This paper analyzes the dynamics of unstable azimuthal thermoacoustic modes in a lean premixed combustor. Azimuthal modes can be decomposed into two counter rotating waves where they can either compete and potentially suppress one of them (spinning) or coexist (standing), depending on the operating conditions. This paper describes experimental results of the dynamical behaviors of these two waves. The experimental data were taken at different mass flow rates as well as different azimuthal fuel staging in a multi-nozzle can combustor. It is shown that at a low flow rate with uniform fuel distribution, the two waves have similar amplitudes, giving rise to a standing wave. However, the two amplitudes are slowly oscillating out of phase to each other, and the phase difference between the two waves also shows oscillatory behavior. For an intermediate flow rate, the dynamics show intermittency between standing and spinning waves, indicating that the system is bistable. In addition, the phase difference dramatically shifts when the mode switches between standing and spinning waves. For a high flow rate, the system stabilizes at a spinning wave most of the time. These experimental observations demonstrate that not only the amplitudes of two waves but also the phase difference plays an important role in the dynamics of azimuthal mode. For non-uniform azimuthal fuel staging, the modal dynamics exhibit only an oscillatory standing wave behavior regardless of the mass flow rate. Compared to the uniform fuel staging, however, the pressure magnitude is considerably reduced, which provides a potential strategy to mitigate and/or suppress the instabilities.

High frequency thermoacoustic instabilities are problematic for lean-premixed gas turbines. Identifying which acoustic mode is being excited is important, in that it provides insight into potential mitigation measures and mechanical stress/life. However, the frequency spacing between modes becomes quite close for high frequency instabilities in a can combustor. This makes it difficult to distinguish between the modes (e.g., the first transverse mode vs. a higher order axial/mixed mode) based upon frequency calculations alone, which inevitably have uncertainties in boundary conditions, temperature profiles, and combustion response. This paper presents a methodology to simultaneously identify the acoustic mode shapes in the axial and azimuthal directions from acoustic pressure measurements. Multiple high temperature pressure transducers, located at distinct axial and azimuthal positions, are flush mounted in the combustor wall. The measured pressure oscillations from each sensor are then used to reconstruct the pressure distributions by using a least squares method in conjunction with a solution of a three dimensional wave equation. In order to validate the methodology, finite element method (FEM) calculations with estimated post-flame temperature is used to provide the candidate frequencies and corresponding mode shapes. The results demonstrate the reconstructed mode shapes and standing/spinning character of transverse waves, as well as the associated frequencies, both of which are consistent with the FEM predictions. Nodal line location was also extracted from the experimental data during the instabilities in the pressure data.

High frequency thermoacoustic instabilities are becoming increasingly problematic in modern combustion systems. Understanding which acoustic mode is being excited is important for understanding potential mechanisms and control approaches — for example, influence of a helical shear layer mode on the flame has profoundly different effects on the first tangential acoustic mode, than a higher order axial mode of similar frequency. Nonetheless, the modal density increases with frequency and it becomes increasingly difficult to determine which acoustic mode is self-excited, based upon frequency calculations alone. Moreover, access issues and cost usually limit the number of pressure probes that can be distributed axially and azimuthally in the combustor. This paper presents a methodology for identifying the acoustic mode by using high temperature pressure transducers flush mounted in a combustion chamber. Modal identification is demonstrated with a siren under non-reacting conditions. The siren is mounted on the chamber to excite longitudinal and azimuthal waves. Five acoustic sensors at different axial and azimuthal locations measure the pressure fluctuations simultaneously. Given the forcing frequency and the speed of sound, the pressure distribution in the combustor is reconstructed in the time domain from the measured data by using a least squares method to determine its mode shapes. In addition, the finite element method (FEM) solver is used to provide the eigenfrequencies and corresponding mode shapes. The test results demonstrate that the mode shapes from the reconstructed data and corresponding frequencies are consistent with those predicted from the FEM, which validates the methodology in this study. In addition, the methodology is extended to practical reacting cases without the siren to determine the acoustic mode shapes of naturally occurring instabilities. In these cases, the modal features have strong stochastic features, such as what appear to be stochastic variations in overall amplitude and relative amplitudes of clockwise and counterclockwise waves.

In large assemblies, the perpendicularity of a bolting hole has remarkable effects on the fatigue life and fluid dynamic configuration. While the Computer Aided Design (CAD) model of complexly curved workpieces is hardly satisfied because of manufacturing errors, it is very necessary to measure the normal direction in robotic drilling. One advisable approach is to arrange four laser displacement sensors at the vertices of a rhombus whose center aims at the drilling position. The influencing factors of the measurement precision are firstly discussed in this study, and a novel method to optimize the arrangement size of the displacement sensors for higher precision is introduced. The measurement error for the normal direction consists of the principle error and instrumental error, caused by inconstant curvature of the surfaces and distance measuring errors of instruments, respectively. When the displacement sensors are arranged closer to each other, the principle error will be decreased, whereas the instrumental error will be increased. After the curvature feature of the surface is obtained with the introduced method, the graph of the measurement precision and the arrangement size is plotted. Then, the graph can contribute to developing an optimized design of arrangement size for higher precision. Finally, an example of the curvature obtainment and the arrangement optimization is given. The experimental results show that the optimized design has achieved a higher precision of ± 0.17° for α Y and ± 0.26° for α X , whereas the precision of another design is about ± 0.21° for α Y and ± 0.29° for α X . The proposed optimization method will bring greater benefit for complexly curved surfaces in practical products and it offers a chance to optimize the arrangement during design phase with little costs.

A series of experimental investigations were conducted to visually observe the fundamental features of boiling nucleation of water in micro capillary tubes covered with transparent metal film and ethanol in mini tubes winded with a heating wire as a heater. Normally, boiling nucleation and/or bubble generation were not observed even at very high heat fluxes compared with usual nucleate boiling situations. In mini tubes violent jet flows formed and played an important role of triggering the emission, while in micro tubes the liquid and/or vapor was instantaneously emitted as the applied heat flux reached a certain high value, rather than initialing nucleate boiling and jet flows which was much weaker than exploding emission. After the exploding emission, an ultra thin liquid film formed on the tube wall and evaporated intensely, causing a perceptible wall temperature drop.

A series of experiments was conducted to visually observe the fundamental features of the scale effect on boiling nucleation in mini/micro tubes. Boiling nucleation and/or bubble generation was observed in mini tubes of 1.5 to 2.5 mm and micro tubes of 50 to 200 μm in inner diameter. As heat flux was increased, bubbles were normally observed generating and growing inside the tubes of 2.5 mm. As tube diameter decreased from 1.5 to 0.05 mm, or in mini and micro tubes, the liquid was emitted instantaneously rather than generating bubbles and bubble growth, which is referred as liquid exploding emission in this paper. In mini tubes of D i = 1.5 mm, violent jet flows with macro bubbles were formed, and the liquid was almost totally emitted out of the tube. While in micro tubes of D i = 50–200 μm, the emission was much stronger, and only fog-like jet flow was observed consisted of extremely tiny bubbles, which indicates the mechanism of nucleation is different from that in mini tubes. It is expected that the scale effects intensely influence on not only the onset of emission, but also the strength and nature of emissions.

There are many nonlinear factors in the optimization process. The objective of this study is to determine some effects of these nonlinear factors on the sensitivity of optimum design. A rotor-bearing system is composed of rigid disks, shaft elements with distributed mass and stiffness, and magnetic bearings. To obtain an optimum design, the objectives including shaft weight and amplitude of shaft lateral response as well as the constraints including critical speeds and bending stresses are considered. The inner radii of shaft elements, the bias currents of magnetic bearings, and the axial positions of bearings and disks are chosen as the design variables. The single objective method, the multi-objective method and the multilevel technique are employed to deal with the problem of optimality. Optimum results obtained by applying these methods are compared and discussed in this study. Finally, the sensitivity of optimum design is analyzed to determine what nonlinear effects the position of magnetic bearings have on different initial designs.

This paper investigates thermo-mechanical deformation and stresses of a flip-chip package (FCBGA) with and without underfill materials. Chip carrier is a 2-2-2 build-up substrate with 40 × 40 mm 2 dimension; while bump material employs Sn/37Pb eutectic solder. Temperature-dependent warpage (out-of-plane displacement) of a FCBGA is characterized via shadow moire´ technique. Results of warpage measurement reveal that packages do not follow the same path during thermal loading/unloading cycle (20-220-20 °C) for both FCBGA with and without underfills. This implies that both solder and underfill exhibit inelastic material response. Therefore, it is a necessity to consider nonlinear constitutive response of packaging materials when designing flip-chip packages. It is observed that FCBGA with underfill exhibit more warpage than packages without underfill due to higher CTE mismatch between underfills and silicon dies. Aspect of package geometry such as die-to-substrate thickness ratio is found to play important role in reducing package stresses. Especially, thinner die provides more direct impact to die stresses reduction than thinner substrate does.