Krzysztof Szilder

Computer simulation of marine ice accretion

Marine icing can arguably be considered to be the primogenitor of icing problems, having occasioned grief to mariners long before aircraft or electrical transmission lines were invented. Adopting an historical perspective, we elucidate the nature of the phenomenon and the scientific and engineering approaches which have been embraced to mitigate it. With a view to encouraging other scientists to address this problem, we also identify the critical knowledge gaps which stand in the way of a final solution, paying particular attention to recent developments and future trends in numerical modelling and wind–tunnel experimentation.

Modelling ice accretion on non-rotating cylinders — The incorporation of time dependence and internal heat conduction

Abstract A new model of ice accretion on a non-rotating cylinder has been formulated. While similar in approach to the model by Lozowski, Stallabrass, and Hearty (1983), it features several important innovations. These include internal heat conduction, time-dependence, and solution using a high-level computer language specifically designed for simulating continuous systems.

Novel two-dimensional modeling approach for aircraft icing

A new modeling approach to tackle the challenging problem of in-flight icing prediction is formulated and verified. With use of this new approach, termed morphogenetic modeling, the shape, structural details, and density of aircraft ice accretions are predicted by emulating the behavior of individual fluid elements. A two-dimensional, morphogenetic model is used to predict the ice accretion forming on a cylinder over a range of in-flight conditions. The model predicts rime, glaze, and simultaneous glaze and rime accretions

Simulation of icicle growth using a three-dimensional random walk model

Abstract A discrete three-dimensional random walk model has been developed to simulate icicle growth. Water flow along the icicles surface is divided into fluid elements which follow a stochastic path towards the icicle tip. During its motion, a fluid element may freeze on the icicles lateral surface or at its tip. The fluid elements may also drip from the icicle tip. The influence of the model parameters (the freezing probability, the shedding parameter and the motion parameter) on the icicle geometry and on the efficiency of freezing has been examined. The model predicts a characteristic three-dimensional icicle surface of a stochastic nature. This new model may be used to simulate icicle formation on transmission lines, offshore structures and buildings. A distinct advantage of the random walk model is that it is not limited by the objects geometry.

Some applications of a new, time-dependent cylinder ice accretion model

Abstract A new, time-dependent ice accretion model on a non-rotating cylinder is described briefly. In order to demonstrate the power and versatility of the model, we present some results related to anti-icing, marine icing and helicopter rotor-blade icing. The model results show that the initial cylinder temperature can have a significant effect on both the shape and the mass of the ice accretion. The thermal properties of the cylinder material are also shown to be important when internal conduction and convection from the un-iced downstream face of the cylinder are taken into account.

Numerical simulations of pendant ice formations

A recently published three-dimensional morphogenetic model has been used to predict the growth of icicles and other pendant ice formations. In this model, the liquid flow is divided into a set of fluid elements, and the behaviour of each element is determined individually using a stochastic process. The model provides a numerically efficient representation of water flow along the ice surface, freezing of water and dripping from the lower extremities. Using a simple analysis, the microscopic model parameters may be expressed as functions of the macroscopic physical conditions. This allows the analysis of the ice formation process as a function of atmospheric conditions. Model verification, based on a comparison with published experimental results, demonstrates, quantitatively and qualitatively, the credibility and value of this modelling approach.

A stochastic model of global atmospheric response to enhanced greenhouse warming with cloud feedback

Abstract An atmosphere–ocean climate box model is used to examine the influence of cloud feedback on the change in the climate systems variability in response to enhanced greenhouse warming. The model consists of three nonlinear stochastic differential equations that are simplified forms of the first law of thermodynamics for the atmosphere and ocean and the continuity equation for the atmospheric component of the hydrological cycle. The model is driven by random fluctuations in the mean evaporative flux, which is routed and distributed among the components of the system through the fluxes of energy and moisture. The model suggests that cloud feedback can lead to the occurrence of two climatic regimes into which the present climate may evolve as a result of an enhanced greenhouse warming. In the first regime, the mean values of the model parameters, such as temperature, precipitation and cloudiness, as well as the amplitude and timescale of their fluctuations all increase moderately. In the second regime these mean values increase substantially, and the amplitude and timescale of their fluctuations rise sharply. The model also predicts the existence of climatic hysteresis; that is, for the climate system to return from either of these regimes back to the present regime, a substantial decrease in the long-wave forcing is required.

THE INFLUENCE OF GREENHOUSE WARMING ON THE ATMOSPHERIC COMPONENT OF THE HYDROLOGICAL CYCLE

An atmosphere-ocean climate box model is used to examine the influence of cloud feedback on the equilibria of the climate system. The model consists of three non-linear ordinary differential equations, which are simplified forms of the first law of thermodynamics for the atmosphere and ocean and the continuity equation for the atmospheric component of the hydrological cycle. The mass continuity equation expresses the cloud liquid water content as a function of the evaporation rate from the ocean surface and the precipitation rate. Cloud formation releases latent heat. The model clouds also absorb solar energy at a rate consistent with recent findings. The model simulates snow-ice albedo feedback, water vapour feedback and cloud feedback. The global mean precipitation and surface temperature are analysed as they respond to enhanced greenhouse warming. Model results show that cloud feedback can lead to the occurrence of multiple climate equilibria. Some of these are warmer than the present equilibrium, with increased precipitation, while others are colder, with reduced precipitation. If the cloud feedback is weak, enhanced greenhouse forcing leads to a small alteration of the present equilibrium. If the cloud feedback is strong enough, the climate system can be forced into a warmer and wetter equilibrium.

Stability of quasi-steady flow in an englacial conduit

The stability of water flow in an englacial conduit is examined with particular reference to catastrophic outbursts of water. Quasi-steady flow of water in a conduit is considered, the conduit being simultaneously enlarged by frictional heating and compressed by plastic deformation in response to the pressure difference across the tunnel wall. The conduit is fed by an ice-dammed reservoir. With the aid of simplifying assumptions, we have devised a mathematical model consisting of two time-dependent, non-linear, dimensionless ordinary differential equations, which describe the time evolution of the conduit cross-section and the water depth in the reservoir. The conditions leading to different types of time-dependent flow behaviour are examined. Regions of the parameter space where the water flow is stable and unstable have been identified. In the unstable regime, the process of emptying the reservoir has either an oscillatory or an exponential character. In the stable regime, the systems return to equilibrium, following a perturbation, also exhibits an oscillatory or exponential character. Examples of this time-dependent behaviour are presented. The model has also been used to study the influence of the glacier, conduit and reservoir geometries on the systems stability. The results show that an increase in the horizontal area of the water reservoir or an increase in the slope of the conduit enhance the likelihood of a sudden outburst. However, an increase in the glacier thickness or the conduit length stabilizes the equilibria.

The influence of the Stefan number on the fusion process under harmonic changes of the driving temperature

Abstract The influence of the Stefan number on the one-dimensional fusion process caused by harmonic changes of the air temperature has been investigated. Analytical relations for zero and infinite Stefan number are compared with numerical results for an arbitrary Stefan number. A comparison of the variations of the interface location, surface temperature and surface heat flux has been accomplished using new general expressions for the dimensionless interface location, surface heat flux and Fourier number. A new analytical relation is proposed, describing the movement of the interface for an arbitrary Stefan number and a harmonically changing surface temperature. Cases with identical thermal properties and different thermal parameters in the two phases have been considered. An average driving temperature is defined, which gives the same penetration depth in the liquid and solid phase. This is expressed as a function of the thermal properties of the two phases.