1 Introduction

A very high heat transfer rate between fluid flow and a solid surface can be obtained in the case of impinging jets (IJs). Therefore, jet impingement is used in many industrial processes, such as drying, deicing, and the cooling of electrical equipment and gas turbine blades. As a result, IJs have received substantial attention (see e.g., Martin 1977; Jambunathan et al. 1992; Viskanta 1993; Webb and Ma 1995; Garimella 2013).

Nozzles with round and slotted cross-sections are the two most common geometries. An interesting alternative is an annular nozzle. However, annular IJs can introduce rather complex flow characteristics, including bistable and hysteretic behavior (see, e.g., Shtern and Hussain 1996, Trávníček and Tesař 2003, Vanierschot and Bulck 2007).

Annular jets can be controlled by passive or active flow control methods. For example, Danlos et al. (2008) investigated the active control of an annular jet using acoustic waves to find a new way to reduce jet instabilities. A swirling effect can be introduced by means of an appropriate spacer (twisted tapes, swirling vanes, and helical strips) inserted into the fluid flow; see, e.g., Ianiro and Cardone (2012). Vanierschot and Bulck (2007) designed a swirl generator according to the geometry of a burner, and the swirl was continuously adjustable from zero to the maximum. Another method to generate flow swirling uses a tangential inlet of the working fluid into a chamber upstream of the nozzle; see Chigier and Beer (1964).

Examples closer to the present topic include annular jets with a cross-flow control injection. Trávníček et al. (2003) investigated bistable annular IJs controlled by a steady radial jet issuing from the nozzle centerbody. Switching the jets by an on/off fluidic control was achieved, and a hysteresis effect was identified. Vanierschot et al. (2009) investigated an annular jet controlled by cross-flow injection by means of 24 steady round jets, distributed equidistantly around the nozzle centerbody perimeter. Three flow patterns were revealed at zero swirl, namely, the “closed jet flow,” “open jet flow,” and “Coanda jet flow.” More recently, Trávníček et al. (2014) investigated an annular IJ controlled by 12 radial pulsatile jets issuing from the nozzle centerbody. It was concluded that the local heat/mass transfer can be enhanced at the stagnation circle by approximately 20%. Note that the control jets were synthetic jets in character.

A synthetic jet (SJ) is a fluid jet that is generated (“synthesized”) from a train of fluid puffs by pushing and pulling fluid through an actuator orifice (Smith and Glezer 1998; Holman et al. 2005; Di Cicca and Iuso 2007; Paolillo et al. 2019). SJs are also known as zero-net-mass-flux jets because the time-mean mass flux of the oscillatory flow in the SJ actuator orifice is zero (Pack and Seifert 2001; Cater and Soria 2002). SJs have a wide range of potential applications, such as active flow control (jet vectoring and utilization in external and internal aerodynamics), convective heat transfer, mixing, and thrusters for underwater vehicles. As a result, SJs continue to be of great interest to researchers (e.g., Trávníček and Tesař 2003; Ben Chiekh et al. 2003; Arik 2007; Timchenko et al. 2007; Chaudhari et al. 2010; Persoons et al. 2011; Hong et al. 2020; Smyk et al. 2020).

The objective of the present study is to extend previous knowledge about annular IJs in the case of their active control. It is expected that the hysteretic behavior of annular IJs (revealed previously by Trávníček and Tesař 2003) can be suppressed by means of a swirling effect. For this reason, the annular jet is driven to a swirling motion by synthetic jets. To the best of the authors’ knowledge, such a configuration has not been suggested and studied in the available literature until now. The main motivation for the present study is to experimentally demonstrate and quantify the possibilities of such a configuration.

2 Experimental setup and methods

The experimental setup is presented in Fig. 1. The air (the working fluid) is supplied by a compressor (position 1 in Fig. 1), runs through a flexible pipe, and is maintained at a chosen pressure by a two-stage pressure regulator (2). The flow rate is measured using a flow meter (3): rotameter AALBORG with the repeatability and accuracy ± 0.25% of full scale (FS) and ± 2% FS, respectively. The airflow passed through a flexible plastic tube and a T-shaped connecting tube via a pair of radial inlets (4) to the settling chamber (5) equipped with a honeycomb (6).

Fig. 1
figure 1

Scheme of experimentation: 1—compressed air, 2—air filters and two-stage pressure regulator, 3—rotameters, 4—pair of radial inlets, 5—settling chamber, 6—honeycomb, 7—annular nozzle equipped with SJ actuator, and 8—impingement wall

Full size image

The annular nozzle is pointed vertically downward, and its detailed scheme is shown in Fig. 2. The nozzle’s inner and outer diameters are Di = 28.4 mm and Do = 30 mm. The nozzle was derived from a previous variant; see Trávníček and Tesař (2013). Unlike the previous variant, the present nozzle centerbody (position 2 in Fig. 2) is equipped with an SJ actuator. The actuator consists of a sealed cavity with a diaphragm with a diameter of DD = 16 mm, driven by an electrodynamic transducer originating from a loudspeaker (LP–21008; GM Electronic, 8 Ω, 0.1 W). Eight SJs originate from eight orifices drilled into the cylindrical surface (diameter DE = 25 mm), each with diameter D = 1.2 mm. As shown in Fig. 2(b), these orifices have horizontal axes that are directed sideways at a 45° angle to generate the tangential (swirl) velocity component of the main annular jet. The loudspeaker is fed with a sinusoidal waveform from a sweep/function generator (AGILENT 33220A) via an audio amplifier (BW-11208). An in-house-built digital multimeter with a 13-kHz sampling frequency was used to measure the true root-mean-square (rms) alternating current, voltage, and power; the accuracies were ± 1.6%, ± 0.8%, and ± 2%, respectively.

Fig. 2
figure 2

The annular nozzle and tested configuration: a central cross-section and b cross-section perpendicular to the axis showing nozzles of SJA; 1: outer nozzle body, 2: nozzle centerbody equipped with SJ actuator, 3: air flow supply, 4: loudspeaker, and 5: impingement wall. Dimensions: \(\phi\) Do = 30.0 mm, \(\phi\) Di = 28.4 mm, \(\phi\) DE = 25.0 mm, \(\phi\) = 3.5 mm, \(\phi\) D = 1.2 mm

Full size image

Two configurations were investigated: annular free jets (jets without impingement walls) and annular IJs. To investigate the IJ, a flat impingement wall was installed perpendicular to the annular nozzle axis. In fact, two different walls were used alternately. For flow visualization experiments, a polymethylmethacrylate (PMMA) plate covered by black wallpaper was used. For wall-pressure measurements, a PMMA plate with a 0.9-mm diameter pressure tap was used. The wall pressure was measured by a Greisinger GMH 3156 manometer with a GMSD 2.5 MR transducer with a range, resolution and accuracy of 250 Pa, 0.1 Pa, and 0.75 Pa, respectively. Adjustments of the nozzle-to-wall distance and the position of the pressure tap were made using a manually operated x–r traversing system.

Flow visualization was performed using three methods: water fog technique, smoke-wire technique, and particle image velocimetry (PIV). In the first case, the water fog from an ultrasonic fog generator (Mini-Nebler, FK technics) was inserted into the air pipe supply. Using continuous light, the time-mean flow field patterns (pathlines) were obtained. A digital camera with 1 s exposure was used to record the pictures.

The smoke wire was made from three resistor wires of 0.1-mm diameter, uniformly twisted together (see Trávníček and Tesař 2003). The wire was coated with a fog generation liquid (DANTEC) before each test and heated by the Joule effect of a DC current. The liquid evaporates from the hot wire and condenses rapidly in the air stream into tiny droplets, which trace the airflow. A contrasting white flow pattern on a black background was observed and recorded. Again, a continuous light and a digital camera with 1 s exposure were used.

The PIV experiment was made in the 500 mm × 500 mm × 600 mm transparent (PMMA) box. An aerosol is used for seeding (DEHS-DANTEC DYNAMICS liquid) with droplet sizes between 1 and 3 μm. The PIV system comprises a double-pulsed Nd:YAG laser (Litron, NANO S 65–15, wavelength of 532 nm, 65 mJ) with cylindrical optics. The time delay between the pulses varied between 50 and 100 μs. The images were recorded by a high resolution digital camera (HiSense Neo, 2560 × 2160 pixels, 16 bit) a Tokina 100 mm F2.8 Macro D lens. The sampling frequency was 15 Hz. The pictures were post-processed using adaptive cross-correlation technique (with IA between 16 and 32 px and 50% overlap). In every run, at least 20 pictures were taken, and the results are presented as the time-mean streamlines in this paper.

Flow velocity measurements were made using a Pitot tube. It was a blunt-nosed impact tube with an outer diameter of 0.8 mm. It is worth noting here that the tube diameter is equal to the annular slot width of b = 0.8 mm and smaller than the SJ orifice diameter of D = 1.2 mm. This is the main reason for using a simple Pitot tube; such a small probe can be completely submerged into the small size jet, while the most sophisticated hot-wire probe will exceed from the jet to its surroundings (a typical length of the hot wire is larger). Note that another approach to measure small diameter SJs was presented by Feero et al. (2015): they used a special plated hot wire (spacing of 1.6 mm between prongs and shortened wire sensing length of 0.5 mm), and they measured SJs issuing from orifices with diameters of 2 mm.

The Pitot tube was connected to a manometer (Greisinger GMH 3156 with a transducer GMSD 2.5 MR; the range, resolution, and accuracy were 250 Pa, 0.1 Pa, and 0.75 Pa, respectively). The jet temperature was measured by a Pt100 platinum thermometer (OMEGA, sensor RTD-2-F3105-36-T) with a resolution and accuracy of 0.1 °C and 0.2 °C, respectively. An uncertainty analysis was performed according to the method outlined by Kline and McClintock (1953) for a single sample experiment. Following the law of uncertainty propagation, the velocity uncertainty was estimated to be 9% at the 95% confidence level for velocities higher than 2.8 m/s.

3 Experimental parameters

The Reynolds numbers of the main annular jet are defined as Re = Uav Do/ν and Reb = Uav b/ν, where Uav is the area-averaged time-mean orifice velocity in the annular nozzle exit, b = (Do–Di)/2 is the annular slot width, and ν is the kinematic viscosity of the working fluid.

The majority of the experiments were carried out at a fixed Reynolds number, Re ≈ 5000 (i.e., Reb = 140). Moreover, some experiments were carried out over a wider range of Re from 4000 to 10,000, i.e., Reb = 107–267. The parameters of the experiments are summarized in Table 1.

Table 1 Experimental parameters
Full size table

Due to the low Reynolds numbers, laminar flow can be expected at the annular nozzle exit. However, the jet flow develops toward the transition to turbulence further downstream (cf. Antošová and Trávníček 2023). Moreover, the initiation of the transition process can be promoted and triggered by pulsations of the control SJs.

The eight control SJs are drilled obliquely in the nozzle centerbody (see Fig. 2(b)). For the given geometry, the two characteristic length scales are the emitting orifice diameter D and the stroke length L0. The stroke length L0 is the length of the fluid column that is extruded from the cavity during the extrusion stroke of the actuation period, L0 = U0T, where T is the time period (T = 1/f, f is the driven frequency) and U0 is the time-mean orifice velocity of the extrusion averaged over the entire period. Considering the slug flow model (i.e., a uniform velocity profile issuing from the actuator orifice), the U0 velocity can be evaluated (see Smith and Glezer 1998) as

$$U_{0} = \frac{1}{T}\int\limits_{0}^{{T_{E} }} {u_{0} (t)dt}$$
(1)

where u0(t) is the velocity in the orifice exit and TE is the extrusion time (TE = T/2 at a common sinusoidal waveform). The Reynolds number of the SJ is defined (see Smith and Glezer 1998) as

$$Re_{{{\text{SJ}}}} = U_{0} D/\nu$$
(2)

Flow swirling is characterized by the swirl number S, defined as the ratio of the axial flux of the angular momentum to the axial flux of the axial momentum multiplied by Do/2. Namely, the swirl number can be defined following Chigier and Beer (1964), without the pressure term (the same definition was used more recently by Vanierschot and Bulck 2007):

$$S = \frac{{\int\nolimits_{{\frac{{D_{i} }}{2}}}^{{\frac{{D_{o} }}{2}}} {2\pi \rho u_{A} u_{T} r^{2} dr} }}{{\frac{{D_{o} }}{2}\int\nolimits_{{\frac{{D_{i} }}{2}}}^{{\frac{{D_{o} }}{2}}} {2\pi \rho u_{A}^{2} rdr} }}$$
(3)

where uA and uT are the local axial and tangential velocities at the nozzle outlet, respectively. In the present case, the annular jet slot is relatively small (Di/Do ~ 0.95). Therefore, the swirl number can be evaluated as

$$S\sim U_{{\text{T}}} /U_{{\text{A}}} \sim {\text{ tan }}(\alpha)$$
(4)

where UT and UA are the average axial and tangential velocity components, respectively, and α is the yaw angle of the outlet velocity vector.

4 Results and discussion

4.1 Frequency characteristics and resonance frequency

The frequency characteristic of the SJ actuator was evaluated using the Pitot tube in a frequency range from 800 to 1600 Hz for an input real power of P = I V cos (\(\varphi\)) = 0.1 W, where I, V, and cos (\(\varphi\)) are the effective values of the supplied input electric current and voltage and the power factor, respectively. The Pitot tube was located downstream of one chosen SJ orifice, at an approximate distance of 1.5D = 1.8 mm. Note that such Pitot tube measurements were discussed by Broučková and Trávníček (2015) with the conclusion that a reasonable result can be obtained if the probe is located sufficiently far from the reversing flow region. The frequency characteristic is presented in Fig. 3 as the relationship between the velocity and driving frequency. The maximum SJ velocity (U ~ 4.5 m/s) was obtained at approximately fmax = 1120 Hz (see Fig. 3). This indicates the first resonance of the actuator. Hence, the frequency f = 1120 Hz was chosen as the operating frequency in this study. Considering that the measured velocity U approximately corresponds to the SJ characteristic velocity U0 (see Broučková and Trávníček, 2015), the Reynolds number and the dimensionless stroke length can be estimated as ReSJ = U D/\(\nu\) = 350 and L0/D = 3.4.

Fig. 3
figure 3

Frequency characteristics of the SJ actuator

Full size image

To analyze the resonance behavior theoretically, we can use a simple mechanical model based on a transformation between the potential energy of the diaphragm and the jet kinetic energy during each period (see Broučková and Trávníček 2015). This model is sufficient to find the first resonance, which is of interest in the present study.

Table 2 Parameters of SJs for f = 1120 Hz
Full size table

Considering fluid incompressibility, the potential energy of the diaphragms is transformed into the kinetic energy of the jets during each period. The potential energy of the rigid, piston-like diaphragm can be written in terms of the energy of linear springs with the spring constant of the diaphragm, KP = p/\(\Delta\)y, where p is the (quasisteady) overpressure that causes a quasisteady displacement \(\Delta\)y of the diaphragm. The KP was evaluated by an auxiliary experiment (measurement of the diaphragm displacement of 0.1–0.3 mm produced by a gradual loading by means of tine weights of 10.4–31.9 g) as KP = 4.9 × 106 N/m3.

The kinetic energy of the SJs is assumed to be captured in fluid columns of effective length Le, where Le = L + 8D/(3\(\pi\)) and L is the length of the orifices – see Kinsler et al. (2000). Following the approach described by Trávníček et al. (2005), the first natural frequency of the present actuator can be derived as

$$f_{Theory} = \frac{1}{2c\pi }\frac{D}{{D_{D} }}\sqrt {\frac{{j{\kern 1pt} \,K_{p} }}{{2\rho \,L_{e} }}}$$
(5)

where \(\rho\) is the fluid (air) density, j is the number of SJs (j = 8, see Fig. 2(b)), and c is the shape constant of the diaphragm deflection volume (from c = 0.5 for a paraboloid of an ideally flexible case to c = 1 for a cylinder of an ideally rigid piston). For the present loudspeaker and geometry (Fig. 2) and considering a moderately rigid diaphragm (c = 0.8), Eq. (5) yields fTheory = 1086 Hz. This value is indicated by the arrow in Fig. 3, showing reasonably good agreement with the experimental maximum of the velocity resonance curve.

4.2 Annular free jet without and with flow control

As the first step, the swirl numbers were evaluated by means of smoke-wire flow visualization at the SJ orifice, which revealed the yaw angle \(\alpha\) of the outlet velocity vector. The experiments were made at Re ≈ 5000, i.e., for the orifice velocity of the main annular jet Uav = 2.7 m/s, while the SJ real input power was gradually adjusted from P = 0 to 100 mW; see Table 2. The swirl number was evaluated as S ~ tan(\(\alpha\)); see Eq. (4). The resulting dependence of the swirl number on the input real power is presented in Fig. 4. Understandably, the swirl number increases from S = 0 to 0.23 as the SJ real input power increases from P = 0 to 100 mW. To make the results more general and facilities independent, the SJ velocity was measured for P = 20–100 mW similarly as was described in the previous text (i.e., the Pitot probe was located at the distance of 1.5D = 1.8 mmd ownstream the SJ orifice), and the resultant velocity values were transformed into the Reynolds number estimation as ReSJ = U D/\(\nu\) The ReSJ values were 140–350, and these values are presented in Fig. 4 as the secondary axis on the right hand side of the graph.

Fig. 4
figure 4

Dependence of the swirl number S on the input real power P. The Reynolds number ReSJ is based on the Pitot probe velocity measurements

Full size image

A qualitative flow visualization of the jets without an impingement wall was performed at Re ≈ 5000. Figure 5(a–c) show three typical flow visualization results: (a) without SJs, (b) with weak SJs, P = 40 mW, i.e., S = 0.18, and (c) with moderate SJs, P = 100 mW, i.e., S = 0.23. The results were interpreted using common terminology for annular jets and their zones (Chan and Ko 1978), see Fig. 6.

Fig. 5
figure 5

Flow visualization (water fog technique) of free annular jet (without the wall) for Re ≈ 5000: a without control SJs, b with weak control SJs, P = 40 mW, ReSJ = 233, S = 0.18, and c with moderate control SJs, P = 100 mW, ReSJ = 353, S = 0.23

Full size image
Fig. 6
figure 6

Schematic view of the annular jet and its zones (drawing not to scale, adapted from Chan and Ko 1978): 1: outer nozzle body, 2: nozzle centerbody, 3: stagnation point, 4: point of reattachment, and 5: entrainment

Full size image

In the case without control, Fig. 5(a), the recirculation region typical for annular jets can be expected. The flow field pattern is reasonably symmetrical. When the control is applied, the flowfield is changed. The qualitative visualization results were quantified by means of the velocity measurement. Figure 7 shows the centerline velocity distribution of the main jet without and with SJ control, as measured by the Pitot probe. The real input power of the SJs ranged from P = 0 to 100 mW, i.e., S = 0 to 0.23. The jet without SJ control has a velocity distribution typical for annular jets (Chan and Ko 1978) (see Fig. 6), and three regions (I, II, and III) were identified in Fig. 7:

  1. I.

    Initial merging zone: This region (x/Do ≈ 0–0.2) with zero velocity in Fig. 7 indicates the recirculation region. In fact, the backward velocity direction occurs there (see Fig. 6); however, the Pitot probe experiments cannot evaluate the negative velocities. This region ends at the stagnation point at a distance of xS/Do ≈ 0.2.

  2. II.

    Intermediate zone: This region shows the velocity increasing from zero at the stagnation point (xS) to the local maximum U/Uav = 0.87 at x/Do = 0.47, where the intermediate zone finishes by the reattachment point; see xr in Fig. 6 and xr/Do = 0.47 in Fig. 7.

  3. III.

    Fully merged zone: The region is developed more downstream (x > xr, i.e., x/Do > 0.47). The velocity gradually decreases with increasing x/Do, indicating the fully merged zone (see Fig. 6).

Fig. 7
figure 7

Centerline velocity distribution of the main annular jet at Re = 5000 showing the control effect of SJs, measured by the Pitot tube; three typical zones of annular jets without SJ control are marked: I. initial merging zone, II. intermediate zone, and III. fully merged zone

Full size image

When flow control is applied, all three regions can still be identified. However, a stepwise increase in the power P from 0 to 100 mW (i.e., S = 0 to 0.23) causes a decrease in the maximum velocity ratio (U/Uav) from 0.87 to 0.50. Moreover, increasing the input power causes the positions of the stagnation and reattachment points (xS and xr) to move slightly downstream as is marked by the arrow in Fig. 7. This effect is shown in Fig. 8(a) where the curves are fitted by the third- and fourth-order polynomials, respectively.

Fig. 8
figure 8

Variation of the stagnation and reattachment points caused by the control effect of SJs: a dependence on the input real power of the actuator P and, b dependence on the swirl number S

Full size image

The stagnation point xs (i.e., the end of the initial merging zone) moves slightly downstream with increasing power input, with the exception of the lowest actuation. However, the xs change is rather small, with the position ranging from xs/Do = 0.17 (at P = S = 0) to xs/Do = 0.3 (at P = 100 mW, S = 0.23). The position of the reattachment point xr also moves further downstream with increasing input power P, from xr/Do = 0.47 at P = S = 0 to xr/Do = 0.67 at P = 100 mW, S = 0.23.

Note that the input real power P used in Fig. 8(a) is convenient for a repeatability of experiments. However, the dominant parameters are the swirl number S; therefore, Fig. 8(b) shows the obtained data as a dependence on the swirl number.

4.3 Annular impinging jet without and with flow control

For the case without flow control, two expected flowfield patterns are schematically presented in Fig. 9(a) and (b); see Trávníček and Tesař (2013). Figure 9(c) and (d) shows the smoke-wire visualization results for H = 0.73Do. To reveal flowfield patterns more precisely, the experiments were repeated by means of PIV technique, and the obtained time-mean streamlines are presented in Fig. 9(e) and (f). A hysteretic behavior was identified because two flow patterns A and B were found under the same boundary condition:

Fig. 9
figure 9

Bistable annular impinging jet at Re ≈ 5000: 1: outer nozzle body, 2: nozzle centerbody, 3: impingement wall, 4: central stagnation point on the wall, 5: stagnation circle, 6: reverse stagnation point, and 7: stagnation point, H: nozzle-to-wall spacing: a and b schematic representations of the flow field patterns A and B, c and d smoke-wire flow visualization for H/Do = 0.73, e and f PIV time-mean streamlines for H/Do = 0.73, and g and h wall-pressure distributions relating to patterns A and B for H/Do = 0.80

Full size image

A pattern: A small recirculation area (bubble) of separated flow is located just downstream from the nozzle centerbody. This pattern was obtained when H was gradually reduced (i.e., the nozzle was gradually moved to the impingement wall). On the impingement wall, there is only the central stagnation point on the nozzle axis and no other stagnation formations. Another stagnation point exists in the space between the nozzle centerbody and the wall, see position 7 in Fig. 9.

B pattern: A large recirculation area of separated flow reaches up to the impingement wall, on which there is a stagnation circle. The entire space between the nozzle centerbody and the stagnation circle is filled with the recirculating fluid. This distribution was obtained when H was gradually increased.

This finding is consistent with the previous results by Trávníček and Tesař (2013).

To quantify these visualization results, the wall-pressure distribution was measured. The resulting wall-pressure profiles (pressure pw relative to the barometric pressure) normalized by the dynamic pressure, q = ρUav2/2, are shown in Fig. 9(g) and (h). Two types of wall-pressure distributions were obtained for H = 0.80Do:

A: For the A pattern, the pressure distribution is bell-shaped with the maximum at the central stagnation point. It resembled the bell-shaped pressure distributions known from common (round or slot) impinging jets.

B: For the B pattern, the pressure distribution is saddle-shaped with two off-axis maxima and a smaller local maximum at the jet axis.

These findings agree closely with the bistability results obtained by Trávníček et al. (2014): two different stable flow field patterns can exist for identical parameters, and the resulting field pattern is dependent on the history of nozzle-to-wall movement.

To quantify the occurrence of hysteresis, the stagnation pressure was measured at the central point on the wall (r = 0) at varying nozzle-to-wall distances for the main annular jet without and with flow control. The results are shown in Fig. 10. In the case without control, sudden changes in the pw0/q curve can be identified, namely:

  • The quick drop in the wall pressure for decreasing H; pw0 dropped from approximately pw0/q = 0.67 to 0.19.

  • The sudden rise of pw0 with increasing H; pw0 rose from pw0/q = 0.28 to 0.63.

Fig. 10
figure 10

Measured pressure in the central point on the wall (r = 0) as a function of the relative nozzle-to-wall distances H/Do; the large hysteretic loop is depicted by gray color

Full size image

The hysteretic loop was identified as depicted by the arrows and gray area in Fig. 10. The hysteretic behavior occurs in the range of H = 22–26 mm, i.e., at H/Do = 0.73–0.87. The two flow patterns A and B can be identified, which are consistent with the previous results by Trávníček and Tesař (2013).

In the case with flow control (P = 40 and 100 mW, i.e., S = 0.18 and 0.23, respectively), Fig. 10 shows that the hysteretic behavior is effectively reduced and no large hysteretic loop occurs.

Figure 11(a) and (b) shows smoke-wire visualizations of the main impinging jet under flow control at P = 40 mW and 100 mW, (i.e., S = 0.18 and 0.23, respectively) for H = 0.73Do. To reveal flowfield patterns more precisely, the experiments were repeated by PIV, and the resultant time-mean streamlines are shown in Fig. 11(c) and (d). While the flowfields without flow control were relatively smooth and symmetric (Fig. 9(e) and (f)), the control SJs changed them into non-symmetrical and unsteady fields shown in Fig. 11(c) and (d). Nevertheless, a typical feature of A pattern can be still identified. Namely, the stagnation points in the space between the nozzle centerbody and the wall can be found as shown as positions 7 in Fig. 11(c) and (d). On the other hand, a large recirculation area of separated flow covering entire nozzle-to-wall space, which is typical for B pattern (see Fig. 9(b) and (f)), was never observed in flow control cases as shown in Fig. 11.

Fig. 11
figure 11

Impinging annular jet for Re ≈ 5000, H/Do ~ 0.73: a smoke-wire visualization for weak control SJs, P = 40 mW, ReSJ = 233, S = 0.18, b smoke-wire visualization for moderate control SJs, P = 100 mW, ReSJ = 353, S = 0.23, and c and d PIV time-mean streamlines for the same parameters as a and b, respectively (position 7 indicates the stagnation point, cf. Figure 9(a) and (e))

Full size image

Consistently, large sudden changes in the pw0/q curves indicate switching of flow patterns as shown in Fig. 10 for the case without flow control. However, such large sudden changes were not identified in the cases of flow control, see Fig. 10.

It can be concluded that the control effectively suppresses the bistability and hysteretic effects, and only one flowfield pattern (A) exists there. The main reason is an introduction of the angular momentum into the jet flow, which is quantified by the swirl number, see Eqs. (3) and (4). Note that another reason could be linked with a relationship of the actuation frequency and the natural frequency of jet flows; however, such effect could not be studied in this paper because of relatively narrow frequency characteristics of the present actuator, see Fig. 3.

The Reynolds number effect on the hysteretic behavior for the case without flow control is presented in Fig. 12. The wall-pressure measurement was performed for the given nozzle-to-wall distance H/Do = 0.8. The hysteretic loop was observed from Re ≈ 4000 up to Re ≈ 8000. On the other hand, there is no hysteretic behavior for Re ≥ 9000. This dependence on the Reynolds number can be interpreted as the effect of the fluid viscosity. That is, the viscous forces at lower Re are sufficient to preserve flow field patterns even in the case of gradual changes in the nozzle-to-wall distance H, and thus, the hysteretic loop can occur. On the other hand, the inertial forces overcome viscous forces at higher Re, so the hysteretic loop cannot occur, and gradual changes in H cause a switch between patterns A and B.

Fig. 12
figure 12

Effect of the Reynolds number on the stagnation point wall pressure at H = 0.8Do

Full size image

5 Conclusions

Experimental research on annular free jets and annular impinging jets was conducted both with and without active flow control (radial SJs generating a tangential/swirl component). Most of the measurements were taken for a Reynolds number of 5000, with others taken over a wider range, from Re = 4000 to 10,000.

In the case of a free annular jet, the typical behavior was observed: immediately behind the nozzle exit, the initial merging zone is formed, and further downstream, the jet streams are fully merged at the point of reattachment. The swirling can affect the flowfield: with increasing input power of the control SJs, the point of reattachment moves further downstream, and the axial velocity decreases. For the impinging jet without control, bistability and hysteretic behavior were identified. Two alternative flowfield patterns (either A or B) can exist under the same boundary conditions:

  • An A pattern, a small recirculation area (bubble) of separated flow located just downstream from the nozzle centerbody.

  • A B pattern, a large recirculation area of separated flow reaching up to the impingement wall with a stagnation circle.

The effect of the Reynolds number was evaluated for the case without flow control: bistability was identified for the jets with Re ≤ 8000, for which the viscous forces are sufficient to preserve flowfield patterns even in the case of gradual changes in the nozzle-to-wall distance H; thus, the hysteresis loop can occur. For Re ≥ 9000, the inertial forces overcome viscous forces, so hysteresis and bistability cannot occur.