over-thrusted, using the same two-equation model. And finally, comparisons of the wake behind a propeller were made for the self-propelled conditions of a ducted and nonducted propeller on the same streamlined body. / Ph. D.