The statistical relation between Eulerian and Lagrangian systems of turbulence (β-approach) is derived to improve HAY and PASQUILL'S approximation from the equality of energies of turbulence in both systems. INOUE'S turbulon theory of turbulence is also applied to derive the equation for LagrangianEulerian time-scale ratio, or so-called HAY-PAS-QUILL scale parameter β, which is shown to be evaluated only from Eulerian statistics. Theoretical discussion shows that Lagrangian correlation function and spectrum can be estimated from Eulerian properties, and that β is the function of Lagrangian time and dependents on intensity of turbulence as well as turbulence scale and approaches the ultimate time-scale ratio βe at very large values of time.
Experimental Results on a Pilot Ballistic Range are reported. The ballistic range is designed by the theory of two-stage light gas gun. The experiments were performed under the matching condition of a heavy piston and a model, which is launched with constant acceleration, using Helium gas as driver gas. The obtained velocity of the model (0.3gr weight) is about 3km/sec.
An electric arc heater, of the arc voltage 250V and the arc current 50A, was specially designed and built for the study of a steady arc performance and efficient productions of acetylene through the methane pyrolysis. Hot gaseous reection products were quenched and sampled with a water-cooled probe. Under the conditions of the mass flow rate of methane 30liter/min and the electric input power 10-15 kW, major products in the quenched gas were acetylene and hydrogen. The concentration of the acetylene in the quenched samples reached as much as 23-35mol% on favorable conditions. This experimental results were found better consistent with the estimations calculated on the hypothesis of a chain reaction as to the methane pyrolysis, than the analysis based on the assumptions of equilibrium processes.