Dawn Aerospace is developing a small launch vehicle in the form of a spaceplane, which is powered by a turbopump driven rocket. To reach higher engine efficiency and save weight, there is a need for a small highly-power dense turbine. The efficiency of small turbines strongly depends on the tip gap sizes compared to the blade height. Existing turbine loss models predict large efficiency penalties due to excessive clearance losses, caused by the relatively large tip gap over blade height ratio. To build a competitive small launch vehicle, it is necessary to develop a highly efficient turbine.The objective of the work presented here is to first analyse and then minimize the clearance losses occurring in a representative small turbine for the spaceplane by applying seals on top of the shroud. Turbine loss models presented in the literature are limited to predicting losses for labyrinth seals only. As more advanced seals, like the brush seal, are being used more regularly there is a need for more accurate modelling of clearance losses in shrouded rotors.In order to calculate the leakage through seals, first bulk flow models (BFM) were developed for the labyrinth, annular and brush seal. BFMs use the zeroth-order of a perturbation equation to calculate leakage. Two- and three-dimensional numerical models were developed to simulate the mass flow rate through the seals with the help of commercially available software. Next, the BFMs and numerical models were validated against experimental data obtained from literature. BFMs could predict leakage rates through seals with an accuracy up to 15\%, when suitable empirically determined constants/equations were used. The numerical models performed slightly worse for the annular seals with a minimum accuracy of 25\%, while good predictions were obtained for labyrinth seals and brush seals. Little difference could be seen between 2D and 3D CFD when assessing leakage through shaft seals.The turbine design of Dawn Aerospace was evaluated in CFD and compared to the loss model of Dunham\&Came. First, an unshrouded case was designed to assess the profile and secondary losses arising in the turbine. In the unshrouded case the loss model agreed with CFD. In the case of the shrouded turbine a large discrepancy existed between CFD and the loss model. The difference in loss was attributed to the fact that the loss model massively over predicted the clearance loss of the turbine, by over predicting the leakage over the shroud. A new loss model has been developed which can be used to more accurately predict the clearance loss of a turbine. This improvement is achieved by using Denton's equation for clearance loss and Dunham\&Came's equations for profile and secondary loss. Denton requires the determination of the leakage mass flow rate through the shroud. The leakage mass flow rate is dependent on the inlet, the seal and the outlet. The leakage through the shroud can be calculated with the usage of BFMs. The inlet and outlets of the shrouds are modelled as labyrinth seals while placing the actual sealing system in between. This means that now not only simple labyrinth seals can be predicted, but brush seals as well and possible other seals for which leakage equations are available. It has been shown that the model can accurately predict losses for a range of turbines. The efficiency predictions of the loss model for a range of designed turbines were within 5.6\% when compared to CFD.During the sensitivity analysis on the model it was found that the influence of the inlet and outlet cavity width on the mass flow rate is significant in small turbines. Especially if the sealing mechanism on top of the shroud is simple, which is the case for an annular seal or a single finned labyrinth seal. Whenever multiple fins were adopted or the brush seal is used the inlet and outlet width become less important in the sealing system for reducing leakage rate over shrouds in small axial turbines.