Numerical Investigation of Hybrid Rocket Combustion Chamber Transient Behavior

Abstract

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

Scaling of Hybrid Rocket Motors with Swirling Oxidizer Injection

“…As a result, only one profile is needed while the others can be obtained from the first, scaling the values accordingly. If the profiles of different variables are similar, the same happens for the derivatives of those profiles [5]. Therefore, the use of the Reynolds analogy permits to obtain the heat flux, that is proportional to the thermal gradient and in turn to the enthalpy gradient, from the shear stress, that is proportional to the velocity gradient:…”

“…Furthermore, this smooth trend is also enhanced by a self-compensating mechanism: the enlargement of the port area causes a local decrease of the mass flux, that in turn leads to a local decrease of the regression rate. This is an advantage compared to the coupling among burning area, mass flow, chamber pressure and regression rate in the solid rocket motors, that can lead to a catastrophic failure due to a variation of the burning area [5].…”

“…This is an acceptable approximation, even if this is not exact in a turbulent boundary layer, due to the temporal and spatial fluctuations of the flux quantities, as was experimentally observed by Marxman who estimated the flame thickness to be about 10% of the boundary layer thickness and the flame position to be approximately 10-20% of the boundary layer thickness above the solid fuel surface, not exactly where the concentration of the combustion reactants equals the stoichiometric conditions. For hybrid rocket motor typical operating conditions the chemical reactions rate is much greater than the rate of mixing of the reactants in the turbulent flame, allowing to consider the combustion as controlled by the diffusion and as occurring with an infinite fast rate at the flame [5]. This is represented by a small Damköhler number, that is defined as the ration between the chemical time scale τ c and the turbulent time scale τ t :…”

“…This happens because enhancing the regression rate causes an increase of the fuel mass injected from the grain wall into the boundary layer, that reduces the convective heat transfer to the surface, which in turns leads to a decrease of the regression rate. This effect is called blocking effect [5,18].…”

“…This phenomenon causes the shift of the point of minimum regression rate to axial positions further downstream, because the effect of the local mass flux G on the regression rate is more important than the one of the axial position x, and thus the decrease of the local mass flux enhances the effects of the boundary layer growing [5,18].…”