Low Temperature Simulation of Subliming Boundary-Layer Flow in Jupiter Atmosphere

Abstract

A method of low temperature, approximate simulation for the sublimation of a graphite heat shield under the Jovian entry condition is studied. A set of algebraic equations was derived to approximate governing equations and boundary conditions based on the order-of-magnitude analysis. Characteristic quantities, such as wail temperature and subliming velocity, are predicted. Similarity parameters needed to simulate the most dominant phenomena of the Jovian entry flow are also given. An approximate simulation of the sublimation of a graphite heat shield is given with an air-dry ice model. The simulation with the air-dry ice model may be experimentally conducted at a lower temperature of 3000-6000 K instead of at the entry condition ot 14000 K. The rate of sublimation of the graphite predicted by the present algebraic approximation agrees to the order of magnitude with extrapolated data. The limitation of the Simulation method and its utility are discussed. Nomenclature [DL]= dimensionless variables; in general, lower case letters [DN\ = dimensional variables; in general, upper case letters A = deceleration encountered by the probe Bo ht Bo c = hydrogen (or air) and C n (or CO 2 ) gas Boltzmann number C n = refers to gas evaporated from the graphite with a molecular weight of approximately 30 C p = specific heat at constant pressure Ev a = evaporation parameter, the ratio of the latent heat of evaporation to the radiation flux [Eq.(25)] E ht E c =Eckert number of hydrogen (or air) and C n (or CO 2 ) gas [Eqs. (8) and (13)] e h ,e c = respectively, the ratio of hydrogen (or air) and C n (or CO 2 ') gas temperature boundary layer thickness to the radius L [Eq. (23) and Fig. 1] F h ,f h = [DN] and [DL], radiation flux in hydrogen (or air) boundary layer F C9 f c =[DN] and [DL] radiation flux in C n (or CO 2 ) gas boundary layer G h ,G c = inverse Froude number for hydrogen (or air) and C n (or CO 2 )gas [Eqs. (13) and (8)] k = thermal conductivity L v = latent heat of sublimation L = base radius of the graphite heat shield M -molecular weight Pr h ,Pr c = Prandtl number for hydrogen (air) and C n 'gas [Eqs. (8) and (13)] P e = equilibrium pressure of C n (or CO 2 ) vapor [Eq. (20)] P t p =[DN\ and [DL] pressure defined in Eqs. (I) and (2) Re h -hydrogen Reynolds number [Eq. (8)] Re c = C n gas Reynolds number [Eq, (13)] = universal gas constant [Eq. (20)] = [DN\ and [DL], distance from the graphite surface to the axis of symmetry [Eq. (1) and Fig, i]= temperature at hydrogen-C,, gas interface = temperature at the edge of hydrogen boundary layer = wall temperature or graphite surface temperature = average hydrogen (or air) temperature in the boundary layer, taken to be (T,-+ T^J/2 [Eqs.( 19) and (25)] = dimensionless time [Eq. (1)] = X component of velocity -X component of velocity at hydrogen-C,, gas interface [Eq, (22)] = X component of velocity at the edge of hydrogen boundary layer -velocity components for hydrogen and C n gas (air and CO 2 ) along the probe surface [Eqs. (!) and (2)] = velocity components for hydrog...