As the space business is shifting from pure performances to affordability a renewed interest is growing about hybrid rocket propulsion.
Hybrid rocket motors are attractive for their inherent advantages like simplicity, reliability, safety and
reduced costs. Moreover hybrid motors are easy to throttle and thus they are ideal candidate when soft-landing or energy management capabilities are required.
This thesis is mainly involved with a theoretical/numerical study of hybrid transient behavior.
The study of transient behavior is a very important aspect in the development of affordable, efficient, stable hybrid motors, particularly when throttling and controllability is concerned.
Moreover transient behavior is important also for motors that work at a fixed operating point, not only in the prediction of ignition and shutdown phases but particularly in the analysis of instabilities.
The prediction and reduction of instabilities are one of the main challenge in hybrid propulsion (as in general in all rocket motors).
The aim of this doctoral thesis is to investigate and simulate hybrid rocket transient behavior through the development of a numerical code.
The numerical code is composed by several independent parts coupled together, each one referring to a different subsystem of the hybrid rocket motor.
Due to budget and time constraints it has not been possible to perform a dedicated experimental activity for this thesis. However the numerical results have been compared with experimental data obtained from literature, from CISAS partners (like NAMMO), and from other CISAS experimental activities performed both before and during this doctoral period.
Each subsystem of the hybrid propulsion unit and its related codes are described in a different chapter.
In the first chapter hybrid boundary layer steady combustion is introduced together with a discussion about the effect of steady hybrid regression physics on the shift of motor operating parameters with time.
In the second chapter typical necessary or intentional transient events occurring during the operation of a hybrid rocket (ignition, throttling and shutdown) are classified and described.
With chapter 3 begins the description of the several sub-models defining hybrid rocket transient behavior.
In this chapter the attention is focused on the numerical modeling of the solid grain thermal behavior.
The main object of this work is to determine the response of the solid fuel to variations of the heat flux on the surface.
A 1D numerical model of transient grain thermal response has been developed with this goal.
The model is based on the work performed by Karabeyoglu and solves the temperature profile in the direction normal to the surface.
In the first paragraph a model suited for classical polymeric fuels is developed.
In the second paragraph the grain model is coupled with the boundary layer response in order to investigate typical hybrid low frequency instabilities.
In the third paragraph a version of the original grain model suited for liquefying propellants is developed.
In fact recently a new class of fast burning fuels has been discovered at Stanford University. These fuels form a liquid layer on the melting surface during combustion, hence the term 'liquefying fuels'. Entrainment of droplets from the liquid-gas interface creates the desired high regression rate by increasing the rate of fuel mass transfer. Several researchers included people at CISAS have experimental confirmed that paraffin-based fuels burn at surface regression rates 3 to 4 times that of conventional hybrid fuels.
Others following studies showed with the use of visualization experiments the presences of waves on the liquid surfaces and droplets entrained by the gas flow, confirming original theoretical predictions.
The third paragraph is divided in three parts. In the first part the model developed to predict the regression rate and the thermal profile inside a paraffin fuel is presented. The second part deals with the phenomenology of supercritical entrainment. Finally the third part discusses the problem of the closure of the equations to take into account the space-time variability of the entrainment phenomenon.
In chapter 4 the attention is focused on the gas dynamic inside the hybrid combustion chamber. For this purpose two time-varying numerical models are developed.
The aim of these unsteady codes is to determine the transient behavior of the main parameters of the hybrid rocket motor. The combustion chamber model represents the core of the hybrid rocket motor simulation.
In fact the combustion chamber model gives directly the main parameter of a propulsion system, that is, motor thrust.
The sub-models presented in the previous and the next chapters define the input parameters for the combustion chamber model. In fact the grain model of chapter 3 determine the fuel mass flow while the tank and feed lines model of chapter 5 gives the oxidizer mass flow.
In the first part of this chapter a global 0D time-varying numerical model of the combustion chamber is developed.
The code is then coupled with the grain model described in the previous chapter to account for the transient fuel production. It follows a brief discussion about the main hybrid rocket motor characteristic times and their relative values.
In the second part a 1D time-varying numerical model of the combustion chamber is developed.
The unsteady 1D code is able to simulate all the features of the 0D code. It should add the acoustic response of the system and the spatial variation of the fluid-dynamic unknowns along the flow direction, increasing the accuracy of the results at the expense of an higher computational effort.
Chapter 5 end the description of the several sub-models of the hybrid rocket propulsion system.
Together with chapter 3 and 4 it composes the code describing hybrid rocket transient behavior.
In this chapter the attention is focused on the numerical modeling of the oxidizer path. This includes the sub-systems ahead of the combustion chamber like the pressurization system, the main tank and the feed lines. Moreover it considers also the injector elements and some aspects of droplets vaporization and atomization in the combustion chamber.
This work is complementary to the one described in chapter 3, defining the input parameters for the core of the code, that is the chamber gas-dynamic model shown in chapter 4.
The main object of this work is to determine how the feed system affects the performance parameters of the hybrid motor with time. For this purpose the prediction of several unknowns like the oxidizer mass flow, tank pressure and the amount of residual gases is obtained through the modeling of the principal subsystem behavior.
Moreover the full transient coupling between the feed system and the combustion chamber is also investigated.
This chapter is divided in three parts.
The topic of the first paragraph regards the main tank and the pressurization system.
After a brief description of the main alternatives the discussion goes on with the numerical modeling of the typical solutions adopted for hybrid rockets (i.e. pressure-regulated, blowdown and self-press).
First of all a numerical model of a pressure fed tank is developed.
The code is able to predict several parameters like masses, densities, temperatures and pressures of the gas in the ullage volume and in the pressurant tank, the pressurant mass flow and the filling level of the tank.
The model takes into account several aspects like heat losses, liquid oxidizer evaporation, eventual gas phase combustion of the pressurant gas, the use of by-pass and digital valves.
Later a numerical model of a self pressurized tank is developed.
The code is able to determine the oxidizer mass, temperature, pressure, density and the vapor/liquid volume/mass fractions during the discharge.
The numerical results are compared with experimental hot tests performed at CISAS.
The second paragraph takes into account the full transient coupling between the feed system and the combustion chamber. The main challenge is to determine the instantaneous liquid mass flow and the relation between the liquid oxidizer and the gaseous oxidizer that takes part in the hybrid motor combustion processes (i.e. droplets vaporization). In this way it is possible to simulate feed system coupled instabilities.
The third paragraph deals with the prediction of the mass flow through the injector elements. In particular the behavior of self-pressurized systems is investigated. In this case the chamber pressure is below the vapor pressure of the liquid inside the tank. Consequently cavitation and flashing occur inside the injector elements. This kind of two-phase flow with vaporization involves several important modeling issues.
Different models are compared with cold-flow tests performed at CISAS in order to check the accuracy of their predictions.
In chapter 6 some advanced techniques developed to increase the regression rate and combustion efficiency of hybrid rockets are investigated with a particular focus on their influence on the transient behavior of the motor, particularly regarding combustion instabilities. The two methods studied in this thesis are the use of a diaphragm in the midst of the grain and the use of a swirling oxidizer injection.
The reason for this choice is related to the fact that both solutions have been tested (among others) at CISAS and look very promising with respect to the overcoming of historical hybrid weaknesses.
Even if working in very different ways both methods induce a strong increase of the turbulence level and mixing of the reactants in the combustion chamber, promoting a more complete combustion and an higher heat flux on the grain surface.
Beside improving significantly hybrid performances this two techniques can affect the stability behavior of an hybrid motor directly (i.e. modifying the flowfield in the chamber) and indirectly (e.g. reducing the chamber length due to increased regression rate).
In the final chapter a summary of the activities carried out and the results achieved is given
