An experimental investigation of the regression-rate characteristics of hydroxyl-terminated polybutadiene (HTPB) solid fuel burning with oxygen was conducted using a windowed, slab-geometry hybrid rocket motor. A real-time, x-ray radiography system was used to obtain instantaneous solid-fuel regression rate data at many axial locations. Fuel temperature measurements were made using an array of 25-¹m ne-wire embedded thermocouples. The regression rates displayed a strong dependence on axial location near the motor head-end. At lower mass ux levels, thermal radiation was found to signi cantly in uence the regression rates. The regression rates were also affected by the addition of activated aluminum powder. A 20% by weight addition of activated aluminum to HTPB increased the fuel mass ux by 70% over that of pure HTPB. Correlations were developed to relate the regression rate to operating conditions and port geometry for both pure HTPB and for HTPB loaded with certain fractions of activated aluminum. Thermocouple measurements indicated that the fuel surface temperatures for pure HTPB were between 930 and 1190 K. The HTPB activation energy was estimated at 11.5 kcal/mole, suggesting that the overall regression process is governed by physical desorption of high-molecular weight fragments from the fuel surface. NomenclatureE a = activation energy, kcal/mole, see Eq. (3) G = local mass ux, kg/m 2 -s G o = oxidizer mass ux, kg/m 2 -s, see Eq. (1) h = port height between fuel slabs, m, see Eq. (1) p = pressure, MPa, see Eq. (1) Re x = Reynolds number R u = universal gas constant, kcal/mole-K, see Eq. (3) r = solid-fuel regression rate, mm/s, see Eq. (1) T s = fuel surface temperature, K, see Eq. (3) x = axial location, m, see Eq. (1) j = gas absorption coef cient, (m-MPa) ¡ 1 , see Eq.(1) q f r = fuel mass ux, g/cm 2 -s, see Eq. (3)

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A series of static engine rings, thermal pyrolysis experiments, and gas chromatograph/mass spectrometer tests were conducted to investigate the solid-fuel regression rate and heat-transfer behavior in a lab-scale hybrid rocket motor burning hydroxyl terminated polybutadiene/gaseous oxygen. A real-time, X-ray radiography system was used to determine the local, instantaneousregression rates. A data analysis program was developed to help correlate the experimental data. The semi-empirical regression-rate correlation showed that, in addition to convection, radiation from soot and variable uid properties across the boundary layer had signi cant effects on regressionrate behavior. The radiant heat ux from soot was relatively more signi cant under low mass ux and low oxidizerto-fuel ratio conditions. Radiation from CO 2 , H 2 O, and CO was quite small compared to convection and soot radiation. The nondimensional regression-rate correlation agreed with the experimental data to within § 3%. Stanton-and Nusselt-number correlations were also developed and found to depend on both ow regime and radiant heat ux. The regression-rate correlations predicted independent data from both a lab-scale tube burner and the 11-in. (28 cm) JIRAD motor to very reasonable accuracy. NomenclatureA = Arrhenius preexponential constant, mm/s B = blowing parameter, ½ f r=.Gc f =2/ or Eq. (20) B mod = modi ed blowing parameter, B exp.q 00 r =q 00 c / c = fuel speci c heat, J/kg-K c f = skin-friction coef cient c p = gas isobaric speci c heat, J/kg-K D = mass diffusivity, m 2 /s Da = Damköhler number D h = hydraulic diameter, cm E a = activation energy, kcal/mol F = function de ned in Eq. (22) G = local, bulk mass ux, kg/m 2 -s h = enthalpy, J/kg; port height, mm L = length of fuel slab, 58.4 cm Nu = Nusselt number Pr = Prandtl number p = pressure, atm or MPa q 00 = heat ux, W/m 2 R = function de ned in Eq. (34) Re = Reynolds number R u = universal gas constant, kcal/kg-K r = regression rate, mm/s St = Stanton number T = temperature, K t = time, s u = streamwise velocity component, m/s w = fuel web thickness, mm x = axial location, cm Y i = species mass fraction ® = absorptivity = heat of formation, J/kg 1H r = heat of reaction per unit mass reactants, J/kg 1H v = heat of vaporization, J/kg " = emissivity, or turbulence dissipation rate, m 2 /s 3 µ = temperature ratio, T ;avg =T s · = absorption coef cient ¹ = viscosity, Ns/m 2 ½ = density, g/cm 3 ¾ = Stefan-Boltzmann constant Subscripts avg = average c = convective eff = effective = ame g = gas phase o = oxidizer, or reference r = radiant s = surface or soot t = turbulent

This study is focused on the tangential boundary layers of a bidirectional vortex, specifically those forming at the core and the sidewall of a swirl-driven cyclonic chamber. Our analysis is based on the regularized, tangential momentum equation which is rescaled in a manner to capture the forced vortex near the chamber axis and the no slip requirement at the sidewall. After identifying the coordinate transformations needed to resolve the rapid changes in the regions of nonuniformity, two inner expansions are constructed. These expansions are then matched with the outer, free vortex solution that is sandwiched between the core and the hard wall. By combining inner and outer expansions, uniformly valid approximations are subsequently obtained for the swirl velocity, vorticity, and pressure. These are shown to be strongly influenced by a dimensionless grouping that we refer to as the vortex Reynolds number, V. This keystone parameter appears as a ratio of the mean flow Reynolds number and the product of the swirl number and the chamber aspect ratio. Based on V, several fundamental features of the bidirectional vortex are quantified. Among them are the thicknesses of the viscous core and sidewall boundary layers; these decrease with V 1/2 and V, respectively. The converse may be said of the peak velocity which increases with V 1/2. In the same vein, the angular speed of the rigid-body rotation of the forced vortex is found to be linearly proportional to V. Our laminar swirl velocity is reminiscent of Sullivan's two-cell vortex except for its additional dependence on the aspect ratio of the chamber. For the purpose of verification, theoretical predictions are compared to particle image velocimetry measurements and Navier-Stokes simulations at high vortex Reynolds numbers. By properly accounting for the turbulent eddy viscosity in the analytical model, local agreement is obtained with both laboratory measurements and computer simulations.

waterspouts, hurricanes, fire whirls, or cosmic jets (see Penner 1 and Königl 2). At the other end, one is concerned with the deliberate generation of swirl motions in thermal and physical transport applications whose performance is commensurate with the level of mixing, heat transfer, combustion, chemical dispensing, atomization, or filtration. So far different methods have been employed to trigger swirl in cylindrical or conical chambers using, for example, tangential fluid injection, inlet swirl vanes, S