Mathematical and numerical model of directional solidification including initial and terminal transients of the process

Abstract The, developed in this study, simple model and numerical solution of diffusion growth of the solid phase under the conditions of directional solidification allow for the effect of constituent diffusion in both liquid and solid phase and assume the process run in which (like in reality) the preset parameter is the velocity of sample (pulling velocity) at a preset temperature gradient. The solid/liquid interface velocity is not the process parameter (like it is in numerous other solutions proposed so far) but a function of this process. The effect of convection outside the diffusion layer has been included in mass balance under the assumption that in the zone of convection the mixing is complete. The above assumptions enabled solving the kinetics of growth of the solid phase (along with the diffusion field in solid and liquid phase) under the conditions of diffusion well reflecting the process run starting with the initial transient state, going through the steady state period in central part of the casting, and ending in a terminal transient state. In the numerical solution obtained by the finite difference method with variable grid dimensions, the error of the mass control balance over the whole process range was 1 -2 %

An institutional perspective on entrepreneurial ecosystems: variation, evolution, agency in and across organisational fields

Entrepreneurial ecosystems (EEs), understood as a type of organisational environment conducive to fostering high-growth and technology oriented startups, are currently deemed important for economic and employment growth. However, while the flagship case of Silicon Valley is widely researched and invoked, our knowledge of variation in how EEs develop is limited, and insufficiently theorised. In response, this thesis adopts an institutional perspective, conceptualising EEs as organisational fields, and addressing how the interplay between agency and structure result in different developmental trajectories of location-based EEs. The thesis consists of three empirical papers that examine several cases of EEs in Japan and India focused on Information and Communication Technology. The in-depth inductive studies are anchored in interview and participant observation data generated during multiple fieldwork visits. The findings illuminate key novel concepts: 1) a field development mechanism of intra-field cross-generational support (uncovered in an emerging field of Tokyo EE examined in relation to domestic large corporations); 2) a comparative framework of Varieties of Entrepreneurial Ecosystems (derived from an analysis of Tokyo and Bangalore – the biggest EEs in their respective countries); 3) an institutional infrastructure-related element of place cohesion (identified from a comparison of Osaka-Kyoto and Fukuoka – smaller EEs developing within one institutional context where the dominant EE is already present). Together, the papers show that differences in EE developmental trajectories stem from the interplay of EE stakeholders’ agency to develop a desired EE institutional infrastructure (which is similarly conceptualised across locations), and the underlying elements for such infrastructure (which can be very time- and location-specific). Particular agency-related mechanisms that are crucial to EE development, depend on the EE relations to other fields. Overall, the thesis contributes to the scholarship on EEs and organisational fields, enhancing more contextualised understanding of EEs, and suggesting how to better study fields in a comparative and interconnected perspective. </p

Kinetic model of ductile iron solidification with experimental verification

Abstract A solidification model for ductile iron, including Weibull formula for nodule count has been presented. From this model, the following can be determined: cooling curves, kinetics of austenite and eutectic nucleation, austenite and eutectic growth velocity, volume fraction, distribution of Si and P both in austenite and eutectic grain with distribution in casting section. In the developed model of nodular graphite iron casting solidification, the correctness of the mathematical model has been experimentally verified in the range of the most significant factors, which include temperature field, the value of maximum undercooling, and the graphite nodule count interrelated with the casting cross-section. Literature offers practically no data on so confronted process model and simulation program

Modelowanie metodą automatu komórkowego zmian objętości podczas krzepnięcia żeliwa z grafitem kulkowym

Volume changes of the binary Fe-C alloy with nodular graphite were forecast by means of the Cellular Automaton Finite Differences (CA-FD) model of solidification. Simulations were performed in 2D space for differing carbon content. Dependences of phase density on temperature were considered in the computations; additionally density of the liquid phase and austenite were deemed as a function of carbon concentration. Changes of the specific volume were forecast on the base of the phase volume fractions and changes of phase density. Density of modeled material was calculated as weighted average of densities of each phase.W pracy przedstawiono wyniki symulacji zmian gęstości żeliwa sferoidalnego w układzie dwuskładnikowym Fe-C, wykorzystując do tego celu model oparty na metodzie automatu komórkowego i różnic skończonych. Symulacje wykonane były dla dwuwymiarowej przestrzeni dla różnych zawartości węgla. Zmiany gęstości wszystkich faz uwzględniano jako zależności temperaturowe. Dodatkowo dla cieczy i austenitu uwzględniono też zależność gęstości od zawartości węgla. Przy obliczaniu zmian objętości właściwej układu brano pod uwagę gęstości poszczególnych faz oraz ich udział objętościowy

Numerical model of continuously cast strand and its application for simulation of continuous casting of structural steel blooms

Przedstawiono założenia wyjściowe i wyniki modelowania krzepnięcia wlewków stalowych o przekroju kwadratowym 160×160 mm odlewanych ze stali gatunku B1 w łukowej instalacji COS. Przeprowadzono modelowanie krzepnięcia wlewków. W modelowaniu wykorzystano oprogramowanie ProCAST (ESI Group). Wykazano możliwość prognozowania pola temperatury we wlewku oraz profilu przestrzennego strefy ciekłej i dwufazowej (ciekło-stałej).The input assumptions and simulation results for solidification modelling of 160×160 mm blooms produced from low alloy structural steel in the bow - type continuous casting machine are presented. The modelling of solidification was carried out by means of ProCAST software (ESI Group). The abilities of forecasting the temperature field in the cast strand as well as space distribution of liquid and two-phase (liquid and solid) fraction are shown

Computer modelling of solidification of semi-industrial square cross-section ingot using ProCAST software

Dla modelowania procesu krzepnięcia wlewka stacjonarnego wykorzystano oprogramowanie ProCAST, stosowane dotychczas w modelowaniu procesów ściśle odnoszących się do procesów odlewniczych. Przedmiotem modelowania był proces stygnięcia stacjonarnego wlewka o wymiarach 100×100×1100 mm we wlewnicy, od momentu rozpoczęcia zalewania metalu do zakończenia krzepnięcia, wraz z procesami tworzenia struktury, skurczu metalu i tworzenia jam skurczowych. Analiza porównawcza dla dwóch typów stali wskazuje na istotne różnice w polu temperatury i kinetyce wzrostu fazy zakrzepłej w trakcie procesu zalewania i krzepnięcia wlewków. Rezultaty modelowania wskazują na duże możliwości symulacji komputerowej dla odtworzenia procesu krzepnięcia wlewka, a przez to przeprowadzenia eksperymentów numerycznych dla optymalizacji technologii.For modeling of stationary ingot solidification process ProCAST software was used. So far, this software has been used in processes related strictly to foundry processes. The subject of modeling was cooling of stationary square ingot of 100×100×1100 mm in the mould, from the beginning of pouring liquid metal until the end of solidification, along with the processes of metal structure formation , metal shrinkage and formation of shrinkage cavities. The comparative analysis for two types of steel shows significant differences in temperature field and kinetics of solidified phase growth while pouring and solidification of ingots. The results of modeling show great possibilities of computer simulation for reproduction of the real solidification process, and thus for conducting numerical experiments for optimization of technology

Modelling of eutectic saturation influence on microstructure in thin wall ductile iron casting using cellular automata

The mathematical model of the globular eutectic solidification in 2D was designed. Proposed model is based on the Cellular Automaton Finite Differences (CA-FD) calculation method. Model has been used for studies of the primary austenite and of globular eutectic grains growth during the ductile iron solidification in the thin wall casting. Model takes into account, among other things, non-uniform temperature distribution in the casting wall cross-section, kinetics of the austenite and graphite grains nucleation, and non-equilibrium nature of the interphase boundary migration. Calculation of eutectic saturation influence (Sc = 0.9 - 1.1) on microstructure (austenite and graphite fraction, density of austenite and graphite grains) and temperature curves in 2 mm wall ductile iron casting has been done