Measurement on the cavitating vortex shedding behind rectangular

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Measurement on the cavitating vortex shedding behind rectangular obstacles

This article has been downloaded from IOPscience. Please scroll down to see the full text article. 2010 IOP Conf. Ser.: Earth Environ. Sci. 12 012066 (http://iopscience.iop.org/1755-1315/12/1/012066) View the table of contents for this issue, or go to the journal homepage for more

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25th IAHR Symposium on Hydraulic Machinery and Systems IOP Conf. Series: Earth and Environmental Science 12 (2010) 012066

IOP Publishing doi:10.1088/1755-1315/12/1/012066

Measurement on the cavitating vortex shedding behind rectangular obstacles F Hegedűs1, C Hős1, Z Pandula1 and L Kullmann1 1

Department of Hydrodynamic Systems, Budapest University of Technology and Economics Műegyetem rkp. 1, Budapest 1111, Hungary E-mail: [email protected]

Abstract. Measurement results on the cavitating vortex shedding behind sharp-edged rectangular bodies are presented, intended to provide benchmark cases for the validation of unsteady cavitation models of CFD codes. Rectangular bodies of increasing aspect ratio (1, 2, 3 and 4) were used with a constant 25mm height (12.5% blockage ratio). The water velocity in the 0.2x0.05m test section of the channel was varied between 1 and 12 m/s resulting in a Reynolds number in the range of (0.4-3.5)x105. Pressure signals were measured at several locations, notably in the wake. Dominant frequencies and Strouhal numbers are reported from cavitation-free flow (classic von Kármán vortex shedding) up to supercavitation as a function of the free-stream Reynolds number. The results are in good agreement with the literature in case of the square cylinder. We experienced a slight increase of the dominant Strouhal number with increasing aspect ratio. This result is somewhat inconsistent with the literature, in which a fall of the Strouhal number can be observed at side ratio 2. This may be the consequence of the different ranges of Reynolds numbers. It was also found that between the inception of cavitation and the formation of supercavitation the Strouhal number is not affected by cavitation.

1. Introduction Cavitation is known as a destructive phenomenon and avoiding it in hydraulic machinery is of essential interest in the engineering. The numerical simulation of cavitation is challenging due to the complex physical properties of multiphase flows. Our main aim is to provide benchmark cases for such CFD simulations. Cylinders of rectangular cross section with side ratios between 1 and 4 were studied, which have the advantage of simple geometry and well-defined separation points. Although there are many studies dealing with cavitational flows, e.g. hydrofoils (Foeth [1], Lohrberg [2]), circular cylinder (Saito [3]), confuser-diffuser test section (Stutz [4-5]), triangular cylinder and sphere (Schmidt [6]), only few studies concern with this simple geometry, for instance Wienken [7]. The flow around rectangular cylinders was extensively studied only if no cavitation occurs. These experiments were usually performed in wind tunnels. Okijama in [8] examined rectangular cylinders with different side ratios (B/H=1 to 4) in the range of Reynolds numbers (Re) between 70-20000. The Strouhal number for the square cylinder was approximately constant and changed slightly between 0.13-0.14. In the case of B/H=2 the Strouhal number definitely increased with increasing Reynolds number below Re=500. At this point there is a discontinuity in the Strouhal number curve, namely, the Strouhal number falls and remains nearly constant at 0.08-0.09. In case of B/H=3 there is more than one peak in the spectrum in the range of Re=1000-3000, that is, more than one Strouhal number can be associated with a certain value of Reynolds number. At higher Reynolds numbers the Strouhal number approaches 0.16-0.17. Finally in the long model with B/H=4 the Strouhal number is nearly constant 0.14. The blockage ratio was 0% (no walls enclosed the model). Sarioglu [9] studied rectangular cylinders as well with B/H=1 and 2 at Re=13159, 53786 and 99714. The blockage ratio was 10.94%. In both cases the Strouhal number was constant at 0.12-0.13 and 0.08-0.09 respectively not depending on the Reynolds number. Lyn [10] examined the same test case with B/H=1 at Re=21400. The result showed good agreement with that of Okijama [8], St=0.132. The following papers obtained the same experimental outcome in case of B/H=1: Saha [11], Davis [12] and Nakagawa [13]. Davis [12] used relatively low Reynolds numbers (100-1850), but the effect of the blockage ratio was examined. It was

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clearly seen that with the increase of the blockage ratio (0%, 16.6%, 25%) the Strouhal number (~0.13, ~0.16, ~0.17) increased as well. As for the numerical simulation, the results usually show good agreement with the experimental data. Kim [14] performed large eddy simulation for a square cylinder at Re=3000 with blockage ratios 0% and 20%. The Strouhal numbers were 0.125 and 0.124 respectively. It is worth to note that the Strouhal number in case of blockage ratio 20% should be greater according to Davis [12]. Sohankar [15] also used large eddy simulation but at Re=105 the blockage ratio was 6% and the Strouhal number was 0.13. The present study intends to provide benchmark cases to CFD simulations comparing the experimental results with those found in the literature. The basis of the comparison is the Strouhal number of the vortex shedding at different Reynolds numbers. The measurement is based on pressure signal recorded in the side walls of test section and on the upper wall of the rectangular cylinder.

2. Experimental set-up The schematic draw of the cavitation channel of the Department of Hydrodynamic Systems of the Budapest University of Technology and Economics can be seen in Fig.1. The channel is 4.9m high and 5.7m long and most of it was built up by ∅400mm and ∅500mm conduits. The 1m long test section is made of stainless steel and Plexiglas. In the closed system the water is circulated by an axial pump which is driven by a 34kW electric motor. The revolution speed is controlled by a frequency converter, thus arbitrary revolution speeds can be set in the range of 30-730 rpm. Directly in front of the test section there is a confuser in which the flow velocity increases significantly due to the large change in cross section. The achievable maximal mean velocity is approximately 12m/s depending on the geometry of the test body. The elbow connected to the confuser section includes guide vanes to avoid flow separation. The test section has a rectangular cross section of 50mm x 200mm. The model of 25mm height and side lengths of 25, 50, 75 and 100mm is placed 240mm after the middle of the test section. At the downstream side of the test section a reservoir is located providing constant downstream overpressure, which was H0=1.28m of water column throughout the experiments.

Fig. 1 Geometry of the cavitation channel and the test section. During the measurements five pressure transducers and one ultrasonic flowmeter were used. The arrangement of the pressure taps is shown in Fig.2. There was one pressure tap on the top of the models placed 12.5mm after the leading edge (S1, HBM P6A 10bar), and one pressure tap was in the test section after 12.5mm of the trailing edge (S2, HBM P6A 10bar). The pressure difference on the confuser was measured with a mercury-filled single tube manometer, a reversed U-tube manometer containing air above the water and a pressure difference transducer (S3, HBM PD1 1bar). For the absolute pressure level pressure signal was recorded in front of the model (S4, HBM P6 10bar). The last pressure tap was assembled 625mm after the model and 50mm above the centre line (S5, HBM P6 10bar). The ultrasonic flowmeter was placed at the suction tube of the

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circulating pump (S6). The measured signals were recorded by a PC through an HBM 840X type A/D converter. The ultrasonic flowmeter was manufactured by FLEXIM, type UMADM5X07-PU1-2EN. The results will be interpreted with the help of dimensionless numbers; namely the Thoma’s cavitation number, the Reynolds number and the Strouhal number defined as

σ =2

pr − pv , ρ U2

Re =

UH

and

ν

St =

fH , U

(1a-c)

where pr is the freestream reference pressure, pv is the vapour pressure, ρ is the density and ν is the kinematic viscosity of the liquid, U is the mean velocity in the test section (before the obstacles), H is the height of the cylinder and f denotes frequency.

Fig. 2 Sensor arrangement

3. Results 3.2 Square cylinder Figure 3 shows a typical waterfall diagram of the pressure signals measured by sensor S1 (upper horizontal wall of the cylinder, see Fig.2.c.) for a square cylinder with 25mm length. Each spectrum was normalized by its maximum. For low and medium pump revolution numbers (flow velocities), we experienced a single dominant frequency and its linear increase with flow velocity, corresponding to von Kármán vortex shedding frequency. The first harmonic with double frequency is also clearly seen in this range. Between approx. 350 and 500 rpm, there is an intermediate range with wide frequency content, where the appearing frequencies are beneath the dominant one. Finally, above approximately 500 rpm, only a very low-frequency component is present corresponding to the appearance of a massive cavitating cloud (supercavitation). The measurements were also performed at different sample rates (600Hz, 1200Hz, 2400Hz) but the higher sample rates did not yield any additional information, therefore the sample rate 600Hz was used in later experiments.

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Fig. 3 Waterfall diagram; B/H=1, sensor S1. The same data set is represented again in Fig.4., where the Reynolds number and Strouhal number defined by (1b) and (1c) are used instead of the pump revolution number and frequency. The scatter plot depicts the peaks above the 30% of the actual spectrum. It can be clearly seen that up to the occurrence of cavitation (Re=2x105, σ=4.89) the dominant Strouhal number is constant and its value is 0.15, which is in good agreement with the literature value of 0.13 given in [12] and [15]. The difference is presumably due to the different blockage ratio, which was 12.5% in our case. Concerning to the inception of cavitation, Wienken in [7] experienced the onset at Re=105, σinc=5.75, which is again a fairly good agreement. Figure 5 presents the same type of diagram for the spectra of the pressure signals measured in the wake by sensor S5 (625mm beneath the cylinder and 50mm above the centre line, see Fig.2.a.). It is interesting that the low-frequency range appears at lower Reynolds numbers and the frequency content is “denser”, which suggests that although the vortex generation frequency is still periodic on the upper and lower horizontal walls, this periodicity is destroyed by the interaction of the vortices in the wake. Figure 6 presents three photos of the measurements at different Reynolds numbers.

Fig. 4 Strouhal number versus Reynolds number at sensor S1 (top of the cylinder); B/H=1. The vertical red li nes indicate the parameter values where the photos shown in Fig. 6. were shot.

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Fig. 5 Strouhal number versus Reynolds number using sensor S5 (after the cylinder); B/H=1. The vertical red lines indicate the parameter values where the photos shown in Fig. 6. were shot.

Fig. 6 Photos at different Re numbers, left: Re=2.46⋅105 (σ=3.16), centre: Re=2.92⋅105 (σ=2.16), right: Re=3. 38⋅105 (σ=1.50); B/H=1. 3.2 Rectangular cylinders Figures 7, 9 and 11 depict the most dominant frequencies of the power spectra of the pressure signals at sensor S5 for rectangular cylinders with B/H=2, 3 and 4, respectively. A common feature of these scatter plots is the massive “cloud” of the Strouhal numbers decreasing with increasing Reynolds number. At this point it is not clear if these frequencies are only background noise or they have physical meaning, e.g. the loss of coherence as reported in [11]. Let us also mention that researchers (e.g. [11]) also experienced a shift in the frequencies towards the origin with increasing Reynolds number. Although it is not clearly seen, the dominant frequency is still present in these figures. For B/H=2, the average value is 0.19, which slightly increases with increasing the B/H values: 0.20 for B/H=3 and 0.21-0.22 for B/H=4. This is somewhat inconsistent with the literature results measured at lower Reynolds numbers; in [8] Okijama measured with rectangles of B/H=1…4 up to Re=2x104, in [9] Sarioglu measured with B/H=1 and 2 up to Re=105 and they both experienced a fall of the Strouhal number at B/H=2 to St=0.08-0.09. Concerning to the inception of cavitation, we experienced a slight decrease in the cavitation number (σ=4.89, 4.46, 4.31 and 4.31 for B/H=1, 2, 3 and 4). As cavitation appears first at the leading edge of the cylinder, the almost constant nature of the cavitation coefficient is not surprising. The cavitation number corresponding to supercavitation also does not change significantly; the reason is as explained before. Figures 8, 10 and 12 show the photos shot at different Reynolds numbers.

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Fig. 7 Strouhal number versus Reynolds number using sensor S5 (after the cylinder); B/H=2.

Fig. 8 Photos at different Re numbers, left: Re=2.61⋅105 (σ=2.81), centre: Re=3.10⋅105 (σ=1.90), right: Re=3.58⋅105 (σ=1.36); B/H=2.

Fig. 9 Strouhal number versus Reynolds number using sensor S5 (after the cylinder); B/H=3

Fig. 10 Photos at different Re numbers, left: Re=2.63⋅105 (σ=2.72), centre: Re=3.12⋅105 (σ=1.83), right: Re= 3.62⋅105 (σ=1.32) B/H=3.

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Fig. 11 Strouhal number versus Reynolds number using sensor S5 (after the cylinder); B/H=4.

Fig. 12 Photos at different Re numbers, left: Re=2.63⋅105 (σ=2.72), centre: Re=3.13⋅105 (σ=1.80), right: Re= 3.62⋅105 (σ=1.32) B/H=4.

4. Summary Unsteady cavitating vortex shedding was studied at high Reynolds numbers (>5x104) behind rectangular cylinders of aspect ratios 1, 2, 3 and 4 with blockage ratio 12.5%. The power spectra and the dominant frequencies of the pressure time signals in the wake were presented as a function of the Reynolds number. In the case of the square obstacle, a quantitative accordance was found with the literature in the sense that although we were unable to find measurements at such high Reynolds numbers, our Strouhal numbers provide a natural extension of the existing data: several researchers report that if the Reynolds number exceeds 104, the dominant Strouhal number seems to stabilize around 0.13-0.14. We also found that the frequency content of the power spectra in the wake is wider and the low-frequency noise-like components occur at lower Reynolds number compared to that one measured at the top of the obstacle. Unless the state of supercavitation is reached, cavitation does not affect the Strouhal number. In the case of rectangles with higher aspect ratio (B/H=2,3 and 4), the noise-like content of the spectra increases and it becomes more cumbersome to identify the dominant frequencies. Broadly speaking, we experienced a slight increase in the Strouhal number (0.19, 0.20 and 0.21 for B/H=2,3 and 4, respectively), although in the case of B/H=2 the measurements were especially noisy. Concerning inception of cavitation, the aspect ratio did not have a significant impact; we experienced a fairly constant value of σinc=4.89, 4.46, 4.31 and 4.31 for B/H=1, 2, 3 and 4. The fact that the Strouhal numbers are not affected significantly by moderate cavitation suggests that in unsteady CFD computations intended to capture the dynamics not the cavitation model is of primary importance but the unsteady turbulence modeling governing the vortex dynamics.

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Acknowledgments The cavitation channel and instrumentation described in this paper was supported by a grant from National Scientific Research Found (OTKA), Hungary, project No: 061460.

Nomenclature Re St

σ

B H Ho n

Reynolds number [-] Strouhal number [-] Thoma’s number [-] Cylinder length [m] Cylinder height [m] Downstream overpressure [mwc] pump rotor speed [rpm]

Freestream reference pressure [Pa] Vapour pressure [Pa] Water density [kg/m3] Water kinematic viscosity [m2/s] Mean velocity at the test section [m/s] Frequency [Hz]

pr pv

ρ ν

U f

References [1] [2] [3] [4] [5] [6] [7] [8] [9] [10] [11] [12] [13] [14] [15] [16]

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