Nomenclature
- D
-
Source jet diameter
- NPR
-
Nozzle Pressure Ratio
- V
-
actuator cavity volume
- REM
-
Resonance enhanced microactuator
- h
-
distance between source jet and actuator block
1.0 Introduction
In a classical coaxial jet configuration, two fluids flow separately through an inner core and an annular space and meet at the exit plane before their injection. This method effectively mixes two distinct fluids moving at higher flow velocities. For example, in applications like a gas turbine or combustion chamber of a rocket engine, these fluids could be oxidisers, such as gaseous or liquid oxygen, and fuel in its liquid or gaseous phase. Another example where extreme flow conditions experience significant challenges for mixing is a hypersonic combustor, where the microscopic convective time scale is of the order of milliseconds. Such a tiny time scale demands robust flow control actuators that enhance microscale mixing at high speed and positively alter the macroscopic phenomena associated. Although the mixing ultimately happens at the molecular level, active flow control techniques can tailor the flow dynamics at micro and macro scales of such systems in favour of rapid diffusion at the molecular level [Reference Ritchie, Mujumdar and Seitzman1–Reference Broadwell and Mungal3]. Effective and controlled mixing leads to higher combustion efficacy, longer life, reduced combustor size, stable operations and fewer emissions/pollutants.
Active flow control schemes can favourably alter the entrainment process. The vorticity dynamics resulting from the shear layer instability modification play a significant role in the overall efficiency of the mixing process. Among many control strategies in the literature, passive methods proposed for improved mixing in high-speed systems use flush-mounted or intrusive injectors to generate streamwise, counter-rotating vortices for rapid nearfield mixing of the incoming air and fuel [Reference Kraus and Cutler4–Reference Hsu, Carter, Gruber and Tam12]. Beyond such classical passive coaxial configuration, a few studies explore active schemes such as powered resonance tubes (PRT) or Hartmann-Sprenger tubes as an option to excite the high-energy shear layer at high frequency [Reference Hongbin, Zhi, Fei, Lihong, Shenglong and Xinyu13].
Schematic of the pulsed coaxial injector system and its operating modes: (a) pulsed coaxial flow, (b) steady coaxial flow, (c) annular flow alone without actuation.
With an intention to improve mixing at supersonic and hypersonic flow conditions, the current paper presents the design and experimental studies on an active coaxial injector configuration, as shown in Fig. 1a. This design could tailor the instabilities of an injected co-flowing fluid using a pulsed supersonic air jet blasting up to 20kHz with a bandwidth of 10kHz. The injector assembly design shown in Fig. 1a has four major components: (1) an under-expanded source jet from a steel tube of 1.5mm diameter (ID) enters (2) an injector assembly made of three plates with internal cavities fabricated with the desired cavity volume of 20.3mm3, and (3) another steel tube (1mm ID, 1.5mm OD) that allows pulsed jet flows out of the cavities, and (4) a separate fluid passage that opens up around the 1mm steel tube through a circular orifice of 1.95mm diameter forming an annular space at the exit of the assembly. This annular space forms a circular slit with a 1.5mm radius and a thickness of 230 micrometers, as indicated in Fig. 1a. This coaxial annular orifice injects a steady fluid stream while the central steel tube exits a pulsed actuation air jet. Both fluids meet coaxially at the exit plane of the assembly, as shown in Fig. 1a. The first three components shown in Fig. 1a, i.e., an under-expanded steady jet, a cavity that forms the boundaries for fluid resonance phenomena, and the high-frequency pulsed jet that flows out from the cavity, which is called a resonance-enhanced microjet (REM), constitute the actuator system that is integrated into the coaxial injector assembly. Solomon et al. have extensively researched REM actuators and suggested a semi-empirical design correlation that predicts their pulsing frequency. For the continuity of this paper, the critical aspects of the REM actuator design are discussed next, and more details of previous studies are available in Refs [Reference Solomon, Foster and Alvi17–Reference Solomon19].
The most crucial parameter that defines the resonance frequency of the REM actuator (elements 1, 2 and 3 in Fig. 1a) is the cavity volume (V). The nozzle pressure ratio of the source jet (NPR), the distance of the cavity from the source jet nozzle entrance (h), the diameter of the source nozzle (D), and the area ratio (ratio of the inlet to the outlet flow area of the cavity) are the other key parameters that affect the resonance phenomena and its frequency response. These parameters essentially decide the mass flow to the cavity, boundary conditions for resonance and net mass accumulation within the cavity. Studies by Uzun et al. [Reference Uzun, Solomon, Foster, Oates, Hussaini and Alvi16], who have numerically simulated the REM actuator system, provide significant insights into the flow physics of the resonance phenomena. The under-expanded source jet essentially ‘fills up’ the cavity as the net mass flow rate (inflow-outflow) is designed to be positive, leading to its pressurisation while the REM jet flows outside. The cavity pressure rises to an equilibrium static pressure value; the limit is decided by the degree of under-expansion of the source jet. The increased cavity pressure resists supersonic inflow by normal and oblique shock formation at the cavity entrance that diverts the source flow outside (‘spilling phase’). The diverted flow causes pressure relief within the cavity as the REM jet still flows out of it. This low pressure allows the source jet to flow again into the cavity, and this cycle repeats itself, causing large pressure fluctuations, driving the REM flow from the cavity in a pulsing mode. It is important to note that an under-expanded source jet (element 1 in Fig. 1a) is essential for the resonance phenomena. The resonance phenomena trigger only for a range of NPR = 4.0 – 6.8 (nozzle pressure ratio) of the source jet. The source jet is highly under-expanded at this pressure, with periodic shock cells in the jet core. Due to the presence of shock cells, the static pressure of the jet at the centreline varies periodically in the axial direction, which is responsible for boundary conditions essential for the ‘filling and spilling’ phenomena, pressure fluctuations inside the cavity, and pulsed REM actuator jet output from the cavity. Under suitable geometric and flow conditions, such a design can generate unsteady supersonic jets over a large bandwidth of 1–60kHz [Reference Solomon19].
In the pulsed mode of operation, the inner actuation jet velocity U1 varies periodically from ∼0–400m/sec at a design frequency of 15.5kHz, providing a highly unsteady velocity profile to the annular flow at the exit, as indicated in Fig. 1a. To achieve pulsed mode, the parameter h/D is kept at 1.3 where h is the distance of source nozzle from the actuator, and D is the diameter of source jet. The source pressure is maintained at 65 psi, with a nozzle pressure ratio NPR = 5.8. In this mode, the instabilities of the injected co-flowing fluid can be tailored using the pulsed supersonic actuation jet operating in a frequency range of 1–60kHz [Reference Solomon19]. The coaxial annular stream exits with a constant velocity of U2, depending on the injection pressure. The annular stream velocity is kept at 70m/sec for the present experiments. In the pulsed actuation mode of operation, the shear layer of the annular fluid is exposed to the ambient air on one side and the central pulsing jet on the other. Figure 1b shows a representative flow pattern of the flowfield at the exit when the nozzle assembly operates in a steady actuation mode. This mode of operation can be achieved by placing the source jet (element 1 in Fig. 1a) flush with the actuator cavity where h/D = 0. For this case, the steady annular coaxial jet interacts with an under-expanded central actuation jet at the nozzle exit. Note that both in the pulsing and steady modes of actuation, the input pressure to the source nozzle is maintained at 65psi. Figure 1c shows flow features when the injector operates in no actuation mode, i.e., only the annular stream flows through the injector in this mode of operation. The source jet pressure is maintained at 0psi in this case. More details of the actuator used in the coaxial configurations, its early development, and prior implementation for various high-speed flow control applications are available in Refs [Reference Solomon, Cairnes, Nayak, Jones and Alexander14–Reference Lozano, Smith, Mungal and Hanson23].
2.0 Experimental details
2.1 Facility description
2.1.1 Set up for particle image velocimetry (PIV) and planar laser-induced fluorescence (PLIF)
The PIV and PLIF imaging uses a setup, as shown in Fig. 2, established recently at Tuskegee University with support from the US National Science Foundation. The critical component of this setup is a Quantel EverGreenTM Nd-YAG dual-pulsed laser with a choice of pulse energies up to 200mJ at 532nm and 30mJ at 266nm with a repetition rate of 15Hz. PIV experiments use laser pulses at 532nm. PLIF experiments use laser pulses at 266nm. A Powerview LS-LCD camera (29 MP, 6600 × 4400) with high quantum efficiency, low noise with 1.8 frames/s, selectable 12-bit or 14-bit output, and a 100 mm f/2.8 camera lens with appropriate filters acquires the images. An eight-channel digital pulse synchroniser with 250ps resolution controls the laser pulses and the trigger for the camera. A UV optic periscope and adjustable laser sheet optics (LSO) with 266/532mm AR coat create a thin laser sheet at an appropriate test plane in the flowfield generated by the pulsed coaxial assembly. A six-jet atomiser-9306 TSI generates olive oil droplet seeding in the annular CO2 stream for PIV measurements. For PLIF measurements, a second six-jet oil droplet generator-9307-6 TSI was used for generating acetone vapour for seeding the annular stream of CO2 gas. Figure 2 also shows the actuator block, the source jet nozzle fixed to a three-stage micro-gauge, the laser optics and their relative locations to PIV and PLIF cameras. The micro gauges have a resolution of 0.01mm for fine adjustment and alignment, which is critical for the experiments.
PLIF and PIV setup established at Tuskegee University for the present study.
2.1.2 PIV data acquisition and processing method
The PIV image acquisition and analysis used the INSIGHT4G software. The field of view for PIV measurement is 20mm across the flow and 50mm in the streamwise direction. The major challenge for image acquisition is the flow scale (order of mm) and the higher speed of the coaxial stream resulting from the supersonic jet actuation. The actuation jet in steady mode operates at a supersonic speed of 400 ± 52m/sec. The pulsing actuation provides a velocity fluctuation of ∼0–400m/sec to the particle-seeded annular flow. The image acquisition parameters, such as time between the laser pulse (Δt), laser pulse delay and PIV exposure time, were fine-tuned considerably to achieve image pairs with sufficient particle movements in various operating conditions. For the steady and unsteady actuation cases, the Δt is chosen at 0.40 microseconds, which will give 157 micrometers (
$\mu $
m) movement of seed particles at a velocity of 350m/sec.
Since the image resolution of the camera is 23
$\mu $
m/pixel, the seed particle will move at least 6–8 pixels distance at this measurement speed. The Δt is chosen at a higher value of 2
$\mu $
s for measuring the low-velocity field of the annular flow moving at 70m/sec near the injector exit. The laser pulse repetition rate was kept at 1.5 for all measurements. Since the Δt of the laser is extremely short at 400ns, and the camera shutters have to close and adjust with the signals physically, there exists an actual delay in the timing for the camera exposure as opposed to the observation in the timing diagram. The laser pulse delay time is fine-tuned to keep the two camera exposures in sync with the double laser pulses, with an extremely short Δt. For 2D spatial calibration, a measured distance in the image, the outer tube diameter is 1.5mm, measured within the image, and used for calibration. A background removal technique generates cleaner and continuous vector fields during preprocessing. This technique uses the Image Generator plugin to calculate the minimum pixel intensity of the input images. This minimum intensity is subtracted from the raw images by the Image Calculator, which sets its operation parameter to subtraction and its operand parameter to the image and passes in the generator image. An appropriate processing mask is used for processing data in a region of interest, 19 pixels from the nozzle.
Representative instantaneous raw images of the flowfield at three different modes of operation.
Figure 3a and 3b shows representative instantaneous raw images of the PIV and PLIF flowfield with olive oil seed particles for PIV and acetone vapour for PLIF at three different modes of operation, as described earlier in Fig. 1. Figure 3a(i) and 3b(i) are an instantaneous phase of the annular seeded jet actuated with a high-frequency actuation jet operating at 15.5kHz when the source jet nozzle maintained at 65psi. The inner diameter (ID) of the annular nozzle is 1.96mm. The actuation jet exits from a nozzle of 1mm ID and 1.5mm OD, which gives an annular exit dimension of 1.5mm diameter and 460-micrometer thickness, as indicated in Fig. 3. Adjusting the parameter h/D, the actuation mode can be switched from steady to pulsing at the same input pressure. At this pressure, the actuation jet velocity at the exit is sonic (∼350m/sec). As an under-expanded jet, the actuation jet expands to supersonic speed (∼400m/sec) outside the coaxial assembly. Figure 3a(ii) and 3b(ii) show the annular seeded jet actuated with a steady actuation jet from a source nozzle maintained at 65psi. Figure 3a(iii) and 3b(iii) correspond to a seeded annular jet at an exit velocity of 70m/sec without a co-flowing actuation jet at the centre.
The classic PIV processing algorithm is used for processing the images. Considering the intensive vorticity in the actuated flows, an additional PIV plugin, Use Image Deformation, which accounts for image deformation, has been used in the image processing approach for the highest accuracy. This plugin fixes the grid engine to Deformation Grid and the spot mask engine to Deformation Mask. The accuracy comes from the Deformation Grid, which performs subpixel deformation of particles across frames A and B. The Deformation Mask uses this subpixel deformation performance to condition and modify the spots. The deformation grid settings were set to 3 and 2 for the primary and secondary iterations. The interrogation window is selected from an initial size of 48x48 to a final dimension 24x24. Having these differing spot dimensions between final and starting spot sizes increases the grid resolution by shortening the spatial area of one grid square, which occurs due to a determining factor. This allows the processor to draw more vectors as more interrogation spots are available. For a Recursive Nyquist Grid, a final spot size smaller than the starting spot size increases vector rows and columns by a factor of 2, which results in 4 times the number of vectors drawn with each pass. A similar effect is seen with the Deformation Grid plugin.
The correlation engine was set to DirectCorrelator to determine the particle movement between frames A and B by calculating and subtracting the mean intensity of spots and then summing the product of pixel intensities at each pixel offset. To further increase the accuracy of the DirectCorrelator, the engine adjusts the correlation map by an autocorrelation factor. The size of this map is limited by the maximum displacement value, which is a parameter that limits the maximum allowed displacement of a particle based on the ratio between the starting spot A and the starting spot B, which is 1 in this case. This variable is vital to limit bad/random vectors because extreme vectors can be filtered out by limiting how much a particle can be displaced. But in areas where particle displacement is too low, missing sectors in the vector field can occur, which are sections of the grid where vectors are absent. Therefore, because of its low speed, we set the maximum displacement value (a non-dimensional parameter used in the correlator) for the low velocity coaxial annular flow to 0.35, causing lower overall particle displacement. For processing the annular flow without supersonic actuation, extreme vectors aren’t something to worry about, so a value of 0.35 allows for more vectors of different magnitudes to be drawn. To process the vector field of annular flow with supersonic, steady, and pulse actuation, the maximum displacement value was set to 0.15 because extreme vectors are very likely in these flow types. Hence, 0.15 ensures a tight restriction that allows for a cleaner image. The Gaussian Peak algorithm was chosen for the peak engine to locate the displacement peak defined by the correlation engine. It locates the peak with subpixel accuracy by fitting a Gaussian curve to the highest pixel and its four nearest neighbours. We get our located peak from the application of two 3-point fits; one fit is done in the ‘x’ direction with the peak pixel and neighbours to the left or right of it, and one fit is done in the ‘y’ direction with the peak pixel and neighbours above and below it. The GaussianPeak and DirectCorrelator were used for the image pair analysis for the vector field prediction.
Double Correlation was enabled within the processing plugin to validate vectors and clean the vector field before post-processing. It validates vectors by taking the ratio between two correlation maps and measuring that ratio against the tolerance value, which was set to 3.5. One of the two correlation maps is the correlation map of the central vector in a square area; the other is the product correlation map acquired from multiplying the correlation maps of every vector surrounding that central vector. Any ratio above 3.5 invalidates that central vector, whereas any below 3.5 doesn’t. The default tolerance value is 2, so a value of 3.5 was used so that there was some leeway given to the vectors while still maintaining some restriction to reduce bad/erroneous vectors. It’s important to note that too tight a restriction will invalidate vectors of higher magnitudes. So, while the vector field may look good and represent flow behaviour, further analysis will show a flow that’s not within the velocity range it’s supposed to be (i.e., supersonic actuation may appear to not be in the sonic or supersonic range). Within the processing, three secondary peaks were also exported; these will be used later in post-processing.
The post-processing for all flow types uses a Global Validation, a Local Validation and a Vector Field Conditioning plugin to clean up the vector field. The ‘Local Validation’ comes before the ‘Vector Field Conditioning’ by convention, but is recommended so that holes in the field can be better filled once the vectors are determined to be good. The Global Validation plugin was set to the ‘standard deviation’ range type, with a standard deviation factor of 4.5. Across the whole vector field, this plugin will determine what constitutes a valid vector by detecting invalid vectors that don’t meet the requirements of the standard deviation factor. The factor determines the range of valid velocities from a central point valued at the mean velocity. For a vector to be considered valid, it is required that its velocity falls within this range, and a factor of 4.5 produces some room for vectors to be considered good but still applies a tight restriction so that errant vectors won’t be regarded as reasonable. This plugin is suitable for removing completely erroneous data. Using the Mean Test, the Local Validation plugin was used to validate vectors in a neighbourhood of 5x5. The tolerance was set to 2.5 in both the U and V directions. When the local validation operates, it calculates a reference vector based on the mean of a 5x5 neighbourhood, using each vector in that neighbourhood; the reference vector is then compared to the current vector of the neighbourhood. The difference between the current and reference vector is compared to the tolerance. If the difference is less than the tolerance, the current vector is suitable, and if it’s higher, then the current vector is bad. The default tolerance was 2, but the tolerance was changed to 2.5 to give a little extra leeway to some vectors while still keeping a tight restriction. A difference higher than the tolerance means that the current vector drawn during processing is way higher than it should be, and 2.5 ensures that those types of vectors are invalidated. In this plugin, Valid Secondary Peak and Local Median were enabled to replace those bad vectors. The valid Secondary Peak uses the three secondary peaks exported during processing for replacement, and the Local Median uses the local median of the 5x5 neighbourhood. Both replacement methods are enabled to increase the replacement rate of bad vectors.
The Vector Field Conditioning plugin will fill any holes resulting from failed vector validation. The plugin was set to recursively fill the holes of a 7x7 neighbourhood using the mean vector of that local area as the filler vector. The Recursive Filling will do repeated passes of filling, first using the most valid neighbours for replacement vectors; then the second pass uses the second most valid neighbours; valid neighbours can be both measured and interpolated vectors. In this plugin, smoothing was enabled, with a Gaussian Kernel of 1 in a 5x5 neighbourhood. Enabling this parameter adds a low-pass filter to the vector field after filling holes, tilting vectors towards their intended horizontal or vertical direction. This reduces some of the noise caused by random particle displacements. This process ultimately produces a clean but interpolated vector field.
2.1.3 PLIF data acquisition and processing
For PLIF data acquisition, the annular stream is seeded with saturated acetone vapour from the six-jet oil droplet generator-9307-6TSI. The PLIF measurement uses an ultra-thin laser sheet of 266nm wavelength to fluoresce the absorbing species (acetone) in a given measurement volume. Many studies report that acetone fluorescence has a linear variation with concentration and laser power [Reference Lozano, Smith, Mungal and Hanson23, Reference Lozano, Yip and Hanson24]. Acetone absorbs ultraviolet light (225 – 320nm) but fluoresces in the blue (350 – 550nm). This study uses CO2 as an annular stream and compressed nitrogen for generating high-frequency actuator jet pulses. Since the resulting fluorescence is proportional to the amount of the absorbing species in the measurement volume, measuring the intensity of light from the fluorescent molecules captured using an appropriate camera with a filter will quantify the mixing of the annular stream with the unseeded actuation jet. The mixture fraction calculated at each location usually represents the mixing characteristics of the flow. From raw images, the intensity of acetone in the flowfield is analysed using MATLAB and INSIGHT4G software.
2.1.4 Measurement uncertainties
The source jet pressure measurement has an uncertainty of ±0.1psi. The micro-gauge used for linear movements of the nozzle block for varying the parameter h/D has an uncertainty of ±0.01 mm. A TSI Mass Flow Multi-Meter 5300-4 measures the flow rate of CO2 with ±2% reading accuracy for measurements up to 300L/min. A high-pressure compressed nitrogen tank (2000psi) supplies air to the source jet nozzle and the pulsed jet injector assembly. A multi-channel oscilloscope monitors all signals used for measurements for accuracy. The uncertainty of velocity measurements in PIV is estimated from ±3% to ±13% (using the INSIGHT4G software) and is reflected in the particle speed estimate as 20 ± 0.6m/sec for low subsonic and 400 ± 52m/sec for supersonic speeds. The uncertainty of PLIF intensity measurements is estimated at ±6%-16%. The error sources for intensity measurement include laser intensity variation, fluorescence quenching, camera-related noise, optical artifacts, and imprecise calibration. In the present experiments, the uncertainty of vorticity is calculated as ±5%–15%. Since the overall mixing effectiveness is directly related to the estimation of velocity, vorticity and pixel intensity measurement, the uncertainty of these parameters will propagate to the overall mixing effectiveness, which can be estimated using Monte Carlo and sensitivity analysis. In this method, each variable’s uncertainty is randomly varied within its known uncertainty ranges (typically assuming a Gaussian or uniform distribution), and the output (e.g., mixing effectiveness metric) is recalculated using several iterations to build a distribution of possible outcomes. The confidence interval of this output distribution quantifies the overall uncertainty in the result. This method estimates that the final mixing effectiveness uncertainty varies from 8% to 22% (±8% for the lowest and ±22% for the largest measurements).
2.2 Design details of the coaxial injector assembly
Figure 4 shows the design details of the pulsed coaxial injector assembly (actuator block indicated in Fig. 1) fabricated with three brass plates. The top plate contains a 3mm long, 1.3mm diameter cavity through which an under-expanded actuator source jet enters the nozzle block. The second plate has another internal hole. A 1mm (ID) steel tube (with 1.5mm OD) connects the cavity in the second plate and directs the air jet to flow out from the base of the third plate. The last plate has a 1.96mm orifice, so when combined with the second plate and the steel tube with 1.5mm OD, an annular space is formed outside the 1mm tube (ID). The internal cavity in plate 3 connects to a steady fluid (CO2) supply line through a steel tube. The design ensures no interaction or coupling between the coaxial fluids before they reach the exit plane of the assembly.
Design details of the coaxial injector: (a) front, side and top views, (b) photograph of the pulsed coaxial injector.
This assembly has a total internal cavity volume of 20.6mm3. An under-expanded source jet supplied from a nozzle of 1.5mm exit diameter (D) enters the assembly through a 1.3mm orifice on the first plate. This source jet produces pulsed flow through the 1mm diameter tube integrated into the second and third plates under suitable resonance conditions. This design allows olive oil-seeded or acetone-seeded fluid stream (CO2) injection through the annular space while the central tube delivers a pulsed or steady actuation air jet (N2). Experiments use two control parameters, h/D or nozzle pressure ratio, NPR, for frequency control. The present study uses h/D = 1.3 and NPR = 5.8 to achieve a pulsing frequency of 15.5kHz.
3.0 Results and discussions
3.1 Frequency characterisation of the pulsed coaxial assembly
Figure 5 shows the frequency spectra of the actuator integrated into the nozzle assembly measured using a GRAS 1/4-inch Free-Field Microphone with a sensitivity of 4mV/Pa. National Instruments 9,234, a 24-bit, 51.2kHz data-acquisition module, acquires the microphone data using LabVIEW.
Spectrum of coaxial jets used for this study: (a) frequency sweep of the actuator, (b) spectra of pulsed, steady modes and no actuation cases as shown in Fig. 1.
Fast Fourier transformation (FFT) of time series with 2048 data points and a Hanning window with 50% overlap, computes acoustic spectra used in the analysis. Figure 5a represents the frequency sweep of the actuator system from 11 to 20kHz. Figure 5b shows the spectra of the actuator’s steady, pulsed and no-actuation modes, corresponding to configurations shown in Fig. 1a–c. The pulsed coaxial flow shows a distinct frequency at 15.5kHz. In contrast, the steady coaxial injection shows no specific tones in the spectra besides broadband noise. In steady actuation, energy is in broadband and is focused at 15.5kHz for pulsed actuation. The primary source for this discrete peak is the formation and propagation of high-frequency compressible vortexes that result from the pulsing action of the actuator source jet. An elaborative discussion of this unsteady phenomenon has been reported earlier by Solomon et al. [Reference Solomon, Cairnes, Nayak, Jones and Alexander14, 25]. In addition, the actuator’s pulsed operation results from a ‘filling and discharge’ phenomenon, causing Mach disc oscillations of the actuator source jet. The discrete tones in the pulsed actuator spectra are directly related to these two processes. The frequency of Mach disc oscillations and the high-frequency compressible vortexes were also measured previously using high-speed image analysis, confirming the tonal peaks in the microphone data [Reference Solomon, Cairnes, Nayak, Jones and Alexander14].
The spectra of the acetone-seeded annular jet stream show low-amplitude broadband noise, indicating natural instabilities in the flow. The present experiments use pressure and the flow rate of CO2 (annular stream) at 8psi and 4.7lit/min, respectively. For a given annular exit area of 1.08mm2, this flow rate gives an estimated exit velocity of U2 ∼70m/sec for the annular stream. The exit velocity U1 of the pulsed jet varies from 0 to 400m/sec during the cycle, giving rise to a range for velocity ratio U1/U2∼0–6. The exit flow area ratio A 1 /A 2 of the present configuration is 0.72, where A1 is the area of the exit of the actuator flow, and A2 is the area of the annular space. With a pressure ratio of fluids exiting the assembly (Pact/Pstream) that varies in the range of 1- 13 during the pulsed coaxial injection process, the momentum of the actuation jet dominates the flowfield for most of the pulsing cycle.
3.2 Instantaneous PLIF and PIV field (acetone concentration, velocity and vorticity)
3.2.1 Acetone-seeded annular stream without coaxial actuation jet
Figure 6a(iii) shows a representative instantaneous PLIF image of the annular stream where the acetone-seeded annular stream is injected through the coaxial assembly without an actuation jet, and the streamwise intensity profiles of this image at three selected locations as marked in the figure. Ideally, the saturated vapour exiting the nozzle fluoresces with maximum intensity (red colour in PLIF image) and unseeded actuation jet and ambient air with zero intensity (black colour in PLIF image). The maximum intensity is observed at the exit plane with a value of ∼1,000 (this is a non-dimensional number proportional to the intensity of light falling on a given pixel), and the minimum value of 0 is noted at a location just outside the nozzle before the annular stream converges at the centre. This location has a small pocket of air without acetone vapour. Also, the ambient air has a minimum intensity (∼0) as it is not seeded with acetone vapour. Assuming a linear variation between these two extreme values, the intensity of light fluorescence measured at a given location represents the local mixing of acetone with the surrounding unseeded streams or ambient air.
Instantaneous velocity (m/sec), vorticity (1/s) and acetone concentration fields of the seeded annular stream. a) Co-axial stream without actuation b) Co-axial stream with steady actuation.
The high magnification optics and a high-resolution camera (27MP) capture fine details of these high-speed microscale flows and their mixing characteristics in the PLIF images. For an acetone-seeded annular stream at 4.7psi and 5lit/min, PLIF images show the formation of a saturated core up to 20 diameters, as noted from the profiles in Fig. 6a (iii). The acetone intensity of annular flow at the centreline of the stream is measured as ∼800 for the core, then drops to 200 far downstream. The acetone intensity profiles also indicate that the annular stream then seems to mix well with the ambient air further downstream by the natural diffusion mechanism. The blue curve in the profile shows the distribution of seed particles in the streamwise direction at the centreline of the injector. The red and green profiles show the streamwise distribution of seed particles at the top and bottom centre locations of the coaxial stream, as indicated in Fig. 6a (iii). These PLIF profiles represent the acetone concentration in the flow at various locations and provide information on its distribution in the flowfield. All the profile curves show the same intensity value of ∼200, indicating well-mixed with the unseeded ambient air far downstream locations. The discrete peaks and varied intensity profiles at the top and bottom locations indicate unsteadiness and instabilities in the shear layer of the annular stream.
Figure 6a(ii) shows a representative instantaneous velocity field of the seeded annular flow without a coaxial actuation jet, corresponding to the acetone intensity field in Fig. 6a(iii). The annular stream from the nozzle exits with a maximum stream velocity measured up to 70 m/s. The core of the annular stream is visible up to 20mm from the exit. The stream slowly dissipates into the ambient air, and the velocity drops to 10–20m/sec at 30mm from the injector exit. The instantaneous velocity field also captures the natural instabilities present in the shear layer of the annular flow. Figures 6a (iii) and (ii) indicate a higher acetone concentration at locations where the flow velocity is measured as high. Figure 6a(i) indicates the vorticity field of the injector corresponding to the velocity vectors shown in Fig. 6a(ii). The top and bottom annular flow regions form a vorticity core with a maximum magnitude of ±50,000/s. Beyond this length, the vorticity core disintegrates and dissipates to a lower magnitude. Note that the annular stream experiences shear on both the inner and outer sides of the stream.
3.2.2 Acetone-seeded annular stream with steady coaxial actuation jet
Figure 6b(i–iii) shows representative instantaneous acetone intensity, velocity and vorticity fields of the seeded annular flow with a steady jet actuation at the centre. An under-expanded jet at NPR = 5.8 is used for steady supersonic actuation. The steady jet actuation accelerates and entrains the acetone-seeded annular flow as it moves downstream. Figure 6b(iii) shows minimal entrainment near the nozzle exit for this configuration. The highly under-expanded characteristic of the actuation jet and its strong compressible shear layer restricts the diffusion of the seeded annular stream near the nozzle exit. The intensity of acetone is observed with a value of 1,000 at the top and bottom profiles, similar to that of the annular stream without actuation discussed in Fig. 6a(iii). Due to steady jet actuation, the seed particles in the annular stream attain a maximum speed of 400m/sec at the core after moving through a distance of 5 to 20mm from the nozzle exit, as observed in the velocity field shown in Fig. 6b(ii). The overall velocity of the annular stream is increased significantly due to the high-momentum steady actuation jet.
Figure 6b(i)shows the instantaneous vorticity field of the seeded annular jet actuated with the steady under-expanded jet. As expected, the actuation causes continuous and intensive double vorticity streaks in the annular stream. The high vorticity magnitude (200,000/s) indicates that the actuation jet imparts intensive shear to the annular stream at the core. The magnitude of maximum vorticity has increased four times due to the steady jet actuation at the centre core of the annular stream. The continuous vorticity streaks have extended up to 20mm in the streamwise direction. The data quantitatively confirms the effects of steady actuation that significantly increased the velocity and vorticity of the annular fluid in the streamwise direction. The impact of this flow dynamics modification is visible in the intensity profile shown in Fig. 6b (iii). The steady actuation resulted in a sudden drop in the acetone intensity of the annular flow from a value of 1,000 to 100 from the exit to a 10d downstream location compared to the case without actuation, where the drop is seen more gradually and over a distance of 20d from the exit. The intensity value at the centre of the actuation jet is almost zero until 20d from the exit due to its coherent structure with shock patterns that prevent diffusion of the acetone-seeded annular stream into its core. The slowdown of the actuation jet further downstream allows some mixing with the annular acetone-seeded jet. A high-velocity actuation jet quickly reduces the intensity of annular flow, as observed in Fig. 6b (iii).
Instantaneous velocity (m/sec), vorticity (1/s) and acetone concentration fields of the seeded annular stream.
3.2.3 Acetone-seeded annular flow with supersonic pulsed coaxial actuation at 15.5kHz
Figures 7 and 8 show instantaneous acetone intensity, velocity, and vorticity fields for four different pulsing phases of a coaxial annular stream when the actuation jet pulses at 15.5kHz. Figure 7a represents the instantaneous fields at the beginning phase (0) of the pulsed actuation observed with an evolving vortex near the nozzle. This vortex evolves, grows and moves downstream in the streamwise direction in phase 90o, as observed in Fig. 7b. As evident in phase 180o shown in Fig. 8a, the growth and entrainment of annular fluid increase as it moves further downstream. At phase 270o (Fig. 8b), the pulsed vortex weakens considerably with interaction with the annular fluid and the air in the ambiance. The representative PLIF and PIV fields of pulsed actuation at various phases of actuator operation confirm that the active injection offers significant velocity fluctuations in the mean flow of annular fluid. For example, a comparison of instantaneous images at phases 90o and 180o reveals velocity fluctuations in a range of ∼100–400m/sec in the streamwise location 10–20mm from the nozzle exit. The evolving vortex, its growth and its movement downstream in the streamwise direction are captured in both PLIF and PIV images. Such a highly unsteady vorticity field leads to enhanced mixing between the annular fluid and the high-velocity actuation jet. The maximum magnitude of the vorticity is observed to be the same in both steady and pulsed actuation cases.
Instantaneous velocity (m/sec), vorticity (1/s) and acetone concentration fields of the seeded annular stream.
The intensity profiles at the centre (blue curves) of four different phases of pulsed actuation (0o, 90o, 180o and 270o) in Figs 7a(iii), 7b(iii), 8a(iii) and 8b(iii) show an interesting phenomenon of annular fluid transport by the evolving vortex of the actuation jet. The shear layer intensity profiles (red and green curves) with discrete peaks indicate a disintegrated shear layer of the acetone-seeded annular stream. The shock wave that precedes the evolving vortex of the actuation stream might be responsible for this breakdown. The vortex front entrains and transports the acetone-seeded annular stream, as indicated in Fig. 7a(iii). The instantaneous phase at 90o (Fig. 7b(iii) shows the further movement of this entrained transportation of the annular stream to 10d-20d downstream. The diffusion and growth of the vortex cause a drop in intensity value from 400 to 200. At 180o, the vortex diffuses further, resulting in a lower intensity, as seen in Fig. 8a(iii). Figure 8b(iii) shows the final phase 270o, where the actuation jet velocity drops and the annular stream momentum predominates the flow domain with a relatively diffused acetone intensity and increased mixing characteristics at the centre.
3.3 Averaged PLIF and PIV flowfield images and mixing characteristics
Figure 9a–c shows the averaged acetone intensity, velocity and vorticity fields of 260 images of annular fluid without actuation. Figures 10a–c and 11a–c present the same results for annular fluid with pulsed and steady actuation, respectively. Due to the steady actuation, the core of annular fluid velocity and vorticity fields extended significantly from the nozzle exit in the streamwise direction. The maximum value of vorticity magnitude increases to ∼400% due to steady jet actuation, and the velocity ranges from 70 to 300m/sec. A comparison of Figs 10 and 11 show that pulsed actuation leads to a lower average velocity for the annular stream than steady actuation. This observation is as expected due to the vortex formation in the pulsed flow. The average intensity of the vorticity field was also reduced in this case, as evident from Figs 10c and 11c. The steady and pulsed actuation cases show two distinct patterns of annular stream diffusion. The high-momentum steady actuation jet entrains the annular fluid to its core and increases speed to supersonic, with less diffusion to the ambient air. Its diffusion characteristics increase as the velocity decreases beyond 30mm from the exit. For pulsed actuation, entrainment and diffusion begin at the nozzle exit and progress uniformly in the streamwise direction due to the evolving compressible vortex. This process leads to a more diverging flowfield and attributes enhanced mixing characteristics than steady actuation. Since each instantaneous image contains information on 4–5 cycles, the average image represents ∼1,000 cycles for the pulsed injection case. These averaged images provide a comprehensive view of all three cases’ mixing characteristics and provide reasonably accurate quantitative estimates of mixing effectiveness between the cases.
Average velocity (m/sec), vorticity (1/s) and acetone concentration fields of the annular stream without actuation.
Average velocity (m/sec), vorticity (1/sec) and acetone concentration fields of the annular stream with 15kHz actuation.
Average velocity (m/sec), vorticity (1/sec) and acetone concentration fields of the annular stream with steady actuation.
The intensity of each pixel in the averaged PLIF image is proportional to the average acetone concentration around that elemental volume for the image sequences selected. The average of all pixel intensity is an estimate of the acetone concentration in a given field of view for a particular case. For the first case, the annular stream jet alone, this number is 44.3. For the second case, when an unseeded steady actuation jet flows through the core, the acetone content we measure as average intensity in the same field of view changes due to fast relative motion between the streams. The average intensity of pixels measured for this case is 7.5. The same calculation for pulsed injections shows this average intensity value as 15.9. This calculation estimates that the mixing effectiveness of pulsed coaxial injection is 114 ± 23% more than that of steady coaxial injection. The enhanced mixing characteristics of the pulsed coaxial injection system are attributed to the entrainment and growth of high-frequency vortex generated by the pulsed jets and through the shock wave diffusion through the interface of the seeded and unseeded flow downstream.
Figure 12 shows the jet spreading of the annular stream without actuation (acetone-seeded jet). The jet spreading rate is estimated at 0.15. The jet spreading rate of standard turbulent round jets has been reported to be 0.1 to 0.15 in the literature. Figure 13a–d shows the normalised acetone intensity profiles of the annular stream image shown in Fig. 9a at various x/d locations. As indicated. x/d = 0 is the exit plane of the nozzle. These profiles show the natural diffusion characteristics of the annular stream. As anticipated in turbulent mixing, the stream diffuses as it moves forward, generating bell-shaped Gaussian distribution curves at various x/d locations up to x/d = 15. (d = 1.5 mm). The intensity curve at x/d = 0 shows double maximum values, a characteristic of annular streams. Note that the acetone intensity is almost flat (∼0.01) away from the centreline of the annular flow x/d = 0. The profile is symmetric for all x/d locations except at x/d = 0 (due to the slight geometric asymmetry of the injector exit plane due to the fabrication imperfection).
Jet spreading rate of the annular stream without actuation (seed jet).
PLIF intensity profiles of the seeded annular stream at various streamwise locations.
Figure 14a–f compares the average intensity profiles of pixels at various streamwise locations of the averaged images shown in Figs 9a, 10a and 11a, respectively, for the annular seed jet alone, with steady actuation and pulsed actuation. The acetone seed jet profiles (green curve) show two maxima up to x/d = 2 and diffuse into a single jet structure. Seed density remains high in the core region and drops in the streamwise direction, as expected, and the jet width increases gradually as the jet diffuses in the downstream direction. The steady and pulsed coaxial flow (blue and red curves) profiles also show two distinct peaks in all streamwise locations at x/d = 0. A slight geometric asymmetry at the exit nozzles creates more seeded acetone jet flow at the top than at the bottom. Since pixel intensity directly correlates to the seed density, this results in an asymmetric intensity profile with higher intensity at the top location of the assembly observed in Fig. 14.
Normalised intensity profiles of averaged images at various x/d locations.
The intensity profiles in all x/d locations indicate that the pulsed coaxial flow (red curves) creates a significantly improved distribution of seeded acetone in the field of view than the steady jet operating at the same pressure (blue curves). Profiles 14a–f indicate that the mixing of the annular acetone-seed jet and the unseeded actuation jet increases as it flows downstream. As discussed in Figs 7 and 8, this enhanced mixing is attributed to the entrainment and growth of high-frequency vortex generated by the pulsed jets and through the shock wave diffusion through the interface of the seeded and unseeded flow downstream. Comparison of the jet width of steady and pulsed coaxial also gives indications of significantly improved mixing between the seeded jet and unseeded supersonic actuation jet when pulsing at 15.5kHz. The profiles examined at various locations of x/d also reflect the mixing effectiveness of pulsed actuation, estimated based on the average image intensity.
4.0 Summary
The paper presents a PLIF and PIV study on an active, supersonic coaxial jet injection assembly integrated with ultra-high frequency pulsed microactuators. The assembly steadily injects a fluid through a 460µm annular space around a 1mm ID, 1.5mm OD sonic nozzle with an exit velocity of 70m/sec. The coaxial nozzle at the centre (1mm ID) issues the supersonic actuation jet in two operation modes: a) as a steady under-expanded jet at 65psi, and b) as a pulsed actuation jet operating at 15.5kHz at the same input pressure. The annular stream seeded with saturated acetone vapour is used for PLIF imaging and mixing studies. The velocity and vorticity field of annular fluid seeded with olive oil with and without actuation were measured using PIV. The PIV data shows that the steady actuation has increased the velocity to 400 ± 52m/sec and introduced four times the intensive shear and extended vorticity streaks in the annular stream. The pulsed actuation resulted in fast-moving, high-frequency compressible air vortices in the injected flowfield. The growth and entrainment of these pulsed vortexes cause a highly unsteady velocity field and vorticity streaks in the annular stream. The current study confirms that the coaxial injector operating in supersonic pulsed mode can provide tailored vorticity in fast-moving fluids and enhance mixing more than 114 ± 23% than a stream actuated with a steady supersonic under-expanded jet and can be used for high-speed flow mixing and control applications.
Acknowledgments
National Science Foundation supports this work through grant 1900177. The authors thank Dr. Phillip Kreth, University of Tennessee Space Institute, TN, for supporting this study.
