A phase averaged PIV study of circular and non-circular synthetic turbulent jets issuing from sharp edge orifices

International Journal of Heat and Fluid Flow 82 (2020) 108536

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A phase averaged PIV study of circular and non-circular synthetic turbulent jets issuing from sharp edge orifices

T

A. Hashiehbaf, G.P. Romano

⁎

Department of Mechanical and Aerospace Engineering, La Sapienza University, Via Eudossiana n18, 00184 Rome, Italy

ARTICLE INFO

ABSTRACT

Keywords: Mixing enhancement Axis switching Synthetic jet Non-circular jet Sharp edge orifice PIV

An extensive experimental study using Particle Image Velocimetry (PIV) on synthetic jets issuing from different orifice shapes is reported. All data are phase and time averaged to derive mean velocity, half-velocity width and rms velocity profiles in the near field of the jet (0 < X/D < 7), at a Reynolds number around 10,000. Different non-circular orifice shapes as rectangular, square, elliptic and triangular are considered and results are compared to those of the circular orifice in order to investigate the effect of asymmetry on the turbulent flow field in view of mixing enhancement. The measurements are carried out on two orthogonal planes to capture three dimensional features of non-circular jets. Results show highest velocity decay rate for elongated orifices, especially the rectangular one, in comparison to the circular one, both in phase and time-averaged plots. Time averaged results show higher velocity decay rate of synthetic jets in comparison to those of continuous ones. It is also observed that, for X/D > 5, only profiles of circular and square jets become partially self-similar. For synthetic jets, higher turbulence content is measured for all orifice shapes at the centerline and close to the orifice exit in comparison to continuous jets.

1. Introduction

the work by Cater and Soria (2002). They investigated a pulsating jet for large Reynolds numbers (Re = 10,000) and small Strouhal numbers (e.g., 0.0015), by increasing the amplitude of oscillation in a piston mechanism. Their main result is that the Reynolds number, based on a velocity scale of the blowing cycle, and the Strouhal number are indeed the two dominant parameters in determining the jet structure. In these conditions, the self-similar behavior in the mean velocity profiles is reached at a distance from the outlet equal to X/D = 15 (where D is the jet equivalent diameter), which is higher than that obtained more recently by other authors as Di Cicca and Iuso (2007) i.e., X/D = 6, and Chaudhari et al. (2009), X/D = 7. In any case, these distances are smaller than those measured in continuous jets. Di Cicca and Iuso (2007) correlated the earlier self-similarity of axial velocity in synthetic jets, in comparison to continuous ones, to the earlier development of mixing layer instabilities and so far to the local increased mixing. At small Reynolds numbers (Re = 1732) and relatively high Strouhal number (St = 0.041), a series of vortex rings with little entrainment of ambient fluid was observed, as in Watson et al. (2003), so that the selfsimilarity region is delayed, coming closer to that of continuous jets. Trying to summarize all possible patterns, Glezer (1988) proposed a vortex map for laminar, transitional and turbulent conditions, by analysing the developing vortex rings in the ejection phase. This was further investigated also by Shuster and Smith (2007) who studied the

Synthetic jets are those jets generated without any steady flow in the background, i.e., the average mean velocity during one blowingsuction cycle is zero, even if momentum flux is different from zero (Mohseni and Mittal, 2014). This is due to the fact that there are always vortices escaping from the orifice in the ejection phase which would not be totally drawn back during successive suction, thus generating a net momentum flux. In other words, there are non-equal positive and negative peak velocities in the ejection and suction phase, respectively. Specifically, the maximum velocity in the ejection phase always occurs at the centreline of the turbulent jet, whereas it occurs far from the centreline of the jet (nearly at the edges of the orifice) in the suction phase (Shuster and Smith, 2007). There are different mechanisms for producing such jet such as piston-cylinder alternation (Gilarranz et al., 2005), oscillating membrane (Mossi et al., 2005) and acoustic excitation (Tesar and Kordik, 2009). The use of above described mechanisms, allows achieving many important engineering applications of such noncircular synthetic jets, as those in cooling of electronic devices or turbine blades, drag reduction over aerofoils, underwater vehicle propulsion and pulsatile injectors in combustors (Lee et al., 2016; Amitay et al., 2001; Mangatea et al., 2019). One of the fundamental investigations in the area of synthetic jets is ⁎

Corresponding author. E-mail address: [email protected] (G.P. Romano).

https://doi.org/10.1016/j.ijheatfluidflow.2020.108536 Received 25 January 2019; Received in revised form 7 November 2019; Accepted 1 January 2020 0142-727X/ © 2020 Elsevier Inc. All rights reserved.

International Journal of Heat and Fluid Flow 82 (2020) 108536

A. Hashiehbaf and G.P. Romano

Nomenclature D H K L Re St T U Ucl Uex

Uo urms vrms wrms X Xs Y y0.5(m) Z z0.5 ν

equivalent circular orifice inlet diameter (m) orifice width (m) cycle duty factor stroke length (m) Reynolds number (Re = Uex D/ ) Strouhal number (St = Uex t/D) cycle period (s) mean exit velocity along orifice width (m/s ) velocity at centerline of the jet (m/s) peak exit velocity during ejection phase (m/s)

effect of Reynolds number and stroke length in an extensive range (Re = 1000–10,000, L/D = 1–3). They observed ‘’trailing jet’’ formation at stroke lengths 4 < L/D < 5, as also proposed by Gharib et al. (1998), while no vortex ring was observed for L/D < 0.6. Regarding the shape of the orifice, Watson et al. (2003) performed qualitative measurements on the effect of such a parameter on vortex structure formed in the near field of a pulsatile jet, observing that even with the same velocity peak value at the exit plane of each orifice, the developed vortex rings from rectangular jets were completely turbulent while being laminar for the circular one. Smith and Glezer (2007) extended the investigation to plane synthetic jets, in a nearly laminar flow regime, due to a quite large Strouhal number (St > 0.03), according to criterion reported in Cater and Soria (2002). In agreement with previously reported measurements, they found that the fully developed self-similar axial velocity was achieved much closer to the orifice exit (X/H > 10), in respect to continuous plane jets (X/H > 40). They showed that time averaged cross-wise profiles of axial velocity and turbulent fluctuations, for both synthetic and continuous jets, are similar to each other, the only difference being related to the decrease of centreline velocity as x 0.58 , in comparison to the decay x 0.5 of continuous jets. O’Farrell and Dabiri (2013) investigated the vortex ring formation on elliptic orifices with aspect ratio, AR, equal to 2 and 4 and also oval orifice. They extended the definition of formation number

mean exit velocity during ejection phase (m/s) mean Stream-wise rms velocity (m/s) mean Cross-wise rms velocity (m/s) mean Span-wise rms velocity (m/s) stream-wise coordinate (m) saddle back point lateral coordinate (m) half-velocity width in y direction (m) cross-wise coordinate (m) half-velocity width in z direction (m) dynamic viscosity of the fluid (m2/s)

previously introduced by Gharib et al. (1998) for non-circular vortex rings. Also Lio et al. (2007) investigated the effects of different orifice shapes, showing that vortices formed on the minor axis of elongated orifices move towards the jet axis and grow faster in respect to those at the major one, which move away from the jet. This leads to the wellknown axis switching phenomenon, observed in non-circular continuous jets (Hashiehbaf and Romano, 2013). As a consequence, vortex rings formed in circular orifice move faster downstream in respect to those from rectangular ones. Wang et al. (2018) investigated the effect of orifice shape with different aspect ratio on mixing enhancement in the near field of the jet (X/D < 10). They reported occurrence of two axis switching for both rectangular and elliptic orifices for AR = 3, but only one for AR = 5. Shi et al. (2019) investigated circular and elliptic synthetic jets with different aspect ratio in the laminar regime, concluding that low aspect ratio elliptic nozzles have higher entrainment rate in respect to circular ones and reported that increases of stroke length results in decreasing of the number of axis switching. Wang et al. (2010) investigated the effect of duty cycle factor K (K=T2/T1, where T2is the suction stroke period and T1is the ejection stroke period) on pulsed planar orifice jets with aspect ratio AR = 100. They showed that the vortex formed at the orifice moves faster downstream for high values of K in respect to smaller ones, whereas the distance between

Fig. 1. Schematic view of the experimental setup with flow from left to right from the orifice. 2

International Journal of Heat and Fluid Flow 82 (2020) 108536

A. Hashiehbaf and G.P. Romano

vortex pairs is much larger for higher K in comparison to smaller ones. The resulting effect is a higher spreading rate in comparison to the continuous and mixed pulsed jets (Mossi et al., 2005; Tesar and Kordik, 2009). Regarding mean square velocity fluctuations, Di Cicca and Iuso (2007) noted a reduction of turbulence by increasing the frequency for a fixed stroke length, in agreement with findings of Pratomo and Bremhorst (2006). Frequency and amplitude of forcing oscillations also contribute to this effect, as observed by Qayoum et al. (2010), the higher being the frequency, the lower the fluctuating velocity. The observation of results obtained in literature for continuous jets, suggests that the shape of orifice could have a dominant effect on the developing mean and fluctuating velocity fields, in addition to the dependence on stroke length and Reynolds number (Falchi et al., 2010). Moving from here, the aim of this paper is to investigate differences among vortex generation and development in pulsed jets, downstream orifices of different shape in fully turbulent conditions, which are extremely interesting for engineering application. The attention is focused onto mean and fluctuating velocity fields, by looking at phase and time averaged results in view of possible mixing enhancements. Specifically, the results obtained on velocity decay and self-similarity will be

Table 1 Orifice characteristic size. Orifice type

Major axis(mm)

Minor axis(mm)

Area (mm2)

Circular Rectangular Elliptic Triangular Square

20.0 10.2 11.5 23.3 17.7

20.0 30.7 34.7 13.5 17.7

100π 100π 100π 100π 100π

compared among the different orifice shapes and among pulsating and continuous conditions. 2. Experimental facility, measurement technique and data analysis A sketch of the experimental setup and real images of high quality (sharp edge, roundness less than 0.5 mm) manufactured non-circular orifices are shown in Figs. 1 and 2. Five different orifice shapes are cut through a plate as orifice jets, the geometrical configurations employed in present experiments being circular, rectangular, squared, elliptical and triangular. The plate dimensions on the measurement planes (X-Y &

Fig. 2. Real images of orifice orifices (a) and detailed dimension of the rectangular orifice and wide chamber (b). 3

International Journal of Heat and Fluid Flow 82 (2020) 108536

A. Hashiehbaf and G.P. Romano

X-Z) are also depicted in Fig. 2b for the rectangular orifice as an example. As a matter of fact, in an orifice jet it is not possible to consider fully developed flow, so it is not possible to use hydraulic diameter concept. Therefore, the orifice inlet area is fixed for all configurations as equal to the inlet area of circular orifice used for comparison (D = 2 cm), the details being given in Table 1. Due to reciprocating motion of the piston, driven by a linear motor, the water flows into the wide chamber (test section) from the small chamber, through the same sharp edge orifices and the same facility used for continuous jets (Hashiehbaf and Romano, 2013). Finally, the water flows out from a large, circular, opening (20 cm in diameter) made on a Plexiglas plate. Both the water inlet and outlet were connected to a constant-head container through two one-way valves. Theoretically, these valves should cancel the backflow through the orifice during the backward motion of the piston, so far allow keeping the same inlet conditions at each pulse. In practice, this will not be exactly the case as reported at the beginning of Section 3. The linear motor driving the piston is controlled by LABVIEW software on a PC, allowing different specific velocity programs to be fed to the piston. Both vertical and horizontal mid-planes of the wide chamber are illuminated separately by a Nd-YAG laser (covering X-Y & X-Z plane) in double pulse mode. The number of laser pulses is synchronized to the period of piston velocity program, which results in 20 pulses at 10 Hz for each cycle. The light sheet thickness is approximately 2 mm. The water was seeded with hollow glass particles (8–10μm diameter), allowing to follow the fluid flow oscillations up to 105 Hz (Stokes frequency). A high speed CMOS camera is mounted perpendicular to the light sheet, working at full resolution (1024 × 1024 pixel) and capturing 500 frames/s, by following a trigger signal synchronised with the motion of the piston (therefore the time interval between double PIV images in 2 ms). The region of interest is divided into two 8 cm × 8 cm window size (with an overlapping of 2 cm between two windows), covering seven and four equivalent diameters from the orifice exit in streamwise and vertical directions, respectively. The whole cycle period is divided into 20 phases, each producing the minimum time resolution of 0.1 s (considering that the frequency of the piston is 0.5 Hz). To ensure statistical convergence, five different acquisitions, each containing 2000 images, are carried out in each window. The phase averaging method is employed here for averaging the instantaneous velocity fields acquired in each phase of the cycle. Thus, for each phase, 500 images are available for each phase averaging (10,000 total images/20 phases), which have been proved to be large enough for convergence of first and second-order statistics (variations less than ± 5% for the average after 50 cycles and after 200 cycles for the rms velocity). Mean velocity, streamwise and lateral rms velocity fields are obtained using a PIV image analysis software (LaVision GmbH), with final interrogation window of 32 × 32 pixels with 75% overlap which results in a grid data of 128 × 128 vectors. Therefore, the distance between two data points is 0.625 mm. The piston displacement is feedback controlled by a PC, therefore, if there is any difference between the input signal and the output displacement larger than 0.2 mm, the piston motion is modified accordingly. Hence, since the average piston stroke length is around 13.7 cm, the maximum error regarding the piston position is approximately 0.14%. Basically, this is also the relative error on the timing of the piston, thus the possible lag in phase averaging procedures (being timing error on laser emission much smaller than this). A sinusoidal input velocity program with a time period of T = 2 s is selected for producing the pulsation in the flow, whereas the amplitude of oscillation is related to the stroke volumes ejected through the orifice (90 mL). Each input signal for the piston is given in the form of 200 data points, allowing to reach a Reynolds number equal to 10,000 based on the peak exit velocity (ReUex ) and 2000 based on the average velocity (ReU0 ), with a Strouhal number equal to 0.022.

Phase averaged statistics is evaluated by using the triple decomposition method proposed by Hussain and Reynolds (1970) and by Reynolds averaging over the total number of images captured at each time interval (phase) (5–1)

un (x, t) = u n (x, t) + u¯n (x) + u˜n (x, t) th

where un is the n instantaneous velocity component, u¯n is the timeaveraged velocity component, u˜n is the phase-correlated velocity component and u n is the turbulent fluctuation. They are defined as following T

1 T

u¯n (x) = lim T

un (x, t)dt

un (x, t) = lim N

(5–2)

0

1 N

N

un (x, t +

)

(5–3)

n=0

u n (x, t) = un (x, t)

un (x, t)

(5–4)

u˜n (x, t) = un (x, t)

u¯n (x)

(5–5)

where 〈un(x, t)〉 is the phase-averaged velocity component, N is the number of the instantaneous velocity fields at the same phase, α is an integer and τ is the period of the coherent contribution, which in this study is considered as the period of forcing generating the synthetic jet. By knowing the total number of 40 images acquired in each cycle (based on the laser pulse rate and pulse number in each second), it is possible to consider that the first and second image are correlated in time similarly to the (1 + 40)th & (2 + 40)th in the second cycle, the (1 + 80)th & (2 + 80)th in the third cycle and so on. Thus all of them belong to the first phase (t/T = 0.1) and averaging over all image pairs will give the phase average at this specific phase. The same procedure would be repeated for the 3rd and 4th images and also (3 + 40)th & (4 + 40)th, (3 + 80)th & (4 + 80)th,… to produce the images pairs for averaging in the second phase (t/T = 0.2) and so on until all time intervals of the cycle are considered. The mean ejection velocity is computed from integration of velocity profile in ejection phase as the velocity scale for normalization, based on the definition of Glezer (1988).

U0 =

0

T 2

u (t ) dt (5–6)

T

where u(t) is the exit velocity profile and T is period of oscillation. Due to the complex nature of the phenomenon, an uncertainty analysis based on the approach of Sciacchitano (2016) is performed for all orifice types at two selected phase instants, for more comprehensive understandings the results being presented in Tables 2 and 3. 3. Results and discussion The axial velocity is evaluated for each of the 20 phases, by averaging the local instantaneous exit velocity (as close as possible to the orifice exit, X/D ≈ 0.1) along the orifice width and normalizing it by Table 2 Estimated values of error on mean and rms velocities at jet centerline for reverse flow (t = 0.7T). Orifice shape

Circular Square Triangular Elliptic Rectangular

4

Mean velocity (U) Centerline mean error

Fluctuating velocity Urms Centerline mean error

Fluctuating velocity Vrms Centerline mean error

5.51% 6.1% 3.38% 6.04% 4.95%

7.93% 7.67% 9% 8.12% 8.44%

4.48% 4.27% 4.41% 6.58% 4.97%

International Journal of Heat and Fluid Flow 82 (2020) 108536

A. Hashiehbaf and G.P. Romano

present jet configurations, from spatial profiles at the inlet section and at the different phases (being an integral quantity, it is not so much affected by poor resolution in phase) and is presented in Table 4. The results show that the value of volumetric efficiency changes from a minimum ε≈0.75 for the square geometry to a maximum ε≈0.82 for the rectangular one, giving a maximum difference around 9%. Therefore, considering the rather small amount of this difference, it is possible to state that the present jets are forming at the same inlet and boundary conditions and that eventually the small differences are affecting the unwanted backflow (which is not considered in detail in this paper).

Table. 3 Estimated values of error on mean and rms velocities at jet centerline around peak ejection (t = 0.4T). Orifice shape

Circular Square Triangular Elliptic Rectangular

Mean velocity (U) Centerline mean error

Fluctuating velocity Urms Centerline mean error

Fluctuating velocity Vrms Centerline mean error

1.68% 1.46% 1.37% 2.06% 2.4%

4.1% 5% 7.92% 4.4% 5%

4.64% 4.15% 4.91% 4.17% 4.7%

3.1. Phase averaged data Based on relation (5–6), the normalized phase averaged axial velocity contour maps for different orifices under investigation are shown in Fig. 4 for t/T = 0.3, 0.35, 0.4, 0.45 and 0.75 in each figure. Ejected vortices can be observed in all orifice types, with the highest velocity being measured for circular orifice (U/U0=6.175) and triangular orifice (U/U0=5.831). Despite, by looking at the circular orifice at t/ T = 0.45 (Fig. 4a), it is evident that a second vortex, separated from the leading one, exists in the flow field. This is related to the observation made by Gharib et al. (1998) of a limiting maximum circulation and vorticity in the growth of an isolated vortex, the circulation in excess being responsible for the generation of other vortices. This phenomenon is only partially observed for square and triangular orifices, with a kind of merging among two separated vortex cores (Fig 4b and c). For elongated orifices (rectangular and elliptic), separated maxima of axial velocity are not observed behind the leading vortex and this could be due to the severe axis switching observed in these type of jets (Fig. 4d, e and –f). The axis switching phenomenon could be recognized by looking at major axis evolution of rectangular orifice shown in Fig. 4f at t/T = 0.35–0.4. At the beginning of the suction phase (t/T = 0.75), close to the orifice exit, negative values can be seen for all configurations in the form of dark blue regions on the left hand side of Fig. 4. Indeed, the position where the negative velocity values change sign is named saddle back and is evaluated from Fig. 4 and labeled as Xs in each plot. This position is slightly dependent on the orifice type and for all occurs at X/ D less than unity, the rectangular orifice showing the shortest saddle back point distance from the orifice exit (less than 0.9). To identify in higher detail phase averaged vortices, vorticity maps are reported in Fig. 5 at t/T = 0.3, 0.35, 0.4 and 0.45. In each map, three phase averaged plots are overlapped: absolute normalized value of vorticity (color lines, scale on the right), velocity vectors and axial velocity color maps normalized by average velocity in ejection phase (color background, scale on the left). Accordingly to Fig. 5a, for the circular jet, the absolute value of velocity is decreasing by 25% from t/ T = 0.3 to t/T = 0.45 and vorticity also decreases for first vortex from t/T = 0.3 to t/T = 0.4. The generation of the second vortex is clearly observed in this sequence, as also the strongly reduced amount of vorticity associated in comparison to the leading vortex. The second vortex is generated at t/T = 0.4–0.45, in agreement with first vortex pinch off from the trailing jet, starting from t/T = 0.3 and completed at t/T = 0.45. As already pointed out in the comments to Fig. 4, this secondary vortex ring has been observed in impulsive starting circular jets (Gharib et al., 1998) and in the present experiments could be retained as a consequence of an ambient fluid almost at rest before starting a new ejection phase at each cycle. The pinch off phenomenon is not observed for any of the other jet configurations, so that this exemplifies a completely different vortex structure in circular orifice, which is also the reason for high turbulence fluctuations at the centerline, as described later. For the square jet, reported in Fig. 5b, the overall content of velocity and vorticity is lower in respect to the circular one, however basically showing similar trailing jet behavior, except for the lack of any pinch off. A second very weak vortex appears

Fig. 3. Normalized averaged axial velocity at the exit of the orifice for different orifices. Table 4 Estimated values of volumetric efficiency for the different jets. Orifice

Average exit velocity (m/s)

ε

Circular Square Triangular Elliptic Rectangular

0.10 0.10 0.11 0.10 0.11

0.78 0.75 0.79 0.80 0.82

the time averaged exit velocity. Values are plotted in Fig. 3 for the different orifice shapes over the whole time period, also as a check of inlet conditions for the different jets. The behavior of all jets is quite similar, except possibly for the rectangular orifice, which is showing some delay and change expecially during the backward motion of the piston, i.e., the suction phase. This could be related to the different vortex evolution mechanism across the different orifices, which will be detailed in the following. Peak ejection velocity is around four times larger than the suction velocity, in agreement with results of Jain et al. (2011). As stated in Section 2, the whole fluid volume pumped by the piston is passing through the orifices whatever their shape, but curves in Fig. 3 are non-symmetrical during injection and suction phases, due to the closure of the valve during the latter. Specifically, the fluid exhibits an unwanted small backflow into the settling chamber due to the deformation of the wide chamber and to imperfections in the hydraulic circuit. During suction, the maximum backward velocity occurs at the edge of orifices as will be shown in the following. Actually, this also indicates that the present jets are no longer ZNMF (or pure synthetic jets), the present condition being more strictly considered as related to hybrid synthetic jets (Tesar et al., 2006; Trávníček et al., 2006). So far, it is important to characterize the amount of deviation from a pure synthetic jet and if this amount would be almost the same for all orifices. This can be quantified by using the volumetric efficiency ɛ, i.e., . the ratio of the net output fluid volume to the total displaced volume pumped during the oscillation period. This quantity is derived for the 5

International Journal of Heat and Fluid Flow 82 (2020) 108536

A. Hashiehbaf and G.P. Romano

Fig. 4. Axial velocity (U/U0) contours in X-Y plane and X-Z plane (for rectangular orifice) during the ejection phases (from the top of each figure: t/T = 0.3, 0.35, 0.4, 0.45) and suction phase (t/T = 0.75) for the tested jets. t/T = 0.3 t/T = 0.35 t/T = 0.4 t/T = 0.45 t/T = 0.75 (a) circular, t/T = 0.3 t/T = 0.35 t/T = 0.4 t/T = 0.45 t/T = 0.75 (b) square, t/T = 0.3 t/T = 0.35 t/T = 0.4 t/T = 0.45 t/T = 0.75 (c) triangular, t/T = 0.3 t/T = 0.35 t/T = 0.4 t/T = 0.45 t/T = 0.75 (d) elliptic, t/T = 0.3 t/T = 0.35 t/T = 0.4 t/T = 0.45t/T = 0.75 (e) rectangular (minor axis), t/T = 0.3 t/T = 0.35 t/T = 0.4 t/T = 0.45t/T = 0.75 (f) rectangular (major axis). 6

International Journal of Heat and Fluid Flow 82 (2020) 108536

A. Hashiehbaf and G.P. Romano

Fig. 4. (continued)

7

International Journal of Heat and Fluid Flow 82 (2020) 108536

A. Hashiehbaf and G.P. Romano

Fig. 4. (continued)

around t/T = 0.4. Regarding the triangular case, Fig. 5c, the content of vorticity is comparable to the circular nozzle for all t/T, but decay of absolute normalized velocity is faster and not symmetric. The trailing jet evolution is also non-symmetrical, without any trace of a second vortex or of pinch off.

On the other hand, the behavior of elongated orifices is rather specific, both elliptic and rectangular orifices showing vorticity values less than one half of the previous described ones, the value of absolute velocity being also lower (Fig. 5d and e). The shape of the whole configuration is also completely different from the previous ones, being 8

International Journal of Heat and Fluid Flow 82 (2020) 108536

A. Hashiehbaf and G.P. Romano

Fig. 5. Normalized absolute vorticity contours overlapped on phase averaged velocity vectors and color maps of axial velocities for (a) circular orifice, (b) square orifice, c) triangular orifice, (d) elliptic orifice, (e) rectangular (minor axis) orifice (f) rectangular (major axis) orifice at t/T = 0.6, 0.7 0.8 & 0.9 t/T = 0.3 t/T = 0.35 t/T = 0.4 t/T = 0.45 (a,) circular t/T = 0.3 t/T = 0.35 t/T = 0.4 t/T = 0.45 (b) square, t/T = 0.6 t/T = 0.7 t/T = 0.4 t/T = 0.45 (c) triangular, t/T = 0.3 t/T = 0.35 t/T = 0.4 t/T = 0.45 (d) elliptic, t/T = 0.3 t/T = 0.35 t/T = 0.4 t/T = 0.45 (e) rectangular (minor axis), t/T = 0.3 t/T = 0.35 t/ T = 0.4 t/T = 0.45 (f) rectangular (major axis). 9

International Journal of Heat and Fluid Flow 82 (2020) 108536

A. Hashiehbaf and G.P. Romano

Fig. 5. (continued)

10

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A. Hashiehbaf and G.P. Romano

Fig. 5. (continued)

11

International Journal of Heat and Fluid Flow 82 (2020) 108536

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Fig. 6. Normalized streamwise rms of velocity fluctuations in X-Y plane for different shapes, t/T = 0.4. (a) circular, (b) square, (c) triangular, (d) elliptic, (e) rectangular (minor axis), (f) Rectangular (major axis).

calculated by averaging over instantaneous fluctuating velocities in each phase and are scaled by the averaged velocity at outlet (U0). In addition some sample contour label is added to each field for more details. By looking at the results, some similarities (shape of contour) among the square, circular and triangular orifices from one side and on the other hand between elongated orifices (rectangular and elliptic) are observed. This similarity is also visible for continuous jets at comparable Reynolds numbers (Re = 8000) (Hashiehbaf and Romano, 2013). The deformation of the initial shape of orifices due to the axis switching phenomenon is detectable by looking at the velocity field of elongated orifices at X/D ≈ 2.5D, where the jet half width expands until y/ D ≈ 2D. The inverse condition occurs for the major axis of rectangular orifice in the aforementioned range, thus proving the completion of axis switching for this orifice type as shown in Fig. 6f. For the square and

the vortex displaced at a higher distance from the centerline. This is compensated by a lower travelled distance along the streamwise axis at similar phases, especially for the rectangular jet. Therefore, it is interesting to investigate the behavior of vortex rings along the major side of the rectangular orifice as shown in Fig. 5f, absolute velocities being much higher in this plane in respect to the minor side. A second vortex following shortly after the first is observed, similarly to the circular orifice with comparable velocity. Unlike the circular case, pinch off is replaced by the merging of the two vortices due to higher convection velocity of the second one. This is due to axis switching at t/T = 0.45, where jet width increases to reach that of the other side. Regarding fluctuating velocity fields, contour plots of streamwise and crosswise rms velocities are shown in Figs. 6 and 7 at t/T = 0.4 as a sample phase (more or less corresponding to the phase of maximum ejection velocity for all jets, t = 0.8 s in Fig. 3). These fields are 12

International Journal of Heat and Fluid Flow 82 (2020) 108536

A. Hashiehbaf and G.P. Romano

Fig. 7. Normalized crosswise rms of velocity fluctuations in X-Y plane for different shapes, t/T = 0.4. (a) circular, (b) square, (c) triangular, (d) elliptic, (e) rectangular (minor axis), (f) rectangular (major axis).

triangular jets, the occurrence of axis switching can be verified by looking at the edge of square orifice at X/D ≈ 2.5D and apex of triangular orifice at X/D ≈ 1, respectively. Again, specifically for the triangular jet, these results are in agreement with the continuous regime (Quinn, 2005). It is also interesting to note that the vortex which is formed at X/D ≈ 2 has an almost circular shape, since the apex of triangular orifice cannot be observed anymore after X/D = 1 and that the circular jet shows higher fluctuations in respect to other configurations at X/D ≈ 3. High values of rms velocity for circular and nonelongated jets seem to be associated to fluctuations in the positions and intensity of vortices at different phases, whereas for elongated orifices, peak rms velocity depends on fluctuations in the occurrence of axis switching. Circular vortices ejected from the orifice move downstream

faster than the others (as noticed in phase plots of axial velocity for circular orifice, Fig. 4a), thus bringing more turbulence content into the flow field. In addition, rms velocity contours show activity also at the centerline of the jet for all configurations, even very close to the orifice due to vortex oscillations at each phase. By looking at low turbulence content regions at the centerline of the jet, the merging process of shear layers could be clearly observed in crosswise rms velocity plots (Fig. 7), occurring for all shapes after X/D = 2, while minor axis of elongated orifices show higher activity (narrower low content rms velocity region) close to the centerline in respect to other configurations. Due to the complexity of the reported fields, it is worth here to consider the uncertainty analysis for all presented rms velocity fields at t/T = 0.4, as presented in Table 3. 13

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Fig. 8. Axial profile of time averaged streamwise velocity at the centerline of pulsed jets and comparison with results for continuous jets (Hashiehbaf and Romano, 2013).

Fig. 9. Axial profile of time averaged half velocity width at the centerline of pulsed jets and comparison with results for continuous jets (Hashiehbaf and Romano, 2013).

3.2. Time averaged data

other configurations, as observed also in continuous jets (Hashiehbaf and Romano, 2013). In addition, the elliptic orifice in pulsating regime shows a higher rate than in continuous regime until X/ D = 4, but further downstream, the opposite takes place. Present results on rectangular orifice in the horizontal plane (X-Z plane) show the existence of axis switching at X/D = 1, which is located closer to the orifice exit in comparison to the continuous regime (X/D = 2), thus indicating higher mixing in the very near field of the jet. Actually, the high rms velocity regions close to orifice shown in Fig. 7 can be well correlated to earlier axis switching taking place in pulsating regime. The results of Di Cicca and Iuso (2007) and Oren et al. (2009) are also shown in the figure, presenting good agreement with current results. The vertical profiles of streamwise velocity measured for different orifices at nine different axial distances are presented in Fig. 10a to –f to investigate possible self-similarity of pulsating jets. As can be observed, profiles of circular jet collapse approximately on a single curve (which corresponds to results by Di Cicca and Iuso (2007) only for X/D ≥ 5. This is also partially observed for the triangular jet for X/D ≥ 5 and major axis of rectangular orifice for X/D ≥ 3. On the other hand, no self-similarity is observed for the minor axis of elongated orifices and square orifices within the test region. Although it is not easy to conclude that initial entrainment has an effect on self-similarity of velocity profile, it is observed that orifices with reduced entrainment very close to the orifice exit, visible in terms of negative axial velocities at the boundaries of the jet, do not show self-similar behavior (at least in the current test region up to X/D = 7). In comparison to continuous jets, a noticeable entrainment is observed for pulsating ones due to the starting vortices at the orifice, which is not present in the continuous regime for the same orifice types (Hashiehbaf and Romano, 2013). This is pointed out by the negative velocities immediately after orifice exit, which are observed up to 1.5 D for the circular orifice, up to 0.6D for the square orifice and around 1D for major axis of rectangular orifice. The situation for the triangular orifice is complex due to the 180∘ axis rotation which takes place at X/ D ≈ 1. Thus, it can be noticed that all entrainment taking place up to X / D=0.6 is at the flat side of the triangle, whereas further downstream,

3.2.1. Streamwise velocity profiles The effect of a pulsating regime on the streamwise velocity decay rate at the centerline of the jet is shown in Fig. 8 for different orifice shapes. The data from rectangular and triangular continuous jets are also added in the graph for comparison (Hashiehbaf & Romano (Wang et al., 2018)). The two elongated orifices show similar behaviors by reaching the highest decay rates in comparison to circular, triangular and square orifices, which have similar trends. These observations are qualitatively similar to those reported in the continuous regime, especially for Re = 8000 (Hashiehbaf and Romano, 2013). It is interesting to mention that even the lowest decay rate in pulsating regime (circular orifice) is still higher than elongated orifices in the continuous conditions. A maximum in streamwise velocity just after the jet exit, i.e., around X / D 1 1.5, has been observed as also in continuous jets. This is a consequence of the vena contracta phenomenon, typical of orifice jets. To investigate the decay rate in more details, two decay rate x x equations, a ( D ) b= 0.58 and a ( D ) b= 1 as proposed in Smith and Glezer (2007) and O'Farrell and Dabiri (2013), are applied to data with a nonlinear least square fitting based on residuals, R2, to determine a and b as reported in Table 5, the value of b being changed in the range −0.5 to −1. According to Table 5, decay rate of circular, square and triangular x orifices are well-matched by a power law ( D ) 0.58 with R2 around 0.98, with best fit in the range b=−0.58÷−0.65 (R2 larger than 0.99). On x the other hand, elongated orifices follow the behavior ( D ) 1, with R2 larger than 0.9, with best fit in the range b=−0.85÷−1 (R2 larger than 0.93). Indeed, this shows that a different decay rate, as derived by axial evolution of vortical structures depicted in Figs. 4, , –6, is attained by the different pulsed jets depending on the orifice shape. The related half-velocity width development is shown in Fig. 9, with added results of Hashiehbaf and Romano (2013) for square and elliptic orifices in continuous regime for comparison. In agreement with results from the centerline velocity decay presented in Fig. 8, elongated orifices in pulsating regime show the highest growth rate in respect to

Table 5 Calculation of residuals (R2) and constant a based on power laws (Smith and Glezer, 2007; O'Farrell and Dabiri, 2013) and best data fit. R2 value

a

Orifice Shape

Range

b=−0.58

b=−1

(best fit)

b=−0.58

b=−1

best fit

Circular Square Triangular Rectangular Elliptic

3
0.985 0.983 0.994 0.744 0.845

0.667 0.695 0.344 0.946 0.901

0.992 0.993 0.994 0.946 0.938

1.797 1.645 1.781 1.157 1.370

3.252 2.976 3.218 2.11 2.487

1.985 (b=−0.65) 1.818 (b=−0.65) 1.781 (b=−0.58) 2.11 (b=−1) 2.015 (b=−0.85)

14

(b=−0.65) (b=−0.65) (b=−0.58) (b=−1) (b=−0.85)

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Fig. 10. Vertical profiles of streamwise velocity for (a) circular orifice, (b) square orifice, (c) triangular orifice, (d) elliptic orifice, (e) rectangular orifice (minor axis), (f) rectangular orifice (major axis).

Fig. 11. Time averaged streamwise rms of velocity fluctuations at the centerline of the jet for various orifices.

Fig. 12. Time averaged crosswise rms of velocity fluctuations at the centerline of the jet for various orifices. 15

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A. Hashiehbaf and G.P. Romano

rectangular and triangular orifices in continuous regime are added for comparisons. According to Fig. 11, the circular and triangular orifices show the highest and lowest values respectively, whereas the elongated orifices are in the middle of aforementioned values. As Kumar et al. (2019) described, the reason for such a behavior could be related to the enhanced travelled distance of vortices released downstream of the circular orifice in respect to other orifice shapes (due also to pinch off observed in Fig. 5 only for this shape), resulting in high rms velocity even far from the orifice. These results are also in agreement with findings of Crispo et al. (2016) who showed lower turbulence fluctuations at the centerline of non-circular pulsed jets, due to the lack of vortex rings convected downstream and generating high rms velocities. On the other hand, for crosswise rms velocities (Fig. 12), nearly all configurations show similar behaviors, with slightly higher values for elliptic and circular orifices in the range 2
Fig. 13. Velocity fluctuation rms ratios at the centerline of the jet for various orifices.

no entrainment is observed. The reason that velocity profiles are not symmetrical for this type of orifice up X / D = 0.6 is related to the aforementioned axis switching which is going to be completed till X / D=1 and makes the rotation of triangular orifice apex in this region. For rectangular orifice, no entrainment is reported at the exit along the minor axis, while on the major axis entrainment is observable up to X / D = 0.6. 3.2.2. R.M.S. velocity profiles The axial profiles of streamwise and crosswise rms velocities are shown in Figs. 11 and 12 for all configurations, the errors on these quantities being also provided in Tables 2 and 3. The spanwise rms velocity (w-component) for the rectangular orifice is also shown in Fig. 12 as measured on the orthogonal plane. In addition, results of

Fig. 14. Lateral distribution of streamwise velocity fluctuations rms at different positions, (a) X/D = 1, (b) X/D = 2, (c) X/D = 3, (d) X/D = 5. 16

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A. Hashiehbaf and G.P. Romano

Fig. 15. Lateral distribution of crosswise and spanwise velocity fluctuations rms at different positions, (a) X/D = 1, (b) X/D = 2, (c) X/D = 3, (d) X/D = 5.

and rectangular continuous jets (the last along the major axis) are also added in the graph for comparison. For ideal isotropic flows, these ratios should be equal to 1, while the value 1.3 was reported for circular jets from orifices (Mi et al., 2007). The circular synthetic jet shows the most anisotropy among all orifice types never reaching unity or even 1.3, while the rectangular orifice in the major axis and the triangular one approach the previous values only for X/D > 4 and all the other configurations rapidly converge towards constant values. Despite, regardless of the very near field (X/D < 3), where synthetic jets are more anisotropic in comparison to continuous ones, further downstream, the behavior of these two types of jets become similar, which is a proof on the similarity of turbulent pulsating jets with continuous ones in the middle-far region from the orifice. To investigate how much the present results are valid all over the field, the lateral distribution of streamwise, crosswise and spanwise rms velocities are illustrated in Figs. 14 and 15 at four positions, X/D = 1, 2, 3 and 5. Results of streamwise rms show that at all X/D positions, the circular orifice gets the highest values close to the centerline of the jet from Y/D < 0.4 at X/D = 1 until Y/D < 0.7 at X/D = 5. This is in accordance with observations in Fig. 11, where circular orifice has the highest values at jet centerline. By moving towards shear layers, elongated orifices show the highest values in respect to the others. This proves that high rms velocity of the circular jet is mainly due to high velocity of vortices moving close to the centerline of the jet as was previously observed in the centerline velocity and fluctuating velocity profiles. Circular, square and triangular orifices show similar behavior far away from the centerline as in the case of continuous jets (Hashiehbaf and Romano, 2013). On the other hand, at X/D = 2–3, there is a sudden increase in the lateral extension of elongated jets, which is attained also for other configurations at X/D = 5. At this distance, results of Shuster and Smith (2007) for circular orifice at X/ D = 7.5 are also added for comparison, the observed difference being

associated to the different streamwise location. Also crosswise rms velocities, presented in Fig. 15, of circular orifice show higher values close to the centerline (until y/D = 0.4), whereas at X/D = 5 all other orifices have already reduced energy content to less than 15%. Results of Shuster and Smith (2007) are also added for comparison. Also crosswise rms shows the lowest values for triangular orifice, especially close to the centerline. So far, considering transverse profiles, it can be noted that while in near field (X/D < 6) and close to the centerline of the jet (y/ D < 0.4), the circular pulsed jet is a good candidate for mixing enhancement, far from the centerline, elongated orifices could play a relevant role in mixing enhancement. 6. Conclusion A detailed Particle Image Velocimetry (PIV) study is presented for different sharp edged circular and non-circular orifices, in order to investigate details of the flow fields of the resulting jets in pulsating regime and to compare them with results in the continuous regime. In all conditions, the vena contracta (due to the sharp edge orifices) and axisswitching phenomena (due to the non-unitary aspect ratio) are observed but with different locations and intensities depending on the shape and regime. The velocity data acquired in pulsatile regime are averaged in phase with the piston forcing, to allow extracting detailed information on vortex position and evolution, and also in time, to allow easier comparison with the continuous jet results. From phase average results, it is possible to point out the shape and extension of main vortical structures generated in the forward phase (ejection), as also some reverse flow during the backward piston motion (suction). Trailing jet accompanied by leading vortices is the main underlying pattern of vortex structures in all configurations. Pinch off of vortices is observed only for circular case, which results in conveying high turbulence content further downstream with higher velocity in 17

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respect to other configurations. Time averaged results show that, by considering the same orifice type, the axis switching occurs earlier in pulsating regime in respect to continuous one, thus suggesting more mixing in very near field of the jet. This is well correlated to higher rms velocities close to the orifice exit (X/D<1), indicating more large scale mixing in comparison to the continuous regime. Axis switching is also observed for time averaged results, where secondary vortex velocity exceed leading vortex and vortex merging takes place. Both phase and time averaged data show similar behaviors between circular and square orifices from one hand and between elongated orifices on the other hand in most cases (from the point of jet configuration). Furthermore, in the pulsating regime, higher anisotropic behavior (especially in the near field of the jet) can be noticed in respect to the continuous one. Higher spreading rate and faster velocity decay rate (at the centerline of the jet), in comparison to all those in continuous regime, indicate mixing enhancement at these locations. From the transverse velocity and rms velocity profiles, it is found that in the very near field of the jets and close to the centerline, elongated orifices in addition to the circular orifice show possible mixing enhancements. These are significant in shear layers, especially after X/D = 3, due to high expansion of these type of jets (a consequence of faster velocity decay rate) and to the severe axis switching related to elongated orifices in pulsating regime (in comparison to continuous regime). On the other hand, for circular orifice, this enhancement is observed next to the centerline of the jet, due to the presence of fast moving vortices, carrying high turbulence content, so far indicating that the circular orifice is also a good candidate for mixing enhancement in the pulsating regime.

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