Investigation of dynamic mixedness characteristics of a transverse acoustically excited turbulent jet by high-repetition-rate acetone tracer Planar laser-induced fluorescence technique

doi:10.21203/rs.3.rs-2199112/v1

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Investigation of dynamic mixedness characteristics of a transverse acoustically excited turbulent jet by high-repetition-rate acetone tracer Planar laser-induced fluorescence technique

https://doi.org/10.21203/rs.3.rs-2199112/v1

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published 01 May, 2023

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The dynamic mixedness characteristics of a bluff-body stabilized turbulent jet under transverse acoustic excitations are investigated using high-repetition-rate acetone planar laser-induced fluorescence (PLIF) at 7 kHz and multipoint scanning hot-wire measurements. Acetone mixedness imaging is made for the turbulent jet to assess the interaction between the turbulent jet and the imposed transverse acoustic excitations at a driving frequency of 50 Hz. The high-repetition-rate acetone PLIF images show that the acetone mixedness distribution swings left and right frequently under the transverse acoustic excitation, and the deflection angle can reach about 6°. The mixedness area of a turbulent jet flow can also be increased by 13.3% when excited by a transverse acoustic wave. Meanwhile, the sequence of acetone instantaneous PLIF images illustrates how the wrinkled edges are generated when acoustic excitations are imposed. The curvature of the acetone PLIF interface shows that the portion of large curvatures increases to 1.6 times after applying an acoustic wave of 123 dB. Multipoint hot-wire measurements further stress that the turbulence intensity at the transverse acoustic excitation of 123 dB increases to be about 1.3 times the natural turbulence. The proper orthogonal decomposition results show that the large and small scales of the jet wrinkles both increase with the sound pressure level. RANS transient simulation also implies that a stronger turbulent kinetic energy distribution and distorted velocity streamlines can be achieved inside the turbulent jet due to the transverse acoustic excitation. They can further lead to increased mixing between the turbulent jet and the surrounding air.

high-repetition-rate acetone PLIF

bluff-body stabilized turbulent jet

transverse acoustic wave

mixedness imaging

Combustion instabilities have been identified as a key focus of detrimental instabilities in many applications, such as rockets (Zhao et al 2015; Zhao et al 2022), gas turbines (O'Connor et al 2012; Zhao et al 2016), and scramjets (Feng et al 2021; Feng et al 2022; Tian et al 2021; Tian et al 2023). Of particular interest are the effects of thermo-acoustic interactions on transient combustion phenomena (Ducruix et al 2003; Meier et al 2010; Tian et al 2022). Transverse acoustic excitation can bring a dramatic force perpendicular to the turbulent flow, and it has been classified as one of the detrimental instabilities in liquid rockets and gas turbines (Chen et al 2018; O'Connor et al 2015). For example, Roa et al. proposed that transverse acoustic–chemical interactions can cause sound amplification, changes in sound speed and frequency, and sound-induced changes in equivalence ratio and reaction rate (Roa et al 2021).

Experimental and computational research on laminar (Paweł et al 2018; Sim et al 2020) and turbulent flames (Baillot et al 2021; Smith et al 2018) excited by transverse acoustic waves via schlieren and chemiluminescence imaging has been reported. Transverse acoustics with elevated frequency can be used to stabilize the combustion and reduce the production of pollutants (Deng et al 2014; Miglani et al 2014). Under certain conditions of lower frequency and higher sound pressure level (SPL), the potential effects of acoustics could result in the suppression and even extinguishment of flames (Bennewitza et al 2018; Kim et al 1994). Niegodajew et al. studied the effects of transverse acoustic waves (30–50 Hz) on flame extinguishing behavior through schlieren imaging (Niegodajew et al 2018). They found that the flames are more likely to be extinguished by low-frequency acoustic waves. Aspects of those studies focused on characterizing and understanding the average global behavior and flame locations (Li et al 2013; Wang et al 2022). Few considered the instability process between acoustic pressure force and inhomogeneous fuel distribution triggered by transverse acoustic waves.

Fuel/air mixing is particularly important from the perspective of thermodynamic and emission performance (Karthick et al 2017; Papageorge et al 2017). Meanwhile, mixedness is a leading quantity that reflects the mixing state of a system prior to ignition and will determine the causes of failed and successful ignition (Connor et al 2018; Sharaborin et al 2021). Nordeen et al. found via CFD analyses that the turbulent mixing of fuel and air is a highly important process affecting combustion efficiency and the amount of unburned fuel (Nordeen et al 2016).

Acetone tracer LIF is a method that does not affect the fluid properties but is susceptible to laser excitation and fluorescence, providing an accessible method for monitoring the location of the seeded molecular species (Srikrishna et al 2014). This technique has been used for estimating the degree of mixedness in various industrial configurations. There has also been a growing body of research on acetone tracer LIF measurements performed at low repetition rates with the combination of a high-energy laser system and ultralow-noise and high-quantum-efficiency scientific CCD cameras (Li et al 2010; Sjöholm et al 2013). More recently, the emergence of high-speed lasers (i.e., diode-pumped solid state and “burst” lasers) and high-frame-rate cameras recently has facilitated the possibilities of kHz-rate tracer LIF measurements (McManus et al 2015; Miller et al 2014). Given that the output energy from commercial high-speed lasers is somewhat low, high-speed (two-stage) image intensifiers become necessary in many situations to boost the signal for low-light applications. However, these applications focused on unsteady jet flows and engine environments (Cundy et al 2011; Schulz et al 2005); fewer studies about the dynamic evolution of mixedness distribution during transverse acoustic excitation were reported.

In this work, acetone LIF at a repetition rate of 7 kHz was utilized to investigate the dynamic mixedness characteristics of a turbulent jet under transverse acoustic excitation. The temporal evolution of acetone distribution can provide an alternative insight into the dynamic mixedness characteristics during early excitation. Furthermore, multipoint scanning hot-wire measurements and two-dimensional RANS transient simulation are critical to analyzing the contributions of acoustic excitation to dynamic mixedness.

A. Turbulent jet apparatus

The flow examined in this study was a turbulent flow exiting in a laboratory-scale bluff-body stabilized jet (Sun et al 2020; Sun et al 2021; Yan et al 2022), as shown in the red dotted rectangles in Fig. 1. The jet was provided by an inlet pipe with a length of 250 mm and an inner diameter of 20 mm, and the pipe outlet was profiled to a knife-shaped edge. A stainless-steel conical bluff body with a diameter of 14 mm and a half-angle of 45° was mounted on a rod with a diameter of 5 mm. The jet velocities varied from 4.71 m/s to 13.20 m/s, providing Reynolds (Re) numbers of 2000–5600. The Re number was calculated using the formula$\operatorname{Re} ={\rho _0}UD/{\mu _0}$(Li et al 2010; Yan et al 2022), where${\rho _0}$, U, and${\mu _0}$ represent the density, velocity, and viscosity coefficient of the mixture, respectively. The hydraulic diameter D₀ = 2(r₁ − r₀) was used as the characteristic length D when computing Re. r₁ = 20 mm and r₀ = 14 mm represent the outlet and bluff-body plane radius, respectively. The experimental parameters are listed in Table 1.

Table 1

Summary of experimental conditions. Reynolds number, Re, is calculated without transverse acoustic excitations. Turbulence intensity is measured by the hot-wire.
Case	U (m/s)	Re	Turbulence intensity (Yan et al 2022)	SPL (dB)
1	13.20	5600	26%	0
2	13.20	5600	27%	118
3	13.20	5600	33%	121
4	13.20	5600	34%	123
5	9.42	4000	16%	0
6	9.42	4000	25%	121
7	4.71	2000	1%	0
8	4.71	2000	3%	121

Experiments were performed in a turbulent jet of air seeded with 7.63% acetone by volume. A Sevenstar flow controller with an error below 0.2% was adopted to control the flow rate of the carrier air stream. Meanwhile, the acetone was controlled by a micro-suction gear pump with a volumetric flow range of 1–65 mL/min and a manufacturer’s stated accuracy of ± 1% over the full range of flow rates. The preliminary mixture, including the acetone vapor and carrier air, was blended and heated in a 5 m-long, 10 mm-diameter tube. To ensure complete evaporation, the preliminary mixture was further heated in a premixing chamber. A type-K thermocouple was set downstream of the premixing chamber to monitor the mixture temperature. The temperature of the acetone/carrier air mixture was set to 313 K and held within ± 0.5 K after a 10-min working period. The jet-to-ambient density ratio was about 0.96, considering that the ambient temperature was 300 K. Therefore, the mixing rate between the jet and the ambient phenomenon can be considered stable in our work. Moreover, the mass spectrum method was applied to measure the volume fraction of the acetone. The bias between the set values and the mass spectrum results was below 5%.

B. Acoustic generation system

As shown in Fig. 1, the speaker (BMS, 15C362) on the right side 15 cm away from the jet center was controlled for forcing transversely. The amplitude and frequency of the acoustic wave were controlled by an amplifier (Yamaha, P7000S) and a signal generator (Rigol, DG1022U), respectively. The influence of acoustic wave frequency (30–50 Hz) on turbulent flow has been studied by Niegodajew et al. (Niegodajew et al 2018). Therefore, an acoustic frequency of 50 Hz was only used throughout this paper. An acoustic sensor (BSWA, MP201) and a data acquisition instrument were used to measure the SPL at a height of 20 mm above the jet apparatus center with an error below 2%. The SPL related to the intensity of the acoustic wave was defined as SPL = 20log₁₀(p_RMS/p₀) (Sun et al 2020; Yan et al 2022), where p_RMS is the root-mean-square pressure of the acoustic wave, and p₀ = 2×10^− 5 Pa. The SPL parameters are written in Table 1.

C. Measurement system

The measurement system consisted of (1) a high-repetition-rate acetone planar laser-induced fluorescence (PLIF) system and (2) a multipoint scanning hot-wire measurement system.

A schematic of the PLIF experimental setup is shown in Fig. 1. A high-frequency laser system (EO-266-N-100µJ) was operated at 7 kHz, producing approximately 100 µJ/pulse. The laser pulse width was about 5 ns/pulse. A beam splitter was used to separate 1% of the laser to monitor the laser energy fluctuation by using a photomultiplier. A laser sheet system (f_L1 = − 50 mm, f_L2 = + 400 mm, and f_L3=1000 mm) was used to form a light sheet with a height of approximately 32 mm and a thickness of approximately 500 µm. The sheet was passed vertically through the center of the seeded air jet with a height of 3 mm far away from the bluff body. A high-frame-rate camera system including a high-speed camera (CAM HX-7s) and a two-stage image intensifier (EyeiTS-D-Hi-QE Blue-F) was used to capture acetone PLIF images with a resolution of 728×768 pixels. The intensifier was gated at 50 ns at 7 kHz. A band-pass filter (Edmund 413/20) was installed in front of the acetone camera to reject the interference light. Imaging was performed with an effective spatial resolution of approximately 19×19×500 µm per pixel. A total of 9000 images were recorded for each turbulent jet condition. The camera and intensifier exposure time was 10 µs and 50 ns, respectively. A DG535 controller was used to ensure that the laser pulse was inside the interval of camera exposure. Moreover, the timing sequence between the laser pulse and the acoustic wave phase was monitored and recorded using a photoelectric probe and an oscilloscope. A list of quantifiable sources of error and their associated uncertainty for this high-repetition-rate acetone tracer PLIF system are shown in Table 2.

Table 2

List of quantifiable sources of errors and their associated uncertainty for the high-repetition-rate acetone PLIF system.
Source of Error	Uncertainty (%)
Laser intensity fluctuations	2.0%
Acetone mixture fraction bias	5.0%
Beam absorption across the test section	4.6% (Fig. 15)
Camera noise	2.3%
Scattering interference	0.5%
Total uncertainty	7.5%

To investigate the response of turbulent fluctuations under different transverse acoustic intensities, the turbulence intensity in the upward direction was measured using the multipoint scanning hot-wire method. The scanning region was 16 mm above the bluff body to prevent collision between the hot wire and the bluff-body plane, and the scanning integral was about 5 mm. The diameter, accuracy, and sampling rate of the hot wire were 10 μm, 0.1%, and 40 kHz, respectively. The jet outlet cold air rate was set to the sum of air and acetone vapor to simulate the same turbulent jet condition. The turbulence intensity was measured at position B2 located on the centerline of the burner and about 16 mm superior to the bluff body. The results are shown in Table 1.

D. Image processing

Several image processing methods were considered for high-repetition-rate acetone tracer PLIF.

As a statistical property of diffusion fluctuation, the temporal fluctuation in mixedness was employed in this work. It depends on the mixedness ξ= c(x,y)/c₀, where c(x,y) and c₀ are the acetone molar volume fractions (mol/L) for initial and post-diffusion situations (Handa et al 2011; Kang et al 2009), respectively. The acetone PLIF signal S(x,y) nominally scales with the molar volume fraction in a situation with a low acetone molar volume fraction. Therefore, the mixedness ξ relates the acetone PLIF signal distribution S(x,y) to that without diffusion: ξ= S(x,y)/S₀.

The root mean square (RMS) value of the acetone mixedness fluctuation employed here is defined as (Handa et al 2011)

$$\sigma =\frac{{\sqrt {\sum\limits_{{i=1,2 \cdot \cdot \cdot N}} {{{(\xi (x,y) - <\xi (x,y)>)}^2}} } }}{{N - 1}}$$

where N is the number of successive measurements, and < > is the average at a specific pixel (spatial location).

Then, the acetone LIF edge was extracted on the basis of the Canny method (Sekehravani et al 2020), as shown in Fig. 2. The integrated area of mixedness based on the extracted LIF edge was accounted for the degree of diffusion under transverse acoustic excitation. A total of 280 LIF images within 2 acoustic cycles were considered.

Turbulent jet distribution is known to strongly depend on the degree of wrinkling, and jet wrinkling is closely related to curvature distribution (Wan et al 2021; Wang et al 2013). To quantify the turbulent wrinkling made from a large number of instantaneous acetone PLIF images, probability density functions (PDFs) of curvature (κ) were constructed. Then, the curvature was obtained by computing the first and second derivatives of the PLIF normal vectors in the x and y directions along the edge with respect to s in accordance with $\kappa =\dot {x}\ddot {y} - \dot {y}\ddot {x}/{({\dot {x}^2}+{\dot {y}^2})^{3/2}}$, where $\dot {x}=dx/ds$, and $\ddot {x}={d^2}x/d{s^2}$ (Wan et al 2021). The curvature was positive where the radius of curvature of the acetone LIF was concave to the jet mainstream and was negative where the radius of curvature was convex to the surrounding air. The curvature was achieved by edge extraction of the PLIF images, and PDF was counted from all PLIF edge curvatures, as shown in Fig. 2(d). Moreover, 500 time-resolved acetone PLIF images were constructed to achieve the average PDF for a single experimental case.

In a further step, an analysis of the topology relying on proper orthogonal decomposition (POD) scale analysis was used to describe the multiscale nature of a turbulent jet under different acoustic conditions, as well as the dominant behavior or dynamics of a given situation (Nie et al 2019; Shimura et al 2016). Complete time series involving 500 time-resolved images were used for these calculations. The POD used for this study is explained in detail by Shimura (Shimura et al 2016).

E. Numerical simulation

Two-dimensional RANS transient simulations were conducted to identify the influence of transverse acoustic waves on turbulent flow. The Fluent software was applied in this work, and the sketch for the computational domain is shown in Fig. 3. The size of the turbulent jet is consistent with that illustrated in Fig. 1. Inflow and outflow conditions were imposed on the entrance and exit 200 mm above the jet surface. A filling gas containing air and ethylene was chosen, and ethylene was used as the tracer substitute of the acetone. The sound inlet was assigned on the left of the jet, and the direction was from left to right. The number of cells was set to about 160000 in this study.

The acoustic velocity at the sound inlet was set to

$${u_x}(t)={u^{\prime}_s}\sin (2\pi {f_s}t)$$

where u_x(t) and ${u^{\prime}_s}$ represent the instantaneous acoustic velocity and the RMS velocity of the acoustic wave, respectively. ${u^{\prime}_s}$was measured to be about 4.5 m/s for Case 4 by using the hot-wire method. f_s was set to 50 Hz, the same as that in the experimental setup. A similar unsteady acoustic condition has also been reported by our previous work (Sun et al 2021) and other researchers (Chen et al 2016; Li et al 2017). This method is proven suitable for calculating and analyzing the interaction between acoustic waves and turbulent flow (Shalaby et al 2014).

The effect of a transverse acoustic wave on a turbulent jet is studied by high-repetition-rate acetone PLIF and multipoint scanning hot-wire measurement. Figure 4 shows the typical instantaneous/mean acetone mixedness ξ and the related RMS value σ, together with the turbulence results measured by hot wire in different experimental situations. Average images with 2 and 10 recycles for Case 1 are compared, as shown in Fig. 15. The distribution is almost the same. Therefore, 280 images, including 2 recycles, are used to conduct the average processing. Instantaneous PLIF images are captured at a phase of 60° of the acoustic waves. The turbulent jet velocity is 13.20 m/s, providing a Reynolds number of 5600, while the acoustic SPL value increases from 0 dB (Case 1) to 123 dB (Case 4). Without transverse acoustic waves, instantaneous acetone mixedness with a wrinkled and distorted profile due to natural turbulence can be realized directly. The instantaneous mixedness becomes wider and more wrinkled along with the jet propagation direction. ξ = 0.8 iso-surface, as highlighted by blue lines, represents a larger acetone mixedness value. The variation in areas inside the iso-surface can further describe the jet diffusion character. The maximum width of the region inside the iso-surface is calculated at roughly 15 mm. The RMS distribution in the edge region is much larger than that in the center region. The multipoint turbulence intensity distribution is consistent with the RMS value. For instance, the turbulence intensity and the RMS value in the lower location B2 are 14% and 24.35%, respectively. They are less than those in the higher location C2. Meanwhile, the turbulence intensity and the RMS value in the jet edge B3 are about twice as much as those at the jet center B2, as shown in Fig. 4. The locations B1, B2, B3, and C2 are marked in Fig. 4.

When the loudspeaker is activated, the turbulent jet is exposed under acoustic excitation at a constant frequency of 50 Hz and different SPL values. At conditions from 118 dB to 123 dB, the instantaneous acetone mixedness is more wrinkled and broken than that without acoustic excitation. Instantaneous/mean areas inside the iso-surface lines decrease with increasing SPL values, and the majority of acetone mixedness also gets diminished, implying that the mixing between the acetone and the surrounding air is enhanced by the transverse acoustic excitation. The jet streaming is increasingly deflected to the opposite side of the loudspeaker, and this trend becomes more obvious with increasing acoustic pressure from 0 dB to 123 dB. The deflection angle of the turbulent jet calculated from the left line of the iso-surface is calculated to be about 6° in comparison with that in Cases 1–4. The RMS value and the turbulence intensity become wider and larger, respectively. The RMS value at the center location C2 increases from 17–22% after applying the transverse acoustic wave, while the growth rate at the edge location B3 can reach about 1.6 times. Detailed turbulent intensity description is shown in Fig. 9(b). The results indicate that the acetone diffusion and turbulent fluctuation effects inside the turbulent jet region strengthen (O'Connor et al 2012; O'Connor et al 2015; Yan et al 2022).

The flow variation is revealed by the high-repetition-rate images, and different mechanisms are identified. Figure 5 shows an example set of nine sequential high-resolution acetone mixedness distributions under transverse acoustic excitation. The time-varying nature of turbulent diffusion and a steep concentration variation is displayed and introduced in a step of 1 ms. The jet downstream is prone to deflect to the opposite side of the loudspeaker gradually. The iso-surface region begins to decrease and break into pieces, and the evolution of small-scale structures (marked by red circles) stretched by the turbulent energy cascade is observed (O'Connor et al 2012; O'Connor et al 2015). It can be concluded that the introduction of the transverse acoustic wave can induce a turbulent fluctuation in acetone mixedness (O'Connor et al 2015).

To illustrate the fine variation in the flow structure further, a sequence of six mixedness frames under acoustic excitation taken between 4 and 5 ms are presented in Fig. 6. The mixedness distribution of large-scale structures changes slightly per frame, and a fine structure variation is obtained at the edge of the mixedness distribution. As shown in the region at the moment of t₀ + 4.143 ms, two smaller wrinkles adhere to the flow mainstream. Owing to the influence of the transverse acoustic wave, the tiny wrinkles expand and move forward slightly. The areas of these two wrinkles evolve gradually, meet, and merge into a larger one. It implies that the diffusion effect is strengthened by the turbulent fluctuation triggered by the transverse acoustic wave (O'Connor et al 2015).

The instantaneous acetone mixedness images under different phase angles in an acoustic cycle are shown in Fig. 7. The mixedness distribution varies greatly based on the phase angles. In the cases of 0°, 60°, and 120°, the jet downstream is prone to deflect to the right. According to the angles of 180° and 240°, a larger area of mixedness distribution with highly wrinkled and bent edges is formed and deflected to the opposite direction. Meanwhile, the deflection angle at 300° is lower, and its morphology is approximately vertical. The mixing between the turbulent jet and the surrounding air is intensified by this deflection character under transverse acoustic excitation.

To visualize the interaction between the acoustic wave and the turbulent stream at different flow velocities, single-shot PLIF images are required, as shown in Fig. 8. Without acoustic excitation, the mixedness distribution has similar shapes for varied flow velocities. However, the heights and areas of jet mainstream increase with the flow velocity, as shown in the first row of Fig. 8. Jet fragment and asymmetric characters increase after the transverse acoustic wave is increased to 121 dB. More jet downstream becomes wrinkled and deflects to the right, as shown in the second row of Fig. 8. The reason is the increase in turbulence intensity under transverse acoustic excitation. The jet turbulence intensity rises with the whole RMS velocity, including the RMS velocities of the flow and acoustic wave. When the flow outlet velocity decreases, the flow RMS velocity decreases, and the acoustic RMS velocity dominates the entire RMS velocity (Yan et al 2022). Therefore, larger changes can be observed in the lower velocity flow.

The dependence of the areas of acetone distribution and the turbulence intensity inside the jet mainstream at different SPL values are displayed in Figs. 9(a) and 9(b), respectively. The images are binarized using a threshold just above the noise level. A total of 240 LIF images within 2 acoustic cycles are considered, and the integrated area containing signals above the threshold is shown in Fig. 9(a). The area, S, improves with increasing flow velocities. After acoustic excitation is applied, the mean area (marked by solid lines) and the related fluctuation increase, and a sine distribution is obtained in the area fluctuation. According to the turbulent flow with an outlet velocity of 13.20 m/s, the mean acetone areas increase by about 0.67%, 3.93%, and 13.3% after increasing the SPL values from 118 dB to 123 dB. Meanwhile, larger area variations due to transverse acoustic perturbations can be achieved at a lower flow outlet velocity. After the transverse acoustic excitation at 118 dB, the mean acetone areas increase by about 134.3% and 0.4% for the outlet velocities of 4.71 and 13.20 m/s, respectively. At a higher SPL value of 121, the areas and fluctuations continue to increase, except at a lower velocity of 4.71 m/s. The downward trend is caused by the mainstream asymmetry character that a high proportion of jets downstream deflects and deviates from the camera imaging field, showing consistency with the experimental results in Fig. 8.

A strong response of the velocity fluctuation to the transverse acoustic wave can exist in the turbulent field. The turbulence intensity for the cold airflow with a velocity of 13.20 m/s at different regions is measured by the hot wire, as shown in Fig. 9(b). Jet turbulence can be divided into two groups: natural turbulence without acoustic excitation and turbulence excited by the transverse acoustic wave. The former increases by about 25 times after increasing the velocity from 4.71 m/s to 13.20%, as shown in Fig. 9(b) and Table 1. When the SPL increases from 0 dB to 123 dB, the turbulence intensity values at all positions increase obviously. According to the center point B2, the turbulence can reach about 34% after the transverse acoustic excitation, which is 1.3 times as large as the natural turbulence. This phenomenon is due to the turbulent fluctuations introduced by the transverse acoustic wave, which coincides with the experimental results in Figs. 4 and 9(a). Meanwhile, the turbulence intensity at the edge B1 is prone to be influenced by the acoustic wave compared with that in the other locations. The turbulence intensity increases by about 1.7 times after increasing the SPL from 0 dB to 123 dB. The reason is the filtering and attenuating effects of the flow on the acoustic wave (O'Connor et al 2015).

Figure. 10(a) shows the PDF of curvature in each of the acoustic situations, Cases 1–4. The distributions of PDF are approximately Gaussian and are symmetric at the curvature κ = 0, implying that the probability to convex or concave to the surrounding air is similar. This is because the Re number of the turbulent jet is small that turbulent fluctuation can only affect the jet edge, and the jet mainstream is almost complete (Wan et al 2021; Yan et al 2022). The PDF profile decreases slightly with increasing SPL values.

The curvature values are then divided by the ones without acoustic perturbations to obtain a nondimensional measurement of acetone LIF edge curvature (Yan et al 2022), as shown in Fig. 10(b). The normalized PDF, PDF/PDF_0dB, becomes more curved with increasing SPL values. The maximum value of the normalized PDF at the SPL of 123 dB can reach 1.6 at the curvature of ± 12 mm^− 1. This finding indicates that the jet edge becomes more distorted and the portion of large curvatures increases to be 1.6 times after applying the acoustic wave of 123 dB. Such results are similar to those shown in Figs. 4 and 5; i.e., acetone LIF wrinkles more heavily, implying a stronger turbulent fluctuation of the acoustic excitation on the turbulent jet. The curvature distribution is concluded at different flow velocities and the same SPL value, as shown in Fig. 10(c). The normalized PDF becomes curved at a lower flow velocity. Approximately 2.0 and 1.5 of the normalized PDF values are obtained at ± 12 mm^− 1 for Cases 8 and 3, respectively. It indicates that larger variations in the curvature distribution triggered by the transverse acoustic wave are observed with decreasing flow velocity (Yan et al 2022).

In a further step, an analysis of the topology relying on POD analysis is used to describe the multiscale nature of turbulent jets under different acoustic conditions. Complete time series involving 500 time-resolved images are used for these calculations. The evolution of the sum (EVsum) of mode eigenvalues is shown in Fig. 11(a). Most modes contain considerable energy. More than 20 modes must be combined to recover more than 75% of the total kinetic energy, illustrating the high spatial complexity of the analyzed flow topology. The first mode (Mode 0) plays a key role in all modes. In other words, it is impossible to get a better approximation than the Mode 0, except when many modes are considered. The EVsum distribution increases fast with improving SPL values, implying that the turbulent jet starts to change orderly when transverse acoustic excitation is triggered. The fast Fourier transform (FFT) method is then used to analyze the time coefficients of Mode 0, as shown in Fig. 11(b). A clear frequency peak at 50 Hz and its harmonics appear in all curves excited by the transverse acoustic wave. The peak frequency is equal to the acoustic one; thus, it can be identified as the most important oscillation frequency of the jet. Meanwhile, the peak amplitude in the oscillation frequency at the SPL of 123 dB is nearly 3 times that at 118 dB. Therefore, order variation in the turbulent jet structure may occur with the acoustic frequency (Sun et al 2020; Sun et al 2021; Yan et al 2022), and a larger order variation can be obtained in stronger acoustic excitation.

To realize an acceptable reconstruction showing the most important jet structures directly under acoustic excitation, the first three POD modes calculated from one series of acetone PLIF series (500 images) are shown in Fig. 12. From the first row of Fig. 12, the first mode, which has 17% of the energy, indicates a uniform distribution and represents a turbulent jet without any acoustic excitations. The absolute value of energy distribution indicates the probability of occurrence of a jet structure there, and the distribution of plus and minus ones represents that a jet structure occurs in different moments. Around the jet edges, the second and third modes show the convection of small-scale mixture islands. Numbers of these characteristic structures appear more in higher energetic modes and are expected to be consumed rapidly, which may enhance the turbulent fluctuation (Nie et al 2019). The formation of a fine-scale structure and its rapid consumption is statistically meaningful under a higher SPL value, and vortex-like and wave-like structures are found in both POD series. Although they are situated at the same location and show a similar topology, the size and the degree of these structures increase obviously. This finding implies that the turbulent fluctuation inside the jet increases with improving SPL values.

To advance the understanding of the interaction between transverse acoustic waves and turbulent flow, a RANS transient simulation is applied, as shown in Figs. 3 and 13. To validate the numerical simulation, the mean axial velocities v_y on the hot-wire measuring points at the height y = 31 mm are calculated. The simulated axial velocity on each point is achieved from the average result inside the region of 0.1 mm×0.1 mm. The statistical numerical mean axial velocity distribution presents reasonable agreement with the hot-wire results.

Without transverse acoustic waves, the axisymmetric jet takes on a cone shape and locates immediately downstream of the turbulent jet holder (Sun et al 2020; Yan et al 2022). The mixedness distribution of the tracer widens along the jet downstream, which is similar to the results shown in Fig. 4. A larger area of recirculation region occurs inside the jet downstream, and it is located adjacent to the shear layer. It is the existence of the recirculation region which is bringing a larger amount of tracer inside the jet center (Kariuki et al 2015).

Figure. 14 shows the evolution of the simulated turbulent kinetic energy distribution and velocity streamlines after applying the transverse acoustic excitation. Without acoustic excitation, there are two nearly symmetric recirculation regions and a stronger turbulent kinetic energy zone with a triangular shape inside the turbulent jet. After applying the transverse acoustic wave, the velocity streamlines inside the jet become distorted. Meanwhile, two nearly symmetric recirculation regions become asymmetric, and they become nearer to the bluff-body surface. Accordingly, the variation in velocity streamlines leads to the flow deflection after applying the acoustic excitation. The jet stream can be transferred to more areas, and the mixing between the surrounding air and turbulent jet is enhanced directly (O'Connor et al 2015). Moreover, the turbulent kinetic energy distribution strengthens, especially for that close to the recirculation region. The center triangular shape distorts seriously and turns from left to right with the development of the phase angles of the acoustic waves. The deflection directions are similar to those achieved by the acetone PLIF results shown in Fig. 7. These results confirm that the turbulent fluctuation inside the jet becomes stronger (O'Connor et al 2015). Such a process can further lead to more diffusion and larger acetone PLIF curvature, as shown in Figs. 4 and 10.

Mixedness imaging of acetone PLIF at 7 kHz and multipoint scanning hot wire are applied to a bluff-body stabilized jet to investigate the effect of transverse acoustic excitation on the turbulent jet. The acetone mixedness distribution swings back and forth frequently under the transverse acoustic excitation, and the deflection angle can reach about 6°. A fragmented distribution of acetone mixedness is determined under the acoustic excitation, and the portion of large curvatures increases by 1.6 times after applying the acoustic wave of 123 dB. Meanwhile, the generation of wrinkled edges is analyzed from the variation in acetone mixedness distribution during successive acetone PLIF imaging. It implies that the turbulent fluctuation effects in the presence of the transverse acoustic excitation are strengthened. The turbulence intensity results further show that the turbulence intensity at the transverse acoustic excitation of 123 dB can be 1.3 times as large as that without acoustic excitation. Such effects can lead to a growth of 13.3% in the area of acetone mixedness distribution.

As the flow velocity decreases, the variation in the acetone mixedness structure excited by acoustic waves increases. Approximately 134.3% of the increase in the mean acetone area can be obtained at the outlet velocity of 4.71 m/s and SPL of 118 dB. The maximum normalized PDF induced by transverse acoustic waves decreases from 2.0 to 1.5 when the flow velocity is increased from 4.71 m/s to 13.20 m/s. The POD analysis reveals that the turbulent jet starts to oscillate at the driving frequency of the acoustic wave, and the large and small scales of flow wrinkles both increase with SPL.

Two-dimensional RANS transient simulation is used to simulate the response of transverse acoustic waves on the turbulent flow. The results show that the transverse acoustic waves can produce distorted velocity streamlines and a stronger turbulent kinetic energy distribution. These two effects can further increase the mixing between turbulent flow and the surrounding air.

A. Ethical Approval

This work is supported by the National Natural Science Foundation of China (NSFC) (Nos. 11925207, 12172379, and 91741205), the National Key R&D Program of China (Grant No. 2020YFA0405700), and the Foundation of Innovation-oriented Province Construction of Hunan (No. 2019RS2028).

A. Ethical Approval

This declaration is not applicable in our work.

B. Competing interests

The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.

C. Authors' contributions

Bo Yan and Jiajian Zhu wrote the main manuscript text. Yongchao Sun provided the experimental setup and Fluids software. Mingbo Sun and Shuang Chen provided financial support. Fan Li and Qinyuan Li finished the Fluids simulation and prepared Figs. 13, 14. Ge Wu and Yifu Tian finished the acetone PLIF measurements. Minggang Wan prepared Figs. 9 and 10. All authors reviewed the manuscript.

D. Funding

E. Availability of data and materials

The data that support the findings of this study are available from the corresponding author upon reasonable request.

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No competing interests reported.

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Investigation of dynamic mixedness characteristics of a transverse acoustically excited turbulent jet by high-repetition-rate acetone tracer Planar laser-induced fluorescence technique

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