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Two-dimensional, laminar, transient, natural- convection heat and mass transfer in closed, partially filled liquid containers
In the present investigation of crystalline phase internal radiation and heat conduction during the vertical Bridgman growth of a YAG-like oxide crystal, where transport through the melt is dominated by convection and conduction, heat is also noted to be conducted through ampoule walls via natural convection and enclosure radiation. The results of a quasi-steady-state axisymmetric Galerkin FEM indicate that heat transfer through the system is powerfully affected by the optical absorption coefficient of the crystal. The coupling of internal radiation through the crystal with conduction through the ampoule walls promotes melt/crystal interface shapes that are highly reflected near the ampoule wall.
Cooling is critical for the life and performance of electronic equipment. In most cases cooling may be achieved by natural convection but forced convection may be necessary for high wattage applications. Use of conventional type heat sinks may not be feasible from the viewpoint of specific applications and the costs involved. In a heat sink, fins can be attached to the well by ultrasonic welding, by soldering, or with a number of industrially available thermal adhesives. In this paper, the author investigates the heat transfer characteristics of several adhesives and compares them with ultrasonic welding and theoretically calculated values. This experiment was conducted in an air flow chamber. Heat was generated by using heaters mounted on the well. Thermstrate foil, Uniset A401, and Aremco 571 adhesives were tested along with an ultrasonically welded sample. Ultrasonic welding performed far better than the adhesives and Thermstrate foil. This type of experiment can be adapted for a laboratory exercise in an upper level heat transfer course. It gives students an exposure to industrial applications that help them appreciate the importance of the course material.
Two iterative schemes based on the mixed finite element method are developed for analyzing steady natural convection in a melt adjacent to its solid phase. The simplest method decouples the calculation of the field variables and the shape of the melt/solid interface into two interlocked iterations that are performed successively. The second method uses Newton's iteration to solve simultaneously for both types of unknowns and has a quadratic convergence rate. Results for a model problem of melt and solid in a cylindrical ampoule show the Newton algorithm to be a factor of three more efficient.
The Echo Classification from COnvectivity (ECCO) algorithm identifies convective and stratiform types of radar echo in three dimensions. It is based on the calculation of reflectivity texture—a combination of the intensity and the heterogeneity of the radar echoes on each horizontal plane in a 3D Cartesian volume. Reflectivity texture is translated into convectivity, which is designed to be a quantitative measure of the convective nature of each 3D radar grid point. It ranges from 0 (100% stratiform) to 1 (100% convective). By thresholding convectivity, a more traditional qualitative categorization is obtained, which classifies radar echoes as convective, mixed, or stratiform. In contrast to previous algorithms, these echo-type classifications are provided on the full 3D grid of the reflectivity field. The vertically resolved classifications, in combination with temperature data, allow for subclassifications into shallow, mid-, deep, and elevated convective features, and low, mid-, and high stratiform regions—again in three dimensions. The algorithm was validated using datasets collected over the U.S. Great Plains during the PECAN field campaign. An analysis of lightning counts shows ~90% of lightning occurring in regions classified as convective by ECCO. A statistical comparison of ECCO echo types with the well-established GPM radar precipitation-type categories show 84% (88%) of GPM stratiform (convective) echo being classified as stratiform (convective) or mixed by ECCO. ECCO was applied to radar grids for the continental United States, the United Arab Emirates, Australia, and Europe, illustrating its robustness and adaptability to different radar grid characteristics and climatic regions.
A time-averaged error indicator with POD- h Greedy is developed to drive parametric model order reduction (pMOR) for 2D unsteady natural convection in a high-aspect ratio slot parameterized with the Prandtl number, Rayleigh number, and slot angle with respect to the gravity. The error indicator is extended to accommodate the energy equation and Leray regularization. Despite being two-dimensional and laminar, the target flow regime presents several challenges: 1) there is a bifurcation in the angle parameter space; 2) the solution can be multivalued, even at steady state; and 3) the solution exhibits spatio-temporal chaos at several points in the parameter space. The authors explore several reduced-order models (ROMs) and demonstrate that Leray-regularized Galerkin ROMs provide a robust solution approach for this class of flows. They further demonstrate that error-indicated pMOR can efficiently predict several QOIs, such as mean flow, mean Nusselt number and mean turbulent kinetic energy, even in the presence of a bifurcation. Finally, they show that spatio-temporal chaos can lead to lack of reproducibility in both the full-order model and the reduced-order model and that the variance in the full-order model provides a lower bound on the pMOR error in these cases.
The central feature in any flow prediction method is the treatment of the coupling between the momentum and continuity equations. In natural-convection flows, the energy equation also becomes strongly coupled with the momentum equations. Because of the nonlinear nature of the coupling, these equations are solved iteratively. Iterative methods are often prone to slow convergence, divergence, and extreme sensitivity to underrelaxation factors. The aim of the present research is to develop more efficient and reliable solution schemes for the coupled flow equations. Such schemes will significantly reduce the expense of computing complex flows encountered in combustion chambers, gas turbines, heat exchangers, and other practical equipment. In the work completed so far, a technique employing norm reduction in conjunction with the successive-substitution and Newton-Raphson techniques was developed. Also, a block-correction procedure for the flow equations is currently being formulated and tested.
There is interest at NASA, other space agencies, and industry, in the liquefaction of fluids produced through in-situ processes on the surfaces of the Moon and Mars. A multi-center team at NASA recently considered multiple different refrigeration cycles and refrigeration integration methodologies and how these might fit into early liquefaction plants for NASA's exploration initiatives. The rate of liquefaction for these initiatives is quite slow in comparison to large scale terrestrial applications. These studies concluded that, for both structural and heat spreading reasons, integrating the refrigeration tubing on the surface of the storage tank wall is an attractive path to pursue in the near term. In order to develop a technology development path and inform investors, it was desired to investigate the sensitivity of gravity of the processes involved. An analysis of the condensation processes within the tank is performed. The objective is to determine the sensitivity of liquefaction to gravitational effects. The heat transfer mechanisms include forced convection heat removal to the refrigeration system (or cryocooler), conduction through the tank wall heat exchanger, and convection and condensation on the inner tank wall. Gravity affects the liquefaction process via condensate liquid drainage, natural convection in the ullage, and the shape of the liquid-vapor interface within the tank. Analysis of these mechanisms shows that while there is some sensitivity to gravitational level in general, within the bounds of current interest (rate of liquefaction appropriate to Lunar and Martian applications, and cooling capacity of the cryocooler), this sensitivity of liquefaction to gravity is quite small. Thus, system level testing on the Earth should suffice for the performance prediction and demonstration of liquefaction operations as applicable to Lunar and Martian applications.
An outline is given of research on the directional solidification of a liquid, and of the effects of natural convection thereon. Three problems which have been studied are described. Finally, current work on solidification in microgravity conditions is discussed.
Thermocapillary convection in a molten zone of NaNO3 contained in a boat with a free horizontal surface, that is heated from above by a centered wire heater, was studied to simulate flow in zone-melting crystal growth. Using a laser-light-cut technique and fine SiO powder as a tracer, convection in the melt zone was visualized in two different cases. In the first case, the entire melt surface was free, while in the second the melt surface was free only in the immediate vicinity of one vertical wall and was covered elsewhere, this wall being to simulate the melt/crystal interface during crystal growth. It was observed that thermocapillary convection near this wall prevailed in the first case, but was reduced significantly in the second. Since thermocapillary rather than natural convection dominated in the melt, the effect of the partial covering of the melt surface on thermocapillary convection in the melt observed in this study is expected to be similar under microgravity.
It has long been recognized that flow in the melt can have a profound influence on the dynamics of a solidifying interface and hence the quality of the solid material. In particular, flow affects the heat and mass transfer, and causes spatial and temporal variations in the flow and melt composition. This results in a crystal with nonuniform physical properties. Flow can be generated by buoyancy, expansion or contraction upon phase change, and thermo-soluto capillary effects. In general, these flows can not be avoided and can have an adverse effect on the stability of the crystal structures. This motivates crystal growth experiments in a microgravity environment, where buoyancy-driven convection is significantly suppressed. However, transient accelerations (g-jitter) caused by the acceleration of the spacecraft can affect the melt, while convection generated from the effects other than buoyancy remain important. Rather than bemoan the presence of convection as a source of interfacial instability, Hurle in the 1960s suggested that flow in the melt, either forced or natural convection, might be used to stabilize the interface. Delves considered the imposition of both a parabolic velocity profile and a Blasius boundary layer flow over the interface. He concluded that fast stirring could stabilize the interface to perturbations whose wave vector is in the direction of the fluid velocity. Forth and Wheeler considered the effect of the asymptotic suction boundary layer profile. They showed that the effect of the shear flow was to generate travelling waves parallel to the flow with a speed proportional to the Reynolds number. There have been few quantitative, experimental works reporting on the coupling effect of fluid flow and morphological instabilities. Huang studied plane Couette flow over cells and dendrites. It was found that this flow could greatly enhance the planar stability and even induce the cell-planar transition. A rotating impeller was buried inside the sample cell, driven by an outside rotating magnet, in order to generate the flow. However, it appears that this was not a well-controlled flow and may also have been unsteady. In the present experimental study, we want to study how a forced parallel shear flow in a Hele-Shaw cell interacts with the directionally solidifying crystal interface. The comparison of experimental data show that the parallel shear flow in a Hele-Shaw cell has a strong stabilizing effect on the planar interface by damping the existing initial perturbations. The flow also shows a stabilizing effect on the cellular interface by slightly reducing the exponential growth rate of cells. The left-right symmetry of cells is broken by the flow with cells tilting toward the incoming flow direction. The tilting angle increases with the velocity ratio. The experimental results are explained through the parallel flow effect on lateral solute transport. The phenomenon of cells tilting against the flow is consistent with the numerical result of Dantzig and Chao.
The numerical simulation of ongoing traveling heater method (THM) solution growth experiments of CdTe from Te solvent and the influence of a Rotating Magnetic Field (RMF) on control of convection in the solution zone is presented. The application of RMF is pursued as a means to actively control thermo-solutal convection in the solution zone which otherwise would be dominated by buoyancy forces. Numerical simulation and scaling analysis are used to generate a flow-regime map demarcating the boundary separating the buoyancy- and RMF-driven convection in the solution zone. Results indicate that whereas at low gravity levels the application of RMF can completely overwhelm buoyancy-induced convection, at normal gravity levels the successful control of convection by RMF requires use of fairly thin solvent zones. Simulation results also indicate that field strengths required to dominate natural convection on earth may lead to instabilities and transition to turbulence, and an associated deleterious effect on the quality of grown crystals. These and other simulations results are discussed in reference to experimental evidence.
Recent exploration initiatives both by NASA and others have produced interest in the liquefaction of fluids produced through in-situ processes on the surfaces of the Moon and Mars. Liquefaction of fluids in cryogenic temperatures is routinely done at large scale for terrestrial uses, but these processes do not necessarily scale down in an economical or technologically feasible manner for the anticipated rates of initial Lunar or Martian production plants. To understand appropriate processes and scaling parameters, various options should be considered. A multi-center team at NASA considered multiple different refrigeration cycles and refrigeration integration methodologies as well as how these might fit into early liquefaction plants. These studies resulted in the conclusion that integrating the tubing on the storage tank wall (for both structural and heat spreading reasons), preferably the tank which will actually use the fluid, is the nearest path forward. Given that assumption on the general framework of the liquefaction system, there are several different heat transfer mechanisms to consider from a scaling perspective. These include forced convection heat removal to the refrigeration system (or cryocooler), conduction through the tank wall heat exchanger, and condensation (with some natural convection) on the inner tank wall. Analysis of these mechanisms shows that while there is some sensitivity to gravitational level, that within the bounds of current interest (Lunar and Martian applications), this sensitivity does not dominate the liquefaction application. While there will be some effect, perhaps in a limiting manner as the tanks approach some high fill level, system level testing on the Earth should suffice for the performance prediction and demonstration of liquefaction operations as applicable to Lunar and Martian applications. However, as one approaches orbital conditions, this general approach to liquefaction will not be appropriate as the scaling of the heat transfer mechanisms is not appropriate. At this point, other approaches will need to be developed and demonstrated in the micro-gravity environment.
This report summarizes FY26 progress under the Nuclear Energy Advanced Modeling and Simulation (NEAMS) program's high-temperature gas-cooled reactor (HTGR) application driver work, covering a wide range of activities such as code validation and multi-physics code assessment. 1) A detailed SAM model of the High-Temperature Engineering Test Reactor (HTTR) was developed using a unique-block grouping approach, with an extended parallel thermal network method to capture block-to-block conduction and radiation heat transfer, and applied to steady-state simulations of the HTTR 30~MW and 9~MW cases. 2) In another activity, SAM's newly implemented multi-component gas flow model was validated against the Natural convection Shutdown heat removal Test Facility (NSTF) argon ingress experiment, correctly capturing the density-driven suppression and thermal recovery of natural circulation observed when argon is introduced into the air-cooled Reactor Cavity Cooling System (RCCS) loop. 3) For the OECD/NEA High Temperature Test Facility (HTTF) benchmark, we co-led the international benchmark activities as well as the OECD/NEA final benchmark report to be released at the end of this year. 4) Finally, the coupled Griffin-SAM modeling capability for pebble-bed HTGRs was advanced by verifying the Griffin neutronics solution against Serpent Monte Carlo for a realistic non-uniform temperature distribution, resolving several deficiencies in the SAM-to-Griffin temperature transfer scheme, and enabling distinct fuel kernel, moderator, and coolant temperatures for cross section feedback. These new features were demonstrated in a PBR load-following transient.
In the absence of gravity, stirring in a liquid is suppressed because of density differences caused by thermal or compositional gradients. However, other mechanisms resulting in natural convection in a microgravity environment exist. One of the most important mechanisms for liquid metals is surface tension driven convection, which becomes predominant in the low gravity environment. In this case, surface tension differences caused by compositional or temperature gradients have been demonstrated to cause stirring in liquids during experiments performed onboard Skylab. Compositional gradients were created by adding a soap solution to a large water globule, which caused vigorous fluid motion for some moments after the addition.
An ultrasound technique has been developed to non-intrusively image temperature fields in small-scale systems of opaque fluids undergoing convection. Fluids such as molten metals, semiconductors, and polymers are central to many industrial processes, and are often found in situations where natural convection occurs, or where thermal gradients are otherwise important. However, typical thermal and velocimetric diagnostic techniques rely upon transparency of the fluid and container, or require the addition of seed particles, or require mounting probes inside the fluid, all of which either fail altogether in opaque fluids, or necessitate significant invasion of the flow and/or modification of the walls of the container to allow access to the fluid. The idea behind our work is to use the temperature dependence of sound velocity, and the ease of propagation of ultrasound through fluids and solids, to probe the thermal fields of convecting opaque fluids non-intrusively and without the use of seed particles. The technique involves the timing of the return echoes from ultrasound pulses, a variation on an approach used previously in large-scale systems.
For computational simulation of the convection and mixing of stratified fluid in a rotating tank (such as used in Apollo flights) with time-dependent rotation, the Navier-Stokes convection problem was formulated for a circular tank configuration. The final equations results from a general approximate theory for combined forced and contained natural convection in a time-dependent rotating system. The equations are cast in terms of vorticity and stream function in a form convenient for computation, with a transformed coordinate system, and appropriate boundary conditions are derived. Accurate representations for the cryogenic supercritical oxygen thermodynamic properties are used in the computations, and an efficient numerical finite difference scheme and computational method are employed.
The Traveling Magnetic Field (TMF) technique, recently proposed to control meridional flow in electrically conducting melts is reviewed. In particular, the natural convection damping capability of this technique has been numerically demonstrated with the implication of significantly improving crystal quality. Advantages of the traveling magnetic field, in comparison to the more mature rotating magnetic field method, are discussed. Finally, a detailed one-dimensional planar TMF model has been developed and is presented.