Measurement of the Adiabatic Wall Temperature of a Flat Plate in a Supersonic Air-Droplet Flow
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urement of the Adiabatic Wall Temperature of a Flat Plate in a Supersonic Air-Droplet Flow Yu. A. Vinogradova, A. G. Zditovetsa, N. A. Kiseleva, N. V. Medvetskayab, and S. S. Popovicha,* a
Institute of Mechanics, Moscow State University, Moscow, 119192 Russia b Joint Institute for High Temperatures of the Russian Academy of Sciences, Izhorskaya ul. 13, bd. 2, Moscow, 125412 Russia *e-mail: [email protected] Received January 24, 2020; revised March 12, 2020; accepted March 12, 2020
Abstract—The results of the measurement of the surface temperature of a flat plate in a supersonic airdroplet flow are presented. The plate made of duralumin was mounted vertically in the working channel of an aerodynamic setup. The droplets of a liquid (distilled water) were pulverized into an air flow in a plenum chamber through centrifugal atomizers. The mass concentration of the liquid was about 0.36 and 0.27%, the mean droplet diameter according to Sauter was about 110 μm, and the freestream Mach number M = 2.5 and 3.0. The surface temperature was measured by an IR imager. The measured plate surface temperatures for the case of single-phase air flow (without droplets) were compared with those for the air-droplet flow at the same parameters (with respect to the air) in the plenum chamber. To intensify the droplet sedimentation on the plate a shock generator in the form of a wedge was mounted vertically ahead of the plate. Keywords: supersonic air-droplet flow, disperse gas flows, adiabatic wall temperature DOI: 10.1134/S0015462820050146
There has been much research devoted to the interaction between two-phase (disperse) flows and bodies in the flow (see, for example, review [1]). The presence of an even small amount of admixture (fractions of one percent) in the main flow can lead to considerable variations of its parameters on the body surface. In this study, emphasis is placed on the effect of the water droplet admixture in a supersonic air flow on the surface temperature of the body in the flow. It is well known that the greater the flow Mach number the greater the difference between its thermodynamic temperature T and the adiabatic stagnation temperature T*0 . For example, at the sonic velocity of an air flow this difference (T*0 – T)/T*0 is 17%, while at Mach 3 it amounts to 65%. In this case, the gas directly on the adiabatic surface, impermeable for the heat flux, takes a temperature Taw different from both the freestream stagnation temperature and its thermodynamic temperature. To name this temperature, the Russian scientific literature uses several equivalent terms, such as adiabatic wall temperature, recovery temperature, own wall temperature, temperature of a thermally-insulated wall, and equilibrium wall temperature. In this study, we will call it the adiabatic wall temperature, as recommended in [2]. The adiabatic wall temperature is determined by the expression [3]
(
Taw = T0* 1 + r
)(
γ −1 2 γ −1 2 M 1+ M 2 2
)
−1
T0*, M 1 ≈ rT0*, M 1,
(0.1)
where Taw is the adiabatic wall temperature (in the units of
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