A Linear Dynamic Analysis of Vent Condensation Stability

Pressure suppression systems in boiling water reactors are designed to condense a large amount of steam very rapidly by injecting it into a pool of water. It transpires that such condensing flows are unstable and can lead to large oscillatory pressures on the walls of the containment system. This paper presents a theoretical model whose purpose is to attempt to understand why these flows are unstable and to extract the important parameters and frequencies pertaining to the instability. A simple linear dynamic model is constructed comprising linear transfer function for (i) the unsteady steam flow in the vent (ii) the condensation interface and (iii) the pool hydrodynamics. The analysis demonstrates the existence of both stable and unstable regions of operation defined by several non-dimensional parameters including the ratio of the steam flow rate to the effective thermal diffusivity in the water just downstream of the condensation interface and the frictional losses in the vent. Instability frequencies are in the vicinity of the vent acoustic frequencies or the pool manometer frequency depending on the conditions. Though the qualitative dynamic behavior of the model is consistent with the experimental observations, quantitative comparison is hindered by difficulties in accurately assessing the effective thermal diffusivity in the water. Nevertheless the model provides insight into the nature of the instability

A Local Condensation Analysis Representing Two-phase Annular Flow in Condenser/radiator Capillary Tubes

NASA's effort for the thermal environmental control of the Space Station Freedom is directed towards the design, analysis, and development of an Active Thermal Control System (ATCS). A two phase, flow through condenser/radiator concept was baselined, as a part of the ATCS, for the radiation of space station thermal load into space. The proposed condenser rejects heat through direct condensation of ATCS working fluid (ammonia) in the small diameter radiator tubes. Analysis of the condensation process and design of condenser tubes are based on the available two phase flow models for the prediction of flow regimes, heat transfer, and pressure drops. The prediction formulas use the existing empirical relationships of friction factor at gas-liquid interface. An attempt is made to study the stability of interfacial waves in two phase annular flow. The formulation is presented of a stability problem in cylindrical coordinates. The contribution of fluid viscosity, surface tension, and transverse radius of curvature to the interfacial surface is included. A solution is obtained for Kelvin-Helmholtz instability problem which can be used to determine the critical and most dangerous wavelengths for interfacial waves

CFD modelling of a two-phase closed thermosyphon charged with R134a and R404a

This paper examines the application of CFD modelling to simulate the two-phase heat transfer mechanisms in a wickless heat pipe, also called a thermosyphon. Two refrigerants, R134a and R404a, were selected as the working fluids of the investigated thermosyphon. A CFD model was built to simulate the details of the two-phase flow and heat transfer phenomena during the start-up and steady-state operation of the thermosyphon. The CFD simulation results were compared with experimental measurements, with good agreement obtained between predicted temperature profiles and experimental temperature data, thus confirming that the CFD model was successful in reproducing the heat and mass transfer processes in the R134a and R404a charged thermosyphon, including the pool boiling in the evaporator section and the liquid film in the condenser section

Review and status of liquid-cooling technology for gas turbines

A review was conducted of liquid-cooled turbine technology. Selected liquid-cooled systems and methods are presented along with an assessment of the current technology status and requirements. A comprehensive bibliography is presented

Nucleate pool boiling investigation on a silicon test section with micro-fabricated cavities

The basic mechanisms of nucleate boiling are still not completely understood, in spite of the many numerical and experimental studies dedicated to the topic. The use of a hybrid code allows reasonable computational times for simulations of a solid plate with a large population of artificial micro-cavities with fixed distribution. This paper analyses the guidelines for the design, through numerical simulations, of the location and sizes of micro-fabricated cavities on a new silicon test section immersed in FC-72 at the saturation temperature for different pressures with an imposed heat flux applied at the back of the plate. Particular focus is on variations of wall temperature around nucleation sites

Feedback stabilisation of pool-boiling systems : for application in thermal management schemes

The research scope of this thesis is the stabilisation of unstable states in a pool-boiling system. Thereto, a compact mathematical model is employed. Pool-boiling systems serve as physical model for practical applications of boiling heat transfer in industry. Boiling has advantages over conventional heat-transfer methods based on air- or single-phase liquids by enabling extremely high heat-transfer rates at isothermal conditions. This o¿ers solutions to thermal issues emerging in cutting-edge technologies as semi-conductor manufacturing and electric vehicles (EVs). Continuous miniaturisation in micro-electronics is pushing heat-¿ux densities beyond the limits of standard cooling schemes and growing architecture complexity makes thermal uniformity during chip manufacturing increasingly critical. Further development of EVs may bene¿t equally from boiling heat transfer by its utilisation for actuator cooling and thermal conditioning of battery packs. A pool-boiling system consists of a heater that is submerged in a pool of boiling liquid. The theater is the to-be-cooled device (or a thermally conducting element between the device and the boiling liquid) and is heated at its bottom. On top of the heater, heat is extracted by the boiling liquid. In order to exploit boiling to its fullest e¿ciency, unstable modes need to be stabilised to avoid the formation of a thermally-insulating vapour ¿lm on the heater that causes collapse of the cooling capacity and that heralds a dangerous and ine¿cient mode of boiling. The pool-boiling model comprises a partial di¿erential equation (PDE), i.e. the well- known heat equation, and corresponding boundary conditions that represent adiabatic sidewalls, a uniform heat supply at the bottom, and a nonuniform and nonlinear heat extraction at the heater top. This nonlinear boundary condition renders the entire model nonlinear, resulting in multiple equilibria and complex and exciting dynamics. Restriction to uniform temperature distributions within the heater admits description by a model of one spatial dimension (1D). The 1D model is investigated mathematically and the results are compared with those found by the analyses of spatial-discretisations of the model. Two spatial-discretisation schemes, based on a ¿nite-di¿erence method and a spectral method, are investigated. The latter shows far better convergence properties than the former. Moreover, application of full state feedback of the spectral modes (modal control) results in signi¿cantly better properties than by regulation via standard P-control. In practical applications, the heater temperature can only be measured at the heater top. Consequently, an observer is implemented that estimates the spectral modes of the temperature within the heater, which are subsequently used in the feedback-law. The e¿ciency and performance of this controller-observer combination is examined by numerical simulations. A pool-boiling system with an electrically heated wire as heater can be represented by the model as described above, but now with two spatial dimensions (2D). The 2D model can be analysed mathematically only for uniform equilibria, i.e. the equilibria that exist also for the 1D system. For nonuniform equilibria, the mathematical analysis becomes too complex and a spatial discretisation is required to obtain results. A 1D characteristic equation on the ¿uid-heater interface can be obtained by analytical reduction of the 2D eigenvalue problem using the method of separation of variables. The system poles follow from spatially discretising this equation. Because of its outstanding performance for the 1D model, the 2D model is again stabilised by a modal controller (full state feedback) in combination with an observer. Simulations are again performed to determine the e¿ciency of the controller-observer combination. If a thermally conducting foil is considered as heater, the three-dimensional (3D) form of the model must be investigated. This involves essentially the same methodology as described above, resulting in a 2D characteristic equation on the ¿uid-heater interface. However, spatial discretisation of this equation yields large system matrices and requires excessive calculation times. Hence, the 3D system is analysed only at moderate discretisation orders. The above modal control strategy is, as before, applied in combination with an observer to stabilise unstable equilibria and the evolution of the nonlinear system is again investigated and demonstrated by way of simulations. Finally, a series of exploratory experiments, to investigate the application of pool-boiling to thermally condition battery cells in EVs, is considered. Experiments are performed to investigate the ability for thermal homogenisation of the boiling process and the ability to manipulate the boiling process via the pressure in the boiling chamber. Furthermore, the application of pool-boiling to overcome thermal issues in high-end technologies is investigated by numerical simulations

Investigation of flow and heat transfer in a large-scale spent nuclear fuel cooling pond

The recent focus on nuclear power has led to the need for more efficient and economical methods of operating the Spent Nuclear Fuel (SNF) cooling ponds as well as complying with the strict safety and environmental legislations imposed by the IAEA and the UK Government. Like many other industrial applications, the design and operation of the SNF cooling ponds have evolved from experience; trial and error. Since the stored materials in such ponds are radioactive, it is very difficult to perform experimental studies. As a result, a rigorous scientific study based on fundamental principles has to be performed. The present research explores analytically and numerically the main processes that take place across the pond installation. The body of the present study includes four main parts: the first part is involved in modelling the heat loss from the free water surface, mainly due to evaporation, using analytical and single-phase numerical approaches, which represents a critical factor in the modelling of the large-scale cooling ponds. The predicted results were in good agreement with experimental data available in open literature. In the second part, a thermal model using Microsoft Excel spreadsheet was developed for the cooling pond based on an analytical approach. The well-mixed hypothesis was adopted to describe the water zone as well as the humid air zone. Also, the ventilation system was considered within this model. The developed spreadsheet tool was validated against reliable data available for Maine Yankee pool as well as temperature measurements collected from the Sellafield site. This spreadsheet tool is able to describe the transient behaviour with low computational cost, allowing many "what-if" scenarios to be rapidly investigated. In the third part, Computational Fluid Dynamics (CFD) was used to model the cooling pond at both macro and micro levels. The macro level modelling involved in developing a CFD model for Sellafield’s cooling pond where the fuel regions were approximated to porous medium. The computational domain was produced for the water zone only, where the humid air zone was introduced to the model by coupling of the spreadsheet model with the CFD model. This model was validated and used to examine the distribution of water temperature to confirm the reliability of the adopted well-mixed approach in the analytical model. The outcomes from the CFD and spreadsheet models were used to provide some boundary conditions to the micro-level model of the fuel assemblies. The modelling methodology of the fuel assemblies was partially validated with experimental data for heat transfer around vertical cylinder. The maximum temperature of the water within the rack arrangement was determined under various conditions and a correlation was proposed. Finally, a sensitivity study was performed using Taguchi method and the statistical method of ANOVA to assess the influence of the cooling systems as well as the environmental conditions on the thermal performance of the cooling pond. The spreadsheet model was implemented to carry out the calculations. The outcomes from this study were presented in the form of recommendations that may be able to aid the organisation to manage their cooling pond more efficiently and safely during the normal operating conditions as well as recovery from an accident scenario

Extended hydrodynamic theory of the peak and minimum pool boiling heat fluxes

The hydrodynamic theory of the extreme pool boiling heat fluxes is expanded to embrace a variety of problems that have not previously been analyzed. These problems include the prediction of the peak heat flux on a variety of finite heaters, the influence of viscosity on the Taylor and Helmoltz instability mechanisms with application to film boiling and to the peak heat flux in viscous liquids, the formalization of the analogy between high-current-density electrolysis and boiling, and the description of boiling in the low-gravity limit. The predictions are verified with a large number of new data

Recent developments on fractal-based approaches to nanofluids and nanoparticle aggregation

This project was supported by the National Natural Science Foundation of China (Nos. 41572116, 51576114, ​41630317), the Fundamental Research Funds for the Central Universities, China University of Geosciences (Wuhan) (No. CUG160602) and the Natural Science Foundation of Fujian Province of China (No. 2016J01254). The authors of the figures that used in presented review are also highly appreciated.Peer reviewedPostprin