A study on vortex injection in hybrid rocket engines with nitrous oxide and paraffin has been performed. The investigation followed two paths: first, the flowfield was simulated with a commercial computational fluid dynamics code; then, burn tests were performed on a laboratory-scale rocket. The computational fluid dynamics analysis had the dual purpose to help the design of the laboratory motor and to understand the physics underlying the vortex flow coupled with the combustion process compared with axial injection. Vortex injection produces a more diffuse flame in the combustion chamber and improves the mixing process of the reactants, both aspects concurring to increase the c efficiency. A helical streamline develops downstream of the injection region, and the pitch is highly influenced by combustion, which straightens the flow due to the acceleration in the axial direction imposed by the temperature rise. Experimental tests with similar geometry have been performed. Measured performance shows an increase in regression rate up to 51% and a c efficiency that rises from less than 80% with axial injection up to more than 90% with vortex injection. Moreover, a reduction of the instabilities in the chamber pressure has been measured. Nomenclature A t= nozzle throat area a = multiplication coefficient for regression rate G ox = mass flux in combustion chamber L g = grain length M f = mass of burned fuel M m = molar mass _ m tot = mean total mass flow n = exponential coefficient for regression rate O∕F = oxidizer to fuel mass ratio p, pc = pressure, mean chamber pressure R u = universal gas constant r = radial coordinate T = temperature t = time u r , u z , u θ = radial, tangential, and axial velocity z = axial coordinate μ = dynamic viscosity ρ f = density of fuel ρ = density ϕ i , ϕ e , ϕ m = initial, final, and mean diameter of the grain ω = vortex angular velocity

Paraffin-based hybrid rockets offer a great potential towards a green, safer, cheaper and more reliable access to space. As for liquids, the pressurization system has a fundamental impact on hybrid rocket motor performances. In particular, unlike liquid rockets, the oxidizer to fuel ratio cannot be directly controlled in a hybrid motor but it is dependent on the complex coupling between oxidizer mass flow (linked to pressurization) and chamber behavior (fuel regression). Pressure-fed circular port hybrid rockets are attractive for their perceived simplicity. In this paper several solutions for the pressurization system of paraffin-based hybrid rocket motors are investigated. A numerical model has been developed in order to determine the main performance parameters of the hybrid motor with time. For this purposes the prediction of oxidizer and fuel mass flows, tank and chamber pressures, thrust and residual gas in the tank is obtained through the modeling of the principal subsystem's behavior. The lumped parameter code is composed by three sub-model linked together: the combustion chamber, the oxidizer tank and the pressurant tank. In the first part of the paper several solutions are investigated like the blowdown mode, the pressure regulated mode, the use of a cavitating venturi, the use of single and multiple orifices, the use of a digital valve, the heating of the pressurant and finally the eventual combustion of the pressurant. For every technique the main aspects/issues are highlighted. In the second part an equivalent model for self-pressurization is presented. It is shown that if proper designed, self-pressurization is a simple, lightweight and high performing solution. However, because of its temperature sensitivity, for optimal performance a good thermal control is required. Nomenclatureregression rate law coefficients A = area D = diameter c v,p = specific heats (at constant volume, pressure) e = specific energy E = energy = throat erosion rate g = gravitational acceleration G = mass flux h = specific enthalpy = mass flow m = rocket mass M = mass L = length = regression rate O/F = oxidizer to fuel ratio c* = characteristic velocity 1 Ph.D. student, University of Padua, CISAS G. Colombo, francesco.barato@studenti.unipd.it, Student Member Joint Propulsion Conferences 2 = expansion ratio = density T = thrust, temperature V = volume V a = valve position p = pressure = heat flow = heat transfer coefficient R = gas constant = ratio of specific heats = efficiency = time constant x = vapor mass fraction s = specific entropy S = entropy v = velocity = tank mass factor subscripts a = ambient c = combustion chamber cv = cavitating venturi ev = evaporated i = initial, interface inj = injection f = final, frontal l = liquid n = nozzle prop = propellant ox = oxidizer fuel = fuel vap = vapor p = port pt = pressurant tank press = presurant s = exit t = tank, throat v = vapor, valve or orifice w = wall

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This paper deals with an experimental and numerical project intended to study fully tangential vortex injection in a hybrid motor of 1kN class. Due to the knowledge of the CISAS Hybrid Team, the choice for oxidizer has been pressurized nitrous oxide, while paraffin wax has been used as fuel. This investigation follows a previous project where a mixed axial/vortex device has been tested: also if an increase in performance has been observed, a non-uniform grain consumption showed an issue of such device. The work starts with a mission scenario that gives the design drivers for the subsequent preliminary design, performed with an iterative, transient and 0D numerical code. A successive step is the detailed design of the combustion chamber and test bed. The aim of the study was to investigate three objectives: vortex injection and a comparison with axial; throttling behavior at fixed mass flows (reduction of 75% and 50% of oxidizer flow); combustion chamber performance changing its configurations, in particular using inside a mixer. Performance parameters taken into account were chamber pressure oscillations, combustion efficiency and regression rate. In the preliminary phase two different issues have been discovered and solved: the first regards a chamber pressure behavior variation, linked to a too long postchamber; the second is referred to pressure pikes in the ignition phase, solved using a longer prechamber and a different ignition configuration. It has been shown that vortex injection lowers the chamber pressure oscillations respect to axial case from more than 7% down to 4%. Moreover, regression rate has been increased of 41%, and the a coefficient of its law up to 67% from axial. This last value, indeed, shows a constant behavior throttling down the oxidizer mass flow. The increase is due to the higher wall heat flux in the grain surface, given by the higher velocity and thermal gradient of the fluid. Combustion efficiency has been increased with vortex injection given by the higher turbulence flow that enhances the mixing of the reactants. Axial case showed a value of 76% of this last parameter, while vortex case went up to 90%. Coupling of injection and mixer (a diaphragm-like device inside combustion chamber) increases this value up to 96%. A cost analysis has been performed for this project, showing that hybrid propulsion is a low cost technology. NomenclatureO/F = oxidizer to fuel mass ratio a = multiplication coefficient for regression rate n = exponential coefficient for regression rate ρ f , ρ o ,ρ f = density (general oxidizer and fuel) r = radial coordinate z = axial coordinate u r , u θ , u z = radial, tangential and axial velocity ϕ i , ϕ e ,ϕ m = initial, final and mean diameter of the grain μ = dynamic viscosity M f = mass of burned fuel G ox = mass flux in combustion chamber L g = grain length ω = vortex angular velocity T = temperature t = time M m = molar mass R u = Universal gas constant p, p c = pressure, mean chamber pressure A t = nozzle throat area ṁ tot = mean total mass flow

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