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.