ISSN 10637850, Technical Physics Letters, 2013, Vol. 39, No. 8, pp. 734–736. © Pleiades Publishing, Ltd., 2013. Original Russian Text © V.M. Aniskin, A.A. Maslov, S.G. Mironov, 2013, published in Pis’ma v Zhurnal Tekhnicheskoі Fiziki, 2013, Vol. 39, No. 16, pp. 47–54.
Relaminarization in Supersonic Microjets at Low Reynolds Numbers V. M. Aniskin, A. A. Maslov, and S. G. Mironov Khristianovich Institute of Theoretical and Applied Mechanics, Siberian Branch, Russian Academy of Sciences, ul. Institutskaya 4/1, Novosibirsk, 630090 Russia email:
[email protected] Received April 9, 2013
Abstract—Results of measuring the length of the supersonic portion of the air jets that flow out of axisym metric sonic nozzles 10.4 µm–1 mm in diameter are presented. The measurements are carried out in a range of degree of jet noncalculation of 1–30 and in a wide Reynolds number range, including the laminar and tur bulent flow modes. It is shown that the Reynolds number calculated from the nozzle diameter and the outlet parameters of gas is the parameter that governs jet flow. It is found that, for a laminar jet mixing layer, the length of the supersonic portion sharply increases. When the jet mixing layer becomes turbulent, the length of the supersonic portion decreases. The effect of increasing the length of the supersonic portion after its decrease due to the turbulization of flow in a jet and a growth in the Reynolds number is first discovered. DOI: 10.1134/S1063785013080166
Supersonic gas microjets have found wide applica tion in manufacturing processes, aviation, and space exploration. These practical needs have motivated interest in the study of the stability of supersonic jets. In particular, the effect of the Reynolds number of a jet and the absolute nozzle size on the length of the super sonic portion of the jet or the jet range is an important issue. Experimental studies of the gasdynamic structure of underexpanded supersonic jets that flew out of axi symmetric sonic micronozzles with diameter D = 10.4–340 µm in a range of degree of jet noncalculation of 1–4.3 were carried out in [1–3]. For nozzles less than 60 µm in diameter, a substantial increase in rela tive length of the supersonic portion of the jets LC/D was shown compared to the length of the supersonic portion of turbulent macrojets [4, 5] at the same values of n. However, at certain values of n, the length of the supersonic portion of the microjets sharply decreased to values that corresponded to the length of the super sonic portion of the turbulent macrojets. These values of n corresponded to Reynolds numbers Re = 1000– 2000 calculated from the nozzle diameter and the out let flow parameters. To reveal the role of the nozzle scale factor and the Reynolds number of a jet in the change of the relative length of the supersonic portion with varying degree of jet noncalculation n, we measured the characteristics of the shockwave structure and the length of the supersonic portion in an axisymmetric underex panded jet that flew out of a sonic nozzle 1 mm in diameter into a lowpressure chamber. The pressure in the chamber was varied from atmospheric pressure to
10–1 mm Hg. Experiments were carried out using air jets at the room retardation temperature. Similarly to in works [1–3], the value of n was changed by increas ing the pressure in the nozzle at a constant ambient pressure. The diagnostics of the jets was performed using a Pitot tube made of a medical needle with inter nal diameter of 100 µm. It was capable of moving at distance of 200 mm from the nozzle edge along the jet axis using a coordinate device. The pressure in the Pitot tube and the nearjet space was measured by TMD4IV1 differential pressure strain gages, and the air pressure in the nozzle was measured by a standard membrane vacuum gage. The position of the end of the jet supersonic portion LC was determined when the pressure in the Pitot tube reached the value that corre sponded to the Mach number on the jet axis equal to unity. In these experiments, Reynolds numbers for the nozzle 1 mm in diameter corresponded to Reynolds numbers for the micronozzles. The results of measuring the average length of the second, third, and fourth cells of the wave structure of the supersonic jet show a good (within 10–15%) agreement of the average length of the cells with the data measured in the microjets [3] and the turbulent macrojets at degree of jet noncalculation of 1 < n < 4. This is indicative of there being no pronounced effect of the nozzle scale factor on the shockwave structure of the supersonic jets. Figures 1a and 1b illustrate a comparison of the dependences of LC/D on n obtained for some values of micronozzle diameter in [1, 3] and for a nozzle diam eter of 1 mm at close Reynolds number values. The measurement results show a good qualitative and a sat
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Fig. 2. Dependences of relative length of supersonic jet portion on degree of jet noncalculation for effective noz zles with various diameters, µm: (1) 8.9, (2) 5.9, (3) 4.2, and (4) 2.4. Dashed and solid curves are data for turbulent macrojets [4, 5].
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Figure 2 shows the results of determining jet range LC/D at Reynolds numbers that correspond to nozzles less than 10 µm in diameter. It can be seen that, like in Fig. 1, with decreasing effective nozzle diameter, the value of n at which the relative range LC/D begins to diminish shifts toward greater values; the degree of decrease in LC/D also declines. In Figs. 1 and 2, special attention should be paid to the subsequent growth of LC/D after its decrease.
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n Fig. 1. Dependences of relative length of supersonic jet portion on degree of jet noncalculation. Dependences for real nozzles with various diameters, µm: (1) 44.6, (3) 16.1, (5) 21.4, and (7) 10.4. Dependences for effective nozzles with various diameters, µm: (2) 53, (4) 17.7, (6) 23.7, and (8) 11.8. Dashed and solid curves are data for turbulent macrojets [4, 5].
isfactory quantitative agreement of the dependences for the real and effective micronozzles with close diameters. The dependences presented in Fig. 1 are indicative of the fact that the Reynolds number is the TECHNICAL PHYSICS LETTERS
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To understand the causes of variations in the microjet range, we measured fluctuations of mass flow rate using a hotwire anemometer. The anemometer was placed in the middle of the jet normally to its axis. Figure 3 shows the dependences of jet range LC/D on n for the real microjets that flow out of the nozzles 26 and 24.3 µm in diameter. The isolines field of the integral fluctuations of mass flow rate measured by the hotwire anemometer is superimposed over these plots. It can be seen that the decrease in the jet range is accompanied by a sharp increase in the integral fluctu ations of mass flow rate. This was interpreted as a manifestation of the laminarturbulent transition in the mixing layer of the supersonic jet.
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The repeated growth in the length of the supersonic portion is accompanied by a decrease in the fluctua tions of mass flow rate in the jet (Fig. 3a) and, in some cases, by their complete disappearance (Fig. 3b). This phenomenon is similar to the relaminarization of flow observed in boundary layers under certain conditions; in supersonic jets, it was first discovered. The existence of a reversal in the length of the microstructures that flow to the environment was confirmed by schlieren visualization of jet flow. Thus, it is shown that the Reynolds number calcu lated from the nozzle diameter and the outlet flow parameters can be used to model the dependence of the length of the supersonic jet portion on the degree of jet noncalculation in a wide nozzle diameter range. The phenomenon of the recovery of the length of the supersonic portion with increasing Reynolds number of the jet after its decrease due to the transition of the jet to the turbulent flow mode is first discovered.
Acknowledgments. This study was supported by the Russian Foundation for Basic Research (project nos. 110800205a and 120831265mol_a), as well as the Program for Basic Research of the Presidium of the Russian Academy of Sciences (project no. 25/13). REFERENCES 1. V. M. Aniskin, A. A. Maslov, and S. G. Mironov, Pis’ma Zh. Tekh. Fiz. 37 (22), 10 (2011). 2. V. M. Aniskin, S. G. Mironov, and A. A. Maslov, Intern. J. Microscale. Nanoscale. Therm. Fluid Transp. Phe nomenon 3 (1), 49 (2012). 3. V. M. Aniskin, S. G. Mironov, and A. A. Maslov, Microfluidics Nanofluidics 14 (3), 605 (2013). 4. J. W. Shirie and J. G. Siebold, AIAA J. 5 (11), 2062 (1967). 5. V. I. Pogorelov, Zh. Tekh. Fiz. 47 (2), 444 (1977).
TECHNICAL PHYSICS LETTERS
Translated by D. Tkachuk
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No. 8
2013
