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Natural convection heat transfer and fluid dynamics for a pair of vertically aligned isothermal horizontal cylinders
International Journal of Heat and Mass Transfer 54 (2011) 5163–5172
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Natural convection heat transfer and fluid dynamics for a pair of vertically aligned isothermal horizontal cylinders Tim Persoons ⇑, Ian M. O’Gorman, David B. Donoghue, Gerry Byrne, Darina B. Murray Department of Mechanical and Manufacturing Engineering, Parsons Building, Trinity College, Dublin 2, Ireland
a r t i c l e
i n f o
Article history: Received 18 March 2011 Received in revised form 21 August 2011 Available online 8 September 2011 Keywords: Tubular heat exchangers Flow oscillations Particle image velocimetry Thermal plume interaction Vortex sheet
a b s t r a c t This paper discusses the close interaction between local fluid dynamics and natural convection heat transfer from a pair of isothermally heated horizontal cylinders submerged in water. The presence of a second heated cylinder induces heat transfer enhancements of up to 10%, and strong fluctuations in local heat transfer rate. Therefore specific attention is focused on how the local heat transfer characteristics of the upper cylinder are affected by buoyancy induced fluid flow from the lower cylinder. The paper investigates a range of Rayleigh number between 1.8 106 and 5.5 106, and a vertical cylinder spacing between 2D and 4D. Simultaneous local heat flux measurements and flow velocity measurements using particle image velocimetry reveal oscillatory behaviour of the thermal plume, depending on operating conditions. A joint temporal analysis of the data has provided new insights into the governing mechanisms, which enables further optimisation of the heat transfer performance. Ó 2011 Elsevier Ltd. All rights reserved.
1. Introduction Tubular heat exchangers are among the most common devices for exchanging heat between two fluid flows. The time-averaged heat transfer characteristics are well known for forced convection from arrays of horizontal cylinders. However natural convection heat transfer has received less attention and there remain questions regarding the natural convection heat transfer mechanisms, especially for closely packed tube arrays, where thermal plumes interact with the thermal boundary layer around nearby cylinders. Most studies have focused on averaged heat transfer characteristics either for single cylinders [1] or cylinder arrays [2]. The interaction between adjacent cylinders is generally described in terms of an overall heat transfer enhancement. Only a very limited amount of knowledge is available on the influence of plume oscillations from one (upstream) cylinder on the heat transfer from another (downstream) cylinder; this is mainly due to the difficulty in the numerical modelling of the transient flow in the plume region. Some papers discuss the swaying motion caused by a thermal plume from single cylinders as a result of natural convection [3,4]. Low Rayleigh numbers are characterized by stationary two-dimensional laminar plumes. With increasing Ra, the plume starts to oscillate in very irregular flow patterns, especially near the top of the cylinder. At high Rayleigh number (Ra > 1010), the plume transitions ⇑ Corresponding author. Address: School of Mechanical Engineering, Purdue University, 585 Purdue Mall, West Lafayette, IN 47907, USA. Tel.: +1 765 494 5638; fax: +1 765 494 0539. E-mail addresses: [email protected], [email protected] (T. Persoons). 0017-9310/$ - see front matter Ó 2011 Elsevier Ltd. All rights reserved. doi:10.1016/j.ijheatmasstransfer.2011.08.033
to the turbulent regime [4]. A far greater amount of research has been carried out into studying plume swaying motion from thin horizontal heated wires, which can be regarded as line heat sources [5–7]. Relationships for the velocity and temperature of a plume from a single wire have been derived numerically [5]. These numerical predictions agree with experimental data for thin wires at low Rayleigh number, yet at higher Rayleigh number plume swaying is observed experimentally, causing substantial temperature oscillations in the plume centreline [6]. Desrayaud and Lauriat [8] numerically investigated buoyancy induced flow from a horizontal line heat source inside rectangular vessels with adiabatic sidewalls and isothermal top and bottom walls. For rectangular vessels two destabilising mechanisms lead to low frequency motion due to instability of the buoyant plume. These mechanisms depend on the ratio of depth of immersion to vessel width. The oscillation frequency collapses well to f = 0.0657Ra0.433 (0.3 106 < Ra < 8 106) [8] which agrees with earlier results of Noto [7]. These findings for single cylinders may serve as a reference case. Eckert and Soehngen [9] investigated heat transfer from a vertical cylinder pair and found that the induced temperature and velocity fields due to the buoyant plume from downstream cylinders have opposite effects. The heat transfer rate from the upper cylinder was found to decrease with decreasing cylinder spacing due to a decrease in the local temperature difference, while at larger spacing an increase in heat transfer was found to occur due to the higher local fluid velocity having a forced convection effect on the upper cylinder. For the case of a pair of horizontal isothermally heated cylinders, previous studies by the authors involving measurements of the local heat transfer coefficient around the cylinder circumference
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Nomenclature D DR Gr f g H h k Nu Pr q Ra r Sr S Ts, T1 t U, V
cylinder diameter (m) dynamic measurement range Grashof number (gb (Ts T1)D3/m2) frequency (Hz) gravitational acceleration (m/s2) immersion depth (m) local convective heat transfer coefficient (q/(Ts T1)) (W/(m2 K)) thermal conductivity of fluid (W/(m K)) Nusselt number (hD/k) Prandtl number (m/a) local convective surface heat flux (W/m2) Rayleigh number (GrPr) radial coordinate from cylinder centre (m) Strouhal number (fD/Vref) cylinder centre spacing (m) cylinder surface and bulk fluid temperature (K) time (s) horizontal and vertical fluid velocity (m/s)
have revealed a range of cylinder spacings and Rayleigh numbers where beneficial interaction occurs [10,11]. Based on spectral analysis of the local surface heat flux, it was hypothesized that when the plume from the bottom cylinder oscillates out of phase with the plume from the top cylinder, beneficial mixing occurs which explains the heat transfer enhancement. To elucidate these previously obtained results, the objective of this paper is to experimentally investigate the coupled fluid dynamics and heat transfer of natural convection from a pair of isothermal horizontal cylinders. The Rayleigh number ranges between 1.8 106 and 5.5 106, corresponding to the earlier investigations [10,11] and the cylinder centre spacing ranges between 2 and 4 cylinder diameters.
2. Experimental approach 2.1. Natural convection test facility The experimental test facility is designed to approximate the testing of a tubular section of infinite length contained within an infinite fluid medium. The facility uses a pair of isothermally heated copper cylinders with a diameter D = 30 mm. Horizontal and vertical confinement effects are minimized by choosing the end plate spacing greater than 3D [12] and the depth of immersion
Vt Vref 0 0 u, v x, y z
velocity tangential to cylinder (m/s) reference plume velocity (Eq. (1)) (m/s) fluctuation intensity of horizontal and vertical fluid velocity (m/s) horizontal and vertical coordinate (m) coordinate along cylinder axis (m)
Greek symbols a thermal diffusivity of fluid (m2/s) b volumetric expansion coefficient (K1) m kinematic viscosity of fluid (m2/s) q density of fluid (kg/m3) h circumferential coordinate (°) Subscripts s cylinder surface bulk fluid conditions 1 U velocity 0 u turbulence intensity
H greater than 3D [13]. Fig. 1 shows a schematic diagram of the facility built with these considerations in mind, measuring 900 mm high, 900 mm long and 300 mm (10D) wide. Deoxygenated water was chosen as the working fluid for this analysis. Air was deemed unsuitable due to the high temperatures required for the targeted Rayleigh number range, and due to the difficulty of properly insulating an air control volume from the surroundings. The large vessel volume (about 200 l) prevents excessive bulk water temperature drift during testing. 2.2. Local heat transfer measurements The instrumented cylinders are carefully machined and measure D = 30 mm in diameter and 10D long to mitigate end effects (see Fig. 1b). Each cylinder contains two 500 W cartridge heaters embedded along the cylinder axis, using thermal grease to minimise the thermal contact resistance. The minimum distance between the bottom cylinder and the vessel floor is 10D. Each cylinder is instrumented with a flush mounted thermopile heat flux sensor (RdF Micro-Foil™ 27036-2-RdF) and an internally mounted T-type thermocouple. The cylinders can be rotated about their axis to measure the local surface heat flux around the circumference, as shown in Fig. 1b. To minimize radiation losses the cylinder surfaces are polished to reduce the surface emissivity to around 0.10; the emissivity of the Kapton coating on the heat flux sensor is 0.70.
Fig. 1. (a) Diagram of the natural convection test facility and (b) definition of the coordinate system, separation distance S and depth of immersion H.
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The properties of water are evaluated at the film temperature, (Ts + T1)/2. The most accurate reading of the surface temperature Ts is obtained using a surface-mounted 0.3 mm fine wire T-type thermocouple, mounted at the same circumferential position h as the heat flux sensor yet at an axial distance of z = 10 mm from the sensor. This proved to be a more reliable approach than predicting the surface temperature based on one-dimensional heat conduction through the heat flux sensor and the thermocouple embedded in the sensor. For a given test, the Rayleigh number (Ra = Gr Pr = gb(Ts – T1)D3/(ma)) is set by adjusting the difference (Ts – T1) between the surface temperature and the bulk water temperature, which is measured at the same elevation y as the test cylinder. Measurements are only taken once a pseudo steady state is reached. Once the targeted operating parameters are met the cylinder is rotated in 10° intervals for half a revolution. At each interval the heat flux, surface temperature, and bulk fluid temperature are recorded. Preliminary testing has revealed very low frequency oscillations in heat transfer for multiple cylinder configurations. To capture this oscillatory behaviour a sampling time of approximately 220 s and sampling frequency of 40 Hz are applied. For each measurement condition, tests are repeated 5 times to ensure repeatability. The thermopile heat flux sensor signal is conditioned using a 1000:1 Fylde 351UA amplifier and read into a National Instruments 9172 data acquisition system (NI 9215, 16 bit, 0–10 V). Thermocouples are read into the data acquisition system (NI 9219, 24 bit, 0–80 mV) with internal cold junction compensation. The thermocouples were calibrated in situ against a factorycalibrated resistance temperature detector (RTD) probe with an Omega CL 26 digital meter (uncertainty of ±0.3% at 50 °C). An in-situ calibration was carried out for the heat flux sensors mounted on the instrumented cylinders, following the procedures outlined by Reymond et al. [11] and Atmane et al. [13]. Thus, for each sensor, the measured heat transfer was referenced against the Churchill and Chu [14] correlation for natural convection from a single horizontal cylinder. In addition, an energy balance was conducted to equate the measured convective heat flux to the electrical power supplied to the internal cartridge heaters. These independent calibration procedures differed by a maximum of 8%, giving confidence in the results obtained. The heat flux measurement is the main contribution to the uncertainty in the Nusselt number. The maximum measurement uncertainty occurs at the highest Rayleigh number of 5.5 106. Based on a 95% confidence level, the overall estimated uncertainties of the Rayleigh and Nusselt numbers are around 1% and 16%, respectively. Repeatability across multiple tests is very good, with maximum rms fluctuations in Nusselt number below 0.5% for the
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single cylinder tests. More details of the calibration procedures and error analysis are given by O’Gorman [15]. 2.3. Fluid flow measurements 2.3.1. Particle image velocimetry approach Particle image velocimetry (PIV) is used to quantify the time-varying flow field. These measurements are performed simultaneously to the heat transfer measurements described above. Synchronisation of the start of both measurements is achieved using a common trigger signal. Fig. 1a depicts the arrangement of the laser light sheet optics (intersecting the cylinders in the mid-plane of the vessel) and the double-frame camera (Photron Fastcam SA1, 1024 1024 px, 5400 Hz at full frame rate, 12 bit, Sigma 105 mm f/2.8 lens). The light source is a Quantronix Darwin-Duo Nd:YLF twin cavity pulsed laser (15 mJ at 1000 Hz, 527 nm), and the mean light sheet thickness throughout the field of view is approximately 1 mm. With the light sheet entering from the left, the cylinder casts a shadow where no PIV measurements are possible (e.g. see Fig. 2). The camera is aligned nearly perpendicular to the light sheet, so as to minimize light reflections from the cylinder surface and maximize the visible region near the top cylinder surface. Because of the slightly off-perpendicular position (viewing angle of a few degrees), a calibration target was positioned in the water tank prior to the measurements to perform an optical distortion correction using Lavision’s Davis™ 7.2.2 software. Details of the calibration process are given by O’Gorman [15]. Polyamide particles with diameters between 30 and 70 lm and density of 1.03 g/cm3 are used as seeding. The maximum Stokes number (i.e. dimensionless relaxation time) never exceeds 0.2, indicating that the particles closely follow the water streamlines. After optical calibration of the camera setup in ambient conditions, the heating power to the instrumented cylinders is adjusted to meet the required thermal conditions for the given test. As slow frequency oscillations within the flow are expected, the camera frame rate is reduced to its minimum of 50 Hz, providing a maximum test duration of 26 s. Local heat transfer data from the instrumented test cylinders is recorded simultaneously with the PIV images. The tests were restricted to Rayleigh numbers below 6 106, since at higher temperatures the quality of the vectors obtained close to the cylinder surface deteriorated due to differential optical refraction within the thermal plume, causing an elongation of the seeding particle images. This optical aberration is minimized by positioning the camera at a slightly oblique angle (about 5°), thereby minimizing the overall thermal gradients in the light path incident to the camera lens.
Fig. 2. Comparison of turbulence intensity distribution (u0 2 + v0 2)1/2/Vref around the upper of two heated cylinders at Ra = 3.6 106 and S = 3D, using (a) conventional PIV with a pulse separation of 40 ms and (b) multi-pulse separation (MPS) PIV based on three pulse separation values (40, 80 and 160 ms).
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Table 1 Comparison of the dynamic measurement range of the mean velocity and turbulence intensity using conventional and MPS PIV, for Ra = 3.6106 and S = 3D (see Fig. 2). Quantity
Time-averaged Velocity (U2 + V2)1/2 rms turbulence Intensity (u0 2 + v0 2)1/2
sensor position angles of h = 0°, 90°, 135° and 180°. Four horizontal cylinder configurations were tested: a single cylinder and a pair of vertically aligned cylinders with centre spacings 2D, 3D and 4D.
Measurable range For conventional PIV
For MPS PIV [16]
0.028–2.06 mm/s DRU = 70:1 0.063–1.38 mm/s DRu0 = 20:1
0.005–1.86 mm/s DRU = 410:1 0.012–1.36 mm/s DRu0 = 110:1
2.3.2. High dynamic range PIV measurements Since the flow field is characterized by strong velocity gradients and differences in velocity magnitude between the thermal plume and the entrainment region, a novel technique for increasing the dynamic range of standard PIV is applied. The multiple pulse separation (MPS) technique described by Persoons and O’Donovan [16] combines information from sets of images acquired at multiple pulse separations, to automatically determine the locally optimal pulse separation depending on local flow field characteristics. By increasing the dynamic velocity range, MPS PIV obtains more accurate mean flow and turbulence measurements compared to conventional PIV. Fig. 2 shows a sample result comparing (a) conventional PIV and (b) MPS PIV using three pulse separation multiples (1, 2 and 4 the minimum pulse separation of 40 ms). Conventional PIV tends to overestimate turbulence levels in low velocity regions, which has also been noted in other flow fields with a wide velocity range, such as impinging steady and synthetic jet flows [16–18]. This is due to the deterioration of vector quality when the particle displacement magnitude reduces to the minimum resolvable displacement which is about 0.1 pixels in typical laboratory conditions [19], even using advanced multi-grid correlation techniques. Table 1 compares the dynamic measurement range of conventional and MPS PIV. The MPS technique increases the dynamic range for mean velocity and turbulence intensity with a factor of 5.5 compared to conventional PIV, resulting in a considerably higher accuracy. The effect is more pronounced in flows with a wider velocity range [16–18].
3. Experimental results A range of Rayleigh numbers between 1.84 106 and 5.33 106 has been investigated, meaning that the flow is nominally laminar. Simultaneous PIV and heat transfer data were recorded at heat flux
Fig. 3. Effect of Rayleigh number on the time-averaged local Nusselt number along the circumference of a single cylinder (0° = bottom, 180° = top).
3.1. Heat transfer from a single cylinder Firstly, local heat transfer results from single cylinder measurements are presented. Fig. 3 shows the time-averaged local Nusselt number around the circumference of the cylinder, where 0° and 180° represent bottom and top of the cylinder, respectively (see definition in Fig. 1(b)). Fig. 3 shows that the maximum heat transfer rate occurs at the bottom stagnation point (0°) of the cylinder and steadily decreases with increasing angle until approximately 160°, with a sharper rate of decrease occurring over the final 20° of the cylinder circumference. This result is consistent with results for the local Nusselt number distribution about a single cylinder reported by Kuehn and Goldstein [20], Merkin [21] and Reymond et al. [11]. A power law scaling of Nu with Ra is observed with an exponent of 0.32 (R2 > 0.99), which is broadly consistent with the findings reported by Morgan [1] and Churchill and Chu [14]. The accelerated decrease in the local Nusselt number over the final 20° of the circumference is generally attributed to an insulating effect of the buoyant plume forming near top of the cylinder. To verify this, PIV flow visualisation was carried out for the case of a single cylinder and within the target Rayleigh number range of this experiment. For a selected case of Ra = 1.92 106, Fig. 4 shows the time-averaged flow field over a single cylinder as contours of velocity magnitude (U2 + V2)1/2/Vref, where the reference plume velocity Vref is defined as
R V ref ¼
x
Vðx; yÞ dx : b
ð1Þ
The plume width b is defined as the distance between the locations where the upward velocity drops to 25% of the peak velocity. Although the plume width slightly increases with y, the value of Vref according to Eq. (1) is reasonably independent of y. Within the Rayleigh number range investigated the plume width b remained constant at 0.35D (=10.5 mm; evaluated at y = 2D). The plume velocity according to Eq. (1) is typically about 1=4 of the characteristic velocity defined based on the square root of the Grashof number, (Ra/ Pr)1/2m/D. The plume detaches from the cylinder surface at an angle of approximately 159°, confirming that the sharp decrease in the local
Fig. 4. Time-averaged contours of velocity magnitude (U2 + V2)1/2/Vref and velocity vectors showing the buoyant plume above a single cylinder at Ra = 1.92 106 (Vref = 5.1 mm/s, plume width 2b = 0.35D at y = 2D).
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Nusselt number from a single cylinder is a direct result of the formation of the buoyant plume at this location.
3.2. Heat transfer from two vertically aligned cylinders 3.2.1. Heat transfer characteristics Previous work by the authors [10,11] has shown that the heat transfer characteristics of a pair of closely spaced horizontal cylinders are significantly different from those of a single cylinder. Reymond et al. [11] have demonstrated that only when both cylinders are heated a considerable degree of interaction occurs in the surface heat transfer rate from the upper cylinder. For a spacing of 1.5D or greater, the lower cylinder is unaffected by the upper cylinder and the upper cylinder is unaffected by an unheated lower cylinder. Table 2 gives an overview of the circumferentially averaged heat transfer coefficient, both for the single cylinder case and for the upper cylinder at inter-cylinder spacings of 2D, 3D and 4D. For the 2D spacing, a slight decrease in mean Nusselt number can be observed at low Rayleigh number. However for all other cases, an overall heat transfer enhancement is noted. This is in agreement with previous results by Reymond et al. [11]. For a fixed Rayleigh number (Ra = 5.33 106), Fig. 5 shows the effect on the local heat transfer coefficient of the presence of a second heated cylinder at spacings of 2D, 3D and 4D below the primary cylinder. Higher local heat transfer levels are evident, especially near the bottom (0°) and to a lesser extent near the top (180°) of the upper cylinder. For the smallest spacing (S = 2D), local increases of 60–100% are observed near the bottom and top of the upper cylinder. A reduction in heat transfer is observed along the sides of the cylinder, which is insignificant for larger spacings. For the largest spacing investigated (S = 4D), the heat
Table 2 Average Nusselt number of a single cylinder and the upper of a pair of vertically aligned cylinders, with values in brackets representing the relative deviation to a single cylinder case, (Nu Nu0)/Nu0 100%.
Single cylinder(S = 1) Upper cylinder (S = 4D) Upper cylinder (S = 3D) Upper cylinder (S = 2D)
Ra = 1.8 106
Ra = 3.6 106
Ra = 5.3 106
Nu = 16.9 Nu = 18.0 (+6.1%) Nu = 18.2 (+7.2%) Nu = 16.1 (–5.1%)
Nu = 20.7 Nu = 22.8 (+9.2%) Nu = 22.4 (+7.6%) Nu = 22.3 (+7.2%)
Nu = 23.8 Nu = 24.3 (+2.0%) Nu = 26.5 (+10.2%) Nu = 24.5 (+3.1%)
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transfer profile is similar to that of a single cylinder except near the top. For the parameters of the current investigation, the heat transfer characteristics of the lower cylinder were unaffected by the presence of the upper heated cylinder and are therefore not reported here. Fig. 5a shows that the local Nusselt profile of the upper cylinder is strongly dependent on the cylinder spacing. Although only shown for Ra = 5.3 106, this is true for the entire investigated Rayleigh range (1.8 106 6 Ra 6 5.3 106). Fig. 5b shows that the shape of the Nusselt profile at a fixed spacing is very similar under different Rayleigh number conditions. For the cylinder pair, strong fluctuations in heat transfer were noted, in particular near the bottom and top of the upper cylinder. Near the bottom, the thermal plume from the lower cylinder joins the upper cylinder’s boundary layer, whereas near the top (180°) the combined plume detaches. Fig. 6(a) and (b) shows the fluctuations in local Nusselt number at the bottom of the upper cylinder (h = 0°) for an cylinder spacing of (a) S = 3D and (b) S = 4D. At a moderate spacing (S = 3D), Fig. 6(a) shows a stable periodicity in the fluctuations induced by the presence of the lower heated cylinder. At a large spacing (S = 4D), the time trace in Fig. 6(b) shows evidence of two distinct regimes, one at a nearly constant Nusselt number and one exhibiting high amplitude and high frequency fluctuations. 3.2.2. Simultaneous flow field and heat transfer measurements The observation of this oscillatory phenomenon in the heat transfer justified a detailed study of the fluid dynamics. Due to camera memory limitations, the duration of these measurements is restricted to 26 s. Fig. 7 shows a single period of a buoyant plume oscillation in the region between a pair of vertically aligned cylinders at a Rayleigh number of 3.7 106 and a spacing of 3D. From left to right and top to bottom, the plots represent instantaneous flow fields at 2.5 s intervals. Fig. 7 shows that the plume from the lower cylinder does not split and rise symmetrically around the upper cylinder, but instead oscillates back and forth across the upper cylinder. As a result of the swaying motion, the cylinder experiences alternating pockets of high velocity fluid passing along its sides. Studies by Sadeghipour and Asheghi [22] and Sparrow and Niethammer [23] have attributed enhancement of the heat transfer from the upper cylinder to the forced convection effect caused by the plume from the lower cylinder, however these flow field measurements suggest that lateral oscillation of the thermal plume from the lower cylinder is an additional mechanism of heat transfer enhancement from the upper cylinder.
Fig. 5. Time-averaged local Nusselt number along the circumference of the upper cylinder: (a) effect of spacing 2D, 3D and 4D ( Ra = 5.33 106 and (b) effect of Rayleigh number at a fixed spacing S = 2D.
represents the single cylinder case) at
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Fig. 6. Time-resolved local Nusselt number on the bottom of the upper cylinder (h = 0°) at (a) S = 3D and (b) S = 4D, for low and high Rayleigh numbers (1.7 106 and 3.3 106).
Fig. 7. Instantaneous streamline and velocity magnitude plots at t = 0 s to 12.5 s in steps of 2.5 s (left to right, top to bottom) showing one plume oscillation period around the lower stagnation point of the upper cylinder at Ra = 3.7 106 and S = 3D (Vref = 4.2 mm/s, plume width 2b = 0.42D at y = 1D).
Fig. 8 shows the local Nusselt number time trace at a position of 90°, on the left side of the upper cylinder. The circular markers represent the simultaneously measured tangential velocity Vt just above the heat flux sensor. This velocity is determined from the time-resolved PIV data, by averaging the tangential velocity in the boundary layer region up to 0.2D from the cylinder surface:
V t ð90 ; tÞ ¼
1 0:2D
Z
0:7D
V t ðr; h ¼ 90 ; tÞ dr:
ð2Þ
This coherence between the local Nusselt number and local plume velocity highlights the impact of the swaying motion of the plume from the lower cylinder on the heat transfer performance of the upper cylinder. Fig. 8 does show some higher order components in both heat transfer and plume velocities. As shown in Fig. 7, the flow field features a wide range of larger vortices down to smaller eddies. Stochastic phenomena including shedding, merging and dissipation of vortices into small scale turbulence can explain these higher order perturbations observed in Fig. 8.
r¼0:5D
As shown in Fig. 7, the plume alternates between the left and right side of the upper cylinder. Fig. 8 demonstrates that the time-resolved Nusselt number Nu(90°) and the tangential velocity on the same location Vt (90°) correlate well. The spectrum of both signals exhibits a peak fluctuation frequency of 0.065 (±0.003) Hz, with only a minor phase difference between the local velocity and Nusselt number.
4. Discussion 4.1. Positive heat transfer enhancement and plume instability At a spacing of 4D, Fig. 6b shows two distinct regimes occurring in the Nusselt number time trace at the bottom of the upper cylinder, one of high frequency fluctuations and one of relatively
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Fig. 8. Simultaneously acquired time-resolved (–) local Nu on left side of upper cylinder (h = 90°) and (s) near-cylinder tangential velocity Vt (in mm/s) just above the sensor position, at Ra = 3.7 106 and S = 3D (Vref = 4.2 mm/s, plume width 2b = 0.42D at y = 1D).
constant Nusselt number. The preceding discussion suggests that the highly fluctuating Nusselt number is a consequence of oscillation of the thermal plume from the lower cylinder. However this does not explain the steady regime in which the mean Nusselt number is comparable with that of a single cylinder at the same location, as shown in Fig. 9a. These two regimes are indicated with letters A and B in Fig. 9. No fixed periodicity is observed in the alternation between both regimes. Their occurrence is stochastic, with regimes A and B occurring, respectively in 17% and 83% of the total measurement time covering 12 separate tests. Fig. 9b gives a schematic representation of the flow field in both regimes. In regime A, no oscillations of the buoyant plume from the lower cylinder are observed and the plume from the bottom cylinder rises steadily along one side of the upper cylinder, maintaining a constant separation distance from the surface of the upper cylinder. This separation leads to two independent plumes rising above the upper cylinder. In regime B, oscillatory plume motion is observed and a single intertwined plume rises above the upper cylinder. In regime A the flow field around one side of the upper cylinder is similar to that around a single cylinder, thus explaining why the
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heat transfer rate in regime A is comparable to that of a single cylinder (see Fig. 9a). The oscillatory regime B is clearly beneficial, with an averaged heat transfer level of about 50% higher than regime A. A further investigation was carried out to determine the mechanism triggering the instability in the lower cylinder plume, by simultaneously measuring the heat fluxes on the lower and upper cylinder. Fig. 10 presents the local convective heat flux q at the lower stagnation point (0°) on the upper cylinder and the upper stagnation point (180°) of the lower cylinder, for a Rayleigh number of 3.3 106 and two cylinder spacings. The heat flux at the top of the lower cylinder remains almost constant throughout the 400 s test period. This steady heat flux from the lower cylinder and the lack of coherence between the heat flux signals on the upper and lower cylinders suggests that unsteady heating from the lower cylinder is not the driving mechanism for plume oscillation. Therefore PIV measurements were employed to analyse the flow surrounding the upper cylinder in further detail. Fig. 11 shows the velocity distribution around the upper cylinder at the point of plume inflection (i.e. when the lower plume changes direction), for three Rayleigh numbers and a cylinder spacing of 3D and 4D. At plume inflection a strong counter-clockwise vortex is formed to the left of the plume (and vice versa, a clockwise vortex is formed to the right when the plume transitions towards the other side of the upper cylinder). The formation of these vortices creates an unbalance in the lateral forces acting on the plume, which suggests that this mechanism may be responsible for the fluctuating oscillatory motion of the lower cylinder plume. Similar coupled oscillatory plume and vortex formation was observed by Incropera and Yaghoubi [24] using dye injection methods for the case of a circular cylinder confined by a free water surface. The observation of vortex rings by these researchers for the case of a vertically confined cylinder suggests that vertical confinement of the buoyant plume from the lower cylinder by the upper cylinder surface may be the cause of these alternate rotating vortices which drive the swaying oscillatory motion of the lower cylinder plume. A second possible interpretation for the plume swaying is that the vortices formed near the bottom of the upper cylinder are governed by a mechanism similar to Kelvin-Helmholtz instability in wake flows. The shear layers in the wake of a single cylinder in cross-flow are known to interact and form a von Karman vortex street. When expressed as Strouhal number, the dimensionless shedding frequency is quite constant over a wide range of Reynolds numbers based on approach velocity and cylinder diameter
Fig. 9. (a) Comparison between the time-resolved local Nusselt number at h = 0° (i.e. bottom stagnation point) of the upper of two cylinders at S = 4D (black line) to a single cylinder (grey line), both at Ra = 3.3 106. For a pair of cylinders, alternating heat transfer regimes are observed (A = constant Nusselt number and B = fluctuating Nusselt number), as schematically depicted in (b).
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Fig. 10. Simultaneously acquired local heat flux at the lower stagnation point (h = 0°) of the upper cylinder and upper stagnation point (h = 180°) of the lower cylinder, at Ra = 3.3 106 and (a) S = 3D and (b) S = 4D.
Fig. 11. Instantaneous streamline and velocity magnitude plot at the time of plume inflection around the upper of a pair of cylinders at (a–c) S = 3D and (d–f) S = 4D; (a, d) Ra = 1.8 106, (b, e) Ra = 3.6 106, (c, f) Ra = 5.3 106.
(300 < Re < 105) [25]. For the case shown in Fig. 8 (Ra = 3.7 106 and S = 3D), the observed plume fluctuation frequency f = 0.065 (±0.003) Hz becomes:
Sr ¼
fD ffi 0:46ð0:02Þ; V ref
ð3Þ
At the largest separation distance (S/D = 4), a similar value of Sr = 0.54 is found based on Vref (or Sr = 0.36 based on the maximum plume velocity) at a comparable Rayleigh number (Ra = 3.6 106). Further research is required to validate this finding in a wider range of parameters. 4.2. Heat transfer reduction and plume confinement
where Vref is determined according to Eq. (1) as the average plume velocity at a distance of 0.5D below the upper cylinder. Using the peak centreline plume velocity instead as reference velocity in Eq. (3) yields Sr = 0.30 ± 0.01. Although there is a significant difference between pressure-driven flow across a single cylinder and buoyancy-driven flow across a pair of cylinders, the Strouhal number value is of the same order of magnitude as the natural shedding frequency for a cylinder in cross-flow (Sr = 0.19 ± 0.01) [25].
Fig. 5a shows that for small S/D, the local Nusselt number of the upper cylinder is lower than that of a single cylinder. As mentioned in Section 1, heat transfer from the upper cylinder may be negatively affected by a reduced local temperature difference between the upper cylinder and the surrounding fluid, which can counteract any potential enhancement due to plume oscillation. However, the local reduction in heat transfer can be quite significant and addi-
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Fig. 12. Time-resolved local Nusselt number on the upper cylinder at Ra = 3.5 106 and S = 2D and 3D, at h = 50° corresponding to the circumferential location of maximum heat transfer reduction compared to a single cylinder case (see Fig. 5).
tional mechanisms may be at play. The maximum local reduction was found to occur at h = 50° for Ra = 3.5 106 and S = 2D, which is the focus of the following investigation. Fig. 12 compares the local Nusselt number at h = 50° for this case against a spacing of 3D. A low frequency, low amplitude oscillatory pattern is observed at S = 2D, very different from the behaviour at S = 3D. Although not shown here, PIV measurements show a regular swaying motion of the plume at S = 2D, however with a much lower amplitude and frequency compared to those found at the same Rayleigh number and larger spacings, as shown in Fig. 7. Incropera and Yaghoubi [24] found that the behaviour of a buoyant plume confined by a free water surface is strongly dependent on the immersion depth H/D, where H is the distance from the cylinder top to the confining surface. They found that the amplitude of the plume oscillation decreases with decreasing H/D and that the oscillation became negligible for H/D < 0.5. This has been confirmed by Atmane et al. [13]. The reduction in oscillation amplitude in Fig. 12 is consistent with these findings [13,24], suggesting that excessive confinement of the plume by the upper cylinder can be responsible for the smaller fluctuations in heat transfer on the upper cylinder at a spacing of 2D. In addition to the weak plume oscillations at S = 2D, the formation and detachment of counter-rotating vortices on either side of the plume (as seen in Fig. 7 for S = 3D) was not observed at S = 2D. Incropera and Yaghoubi [24] reported that no vortex is formed below the air-water interface for H/D < 0.5, in contrast to larger immersion depths. The lack of vortex formation at this close spacing directly coincides with a large reduction of the local heat transfer of the upper cylinder compared to that found at a larger spacing. This supports the contention that vortex formation acts as an additional enhancement mechanism for increasing heat transfer from the upper cylinder of a pair of isothermal horizontal cylinders aligned in the same vertical plane. 5. Conclusions By combining particle image velocimetry (PIV) and local convective heat transfer measurements using hot-film anemometry, a methodology has been established to simultaneously study fluid dynamics and natural convection heat transfer from a pair of horizontal cylinders. Multiple pulse separation PIV has been successfully applied to increase the dynamic range in measuring the velocity and turbulence fields. In typical conditions, a 5.5 increase in dynamic velocity range has been obtained, resulting in more accurate flow and turbulence fields.
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A single cylinder does not show any significant fluctuations in heat transfer in the Rayleigh number range under investigation (1.8 106 6 Ra 6 5.5 106), and agrees well with established correlations in terms of the average heat transfer rate. However, in the case of two vertically aligned horizontal cylinders (centre spacing from 2D to 4D), a strong periodicity is observed in the local heat transfer rate. Fluctuations are highest around the bottom and top of the upper cylinder, where respectively the lower plume impinges and the upper plume detaches. The average heat transfer rate of the upper cylinder increases by up to 10% depending on Rayleigh number and separation distance, although a slight heat transfer reduction of 5% is observed at a small separation distance and low Rayleigh number (S/D = 2, Ra = 1.8106). The simultaneous flow field and heat transfer results show the interaction of oscillating thermal plumes, and have confirmed the existence of different alternating regimes. Related to the plume swaying, vortex shedding occurs near the bottom of the upper cylinder. After formation, these vortices travel upwards across alternating sides of the upper cylinder, resulting in pockets of high velocity fluid thus contributing to break up and mixing of the thermal boundary layer. At a cylinder spacing of S = 2D, excessive confinement of the buoyant plume from the lower cylinder is believed to be responsible for minimal fluctuations in heat transfer and regions of reduced local heat transfer on the upper cylinder. A temporal analysis shows how the plume velocity affects the local heat transfer rate. Further work is needed to confirm a hypothesis of a constant Strouhal number, reminiscent of vortex shedding in forced flow across a single cylinder. The established methodology of simultaneously acquiring flow field and heat transfer measurements has yielded a better insight into the fundamentals of natural convection heat transfer in this particular case, and enables a further optimisation of the observed heat transfer enhancement towards larger scale systems and industrial applications.
Acknowledgements Dr. Tim Persoons is a Marie Curie research fellow of the Irish Research Council for Science, Engineering and Technology (IRCSET). Ian M. O’Gorman is a postgraduate research scholar of the Irish Research Council for Science, Engineering and Technology (IRCSET). The authors acknowledge the work of Antoine Van Noorte and Pauline Vancraenenbroek, and the financial support of Science Foundation Ireland (SFI 09-RFP-ENM2151).
References [1] V.T. Morgan, The overall convective heat transfer from a smooth circular cylinder, Adv. Heat Transfer 11 (1975) 199–264. [2] G.F. Marsters, Arrays of heated horizontal cylinders in natural-convection, Int. J. Heat Mass Transfer 15 (1972) 921–933. [3] L. Pera, B. Gebhart, Experimental observations of wake formation over cylindrical surfaces in natural convection flows, Int. J. Heat Mass Transfer 15 (1972) 177–180. [4] K. Kitamura, F. Kami-iwa, T. Misumi, Heat transfer and fluid flow of natural convection around large horizontal cylinders, Int. J. Heat Mass Transfer 42 (1999) 4093–4106. [5] B. Gebhart, L. Pera, A.W. Schorr, Steady laminar natural convection plumes above a horizontal line heat source, Int. J. Heat Mass Transfer 13 (1970) 161– 171. [6] A.W. Schorr, B. Gebhart, An experimental investigation of natural convection wakes above a line heat source, Int. J. Heat Mass Transfer 13 (1970) 557–571. [7] K. Noto, Swaying motion in thermal plume above a horizontal line heat source, J. Thermophys. 3 (1989) 428–434. [8] G. Desrayaud, G. Lauriat, Unsteady confined buoyant plumes, J. Fluid Mech. 252 (1993) 617–646. [9] E.R.G. Eckert, E.E. Soehngen, Studies on heat transfer in laminar free convection with the Zehnder–Mach interferometer, AF Technical report, 1948. [10] I.M. O’Gorman, D.B. Murray, G. Byrne, T. Persoons, Natural convection from isothermal horizontal cylinders, in: Proceedings of the ASME International
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T. Persoons et al. / International Journal of Heat and Mass Transfer 54 (2011) 5163–5172 Mechanical Engineering Congress, Florida, 13–19 Nov. 2009, IMECE200911213. O. Reymond, D.B. Murray, T.S. O’Donovan, Natural convection heat transfer from two horizontal cylinders, Exp. Therm. Fluid Sci. 32 (2008) 1702–1709. I. Tokura, H. Saito, K. Kishinami, K. Muramoto, An experimental study of free convection heat transfer from a horizontal cylinder in a vertical array set in free space between parallel walls, ASME J. Heat Transfer 105 (1983) 102–107. M.A. Atmane, V.S. Chan, D.B. Murray, Natural convection around a horizontal heated cylinder: the effects of vertical confinement, Int. J. Heat Mass Transfer 46 (2003) 3661–3672. S.W. Churchill, H.H.S. Chu, Correlating equations for laminar and turbulent free convection from a horizontal cylinder, Int. J. Heat Mass Transfer 18 (1975) 1049–1053. I. O’Gorman, An Experimental Investigation of Natural Convection from a Pair of Vertically Inline Isothermal Horizontal Cylinders, M.Sc. Thesis, University of Dublin, 2010. T. Persoons, T.S. O’Donovan, High dynamic velocity range particle image velocimetry using multiple pulse separation imaging, Sensors 11 (2011) 1–18. T. Persoons, T.S. O’Donovan, D.B. Murray, Heat transfer in adjacent interacting impinging synthetic jets, in: Proceedings of the ASME Summer Heat Transfer Conference, San Francisco, 19–23 July 2009, HT2009-88440.
[18] T. Persoons, A. McGuinn, R. Farrelly, D.B. Murray, High dynamic range wholefield turbulence measurements in an impinging synthetic jet, Exp. Fluids (in review). [19] M. Stanislas, K. Okamoto, C.J. Kähler, J. Westerweel, Main results of the second international PIV challenge, Exp. Fluids 39 (2005) 170–191. [20] T.H. Kuehn, R.J. Goldstein, Numerical solution to the Navier–Stokes equations for laminar natural convection about a horizontal isothermal circular cylinder, Int. J. Heat Mass Transfer 23 (1980) 971–979. [21] J.H. Merkin, Free convection boundary layers on cylinders of elliptic cross section, ASME J. Heat Transfer 99 (1977) 453–457. [22] M.S. Sadeghipour, M. Asheghi, Free convection heat transfer from arrays of vertically separated horizontal cylinders at low Rayleigh numbers, Int. J. Heat Mass Transfer 37 (1994) 103–109. [23] E. Sparrow, J.E. Niethammer, Effect of vertical separation distance and cylinder-to-cylinder temperature imbalance on natural convection for a pair of horizontal cylinders, ASME J. Heat Transfer 103 (1981) 638–644. [24] F.P. Incropera, M.A. Yaghoubi, Buoyancy driven flows originating from heated cylinders submerged in a finite water layer, Int. J. Heat Mass Transfer 23 (1980) 269–278. [25] M.M. Zdravkovich, Flow Around Circular Cylinders. 1: Fundamentals, Oxford University Press, 1997.
Contents lists available at SciVerse ScienceDirect
International Journal of Heat and Mass Transfer journal homepage: www.elsevier.com/locate/ijhmt
Natural convection heat transfer and fluid dynamics for a pair of vertically aligned isothermal horizontal cylinders Tim Persoons ⇑, Ian M. O’Gorman, David B. Donoghue, Gerry Byrne, Darina B. Murray Department of Mechanical and Manufacturing Engineering, Parsons Building, Trinity College, Dublin 2, Ireland
a r t i c l e
i n f o
Article history: Received 18 March 2011 Received in revised form 21 August 2011 Available online 8 September 2011 Keywords: Tubular heat exchangers Flow oscillations Particle image velocimetry Thermal plume interaction Vortex sheet
a b s t r a c t This paper discusses the close interaction between local fluid dynamics and natural convection heat transfer from a pair of isothermally heated horizontal cylinders submerged in water. The presence of a second heated cylinder induces heat transfer enhancements of up to 10%, and strong fluctuations in local heat transfer rate. Therefore specific attention is focused on how the local heat transfer characteristics of the upper cylinder are affected by buoyancy induced fluid flow from the lower cylinder. The paper investigates a range of Rayleigh number between 1.8 106 and 5.5 106, and a vertical cylinder spacing between 2D and 4D. Simultaneous local heat flux measurements and flow velocity measurements using particle image velocimetry reveal oscillatory behaviour of the thermal plume, depending on operating conditions. A joint temporal analysis of the data has provided new insights into the governing mechanisms, which enables further optimisation of the heat transfer performance. Ó 2011 Elsevier Ltd. All rights reserved.
1. Introduction Tubular heat exchangers are among the most common devices for exchanging heat between two fluid flows. The time-averaged heat transfer characteristics are well known for forced convection from arrays of horizontal cylinders. However natural convection heat transfer has received less attention and there remain questions regarding the natural convection heat transfer mechanisms, especially for closely packed tube arrays, where thermal plumes interact with the thermal boundary layer around nearby cylinders. Most studies have focused on averaged heat transfer characteristics either for single cylinders [1] or cylinder arrays [2]. The interaction between adjacent cylinders is generally described in terms of an overall heat transfer enhancement. Only a very limited amount of knowledge is available on the influence of plume oscillations from one (upstream) cylinder on the heat transfer from another (downstream) cylinder; this is mainly due to the difficulty in the numerical modelling of the transient flow in the plume region. Some papers discuss the swaying motion caused by a thermal plume from single cylinders as a result of natural convection [3,4]. Low Rayleigh numbers are characterized by stationary two-dimensional laminar plumes. With increasing Ra, the plume starts to oscillate in very irregular flow patterns, especially near the top of the cylinder. At high Rayleigh number (Ra > 1010), the plume transitions ⇑ Corresponding author. Address: School of Mechanical Engineering, Purdue University, 585 Purdue Mall, West Lafayette, IN 47907, USA. Tel.: +1 765 494 5638; fax: +1 765 494 0539. E-mail addresses: [email protected], [email protected] (T. Persoons). 0017-9310/$ - see front matter Ó 2011 Elsevier Ltd. All rights reserved. doi:10.1016/j.ijheatmasstransfer.2011.08.033
to the turbulent regime [4]. A far greater amount of research has been carried out into studying plume swaying motion from thin horizontal heated wires, which can be regarded as line heat sources [5–7]. Relationships for the velocity and temperature of a plume from a single wire have been derived numerically [5]. These numerical predictions agree with experimental data for thin wires at low Rayleigh number, yet at higher Rayleigh number plume swaying is observed experimentally, causing substantial temperature oscillations in the plume centreline [6]. Desrayaud and Lauriat [8] numerically investigated buoyancy induced flow from a horizontal line heat source inside rectangular vessels with adiabatic sidewalls and isothermal top and bottom walls. For rectangular vessels two destabilising mechanisms lead to low frequency motion due to instability of the buoyant plume. These mechanisms depend on the ratio of depth of immersion to vessel width. The oscillation frequency collapses well to f = 0.0657Ra0.433 (0.3 106 < Ra < 8 106) [8] which agrees with earlier results of Noto [7]. These findings for single cylinders may serve as a reference case. Eckert and Soehngen [9] investigated heat transfer from a vertical cylinder pair and found that the induced temperature and velocity fields due to the buoyant plume from downstream cylinders have opposite effects. The heat transfer rate from the upper cylinder was found to decrease with decreasing cylinder spacing due to a decrease in the local temperature difference, while at larger spacing an increase in heat transfer was found to occur due to the higher local fluid velocity having a forced convection effect on the upper cylinder. For the case of a pair of horizontal isothermally heated cylinders, previous studies by the authors involving measurements of the local heat transfer coefficient around the cylinder circumference
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Nomenclature D DR Gr f g H h k Nu Pr q Ra r Sr S Ts, T1 t U, V
cylinder diameter (m) dynamic measurement range Grashof number (gb (Ts T1)D3/m2) frequency (Hz) gravitational acceleration (m/s2) immersion depth (m) local convective heat transfer coefficient (q/(Ts T1)) (W/(m2 K)) thermal conductivity of fluid (W/(m K)) Nusselt number (hD/k) Prandtl number (m/a) local convective surface heat flux (W/m2) Rayleigh number (GrPr) radial coordinate from cylinder centre (m) Strouhal number (fD/Vref) cylinder centre spacing (m) cylinder surface and bulk fluid temperature (K) time (s) horizontal and vertical fluid velocity (m/s)
have revealed a range of cylinder spacings and Rayleigh numbers where beneficial interaction occurs [10,11]. Based on spectral analysis of the local surface heat flux, it was hypothesized that when the plume from the bottom cylinder oscillates out of phase with the plume from the top cylinder, beneficial mixing occurs which explains the heat transfer enhancement. To elucidate these previously obtained results, the objective of this paper is to experimentally investigate the coupled fluid dynamics and heat transfer of natural convection from a pair of isothermal horizontal cylinders. The Rayleigh number ranges between 1.8 106 and 5.5 106, corresponding to the earlier investigations [10,11] and the cylinder centre spacing ranges between 2 and 4 cylinder diameters.
2. Experimental approach 2.1. Natural convection test facility The experimental test facility is designed to approximate the testing of a tubular section of infinite length contained within an infinite fluid medium. The facility uses a pair of isothermally heated copper cylinders with a diameter D = 30 mm. Horizontal and vertical confinement effects are minimized by choosing the end plate spacing greater than 3D [12] and the depth of immersion
Vt Vref 0 0 u, v x, y z
velocity tangential to cylinder (m/s) reference plume velocity (Eq. (1)) (m/s) fluctuation intensity of horizontal and vertical fluid velocity (m/s) horizontal and vertical coordinate (m) coordinate along cylinder axis (m)
Greek symbols a thermal diffusivity of fluid (m2/s) b volumetric expansion coefficient (K1) m kinematic viscosity of fluid (m2/s) q density of fluid (kg/m3) h circumferential coordinate (°) Subscripts s cylinder surface bulk fluid conditions 1 U velocity 0 u turbulence intensity
H greater than 3D [13]. Fig. 1 shows a schematic diagram of the facility built with these considerations in mind, measuring 900 mm high, 900 mm long and 300 mm (10D) wide. Deoxygenated water was chosen as the working fluid for this analysis. Air was deemed unsuitable due to the high temperatures required for the targeted Rayleigh number range, and due to the difficulty of properly insulating an air control volume from the surroundings. The large vessel volume (about 200 l) prevents excessive bulk water temperature drift during testing. 2.2. Local heat transfer measurements The instrumented cylinders are carefully machined and measure D = 30 mm in diameter and 10D long to mitigate end effects (see Fig. 1b). Each cylinder contains two 500 W cartridge heaters embedded along the cylinder axis, using thermal grease to minimise the thermal contact resistance. The minimum distance between the bottom cylinder and the vessel floor is 10D. Each cylinder is instrumented with a flush mounted thermopile heat flux sensor (RdF Micro-Foil™ 27036-2-RdF) and an internally mounted T-type thermocouple. The cylinders can be rotated about their axis to measure the local surface heat flux around the circumference, as shown in Fig. 1b. To minimize radiation losses the cylinder surfaces are polished to reduce the surface emissivity to around 0.10; the emissivity of the Kapton coating on the heat flux sensor is 0.70.
Fig. 1. (a) Diagram of the natural convection test facility and (b) definition of the coordinate system, separation distance S and depth of immersion H.
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The properties of water are evaluated at the film temperature, (Ts + T1)/2. The most accurate reading of the surface temperature Ts is obtained using a surface-mounted 0.3 mm fine wire T-type thermocouple, mounted at the same circumferential position h as the heat flux sensor yet at an axial distance of z = 10 mm from the sensor. This proved to be a more reliable approach than predicting the surface temperature based on one-dimensional heat conduction through the heat flux sensor and the thermocouple embedded in the sensor. For a given test, the Rayleigh number (Ra = Gr Pr = gb(Ts – T1)D3/(ma)) is set by adjusting the difference (Ts – T1) between the surface temperature and the bulk water temperature, which is measured at the same elevation y as the test cylinder. Measurements are only taken once a pseudo steady state is reached. Once the targeted operating parameters are met the cylinder is rotated in 10° intervals for half a revolution. At each interval the heat flux, surface temperature, and bulk fluid temperature are recorded. Preliminary testing has revealed very low frequency oscillations in heat transfer for multiple cylinder configurations. To capture this oscillatory behaviour a sampling time of approximately 220 s and sampling frequency of 40 Hz are applied. For each measurement condition, tests are repeated 5 times to ensure repeatability. The thermopile heat flux sensor signal is conditioned using a 1000:1 Fylde 351UA amplifier and read into a National Instruments 9172 data acquisition system (NI 9215, 16 bit, 0–10 V). Thermocouples are read into the data acquisition system (NI 9219, 24 bit, 0–80 mV) with internal cold junction compensation. The thermocouples were calibrated in situ against a factorycalibrated resistance temperature detector (RTD) probe with an Omega CL 26 digital meter (uncertainty of ±0.3% at 50 °C). An in-situ calibration was carried out for the heat flux sensors mounted on the instrumented cylinders, following the procedures outlined by Reymond et al. [11] and Atmane et al. [13]. Thus, for each sensor, the measured heat transfer was referenced against the Churchill and Chu [14] correlation for natural convection from a single horizontal cylinder. In addition, an energy balance was conducted to equate the measured convective heat flux to the electrical power supplied to the internal cartridge heaters. These independent calibration procedures differed by a maximum of 8%, giving confidence in the results obtained. The heat flux measurement is the main contribution to the uncertainty in the Nusselt number. The maximum measurement uncertainty occurs at the highest Rayleigh number of 5.5 106. Based on a 95% confidence level, the overall estimated uncertainties of the Rayleigh and Nusselt numbers are around 1% and 16%, respectively. Repeatability across multiple tests is very good, with maximum rms fluctuations in Nusselt number below 0.5% for the
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single cylinder tests. More details of the calibration procedures and error analysis are given by O’Gorman [15]. 2.3. Fluid flow measurements 2.3.1. Particle image velocimetry approach Particle image velocimetry (PIV) is used to quantify the time-varying flow field. These measurements are performed simultaneously to the heat transfer measurements described above. Synchronisation of the start of both measurements is achieved using a common trigger signal. Fig. 1a depicts the arrangement of the laser light sheet optics (intersecting the cylinders in the mid-plane of the vessel) and the double-frame camera (Photron Fastcam SA1, 1024 1024 px, 5400 Hz at full frame rate, 12 bit, Sigma 105 mm f/2.8 lens). The light source is a Quantronix Darwin-Duo Nd:YLF twin cavity pulsed laser (15 mJ at 1000 Hz, 527 nm), and the mean light sheet thickness throughout the field of view is approximately 1 mm. With the light sheet entering from the left, the cylinder casts a shadow where no PIV measurements are possible (e.g. see Fig. 2). The camera is aligned nearly perpendicular to the light sheet, so as to minimize light reflections from the cylinder surface and maximize the visible region near the top cylinder surface. Because of the slightly off-perpendicular position (viewing angle of a few degrees), a calibration target was positioned in the water tank prior to the measurements to perform an optical distortion correction using Lavision’s Davis™ 7.2.2 software. Details of the calibration process are given by O’Gorman [15]. Polyamide particles with diameters between 30 and 70 lm and density of 1.03 g/cm3 are used as seeding. The maximum Stokes number (i.e. dimensionless relaxation time) never exceeds 0.2, indicating that the particles closely follow the water streamlines. After optical calibration of the camera setup in ambient conditions, the heating power to the instrumented cylinders is adjusted to meet the required thermal conditions for the given test. As slow frequency oscillations within the flow are expected, the camera frame rate is reduced to its minimum of 50 Hz, providing a maximum test duration of 26 s. Local heat transfer data from the instrumented test cylinders is recorded simultaneously with the PIV images. The tests were restricted to Rayleigh numbers below 6 106, since at higher temperatures the quality of the vectors obtained close to the cylinder surface deteriorated due to differential optical refraction within the thermal plume, causing an elongation of the seeding particle images. This optical aberration is minimized by positioning the camera at a slightly oblique angle (about 5°), thereby minimizing the overall thermal gradients in the light path incident to the camera lens.
Fig. 2. Comparison of turbulence intensity distribution (u0 2 + v0 2)1/2/Vref around the upper of two heated cylinders at Ra = 3.6 106 and S = 3D, using (a) conventional PIV with a pulse separation of 40 ms and (b) multi-pulse separation (MPS) PIV based on three pulse separation values (40, 80 and 160 ms).
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Table 1 Comparison of the dynamic measurement range of the mean velocity and turbulence intensity using conventional and MPS PIV, for Ra = 3.6106 and S = 3D (see Fig. 2). Quantity
Time-averaged Velocity (U2 + V2)1/2 rms turbulence Intensity (u0 2 + v0 2)1/2
sensor position angles of h = 0°, 90°, 135° and 180°. Four horizontal cylinder configurations were tested: a single cylinder and a pair of vertically aligned cylinders with centre spacings 2D, 3D and 4D.
Measurable range For conventional PIV
For MPS PIV [16]
0.028–2.06 mm/s DRU = 70:1 0.063–1.38 mm/s DRu0 = 20:1
0.005–1.86 mm/s DRU = 410:1 0.012–1.36 mm/s DRu0 = 110:1
2.3.2. High dynamic range PIV measurements Since the flow field is characterized by strong velocity gradients and differences in velocity magnitude between the thermal plume and the entrainment region, a novel technique for increasing the dynamic range of standard PIV is applied. The multiple pulse separation (MPS) technique described by Persoons and O’Donovan [16] combines information from sets of images acquired at multiple pulse separations, to automatically determine the locally optimal pulse separation depending on local flow field characteristics. By increasing the dynamic velocity range, MPS PIV obtains more accurate mean flow and turbulence measurements compared to conventional PIV. Fig. 2 shows a sample result comparing (a) conventional PIV and (b) MPS PIV using three pulse separation multiples (1, 2 and 4 the minimum pulse separation of 40 ms). Conventional PIV tends to overestimate turbulence levels in low velocity regions, which has also been noted in other flow fields with a wide velocity range, such as impinging steady and synthetic jet flows [16–18]. This is due to the deterioration of vector quality when the particle displacement magnitude reduces to the minimum resolvable displacement which is about 0.1 pixels in typical laboratory conditions [19], even using advanced multi-grid correlation techniques. Table 1 compares the dynamic measurement range of conventional and MPS PIV. The MPS technique increases the dynamic range for mean velocity and turbulence intensity with a factor of 5.5 compared to conventional PIV, resulting in a considerably higher accuracy. The effect is more pronounced in flows with a wider velocity range [16–18].
3. Experimental results A range of Rayleigh numbers between 1.84 106 and 5.33 106 has been investigated, meaning that the flow is nominally laminar. Simultaneous PIV and heat transfer data were recorded at heat flux
Fig. 3. Effect of Rayleigh number on the time-averaged local Nusselt number along the circumference of a single cylinder (0° = bottom, 180° = top).
3.1. Heat transfer from a single cylinder Firstly, local heat transfer results from single cylinder measurements are presented. Fig. 3 shows the time-averaged local Nusselt number around the circumference of the cylinder, where 0° and 180° represent bottom and top of the cylinder, respectively (see definition in Fig. 1(b)). Fig. 3 shows that the maximum heat transfer rate occurs at the bottom stagnation point (0°) of the cylinder and steadily decreases with increasing angle until approximately 160°, with a sharper rate of decrease occurring over the final 20° of the cylinder circumference. This result is consistent with results for the local Nusselt number distribution about a single cylinder reported by Kuehn and Goldstein [20], Merkin [21] and Reymond et al. [11]. A power law scaling of Nu with Ra is observed with an exponent of 0.32 (R2 > 0.99), which is broadly consistent with the findings reported by Morgan [1] and Churchill and Chu [14]. The accelerated decrease in the local Nusselt number over the final 20° of the circumference is generally attributed to an insulating effect of the buoyant plume forming near top of the cylinder. To verify this, PIV flow visualisation was carried out for the case of a single cylinder and within the target Rayleigh number range of this experiment. For a selected case of Ra = 1.92 106, Fig. 4 shows the time-averaged flow field over a single cylinder as contours of velocity magnitude (U2 + V2)1/2/Vref, where the reference plume velocity Vref is defined as
R V ref ¼
x
Vðx; yÞ dx : b
ð1Þ
The plume width b is defined as the distance between the locations where the upward velocity drops to 25% of the peak velocity. Although the plume width slightly increases with y, the value of Vref according to Eq. (1) is reasonably independent of y. Within the Rayleigh number range investigated the plume width b remained constant at 0.35D (=10.5 mm; evaluated at y = 2D). The plume velocity according to Eq. (1) is typically about 1=4 of the characteristic velocity defined based on the square root of the Grashof number, (Ra/ Pr)1/2m/D. The plume detaches from the cylinder surface at an angle of approximately 159°, confirming that the sharp decrease in the local
Fig. 4. Time-averaged contours of velocity magnitude (U2 + V2)1/2/Vref and velocity vectors showing the buoyant plume above a single cylinder at Ra = 1.92 106 (Vref = 5.1 mm/s, plume width 2b = 0.35D at y = 2D).
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Nusselt number from a single cylinder is a direct result of the formation of the buoyant plume at this location.
3.2. Heat transfer from two vertically aligned cylinders 3.2.1. Heat transfer characteristics Previous work by the authors [10,11] has shown that the heat transfer characteristics of a pair of closely spaced horizontal cylinders are significantly different from those of a single cylinder. Reymond et al. [11] have demonstrated that only when both cylinders are heated a considerable degree of interaction occurs in the surface heat transfer rate from the upper cylinder. For a spacing of 1.5D or greater, the lower cylinder is unaffected by the upper cylinder and the upper cylinder is unaffected by an unheated lower cylinder. Table 2 gives an overview of the circumferentially averaged heat transfer coefficient, both for the single cylinder case and for the upper cylinder at inter-cylinder spacings of 2D, 3D and 4D. For the 2D spacing, a slight decrease in mean Nusselt number can be observed at low Rayleigh number. However for all other cases, an overall heat transfer enhancement is noted. This is in agreement with previous results by Reymond et al. [11]. For a fixed Rayleigh number (Ra = 5.33 106), Fig. 5 shows the effect on the local heat transfer coefficient of the presence of a second heated cylinder at spacings of 2D, 3D and 4D below the primary cylinder. Higher local heat transfer levels are evident, especially near the bottom (0°) and to a lesser extent near the top (180°) of the upper cylinder. For the smallest spacing (S = 2D), local increases of 60–100% are observed near the bottom and top of the upper cylinder. A reduction in heat transfer is observed along the sides of the cylinder, which is insignificant for larger spacings. For the largest spacing investigated (S = 4D), the heat
Table 2 Average Nusselt number of a single cylinder and the upper of a pair of vertically aligned cylinders, with values in brackets representing the relative deviation to a single cylinder case, (Nu Nu0)/Nu0 100%.
Single cylinder(S = 1) Upper cylinder (S = 4D) Upper cylinder (S = 3D) Upper cylinder (S = 2D)
Ra = 1.8 106
Ra = 3.6 106
Ra = 5.3 106
Nu = 16.9 Nu = 18.0 (+6.1%) Nu = 18.2 (+7.2%) Nu = 16.1 (–5.1%)
Nu = 20.7 Nu = 22.8 (+9.2%) Nu = 22.4 (+7.6%) Nu = 22.3 (+7.2%)
Nu = 23.8 Nu = 24.3 (+2.0%) Nu = 26.5 (+10.2%) Nu = 24.5 (+3.1%)
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transfer profile is similar to that of a single cylinder except near the top. For the parameters of the current investigation, the heat transfer characteristics of the lower cylinder were unaffected by the presence of the upper heated cylinder and are therefore not reported here. Fig. 5a shows that the local Nusselt profile of the upper cylinder is strongly dependent on the cylinder spacing. Although only shown for Ra = 5.3 106, this is true for the entire investigated Rayleigh range (1.8 106 6 Ra 6 5.3 106). Fig. 5b shows that the shape of the Nusselt profile at a fixed spacing is very similar under different Rayleigh number conditions. For the cylinder pair, strong fluctuations in heat transfer were noted, in particular near the bottom and top of the upper cylinder. Near the bottom, the thermal plume from the lower cylinder joins the upper cylinder’s boundary layer, whereas near the top (180°) the combined plume detaches. Fig. 6(a) and (b) shows the fluctuations in local Nusselt number at the bottom of the upper cylinder (h = 0°) for an cylinder spacing of (a) S = 3D and (b) S = 4D. At a moderate spacing (S = 3D), Fig. 6(a) shows a stable periodicity in the fluctuations induced by the presence of the lower heated cylinder. At a large spacing (S = 4D), the time trace in Fig. 6(b) shows evidence of two distinct regimes, one at a nearly constant Nusselt number and one exhibiting high amplitude and high frequency fluctuations. 3.2.2. Simultaneous flow field and heat transfer measurements The observation of this oscillatory phenomenon in the heat transfer justified a detailed study of the fluid dynamics. Due to camera memory limitations, the duration of these measurements is restricted to 26 s. Fig. 7 shows a single period of a buoyant plume oscillation in the region between a pair of vertically aligned cylinders at a Rayleigh number of 3.7 106 and a spacing of 3D. From left to right and top to bottom, the plots represent instantaneous flow fields at 2.5 s intervals. Fig. 7 shows that the plume from the lower cylinder does not split and rise symmetrically around the upper cylinder, but instead oscillates back and forth across the upper cylinder. As a result of the swaying motion, the cylinder experiences alternating pockets of high velocity fluid passing along its sides. Studies by Sadeghipour and Asheghi [22] and Sparrow and Niethammer [23] have attributed enhancement of the heat transfer from the upper cylinder to the forced convection effect caused by the plume from the lower cylinder, however these flow field measurements suggest that lateral oscillation of the thermal plume from the lower cylinder is an additional mechanism of heat transfer enhancement from the upper cylinder.
Fig. 5. Time-averaged local Nusselt number along the circumference of the upper cylinder: (a) effect of spacing 2D, 3D and 4D ( Ra = 5.33 106 and (b) effect of Rayleigh number at a fixed spacing S = 2D.
represents the single cylinder case) at
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Fig. 6. Time-resolved local Nusselt number on the bottom of the upper cylinder (h = 0°) at (a) S = 3D and (b) S = 4D, for low and high Rayleigh numbers (1.7 106 and 3.3 106).
Fig. 7. Instantaneous streamline and velocity magnitude plots at t = 0 s to 12.5 s in steps of 2.5 s (left to right, top to bottom) showing one plume oscillation period around the lower stagnation point of the upper cylinder at Ra = 3.7 106 and S = 3D (Vref = 4.2 mm/s, plume width 2b = 0.42D at y = 1D).
Fig. 8 shows the local Nusselt number time trace at a position of 90°, on the left side of the upper cylinder. The circular markers represent the simultaneously measured tangential velocity Vt just above the heat flux sensor. This velocity is determined from the time-resolved PIV data, by averaging the tangential velocity in the boundary layer region up to 0.2D from the cylinder surface:
V t ð90 ; tÞ ¼
1 0:2D
Z
0:7D
V t ðr; h ¼ 90 ; tÞ dr:
ð2Þ
This coherence between the local Nusselt number and local plume velocity highlights the impact of the swaying motion of the plume from the lower cylinder on the heat transfer performance of the upper cylinder. Fig. 8 does show some higher order components in both heat transfer and plume velocities. As shown in Fig. 7, the flow field features a wide range of larger vortices down to smaller eddies. Stochastic phenomena including shedding, merging and dissipation of vortices into small scale turbulence can explain these higher order perturbations observed in Fig. 8.
r¼0:5D
As shown in Fig. 7, the plume alternates between the left and right side of the upper cylinder. Fig. 8 demonstrates that the time-resolved Nusselt number Nu(90°) and the tangential velocity on the same location Vt (90°) correlate well. The spectrum of both signals exhibits a peak fluctuation frequency of 0.065 (±0.003) Hz, with only a minor phase difference between the local velocity and Nusselt number.
4. Discussion 4.1. Positive heat transfer enhancement and plume instability At a spacing of 4D, Fig. 6b shows two distinct regimes occurring in the Nusselt number time trace at the bottom of the upper cylinder, one of high frequency fluctuations and one of relatively
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Fig. 8. Simultaneously acquired time-resolved (–) local Nu on left side of upper cylinder (h = 90°) and (s) near-cylinder tangential velocity Vt (in mm/s) just above the sensor position, at Ra = 3.7 106 and S = 3D (Vref = 4.2 mm/s, plume width 2b = 0.42D at y = 1D).
constant Nusselt number. The preceding discussion suggests that the highly fluctuating Nusselt number is a consequence of oscillation of the thermal plume from the lower cylinder. However this does not explain the steady regime in which the mean Nusselt number is comparable with that of a single cylinder at the same location, as shown in Fig. 9a. These two regimes are indicated with letters A and B in Fig. 9. No fixed periodicity is observed in the alternation between both regimes. Their occurrence is stochastic, with regimes A and B occurring, respectively in 17% and 83% of the total measurement time covering 12 separate tests. Fig. 9b gives a schematic representation of the flow field in both regimes. In regime A, no oscillations of the buoyant plume from the lower cylinder are observed and the plume from the bottom cylinder rises steadily along one side of the upper cylinder, maintaining a constant separation distance from the surface of the upper cylinder. This separation leads to two independent plumes rising above the upper cylinder. In regime B, oscillatory plume motion is observed and a single intertwined plume rises above the upper cylinder. In regime A the flow field around one side of the upper cylinder is similar to that around a single cylinder, thus explaining why the
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heat transfer rate in regime A is comparable to that of a single cylinder (see Fig. 9a). The oscillatory regime B is clearly beneficial, with an averaged heat transfer level of about 50% higher than regime A. A further investigation was carried out to determine the mechanism triggering the instability in the lower cylinder plume, by simultaneously measuring the heat fluxes on the lower and upper cylinder. Fig. 10 presents the local convective heat flux q at the lower stagnation point (0°) on the upper cylinder and the upper stagnation point (180°) of the lower cylinder, for a Rayleigh number of 3.3 106 and two cylinder spacings. The heat flux at the top of the lower cylinder remains almost constant throughout the 400 s test period. This steady heat flux from the lower cylinder and the lack of coherence between the heat flux signals on the upper and lower cylinders suggests that unsteady heating from the lower cylinder is not the driving mechanism for plume oscillation. Therefore PIV measurements were employed to analyse the flow surrounding the upper cylinder in further detail. Fig. 11 shows the velocity distribution around the upper cylinder at the point of plume inflection (i.e. when the lower plume changes direction), for three Rayleigh numbers and a cylinder spacing of 3D and 4D. At plume inflection a strong counter-clockwise vortex is formed to the left of the plume (and vice versa, a clockwise vortex is formed to the right when the plume transitions towards the other side of the upper cylinder). The formation of these vortices creates an unbalance in the lateral forces acting on the plume, which suggests that this mechanism may be responsible for the fluctuating oscillatory motion of the lower cylinder plume. Similar coupled oscillatory plume and vortex formation was observed by Incropera and Yaghoubi [24] using dye injection methods for the case of a circular cylinder confined by a free water surface. The observation of vortex rings by these researchers for the case of a vertically confined cylinder suggests that vertical confinement of the buoyant plume from the lower cylinder by the upper cylinder surface may be the cause of these alternate rotating vortices which drive the swaying oscillatory motion of the lower cylinder plume. A second possible interpretation for the plume swaying is that the vortices formed near the bottom of the upper cylinder are governed by a mechanism similar to Kelvin-Helmholtz instability in wake flows. The shear layers in the wake of a single cylinder in cross-flow are known to interact and form a von Karman vortex street. When expressed as Strouhal number, the dimensionless shedding frequency is quite constant over a wide range of Reynolds numbers based on approach velocity and cylinder diameter
Fig. 9. (a) Comparison between the time-resolved local Nusselt number at h = 0° (i.e. bottom stagnation point) of the upper of two cylinders at S = 4D (black line) to a single cylinder (grey line), both at Ra = 3.3 106. For a pair of cylinders, alternating heat transfer regimes are observed (A = constant Nusselt number and B = fluctuating Nusselt number), as schematically depicted in (b).
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Fig. 10. Simultaneously acquired local heat flux at the lower stagnation point (h = 0°) of the upper cylinder and upper stagnation point (h = 180°) of the lower cylinder, at Ra = 3.3 106 and (a) S = 3D and (b) S = 4D.
Fig. 11. Instantaneous streamline and velocity magnitude plot at the time of plume inflection around the upper of a pair of cylinders at (a–c) S = 3D and (d–f) S = 4D; (a, d) Ra = 1.8 106, (b, e) Ra = 3.6 106, (c, f) Ra = 5.3 106.
(300 < Re < 105) [25]. For the case shown in Fig. 8 (Ra = 3.7 106 and S = 3D), the observed plume fluctuation frequency f = 0.065 (±0.003) Hz becomes:
Sr ¼
fD ffi 0:46ð0:02Þ; V ref
ð3Þ
At the largest separation distance (S/D = 4), a similar value of Sr = 0.54 is found based on Vref (or Sr = 0.36 based on the maximum plume velocity) at a comparable Rayleigh number (Ra = 3.6 106). Further research is required to validate this finding in a wider range of parameters. 4.2. Heat transfer reduction and plume confinement
where Vref is determined according to Eq. (1) as the average plume velocity at a distance of 0.5D below the upper cylinder. Using the peak centreline plume velocity instead as reference velocity in Eq. (3) yields Sr = 0.30 ± 0.01. Although there is a significant difference between pressure-driven flow across a single cylinder and buoyancy-driven flow across a pair of cylinders, the Strouhal number value is of the same order of magnitude as the natural shedding frequency for a cylinder in cross-flow (Sr = 0.19 ± 0.01) [25].
Fig. 5a shows that for small S/D, the local Nusselt number of the upper cylinder is lower than that of a single cylinder. As mentioned in Section 1, heat transfer from the upper cylinder may be negatively affected by a reduced local temperature difference between the upper cylinder and the surrounding fluid, which can counteract any potential enhancement due to plume oscillation. However, the local reduction in heat transfer can be quite significant and addi-
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Fig. 12. Time-resolved local Nusselt number on the upper cylinder at Ra = 3.5 106 and S = 2D and 3D, at h = 50° corresponding to the circumferential location of maximum heat transfer reduction compared to a single cylinder case (see Fig. 5).
tional mechanisms may be at play. The maximum local reduction was found to occur at h = 50° for Ra = 3.5 106 and S = 2D, which is the focus of the following investigation. Fig. 12 compares the local Nusselt number at h = 50° for this case against a spacing of 3D. A low frequency, low amplitude oscillatory pattern is observed at S = 2D, very different from the behaviour at S = 3D. Although not shown here, PIV measurements show a regular swaying motion of the plume at S = 2D, however with a much lower amplitude and frequency compared to those found at the same Rayleigh number and larger spacings, as shown in Fig. 7. Incropera and Yaghoubi [24] found that the behaviour of a buoyant plume confined by a free water surface is strongly dependent on the immersion depth H/D, where H is the distance from the cylinder top to the confining surface. They found that the amplitude of the plume oscillation decreases with decreasing H/D and that the oscillation became negligible for H/D < 0.5. This has been confirmed by Atmane et al. [13]. The reduction in oscillation amplitude in Fig. 12 is consistent with these findings [13,24], suggesting that excessive confinement of the plume by the upper cylinder can be responsible for the smaller fluctuations in heat transfer on the upper cylinder at a spacing of 2D. In addition to the weak plume oscillations at S = 2D, the formation and detachment of counter-rotating vortices on either side of the plume (as seen in Fig. 7 for S = 3D) was not observed at S = 2D. Incropera and Yaghoubi [24] reported that no vortex is formed below the air-water interface for H/D < 0.5, in contrast to larger immersion depths. The lack of vortex formation at this close spacing directly coincides with a large reduction of the local heat transfer of the upper cylinder compared to that found at a larger spacing. This supports the contention that vortex formation acts as an additional enhancement mechanism for increasing heat transfer from the upper cylinder of a pair of isothermal horizontal cylinders aligned in the same vertical plane. 5. Conclusions By combining particle image velocimetry (PIV) and local convective heat transfer measurements using hot-film anemometry, a methodology has been established to simultaneously study fluid dynamics and natural convection heat transfer from a pair of horizontal cylinders. Multiple pulse separation PIV has been successfully applied to increase the dynamic range in measuring the velocity and turbulence fields. In typical conditions, a 5.5 increase in dynamic velocity range has been obtained, resulting in more accurate flow and turbulence fields.
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A single cylinder does not show any significant fluctuations in heat transfer in the Rayleigh number range under investigation (1.8 106 6 Ra 6 5.5 106), and agrees well with established correlations in terms of the average heat transfer rate. However, in the case of two vertically aligned horizontal cylinders (centre spacing from 2D to 4D), a strong periodicity is observed in the local heat transfer rate. Fluctuations are highest around the bottom and top of the upper cylinder, where respectively the lower plume impinges and the upper plume detaches. The average heat transfer rate of the upper cylinder increases by up to 10% depending on Rayleigh number and separation distance, although a slight heat transfer reduction of 5% is observed at a small separation distance and low Rayleigh number (S/D = 2, Ra = 1.8106). The simultaneous flow field and heat transfer results show the interaction of oscillating thermal plumes, and have confirmed the existence of different alternating regimes. Related to the plume swaying, vortex shedding occurs near the bottom of the upper cylinder. After formation, these vortices travel upwards across alternating sides of the upper cylinder, resulting in pockets of high velocity fluid thus contributing to break up and mixing of the thermal boundary layer. At a cylinder spacing of S = 2D, excessive confinement of the buoyant plume from the lower cylinder is believed to be responsible for minimal fluctuations in heat transfer and regions of reduced local heat transfer on the upper cylinder. A temporal analysis shows how the plume velocity affects the local heat transfer rate. Further work is needed to confirm a hypothesis of a constant Strouhal number, reminiscent of vortex shedding in forced flow across a single cylinder. The established methodology of simultaneously acquiring flow field and heat transfer measurements has yielded a better insight into the fundamentals of natural convection heat transfer in this particular case, and enables a further optimisation of the observed heat transfer enhancement towards larger scale systems and industrial applications.
Acknowledgements Dr. Tim Persoons is a Marie Curie research fellow of the Irish Research Council for Science, Engineering and Technology (IRCSET). Ian M. O’Gorman is a postgraduate research scholar of the Irish Research Council for Science, Engineering and Technology (IRCSET). The authors acknowledge the work of Antoine Van Noorte and Pauline Vancraenenbroek, and the financial support of Science Foundation Ireland (SFI 09-RFP-ENM2151).
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