Solid-Fuel Pyrolysis Phenomena and Regression Rate, Part 2: Measurement Techniques

Abstract

Nomenclature A= Plasma capacitance gauge area, m 2 A p = instantaneous grain port cross-sectional area, Eq. (4), cm 2 a = classical regression law constant, Eq. (1) b = curve-fit exponent C = mechanical wave velocity, m/s C = general constant, Eq. (6) dP/dt = pressure gradient, MPa/s G 0 = oxidizer mass flux, Eq. (1), kg/cm 2 · s I (θ) = x-ray intensity arriving at the input screen of the image intensifier at an angle of θ , R/s I 0 = initial x-ray intensity, R/s k = wave number k P = wave velocity variation coefficient with respect to pressure, MPa −1 k T = wave velocity variation coefficient with respect to temperature, K −1 168 F. CAUTY ET AL. L (θ) = interaction length of x ray and material, m 0 = initial thickness, m m = linear attenuation coefficient of photoelectric absorption, m −1 m 0 = oxidizer mass flow rate, Eq. (3), kg/s n = classical regression law exponent, Eq. (1) P = pressure, MPa R f = cumulative web regression at time t f , Eq. (8), cm R p = initial grain port radius at t = 0, Eq. (4), cm R t = cumulative web regression at time t, Eq. (2), cm r = instantaneous surface regression rate, Eq. (1), cm/s r b , R b = burning rate, mm/s T = temperature, K t = time, Eq. (6), s t f = elapsed time between first and last data point, s ΔC = capacitance change ε = permittivity or dielectric constant λ = wavelength, m σ P = initial temperature sensitivity of the burning rate at constant pressure, K −1 τ = propagation time, μs Subscripts φ = phase shift, deg b = burning c = cutoff G = grain P = pressure ref = reference conditions T = temperature 0 = initial conditions

Determining the time-resolved mass flow rates of hybrid rocket fuels using laser absorption spectroscopy

“…It remains challenging to accurately evaluate the combustion efficiency of a hybrid rocket engine in real time. However, in the case of an engine that exhibits stable operation and with the exception of obvious changes during the ignition and flameout stages, the combustion efficiency is close to constant [33]. Therefore, the average combustion efficiency is typically used:…”

“…Overall, all the above methods are based on tracking variations in the geometric shape of the fuel grain without paying attention to the combustion characteristics, and cannot quantify the actual fuel participating in combustion. In recent years, a pressure-based measurement method has been proposed, which takes into account the variation of the thermodynamic properties of the fuel grain to predict thermo-fluid-dynamic parameters as a function of the regression rate [33,34]. However, it is based on many assumptions such as disregarding combustion in the post-chamber and the regression rate is constant all over the grain axis, which needs to be further verified before being widely used.…”