The numerical study of energy separation in a two-cascade Leontiev tube

Abstract

Abstract. This paper presents results of numerical modeling of energy separation for heliumxenon gas mixture flow in a two-cascade Leontiev tube with central and outer (annular) supersonic nozzles. The Mach number and stagnation temperature distributions in longitudinal section and the heat-transfer intensity from the subsonic to supersonic flow have been obtained. The dependences of the cooling effect, the temperature efficiency factor and the adiabatic efficiency on a stagnation pressure in the receiver have been investigated. IntroductionIt is known that various physical effects lead to energy separation in the gas flow without heat transfer between the gas and external heat-sources (to temperature stratification). The most famous energyseparation effect is the Ranque-Hilsch effect in the vortex tube [1][2][3]. This effect has been used for building the aircraft air-conditioning system, cooling systems with a swirl gas flow, and small refrigerators [4,5].In the Leontiev tube, the heat flux appears due to the temperature differences between the subsonic and supersonic parts of the flow when the expanding supersonic part of the flow is cooled. The dissipation of kinetic energy of the stagnating supersonic flow near the wall increases its temperature but for the low-Prandtl gas mixture the recovery temperature on the wall is lower than the temperature of the subsonic part of the flow. As a result, the heat transfers across the heat-conducting separating wall from the supersonic part of the flow to the subsonic part even if the stagnation parameters for both parts of the flow are equal.The energy-separation method in a compressible flow was suggested and theoretically analyzed in [6,7]. There it was shown theoretically that the heat transfer across the heat-conducting separating wall depended on the recovery temperature on the wall from the side, flown by the supersonic part of gas under the adiabatic conditions. To decrease the recovery temperature and increase the energy separation effect, it was suggested to use the low-Prandtl gas mixtures (helium-xenon, hydrogenxenon etc.) [8][9][10], to blow some part of gas into the high-speed flow, to suck some part of gas from the low-speed flow [7,[11][12][13][14], or to use the wall with various surface reliefs [15].The experimental investigations of heat transfer in the single Leontiev tube with a central cylindrical channel [16,17] show the energy separation in the airflow with Prandtl number equal to 0.71. The authors obtain the static pressure distribution on the nozzle wall, and temperature and Mach number distributions in the outer cross section of the tube for the subsonic and supersonic parts of the flow. The results of numerical modeling of energy separation in the trans-and supersonic external flows are presented in monograph [18]. The study was performed for various gas mixtures with

Numerical modeling of energy-separation in cascaded Leontiev tubes with a central body

“…Fig. 4 presents data on the degree of cooling, temperature efficiency factor and adiabatic efficiency [4] of energy separation in single and cascaded Leontiev tubes, depending on the ratio of cooled air or helium-xenon mixture.…”