Addressing Propulsive Efficiency Drawbacks Associated with High Regression Rate Liquefying Hybrid Rocket Fuels Through the Modification of Thermal and Mechanical Properties

Paraffin-based liquefying hybrid rocket fuels have been shown to demonstrate significantly increased regression rates over traditional HTPB largely due to the formation of a hydrodynamically unstable melt layer. The rate of fuel mass entrainment in the combusting boundary layer is related to the dynamics of heat transfer in the melt layer along with its mechanical properties including viscosity and surface tension. Heat is transferred to the fuel grain via convection and radiation and is dispersed throughout the fuel itself through diffusive conduction. The balance of thermal flux at the fuel surface determines its temperature and governs fuel melting. Assuming little convective transfer through the melt layer, the rate fuel regression is proportional to powers of operating pressure and oxidizer mass flux though the port. It is inversely proportional to powers of fuel melt viscosity and surface tension and therefore the operating melt layer thickness. As a result, regression rate tends to increase as melting point and carbon chain length decrease. 

Raw paraffin is a translucent, waxy, brittle solid being easily penetrated by thermal radiation from the combustion zone. This leads to several issues with realistic implementations of paraffin-based fuels. In the worst case, thermal radiation fails to be absorbed by the relatively thin fuel grain and heats the fuel liner. This causes the fuel to begin melting form the outside in, causing the fuel grain to fail structurally and potentially eject unburned fuel. In the less exaggerated case, fuel mass injection increasingly outpaces the rate of oxidizer injection over the firing duration, harshly limiting the operating cycle of the motor. It also causes a departure from the optimal oxidizer to fuel ratio and performance. Using pure paraffin, this ratio is approximately 7.0 with respect to mass, making ideal performance levels difficult if not impossible to achieve due to limitations with the oxidizer feed system and mixing of fuel and oxidizer. Fuel and oxidizer are transported advectively into the thin combustion layer from opposite sides, making it difficult to effectively combust the fuel with large quantities of oxidizer.

The problems with oxidizer and fuel mixing can be partially solved using a high performance injector that creates a turbulent or swirling flow in the fuel port. An commercial X-form injector has been purchased and cold-flow tested with liquid nitrous oxide supplied by the completed oxidizer feed system. The resulting flow rate at a target operating pressure of 500 psi is approximately 175 g/sec. Using this configuration, an oxidizer to fuel ratio of approximately 2:1 is attainable. It would be necessary to increase the orifice area significantly in order to increase this ratio towards to optimal domain. However, significant metallization of the fuel using magnesium powder is shown to both increase performance and lower the optimal oxidizer to fuel ratio. For a magnesium loading of 40%, the injector orifice area still must be enlarged by a factor of 2. However, in smaller motors, there may be insufficient "residence time" in the combustion chamber for the magnesium to fully combust, lower the oxidizer to fuel ratio, and contribute favorably to the performance. Also, while opacifying the fuel and reflecting thermal radiation, magnesium also conducts heat into the fuel grain. An increase in regression rate beyond the optimal point or a structural failure of the fuel may result from high magnesium loadings. Several will be tested.

In order to improve the fuel's strength and mechanical properties during grain production, cellulose fibers will be added. Their effect on fuel density and regression performance will be characterized. An opaque fuel that is absorbent to thermal radiation at the surface is desired for an increased and pressure-dependent regression rate. Graphite and activated charcoal will be tested for this purpose. Graphite powder is expected to produce a fuel that absorbs thermal radiation but may conduct heat into the fuel grain. Activated charcoal presents a high degree of microporosity and may function as an insulator when used in the fuel. Its dark color will likely absorb heat similarly to graphite. Activated charcoal may lower the fuel density and thus density specific impulse. A combination of the additives discussed herein may vastly improve the fuel's performance and mechanical properties during grain production and firing.

Nitrous Oxide Injector Cold Flow Test

Today I performed a cold flow test of the nitrous oxide feed system. The test encompassed procedures for tank filling along with the flow of nitrous oxide through the entire system at pressure. No leaks or flaws were found in the system. The injector and forward closure also performed flawlessly.

The flow duration was approximately 4 seconds when the nitrous oxide was discharged from its tank at 750psi into the open air. Given the effective tank volume of about 1000 cm^3 and nitrous density of 1.228 g/cm^3 the flow rate was approximately 300 g/sec. Since the flow rate is proportional to the square root of the pressure drop, an operating pressure of 500psi inside the motor would produce:

Oxidizer Mass Flow Rate ~ 175 g/sec

Flow Duration ~ 7 sec

The initial core diameter of the fuel grain is approximately 1cm to begin and 3cm at the end. Averaging of the cross-sectional area using integration yields

Avg Port Area = .0003404 meters^2

Avg Port Radius = 1.04 cm

Provided with the oxidizer mass flow rate and average port area, the expected average oxidizer mass flux is found

Gox ~ 510 Kg/M^2

Given the regression equation for HTPB given by Chiaverini et al. 2001, regression rate can be found if HTPB were used as the fuel.

dr/dt HTPB = .049 * Gox^0.61

dr/dt HTPB ~ 2.19 mm/sec

The fuel grain length is approximately 35 cm and the density is about 1g/cm yielding

Fuel Mass Flow Rate ~ 50 g/sec

O/F HTPB ~ 3.45

Provided with the regression rate equation for a polymer/paraffin combination of 50% given by Tsong-Sheng Lee et al. "Combustion Characteristics of a Paraffin-Based Fuel Hybrid Rocket"

 dr/dt 50%Paraffin = .026 * Gox^0.8076

dr/dt 50%Paraffin ~ 4.00 mm/sec

Fuel Mass Flow Rate ~ 90 g/sec

O/F 50%Paraffin ~ 1.90

Ablative Precombustion Liner

An ablative liner was made in order to shield the section of motor casing surrounding the injector from the intense heat produced during firing of the rocket motor. Initially I considered graphite for this section, however, several drawbacks became apparent with this material. Graphite has a low shear strength and may crack under the high mechanical loads exerted during machining and firing considering the small thickness needed. The liner must operate in a highly oxidizer rich environment. At high temperatures, graphite is easily oxidized into carbon dioxide, leading to substantial erosion in the presented application. New liners would have to be machined prior to each firing, raising issues with cost and labor time.

A temperature resistant graphite epoxy ablative liner was selected instead. New liners are easily made in bulk and are replaced after each firing. Graphite powder was mixed with West Systems epoxy and microballoons in order to produce an opaque, thermally resistant layer 4 mm thick that will be consumed at a significantly lower rate than the fuel grain itself. A "doughnut" of APCP propellant with substantial ferric or cupric oxide content will be mounted inside the liner with high temperature RTV rubber as a pre-heater.

After the ablative coating was mixed, the volume needed to produce the necessary thickness over a length substantial enough for several liner sections was measured out. The coating was poured into a paper propellant liner tube with ends sealed with waxed paper. Next, the tubing was centered and spun axially at a high rate on my lathe in order to deposit an even 4 mm thick coat on the inside of the liner tube.

The length of coated liner tubing was cut into five even 2.25" lengths which will serve as ablative liners for individual trials. Interestingly, the microballoons separated from the graphite mixture during the centrifugation due to a difference in density. Appearing at the surface of the ablative coating, the microballoons may actually slow the rate of liner consumption due to their properties as insulators and light color, demonstrating low thermal absorption. Also, bubbles of air are forced out of the epoxy and towards surface by this process. I don't expect this to present any significant challenges with regard to bulk ablative characteristics as the bubbles only exist at the surface and don't penetrate more than 1 mm into the liner itself.

The following images demonstrate the orientation of the ablative liner with respect to the injector/forward closure. The ablative liner along with the fuel grains exist within a continuous phenolic liner tube capped at both ends with the nozzle and the forward closure.

Note that the pressure tap in the forward closure is not obscured by the ablative liner.

Injector and pressure tap positioned within the ablative liner

Pressure Transducer Calibration

After constructing the 12V power supply, I calibrated the output voltage from the transducers against simulated input pressures. Six resistors were used. The following table summarizes the results:

Calibration Resistance(Kohm)    Pressure(psi)    Transducer1(mV)    Transducer2(mV)

33                                                   1694.92               28.60                         28.26

39                                                   1434.62               24.94                         25.65

56                                                     999.80               17.13                         17.89

68                                                     823.67               13.80                         14.62

100                                                   560.51                 9.15                           9.89

180                                                   311.75                 4.66                           5.50

The following equation summarizes the relationship between resistance and pressure as given by the pressure transducer information sheet.

P=5558.781 * R^(-.99808393)

Here are the calibration curves that will be used to convert  the output voltages from the setup into internal pressures of the feed system and combustion chamber.

Pressure 1 = 54.989675 + 55.330104*P1 Voltage

Pressure 2 = 8.0671329 + 55.608625*P2 Voltage

The last data point at 33Kohm was removed from both plots since it was a considerable outlier from the trend produced by the other data points. It is acceptable to remove this point since it corresponds to a pressure well above the operating range of the motor or oxidizer feed system. 

Here is a picture of the calibration setup:

Setup

Nitrous Injector Machining

Yesterday I completed the machine work one the forward closure and nitrous injector per the specs given in the motor schematic. Here are a few images of the forward closure with the injector installed. The injector itself contains a compression fitting for the thermoplastic tubing that prevents nitrous flow prior to ignition. A pressure tap (small hole on the right side of the injector face in the image below) was drilled through the closure and adapted to 1/16" NPT in order to measure motor internal pressures and the pressure drop across the injector.

Nitrous Oxide Injector Face and Pressure Tap

Forward Closure With Nitrous Feed and Pressure Tap Threading

Fuel Additives

Several fuel additives will be investigated for favorable augmentation of the paraffin's thermal and mechanical properties. Paraffin alone is a brittle, translucent solid. This means that thermal radiation from the combustion zone is allowed to penetrate the fuel grain. radiant heating within the fuel grain can reduce the performance of the hybrid system in terms of total impulse since the paraffin will be depleted too quickly and incompletely combusted with the oxidizer. In the worst case, this radiation heats the liner and melts the fuel from the outside in. These effects make pure paraffin fuels poor for long duration firings. Also, paraffin has a propensity to crack under the mechanical loads and thermal gradients found withing a large scale hybrid rocket motor. High regression rate fuels in general exhibit problems in that the high O/F ratios required for efficient combustion often cannot be met because of limitations associated with oxidizer injection and a surplus of unburned fuel.

In theory, the addition of a light metal to the fuel could solve several of these problems, while significantly improving the density specific impulse performance of the fuel. The metal opacifies the fuel, reflecting thermal radiation, preventing it from penetrating the fuel grain. Also, the metal lowers the optimal O/F ratio in terms of characteristic velocity, meaning that the fuel can be more completely combusted with achievable oxidizer flows, allowing for increased burn durations.

 

In reality, however, the metal may not have enough "residence time" (Fintel) in the combustion chamber of a smaller motor to effectively contribute to performance. Aluminum, in particular, may not contribute substantially to performance because it forms an inhibiting oxide coating. Magnesium doesn't form an inhibiting coating and it offers a theoretical performance comparable to that of Aluminum. Magnesium will be tested as a possible additive. At the very least, the metallized propellant will reflect the majority of the thermal radiation that could compromise the fuel grain. Another drawback of metallizing the fuel is that rates of conductive heat flux into the grain are increased, possibly having a similar effect as the radiation.

Graphite is another additive that opacifies the fuel. Unlike a metal, graphite absorbs thermal radiation and transfers it to the surrounding fuel. This effect results in a higher, pressure-dependent, regression rate. The drawback is that graphite also conducts a substantial amount of heat back into the fuel grain. Activated charcoal and carbon black display similar thermal absorption properties to graphite except activated charcoal exhibits a massive surface area due to high porosity on a nano scale. Hence, activated charcoal is an effective insulator. Moreover, activated carbon's micropores provide good conditions for adsorption to occur, making it a potential catalyst in some reactions. The use of activated carbon in conjunction with nitrous oxide and a metallized fuel may speed up the combustion process, decreasing the necessary residence time for the magnesium within the motor.

Finally, the fuel grain itself can be strengthened against the mechanical and thermal loads with the addition of polymeric fibers like cellulose. Anything from dietary fiber to a cloth fiber matrix may supply this added structural integrity. These combustible additives will be investigated in the hybrid rocket's fuel grain. Adding these polymers will present unique challenges to fuel grain fabrication techniques.