The Ekman spiral is described by a coupled system of differential equations originally discussed by Walfrid Ekman (Ekman, 1905). This system is a simplified version of the Navier­Stokes equations. The differential equations, as discussed in Ekman’s paper, concern the currents of the ocean. However, it is also possible to interpret these equations so as to describe and predict the flow of wind. The research as presented is not only inspired by Walfrid Ekman’s original paper, but also by the master thesis from de Jong (2021). The main contribution of this thesis is to include the influence of a constant vertical wind speed on the classical Ekman spiral. After stuyding the classical Ekman spiral, the inclusion of a constant vertical wind speed is done step­wise. First, the vertical wind speed is discussed without having any vertical Coriolis forces. The classical Ekman spiral and the Ekman spiral with vertical wind, but no vertical Coriolis force, were solved exactly. Then, the vertical wind speed is included fully, giving rise to a non­linear coupled system of differential equations. For the non­linear system, an algorithm for solving it analytically using a general perturbation method is proposed. Next, the hodograph of the non­linear equations of motion including a constant vertical wind speed, is made using Euler’s Explicit numerical method and a shooting problem is solved.

Decreasing NOx emissions is becoming increasingly important as it has many lifechanging implications on humanity and nature. In this work several models were constructed to simulate the combustion of methane in a cement rotary kiln, and it was investigated whether oxygen-enhanced combustion leads to less NO_x production for the obtained models. This was done using the Cantera software package with Python. Starting off with a single zero-dimensional reactor equipped with a reduced one-step global reaction mechanism, which was expanded to include two-step and four-step reaction mechanisms. Combustion inside this homogeneous reactor was simulated for various stoichiometric conditions for an initial temperature of 1000K. Subsequently, a one-dimensional model of chained reactors to simulate flow was considered, equipped with both the two-step and four-step mechanisms. This was realized using the scalar convection-diffusion equation to compute the flow throughout the reactor. All aforementioned models were adjusted to replace air with oxygen-enhanced air, containing higher levels of oxygen for every iteration. The simulated
temperature evolution was examined using the exponential relationship of temperature and thermal NO_x.