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Journal ArticleDOI

A CFD study of flow quantities and heat transfer by changing a vertical to diameter ratio and horizontal to diameter ratio in inline tube banks using URANS turbulence models

01 Dec 2017-International Communications in Heat and Mass Transfer (Elsevier BV)-Vol. 89, pp 18-30

AbstractThis paper reports the effect of changing the aspect ratio on the heat transfer and flow quantities over in-line tube banks. Two types of in-line arrangements were employed; square and non-square configurations. The models that were examined are a standard k-e model, SST k-ω model, v2-f model, EB k-e model and EB-RSM model. The closer results to the experimental data and LES were obtained by the EB k-e and v2-f models. For the square pitch ratios, the solution has faced a gradual change from a strong asymmetric to asymmetric and then to a perfect symmetry. The strong asymmetric solution was found by the very narrow aspect ratio of 1.2. However, the behaviour of cases of 1.5 and 1.6 became less strong than that predicted in the case of 1.2. In the larger aspect ratio of 1.75, the flow behaviour is seen to be absolutely symmetric for all variables under consideration except Nusselt number. For the very large pitch ratio of 5, the flow has recorded maximum distributions for all parameters on the windward side of the central tube with a perfect symmetric solution around the angle of 180° while the vortex shedding frequency has recorded minimum value and the Strouhal number; therefore, has given the smallest value. However, for the non-square pitch ratio of constant transverse distance, the solution is still asymmetric for all parameters with merely one stagnation at the angle of 52° at the case of the 1.5 × 1.75 while by increasing the longitudinal distance to 2 and 5, the solution provided a comprehensive symmetry for all variables with two vortices are fully developed mirrored in shape on the leeward side of the central tube. On the contrary, for the non-square pitch ratio of constant longitudinal distance, the flow of the case of 1.75 × 1.5 provided two stagnation locations at around 52° and 308° with a very similar solution to the case square ratio of 1.75 for all variables whereas by increasing the transverse distance to 2 and 5, the solution recorded was not perfectly symmetric resulting in two different vortices and one stagnation position located at the leading edge of the cylinder provided by the case of 5 × 1.5. In terms of vortex shedding effect, the reduction in the Strouhal number at a constant transverse pitch is less steep than those at a constant longitudinal pitch.

Topics: Strouhal number (58%), Aspect ratio (57%), Vortex shedding (56%), Nusselt number (53%), Turbulence (52%)

Summary (4 min read)

Introduction

  • This paper reports the effect of changing the aspect ratio on the heat transfer and flow quantities over in-line tube banks.
  • In addition to that, the new turbulence model EB k-ε would be used in such application which was not used in literature as well.

2.1. Flow Periodicity

  • The periodic boundary conditions can be described as an assortment of boundary conditions which can be selected in order to discretize very large systems by employing a small section from the system.
  • In general, the simulation of tube bundles can be significantly simplified by knowing the fact that the flow repeats itself after passing the entrance by a certain length which in turn leads to allow the flow to be periodic at the certain cyclical boundaries.
  • The periodic boundary condition as commonly known has a specific condition which is the flow goes out from the one domain is forced to return back to be inflow to another one and thereby the directions would be infinite.
  • Generally, the periodic boundary condition should be specified by either a constant pressure drop or a constant mass flow rate between the inner and outer domains.

2.2. Computational Mesh Generation

  • The present work has been undergone to study the mesh resolution depending on the case of (ST/D=SL/D=1.6) and similarly the other subsequent cases have been conducted by considering the similar grid parameters.
  • Four meshes are examined in order to select the more efficient one according to the accuracy of the results and the stability of the solution.
  • These meshes are named; coarse, intermediate, fine and very fine meshes.
  • Sixteen cases are simulated and their cell densities and mass flow rates are summarized in table 1.

2.3. Tube bundle domain

  • Many preceding periodic investigations have been done such as (Beale and Spalding, 1999, Benhamadouche et al., 2005 and Afgan 2007) concluded that the domain of 2X2 has to be enough in terms of capturing both the unsteady flow physics and mean interested mean characteristics.
  • Nevertheless, the domain of 4X4 tubes was investigated numerically by (Benhamadouche et al., 2005 and West 2013) to provide the same flow patterns with another important feature which is there is no difference in the mean characteristics.
  • They also reported that the minimum spanwise direction must be twice the tube diameter (Lz=2D) in order to sufficiently cover the flow physics which take place through the inline tube bundles.

3.1 Mesh independence study

  • The most important step in the CFD simulations is to achieve a mesh that creates an opportunity to give more accurate results and faster convergence.
  • Figure 1 illustrates the pressure coefficient distribution around the central tube using four meshes.
  • The more accurate result compared to the very fine grid has been provided by the fine mesh and also the solution is nearly stable as well as the grid provided an independent solution.
  • In terms of wall treatment, the type of (all-y+ wall treatment) has been employed which is available in the STAR CCM+ solver.

3.2 The turbulence modelling selection

  • The square pitch ratio of 1.6 is chosen in order to judge the performance of different RANS models comparing with the measurements of Aiba et al. (1982) at the Reynolds number of 41000 and LES predictions of Afgan (2007) for 2D URANS and 3D URANS calculations.
  • The two parameters are selected for the comparisons which are the normalized pressure coefficient distribution around the central tube and the normalized velocity profile at the wake of the central column.
  • In addition to that, the flow patterns using velocity streamlines for 2D URANS cases are selected to compare with the LES flow pattern reported by Afgan (2007).

3.2.1 The normalized pressure coefficient distribution

  • Figure 2 shows the normalized pressure coefficient, Cp, profile around the central tube for square pitch ratio of 1.6 for 2D URANS , and 3D URANS , calculations.
  • It is obvious that the experimental data (just available for half cylinder 0°-180°) and LES results provided high stagnation pressure on the stream-wise direction located around 45° while the low pressure located at 90°.
  • The LES predicted another low-pressure location at 215°.
  • Fortunately, all the, 2D URANS and 3D URANS calculations seem to provide good agreement with experimental data and LES prediction in some regions like stagnation point and the minimum pressure except the k-ɛ model.
  • Some of them could not match the experimental data and LES prediction in other regions, especially at the second half of cylinder (180°-360°).

3.2.2 The normalized velocity profiles at the wake of the central tube

  • The k-ɛ model failed to predict the peaks in the same locations shown by the measurements and LES just in 2D URANS case while the EB-RSM shows good agreement above the central tube but was far away from the experimental data below the central tube.
  • The k-ɛ model gave a better prediction in the 3D case but still not close to the measurements and LES.
  • Nevertheless, the behaviour of the three rest turbulence models (SST k-ω, v2-f and EB k-ɛ) is approximately the same in all cases and in all regions as well.
  • In all cases, their results are nearly close to the experimental data and LES above y=0.04m, whereas below y=0.04m, their behaviour is better and their path is more uniform.

3.2.3 Flow patterns

  • Figure 4 presents the flow patterns predicted by URANS models compared with the LES prediction of Afgan (2007) for the square pitch ratio of 1.6.
  • In spite of the fact that the k-ɛ model is valid for most engineering applications with results reasonably accurate, its performance becomes very poor in flow with large pressure gradients, high streamline curvature and strong separation.
  • Eventually, the results in the next sections are presented either by the EB k-ɛ model or v2-f model or both.
  • With increasing the pitch ratio for limited value (say <5), the flow is able to show more uniform presentation and nearly symmetric behaviour like the case of 1.75 with two stagnation points at around 50° and another one around 310° as presented in Figure 5d.
  • By increasing the transverse distance to 2, the tube walls became slightly far away from each other and thus the restriction against the flow has been gradually reduced.

3.4 Time-averaged velocity profiles

  • The time-averaged velocity distributions divided by the mean velocity at the wake of the central column of the tubes for square inline configurations are presented in Figure 7.
  • The results are represented for 2D and 3D simulations by two turbulence models; v2-f and EB k-ɛ.
  • This is could be due to the narrow space between tubes that does not allow the flow to move easily and; therefore, when the flow hit the tube, the flow is forced to be deviated from the centreline leading to creating maximum deviated behaviour.
  • One can easily notice two things in Figure (7b); the deviation of the velocity stream is significantly reduced and the flow tries to be symmetric.
  • The second observation is that the thickness of the profile between tubes became bigger due to increasing the pitch ratio which require bigger mass flow rate and; therefore, the maximum ratio of (U/Uo) decreased from 3.8 to 3.2.

3.6 Flow patterns

  • The flow pattern of fluid can easily characterize the pressure drop and heat transfer in tube bundles.
  • This is due to the mutual interference of the flow which leads to cause a presence the interesting and unexpected phenomena.
  • Another feature one can be taken into account which is the fluid acts to flow diagonally among the tubes instead of following in the stream-wise direction.
  • Figure 11 shows the time-averaged velocity streamlines for 2D non-square pitch ratios at a constant longitudinal distance using the EB k-ɛ model.
  • If one compares the square pitch ratio of 1.5 shown in figure 13b with the case of 1.75X1.5 observed in Figure 11a, the flow is still denominated by the asymmetrical behaviour with something is interesting can be noted which is the bubble sizes became bigger and also filled the recirculation regions.

3.7 The Nusselt number distribution around the second tube

  • In general, the calculations of the Nusselt number of the in-line tube bundles are strongly dependent on three variables.
  • All of these variables are set to be constant in the present work.
  • Therefore, approximately all the maximum values shown in figure 13, are close to each other while the locations of them are different due to the flow deflection through tube banks.
  • That gives an idea that the flow tries to be symmetric but needs further relaxation in the pitch ratio.
  • By further increasing the transverse distance to 5, the flow has now been able to provide a perfect symmetry at around 180° and the Nu distribution has concentrated just on the windward side of the central tube (360°-0°).

3.8 Vortex shedding

  • Figure 14 presents the variation of stream-wise velocity with time at a point just behind the central tube in the case of square pitch ratio of 1.6.
  • For this vortex shedding, it is noticed that the period of time is nearly 0.0225 sec and the corresponding frequency is 44.4 Hz.
  • Therefore, the non-dimensional Strouhal number can be computed by multiplying the frequency by the tube diameter and the free-stream velocity.
  • The smaller the square pitch ratios, the larger the Strouhal number would occur.
  • When the square pitch ratio has been relaxed to 1.5, 1.6, 1.75 and 5, the space between tubes has gradually increased and turbulence accordingly decreased.

4. Conclusion

  • Computational investigations were performed for square and non-square in-line tube bundles to study the effect of changing the aspect ratios on the pressure coefficient distribution, velocity profile, turbulence intensity, flow patterns, Nusselt number distribution, and vortex shedding.
  • Five turbulence models were tested, namely (EB RSM, SST k-ω, standard k-ɛ, v2-f and EB k-ɛ) and after comparing the results of the square ratio of 1.6 with the experimental data of Aiba et al. (1982) and the LES prediction of Afgan (2007), the best turbulence model was selected for presenting the results.
  • The best results are achieved by the EB k-ɛ model and the v2-f model also provides good results.

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The University of Manchester Research
A CFD study of flow quantities and heat transfer by
changing a vertical to diameter ratio and horizontal to
diameter ratio in inline tube banks using URANS
turbulence models
DOI:
10.1016/j.icheatmasstransfer.2017.09.015
Document Version
Accepted author manuscript
Link to publication record in Manchester Research Explorer
Citation for published version (APA):
Abed, N., & Afgan, I. (2017). A CFD study of flow quantities and heat transfer by changing a vertical to diameter
ratio and horizontal to diameter ratio in inline tube banks using URANS turbulence models. International
Communications in Heat and Mass Transfer, 89, 18-30. https://doi.org/10.1016/j.icheatmasstransfer.2017.09.015
Published in:
International Communications in Heat and Mass Transfer
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Download date:09. Aug. 2022

International Communications in Heat and Mass Transfer 89 (2017) 1830
A CFD study of flow quantities and heat transfer by changing a vertical to diameter ratio and
horizontal to diameter ratio in inline tube banks using URANS turbulence models.
Nabeel Abed*, Imran Afgan
1
* Corresponding author: Nabeel Abed
Email: nabilkhalil90@gmail.com
Mobile: +9647803021102
Mechanical Technical Department, Institute of Anbar, Middle Technical University, Iraq.
1.
Imran Afgan
Email: Imran.afgan@manchester.ac.uk
Phone: +44(0)1612754334
School of Mechanical, Aerospace, and Civil engineering, University of Manchester, UK.
Abstract
This paper reports
the effect of changing the aspect ratio on the heat transfer and flow quantities over
in-line tube banks. Two types of in-line arrangements were employed; square and non-square
configurations. The models that were examined are a standard k-ε model, SST k-ω model, v2-f model,
EB k-ε model and EB-RSM model. The closer results to the experimental data and LES were obtained
by the EB k-ε and v2-f models. For the square pitch ratios, the solution has faced a gradual change
from a strong asymmetric to asymmetric and then to a perfect symmetry. The strong asymmetric
solution was found by the very narrow aspect ratio of 1.2. However, the behaivour of cases of 1.5 and
1.6 became less strong than that predicted in the case of 1.2. In the larger aspect ratio of 1.75, the flow
behaviour is seen to be absolutely symmetric for all variables under consideration except Nusselt
number. For the very large pitch ratio of 5, the flow has recorded maximum distributions for all
parameters on the windward side of the central tube with a perfect symmetric solution around the angle
of 180° while the vortex shedding frequency has recorded minimum value and the Strouhal number;
therefore, has given the smallest value.
However, for the non-square pitch ratio of constant transverse
distance, the solution is still asymmetric for all parameters with merely one stagnation at the angle of
52° at the case of the 1.5X1.75 while by increasing the longitudinal distance to 2 and 5, the solution
provided a comprehensive symmetry for all variables with two vortices are fully developed mirrored in
shape on the leeward side of the central tube. On the contrary, for the non-square pitch ratio of
constant longitudinal distance,
the flow of the case of 1.75X1.5 provided two stagnation locations at
around 52° and 308° with a very similar solution to the case square ratio of 1.75 for all variables
whereas by increasing the transverse distance to 2 and 5, the solution recorded was not perfectly
symmetric resulting in two different vortices and one stagnation position located at the leading edge of

International Communications in Heat and Mass Transfer 89 (2017) 1830
the cylinder provided by the case of 5X1.5. In terms of vortex shedding effect, the reduction in the
Strouhal number at a constant transverse pitch is less steep than those at a constant longitudinal pitch.
Keywords: Heat transfer, Flow quantities, inline tube bundles, URANS turbulence models.
HIGHLIGHTS:
1- URANS turbulence models in inline tube bundles.
2- The behaviour of flow in square and non-square inline tube bundles.
3- Heat Transfer and vortex shedding in inline configuration.
Corresponding author: Nabeel Abed
Author affiliation: Assistant lecturer
Email: nabilkhalil90@gmail.com
Mobile: +9647803021102
Mechanical Technical Department, Institute of Anbar, Middle Technical University, Iraq.
Author
1- Imran Afgan
Author affiliation: Assistant professor
Email: Imran.afgan@manchester.ac.uk
Phone: +44(0)1612754334
School of Mechanical, Aerospace, and Civil engineering, University of Manchester, UK.
1. Introduction
The flow through the tube banks has been encountered in a large number of heat exchanger
applications in the engineering field in order to exchange the thermal energy (heat) from tube banks as
much as possible. However, many numerical and experimental investigations have been made to study
the effect of heat transfer, pressure drop, vortex shedding, and vibration over cross flow, parallel flow
and oblique flow on both types of flow, laminar and turbulent flows using both configurations; in-line
and staggered configurations. The flow can be characterized by transverse and longitudinal pitch-to-
diameter ratios. By increasing the rows number, the turbulence level and the coefficient of heat transfer
have increa
sed significantly and would not be a significant change after a few rows in terms of the
level of turbulence, and consequently, the heat transfer coefficient becomes constant.

International Communications in Heat and Mass Transfer 89 (2017) 1830
Many experimental and numerical investigations have been carried out on both inline and staggered
configurations for a wide range of parameters. Experimental data of heat transfer over inline tube
banks had been provided by (Aiba et al., 1982). Traub (1990) examined the effect of turbulence
intensity on heat transfer and pressure drop on in-line and staggered configurations. Other
experimental studies showed the flow regimes in inline and staggered arrangements reported by Ishigai
et al. (1973), Zdravkovich (1987) while Lam and Lo (1992) just for an inline configuration.
Benhamadouche (2005) and Afgan (2007) have reported numerical investigations using Large Eddy
Simulation (LES). Lam, et al. (2008) reported a simulation study on cross flow around square in-line
arrangement using finite volume method at Reynolds number of 100 and 200 with a wide range of
aspect ratio.
In (1992) Lam and Lo carried out an experimental water tunnel investigation to study the
frequency of vortex shedding and the wake formation on a four tubes placed in a square arrangement
and subjected to cross-flow at a very low Reynolds number. Konstantinidis et al. (2000) studied the
water flow around in-line bank tubes in two dimensions, under conditions of steady and pulsating cross
flow, using flow visualization and laser Doppler anemometry to provide the detailed characterization
of the flow. In (2005) Liang and Papadakis examined the influence of pulsating flow on convective
heat transfer and flow field over an array of in-line tubes at Re of 3400, employing the technique of
(LES). It was pointed out that with decreasing the aspect ratio; the flow pattern deviated from
symmetric to asymmetric. In addition to that, the mean flow has to move in a diagonal direction
through the bundle domain. Afgan (2007) and Ladjedel, et al. (2013) carried out the study of turbulent
flow over in-line tube bundles by using different models of RANS approach. It was also found that the
RANS models gave a good attitude in terms of capturing the transient behaviour of flow. Additionally,
it provided good agreement with the experimental measurements. However, only the k-ε model
suppressed the fluctuations of flow.
As presented so far, the gap found in literature survey that need to pay attention for being the change
of the transverse pitch (keeping the longitudinal pitch as a constant) and the change of the longitudinal
pitch (keeping the transverse pitch as a constant) in a deep study with changing the both pitches in the
same investigation at the same Reynolds number which was not covered in the literature. In addition to
that, the new turbulence model EB k-ε would be used in such application which was not used in
literature as well. All these issues would be taken into account in more details in the present work.

International Communications in Heat and Mass Transfer 89 (2017) 1830
2. Numerical procedure
2.1. Flow Periodicity
The periodic boundary conditions can be described as an assortment of boundary conditions which can
be selected in order to discretize very large (infinite) systems by employing a small section from the
system. In general, the simulation of tube bundles can be significantly simplied by knowing the fact
that the flow repeats itself after passing the entrance by a certain length which in turn leads to allow
the flow to be periodic at the certain cyclical boundaries.
The periodic boundary condition as commonly known has a specific condition which is the flow goes
out from the one domain is forced to return back to be inflow to another one and thereby the directions
would be infinite. Generally, the periodic boundary condition should be specified by either a constant
pressure drop or a constant mass flow rate between the inner and outer domains.
2.2. Computational Mesh Generation
The present work has been undergone to study the mesh resolution depending on the case of
(ST/D=SL/D=1.6) and similarly the other subsequent cases have been conducted by considering the
similar grid parameters. Four meshes are examined in order to select the more efficient one according
to the accuracy of the results and the stability of the solution. These meshes are named; coarse,
intermediate, fine and very fine meshes. Sixteen cases are simulated and their cell densities and mass
flow rates are summarized in table 1.
Table 1: Number of cells and mass flow rates (kg/s) of the cases used in the present work.
Square pitch ratios
Non-square pitch ratios
2D
3D
case
Cell
Density
Mass flow
rate
Cell
Density
Mass
flow rate
case
Cell
Density
Mass flow
rate
1.2X1.2
11008
0.00011075
1100800
0.005537
1.5X1.75
21504
0.000415
1.5X1.5
11840
0.0002768
1184000
0.01384
1.5X2
27680
0.0005537
1.6X1.6
29952
0.000332
2995200
0.0166
1.5X5
84032
0.002215
1.75x1.75
66560
0.000415
6656000
0.0207
1.75X1.5
21504
0.0002768
5X5
74752
0.002215
7475200
0.11075
2X1.5
27680
0.0002768
5X1.5
84032
0.0002768

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References
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Abstract: One is dismayed if not surprised by the disorderly state of a topic of such practical importance. An attempt is first made to categorize various cluster arrangements in terms of the number of pipes (cylinders), their mutual spacing and orientation to the oncoming current. The second step classifies the basic interference flow regimes in the subcritical, critical and postcritical states, for two pipes only, in all possible arrangements. The third step goes further and considers various clusters and distinguishes between the basic interference flow regimes, however modified they may be, and the additional ones for particular orientations. This approach allows some qualitative interpretation and even the prediction of the forces exerted on any of the pipes in the cluster, for various orientations. The following clusters are discussed in some detail: aligned, triangular, square, staggered, all with pipes of the same size, and clusters with pipes of different diameters, i.e. small pipes arranged circumferentially around a big central one. This field is an example of ad hoc testing, leading to a proliferation of undigested and uncorrelated data.

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"A CFD study of flow quantities and ..." refers background in this paper

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    [...]


Journal ArticleDOI
Abstract: Successful numerical simulations can reveal important flow characteristics and information which are extremely difficult to obtain experimentally. Two- and three-dimensional (3-D) numerical simulations of cross-flow around four cylinders in an in-line square configuration are performed using a finite-volume method. For 2-D studies, the Reynolds numbers (Re) are chosen to be Re=100 and 200 and the spacing ratio L/D is set at 1.6, 2.5, 3.5, 4.0 and 5.0. For the 3-D investigation, the simulation is only performed at a Re=200, a spacing ratio L/D=4.0 and an aspect ratio H/D=16. The 2-D studies reveal three distinct flow patterns: (I) a stable shielding flow; (II) a wiggling shielding flow and (III) a vortex shedding flow. A transformation of the flow pattern from (I) to (II) at Re=100 will increase the amplitude of the maximum fluctuating pressure on the downstream cylinder surface by 4–12 times, while a transformation of the flow pattern from (II) to (III) will enhance the maximum fluctuating pressure amplitude by 2–3 times. There is a large discrepancy between 2-D simulation and flow visualization results at L/D=4.0 and Re=200. A probable cause could be the strong 3-D effect at the ends of the cylinder at low H/D. It was found that, for an in-line square configuration at critical L/D and when H/D is lower than a certain value, 3-D effects are very significant at the ends of the cylinders. In such cases, a time-consuming 3-D numerical simulation will have to be performed if full replication of the flow phenomenon were to be achieved.

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Journal ArticleDOI
Hugh Goyder1
Abstract: Heat exchanger tube bundles may fail due to excessive vibration or noise. The main failure mechanisms are generated by the shellside fluid that passes around and between the tubes. This fluid may be a liquid, gas or multi-phase mixture. The most severe vibration mechanism is a fluidelastic instability, which may cause tube damage after only a few hours of operation. Clearly, such extreme causes of vibration must always be avoided. In contrast buffeting due to flow-turbulence causes very little vibration. However, after many years of service such remorseless low level vibration will produce tube wall thinning, due to fretting, which may be unacceptable in a high-integrity heat exchanger. Consequently, the issues of life cycle and integrity must frequently be included in heat exchanger specification. This paper reviews the various mechanisms that cause vibration and noise. Particular attention is given to methods for achieving good tube support arrangements that minimize vibration damage. References to the most recent sources of data are given and good working practice for the design and operation of standard and high-integrity heat exchangers is discussed.

77 citations


Journal ArticleDOI
Abstract: This paper is concerned with the results of numerical calculations for transient flow in in-line-square and rotated-square tube banks with a pitch-to-diameter ratio of 2:1, in the Reynolds number range of 30–3000. Transient-periodic behaviour is induced by the consideration of two or more modules, with a sinusoidal span-wise perturbation being applied in the upstream module. There is a triode-like effect, whereby the downstream response to the stimulus is amplified, and there is a net gain in the crosswise flow component. When an appropriate feedback mechanism is provided, a stable transient behaviour is obtained, with alternate vortices being shed from each cylinder. Flow visualization studies of the results of the calculations are presented together with quantitative details of pressure drop, lift, drag and heat transfer. For the staggered bank, a wake-switching or Coanda effect was observed as the serpentine-shaped wake attached to alternate sides of the downstream cylinder. The induced response is independent of the amplitude and frequency of the applied disturbance, including the case of spontaneous behaviour with no excitation mechanism. For the in-line case where each cylinder is in the shadow of the previous one, the motion is less pronounced; however, a shear-layer instability associated with the alternating spin of shed vortices was observed. In this case, the response was found to be somewhat dependent on the frequency of the applied disturbance, and a transient motion could not be induced spontaneously in the absence of an explicit feedback mechanism. Calculated Strouhal numbers were in fair agreement with experimental data: for the staggered geometry, they had values of between 0·26 and 0·35, or from −21 to +6% higher than measured values, while for the in-line geometry, the Strouhal numbers ranged between 0·09 and 0·12, or about 20–40% lower than experimental values.

77 citations