The growing environmental concerns has put a lot of political & ethical pressure on the conventional industrial practices. The research community is ever so eager to investigate new technologies that can offer an efficient and environmentally sound solution to the issues caused by the polluting industrial processes. One of the potential solution is an Organic Rankine Cycle (ORC) which is proven to be an effective technology to efficiently extract energy from low-temperature sources. The ORC is basically a Rankine cycle but employs a high molecular weight organic fluid as the energy carrier. The peculiar non-classical gas dynamics behaviour of these fluids during dry expansion close to the vapour saturation line (in the dense gas region) poses certain challenges on the turbine design. Furthermore, the low speed of sound in organic fluids and high expansion ratio required in an ORC turbine leads to highly supersonic flows in the turbine. Such high speed flows within a turbine stage are susceptible to high shock losses, if necessary corrective steps are not taken during early design phase. This has sparked a wave of interest in the scientific community to come up with an efficient supersonic ORC turbine design guidelines. The design of a supersonic turbine rotor is crucial to ensure efficient performance of the turbine. In the mid-20th century, a supersonic impulse rotor design methodology for axial turbines was proposed that boasts shock-free turning of supersonic flows using the vortex-flow theory. This procedure relies on Method of Characteristics (MOC) to solve hyperbolic governing PDEs. The method got enriched later with the capability to account for dense gas effects on the rotor geometry which is essential for ORC applications. However, there are no such design guidelines available in the literature to generate a radial rotor blade especially for supersonic flows. The conventional 1D preliminary design methods, generally available for radial rotor blades, are not very reliable in supersonic flow regime. This calls for a novel design philosophy for supersonic radial rotors that accounts for supersonic flow phenomenon early in the design phase to ensure efficient turbine performance. The objective of this thesis is to put forth a design methodology for supersonic radial rotors that acknowledges the flow equations in the design procedure. The proposed design ideology is to extend the supersonic axial rotor design procedure by including the fictitious forces' effects in the governing equations to generate a radial rotor using MOC. These pseudo forces (Centrifugal & Coriolis) are experienced by the flow in the radial runner if seen from the rotor's rotating frame of reference. Furthermore, the dense gas effects are also included in the design using the properties from CoolProp library. A design tool is developed in PYTHON that implements the aforementioned ideology in the design procedure. This thesis takes the first step towards developing a fully functional design methodology for supersonic radial rotors. Therefore, a simple case of a constant force's influence on the rotor geometry is studied in this work and compared with the CFD simulations in both perfect & dense gas region. Future research will focus on understanding the complex behaviour of organic fluids in the presence of an external force and modify the design procedure accordingly.

Organic Rankine Cycles (ORCs) are one of the technologies that can play an important role in the reduction of green house emissions. By converting low temperature energy sources in electricity, they are suitable for the exploitation of renewable sources (as solar and geothermal) and industrial waste heat. One of the most critical components in ORCs is the gas turbine, which usually has a radial inflow and one single expansion stage. The difficulties of the turbine design are related to real gas effects of the working fluids (organic compounds) and high expansion ratios, which lead to a supersonic flow at the turbine exit. The objective of this work is to develop a blade design methodology for a transonic turbine rotor. This is done by setting the focus on the blade passage and shaping it as a rotating nozzle. First, theory of rotating nozzles is developed, assuming the flow to be one dimensional and isentropic. Relations with respect to chocked conditions and the analytic solution to the flowfield are derived. Afterwards, the blade designmethodology is developed based on the rotating nozzle theory. Inputs of the methodology are total conditions, mass flowand static pressure at the rotor inlet, static pressure at the rotor outlet. Both the theory developed and the blade design methodology are validated. The relations derived for a one dimensional flow through an isentropic nozzle are valid for an ideal gas, while validation for real gas is not carried out. The location of the physical throat and its cross sectional area are determined and the analytic solution method of the flow field is proved to be precise. The blade design methodology is based on a one dimensional approximation and represents a first step towards a more precise blade design: the flow conditions along the nozzle mid line follow the expected trend. However, the boundary conditions are not respected and the flow varies considerably far from the mid line. Additional levels of complexity (as 2D approximation) have to be implemented in future work.