## 1 Introduction
Generally, the design objective is to maximize the volume loading (defined as the fuel volume divided by the chamber envelope volume), avoiding solutions that lead to a fuel-grain-length-to-diameter ratio (L/D) too low or too high [42; 43; 44], which negatively affects packaging and inert mass. Regression rate tailoring has been investigated by using computational fluid dynamics (CFD) tools and by performing experimental tests [45], showing the possibility of changing grain consumption by over 50% by varying the injection swirl number while keeping high combustion efficiencies. The most advanced hybrid rocket simulations are able to estimate the regression rate directly from the internal flowfield through mass, species and heat balances at the fuel surface, both for classical fuels [46; 47] and also the more complex liquefying fuels [48; 49; 50]. Swirl injection has been also simulated numerically [51], confirming its peculiar flowfield and characteristics. CFD simulations are an effective tool to rapidly analyze multiple scenarios, providing detailed comparisons of the results. However, their reliability is highly dependent on the associated validation tests [52], which limit results generalization to different parameters, propellants and/or configurations. Thus, experimental tests are still a necessary parallel choice, although more time consuming and expensive. The experimental variation of the \(SN\) is enabled by the geometrical swirl number (\(SN_{g}\)). The \(SN_{g}\) is defined as the reference swirl number at the injection, and it depends only on the geometrical characteristics of the swirl injector plate. It is calculated using the following formula [53]:  
\[SN_{g}=\frac{R_{inj}(R_{inj}-R_{h})}{NR_{h}^{2}} \tag{2}\]  
The \(SN_{g}\) is a useful parameter to perform the regression rate tailoring in vortex hybrid motors as it permits an easy and direct test results comparison just considering the injector plates' geometry and requires no difficult and intricate measurements of the internal flow field velocity components. In addition, previous works proved the existence of an approximately linear-like relation between the geometrical swirl number and the surface regression rate [45]. This work is part of the PHAEDRA (Paraffinic Hybrid Advanced Engine Demonstrator for Rocket Application) project coordinated by the Italian Space Agency [54]. The project aim is to develop a hybrid motor demonstrator for upper stage as reference application in order to investigate and exploit hybrid rocket engine (HRE) re-ignition capabilities, thus bringing hybrid motor technology to a large scale [55]. This paper focuses on the experimental investigation performed on a hybrid lab-scale motor to obtain the desired values of the regression rate and performance. These parameters were identified by the prime contractor Avio during the preliminary analysis phase. The study reported hereafter investigates the regression rate obtained coupling different swirl injectors with different fuel types. The experimental setup consists in a lab-scale HTP hybrid rocket motor with a single-port grain. Two different fuels blend formulations based on paraffin (named as F8 and F5) and a third HDPE classical plastic fuel are tested; one of the former (F8) is coupled with a \(SN_{g}\) greater than 2, while the latter (F5 and the HDPE) are coupled with low swirl numbers (between 0.5 and 1.0). The two paraffin blend fuels were provided by Politecnico di Milano, a partner of the project, and they were developed in previous phases of PHAEDRA. The results retrieved from the test campaign are reported in the following chapters. This study shows the great potential of having two variables (i.e., fuel formulation and \(SN_{g}\)) to tailor the fuel regression rate and optimize the combustion chamber design. Eventually, high values of combustion efficiency were obtained, even with the use of a lower \(SN_{g}\), compared with the ones found in previous literature.