Virgil E. Schrock

Diffusion Layer Theory for Turbulent Vapor Condensation With Noncondensable Gases

In turbulent condensation with noncondensable gas, a thin noncondensable layer accumulated and generates a diffusional resistance to condensation and sensible heat transfer. By expressing the driving potential for mass transfer as a difference in saturation temperatures and using appropriate thermodynamic relationships, here an effective condensation thermal conductivity is derived. With this formulation, experimental results for vertical tubes and plates demonstrate that condensation obeys the heat and mass transfer analogy, when condensation and sensible heat tranfer are considered simultaneously

An investigation of condensation from steam–gas mixtures flowing downward inside a vertical tube

Abstract This research investigates experimentally local heat transfer from condensation in the presence of noncondensable gases inside a vertical tube. Using a novel experimental apparatus for accurately measuring local heat fluxes, an extensive data base has been obtained for the condensation of pure steam, steam–air mixtures and steam–helium mixtures. Three different correlations, implementing the degradation factor method, diffusion layer theory, and mass transfer conductance model, are presented. The correlation using the simple degradation factor method has been shown to give satisfactory engineering accuracy. However, this method is based on very simplified arguments that do not fully represent the complex physical phenomena involved. Based on diffusion layer theory and a mass transfer conductance model, more physically based correlations were developed for the heat transfer of vapor-gas side. The total heat transfer coefficient predicted by the correlations from these two mechanistic models are in close agreement with experimental values.

Diffusion layer modeling for condensation in vertical tubes with noncondensable gases

Abstract Noncondensable gases significantly modify the mechanism of condensation for cocurrent downward flow in vertical tubes. Two-dimensional experimental measurements presented here show similarity between gas concentration distributions and the temperature distributions encountered in laminar and turbulent heat transfer. Thus the analogy between heat and mass transfer, coupled with a reasonable condensate film model, can provide predictions of the local condensation rate. This work presents a simple 9-step iterative calculation procedure for calculating the local heat flux. The empirical model, based on a modified Dittus-Boelter formulation and utilizing an effective condensation thermal conductivity, converges with 2 to 10 iterations at each axial location. Experimental results from several investigators are compared with the predictions of the model, with good agreement.

Blast venting through blanket material in the HYLIFE ICF reactor

This work presents a numerical study of blast venting through various blanket configurations in the HYLIFE ICF reactor design. The study uses TSUNAMI -- a multi-dimensional, high-resolution, shock capturing code -- to predict the momentum exchange and gas dynamics for blast venting in complex geometries. In addition, the study presents conservative predictions of wall loading by gas shock and impulse delivered to the protective liquid blanket. Configurations used in the study include both 2700 MJ and 350 MJ fusion yields per pulse for 5 meter and 3 meter radius reactor chambers. For the former, an annular jet array is used for the blanket geometry, while in the latter, both annular jet array as well as slab geometries are used. Results of the study indicate that blast venting and wall loading may be manageable in the HYLIFE-II design by a judicious choice of blanket configuration.

Scaling for integral simulation of mixing in large, stratified volumes

In this paper we develop scaling relationships for mixing in large stratified volumes, both for steam/nitrogen mixtures in containment compartments and for water in suppression pools. The results apply to scaling for integral tests of passive reactor containment systems. Buoyant jets from injected fluids and buoyant wall jets generated by hot and cold surfaces provide the primary mixing in these passive systems. The buoyant jets entrain and transport the stratified fluid, mixing the fluid and reducing the vertical temperature and concentration gradients. We show that scaling for mixing can be satisfied simultaneously with scaling for two-phase natural circulation. The scaling requires a reduced height, accelerated time facility. Accelerated time scaling is advantageous for studying long-term behavior of interest in passive systems, while reduced height improves long-term heat loss, decreases power requirements, and makes simulation of blow-down mixing feasible.

The Soft-Sphere Equation of State for Liquid Flibe

AbstractMolten Flibe (Li2BeF4) salt is a candidate material for the liquid blanket in the HYLIFE-II inertial confinement fusion reactor. The thermodynamic properties of the liquid are very important for the study of the thermohydraulic behavior of the concept design, particularly, the compressible analysis of the blanket isochoric heating problem. In this paper, a soft sphere model equation of state, which was used for describing liquid metals previously, is deployed with slight modifications for fitting the available experimental data for liquid Flibe. It is found that within the available temperature range the model gives a good agreement with experimental data for density, enthalpy and speed of sound. Additionally the model provides reasonable isotherms, spinodal line and predicts a “critical point”. The results show that the model has good thermodynamic behavior, although for a material like Flibe the “critical point” phenomenon is more complex than for pure component material.

Rayleigh-Taylor instability of cylindrical jets with radial motion

Abstract Rayleigh–Taylor instability of an interface between fluids with different densities subjected to acceleration normal to itself has interested researchers for almost a century. The classic analyses of a flat interface by Rayleigh and Taylor have shown that this type of instability depends on the direction of acceleration and the density differences of the two fluids. Plesset later analyzed the stability of a spherically symmetric flows (and a spherical interface) and concluded that the instability also depends on the velocity of the interface as well as the direction and magnitude of radial acceleration. The instability induced by radial motion in cylindrical systems seems to have been neglected by previous researchers. This paper analyzes the Rayleigh–Taylor type of instability for a cylindrical surface with radial motions. The results of the analysis show that, like the spherical case, the radial velocity also plays an important role. As an application, the example of a liquid jet surface in an Inertial Confinement Fusion (ICF) reactor design is analyzed.

An Approximate Method for Analyzing Transient Condensation on Spray in HYLIFE - II

The HYLIFE-II conceptual design calls for analysis of highly transient condensation on droplets to achieve a rapidly decaying pressure field. Drops exposed to the required transient vapor pressure field are first heated by condensation but later begin to reevaporate after the vapor temperature falls below the drop surface temperature. An approximate method of analysis has been developed based on the assumption that the thermal resistance is concentrated in the liquid. The time dependent boundary condition is treated via the Duhamel integral for the pure conduction model. The resulting Nusselt number is enhanced to account for convection within the drop and then used to predict the drop mean temperature history. Many histories are considered to determine the spray rate necessary to achieve the required complete condensation.

Droplet Condensation in Rapidly Decaying Pressure Fields

Certain promising schemes for cooling inertial confinement fusion reactors call for highly transient condensation in a rapidly decaying pressure field. After an initial period of condensation on a subcooled droplet, undesirable evaporation begins to occur. Recirculation within the droplet strongly impacts the character of this condensation-evaporation cycle, particularly when the recirculation time constant is of the order of the pressure decay time constant. Recirculation can augment the heat transfer, delay the onset of evaporation, and increase the maximum superheat inside the drop by as much as an order of magnitude

The pressure relaxation of liquid jets after isochoric heating

During isochoric heating by fast neutron irradiation, a high pressure is almost instantaneously built up inside the falling liquid jets in a HYLIFE (ICF) reactor. It has been suggested that the jets will breakup as a consequence of negative pressure occurring during the relaxation. This is important to both the subsequent condensation process and the chamber wall design. In this paper the mechanism of the relaxation of liquid jets after isochoric heating has been studied with both incompressible and compressible models. The transient pressure field predicted is qualitatively similar for both models and reveals a strongly peaked tension in the wake of a rarefaction wave. The pressure then rises monotonically in radius to zero pressure on the boundary. The incompressible approximation greatly over predicts the peak tension, which increases with time as the rarefaction wave moves toward the center of the jet. Since the tension distribution is as a narrow spike rather than uniform, a cylindrical fracture is the most likely mode of failure. The paper also discusses the available methods for estimating liquid tensile strength.