Vortex Shedding Influence on Hybrid Rocket Pressure Oscillations and Combustion Efficiency

Abstract

Numerical simulation is performed and compared with a firing test of an H 2 O 2 ∕polyethylene hybrid rocket engine equipped with a catalyzer. The simulation is performed assuming an axisymmetric flow, unsteady Reynolds-averaged Navier-Stokes equations are solved based on a single-phase flow. Stable pressure oscillations are observed during the firing test and could be explained by the simulation with the formation of large-scale vortices at the end of the fuel grain and in the postcombustion chamber. These vortices transport unburnt fuel to the nozzle and play a major role in the mixing process in the postchamber. Two semi-empirical approaches are applied and provide a good order of magnitude for the frequency and frequency shift during the firing test. Another simulation has been performed with an added oxidizer postchamber injection. It revealed that small-scale vortices along the fuel grain in the baseline case are probably generated by the oscillatory motion of the flow due to pressure fluctuations in the engine. Nomenclature C μ = turbulence model constant c = speed of sound, m · s −1 c th = theoretical characteristic velocity, m · s −1 D = fuel port diameter, m D t = nozzle throat diameter, m f = frequency, Hz k = turbulence kinetic energy, m 2 · s −2 k Ross = ratio of vortex transport velocity to freestream velocity L = total combustion chamber length, m L f = fuel grain length, m L pre ch = length of the prechamber, m L Ross = distance between shear layer initiation and impingement point, m l = exhaust nozzle length, m M = Mach number m = stage number (number of coherent structures) _ m = mass flow rate, kg · s −1 O∕F= oxidizer-to-fuel mixture ratio p = pressure, Pa Q = Q criterion, rad 2 · s −2 R = specific gas constant, J · kg −1 · K −1 R f = fuel port radius, m r = distance from wall, m S = symmetric part of velocity gradient tensor S D = Strouhal number based on end-port diameter T = temperature, K T Ross = period, s U = freestream velocity, m · s −1 U vortex = vortex transport velocity, m · s −1 V = combustion port total volume, m 3 V x = axial velocity, m · s −1 x = axial position, m Y = mass fraction y = radial position, where y equal to zero is the axis, m α = empirical constant Δt = correction factor, s η c = combustion efficiency κ = von Kármán constant ρ = density, kg · m −3 τ bl = boundary-layer delay time, s ψ = function of isentropic coefficient Ω = skew-symmetric part of velocity gradient tensor ω = turbulence specific dissipation rate, s −1 Subscripts 1L = first longitudinal acoustic mode end = end of firing test H = Helmholtz mode hy = hybrid intrinsic instability ini = beginning of firing test ox = oxidizer

Effect of Protrusion on Combustion Stability of Hybrid Rocket Motor

“…Their studies were mainly focused on the formation of the large-scale vortices in the post-combustion chamber and its influence on small-scale vortices formed near the fuel surface as a result of the cross-flow of fuel and axially convicted product gases. Messineo et al [38] further studied the frequency shifts and jumps of hydrodynamic instabilities provoked by the vortex shedding in a hybrid rocket motor. French research group ONERA reported that the use of protrusions or diaphragms can significantly suppress combustion instabilities [12].…”

Modeling of High Density Polyethylene Regression Rate in the Simulation of Hybrid Rocket Flowfields

“…In fact, when the pyrolysis reaction rates were obtained from thermogravimetric analyses, they were expressed in terms of reaction speeds with a pre-exponential factor A in sec −1 , while the pre-exponential constant A of Equation (16) was expressed in m/s and was obtained from curve fitting of surface regression experiments. When the form of Equation 14was used, a pre-exponential termÂ, which varied with temperature, could be computed from the pre-exponential factor, the fuel thermal diffusivity, and the non-dimensional regression rate from Equation (15). Tables 5 and 6 list the activation energy and the pre-exponential constant (see Table 5) or the pre-exponential factor (see Table 6) for the different HDPE pyrolysis laws.…”

“…Indeed, the extension of those models to new motors that can be different in geometry, scale, etc., is hardly possible without the availability of existing experimental data for each motor. For these reasons, there is a renewed interest in the development of more accurate and advanced models based on Computational Fluid Dynamics (CFD) [3][4][5][6][7][8][9][10][11][12][13][14][15] that are capable of representing more accurately the physico-chemical phenomena involved. The numerical modeling of the fluid dynamics and the combustion process in the fuel port area and nozzle of a hybrid rocket is a challenging task as it involves strongly-interacting multiphysics processes such as fluid dynamics, fuel pyrolysis [16,17], atomization and vaporization of the oxidizer, mixing and combustion in the gas phase [11][12][13]18], thermochemical erosion of the nozzle [3,19], particulate formation, and the radiative characteristics of the flame.…”

“…The in-house computational tool used for the simulations, and its gas-surface interaction capability has been validated for high-speed re-entry flows [24], for the analysis of Hydroxyl-Terminated Polybutadiene (HTPB) fuel grains [3,4,25], and for hybrid rocket nozzle thermal protection systems' ablation [3,19,26]. Recent literature works focusing on HDPE fuel grains in hybrid rockets either used commercial CFD tools with user-defined functions to compute the fuel mass flux as a function of the wall heat flux [8,14] or in-house CFD code [15] with imposed fuel mass flux using the mean regression rates measured during the firing test. Thermal radiation was not taken into account in [14,15].…”

“…Recent literature works focusing on HDPE fuel grains in hybrid rockets either used commercial CFD tools with user-defined functions to compute the fuel mass flux as a function of the wall heat flux [8,14] or in-house CFD code [15] with imposed fuel mass flux using the mean regression rates measured during the firing test. Thermal radiation was not taken into account in [14,15]. Interestingly, the work in [8] showed that the regression rate was underestimated by 30% for high-density polyethylene grains when radiative heat exchange was not accounted for.…”