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Aspect ratio effect on flow-induced forces on circular cylinders in a cross-flow

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Abstract

Finite-span circular cylinders with two different aspect ratios, placed in a cross-flow, are investigated experimentally at a cylinder Reynolds number of 46,000. Simultaneous measurements of the flow-induced unsteady forces on the cylinders and the stream velocity in the wake are carried out. These results together with mean drag measurements along the span and available literature data are used to evaluate the flow mechanisms responsible for the induced unsteady forces and the effect of aspect ratio on these forces. The coherence of vortex shedding along the span of the cylinder is partially destroyed by the separated flow emanating from the top and by the recirculating flow behind the cylinder. As a result, the fluctuating lift decreases drastically. Based on the data collected, it is conjectured that the fluctuating recirculating flow behind the cylinder is the flow mechanism responsible for the unsteady drag and causes it to increase beyond the fluctuating lift. The fluctuating recirculating flow is a direct consequence of the unsteady separated flow. The unsteady forces vary along the span, with lift increasing and drag decreasing towards the cylinder base. When the cylinder span is large compared to the wall boundary layer thickness, a submerged two-dimensional region exists near the base. As the span decreases, the submerged two-dimensional region becomes smaller and eventually vanishes. Altogether, these results show that fluctuating drag is the dominant unsteady force in finite-span cylinders placed in a cross-flow. Its characteristic frequency is larger than that of the vortex shedding frequency.

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Abbreviations

a :

span of active element on cylinder, = 2.5 cm

C′ D :

local rms drag coefficient, 2D′/ϱ U ∞ 2 da

C′ L :

local rms lift coefficient, 2l′/ϱ U ∞ 2 da

C D :

local mean drag coefficient, 2D/ϱ U ∞ 2 da

C D :

spanwise-averaged C D for finite-span cylinder

(C D ) 2D :

spanwise-averaged mean drag coefficient for two-dimensional cylinder

C p :

pressured coefficient

-(C p ) b :

pressure coefficient at θ = π

d :

diameter of cylinder, = 10.2 cm

D :

fluctuating component of instantaneous drag

D′ :

local rms of fluctuating drag

D :

local mean drag

E D :

power spectrum of fluctuating drag, defined as \(\int\limits_0^\infty {\mathop E\nolimits_D (f)df = D\prime ^2 } \)

E L :

power spectra of fluctuating lift, defined as \(\mathop \smallint \limits_0^\infty E_L (f) df = L^{'2} \)

f D :

dominant frequency of drag spectrum

f L :

dominant frequency of lift spectrum

f u :

dominant frequency of velocity spectrum

h :

span of cylinder

H :

height of test section, = 30.5 cm

L :

fluctuating component of instantaneous lift

L′ :

local rms of fluctuating lift

R Du (τ):

cross-correlation function of streamwise velocity and local drag, \(\overline {D(t) u(t + \tau )} /D' u'\)

R Lu (τ):

cross-correlation function of stream wise velocity and local lift, \(\overline {L(t) u(t + \tau )} /L\prime u\prime \)

Re :

Reynolds number, U ∞ d/y

S L :

Strouhal number based on f L ,f L d/U ∞

S D :

Strouhal number based on f D ,f D d/U ∞

S u :

Strouhal number based on f u , f u d/U ∞

t :

time

u :

fluctuating component of instantaneous streamwise velocity

U :

mean streamwise velocity

∞ :

mean stream velocity upstream of cylinder

x :

streamwise distance measured from axis of cylinder

y :

transverse distance measured from axis of test section

z :

spanwise distance measured from cylinder base

θ :

angular position on cylinder circumference measured from forward stagnation

ν :

kinematic viscosity of air

ρ :

density of air

τ :

time lag in cross-correlation function

φ D :

normalized spectrum of fluctuating drag

φ L :

normalized spectrum of fluctuating lift

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Author notes

  1. F. Baban

    Present address: The Aerospace Corporation, P.O. Box 92957, 90089-1454, Los Angeles, CA, USA

Authors and Affiliations

  1. Mechanical and Aerospace Engineering, Arizona State University, 85287, Tempe, AZ, USA

    F. Baban & R. M. C. So

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  1. F. Baban
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  2. R. M. C. So
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Baban, F., So, R.M.C. Aspect ratio effect on flow-induced forces on circular cylinders in a cross-flow. Experiments in Fluids 10, 313–321 (1991). https://doi.org/10.1007/BF00190247

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  • DOI: https://doi.org/10.1007/BF00190247

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