Literature Review
Abstract
Innovations and modifications that produce cost reductions and enhance performance have driven the evolution of the classic solid rocket and the liquid bipropellant rocket into hybrid models that integrate the predominant solid and liquid model features into more sensical, more economical fabrications of design. The commercial spacecraft demands for aerospace propulsion have also evolved to include a market for environmentally sustainable hybrid rocket engines that has yet to fully mature to the Technology Readiness Level (TRL). Numerical modeling has been used as a tool to test the feasibility of new solid fuel types. ABS has been considered as an alternative to HTPB as the fuel grain material for hybrid rocket motors. However, the manufacture of hybrid motor fuel grains has not produced comparable thrusts to the solid rocket motor. This study investigates the port shapes of the ABS fuel grain in order to identify and measure the impact of the port shapes on the hybrid rocket motor performance.
Key Terms: hybrid rocket regression rate, hybrid fuel grains, liquid oxidizer, chamber pressure, flight vehicle testing, propellants, abs, O/F oxidizer-to-fuel ratio, payload, burn rate
2. Review of Literature
Whitmore, Peterson & Eilers (2011) presented that launch vehicles that are operationally ready and that pose less risk are required in order for the commercial market for space flights to increase in viability. Chidambaram & Kumar (2015) described hybrid rocket motors as reliable, flexible, economical and safe. Karabeyoglu, Stevens, Geyzedl, Cantwell & Micheletti (2011, p. 1) described the hybrid rocket as a technological “tipping point” in the form of small, short term investments that yield green, cost effective, safe, and high performing systems that are in demand for space missions. Further, successful commercial spacecraft are also defined as producers of safe and cost efficient flight operations within civilian environments (Whitmore et all 2011; Quigley, 2014).
2.1 Hybrid Rocket Motor Design
In the past few decades, aerospace researchers have developed a diversity of potential designs for hybrid rockets that vary in size, fuel type, benign propellant formulas and other primary components (Quigley, 2014; Costa & Vieira, 2010). The hybrid rocket performance depends heavily upon the mixing of oxidizer and fuel in the combustion chamber, a process that has been configured from many aspects of the hybrid rocket design. The commercially ideal hybrid rocket design emphasizes small sizes and payloads and decreases susceptibility to chemical explosion by storage of the fuel as solid and storage of the oxidizer as liquid and provides for desirable propulsive performance. Tian, Sun, Guo & Wang (2015) described the hybrid rocket design as reliable, less pollutant, cost efficient and safe. The hybrid design has also been found to reduce instances of propellant de-bonds or cracks and is less complex, as the hybrid rocket requires only one liquid containment and delivery system (Costa & Vieira, 2010).
Contrastingly, the futuristic potential of the hybrid rocket motor is tainted by disadvantages of the hybrid rocket design, to include the loss of efficiency in the low combustion, complex geometries, chugging, and regression rates and longitude instability (Chidambaram & Kumar, 2015; Tian et al 2015; Karabeyoglu et al 2001). Whitmore et al (2015) presented that limitations of commercial hybrid rocket motor use stem from ballistics of the inner motor which produce regression rates that are approximately 25% to 35% less than solid fuel designs with the same impulse and thrust. Solutions to low burning fuel speeds consist of approaches that use additives that are highly energetic and paraffin based materials.
2.1.1 Port Fuel Grains
The hybrid rocket motor has been designed based upon several theoretical precepts that aim to increase performance and cost efficiency. Karabeyoglu et al (2011) presented a simple single circular port design in which a LOX/parrafin-based rocket technology replaced the Orion 38 to demonstrate the capabilities of advanced hybrid rocket motor designs. The drivers for optimal specific impulse performance for the LOX/paraffin-based system consist of theoretical performance, combustion efficiency, O/F shift, nozzle erosion, and Mean O/F (Karabeyoglu et al 2011). The performance of the LOX/paraffin-based system was an indication of significant development cost savings, high fault tolerance, and inherently safe rocket engine manufacturing, storage, testing, and operation.
Whitmore, Walker, Merkley & Sobbi (2015) studied hybrid rocket motors with helical port shapes, noting disadvantages of multi-port designs to include reduced fuel regression with each additional port, uneven port burning, higher unburned mass fractions and increased instances of the feed coupling instabilities. In juxtaposition to cylindrical port shapes, the study outcomes indicated that helical fuel grains produced significantly higher regression rates which diminished as the helical shape became more cylindrical. Further, the convective heat transfer was found to be enhanced significantly and which also influenced the increased regression rate.
Kim, Lee, Kim et al (2009) and Costa & Vieira (2010) investigated the combustion components of a cylindrical multi-port fuel grain and found that the port number shifts the O/F ratio positively toward optimum value up to 4 ports and the oxidizer mass flux toward its typical range. The study included a research of the port number; distance between the ports; and pressure drop and thrust of a merging port during firing. The multi-port effect was observed by increased regression rates 4 and 5 in respect of the single port. Kim et al (2009) also determined that the PE fuel regression rate is smaller than the rate for PMMA fuel from tests of a single port.
2.2 Hybrid Rocket Motor Propulsion
Hybrid propulsion systems are characterized by a propellant component stored in the liquid phase and one stored in the solid phase; a design that enhances safety, enables restart features, and increased specific and density specific impulses in juxtaposition to solid rocket models (Tian et al 2015; Karabeyoglu et al 2001). The hybrid rocket motor may be restarted several times until the motor fuel grain has been consumed or the nozzle has become extended beyond its design life limits. Quigley (2014) contributed that hybrid rockets have thrust modulation features that are retained from the solid rocket design along with the requirement of only one propellant tank; which increases volumetric efficiency and simplicity of the hybrid. Costa & Vieira (2010) found that the use of aluminum in the propellant increases the specific impulse and induces reductions in the optimal O/F ratio.
Propulsion system optimization is complex, as combined variables are dependent upon rocket trajectory and time (Costa & Vieira, 2010). Gariani, Maggi & Glafetti (2010) described the flame structure of the hybrid rocket motor as a “complex interaction between heat transfer, fluid dynamics, radiation and chemical kinetics. The combustion process occurs within a solid fuel grain by gaseous, storable or cryogenic oxidizer injection.
Costa & Vieira (2010) conducted a preliminary analysis of the mass distribution in hybrid propulsion systems and contrasted the performances of ground launched and air launched hybrid rockets. Figure 1 shows a hybrid rocket configuration with paraffin and aluminum mix as the propulsion propellant:
Figure 1. Hybrid Rocket with Paraffin/Aluminum Propulsion Propellant (Costa & Vieira, 2010)
The hybrid propulsion systems use the propellants in different phases, with controlled oxidizer flow rates that allow for restarts (Costa & Vieira, 2010; Quigley, 2014). Further, as the port size of the hybrid model increases, the fuel burn rate decreases, irrespective of the oxidizer flux.
2.3 ABS and Average Regression Rate on Gox
The low regression rate is a setback of hybrid rocket design in that combustion depends upon a slow fuel melting mechanism. Kim et al (2009) agreed that the low fuel burning flow that results from low regression rates is a primary setback of hybrid rocket motors; particularly for use in commercial developments. However, Direct Digital Manufacturing (DDM) technology has added potential to revolutionize hybrid rocket fuel grain fabrication due to advancements in robotics and factory automation (Whitmore et al 2011).
Regression rate improvement strategies include heat transfer improvements by perturbed flow; improvements to the injector design, and energetic additives to the (Chidambaram & Kumar, 2015; Whitmore et al 2015). Tian et al (2015) deployed two types of grain configuration into one chamber in order to improve the efficiency of combustion and the regression rate.
Hydroxyl-terminated polybutadiene (HTPB) is a common thermosetting polymer that is used as a binder for the solid propellant fuel grains. Acrylonitrilebutadiene-styrene (ABS) is an alternative thermoplastic that can be produced in a cost efficient manner and in a diversity of shapes (Whitmore et al 2011). Industrial (ABS) products consist primarily of butadiene, styrene and acrylonitrile.
ABS fuel grains increase the regression rate of hybrid rocket fuel grains by increasing surface area. Quigley (2014) used an ABS/Nitrous Oxide rocket to explore the versatility, economy, safety and durability of hybrid rockets. The study outcomes validated the nozzle design which can be used for 3D printed and regeneratively cooled nozzles for hybrid rocket engines and aft-end vortex oxidizer injections to enhance regression rates.
Tian et al (2015) concluded that segmented grain configurations increase the after-section grain regression rates and reshapes the distributions on surfaces. The regression rate may be measured by a weighting method and also by direct measurement. Marxman & Gilbert (1963) presented that hybrid rocket motor average regression rates increase exponentially with oxidizer mass flux, which is derived by:
r ̇ = a · G ̇ nox
where G ̇ nox represents the oxidizer mass flux. The n exponent represents the 0.5 to 0.8 range. The oxidizer mass flux is calculated by the division of oxidizer mass flow rate by port gross sectional areas.
Chidambaram & Kumar (2015) conducted a numerical study of the outcomes for solid oxidizers and mixed fuel grains on the performance of a GOX hybrid rocket motor. The effect of the Gox regression rate was also considered which measured as a constant 132 kg/(m2s). The research consisted of simulations and parametric investigations in order to discover effects of grain scaling for specified compositions. The scaling revealed that grains with different port diameters exhibit specific pulse performances that are similar when the inlet Gox and port L/D ration are maintained. The outcomes of the study indicated that AP pyrolysis products and decomposition “react with fuel vapors which form premixed flames near the surface”, increasing the heat feedback and enhancing the rate of regression (Chidambaram & Kumar, 2015, p. 15). Reductions in the mean regression rate were found as the grain port diameter increased. Further, the outcomes also indicated that C* enhancements are limited to fuel grains with L/D<18 as a result of oxygen depletion. Gariani et al (2010) concluded that regression rate studies that have been based upon a classic analysis of hybrid combustion that only assumes boundary layers is insufficient and demands more detailed analyses. 2.4 Numerical Models
The reliable numerical tool can analyze combustion, investigations of fuel formulations, and estimations of the hybrid engine performance. The applications for Computational Fluid Dynamics (CFD) algorithms have increased in regard to chemically reacting flow modeling, particularly for modeling transonic aerodynamic flows. However, Venkateswaran et al (2001) concluded that CFD algorithms are challenged by multi-phase flows due to liquid phase incompressible flow, vapor phase low speed compressible flow, and two phase transonic and supersonic flows.
The 3D numerical models are created with turbulence, fluid dynamics, gas phase combustions and solid fuel pyrolysis (Tian et al 2015). Venkateswaran & Merkle’s (2000) computational model provided a numerical simulation for the hybrid rocket engine flow field. Cheng’s et al numerical model solved the Naiver-Stokes equations using a Lagrangian-Eulerian platform which solved for the 3D flow field for two hybrid motors and a number of port configurations.
Numerical tools have played a primary role in modifications and innovations to small space craft design. Issues such as stiffness in the presence of high aspect ratio cells have been addressed through modifications by algorithm and combustion issues that consist of strong effects that are non-linear and that are highly significant at the beginning of the computation (Venkateswaran & Merkle, 2000; Tian et al 2015). Here, the algorithm may provide convergence that is efficient for solving practical combustion issues in light of turbulence, dominant viscous effects, combustion heat release, and grid-stretching.
The numerical model created by Marxman & Gilbert (1963) excludes considerations for finite-rate chemistry, operating conditions, and chamber pressure. However, Ramakrishna et al (2002) conducted a numerical study of composite AP sandwich propellant in which 5 step reaction approximated the solid pyrolysis and gas phase chemical reactions.
2.4.1 k-ε turbulence model
The k-ε turbulence model was developed in the 1970s as the outcome of the equations for k and for ε along with the eddy-viscosity stress-strain association where ε constitutes the dissipation rate for k (Ramakrishna & Mukunda, 2002; Scott-Pomerantz, 2004). The k-ε model produces stable, convergent calculations, feasible predictions for the flows, and the implementation of the k-ε model is relatively simple. The rate of dissipation per unit mass for ε can be defined as:
If k and ε both are known, the turbulent viscosity can be modeled as:
where k represents turbulent kinetic energy and ε represents the turbulent energy dissipation rate with all others as positive constants and can be derived from Naiver-Stokes equations (Ramakrishna & Mukunda, 2002; Scott-Pomerantz, 2004). However, the k-ε model has produced unstable predictions for rotating, unconfined, and swirling flows and have been classified as valid for only fully turbulent flows. The multi-phase flows are associated with several applications to include cavitation, sprays and heat exchange. Further, the computations encompass a diversity of levels for modeling that apply to both compressible and incompressible flow regimes.
2.5 Combustion Efficiency
Hybrid rocket combustion depends upon the nature of the fuel and is driven primarily by boundary-layer fluid mechanics whereas the regression rate is derived from the boundary-layer heat transfer. Combustion takes place above the fuel surface in the boundary layer. Mechanisms that exist within the combustion process include fuel sublimation, oxidizer gasification, gaseous fuel diffusion, and flame chemical reactions. Lower regression rates increase the high oxidizer-to-fuel (O/F) ratios, which provoke unstable combustion along with nozzle erosion, motor duty cycle reductions, and erosive burning (Whitmore et al (2015).
Kim et al (2009) investigated the impact of fuel type, port distance, and port number on the regression rate along with the merging between ports in regard to both small and large combustors. A comparison was made between the small scale grain and multi-port large scale which yielded an overall regression to oxidizer flux for the non-merging large scale grain. The oxidizer mass flux can be defined as:
where Rpi represents the initial port radius, Rpf represents the final port radius, and N represents port number. A gap of significant size was observed for oxidizer mass flux. Further, high pressure radiative heat in low range oxidizer mass flux increases the regression rate in multi-port environments (Kim et al 2009). Figure 2 shows the overall regression rate curve is irrespective to the port number change, which fluctuates between 1 and 5:
Figure 2. Overall Regression versus Oxidizer Mass Flux: Large Motor
Here, the port number is proportional to the fuel burning mass under conditions where no merging events exist between the adjacent ports. Tian et al (2015) concluded that grain length combinations play a significant role in the adjustments of oxidizer-to-fuel ratios in segmented grain motors. Whitmore et al (2015) contributed that increases to the oxidizer mass flux may increase fuel regression rates with the effect of limitations at higher flux rates.
Gariani et al (2010) presented a combustion model for flame structure simulation that is typically characterized in the hybrid rocket. Typical outcomes were recorded for combustion process dependence on the rate of oxidizer mass flow. A model of particle combustion is developed from Beckstead’s Law with outcomes from a four particle test case.
Karabeyoglu et al (2001) also contributed that, according to classic theory of hybrid combustion, a hydrodynamically unstable layer leads to significant amounts of droplet entrainment that travels from the melt layer to the gas stream. A linear stability treatment highlighted the possibility that hybrid melt layers may develop instabilities that are insufficient to invoke the entrainment process (Karabeyoglu et al 2001). The linear stability theory applies to hybrid propellants which form liquid layers upon the fuel grain and has also been used to test other materials in the same capacity. Karabeyoglu et al (2001) concluded that extra mass transfer may increase regression rates by an order of magnitude that is larger than the estimations derived by using classical theory due to reductions in heat gasification, blocking factors in the boundary layer, and high heat transfers.
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