Experimental Measurement and Modeling of Regression Rate Phenomena in Solid Fuel Ramjet Combustors
Creators: name: Evans, Jay Vincent
Publisher: name: Purdue University Graduate School
Year: 2023
Subjects: classificationCode: 400106
subject: Hypersonic propulsion and hypersonic aerothermodynamics

description: Instantaneous fuel regression rate within a solid fuel ramjet combustor was characterized using X-ray radiography and ultrasonic transducer measurements. Experiments were performed with cylindrical, center-perforated hydroxyl-terminated polybutadiene (HTPB) fuel grains at three mass fluxes (407-561 kg/m2-s) with consistent inlet total temperatures and chamber pressures. Ultrasonic transducer measurements demonstrated changes of web thickness ranging from 7.50-9.85 mm and regression rate measurements ranging from 1.35-1.74 mm/s. Local maxima of change in web thickness due to flow reattachment and erosive burning were consistently measured with the ultrasonic transducers. Changes in port radius on the order of 8-9 mm and regression rates of approximately 1.25 mm/s were deduced from the X-ray radiography images. Structure of the flow reattachment region was evident in measurements from the X-ray radiography images captured near the combustor entrance while images captured at the mid-length of the combustor exhibited more uniform fuel regression profiles. Ultrasonic measurements of change in web thickness were consistently greater in magnitude relative to X-ray radiography measurements. X-ray radiography imaging allowed for the more accurate measurement of fuel regression with the greatest axial spatial resolution while ultrasonic transducer measurements yielded the greatest radial spatial resolution. The change in web thickness calculated with weight-based techniques yielded smaller magnitude measurements of change in web thickness relative to X-ray radiography.Time-dependent measurements of web thickness and regression rate along the port of aluminum-loaded and boron carbide-loaded, hydroxyl-terminated polybutadiene (HTPB) fuel grains were measured in a solid fuel ramjet combustor with X-ray radiography. The combustor was operated at three mass flux conditions, ranging from 397-532 kg/m2-s, with consistent chamber pressures and upstream-of-combustor total temperatures of 1313 kPa and 748 K, respectively. A cross-correlation-based edge detection scheme was used to extract the fuel grain edges within X-ray radiography images collected at 15 Hz. Cross-section photographs of the post-combustion fuel grain surfaces exhibited evidence of flow reattachment and large aft-end regression. Aluminized fuel grains exhibited average weight-based regression rates of 1.29-1.48 mm/s, and boron carbide-loaded fuel grains yielded average regression rates of 1.21-1.38 mm/s. Head-end X-ray measurements of change in port radius indicated flow reattachment, particularly for the bottom (theta = 180) edge of the fuel grain. The absolute maximum of change in port radius, which ranged between 8.56-10.31 mm for aluminized fuel grains and 8.22-9.40 mm for boron carbide-containing fuel grains, did not always coincide with the flow reattachment location. Time-averaged regression rate profiles measured with X-ray radiography were relatively uniform along the port axis but smaller in magnitude compared to the weight-based measurements; 1.17-1.35 mm/s for the aluminum-loaded fuel grains and 1.07-1.24 mm/s for the boron carbide-loaded fuel grains. Pre-ignition fuel regression, on the order of 1.5 mm, was determined to be the cause of the over-prediction of regression rate by weight-based measurements compared to X-ray measurements.The weight-based average regression rates measured in tests conducted with the axisymmetric solid fuel ramjet test article in its various configurations were compared to quantify the effects of average port air mass flux, bypass air addition, carbon black addition, and metal particle addition on regression rate. Baseline tests without an aft-mixing section or bypass air addition fuel grains containing carbon black yielded a regression rate coefficient of a = 5.33E-2 and an exponent of n = 0.50 for p4 = 1179-1298 kPa. Including an aft-mixing section without bypass air addition yielded regression rates of 0.94-1.04 mm/s due to the increased residence time. Bypass air addition of 14\% bypass ratio reduced the regression rate to 0.83-0.92 mm/s, and 30% bypass ratio reduced the regression rate to 0.80-0.82 mm/s. For otherwise equal tests, adding carbon black to the fuel grain increased the regression rates from 0.76-0.78 mm/s to 0.83-0.92 mm/s (6-21%). Aluminized fuel grains exhibited an increase in regression rate coefficient over the baseline fuel grains from a = 5.33E-2 to a = 6.30E-2 (18%), but the regression rate exponent remained at n = 0.50. Boron carbide (B4C) addition reduced the regression rate exponent to n = 0.46 but increased the regression rate coefficient to a = 7.55E-2; a 42% increase.A simplified solid fuel ramjet combustion model which includes (1) turbulent heat convection, (2) radiation, (3) radiation-coupled surface blowing, (4) unsteady sub-surface heat conduction, (5) solid fuel regression, (6) gas-phase combustion, and (7) fuel port hydrodynamics was developed for regression rate prediction over a range of combustor geometries and operating conditions. Turbulent convection was modeled with empirical correlations relating non-dimensional boundary layer transport numbers. Radiative heat transfer was estimated using modified empirical correlations for radiation in a slab hybrid rocket combustor. Hybrid rocket combustion theory was used to model surface blowing. The condensed-phase heat transfer was modeled by solving the unsteady, variable thermophysical property, regressing surface heat equation with an explicit time-integration, finite volume scheme on a non-uniform grid. A general Arrhenius expression was used to estimate the fuel regression rate. Chemical equilibrium calculations for a stoichiometric HTPB/air diffusion flame were used to model the gas-phase combustion. The port gas dynamics were modeled with compressible flow ordinary differential equations. The results of these individual physical processes were examined in detail for a high mass flux (G_air = 561 kg/m2-s) case. Experiments performed in the axisymmetric solid fuel ramjet combustor were simulated in the model, which yielded a lower regression rate versus mass flux exponent of n = 0.39 compared to the experimentally-obtained n = 0.50. A larger parameter sweep of the model yielded a mass flux exponent of n_1 = 0.30, a pressure exponent of n_2 = 0.04, and an inflow total temperature exponent of n_3 = 0.39. These exponents are less than those observed in other works, but the model successfully captured the relative influence of mass flux, chamber pressure, and inflow total temperature.A combustion diagnostic consisting of X-ray radiography and thermocouples embedded within the fuel grain was successfully applied and demonstrated in a solid fuel ramjet slab combustor. One representative test condition with an air mass flowrate of 1 kg/s, an upstream-of-combustor static pressure of 560 kPa, and an upstream-of-combustor total temperature of 639 K was examined. Changes in web thickness of approximately 4 mm and steady-state regression rates of 0.35 mm/s were measured at the thermocouple locations. Condensed-phase temperature measurements yielded fuel grain surface temperatures of 820 K and temperature profiles which were compared to theoretical Michelson profiles. The Michelson profile closely matched the thermocouple-measured temperature profile at one axial location. Sub-surface conductive heat fluxes of 0.35 MW/m2, heat fluxes required to vaporize solid fuel of 0.60 MW/m2$, and surface heat fluxes of 0.95 MW/m2$ were estimated using the condensed-phase temperature profiles.