Research Papers: Fundamental Issues and Canonical Flows

Axial Flutter Effects on the Axisymmetric Turbulent Boundary Layer Along Long Thin Circular Cylinders

[+] Author and Article Information
Stephen A. Jordan

Naval Undersea Warfare Center,
Newport, RI 02841
e-mail: stephen.jordan@navy.mil

Contributed by the Fluids Engineering Division of ASME for publication in the JOURNAL OF FLUIDS ENGINEERING. Manuscript received July 27, 2015; final manuscript received March 22, 2016; published online June 6, 2016. Assoc. Editor: Mark F. Tachie.This material is declared a work of the U.S. Government and is not subject to copyright protection in the United States. Approved for public release; distribution is unlimited.

J. Fluids Eng 138(9), 091203 (Jun 06, 2016) (11 pages) Paper No: FE-15-1513; doi: 10.1115/1.4033370 History: Received July 27, 2015; Revised March 22, 2016

Experimental observations of towed sonar arrays as characterized by long thin circular cylinders indicate transverse motions that are clearly identified by low-amplitudes, low-wavelengths, and low-frequencies. Although the cylinder length (L) to radius (a) is commonly large [L/a = O(103)] with high Reynolds numbers [O(104)], the corresponding length scale involving the average skin friction [CfL/a = O(10)] remains within the many experimental determinations of short to moderate length cylinders that experience oscillatory instabilities. Prior to the present investigation, any detrimental effects of these oscillatory instabilities on the thin cylinder flow physics that serve construction of the respective semi-empirical and semi-analytical models remained chiefly unknown. Herein, we began examining those turbulent statistics via fine-scale numerical simulations to critique the pragmatic adequacy of the representative design models. We were concerned in particular about the streamwise effects on the turbulent boundary layer (TBL), skin friction and wall pressure evolutions as well as the radial distributions of the leading normal and shear Reynolds stresses. Fortunately, no major deviations (within 10%) were discovered in the TBL statistics over a characteristic range of Reynolds numbers and TBL thicknesses as compared to the axisymmetric state. However, acute spikes (both subharmonics and harmonics) were detected in the wall pressure autospectra similar to that suspected in the towed cylinder experiments, which were conducted in large tow tanks and lake-type basins. These spikes are of paramount importance and should be explored further because they may lead to signal-to-noise ratios above acceptable limits.

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Fig. 1

A typical snapshot of an instantaneous asymmetric velocity field and suspected low-frequency spikes of wall pressure spectra (highlighted inside box) of a towed thin cylinder at high-Re [12]. The thin cylinder is the approximate location of the array; (a) velocity vectors and (b) wall pressure spectra.

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Fig. 2

Sketch of the turbulent inflow and external kinematics for simulating TBLs along long fluttering cylinders

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Fig. 3

Comparisons of the measured mean axial velocities [21,22] and Reynolds shear stress [23] (symbols) against the LES results [24] (lines); (a) mean axial velocity with numbers as δ/a, Rea and a+ and (b) Reynolds shear stress with numbers as δ/a, a+ and Reθ

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Fig. 4

Model predictions [29] of the skin friction coefficient (Cf) longitudinal evolution for an axisymmetric turbulent flow

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Fig. 5

Comparisons of the measured Reynolds normal stress [22,23] (symbols) against the LES results (lines) and wall pressure spectra (first test case only); (a) Reynolds normal stress where numbers are δ/a, a+ and Reθ and (b) pressure spectra with white dashed lines indicating the convective ridge velocity (uc)

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Fig. 6

Skin friction coefficient (Cf) of the first test case (Rea = 586) in Tables 1 and 2; (a) α = 1 deg and (b) α = 2 deg

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Fig. 8

Axial evolution of the skin friction coefficient (Cf) for the second (Rea = 7475) and fourth (Rea = 14,750) test cases; (a) Rea = 7475 and (b) Rea = 14,750

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Fig. 9

Composite of skin friction coefficients against parameter Rea/(δ/a)

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Fig. 12

Scaled TBL thickness of the first (Rea = 586) and fourth (Rea = 14,950) test case; (a) Rea = 586 and (b) Rea = 14,950

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Fig. 13

Mean axial velocity of first (Rea = 586) and fourth (Rea = 14,950) test cases; (a) Rea = 586 and (b) Rea = 14,950

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Fig. 14

Wall pressure autospectra (wavenumber-frequency) of the second (Rea = 7475) and fourth (Rea = 14,950) test cases

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Fig. 15

Wall pressure autospectra of the test cases in Table 1 at imposed frequencies (a) f = 3 Hz and (b) f = 5 Hz

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Fig. 11

Profiles of the Reynolds normal stresses for the first (Rea = 586) and fourth (Rea = 14,950) test cases with abbreviated shear stress notations u2 = vx′vx′¯/uτ/Uo, v2 =  vr′vr′¯ /uτ/Uo and w2 = vφ′vφ′¯ /uτ/Uo; (a) Rea = 586 and (b) Rea = 14,950

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Fig. 10

Profiles of the Reynolds shear stresses for the second (Rea = 7475) and fourth (Rea = 14,950) test cases; abbreviated shear stress notations are uv′ =  vx′vr′¯/uτ2 and uw′ = vx′vφ′¯/uτ2; (a) Rea = 7475 and (b) Rea = 14,950

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Fig. 7

Profiles of the Reynolds shear stresses for the first test case (Rea = 586); abbreviated shear stress notations are uv′ =  vx′vr′¯/uτ2 and uw′ =  vx′vφ′¯/uτ2; (a) α = 1 deg and (b) α = 2 deg




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