Research Papers: Fundamental Issues and Canonical Flows

Study of the Reynolds Number Effect on the Process of Instability Transition Into the Turbulent Stage

[+] Author and Article Information
N. V. Nevmerzhitskiy

Russian Federation Nuclear Center,
Nizhniy Novgorod region,
Sarov, Russia
e-mail: postmaster@ifv.vniief.ru

E. A. Sotskov, E. D. Sen'kovskiy, O. L. Krivonos, A. A. Polovnikov, E. V. Levkina, S. V. Frolov, S. A. Abakumov, V. V. Marmyshev

Russian Federation Nuclear Center,
Nizhniy Novgorod region,
Sarov, Russia

Contributed by the Fluids Engineering Division of ASME for publication in the JOURNAL OF FLUIDS ENGINEERING. Manuscript received March 10, 2013; final manuscript received May 15, 2014; published online July 9, 2014. Assoc. Editor: David Youngs.

J. Fluids Eng 136(9), 091207 (Jul 09, 2014) (9 pages) Paper No: FE-13-1145; doi: 10.1115/1.4027774 History: Received March 10, 2013; Revised May 15, 2014

The results of the experimental study of the Reynolds number effect on the process of the Rayleigh–Taylor (R-T) instability transition into the turbulent stage are presented. The experimental liquid layer was accelerated by compressed gas. Solid particles were scattered on the layer free surface to specify the initial perturbations in some experiments. The process was recorded with the use of a high-speed motion picture camera. The following results were obtained in experiments: (1) Long-wave perturbation is developed at the interface at the Reynolds numbers Re < 104. If such perturbation growth is limited by a hard wall, the jet directed in gas is developed. If there is no such limitation, this perturbation is resolved into the short-wave ones with time, and their growth results in gas-liquid mixing. (2) Short-wave perturbations specified at the interface significantly reduce the Reynolds number Re for instability to pass into the turbulent mixing stage.

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Grahic Jump Location
Fig. 1

Experimental scheme

Grahic Jump Location
Fig. 2

Motion picture of test No. 902 (glycerine, Remax = 103, ν = 1.18 × 10−3 m/s2, gmax = 1466 m2/s): the propagation of the single perturbation in the form of a jet directed in the air is observed at the interface. J is the technological joint of the acceleration channel sections.

Grahic Jump Location
Fig. 3

Motion pictures of experiments in group I: the large jet is propagating at the surface of water solution of glycerine; in time, the separate gas bubbles directed in liquid are formed at the surface, which is free from the jet. J, technological joint of the acceleration channel sections; ES, elastic substance. (a) Test No. 915 (96% of glycerine, Remax = 1.9 × 104, ν = 0.67 × 10−3 m/s2, gmax = 15,485 m2/s); (b) test No. 983 (94% of glycerine, Remax = 2 × 104, ν = 0.38 × 10−3 m/s2, gmax = 7560 m2/s).

Grahic Jump Location
Fig. 4

Liquid jet penetration into gas hJET(2S) in experimental group I: the interface oscillation is occurred in area I, the jet is formed in area II (its growth rate depends on the values of viscosity and acceleration), the jet growth rate in area III becomes almost constant (except test No. 904, where the value of the viscosity is considerable)

Grahic Jump Location
Fig. 5

Dependence of the Reynolds number Re on displacement 2S in experimental group I

Grahic Jump Location
Fig. 6

Dependencies of the growth rate of liquid jet βJ on the Reynolds number Re. (a) Re was determined at 2S ≈ 120 mm and (b) Re was determined at 2S ≈ 280 mm

Grahic Jump Location
Fig. 7

Motion pictures of experiments in group II: the initial perturbations lead to rapid generation of the mixing zone of substances even at relatively low value of Re. G.S. – glycerine solution; TMZ – turbulent mixing zone; J – technological joint of the acceleration channel sections. (a) Test No. 919 (80% of glycerine, λ = 0.4 mm, Remax = 3 × 104); (b) test No. 921 (95% of glycerine, λ = 3 mm, Remax = 3.3 × 103); and (c) test No. 916 (80% of glycerine, Remax = 2.4·× 105, natural perturbations with the size of λ ≤ 0.01 mm).

Grahic Jump Location
Fig. 8

Dependence of gas penetration into liquid hLH on displacement 2S in experimental group II. Test Nos. 916 and 918 are without initial perturbations specified; in test No. 919—λ = 0.4 mm, in test No. 921—λ = 3 mm, in test No. 923—λ = 0.4 mm, in test No. 924—λ = 0.4 mm (data on the plot are approximated)

Grahic Jump Location
Fig. 9

Dependencies of the Reynolds number Re(t) and Re(2S) in experimental group II

Grahic Jump Location
Fig. 10

Motion pictures of experiments in group III: the time of instability transition into the turbulent stage decreases with the increase of Re. TMZ – turbulent mixing zone; J – technological joint of the acceleration channel sections; AR – auxiliary reference mark. (a) Test No. 959 (glycerine, Remax = 8 × 102); (b) test No. 957 (glycerine, Remax = 2 × 103); and (c) test No. 956 (glycerine, Remax = 7.6 × 103).

Grahic Jump Location
Fig. 11

Time dependence of the Reynolds number Re for experimental group III

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Fig. 12

Dependence of the time of perturbation growth transition into the turbulent stage τ on the hyperbolic logarithm of the Reynolds number



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