Effect of Thermodynamic Parameter on Cavitation in Rocket Inducer

Cavitation is physically “a vaporization of liquid” which needs latent heat for phase change. A cavity grows in the liquid, so the latent heat of vaporization can only be supplied by the liquid surrounding the cavity. Thus, the liquid close to the interface region of the cavity is cooled down. In general, cryogenic liquids are very thermosensitive. For liquid hydrogen and oxygen used in rocket propulsion, the temperature in the cavity, i.e., the vapor pressure in the cavity, is lower than those of the liquid bulk. Thanks to this thermal effect, cavitation in cryogenic liquids is less developed than that in water at room temperature. This thermal effect on cavitation is beneficial in that it improves cavitation performance and alleviates cavitation instabilities in space inducers. In previous works, we investigated the relationship between the thermodynamic effect and the cavitation instabilities, e.g., rotating cavitation and cavitation surge, with a focus on the cavity length as an indication of cavitation. In the present work, first, aspects of cavitation in an inducer were observed by direct optical visualization in liquid nitrogen. Second, joint experiments in liquid nitrogen and cold water were conducted on a cavitaing inducer. In nitrogen experiments, operating conditions, i.e., rotational speed and liquid temperature, were varied to determine the cavitation scaling law. Through these experimental results, characteristic times, namely, the transit time for bubble growth and the characteristic thermal time introduced from the thermal property, were investigated as a cavitation thermodynamic parameter. It was found out that the adjustment of cavitation number has a good correlation with the ratio of the transit time and the characteristic thermal time. * Received 3 December 2012 *1 Space Transportation Propulsion Research and Development Center, Space Transportation Mission Directorate (宇宙輸送ミッション本部 宇宙輸送系推進技術研究開発センタ-) *2 Space Transportation Propulsion Research and Development Center, Space Transportation Mission Directorate (宇宙輸送ミッション本部 宇宙輸送系推進技術研究開発センタ-) Present affiliation : IHI Corporation, Aero-Engine & Space Operations ((株)IHI、航空宇宙事業本部) *3 Space Transportation Propulsion Research and Development Center, Space Transportation Mission Directorate (宇宙輸送ミッション本部 宇宙輸送系推進技術研究開発センタ-) Present affiliation : Kanazawa Institute of Technology, Department of Mechanical Engineering (金沢工業大学工学部) *4 Kyushu University, Department of Mechanical Engineering (九州大学工学研究院) This document is provided by JAXA 2 JAXA Reserch and Development Memorandum JAXA-RM-12-006E INTRODUCTION Pioneering works of the thermodynamic effect on cavitation performances were conducted by Stepanoff [1] and Cooper [2], who used B-factor (B=Vv/Vl) as a thermal cavitaion criterion to explain the difference of NPSH requirement between water and other liquids. Stepanoff investigated the thermodynamic effect on cavitation with regard to the reduction of pump performance (i.e., the measurable cavitation effect of head breakdown Δψ/ψo = 3%) as an indication of cavitation. Figure 1 shows that the explanation of Stepanoff’s NPSH adjustment Δht, where C1 and C2 are 3% head breakdown as the reduction of pump performance. Stahl et al. [3] assumed that “the same value of B=Vv/Vl would mean the same extent of cavitation condition and the same damage to the performance. ” Furthermore, Stepanoff proposed that “such reductions of NPSH values below their cold water test values will be referred to as ‘NPSH adjustments’ rather than ‘NPSH corrections’an obvious misnomer. ” In other words, Stepanoff’s classical B-factor could be understood as a non-dimensional temperature parameter B=ΔT/ΔT*, in which ΔT is the temperature difference between the liquid at infinity and the cavitating region, and Δ T* =ρvL/ρlCpl which depends only upon the fluid property is the characteristic temperature difference by simple heat balance. Brennen [4] proposed the thermodynamic parameter Σ (Eq. (1)) from the analysis of the dynamics of a single sphere bubble based on the assumption that heat transfer to the interface between a bubble and the surrounding liquid occurs due to the conductive nature. This thermodynamic parameter Σ has the units of m/s. Figure 2 shows the thermodynamic parameter Brennen’s Σ vs. non-dimensional temperature T/Tc (Tc: critical temperature), Σ increases at an exponential rate in water and other liquid when the temperature increases to near the critical temperature.