- Email: [email protected]
Experiments on circular cylinders in crossflow at Reynolds numbers up to 7 million
ARTICLE IN PRESS
Journal of Wind Engineering and Industrial Aerodynamics 96 (2008) 880–886 www.elsevier.com/locate/jweia
Experiments on circular cylinders in crossflow at Reynolds numbers up to 7 million S.J. Zan Aerodynamics Laboratory, National Research Council Canada, Ottawa, Canada Available online 26 July 2007
Abstract This paper describes a series of experiments conducted on polished circular cylinders in the Reynolds number range from 100,000 to 7 million. The experiments were conducted in a pressurized wind tunnel wherein Mach number and Reynolds number could be independently varied. Three models were used with aspect ratios of 10, 5 and 2.5. Measurements were also made in two gridgenerated turbulent flows with intensities of 5% and 13%. In addition to force balances at each end of the models, 32 pressure taps were embedded in a circumferential ring at mid-span and along the leeward generator. Both time-averaged and unsteady data are discussed. The pressure-tap data provide a detailed understanding of the unsteady flow, including vortex shedding, around the cylinder in different flow regimes. The presence of turbulence can change the flow state and hence the steady and unsteady loads. Compressibility effects are shown to exist above a Mach number of 0.3. Crown Copyright r 2007 Published by Elsevier Ltd. All rights reserved. Keywords: Strouhal number; Circular cylinder; Reynolds number; Mach number; Turbulence
1. Introduction Our understanding of the complex fluid mechanics and steady and unsteady loading on circular cylinders at Reynolds numbers in excess of a few hundred thousand remains incomplete. It is known that the fluid mechanics are influenced by free-stream turbulence, by the surface roughness of the model, and by the ‘‘two-dimensionality’’ of the flow. This study was undertaken to expand the knowledge base for smooth cylinders to include the
E-mail address: [email protected] 0167-6105/$ - see front matter Crown Copyright r 2007 Published by Elsevier Ltd. All rights reserved. doi:10.1016/j.jweia.2007.06.015
ARTICLE IN PRESS S.J. Zan / J. Wind Eng. Ind. Aerodyn. 96 (2008) 880–886
881
effects of compressibility, aspect ratio, and free-stream turbulence. It complements earlier work on roughened cylinders by Zan and Matsuda (2002). The descriptions of the state of the flow around a circular cylinder are subject to debate, with terms such as ‘‘supercritical’’ and ‘‘postcritical’’ used inconsistently by different authors. To avoid confusion, this paper will adopt the naming convention suggested by Zdravkovitch (1997). Those terms are based on the physical state of the boundary layer, specifically where the transition occurs. In the present context, the relevant regime is transition in the boundary layer, TrBL. For smooth cylinders in low turbulence flow, the TrBL regime has a lower Reynolds number bound of 100K1 to 200K and an upper bound of 3M to 5M. The TrBL regime is further sub-divided into the TrBL0 (drag coefficient decreasing and separation moving aft), TrBL1 (laminar bubble on one side of the cylinder), TrBL2 (two laminar bubbles), TrBL3 (spanwise disruption of bubbles) and TrBL4 (elimination of bubbles) regimes, all of which can occur as Reynolds number increases. The Strouhal number and magnitude of steady and unsteady loads are a reflection of the specific flow regime. As will be shown, turbulence can have large effects on the Reynolds number range over which these sub-regimes exist, and can eliminate some completely. 2. Experimental details 2.1. Models and instrumentation Three aluminum models with the same normalized surface roughness, k/D ¼ 106, were used in these tests. The diameters were 38, 75 and 150 mm. A model was mounted on a pair of two-component balances located outside the wind tunnel, but within the wind-tunnel plenum (Fig. 1). A boundary-layer suction system on both walls confers higher effective aspect ratios than suggested by the geometry. The model-mounting arrangement and wallsuction system are described in detail in Zan and Matsuda (2002). In addition to the external balances, the model was instrumented with 24 pressure taps arranged around the circumference of the model at mid-span and with eight pressure taps installed across the leeward generator. The spanwise variation in base pressure is an effective indicator of the flow state in the TrBL regime (Zan and Matsuda, 2002). A hotfilm anemometer was also inserted into the wake to record shedding frequencies. It was located 5.2 diameters downstream of each model and 0.4 diameters above each model centerline. All data were acquired at 4.8 kHz per channel. 2.2. The wind tunnel The tests were carried out in the 0.38 m 1.5 m two-dimensional test section of the trisonic blowdown wind tunnel at the Aerodynamics Laboratory (Ohman et al., 1970). The facility is pressurized and was operated at a constant Mach number (Mo0.4) and variable pressure for a given run. The total pressure, hence Reynolds number, can vary by an order of magnitude at the same flow speed, with a maximum pressure of 11.5 bar. The floor and ceiling are ventilated, eliminating the requirement for blockage corrections. 1
Following Zdravkovitch, K is used to denote 103 and M to denote 106, thus 20 K ¼ 20 103.
ARTICLE IN PRESS 882
S.J. Zan / J. Wind Eng. Ind. Aerodyn. 96 (2008) 880–886
Fig. 1. Schematic of model installation.
The background turbulence level in this facility is about 0.5%. In order to increase the turbulence level, two grids were designed and fabricated for these experiments. The streamwise turbulence intensities and integral length scales were 5% and 33 mm, and 13% and 74 mm.
3. Results and discussion 3.1. Strouhal number in smooth flow Schewe (1983) published a comprehensive study on the relationship between Strouhal number, St, and Reynolds number, Re, throughout the TrBL regime for a polished cylinder in smooth flow. In general terms, these results agree with the trends of that work, but there are some differences of note. Fig. 2 presents the relationship, primarily inferred from balance data, between Strouhal number and Reynolds number in smooth flow from all models used in these experiments. The transition to TrBL1 (St0.3) at a Reynolds number just above 300K is evident and agrees with Schewe. The 38 and 75 mm diameter models are consistent in this regard. The 150 mm diameter model could not be tested at Reynolds numbers below 400K. The emergence of the TrBL2 regime (St0.48) occurs for a Reynolds number of about 350K, again in agreement with Schewe. This shedding is weak, but was detected from PSDs of the balance, a pressure tap at 1441 from the windward generator and wake data (Fig. 3). All PSD magnitudes are scaled for clarity. In contrast to shedding in the TrSL and TrBL0 regimes wherein shedding can be detected at virtually any pressure tap around the circumference, in the TrBL2 regime shedding was typically detected at pressure taps in the range 90–1621 from the windward generator. Further, the magnitude of the shedding normalized by the dynamic pressure was reduced by an order of magnitude in the TrBL2 regime. It is possible that a free-to-respond model could couple with weak shedding to reinforce the shedding and lead to larger unsteady loads. However, given the relatively weak shedding strength and the fact that the pressure fluctuations act over a relatively
ARTICLE IN PRESS S.J. Zan / J. Wind Eng. Ind. Aerodyn. 96 (2008) 880–886 75 mm dia
38 mm dia
883
150 mm dia
Strouhal number
0.6 0.5 0.4 0.3 0.2 0.1 0.0 100K
1M Reynolds number
10 M
Fig. 2. Strouhal–Reynolds number relationship in smooth flow.
0.01 hot wire
PSD
000.1
1E-04
normal force
p tap
1E-05 0
0.5
1
1.5
fD/U Fig. 3. PSDs of 3 signals at Re ¼ 371K, smooth flow.
small arc on the surface, it would not be expected that the coupling would produce large loads. Above a Reynolds number of about 500K, the TrBL2 regime was not detected via the balance spectra and the spanwise variation in base pressure indicated the flow was highly three-dimensional. Wake and pressure-tap spectra however, indicated an St0.55 for Re as high as 700K (Fig. 4). Schewe reported the TrBL2 regime weakened with increasing Re, but remained for Re as high as 2M. Over the Reynolds number range 700K–1.5M, balance data showed a broad peak at fD/U0.1 and pressure taps within 751 of the windward generator indicated a weak narrow peak at fD/U0.19 (Fig. 5). No characteristic frequencies were detected in the wake. These pressure-tap locations confirm the hypothesis of Schewe that the lowfrequency excitation is not vortex shedding. In Schewe, two spectral peaks were reported spanning a Reynolds number range from 1.5M to 2M. For Reynolds numbers ranging from 2M to 5M, the current results indicate St0.2, as vortex shedding re-emerges and the broad peak at fD/U ¼ 0.1 fades. Above a Reynolds number of 5M, these data (150 mm diameter model only) indicated the Strouhal number remains at 0.2, whereas Schewe and others indicate that St rises to about 0.27 as Re increases above 5M. The aspect ratio in the current test was 2.5, whereas experiments for
ARTICLE IN PRESS S.J. Zan / J. Wind Eng. Ind. Aerodyn. 96 (2008) 880–886
884
0.1 0.01 PSD
hot wire
0.001 p tap at 72 deg
1E0-4 1E0-5 0
0.2
0.4 fD/U
0.6
0.8
Fig. 4. PSDs at Re ¼ 689K in smooth flow.
1 hot wire
PSD
0.1 0.01
normal force p tap at 54 deg
0.001 1E0-4 0
0.2
0.4 fD/U
0.6
0.8
Fig. 5. PSDs of 3 signals at Re ¼ 958K, smooth flow.
which St0.27 had aspect ratios in excess of 10. St0.22 was reported in James et al. (1980) for a model with aspect ratio o5. It may be that a further increase in Reynolds number on a low-aspect-ratio model would result in an increase in the Strouhal number. Results in the blowdown wind tunnel from a roughened model (k/D104) indicated St0.25 for Re4900K (Zan and Matsuda, 2002). Shih et al. (1993) showed that for roughened models at Re41M, St was independent of Re and that St decreased as roughness increased. The value of St at high Re for various surface conditions is important for many real-world applications and further understanding of these differences is required. 3.2. Strouhal number in turbulent flow In turbulent flow, the situation is changed dramatically. Results from the 5% turbulent flow are shown in Fig. 6. The data indicate a rise in St for Re4100K, consistent with Bearman (1969), followed by a region without coherent shedding and a re-emergence of shedding with St falling as Re is increased. Due to loading restrictions on the grid, the test Reynolds number in turbulent flow was limited to 2M. Turbulence has led to the reemergence of strong, coherent shedding at a lower Reynolds number than that for smooth flow, consistent with the Zan and Matsuda results for roughened models. In 13% turbulence vortex shedding was still detected in the balance and pressure-tap PSDs, with
ARTICLE IN PRESS S.J. Zan / J. Wind Eng. Ind. Aerodyn. 96 (2008) 880–886 75 mm dia
38 mm dia
885
150 mm dia
Strouhal number
0.4 0.3 0.2 0.1 0.0 100K
1M Reynolds number
10 M
Fig. 6. Strouhal–Reynolds number relationship in 5% turbulent flow.
0.7
CD
0.6
0.5 M = 0.20 M = 0.25
0.4
M = 0.30 M = 0.35 M = 0.4
0.3 1
0
2 Re (millions)
3
4
Fig. 7. CD vs. Re at various Mach numbers.
St0.25 independent of Reynolds number. Given that flow conditions in nature are often turbulent, the premise inherited from smooth flow tests of weak shedding is not necessarily conservative. 3.3. Effect of Mach number Bluff bodies are not often exposed to high-speed flows, although it is noted that design wind speeds in typhoon-prone areas can reach 95 m/s (Mach number, M0.28). Further, in atmospheric wind tunnels, an increase in model Reynolds number is sometimes effected by increasing the flow speed. It was thus of interest to determine how high a flow speed one could employ in an experiment. Fig. 7 plots the time-averaged drag coefficients for the 75 mm diameter model as a function of Reynolds number at different Mach numbers. The data are restricted to Reynolds numbers in the range 500K to 4M which represents the lowest Re obtained at M ¼ 0.4 and the highest Re attained at M ¼ 0.2. For Mach numbers less than 0.3 the results collapse, but increases in drag are noted for M40.3, and the
ARTICLE IN PRESS 886
S.J. Zan / J. Wind Eng. Ind. Aerodyn. 96 (2008) 880–886
increases are more severe as flow speed increases. At a Mach number of 0.4, the pressure coefficient at which the local velocity is sonic is 3.66. In the TrBL2 regime, the timeaveraged Cp at 901 from the windward generator was about 3, so it is not surprising to see the drag rise associated with increasing Mach number. A sharp-edged body, for which Cp values are more negative, would be expected to display a greater sensitivity to Mach number effects. 4. Conclusions Experiments conducted on polished circular cylinders at Reynolds numbers up to 7M have yielded results consistent with, but not identical to, previously published work. In particular, the value of the Strouhal number for Re45M was lower than previously reported results, possibly due to the model aspect ratio. Pressure-tap data demonstrated for the first time that shedding in the TrBL2 regime was limited to a narrow arc on the cylinder. The research also showed that the low-frequency excitation at Reynolds numbers of about 1M existed only on the windward side of the model and thus cannot be vortex shedding as previously believed. Turbulence was shown to have a major impact on the flow state, particularly in that it promotes the return of strong coherent shedding at Reynolds numbers significantly lower than that for smooth flow. Compressibility effects were observed for Mach numbers greater than 0.3. References Bearman, P.W., 1969. On vortex shedding from a circular cylinder in the critical Reynolds number regime. J. Fluid Mech. 37 (part 3), 577–585. James, W.D., Paris, S.W., Malcolm, G.N., 1980. Study of viscous crossflow effects on circular cylinders at high Reynolds numbers. AIAA J. 18 (9), 1066–1072. Ohman, L.H., et al., 1970, The NAE high Reynolds number 15 in 60 in two-dimensional test facility, Part 1. General Information. NRC-NAE-LTR-HA-4, National Research Council of Canada, April 1970. Schewe, G., 1983. On the force fluctuations acting on a circular cylinder in crossflow from subcritical up to transcritical Reynolds numbers. J. Fluid Mech. 133, 265–285. Shih, W.C.L., Wang, C., Coles, D., Roshko, A., 1993. Experiments on flow past rough circular cylinders at large Reynolds numbers. J. Wind Eng. Ind. Aerodyn. 49, 351–368. Zan, S.J., Matsuda, K., 2002. Steady and unsteady loading on a roughened circular cylinder at Reynolds numbers up to 900,000. J. Wind Eng. Ind. Aerodyn. 90, 567–581. Zdravkovitch, M.M., 1997. Flow Around Circular Cylinders. Fundamentals, vol. 1. Oxford University Press, Oxford, UK.
Journal of Wind Engineering and Industrial Aerodynamics 96 (2008) 880–886 www.elsevier.com/locate/jweia
Experiments on circular cylinders in crossflow at Reynolds numbers up to 7 million S.J. Zan Aerodynamics Laboratory, National Research Council Canada, Ottawa, Canada Available online 26 July 2007
Abstract This paper describes a series of experiments conducted on polished circular cylinders in the Reynolds number range from 100,000 to 7 million. The experiments were conducted in a pressurized wind tunnel wherein Mach number and Reynolds number could be independently varied. Three models were used with aspect ratios of 10, 5 and 2.5. Measurements were also made in two gridgenerated turbulent flows with intensities of 5% and 13%. In addition to force balances at each end of the models, 32 pressure taps were embedded in a circumferential ring at mid-span and along the leeward generator. Both time-averaged and unsteady data are discussed. The pressure-tap data provide a detailed understanding of the unsteady flow, including vortex shedding, around the cylinder in different flow regimes. The presence of turbulence can change the flow state and hence the steady and unsteady loads. Compressibility effects are shown to exist above a Mach number of 0.3. Crown Copyright r 2007 Published by Elsevier Ltd. All rights reserved. Keywords: Strouhal number; Circular cylinder; Reynolds number; Mach number; Turbulence
1. Introduction Our understanding of the complex fluid mechanics and steady and unsteady loading on circular cylinders at Reynolds numbers in excess of a few hundred thousand remains incomplete. It is known that the fluid mechanics are influenced by free-stream turbulence, by the surface roughness of the model, and by the ‘‘two-dimensionality’’ of the flow. This study was undertaken to expand the knowledge base for smooth cylinders to include the
E-mail address: [email protected] 0167-6105/$ - see front matter Crown Copyright r 2007 Published by Elsevier Ltd. All rights reserved. doi:10.1016/j.jweia.2007.06.015
ARTICLE IN PRESS S.J. Zan / J. Wind Eng. Ind. Aerodyn. 96 (2008) 880–886
881
effects of compressibility, aspect ratio, and free-stream turbulence. It complements earlier work on roughened cylinders by Zan and Matsuda (2002). The descriptions of the state of the flow around a circular cylinder are subject to debate, with terms such as ‘‘supercritical’’ and ‘‘postcritical’’ used inconsistently by different authors. To avoid confusion, this paper will adopt the naming convention suggested by Zdravkovitch (1997). Those terms are based on the physical state of the boundary layer, specifically where the transition occurs. In the present context, the relevant regime is transition in the boundary layer, TrBL. For smooth cylinders in low turbulence flow, the TrBL regime has a lower Reynolds number bound of 100K1 to 200K and an upper bound of 3M to 5M. The TrBL regime is further sub-divided into the TrBL0 (drag coefficient decreasing and separation moving aft), TrBL1 (laminar bubble on one side of the cylinder), TrBL2 (two laminar bubbles), TrBL3 (spanwise disruption of bubbles) and TrBL4 (elimination of bubbles) regimes, all of which can occur as Reynolds number increases. The Strouhal number and magnitude of steady and unsteady loads are a reflection of the specific flow regime. As will be shown, turbulence can have large effects on the Reynolds number range over which these sub-regimes exist, and can eliminate some completely. 2. Experimental details 2.1. Models and instrumentation Three aluminum models with the same normalized surface roughness, k/D ¼ 106, were used in these tests. The diameters were 38, 75 and 150 mm. A model was mounted on a pair of two-component balances located outside the wind tunnel, but within the wind-tunnel plenum (Fig. 1). A boundary-layer suction system on both walls confers higher effective aspect ratios than suggested by the geometry. The model-mounting arrangement and wallsuction system are described in detail in Zan and Matsuda (2002). In addition to the external balances, the model was instrumented with 24 pressure taps arranged around the circumference of the model at mid-span and with eight pressure taps installed across the leeward generator. The spanwise variation in base pressure is an effective indicator of the flow state in the TrBL regime (Zan and Matsuda, 2002). A hotfilm anemometer was also inserted into the wake to record shedding frequencies. It was located 5.2 diameters downstream of each model and 0.4 diameters above each model centerline. All data were acquired at 4.8 kHz per channel. 2.2. The wind tunnel The tests were carried out in the 0.38 m 1.5 m two-dimensional test section of the trisonic blowdown wind tunnel at the Aerodynamics Laboratory (Ohman et al., 1970). The facility is pressurized and was operated at a constant Mach number (Mo0.4) and variable pressure for a given run. The total pressure, hence Reynolds number, can vary by an order of magnitude at the same flow speed, with a maximum pressure of 11.5 bar. The floor and ceiling are ventilated, eliminating the requirement for blockage corrections. 1
Following Zdravkovitch, K is used to denote 103 and M to denote 106, thus 20 K ¼ 20 103.
ARTICLE IN PRESS 882
S.J. Zan / J. Wind Eng. Ind. Aerodyn. 96 (2008) 880–886
Fig. 1. Schematic of model installation.
The background turbulence level in this facility is about 0.5%. In order to increase the turbulence level, two grids were designed and fabricated for these experiments. The streamwise turbulence intensities and integral length scales were 5% and 33 mm, and 13% and 74 mm.
3. Results and discussion 3.1. Strouhal number in smooth flow Schewe (1983) published a comprehensive study on the relationship between Strouhal number, St, and Reynolds number, Re, throughout the TrBL regime for a polished cylinder in smooth flow. In general terms, these results agree with the trends of that work, but there are some differences of note. Fig. 2 presents the relationship, primarily inferred from balance data, between Strouhal number and Reynolds number in smooth flow from all models used in these experiments. The transition to TrBL1 (St0.3) at a Reynolds number just above 300K is evident and agrees with Schewe. The 38 and 75 mm diameter models are consistent in this regard. The 150 mm diameter model could not be tested at Reynolds numbers below 400K. The emergence of the TrBL2 regime (St0.48) occurs for a Reynolds number of about 350K, again in agreement with Schewe. This shedding is weak, but was detected from PSDs of the balance, a pressure tap at 1441 from the windward generator and wake data (Fig. 3). All PSD magnitudes are scaled for clarity. In contrast to shedding in the TrSL and TrBL0 regimes wherein shedding can be detected at virtually any pressure tap around the circumference, in the TrBL2 regime shedding was typically detected at pressure taps in the range 90–1621 from the windward generator. Further, the magnitude of the shedding normalized by the dynamic pressure was reduced by an order of magnitude in the TrBL2 regime. It is possible that a free-to-respond model could couple with weak shedding to reinforce the shedding and lead to larger unsteady loads. However, given the relatively weak shedding strength and the fact that the pressure fluctuations act over a relatively
ARTICLE IN PRESS S.J. Zan / J. Wind Eng. Ind. Aerodyn. 96 (2008) 880–886 75 mm dia
38 mm dia
883
150 mm dia
Strouhal number
0.6 0.5 0.4 0.3 0.2 0.1 0.0 100K
1M Reynolds number
10 M
Fig. 2. Strouhal–Reynolds number relationship in smooth flow.
0.01 hot wire
PSD
000.1
1E-04
normal force
p tap
1E-05 0
0.5
1
1.5
fD/U Fig. 3. PSDs of 3 signals at Re ¼ 371K, smooth flow.
small arc on the surface, it would not be expected that the coupling would produce large loads. Above a Reynolds number of about 500K, the TrBL2 regime was not detected via the balance spectra and the spanwise variation in base pressure indicated the flow was highly three-dimensional. Wake and pressure-tap spectra however, indicated an St0.55 for Re as high as 700K (Fig. 4). Schewe reported the TrBL2 regime weakened with increasing Re, but remained for Re as high as 2M. Over the Reynolds number range 700K–1.5M, balance data showed a broad peak at fD/U0.1 and pressure taps within 751 of the windward generator indicated a weak narrow peak at fD/U0.19 (Fig. 5). No characteristic frequencies were detected in the wake. These pressure-tap locations confirm the hypothesis of Schewe that the lowfrequency excitation is not vortex shedding. In Schewe, two spectral peaks were reported spanning a Reynolds number range from 1.5M to 2M. For Reynolds numbers ranging from 2M to 5M, the current results indicate St0.2, as vortex shedding re-emerges and the broad peak at fD/U ¼ 0.1 fades. Above a Reynolds number of 5M, these data (150 mm diameter model only) indicated the Strouhal number remains at 0.2, whereas Schewe and others indicate that St rises to about 0.27 as Re increases above 5M. The aspect ratio in the current test was 2.5, whereas experiments for
ARTICLE IN PRESS S.J. Zan / J. Wind Eng. Ind. Aerodyn. 96 (2008) 880–886
884
0.1 0.01 PSD
hot wire
0.001 p tap at 72 deg
1E0-4 1E0-5 0
0.2
0.4 fD/U
0.6
0.8
Fig. 4. PSDs at Re ¼ 689K in smooth flow.
1 hot wire
PSD
0.1 0.01
normal force p tap at 54 deg
0.001 1E0-4 0
0.2
0.4 fD/U
0.6
0.8
Fig. 5. PSDs of 3 signals at Re ¼ 958K, smooth flow.
which St0.27 had aspect ratios in excess of 10. St0.22 was reported in James et al. (1980) for a model with aspect ratio o5. It may be that a further increase in Reynolds number on a low-aspect-ratio model would result in an increase in the Strouhal number. Results in the blowdown wind tunnel from a roughened model (k/D104) indicated St0.25 for Re4900K (Zan and Matsuda, 2002). Shih et al. (1993) showed that for roughened models at Re41M, St was independent of Re and that St decreased as roughness increased. The value of St at high Re for various surface conditions is important for many real-world applications and further understanding of these differences is required. 3.2. Strouhal number in turbulent flow In turbulent flow, the situation is changed dramatically. Results from the 5% turbulent flow are shown in Fig. 6. The data indicate a rise in St for Re4100K, consistent with Bearman (1969), followed by a region without coherent shedding and a re-emergence of shedding with St falling as Re is increased. Due to loading restrictions on the grid, the test Reynolds number in turbulent flow was limited to 2M. Turbulence has led to the reemergence of strong, coherent shedding at a lower Reynolds number than that for smooth flow, consistent with the Zan and Matsuda results for roughened models. In 13% turbulence vortex shedding was still detected in the balance and pressure-tap PSDs, with
ARTICLE IN PRESS S.J. Zan / J. Wind Eng. Ind. Aerodyn. 96 (2008) 880–886 75 mm dia
38 mm dia
885
150 mm dia
Strouhal number
0.4 0.3 0.2 0.1 0.0 100K
1M Reynolds number
10 M
Fig. 6. Strouhal–Reynolds number relationship in 5% turbulent flow.
0.7
CD
0.6
0.5 M = 0.20 M = 0.25
0.4
M = 0.30 M = 0.35 M = 0.4
0.3 1
0
2 Re (millions)
3
4
Fig. 7. CD vs. Re at various Mach numbers.
St0.25 independent of Reynolds number. Given that flow conditions in nature are often turbulent, the premise inherited from smooth flow tests of weak shedding is not necessarily conservative. 3.3. Effect of Mach number Bluff bodies are not often exposed to high-speed flows, although it is noted that design wind speeds in typhoon-prone areas can reach 95 m/s (Mach number, M0.28). Further, in atmospheric wind tunnels, an increase in model Reynolds number is sometimes effected by increasing the flow speed. It was thus of interest to determine how high a flow speed one could employ in an experiment. Fig. 7 plots the time-averaged drag coefficients for the 75 mm diameter model as a function of Reynolds number at different Mach numbers. The data are restricted to Reynolds numbers in the range 500K to 4M which represents the lowest Re obtained at M ¼ 0.4 and the highest Re attained at M ¼ 0.2. For Mach numbers less than 0.3 the results collapse, but increases in drag are noted for M40.3, and the
ARTICLE IN PRESS 886
S.J. Zan / J. Wind Eng. Ind. Aerodyn. 96 (2008) 880–886
increases are more severe as flow speed increases. At a Mach number of 0.4, the pressure coefficient at which the local velocity is sonic is 3.66. In the TrBL2 regime, the timeaveraged Cp at 901 from the windward generator was about 3, so it is not surprising to see the drag rise associated with increasing Mach number. A sharp-edged body, for which Cp values are more negative, would be expected to display a greater sensitivity to Mach number effects. 4. Conclusions Experiments conducted on polished circular cylinders at Reynolds numbers up to 7M have yielded results consistent with, but not identical to, previously published work. In particular, the value of the Strouhal number for Re45M was lower than previously reported results, possibly due to the model aspect ratio. Pressure-tap data demonstrated for the first time that shedding in the TrBL2 regime was limited to a narrow arc on the cylinder. The research also showed that the low-frequency excitation at Reynolds numbers of about 1M existed only on the windward side of the model and thus cannot be vortex shedding as previously believed. Turbulence was shown to have a major impact on the flow state, particularly in that it promotes the return of strong coherent shedding at Reynolds numbers significantly lower than that for smooth flow. Compressibility effects were observed for Mach numbers greater than 0.3. References Bearman, P.W., 1969. On vortex shedding from a circular cylinder in the critical Reynolds number regime. J. Fluid Mech. 37 (part 3), 577–585. James, W.D., Paris, S.W., Malcolm, G.N., 1980. Study of viscous crossflow effects on circular cylinders at high Reynolds numbers. AIAA J. 18 (9), 1066–1072. Ohman, L.H., et al., 1970, The NAE high Reynolds number 15 in 60 in two-dimensional test facility, Part 1. General Information. NRC-NAE-LTR-HA-4, National Research Council of Canada, April 1970. Schewe, G., 1983. On the force fluctuations acting on a circular cylinder in crossflow from subcritical up to transcritical Reynolds numbers. J. Fluid Mech. 133, 265–285. Shih, W.C.L., Wang, C., Coles, D., Roshko, A., 1993. Experiments on flow past rough circular cylinders at large Reynolds numbers. J. Wind Eng. Ind. Aerodyn. 49, 351–368. Zan, S.J., Matsuda, K., 2002. Steady and unsteady loading on a roughened circular cylinder at Reynolds numbers up to 900,000. J. Wind Eng. Ind. Aerodyn. 90, 567–581. Zdravkovitch, M.M., 1997. Flow Around Circular Cylinders. Fundamentals, vol. 1. Oxford University Press, Oxford, UK.