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Evaluation of the Homologous Series of Normal Alkanes As Hybrid

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Evaluation of the Homologous Series of Normal Alkanes As Hybrid 41st AIAA/ASME/SAE/ASEE Joint Propulsion Conference & Exhibit AIAA 2005-3908 10 - 13 July 2005, Tucson, Arizona 41st AIAA/ASME/ASEE Joint Propulsion Conference, Tucson AZ, July 2005 AIAA 2005-3908 EVALUATION OF HOMOLOGOUS SERIES OF NORMAL-ALKANES AS HYBRID ROCKET FUELS M. Arif Karabeyoglu*, Brian J. Cantwell‡, and Jose Stevens¶ Stanford University Stanford, CA and Space Propulsion Group Inc. Sunnyvale, CA Abstract The liquid layer hybrid combustion theory which was developed to predict the regression rate behavior of hybrid rocket fuels burning by forming a liquid layer on their surfaces has been improved. In the enhanced version of the theory, the regression rate equations are cast in a non-dimensional format, normalized by the classical regression rate, and a universal law for the non-dimensional regression rate has been derived. Comprehensive prediction methods for the surface temperature have been developed for the subcritical and the supercritical operating conditions for the molten fuel. Note that each regime is quite different in terms of the underlying surface phenomenon. In the subcritical operation, the temperature is dictated by the physical phase transformation process whereas in the supercritical case, pyrolysis chemistry governs the surface phenomenon. The enhanced theory has been applied to the homologous series of normal alkanes (C2H2n+2) which are fully saturated hydrocarbons with varying numbers of carbon atoms. It has been demonstrated that the regression rate predicted by the theory matches the data obtained from the motor tests with reasonable accuracy. The motor test data used in the comparison was based on a wide range of practical fuel systems composed of n-alkane molecules including liquid pentane (n=5), paraffin waxes (n=28-32), PE waxes (n=60-80) and, finally, the high density polyethylene polymer (n > 100,000). 1. Nomenclature Ev : Activation energy for viscous flow Fr : Heat transfer correction factor for surface Acc : Evaporation equation coefficient roughness aent : Entrainment coefficient G , Gox : Local, instantaneous mass flux, oxidizer al : Average gray body absorption coefficient mass flux in the liquid phase h : Melt layer thickness a p : Pyrolysis reaction rate coefficient for the hm , he : Effective heats Arrhenius form hs , hb : Enthalpies at the surface and flame at : Thickness parameter hv : Effective heat of gasification B , Bg : Blowing parameter and evaporation I , I p : Reaction layer integrals blowing parameter K: Entrainment parameter coefficient B1 , B2 , B3 : Thermal variables k : Boltzmann’s constant, reaction exponent C : Specific heat k p : Pyrolysis reaction rate coefficient C , C : Blowing correction coefficients B1 B2 Lm , Lv : Latent heat of melting and vaporization C f , C fo : Skin friction coefficient with and without L : Latent heat of vaporization at the normal v,Tb blowing boiling temperature C , C : Stanton number with and without blowing H Ho M cr : Critical molecular weight for Ea : Activation energy for pyrolysis entanglement * President/CTO, Space Propulsion Group Inc., Consulting Professor, Stanford University, Member AIAA ‡Chairman and Edward C. Wells Professor, Dept. of Aeronautics and Astronautics, Stanford University, Fellow AIAA ¶ Senior Engineer, Space Propulsion Group Inc. 1 American Institute of Aeronautics and Astronautics Copyright © 2005 by Arif Karabeyoglu. Published by the American Institute of Aeronautics and Astronautics, Inc., with permission. AIAA 2005-3908 M m : Molecular weight of the monomer Tmelt : Effective temperature of the melt layer M w : Molecular weight of the alkane CnH2n+2 Tp : Temperature at which the pyrolysis m& cond : Condensation mass flux into fuel surface reactions start m& ent : Entrainment component of mass flux Tsolid : Effective temperature of the solid from fuel surface u: Temperature gradient variable Y: Quantity predicted by the ABC method m& evap : Evaporation mass flux from fuel surface x p , xl , xs : Normal distance in the pyrolysis, liquid m& v : Net vaporization mass flux from fuel surface and solid zones Y f : Fuel mass fraction N a : Avogadro’s number n: Carbon number Y fb : Fuel mass fraction at the flame n : Effective carbon number of the pyrolysis e Y fs : Fuel mass fraction at the surface products Yo , Y∞,0 : ABC method parameters no : Offset carbon number for the ABC z : Axial distance along the port prediction method α : Mass flux exponent n : Number density of the molecules on unit σ α , α : Reaction layer thickness variables surface 1 2 β : Thickness exponent, ABC prediction ()O / F : Oxidizer to fuel ratio at the flame f method parameter PD: Polydispersity δ l : Characteristic thermal thickness in liquid Pa : Pressure for normal boiling temperature, 1 atm δ p : Thickness of the pyrolysis layer Pc : Chamber pressure δ r : Thickness of the radiation absorption Pcr : Critical pressure layer (1 al ) Pf : Partial pressure of fuel at the surface IG ∆H f ,298 : Heat of formation of the ideal gas at 298 Q& r , Q&c : Radiative and convective heat flux at the K surface s ∆H f ,Ta : Heat of formation of the solid at ambient Q& : Total heat flux at the surface s temperature q p : Heat of pyrolysis ∆h : Enthalpy difference between the flame and the surface Rent : Entrainment parameter ∆Yo , ∆Y∞ : ABC method parameters Rhv , Rhe : Ratio of effective heat of gasifications for entrainment and vaporization ε : Activation energy for evaporation per molecule R : Ratio of thermal to radiative thickness in l φ ,φ : Non-dimensional regression rate the liquid ent parameters, total and entrainment Ru : Universal gas constant φv , φcl : Non-dimensional regression rate r& : Total regression rate r : Regression rate predicted by classical parameters, vaporization and classical &cl γ : ABC method parameter theory κ : Thermal diffusivity ()r&cl ref : Regression rate for the HDPE polymer λl : Thermal conductivity r&ent , r&v : Entrainment and vaporization µ : Viscosity components of the regression rate µ : Molecular mass 2s : Number of quadratic terms among which mol the activation energy is distributed µTg , µcr : Glass transition and critical viscosities T: Temperature υ : Oscillation frequency of the molecules in Ta : Ambient temperature the liquid phase Tb : Normal boiling temperature θ : Non-dimensional temperature ρ : Density Tg : Average gas phase temperature, glass transition temperature ρs : Solid density Tm ,Ts : Melting and surface temperatures σ : Surface tension 2 American Institute of Aeronautics and Astronautics AIAA 2005-3908 ψ : Non-dimensional thickness parameter by materials that are solids at standard conditions if ζ : Temperature difference variable they form a low viscosity melt layer at the combustion surface. Subscripts: In fact, increased regression rates by several hundred ent : Entrainment percent have been observed with solid cryogenic g : Gas hybrids by researchers at the Air Force Research l : Liquid Laboratory (AFRL)2,3,4 and ORBITEC5,6. The AFRL ox : Oxidizer program was concentrated on burning several frozen s: Surface organic liquids including normal pentane with gaseous oxygen in a small test motor. As discussed in Superscripts: references 2 and 3, the measured regression rates for ^ : Molar based quantity cryogenic pentane are 3-4 times larger than the - : Non-dimensional quantity reported regression rates for the conventional fuel, HTPB, under the same oxidizer mass flux condition. 2. Introduction Similarly, ORBITEC conducted tests using solidified Despite their safety and cost advantages over solid and kerosene and methane with gaseous oxygen and liquid systems, conventional hybrid rockets possess solidified oxygen with gaseous methane (i.e. a reverse one very significant shortcoming: very low fuel hybrid configuration) with small AFRL scale motors. regression rates. For many practical applications, this In the process of developing a production technique for leads to a complex, multi-port grain design such as the frozen methane fuel grains, ORBITEC has also commonly used wagon wheel configuration. The multi- performed a limited number of tests with a low port design presents serious shortcomings, which molecular weight paraffin wax. The oxidizer mass significantly degrade the overall performance, fluxes corresponding to the measured regression rates reliability and cost effectiveness of a hybrid propulsion for the paraffin tests were not reported. Similar to the system. AFRL results, solid kerosene and methane showed very high burning rates relative to the polymeric Fundamentally, the limit on regression rate for classical hybrids. However regression rate data for conventional hybrid fuels is set by the physical methane and kerosene is not adequate to make a phenomena of heat and mass transfer from the meaningful comparison with the other well studied relatively remote flame zone to the fuel surface1. Heat hybrid fuels. transfer to the fuel surface is further reduced by the well-known “Blocking Effect” which is induced by the The main conclusion from these various experiments is radial blowing of the gas from the fuel surface at that the regression rates for cryogenic propellants are relatively high velocities. As a consequence, the many times higher than for conventional hybrids. This regression rates of modern hybrids that utilize observation cannot be explained by a lower heat of polymers as the fuel are much lower than conventional vaporization, which is insufficient to account for the solid rocket burning rates. observed regression rate increase. Recall that in the classical regression
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