Session B5: Thermal Phenomena

Computational Modeling of Radiative Cooling Coupled with Thermoconductivity Using Maple Software: Challenges and Results

Maple is a versatile software package which can go as far as solving partial differential equations (PDEs). Many astrophysical problems (as well as many engineering situations) require coupling of thermoconductivity equation with radiative cooling/heating. Using Maple software for such problems results in serious challenge due to the fact that it requires non-linear boundary condition (black body radiation). Turns out that Maple cannot solve linear PDE with non linear boundary condition. However, Maple can solve some non-linear PDEs with non-linear boundary conditions (!). So if to slightly modify thermoconductivity equation by adding some non-linear terms, then Maple accepts non-linear boundary conditions for it too. Decreasing non-linear terms to insignificant values (for the particular problem in hand) allows accurate modeling of radiative cooling/hating, and thus adapting Maple for wide class of problems. As a few examples, we model radiative cooling of a chunk of molten silicate debris in vacuum (as a result of asteroid collision), the dynamics of radiative cooling and heating of lunar soil during lunar nights and days, daily and yearly variations of Earth soil temperature, radiative cooling of a planet, and cooling of a neutron star. The model we used and the computational results are discussed in the presentation.   

Optimum Cavity Radius Within a Bottle-Shaped Thermoacoustic Engine

Heat energy can be used to generate acoustic energy due to thermoacoustic interactions. These engines can be used to create sound waves without any moving parts, like pistons, and could be used in space to convert solar energy into electricity. This research focused on the optimization of the geometry of bottle-shaped resonators used for thermoacoustic prime movers. These resonators have the advantage of non-harmonic overtones compared with half-wave resonators. The resonators for this research were constructed of concentric cylinders consisting of a neck piece and a cavity. The dimensions were approximately 5 cm with an ID of 2 cm for the neck and 10 cm long with IDs varying from about 2 cm to 12 cm for the cavity, producing operating frequencies ranging from approximately 1.2 to 1.5 kHz, following a theoretical model. Twelve different cavity radii were tested. The optimal cavity radius of 2.06 cm had an onset time that was 27 s faster and an onset temperature difference that was lower by 12\r{ }C than the smallest cavity (a half-wave resonator). Future research will explore the quality factor and optimum stack to surface area ratio of the engines.   

Optimum Stack Position Within a Bottle-shaped Thermoacoustic Engine

Thermoacoustics involves turning heat energy into acoustic energy, or using sound to pump heat. A thermoacoustic engine with a transducer could be used, for example, to convert solar energy incident on a satellite into sound and then into electricity. This research focused on the optimization of stack placement within a bottle-shaped 1.4 kHz engine to achieve maximum acoustic pressure. The prime mover consisted of two connected cylinders: the bottle neck, 5 cm long and 1 cm in radius, and a cavity, 10 cm long and 2 cm in radius, with the stack located within the middle of the neck. Sound intensity is a function of both pressure and velocity; therefore, maximum intensity should be found in between their nodes. However, a phase shift is introduced for the velocity due to the thermoacoustic effect and the optimum position will not be exactly between the nodes. Therefore, 9 different stack positions within the neck were tested to determine the optimum location. The optimum was found to be 39{\%} away from the closed end of the neck, which improved acoustic pressure by 50{\%}. Further testing is planned, to verify the results and test different configurations.   

Nonlinear Model of Onset of Thermoacoustic Engines

\newline Thermoacoustic engines are devices that use heat to produce acoustic oscillations. ~Heat is applied to a heat exchanger within a resonator until an adequate temperature gradient is reached, at which point self-sustained oscillations occur. The buildup of oscillations for devices operating at a few kilohertz only last for a few seconds, but can be indicative of the performance of the device. This research uses a Van der Pol model for the self-sustained oscillations for engines operating near 1.5 kHz. Two parameters emerge from the model based on energy supplied to the system and losses of the system. LabVIEW is used to record data from different thermoacoustic engines, and fit the onset profile to a profile generated from the Van der Pol equation. A best fit of the model to the data yields quantitative comparisons of the gain and loss parameters between the engines.