Modeling the Subsurface Structure of Sunspots

While sunspots are easily observed at the solar surface, determining their subsurface structure is not trivial. There are two main hypotheses for the subsurface structure of sunspots: the monolithic model and the cluster model. Local helioseismology is the only means by which we can investigate subphotospheric structure. However, as current linear inversion techniques do not yet allow helioseismology to probe the internal structure with sufficient confidence to distinguish between the monolith and cluster models, the development of physically realistic sunspot models are a priority for helioseismologists. This is because they are not only important indicators of the variety of physical effects that may influence helioseismic inferences in active regions, but they also enable detailed assessments of the validity of helioseismic interpretations through numerical forward modeling. In this paper, we provide a critical review of the existing sunspot models and an overview of numerical methods employed to model wave propagation through model sunspots. We then carry out an helioseismic analysis of the sunspot in Active Region 9787 and address the serious inconsistencies uncovered by \citeauthor{gizonetal2009}~(\citeyear{gizonetal2009,gizonetal2009a}). We find that this sunspot is most probably associated with a shallow, positive wave-speed perturbation (unlike the traditional two-layer model) and that travel-time measurements are consistent with a horizontal outflow in the surrounding moat.Comment: 73 pages, 19 figures, accepted by Solar Physic

Prediction of the Circumferential Film Thickness Distribution in Horizontal Annular Gas-Liquid Flow

This paper develops a liquid film symmetry correlation and a liquid [11m thickness distribution model for horizontal annular gas-liquid pipe flows. The symmetry correlation builds on the work of Williams et al. (1996). A new correlating parameter is presented. The experimental data used in the correlation is from all three of the horizontal annular flow regions: stratified-annular, asymmetric annular, and symmetric annular. The liquid film thickness model is based on work done by Laurinat et al. (1985). The circumferential momentum equation is simplified to a balance between the normal Reynolds stress in the circumferential direction and the circumferential component of the weight of the film. A model for the normal Reynolds stress in the circumferential direction is proposed. The symmetry correlation is used to close the model equations. Circumferential film thickness distribution predictions are made in the three horizontal annular flow regions and compared to experimental data.Air Conditioning and Refrigeration Project 7

Two-Phase Modeling of Refrigerant Mixtures in the Annular/Stratified Flow Regimes

Air Conditioning and Refrigeration Center Project 4

Optical Measurement of Liquid Film Thickness and Wave Velocity in Liquid Film Flows

Two optical techniques are described for measurement of a liquid film's surface. Both techniques make use of the total internal reflection which occurs at a liquid-vapor interface due to the refractive index difference between a liquid and a vapor. The fIrst technique is used for film thickness determination. A video camera records the distance between a light source and the rays which are reflected back from the liquid-vapor interface. This distance can be shown to be linearly proportional to film thickness. The second technique measures surface wave velocities. Two photosensors, spaced a fIxed distance apart, are used to record the time varying intensity of light reflected from the liquid-vapor interface. The velocity is then deduced from the time lag between the two signals.Air Conditioning and Refrigeration Center Project 4

Characteristics of Refrigerant Film Thickness, Pressure Drop, and Heat Transfer in Annular Flow

Common refrigeration and air conditioning cycles are dependent on two-phase flow for efficient heat transfer with minimal pressure drop. Design of heat exchangers for these systems is aided by an understanding of the refrigerant pressure drop and local heat transfer coefficient. An estimate of the liquid fraction is also important for predicting the charge required in a system. The present work develops a semi-analytical model for predicting liquid fraction, pressure drop, and heat transfer for pure refrigerants in the annular flow regime. The model uses the approach of coupling a uniformly thick, turbulent liquid film layer with a turbulent vapor core. Model predictions are compared to experimental evaporation and condensation data for Rll, R12, R134a, and R22. These refrigerants represent the low, medium, and high pressure ranges found in common refrigeration systems. The uniform film model, when compared to experimental data, provides a reference for understanding some of the mechanisms that are important to refrigerant two-phase flow.Air Conditioning and Refrigeration Project 7