# HFSB-seeding for large-scale tomographic PIV in wind tunnels

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## Abstract

A new system for large-scale tomographic particle image velocimetry in low-speed wind tunnels is presented. The system relies upon the use of sub-millimetre helium-filled soap bubbles as flow tracers, which scatter light with intensity several orders of magnitude higher than micron-sized droplets. With respect to a single bubble generator, the system increases the rate of bubbles emission by means of transient accumulation and rapid release. The governing parameters of the system are identified and discussed, namely the bubbles production rate, the accumulation and release times, the size of the bubble injector and its location with respect to the wind tunnel contraction. The relations between the above parameters, the resulting spatial concentration of tracers and measurement of dynamic spatial range are obtained and discussed. Large-scale experiments are carried out in a large low-speed wind tunnel with 2.85 × 2.85 m^{2} test section, where a vertical axis wind turbine of 1 m diameter is operated. Time-resolved tomographic PIV measurements are taken over a measurement volume of 40 × 20 × 15 cm^{3}, allowing the quantitative analysis of the tip-vortex structure and dynamical evolution.

## Keywords

Vorticity Wind Tunnel Settling Chamber Seeding System Bubble Generator## 1 Introduction

Tomographic PIV has been employed in a wide range of applications since its introduction in 2006 (Elsinga et al. 2006). One of the recognized limitations of this technique is the extent of the measurement volume, limited to a typical size of a few hundreds of cubic centimetres (Scarano 2013), especially in airflow experiments with micron-sized particle tracers. This limitation has hindered the use of tomographic PIV for applications of industrial aerodynamics, where the region of interest may attain the order of a metre. The main factor precluding the upscaling of the technique is the limited laser pulse energy when distributed over a large volume, combined with a small optical aperture to ensure in-focus imaging conditions. As a result, the amount of light collected by the cameras for each particle decreases when increasing the size of the measurement domain. The use of larger tracer particles as a means to increase the scattered intensity has been demonstrated to affect the tracing fidelity, which rapidly degrades due to the increase in the particle inertia (Melling 1997). The neutral buoyancy condition reached with sub-millimetre helium-filled soap bubbles (HFSB) tracers has been recently shown to combine the higher scattered intensity with good tracing fidelity. With a time response in the range of 10–30 μs, these tracers are deemed suitable for quantitative studies in low-speed aerodynamics (Scarano et al. 2015).

The use of HFSB as flow tracers dates back to the visualization of several aerodynamic flows, including the flow around a parachute (Pounder 1956; Klimas 1973), the separated flow around an airfoil (Hale et al. 1971a), wing-tip vortices (Hale et al. 1971b; Babie and Nelson 2010) and jet flows (Ferrell et al. 1985). HFSB tracers have been mostly used to visualize individual path-lines within complex flows. However, the low production rate of 10^{3}–10^{4} bubbles per second (Okuno et al. 1993; Müller et al. 2001; http://www.sageaction.com/) only allows low seeding concentrations, which makes the image analysis via standard cross-correlation-based approaches unsuited. Moreover, uniform tracer dispersion in the airflow cannot be achieved with the use of a single-point source of tracers.

In a previous work from the authors (Scarano et al. 2015), a system was proposed based on a single bubble generator with production rate of approximately 50,000 bubbles per second coupled with a piston–cylinder system. A larger amount of tracers was injected in the settling chamber of a small wind tunnel allowing time-resolved tomographic PIV measurements over a domain of approximately 20 × 20 × 10 cm^{3}.

A number of questions remains open, namely the achievable spatial resolution and spatial dynamic range of large-scale experiments realized with HFSB as flow tracers. The applicability of these systems in large-scale wind tunnels (with test section of 10 m^{2} or larger) has also to be assessed before tomographic PIV can become a viable tool for aerodynamic research at industrial scale.

The present study is structured in two parts. First, the governing parameters of a large-scale seeding system are identified. The relationship between HFSB production rate, spatial concentration and dynamic spatial range (DSR) achievable in the wind tunnel environment is discussed on a theoretical basis. Then, a description of the salient technical aspects of the seeding system is given, which compares the theoretical and the measured increase in bubble concentration with respect to stationary bubble emission. Finally, the technique is applied to study the dynamical evolution of the three-dimensional flow developing from the rotor blade tip of a vertical axis wind turbine (VAWT) of 1 m diameter and 1 m height. The measurements are taken at a rate of 1000 Hz in a volume of 40 × 20 × 15 cm^{3}, which allows following the blade passage and the associated tip-vortex formation, release and spatio-temporal evolution in the inner rotor region. The results obtained with tomographic PIV cross-correlation analysis are compared with the Tomo-PTV approach that follows the VIC+ method (Schneiders and Scarano 2016) in relation to the tip-vortex peak vorticity. The method was successfully applied in the case of a turbulent boundary layer measurement by Schneiders et al. (2016).

## 2 Spatial resolution and dynamic range

In this section, the relationship between the production rate of the HFSB and the DSR achievable in tomographic PIV measurements is discussed. Moreover, the influence of the location where the tracers are injected, namely upstream or downstream the wind tunnel contraction, is considered.

*L*and the particle tracer displacement Δ

*x*namely:

Further studies on the spatial resolution of PIV (Raffel et al. 2007; Astarita 2009; Kähler et al. 2012) suggest referring to the (linear) size of the interrogation window *l* _{I} (or interrogation volume *I* _{V} in tomographic PIV) instead of the particle tracer displacement. This is justified by the fact that the measurement of spatial resolution is directly connected with the size of the interrogation window, which becomes independent of the pulse separation time when multi-pass interrogation methods are used.

*C*. For a uniform distribution of tracers, the interrogation volume reads as

*N*

_{I}represents the particle image number density, defined as the number of particle images per interrogation volume (Keane and Adrian 1990), and

*C*is expressed in number of tracers per unit of volume. Substituting Eq. (3) into Eq. (2) yields

*L*) is typically determined by the geometry of the model under study and the specific flow features of interest. The particle image density is chosen in order to maximize the spatial resolution and the number of particle image pairs for the cross-correlation analysis. As a consequence, the concentration is the parameter most easily varied to achieve the desired DSR. When using HFSB tracers, the concentration is limited by the maximum rate at which they can be released by an emitter. Moreover, given their large size and the limited lifetime (reported to be within 120 s, Bosbach et al. 2009), the tracers are only used once, since they do not circulate around closed-loop wind tunnels. The present discussion is based on the hypothesis that HFSB tracers are released by an emitter at a rate \(\dot{N}\)[bubbles/s] and travel without disturbing the flow within the stream-tube of cross section

*A*corresponding to that of the emitter, with a velocity \(U\). The rate at which the bubbles cross a plane normal to their direction of convection reads as:

A simple example is given here to illustrate the requirements in terms of bubble production rate. Let us assume that a stream-tube with velocity of 10 m/s and a quadratic cross section of 1 × 1 m^{2} is to be seeded at a concentration of 5 bubbles/cm^{3} (*I* _{V} = 1 cm for *N* _{I} = 5). The generation system needs to supply tracers at \(\dot{N}\) = 50 × 10^{6} bubbles/s, which exceeds by three orders of magnitude the production rate of a single generator. The resulting DSR for such conditions would be around 100, which compares well to that of many planar PIV experiments reported in the literature (Raffel et al. 2007).

*C*from the last expression into Eq. (4), the DSR reads now as:

In the last derivation on the right-hand-side term, it is assumed that *A* ≈ *L* ^{2}, i.e. the seeded stream-tube cross section is comparable to the characteristic length of the object of interest. Equation (6) states the dependence of the DSR upon the characteristic length of the measurement volume, the amount of HFSB entering the measurement volume per unit of time and the local stream velocity.

The bubble rate in the measurement volume \(\dot{N}\) is thereby pivotal to achieve the required DSR. High values of \(\dot{N}\) yield a high concentration, which in turn increases the dynamic spatial range. On the other hand, as in every tomographic PIV experiments, the number of ghost particles (Maas et al. 1993) increases rapidly with the density of particle images (Discetti 2013), which affects the accuracy of tomographic reconstruction and motion analysis, as discussed in the work of Elsinga et al. (2011). However, as shown in recent experiment with HFSB (Scarano et al. 2015), the particle image density levels achieved are far below the critical value of 0.05 ppp (particles per pixel) suggested in the work of Elsinga et al. (2006). Finally, the DSR is inversely proportional to the stream velocity \(U\).

Equation (6) can also be interpreted as follows: For a given value of the Reynolds number, higher values of DSR can be achieved increasing the size of the scaled model and reducing the velocity. It may be concluded that scaling up the Reynolds number with the geometrical scale is a more convenient approach than increasing the velocity for achieving a high DSR with HFSB tracers.

*ρ*, where

*ρ*is defined as the ratio between the cross-sectional area of the injector and that of the seeded stream-tube in the test section.

*L*

_{inj}

^{2}, with a constant bubble injection rate into the flow \(\dot{N},\) the seeding concentrations read as:

*ρ*> 1). Conversely, the flow contraction reduces the cross section of the seeded stream-tube scale, which may be regarded as a disadvantage when the measurement region needs to cover large objects. The relationship between the emitter characteristic length and that of the seeded stream-tube is

The ratio expressed in Eq. (9) represents quantitatively the effect of the contraction on the DSR in a tomographic PIV experiment. The dependence upon the 1/6 root indicates that the ratio in Eq. (9) is weakly dependent upon the chosen configuration, however, with a slight advantage in case the emitter is placed directly in the wind tunnel free-stream. Furthermore, in many situations, the access to the settling chamber is limited if not impossible; thus, case *b* remains a more practical choice.

*C*and the DSR upon the size of the emitter

*L*

_{inj}and the seeded stream-tube contraction

*ρ*. The calculation is made assuming free-stream velocity of 8.5 m/s, a bubble emission rate of 8 × 10

^{5}bubbles/s and a particle image number density of 5 (corresponding to the current experiment presented in the remainder). Four values of the contraction ratio

*ρ*are considered, namely 1, 3, 9 and 18, covering a range commonly encountered in low-speed wind tunnels (the last three numbers correspond to the OJF, W-tunnel and LTT wind tunnel, respectively, of the aerodynamics laboratory of TU Delft). The case with unit contraction corresponds to case

*b*where the injector is placed in the test section upstream of the model (present experiment). These results are used to predict the concentration and the DSR for a given seeding system.

Increasing the size of the injector is detrimental to the seeding concentration if additional bubble generators are not added into the system. In Fig. 2 (left), for example, the concentration reduces of one order of magnitude when *L* _{inj} increases from 20 to 100 cm. In contrast, the dynamic spatial range increases with the size of the emitter and of the seeded stream-tube. On the other hand, the dynamic spatial range increases with the size of the seeding injector. In Fig. 2, the working point of the seeding system used in the present experiment (described in the following section) is also shown. The seeding system was used in configuration *b*, with the bubbles injector placed in the test section.

Due to the limited HFSB concentration, typically not exceeding a few bubbles per cubic centimetre, experiments conducted with HFSB are suited for image analysis based on PTV (particle tracking velocimetry) approaches, which requires that the average distance between the particles is large with respect to the average particle displacement (Maas et al. 1993). The equations discussed above remain conceptually valid also for PTV analysis, provided that the image number density is set to unity: *N* _{I} = 1. It is well known that PTV approaches allow higher spatial resolution, whereas cross-correlation approaches yield higher probability of valid vector detection (Adrian 1991). Furthermore, correlation-based techniques yield velocity data defined in a regular Cartesian grid, which is better suited for the computation of spatial derivatives and flow-derived properties as vorticity.

^{7}–10

^{8}bubbles/s. Moreover, the less fundamental, yet very relevant problem of uniformly introducing the tracers upstream of the test section with minimum intrusion to the free-stream flow conditions requires dedicated technical solutions. The remainder of this study describes the concept and the realization of a seeding system that multiplies the instantaneous bubble emission rate from a single generator to produce a quasi-uniform stream of seeded flow in a large-scale wind tunnel.

Dynamic spatial range for relevant Tomographic PIV experiments in air flows

Work in the literature | Measurement domain linear size | Interrogation box linear size | DSR |
---|---|---|---|

| | ||

Elsinga et al. (2006) | 40 | 2.1 | 19 |

Staack et al. (2010) | 50 | 2.5 | 20 |

Schröder et al. (2011) | 63 | 2.7 | 22 |

Kühn et al. (2012) | 840 | 38 | 22 |

Fukuchi (2012) | 160 | 5 | 30 |

Scarano et al. (2015) | 200 | 20 | 10 |

Current study | 400 | 33 | 13 |

## 3 Seeding system

Production rate of different HFSB generators

Research group | Production rate [bubbles/s] |
---|---|

Toyota—Tokyo University | 3000 |

Sage Action Inc. | 300–400 |

RWTH Aachen University | 500 |

DLR | 50,000 |

^{2}; only 550 cm

^{2}are obstructed by the airfoils and therefore contribute to the blockage (considering the total amount of 12 airfoils). However, one should keep in mind that the airfoils are place in two rows of six, which are staggered with respect to each other, thus reducing the blockage. This is considered negligible, <6% blockage, in large wind tunnels with cross section of 1 m

^{2}or larger. Finally, the air flow injected with the HFSB from the seeding probe depends on the stroke of the piston and the injection time. In the present work, the additional air flow rate was 0.04 m

^{3}/s. The latter is rather small in comparison with the air flow crossing the overall cross section of the rake at 10 m/s (approximately 1 m

^{3}/s), and it is certainly negligible when compared to the wind tunnel air flow rate.

*accumulation time*). After that, the piston rapidly moves forward during a time interval \(\Delta t_{1}\) (

*release time*). The total number of bubbles produced during one period of the piston motion is \(\dot{N}_{0} \left( {\Delta t_{0} +\Delta t_{1} } \right)\). In the ideal case where all the produced bubbles are ejected from the system during release, the rate at which the bubbles exit the cylindrical reservoir in \(\Delta t_{1}\) is \(\dot{N}_{1}\):

*gain factor G*of bubble rate obtained by the seeding system compared to a single bubble generator. Assuming that during the accumulation phase, all the bubbles stay in the cylindrical reservoir, whose maximum volume during the accumulation time \(\Delta t_{0}\) is

*V*

_{0}, and the bubbles concentration within the reservoir is:

*C*due to dilution with the air flow crossing the injector during release:

*V*

_{ wt }is the air volume flowing through the diffuser and in which the bubbles are ejected. The term \(V_{wt}\) can be expressed as:

*u*is the velocity of the flow in which the HFSB are injected and is equal to

*U*

_{∞}/

*ρ*in case

*a*(injector in the settling chamber) and

*U*

_{∞}in case

*b*(injector in the test section; see Sect. 2). Substituting Eq. (13) into Eq. (12) and making use of the definition of the gain factor, the expression of the concentration becomes:

Equation (14) shows the dependence of the concentration from the main working parameters of the seeding system. The choice of the bubble generator determines the bubbles production rate, \(\dot{N}_{0} ,\) and therefore is crucial for the optimization of *C*. The latter is directly dependent upon the gain factor, which is varied by changing the accumulation time \(\Delta t_{0}\), provided it does not exceed the bubbles lifetime. The cross section of the seeded stream-tube *A*, determines the air volume flow rate where the bubbles are released and therefore the dilution in the wind tunnel. Increasing *A* reduces the concentration of tracers.

*C*

_{th}) of 3 bubbles/cm

^{3}is expected. This concentration allows tomographic PIV measurements to investigate flow structures of the order of a few centimetres, as it will be done in the next section for the analysis of the blade tip vortex of a vertical axis wind turbine. The concentration observed within the measurements (

*C*

_{meas}) is considerably less than the above one (1 bubble/cm

^{3}) as shown in Fig. 2, left. This difference is ascribed to a number of factors, most importantly, bubbles extinction during their transport from the reservoir to the exit of the injector and bubble collisions inside the reservoir. As a result of the lower concentration, the tomographic PIV analysis is conducted with larger interrogation windows, yielding in turn a lower spatial resolution.

Theoretical and measured bubble concentration for the VAWT experiment

\(\dot{N}_{0} \,({\text{b}}/{\text{s}})\) | \(\Delta t_{0} \,\left( {\text{s}} \right)\) | \(\Delta t_{1}\, \left( {\text{s}} \right)\) | | \(V_{0} \,\left( {{\text{cm}}^{3} } \right)\) | \(A \,\left( {{\text{cm}}^{2} } \right)\) | \(U_{\infty } \,\left( {{\text{m}}/{\text{s}}} \right)\) |
---|---|---|---|---|---|---|

50,000 | 50 | 1 | 50 | 16,000 | 900 | 8.5 |

\(C_{\text{th}}\, \left( {b/{\text{cm}}^{3} } \right)\) | \(C_{\text{meas}} \,\left( {b/{\text{cm}}^{3} } \right)\) | DSR | DSR |
---|---|---|---|

3 | 1 | 28 | 13 |

Concluding, it was noticed that the loss of bubbles upstream of the injector poses some limits to the seeding system described above. A possible solution to comply with this issue will be the use of many bubble generators in parallel installed inside the wind tunnel. A multi-generator system allows producing HFSB directly in the stream of the wind tunnel without transport losses and introduction of the air volume *V* _{0}. The latter alternative, however, requires a large number of nozzles, on the order of *G* for a given \(\dot{N}_{0}\) = 50,000 in order to retrieve the same concentration and DSR obtained for the present seeding system. Although a multi-generator system is not yet available at present time, the analysis performed in the present section can be extended to the latter case, provided that a unitary gain factor (*G* = 1) and the total production rate of all nozzles are considered.

## 4 Wind tunnel experiment

The above described system is used to perform time-resolved tomographic PIV measurements on a scaled model of vertical axis wind turbine (VAWT). The measurements are taken in the Open Jet Facility (OJF) of TU Delft. The wind tunnel features an open test section with closed-circuit. At the end of the contraction, the wind tunnel has an octagonal cross section of 2.85 × 2.85 m^{2}. The air flow is driven by a 500 kW electric motor. In the test section, the free-stream velocity can range from 3 to 35 m/s with a maximum turbulence intensity of 0.5%. The model is a two-blade H-shaped rotor VAWT of 1 m diameter (*D*). The rotor blades are shaped following the NACA0018 profile with 6 cm chord length and installed with zero angle of attack. The blades are tripped by zig-zag stripes in order to force the boundary layer transition from laminar to turbulent regime and avoid the occurrence of laminar separation bubbles. The blade span *H* is 1 m long, yielding an aspect ratio AR = *H*/*D* = 1. Measurements are taken at free-stream velocity *U* _{ ∞ } = 8.5 m/s and rotational speed *Ω* = 800 rpm, yielding a tip speed ratio *λ* = 5. The Reynolds number based on the chord length and the tangential velocity of the blades is *Re* _{c} = 170,000.

*θ*= 0° (windward position). The free-stream velocity is directed along

*x*. The turbine rotates clockwise when seen from the top.

*θ*= 0°.

The turbulence intensity of the stream before it interacts with the wind turbine is assessed by dedicated measurements returning rms fluctuations below 2% of the free-stream. The HFSBs injected in the flow have an average diameter of approximately 300 µm. The bubbles are generated in the same condition as it is described in the work of Scarano et al. (2015) and have a characteristic response time in the order of 10 µs.

The tomographic PIV system consists of a Quantronix *Darwin Duo* Nd:YLF laser (2 × 25 mJ at 1 kHz) and three Photron Fast CAM SA1 cameras (CMOS, 1024 × 1024 pixels, 12-bit and pixel pitch 20 μm). The optical magnification is approximately *M* = 0.05, and the extent of the measured domain is 40 × 20 × 15 cm^{3}. The lens aperture is set to *f*/11 to ensure images in focus over the entire depth. Under these conditions, images are recorded with a particle density of approximately 0.004 ppp (4000 particles/Mpixel) and the typical particle peak intensity is 300 counts.

Image acquisition and processing is performed using the LaVision software *DaVis 8.2.2*. Image pre-processing consists of image background elimination via minimum subtraction and Gaussian filter (3 × 3 pixels). The domain is discretized into 910 × 814 × 456 voxels and reconstructed with 10 iterations of the fast MART algorithm. The objects are interrogated with correlation blocks of 80 × 80 × 80 voxels (3.3 × 3.3 × 3.3 cm^{3}) and 75% overlap factor, yielding 42 × 35 × 23 vectors with a grid spacing of approximately 8 mm. The resulting vector fields are post-processed with the universal outlier detection algorithm (Westerweel and Scarano 2005).

Moreover, Tomo-PTV analysis is performed on the same recordings in the vortex region to evaluate the effects of spatial resolution on the estimates of peak vorticity and vortex core diameter. The method is based on the Vortex-in-Cell (VIC) technique, introduced by Schneiders et al. (2014), and it is used in the analysis of the peak vorticity for comparison with the cross-correlation-based results. The method is used to reconstruct velocity fields on a regular grid from volumetric particle-tracking measurements. The time-resolved reconstructions, used for the tomographic PIV, are also used for a tomographic PTV analysis. The locations of the particles are identified with sub-voxel accuracy using a 3-point Gaussian fit. The 3D trajectories allow the determination of the velocity and acceleration through a second-order polynomial fit along seven snapshots. The dense interpolation of the velocity from the sparse PTV-grid onto a regular one is made using an iterative minimization problem of a cost function that is proportional to the difference between the PTV measurements and the VIC+ results. The minimization is constrained by the incompressible flow assumption and the momentum equation in vorticity–velocity formulation. Due to their different dimensions, velocity and acceleration are scaled in the cost function by a factor alpha, which is chosen to be equal to the ratio of the typical magnitude of velocity and acceleration calculated from their root-mean-squared value. The VIC+ step is initialized using a uniform flow in the free-stream direction. The computational domain is chosen 30% lager than the measurement volume with constant boundary conditions based on the free-stream. The mesh spacing equals to 20 voxels. After the computation, the volume is cropped to the measurement volume and the exterior is not considered for data analysis. For full details of the VIC+ method, the reader is referred to Schneiders and Scarano (2016).

### 4.1 Results

*θ*= {0°, 30°, 60°, 90°}, corresponding to time steps of 6 ms. The vorticity was computed with an approximation of a grid point with a second-order central scheme. A more detailed representation is given with the animation Movie 1. In Fig. 9, the column on the left shows the top view of the measured velocity and vorticity field, while the right column gives the lateral view. The large-scale tomographic PIV returns the presence of tip vortices regularly generated by the motion of the retrograding blade from the windward to the upwind position. A portion of the blade is captured inside the measurement volume only for

*θ*= 0° shown in Fig. 9a. When the blade is at

*θ*= 0°, it passes through the condition of zero incidence, where no lift is generated. At this particular location, the blade is not releasing any tip vortex; therefore, the vortical structures present in the measurement domain, indicated as A and B in Fig. 9a, have been released by prior blade passages and convected downstream.

When the blade is in position *θ* = 30°, it releases a tip vortex of finite and measurable strength, labelled with C in Fig. 9b. The vortices A, B and C are convected downstream by the flow field and their mutual distance depends on the tip speed ratio. From the side views of Fig. 9, it is clear that the vortical structures also convect outboard (towards negative values of *Z*), departing downward from the blade tip plane (*Z* = 0). The tip vortex C released by the blade at *θ* = 30° (Fig. 9b) appears weaker than the vortex generated with the blade at higher angle of attack (Fig. 9c, d). The change in the vortex strength is related to the variation of the lift generated as the blades rotate. The observed behaviour agrees with the three-dimensional unsteady RANS simulation of Howell et al. (2010), where strong correlation between the maximum developed lift and maximum strength of the tip vortex was documented.

*X*= 50 mm for 10 successive blade passages at

*θ*= 30°. The tip of the blade is located at

*Z*= 0, the negative values correspond to the outboard region. The instantaneous profiles show pronounced velocity fluctuations inside the rotor region (

*Z*> 0), whereas the outboard region exhibits a more stable behaviour. The variations of the velocity profiles are therefore localized in the turbulent wake of the blades, in which the laminar–turbulent transition of the boundary layer is forced with the tripping procedure. In addition, the wakes generated by the blades in the upwind position (0° <

*θ*< 180°) are transported downstream through the inner region of the rotor. As a result, the velocity field is characterized by higher fluctuations at this location, as reported by the experimental results of Tescione et al. (2014). The interaction between the blades and their own wakes, produced in the previous rotation, influences the flow condition in the pressure and suction sides with a consequent effect on the generation and development of the tip vortices.

*X*= 0 mm. The VIC+ result exhibits a peak vorticity approximately two times higher than that returned with cross-correlation. These discrepancies are ascribed to the higher spatial resolution of the PTV-based algorithm.

Similarly to the analysis made on aircraft wing-tip vortices (Scarano et al. 2002), limited spatial resolution causes peak modulation and vortex diameter overestimation; their combined effect is less detrimental in terms of vortex total circulation, which relates to the integral of vorticity. In Fig. 11, a clear difference of the vortex diameter is not evident. Therefore, the circulation associated with the vortex is expected to be underestimated when measured with tomographic cross-correlation compared to VIC+.

The peak values of vorticity presented in the work of Tescione et al. (2014) are also approximately 300 1/s, but the value only pertains to the *y*-component as obtained from planar and stereoscopic PIV measurements. The three-dimensional structure of the vortices shed from VAWT would require rotating the measurement angle with the blade position to compensate from the rotation of the vorticity vector. For practical reasons, experiments are often conducted at a fixed orientation of the measurement plane that only provides one component of the vorticity vector (not generally aligned with the axis of the vortex). Large-scale tomographic PIV allows the measurement of the three components of the vorticity vector, enabling the three-dimensional inspection of the vortex structure, which is strongly affected by the characteristic flow curvature in the rotor region of VAWT. However, as shown in the current experiments, the limited spatial resolution of this approach poses a caveat on the interpretation of peak vorticity and circulation (Fig. 11c).

Figure 11 shows the axial distribution of peak vorticity in vortex B, as shown in Fig. 9a. The peak vorticity is presented along the stream-wise direction *X*, approximately corresponding to the direction of the vortex axis. The distribution corresponds to the angular position *θ* = 0° of the blade. The instantaneous measurements (thin lines) are presented along with the corresponding phase average (thick line). The peak vorticity decreases monotonically moving downstream, which is consistent with the increase in lift generated by the blade when it rotates from *θ* = 0° to higher values of the phase angle. The results obtained by cross-correlation analysis are significantly below the estimates returned with VIC+, which has also been reported in a study by Schneiders et al. (2016). This is mainly due to the more pronounced effect of spatial filtering associated with the cross-correlation operator. Despite the aforementioned effect, the cross-correlation analysis returns a consistent characterization of the tip-vortex topology, the induced velocity field and the dynamical evolution of the vortex.

*ω*| < 200 1/s), and they are expected to contribute in destabilizing the tip vortices during their dynamical evolution in the rotor wake region.

## 5 Conclusions

In the present study, the relationship between the measurement of DSR and the production rate of tracer particles has been derived for the case of HFSB tracers. A dedicated seeding system has been designed to increase the amount of HFSB injected into the flow to overcome the limited production rate of bubble generators for large-scale measurements. The importance of the location where the tracers are injected has been addressed, and the effects on concentration and DSR have been quantified.

The system has been demonstrated by large-scale tomographic PIV measurements for the investigation of the blade tip vortex of a vertical axis wind turbine. Time-resolved measurements in a volume of 40 × 20 × 15 cm^{3} were taken with a seeding concentration of about 1 bubble/cm^{3}. Data analysis by tomographic PIV describes the flow structure in the rotor region of the VAWT, dominated by large-scale vortices shed from the blade tip. The behaviour of the latter vortex has been described in the near-wake region and its properties examined, in terms of peak vorticity. The comparison of the results from tomographic PIV with a higher resolution PTV analysis based on VIC+ poses a caveat on the quantitative underestimation of peak vorticity, when cross-correlation analysis is used for tomographic PIV at the present level of seeding concentration.

## Notes

### Acknowledgements

The authors wish to thank Jan F. G. Schneiders for the contribution in the analysis of the tomographic data with the VIC+ technique.

## Supplementary material

Supplementary material 1 (MOV 6641 kb)

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