Bluff body flow and vortex—its application to wind turbines

The flow around multiple bluff bodies is an attractive flow phenomenon, and due to the arrangement—side by side, tandem and staggered—a wide variety of flow patterns appear (Bearman and Wadcock 1973, Zdravcovich 1977). The wake characteristics of groups of normal flat plates, consisting of two, three, or four plates placed side by side with slits in between, have been investigated experimentally in a uniform flow with Reynolds numbers, Re(=Uh/ν) of about (1.3–1.9) × 10⁴ (Hayashi et al 1986, Ohya et al 1989). When the slit ratio s/h (the ratio of slit width to plate width) of a row of flat plates is less than about 2.0, the flows through the slits (gap flows) are biased either upward or downward in a stable way, leading to multiple flow patterns for a single slit ratio value, as shown in figure 1. Some regularities are recognized in the wake characteristics of flat-plate rows such as the gap flow direction and the sequence of flow patterns.

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The plates on the biased side show high drag and regular vortex shedding, while those on the unbiased side show the opposite. The origin of the biased flow has also been investigated with water-tank experiments, numerical calculations and wind tunnel experiments. The results show that the origin of the biasing is strongly related to the vortex shedding of each plate of a row. When the slit ratio is moderate, where each plate of a row can shed vortices, the gap flow is engulfed by the stronger vortices and becomes biased. The stability of biased gap flow appears to be particularly dependent on the behavior of the separated shear layer from the slit side of the plate on the unbiased side.

Thus, for a side-by-side arrangement of bluff cylinders with the same geometrical shape placed in a steady flow, multiple modes of flow pattern exist in the wake. For a two-cylinder arrangement, the gap flow can take two discrete biased directions. For an arrangement of three or more cylinders, the number of wake flow patterns increases rapidly since the resulting flow pattern can be any combination of the two modes from each gap between cylinders.

2.2.1. Flow around a rectangular cylinder—critical depth

For a rectangular cylinder placed in a smooth flow it is generally reported that with increasing cylinder depth d the base pressure decreases rapidly until a critical minimum is reached, when the depth is slightly greater than about 0.6 times the height, h. This phenomenon has been investigated by many researchers and is referred to as the critical geometry (or the critical depth) for rectangular cylinders (Bearman and Trueman 1972, Bearman 1980). The principal aim of this investigation is to gain a better understanding of the critical phenomenon for a rectangular cylinder (Ohya 1994).

We have examined in detail the time behavior of the mean base pressure for cylinders with d/h = 0.4, 0.5, and 0.6 and have also visualized the flow around cylinders in combination with base pressure measurement in a uniform smooth flow with Reynolds number, Re(=Uh/ν) of (0.67–6.7) × 10⁴. As a result, a cylinder with d/h = 0.5 shows characteristic time variations in base pressure, with alternating high and low values, almost equal to those for d/h = 0.4 and 0.6 (the critical depth), respectively. This is caused by a sudden change in the flow pattern around the cylinder associated with the vortex formation. For cylinders with depths below the critical value, the flow around the cylinder initially changes gradually with increasing d/h, but when d/h reaches a transitional range around d/h = 0.5, there is an abrupt change in the flow pattern.

The mean base pressure variation with side ratio is shown in figure 2. The side ratios around d/h = 0.5 are in a transitional range where the base pressure Cp_b has alternating low and high values at irregular intervals, corresponding to the abrupt change between the two different flow patterns. If a mean value over a very long period is considered, it indicates a weighted-average value between the low and high values, which has been reported by many researchers. After the transitional range, at around d/h = 0.6, a stable critical flow pattern is established. In the transitional range, the rate of appearance of the critical flow pattern, i.e., the intermittency, is dependent on the characteristics of the approaching flow, the end plates for a model, the model aspect ratio, the Reynolds number and so on. As to the origin of the critical flow patterns, i.e., the abrupt change in wake pattern to the strong roll-up of the separated shear layers, it appears to be caused by an interaction between the separated shear layers and the body downstream of the separation. The detailed mechanism is expected to be clarified as a result of further research.

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2.2.2. Flow around a long flat plate—vortex shedding from flat plates with square leading and trailing edges

Similar irregular switching of wake flow patterns can be observed for a long rectangular plate with the chord-to-thickness ratio, d/h (we call d/h the chord-to-thickness ratio instead of the side ratio in this section) larger than 3 (Cherry et al 1984). This flow phenomenon is categorized as edge-tone flow (Nakamura et al 1991). Vortex shedding from flat plates with square leading and trailing edges with d/h = 3–16 at Reynolds number, Re(=Uh/ν) of (1–3) × 10³, is investigated experimentally in a large wind tunnel. It is shown that this vortex shedding is characterized by the impinging-shear-layer instability, where the separated shear layer becomes unstable in the presence of a sharp trailing edge corner. The Strouhal number, S_d (=fd/U), which is based on the plate's chord d, is approximately constant and equal to 0.6 for d/h = 3–5. With increasing ratio, it increases stepwise to values that are approximately equal to integral multiples of 0.6, as shown in figure 3.

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After the wind tunnel test, we tried to clarify the mechanism of the stepwise increase in Strouhal number S_d, using a numerical simulation of DNS (Ohya et al 1992). During an early phase of the numerical investigation, we tried to obtain the response of the flow to some artificial disturbance to check the possibility of controlling the random modulation in the flow arising from the vortex interactions at the trailing edge. This was successful, but we found later that such random modulations can take place spontaneously without introducing any artificial disturbance into the flow. In one such trial on a flat plate with d/h = 8, we found a transition in vortex shedding from m = 2 to m = 3 that was found in a wind tunnel experiment (figure 3). The plate was initially at zero incidence and was then given a small positive incidence of 0.5 for a short time interval t = 616–694, and the subsequent flow development was observed. Figure 4 shows the time history of the lift fluctuation and it can be seen that for t > 1280, the plate experiences very regular vortex shedding with a zero-mean C_L value. Figure 4 also shows the corresponding streaklines and the change in the flow pattern corresponding to an irregular shedding (m = 2) and a regular vortex shedding (m = 3). It is interesting to note that the value of S_d is just on the basic line plotted in figure 3.

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Thus, we can often observe the critical flow pattern switching for bluff bodies with certain geometrical shapes, in which the flow around the body suddenly changes from one mode to another both for short cylinders and long plates. Although the mechanisms for switching flow patterns are different, the flows around rectangle or cylinder with side ratio (or chord-to-thickness ratio) around d/h = 0.5 and 8, show the two different vortex shedding patterns, corresponding to those flow patterns.

The near wake of a circular cylinder in linearly stratified flows of finite depth, H, was experimentally investigated by means of flow visualization and measurements of vortex shedding frequencies, at Reynolds numbers, Re(=Ud/ν) of 3.5 × 10³–1.2 × 10⁴ and stratification parameters, k_d of 0–2.0. The non-dimensional parameter k_d is defined as k_d = Nd/U, where N is the Brunt–Väisälä frequency, N² = −(g/ρ₀)(dρ/dz), d, the diameter of the cylinder, and U, the approaching flow velocity. The parameter k_d is adopted to quantify the density stratification, and is the inverse of the Froude number.

Experiments were performed in a density-stratified wind tunnel of closed-circuit type. The test section of the wind tunnel was 0.4 m wide, 0.6 m high and 1.7 m long. Designed to generate predefined density-stratified flows, the wind tunnel, except for the contraction and test sections, was divided horizontally into six storeys. A mixture of air and sulfur hexafluoride, SF₆, was injected into each storey from an external source to directly produce density stratification. The wind in the test section was generated by 18 microfans, each driven by a micromotor, and three microfans were mounted side-by-side on each storey. The generated wind velocity, U, ranged from 0 to 1.2 m s⁻¹. For homogeneous flow, the wind velocity was set to U = 0.83 m s⁻¹.

Flow around a circular cylinder (d = 10 cm) was observed in a stratified wind field that had a nearly uniform vertical profile of wind velocity and a linear vertical profile of density. With the flow visualization technique, change in the near-wake flow pattern was examined with respect to the stratification parameter, k_d. Figure 5 illustrates instantaneous flow patterns. The vortex formation and shedding are significantly enhanced at k_d = 0.513 (figure 5(a)) with respect to the homogeneous case. The flow pattern around the circular cylinder suddenly changes in the proximity of k_d = 0.52 (figure 5(b)). At this stratification, strong roll-up of the shear layers that have separated from the cylinder is no longer observed, and vortex formation in the wake is highly suppressed. The pattern of the near-wake flow has shifted from a vortex flow pattern to an internal-wave flow pattern (Ohya and Nakamura 1990, 2013).

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Concurrently with the flow visualization experiments, fluctuating wind velocity measurements were made at the outer edge of the wake of the circular cylinder. From the peak frequency of the wake velocity fluctuations, f_v, the Strouhal number, St (=f_vd/U) was evaluated for homogeneous and density-stratified flows, as shown in figure 6. With increasing k_d, the value of St decreases gradually and becomes approximately 73% of that in homogeneous flow at k_d = 0.513. This means that with increasing k_d, the vortex shedding from a circular cylinder progressively strengthens, while the Strouhal number gradually becomes lower than that for homogeneous flow. This phenomenon can be explained by the effect of the increasingly stable stratification which enhances the two-dimensionality of the near-wake flow of the circular cylinder; the enhanced two-dimensionality of the flow strengthens the roll-up of the separated shear layer. With further increases in k_d, the value of St increases steeply to a large value at around k_d = 0.52 (K = 1, explained below) in response to the change in the flow pattern, as shown in figures 5(a) and (b). Thus, for a horizontal circular cylinder placed in a stable stratified flow, we found a sudden change in the flow pattern. This is subjected to the non-dimensional stability parameter consisting of buoyancy force, inertia force and the ratio of the cylinder diameter to fluid depth. In terms of the stratification parameter K(=NH/πU) which includes the depth of stratified flow, H, the critical phenomenon occurs close to K = 1 for all sizes of circular cylinders investigated. The linear theory predicts that lee waves will develop for K > 1. Thus, in this critical phenomenon, the emergence of a stationary lee wave suppresses the vertical fluid motions of the vortices formed behind an object and causes a sudden change in the flow pattern.

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Based on our research on vortex flows described in section 2, an innovative application of vortex flow to a shrouded wind turbine is made in which the power output of a wind turbine is remarkably enhanced. Unlike the majority of conventional aerodynamic machinery, which tends to minimize vortex shedding, the vortex formation of our 'brimmed' shroud plays an important role in capturing and concentrating wind energy. Furthermore, aerodynamic noise is reduced due to the shroud. In section 2, we learned that the flows around a bluff body are strongly affected by the interaction between the separated shear layers and some rear portion of the body and the strong vortex shedding is directly relevant to the uniform separation of the boundary layer. Namely, the enhanced two-dimensionality of the flow strengthens the roll-up of the separated shear layer. This finding is applied to our new wind turbine as described in section 3.2.1.

To help solve energy problems and mitigate global warming the importance of clean, renewable energy is growing. In addition, in order to prevent massive blackouts caused by disasters, small distributed energy systems have been and continue to be tested. In this testing, there has been an increase in the variety of technologies used to generate clean, renewable energy. Of these methods, wind power generation, which can be conducted over the land and ocean, is attracting increasing attention. However, wind power generation has the following disadvantages: a very wide area needed to gain the energy comparable to thermal and nuclear power generation, noise, bird strikes, and landscape disturbances.

Gilbert and Foreman 1983 examined a diffuser-augmented wind turbine (DAWT) as a part of their research on high-power wind turbines. A DAWT is a wind turbine in which the power is augmented by concentrating the wind energy using a diffuser. Their diffuser is a kind of streamlined body and boundary layer separation along the diffuser never occurs. The streamwise section of the diffuser is similar to an airfoil. In contrast to the design of most DAWTs, we have developed a unique wind turbine with a brimmed diffuser called a 'Wind-Lens turbine' (Ohya et al 2008, Ohya and Karasudani 2010). An example of this turbine is shown in figure 7. A Wind-Lens turbine consists of a downwind-type wind turbine and a structure composed of an inlet shroud, a diffuser and a brim. We have applied fluid engineering technologies regarding vortex dynamics to this Wind-Lens turbine, as explained in the following sections.

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The flow which passes inside the diffuser and the flow which comes around behind the brim generate a large vortex behind the structure, as shown in figure 7. As a result of this low-pressure region due to the vortices, air is drawn into the turbine at a higher rate and accelerates more than with a bare wind turbine. Since wind power generation is proportional to the wind speed cubed, this wind acceleration results in a large increase in power output compared to a conventional wind turbine. Due to this effect, a 3 kW turbine with a rotor diameter of 2.5 m generated 2.5 times more power with a compact Wind-Lens than the same turbine without a Wind-Lens in the field experiment, as shown in figure 8.

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3.2.1. Application of vortex control plates to a Wind-Lens

In general, the vortex shedding from a three-dimensional body tends to be random and is not uniform in the circumferential direction. Therefore, if a uniform flow separation in the circumferential direction is established in a stable segment in some way, the vortex shedding might be strengthened. Small vortex control plates, which are aligned in the circumferential direction on the Wind-Lens, as shown in figure 9, were attached to strengthen the vortex shedding behind the shroud. As a result, the output performance of the Wind-Lens turbine is further improved. As shown in figure 10, the optimal number of control plates is around 6–12. It should be noted that the spacing between two adjacent control plates corresponds to the correlation length of vortex shedding for a bluff body. In general, the correlation length of vortex shedding of a circular cylinder is reported to be 3–4d , where d is the diameter of a circular cylinder. If we use 6–12 control plates for the Wind-Lens, the spacing in the circumferential direction on the Wind-Lens becomes 3—5d_w. Here d_w is the projected width of the Wind-Lens from the approaching flow direction. This is why the cases with 6–12 plates show a small increase in power output.

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In addition to increased power output, a Wind-Lens turbine offers the following advantages: low noise, reduced risk of bird strikes and reduced landscape disturbance. In this section, we focus on the low aerodynamic noise of Wind-Lens turbines. Figure 11 shows an example of a noise survey based on an international standard for measuring noise generated by wind turbines, JIS C1400-11 (IEC 61400-11). There is no appreciable difference in the noise level between a Wind-Lens turbine in operation and one at rest (Fukuoka City Home Page 2012). There are many sources of wind turbine noise including (1) turbulent boundary layer trailing edge noise; (2) laminar boundary layer vortex shedding noise; (3) boundary layer separation noise; and (4) noise associated with blade tip vortex formation (Morris et al 2004). In particular, blade tip vortices can strongly contribute to aerodynamic noise over a broad band of high frequencies (Arakawa et al 2005, Brooks and Marcolini 1986). We focus on blade tip vortices in a Wind-Lens turbine since the blades are enclosed by the Wind-Lens structure and thus the arrangement of the blade tips in a Wind-Lens turbine is quite different to that of a bare wind turbine.

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To clarify the behavior of the blade tip vortices of a wind turbine equipped with a brimmed-diffuser shroud, we conducted a three-dimensional numerical simulation using a large eddy simulation (LES) (Takahashi et al 2012). Since this unique wind turbine consists of not only rotating blades but also a diffuser shroud with a broad-ring brim at the exit periphery, the flow field around the turbine is highly complex and unsteady. In the present numerical analysis, the detailed flow patterns around the rotating blades and the shroud, including the blade tip vortices, were simulated. We used a moving boundary technique in the present CFD simulation to simulate the flow around a rotating blade in order to focus on blade tip vortices.

The simulation results showed a pair of vortices consisting of a blade tip vortex and a counter-rotating vortex which was induced between the blade tip and the inner surface of the diffuser, as shown in figure 12. Since these vortices interacted with each other, the blade tip vortex was weakened by the counter-rotating vortex. Thus, the tip vortex of the Wind-Lens breaks down very rapidly compared with that of the bare wind turbine. The results showed good agreement with previous wind tunnel experiments (Abe et al 2006). In the experiment, mean velocity profiles behind the wind turbines are measured using an x-type hot-wire technique and the tip-vortex structures are detected. As is the case in figure 12, the tip vortices and the induced counter-rotating vortices are shown in figure 13. These two vortices tend to weaken through their interaction. Due to this effect, the strength of the tip vortex for the Wind-Lens turbine becomes weak very rapidly in the downstream region. Such a rapid destruction of the tip vortex may strongly influence the noise reduction of a wind turbine. This is the reason why the Wind-Lens turbine has lower noise than a bare wind turbine.

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