Free-stream turbulence effects on the instantaneous pressure and forces on cylinders of rectangular cross section
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DOI: 10.1007/s00348-002-0562-0
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- Noda, H. & Nakayama, A. Exp Fluids (2003) 34: 332. doi:10.1007/s00348-002-0562-0
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Abstract
Simultaneous measurements of instantaneous pressure distributions on rectangular cylinders of length to height ratio(B/D) of 1.0, 2.5 and 3.0 in smooth nonturbulent and homogeneous turbulent flows were made and the data were analyzed by phase averaging and spectral analysis in addition to more conventional methods. The turbulence in the inflow stream is nearly homogeneous and isotropic with the intensity and the scale of 5% and 1.2–1.5 times the cylinder height, respectively. The main effects of the turbulence in the inflow free stream of this scale and intensity are to laterally move the separated shear flow off the upstream corners and cause intermittent reattachment on the side surfaces of cylinders of B/D of 2.5 and larger. For the cylinder with smaller B/D, the flow does not reattach with or without turbulence in the free stream, and the instantaneous surface pressure distributions fluctuate quite periodically at a frequency corresponding to the Strouhal frequency of the vortex shedding. The effects of the free-stream turbulence appear in the increased fluctuation on the front surface as buffeting due to the impinging turbulence. When the separated shear layers reattach due to the influence of the free-stream turbulence, the reattachment point moves intermittently, the pressure distributions downstream of the reattachment fluctuate periodically, and a mild peak is formed in the spectra at a frequency much larger than the Strouhal frequency.
1 Introduction
Recent advances in numerical methods in fluid-flow simulations have made it possible to simulate various turbulent flows including those past bluff bodies. Simulation of turbulent flows when the incident flow is turbulent is very important in engineering applications such as flows past buildings and bridges in natural winds, but has been very difficult. One of the tasks that need to be performed in developing such simulation methods is to verify against known flows, but detailed experimental data on turbulent flow past bluff bodies in turbulent streams are not available at the present time.
More basic experimental investigations, however, have been made to clarify the effects of the free-stream turbulence. Vickery (1966), Roberson et al. (1972), Lee (1975a) and Miyazaki (1980) have investigated the effects of the intensity of the uniform turbulence in the free stream on the drag coefficient and the pressure distribution on a rectangular cylinder. Lee (1975b) and Petty (1979) investigated the effects of the scale of turbulence while Nakamura and Ohya (1984) studied the combined effects of both strength and scale of turbulence and showed that depending on the ratio of the turbulence scale and the cylinder size, the results can be very different. None of these data, however, are meant for detailed validation of simulation methods. Particularly, there are no data for detailed instantaneous forces and pressures on the body together with the detailed characteristics of the free-stream turbulence taken at the same time. The detailed information of the free-stream turbulence will be a prerequisite for serving as a validation test case.
In the present work, we collect detailed data for the turbulence of the oncoming flow including frequency spectra and two-point correlations without the models, and then simultaneous measurements of the instantaneous pressure distributions on all the surfaces of rectangular cylinder models are made. Though only one kind of free-stream turbulence is generated with a turbulence grid, measurements are made on cylinder models of various length-to-height ratios, so that the effects of the free-stream turbulence can be examined in grossly different flow situations.
2 Experimental methods
Measurement cases and conditions
Case | B/D | Inflow conditions | Re | |
---|---|---|---|---|
Intensity I_{n} (%) | Scale, L_{x} | |||
Case 1 | 1.0 | 0.2 | – | 6.89×10^{4} |
Case 2 | 5.3 | 1.13D | ||
Case 3 | 2.5 | 0.2 | – | 5.16×10^{4} |
Case 4 | 5.3 | 1.50D | ||
Case 5 | 3.0 | 0.2 | – | 5.16×10^{4} |
Case 6 | 5.3 | 1.50D |
3 Experimental results
3.1 Results of characteristics of free-stream turbulence
3.2 Drag and lift coefficients
Aerodynamic characteristics obtained by present measurement and previous studies
Inflow conditions | Re | St | C_{pb} | C_{D} | C′_{D} | C′_{L} | ||||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
Intensity (%) | Scale | |||||||||||||
(a) B/D=I.0 | ||||||||||||||
Present | 0.2 | – | 6.89×10^{4} | 0.131 | –1.483 | 2.164 | 0.207 | 1.180 | ||||||
5.3 | 1.12D | 0.133 | –1318 | 1.989 | 0.203 | 1.105 | ||||||||
Nakaguchi et al. (1968) | Smooth | – | 2~6×10^{4} | 0.13 | –1.50 | 2.10 | – | – | ||||||
Ootsuki et al. (1980) | 0.2 | – | 6.5~7×10^{4} | 0.12 | –1.35 | 2.08 | 0.11 | 0.82 | ||||||
Bearman and Trueman (1972) | Smooth | – | 6.8×10^{4} | 0.13 | –1.40 | 2.19 | – | – | ||||||
Bearman and Obasaju (1982) | Smooth | – | 4.7×10^{4} | 0.125 | –1.65 | – | – | – | ||||||
Mizota and Okajima (1982) | Smooth | – | 7.14×10^{4} | 0.125 | –1.64 | – | – | – | ||||||
Okajima (1982) | Smooth | – | 4.2×10^{4} | 0.13 | –1.47 | – | – | – | ||||||
Durao et al. (1988) | 6 | – | 1.4×10^{4} | 0.138 | – | – | – | – | ||||||
Lyn and Rodi (1994) | 2 | – | 2.2×10^{4} | 0.132 | – | – | – | – | ||||||
Vickery (1966) | Smooth | – | 1.0×10^{5} | 0.118 | –1.31 | – | – | – | ||||||
10.0 | 1.33D | – | 0.120 | –0.71 | – | – | – | |||||||
Roberson et al. (1972) | 0.5 | – | 2.16×10^{4} | – | –1.13 | 1.19 | – | – | ||||||
4.0 | – | 1.97×10^{4} | – | –1.06 | 1.85 | – | – | |||||||
8 | – | 2.02×10^{4} | – | –0.88 | 1.65 | – | – | |||||||
Lee (1975a) | 0.5 | – | 1.76×10^{4} | 0.122 | –1.30 | 2.05 | – | – | ||||||
6.5 | – | 1.14D | 0.126 | –1.18 | 1.93 | – | – | |||||||
Petty (1979) | Smooth | – | 2.9×10^{4} | – | –137 | – | – | – | ||||||
4.0 | 0.9D | – | –1.19 | – | – | – | ||||||||
8.0 | 1.1D | – | –0.96 | – | – | – | ||||||||
Nakamura and Ohya (1984) | 0.12 | – | 6.6×10^{4} | – | –1.50 | – | – | – | ||||||
6.1 | 0.85D | – | –1.20 | – | – | – | ||||||||
10.0 | 1.05D | – | –0.97 | – | – | – | ||||||||
Tamura and Miyagi (1998) | 0.4 | – | 3.0×10^{4} | – | – | 2.09 | – | 1.05 | ||||||
6.5 | 0.76D | – | – | 1.79 | – | 0.74 | ||||||||
14.0 | 0.80D | – | – | 1.49 | – | 0.34 | ||||||||
(b) B/D=2.5 | ||||||||||||||
Present | 0.2 | – | 5.16×10^{4} | 0.070 | –0.746 | 1.562 | 0.054 | 0.256 | ||||||
5.3 | 1.5D | 0.049, | –0.558 | 1.346 | 0.119 | 0.217 | ||||||||
0.169 | ||||||||||||||
Nakaguchi et al. (1968) | Smooth | – | 2~6×10^{4} | 0.07 | –0.62 | 1.32 | – | – | ||||||
Ootsuki et al. (1980) | 0.2 | – | 6.5~7.6×10^{4} | 0.06 | –0.46 | 1.42 | 0.03 | 0.28 | ||||||
Okajima (1982) | Smooth | – | 4.2×10^{4} | 0.06, | –0.53 | – | – | – | ||||||
0.12 | ||||||||||||||
(c) B/D=3.0 | ||||||||||||||
Present | 0.2 | – | 5.16×10^{4} | 0.163, | –0.641 | 1.472 | 0.070 | 0.137 | ||||||
0.049 | ||||||||||||||
5.3 | 1.5D | 0.168, | 0.487 | 1.312 | 0.110 | 0.152 | ||||||||
0.051 | ||||||||||||||
Nakaguchi et al. (1968) | Smooth | – | 2~6×10^{4} | 0.154 | –0.50 | 1.23 | – | – | ||||||
Ootsuki (1980) | 0.2 | – | 6.5~7.6×10^{4} | – | –0.35 | 1.26 | 0.05 | 0.31 | ||||||
Okajima (1982) | Smooth | – | 4.2×10^{4} | 0.15 | –0.44 | – | – | – |
3.3 Instantaneous and phase-averaged surface pressure distributions
It can be seen in Fig. 7 that, in the case of B/D=1.0, the results for the smooth flow and turbulent flow are about the same, and the pressures on all surfaces fluctuate at a frequency corresponding to that of the vortex shedding and the distribution is anti-symmetric about the centerline of the model. The amplitude of fluctuation decreases slightly towards the downstream end of the side surface where a slight phase lag is also seen.
The smooth-flow results for the case of B/D=2.5 shown in Fig. 8 show fewer periodic fluctuations compared with the case of B/D=1.0, but a weak periodic fluctuation is seen in the side-surface pressure distributions. The turbulent inflow case shown in Fig. 8b shows large wavy fluctuations over the downstream half of the side surfaces, though not on the fixed-phase basis, and the waviness is seen to propagate in the downstream direction. This is considered to be due to an unsteady reattachment of the flow separated at the upstream corners. When the reattachment occurs, the fast flow reaches the surface and creates negative peaks in the surface pressure distribution. As the aspect ratio is increased to B/D=3.0, clear periodicity is lost for both smooth and turbulent inflow cases and instantaneous distributions are shown. The overall fluctuations are small when the inflow is smooth and the reattachment occurs more steadily compared with the turbulent inflow case of B/D=2.5. When the inflow is turbulent, the pressure over the downstream half of the side surfaces change with large amplitude and is very much like the case of B/D=2.5, with distinct negative peaks traveling downstream. These results indicate that the turbulence in the free stream causes flapping of the separated shear flow and, for cylinders of B/D=2.5 or larger, it is made to reattach intermittently on the side surface. This causes a fluctuation of the surface pressure near the downstream end of the cylinder. The case of B/D=2.5 is the critical case, in which the flow does not reattach without the free-stream turbulence, but with the turbulence unsteady reattachment occurs.
3.4 Mean and rms pressure coefficients
Next, the pressure fluctuation intensity results are examined. In the case of B/D=1.0, the pressure fluctuation on the front surface in the smooth flow case is very small at the center and increases towards the corners while, in the cases of B/D=2.5 and 3.0, it is small across the entire front surface. This is perhaps related to the fluctuation level on the side surfaces, which is very large for the fully separated case of B/D=1.0 compared with the reattaching cases of B/D=2.5 and 3.0. In turbulent inflow cases of B/D=2.5 and 3.0, the fluctuation level reaches maximum near x/D=2.0. According to Ishizaki and Katsura^{}(1974), the pressure fluctuation level becomes maximum near the reattachment point and the reattachment in the present flow is considered to occur near x/D=2.0. In the case of smooth inflow of B/D=2.5, no clear local maximum is seen and is an indication of no reattachment.
3.5 Power spectral density of fluctuating surface pressure
In the case of B/D=1.0, the flow is fully separated irrespective of the existence of the free-stream turbulence. The spectra on all surfaces shown in Fig. 12 for both smooth and turbulent-flow cases contain strong peaks corresponding to the Strouhal frequency of the vortex shedding. The only difference between the smooth and turbulent cases is seen near the center (y/D=0) of the front surface, where the spectra for the turbulent inflow case look closer to the spectra of the inflow turbulence shown in Fig. 4. Therefore, the free-stream turbulence in the fully separated case merely causes a buffeting by the impinging turbulence. The spectra on the side surfaces are little influenced by the free-stream turbulence, and both cases show higher frequency contributions as the downstream corner is approached. These are smaller peaks at approximately twice the Strouhal frequency and perhaps related higher modes. The spectra on the rear surface contain both the high-frequency contributions and additional lower-frequency contributions near the center of the surface. These low-frequency contributions near the center of the body are considered to be due to the slow oscillation of the recirculating flow just downstream of the body.
In the case of B/D=2.5, the spectra of the fluctuating pressure are very different between the smooth and turbulent inflow cases. The smooth-flow results show peaks near nD/U_{ref}=0.07 that are considered to be due to the vortex shedding, since they are seen on all surfaces except near the center of the rear surface. This low frequency of vortex shedding also agrees with the previous results of Nakaguchi et al. (1968). The peak values are significantly smaller, indicating weaker shedding. The spectra for the turbulent inflow case look very different. Those on the front surface are very close to those of the inflow turbulence, except near the corner (y/D=0.5), where very gentle peaks are seen that correspond to the Strouhal frequency of the smooth-flow case (nD/U_{ref}=0.07). These small peaks, which may be related to the premature vortex shedding that may be starting near the corners, diminish at downstream positions of the side surfaces and disappear altogether at the downstream corner. Here, broad high-frequency contributions due to turbulent fluctuations dominate.
In the case of B/D=3.0, the spectra of pressure on the front surface of even the smooth inflow case do not show distinct peaks. This is consistent with the data of the instantaneous pressure distributions. The spectra of the turbulent inflow case are now almost exactly the same as the inflow turbulence. On the side surfaces, peaks that are not very clear appear at about nD/U_{ref}=0.17 for both cases, and they grow as the downstream corner is approached. Contributions from other frequencies over wider range also grow. On the rear surface, the direct effects of the inflow turbulence are not seen, and the results for both smooth and turbulent inflow cases are almost the same, except the turbulent inflow case shows larger contributions from the high-frequency fluctuations.
3.6 Spanwise correlation of surface pressure
In the case of B/D=1.0, the correlation of the pressure on the side surfaces is reduced slightly due to the turbulent flow. This is in agreement with Nakamura and Ohya's (1984) results. The correlation on the rear surface, on the other hand, is larger. In the cases of B/D=2.5 and 3.0, the high correlations on the side surfaces in the smooth flow are significantly reduced by the turbulent flow. The effects on the correlation on the rear surface are similar to the case of B/D=1.0 and it is larger in the turbulent flow. The main reason for the reduced correlation on the side surface by the free-stream turbulence is considered to be the shift of the reattachment position and its intermittent nature. The fact that the spanwise correlation of the pressures on the rear surface is increased by the free-stream turbulence is due to the increased turbulence downstream of reattachment and in the near wake tending to equalize the correlations on both surfaces.
4 Discussion
While the data presented in the present paper are mainly for documentation of the properties of the fluctuating surface-pressure distributions and the resulting aerodynamic forces, the simultaneously sampled instantaneous pressure distributions together with their spectral analysis allow us to clarify some of the flow physics important to the effects of the free-stream turbulence. It is known that the free-stream turbulence promotes reattachment and changes the overall flow characteristics, but how the instantaneous flow is influenced by the turbulence in the free stream has not been clear. The present data indicate that, when the length to height ratio B/D of the rectangular cross section is either as small as 1.0 or as large as 3.0, the turbulence in the inflow does not alter the overall characteristics of the fluctuation of the flow and the surface pressure. The main effects occur when B/D is in the critical range near B/D=2.5, which corresponds to the range where Nakaguchi et al. (1968) found a sudden change in the vortex shedding characteristics when there is no free-stream turbulence. The way the turbulence in the inflow influences the flow may be summarized as follows. The turbulence with the length scale of the same order as D, which is the scale in the present experiment, acts to shake the position of the shear layer separated off the upstream corners over the distances comparable to this scale. When it shifts towards the surface, it can reach the surface resulting in the flow reattachment. This was indicated by the local reduction of the surface pressure and its propagation in the downstream direction. This was seen to occur intermittently at a frequency higher than the vortex shedding. The periodicity of this motion is weak but shows as a mild peak at the low end of broad spectrum representing turbulent fluctuations. Though it may be confused as a secondary shedding frequency it is better interpreted as the contributions from the large-scale turbulent motion.
5 Conclusions
The present paper presents new and detailed statistics of aerodynamic pressure and forces on rectangular cylinders of various length-to-height ratios in smooth and turbulent streams. The instantaneous and simultaneous measurements of surface pressure at multiple positions on the cylinder surface allowed documentation of instantaneous and fixed-phase distributions of fluctuating pressure as well as other long-time statistics such as spectra and correlations. These clarify much of the effects of the free-stream turbulence and also provide a comprehensive test case for validation of simulation methods.
The turbulence generated in the inflow is very close to isotropic, with spectra and coherence following approximately the Kármán spectrum and Davenport coherence with the length scale of the same order as the cylinder height. The results may be interpreted as the effects of uniform isotropic turbulence.
The main effects are seen when B/D is in the critical range near B/D=2.5. The turbulence in the inflow with the length scale of the same order as D acts to move the position of the shear layer separated off the upstream corners, and this is the main mechanism for promoting reattachment. When the reattachment occurs, the vortex shedding is weakened significantly or suppressed. At the same time, the spanwise correlation of fluctuating pressure on the side surfaces is reduced, while that on the rear surface increases.