Upgrading the Frozen Sonic Flow Method for Arc-Jet Facilities

The arc-jet facilities are used to simulate the aero-heating environment during the high speed planetary entry. The most important parameter to be reproduced is the flow total enthalpy that is highest at the nozzle centerline and decreases toward the nozzle walls. The assessment of the ratio of the centerline enthalpy (i.e. the total enthalpy at the core of the free jet) to the mass–averaged enthalpy is important for an accurate evaluation of the heat flux on the tested model. In fact, this is proportional to the centerline enthalpy; on the other hand the mass–averaged enthalpy is usually measured in the arc-jet facilities. The assessment of the centerline enthalpy in arc-heated flows expanding from high pressure reservoirs, i.e. from equilibrium conditions, relies on the Winovich “sonic flow method”. This method assumes that the flow at the sonic point of a nozzle can be represented by a one-dimensional, isentropic expansion in equilibrium conditions. Jorgensen suggested applying the Winovich method to flows that are in equilibrium through a reservoir up to the beginning of expansion and suddenly freeze at that point (the so-called “frozen sonic point method”). Finally Pope verified that this method can be applied also to high-enthalpy flows freezing upstream the beginning of expansion, provided that the chemical composition of the frozen flow is known. The equation for equilibrium or frozen flow, allowing the evaluation of total temperature (Tt) at the beginning of expansion, reads: mg/ptA*=CF(γ)/(ZTt)1/2 (1) where C=m/R0 and F(γ)=[(2/+1)(+1)/(-1)]1/2. The chemical composition (ci) is evaluated by the measurement of the mass–averaged enthalpy and pressure in the reservoir. The compressibility factor (Z) is computed as Z=1+ then the isentropic exponent (γ) can be evaluated for a chemically frozen mixture of atomic and diatomic species, with frozen vibrational energy, by γ=(4+3Z)/(4+Z), while mg and pt are measured during the test. Once known Tt and the chemical composition, from the JANAF thermo-chemical data, the centerline enthalpy can be calculated by: HCL=Σci(HT+ΔHf,T)i (2) To simplify the data reduction, Pope correlated the values of (HT+ΔHf,T)i in terms of temperature by: (HT+ΔHf,T)i=B1T+B2 (3) Park, for one operating condition of the Interaction Heating Facility (IHF) at NASA Ames Research Center (HN=44.5 MJ/Kg, pt=4.7105 Pa), compared five methods for evaluating enthalpy; two experimental methods for the mass-averaged enthalpy, two experimental methods for the centerline enthalpy and a fully numerical method for both enthalpies. All methods gave values of the centerline to mass-averaged enthalpy ratio of about 1.41. The Small Planetary Entry Simulator (SPES) in Naples is an arc-jet facility operating with simulated air, i.e. a mixture of 80% Nitrogen and of 20% Oxygen. Nitrogen is processed by the arc-heater while cold Oxygen is injected into a reservoir downstream the arc-heater. The reservoir pressure is less than 7.5104 (Pa), therefore the sonic flow method, as modified by Pope, can be applied to evaluate the centerline enthalpy. A rational base, making the results from SPES comparable with those from IHF, is that the enthalpy profile across the nozzle of all arc-heated facilities is characterized by a maximum at the center line. This is basically due to the fact that the arc is concentrate at the center line (argon in IHF and nitrogen in SPES) while the arc flow is surrounded by a cold gas (air in IHF and oxygen in SPES). As for both IHF and SPES the nozzles are water-cooled and the area ratios (A/A*) are similar, you can expect a similar boundary layer development and therefore a similar enthalpy profile across the nozzle exit. Moreover, SPES has been used in the past as pilot facility for SCIROCCO, a 70 MW arc-driven wind tunnel (based on a segmented arc-heater similar to the IHF one). The aim of the present note is upgrading the Pope procedure by: 1) using the most updated version of thermochemical JANAF tables (1998 edition); 2) including the formation of nitric oxide in the air chemical model, 3) considering low-to-moderate enthalpy levels.