The article presents the possibility of using the Cobb-Douglas production function for planning in a turbulent environment. A case study was carried out – the Cobb-Douglas function was used to examine the condition of the Polish hard coal mining industry and the progress which has been made after undertaking certain activities aimed at increasing the competitiveness of coal companies over recent years. Only the correct and confirmed identification of the causes of irregularities in the production process can allow for the introduction of effective remedies. The effectiveness of the solutions proposed by the author has been confirmed thanks to the simulation during which the impact of the proposed production strategy on the parameters of the CD function was examined. Three variants of production functions models were created and production productivity rates and marginal substitution rates were determined. The results enabled the verification of the progress of restructuring as well as identification of the origin of the observed problems and comparison of the current state with the results of analyses carried out in previous years. Scenarios of possible trend developments for the factors introduced into the function model in order to present remedial measures that could improve the process of hard coal extraction were created. The scenarios were created using the ARIMA class models. Which scenario is the most favourable was determined. A computer program, created by the author, for optimising the level and use of labor resources at the level of the entire coal company has been presented.
An important phenomenon of delta wing is the mechanism of vortex core, which indicates the increase in lifting force until the occurrence of the vortex breakdown. The computational fluid dynamics (CFD) is very helpful in visualizing and providing analysis of the detailed data. The use of turbulent models will affect the quality of results in obtaining the vortex breakdown phenomenon. This study used several models of turbulence to capture the occurrence of vortex breakdown and compare it with experiments using water tunnel test facility. The results show that all turbulence models give good results at a low angle of attack (AoA), but at a high AoA the DES model gives the results closest to experimental ones with Cl error value of about 1%. Taking into account the time required and the acceptable level of accuracy, the use of SST and k-omega models is an alternative option for use in the detection of vortex breakdown.