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Complex ladder-like structures recently have been considered as the target design for accelerator applications. The decay heat, during a postulated beyond design-basis loss-of-coolant accident in the target where all normal and emergency cooling fails, is removed mainly by radiation heat transfer. Modeling of the radiation transport in complex ladder-like structures has several challenges and limitations when the standard net-radiation model is used. This paper proposes a simplified lumped, or ‘hot-rung’ model, that considers the worst elements and utilizes the standard net-radiation method. The net-radiation model would under-predict structure temperatures if surfaces were subject to non-uniform radiosity. The proposed model was assessed to suggest corrections to account for the non-uniform radiosity. The non-uniform radiosity effect causes the proposed hot-rung model to under-predict the center-rung temperatures by ≈4–74°C when all parametrics, including temperatures up to 1500°C, were considered. These temperatures are small. The proposed model predicted that an important effect of decreasing the emissivity was smoothing of non-isothermal effects. The radiosity effects are more pronounced when there are strong temperature gradients. Uniform rung temperatures tend to decrease the radiosity effects. We concluded that a relatively simple model that is conservative with respect to radiosity effects could be developed.

A computer program developed to analyze nucleate boiling over a heated surface is described. The model solves the three-dimensional transient conduction equation within the heater. The conduction solution is coupled with closure relationships to mimic the bubble dynamics and the associated heat transfer coefficients. Sample problems are run using a copper surface subject to partial nucleate boiling in saturated water at atmospheric pressure. The results are shown to be in good qualitative agreement with the pertinent experimental observations.

Using a numerical model, the effect of heating methods on saturated nucleate pool boiling is investigated parametrically for smooth and rough nickel and copper heater plates. The boiling curve moved right with decreasing thickness for the smooth and rough nickel and copper heaters in the constant-heat-flux heating method. This trend was reversed in the constant-temperature heating method; the boiling curved shifted left with decreasing heater thickness. However, the later trend was not affected by the heater material and thickness and the surface roughness (mean cavity radius). The boiling curves were identical for the constant internal generation rate and the constant-heat-flux heating method. The use of ac instead of dc resistive heating caused the boiling curve generally to move left. This behavior was not linear with the heat flux, heater material, or surface conditions. No hysterisis was found when the heat flux was increased and then decreased gradually to original values.

A new model has been developed where the coupled transient two-dimensional conduction equation is solved for the heater and the liquid macrolayer, while allowing for the time-wise thinning of the macrolayer. The major conclusions are: (1) dominant evaporation occurs at the liquid-vapor-solid contact point (triple point) and is required to match boiling curve behavior quantitatively; (2) evaporation at the stem interface and bubble-macrolayer interface is negligible (except near critical heat flux); and (3) the results are sensitive to closure relationships, especially to the active site-density correlation.

A new approach to address the effect of surface radiation on a laminar film boiling flow over a horizontal flat plate is suggested. Previously developed approximate expressions of the thermal boundary-layer thickness and the wall shear stress of a moving surface in a flowing liquid are used to circumvent the complicated simultaneous solution of the vapor and liquid flow. Approximate closed-form expressions to predict the wall heat transfer and skin friction are obtained. For a water-steam system at atmospheric pressure within the wall temperature range considered (Tw

Subcooled laminar forced convection film boiling flow on a wedge is analyzed considering the streamwise pressure gradient imposed on the flow and the streamwise buoyancy force acting on the vapor film. A twophase boundary-layer model is proposed, and the local similarity concept is applied to obtain an approximate solution of the governing equations. For a water-steam system at atmospheric pressure considered within this study, wall skin friction results display a strong dependency on the streamwise buoyancy force driving the vapor film and the external pressure gradient. Adverse streamwise buoyancy force acting on the vapor film, which is the case on the lower surface of a horizontally aligned wedge, may cause vapor flow separation. In contrast to wall skin friction dependency, the wall heat transfer parameter shows a secondary dependence on the streamwise pressure gradient and the buoyancy force.

The authors consider the high-heat-flux, pool nucleate boiling region of a horizontal surface and propose a theoretical basis for estimating the constant of proportionality between the mean macrolayer thickness and the mean vapor-stem diameter at critical heat flux. This constant is found to be of the same order of magnitude (−10% difference) as that suggested by Gaertner [5]. While Gaertner's estimate is based on photographic evidence, the current approach uses a theoretical basis together with experimental data.

A simple analysis of the steady laminar forced convection film boiling flow over a horizontal flat plate is presented. A novel analogy drawn between the mobile liquid-vapor interface in forced convection film boiling and a moving surface in a flowing single-phase fluid enables a simple analysis of this complex flow. As a result, easy to apply closed-form expressions to predict theoretical wall heat transfer and skin friction are obtained, circumventing the need for previous complex analyses.

Laminar forced convection film boiling flow on a wedge is analyzed considering the streamwise pressure gradient imposed on the flow and the streamwise buoyancy force (important because of the large density difference between the vapor and liquid) acting on the vapor film. A two-phase boundary layer model is proposed, and the local similarity concept is applied to obtain an approximate solution of the governing equations. Parametric trends in this analysis show that, for a water-steam system at atmospheric pressure considered within this study, the density difference between the vapor and liquid is large enough. As a result, both the streamwise pressure gradient and the buoyancy force exert strong influence on the vapor flow dynamics. Wall skin friction results display a strong dependency on the streamwise buoyancy force driving the vapor film and the external pressure gradient. Previously observed skin friction bucket'' type phenomena with increased heating of the wedge are possible when the buoyancy force is small or negligible. Adverse streamwise buoyancy force action on the vapor film, which is the case on the lower surface of a horizontally aligned wedge, may cause vapor flow separation. In contrast to wall skin friction dependency, the wall heat-transfer parameter shows a secondarymore » dependence on the streamwise pressure gradient and the buoyancy force. 16 refs., 9 figs., 3 tabs.« less

In the previously postulated relationship between the macrolayer thickness in saturated pool boiling and the Helmholtz instability wavelength is further investigated in the ligth of experimental data that recently appeared in the open literature. The study shows that the Helmholtz wavelength in the vapor stems is strongly dependent on parameters affected by surface chemistry. These parameters same order of magnitude as the ones reported in the literature, the Helmholtz instability model was able to successfully predict the macrolayer thickness data. This result suggests that the Helmholtz instability model must not be ruled out, unless further experimental research proves otherwise.