Periodic atomization characteristics of simplex swirl injector induced by klystron effect

Anlong YANG,Shangrong YANG,Yunfei XU,Longfei LI

Science and Technology on Liquid Rocket Engine Laboratory,Xi’an Aerospace Propulsion Institute,Xi’an 710100,China

1.Introduction

Combustion instabilities generated by the coupling of heat release and acoustic pressure in the combustor are very complicated and dangerous phenomena in rocket engines.This problem is particularly troublesome in rocket engines,because it interrupts original energy supplies,generates undesired intense pressure fluctuations,and leads to excessive heat that transfers to combustor walls and injector plates.Although tremendous human,material,and time resources have been invested by many countries since the 1940s to determine ways to manage this problem,1,2because of the complexity of the problem,the generally inaccessible environment of the rocket engine combustion chamber,and the lack of appropriate diagnostic techniques available to study the problem,this problem has not yet been resolved.

It is known that the combustion process can add energy to the system in the occurrence of combustion instabilities.The energy transfer is mathematically expressed in terms of the so-called Rayleigh criterion.3According to the Rayleigh criterion,interaction between the combustion heat release and the acoustic field is the strongest if heat is added in a region of space while the pressure fluctuation is being up to the highest.

It should be noted that there are two significant characteristics of pressure fluctuations in the unstable combustion chamber:their large amplitudes and obvious periodicity.4,5That feature could be crucial to understand combustion instabilities,since the combustion heat release needs to be periodic to catch a stable phase angle to the periodic pressure fluctuation,which is required by Rayleigh criterion.Periodicity of combustion heat release in the occurrence of combustion instabilities has been certified in previous literatures experimentally6,7and numerically.8–10However,there are many other processes in the liquid engine combustion chamber,including injection,atomization,vaporization,mixing and reaction.They all might have an effect on the heat release and might be influenced by pressure fluctuations.Thus,a further question should be asked that whether the other processes also feature the similar periodicity in the occurrence of combustion instabilities.

The best way to find out the answer to this question is to observe all the component processes in rocket engines when combustion instability phenomenon occurs.Unfortunately,any successful observed case does not exist in previous literatures,although Miller et al.4achieved strong spontaneous longitudinal instabilities with peak-to-peak amplitudes of 0.69–1.38 MPa in a model combustor without observation.

Another way to examine the feedback of these processes to combustion instabilities is to set up an environment with large oscillations to observe and analyze the dynamic responses of the processes.This environment should approach that of naturally occurring combustion instabilities in real engines.11Hardi et al.12conducted an experiment in which a condition similar to unstable combustors’was provided.The breakup and atomization behavior of the central LOx jet was characterized using the high-speed shadowgraph imaging.There was not evident periodicity displayed by injection or atomization in their experiment.Nevertheless,there are three differences between their experiment and the spontaneous combustion instability cases.First,in their experiment,the large acoustic oscillations were excited by a toothed exciter wheel rather than the heat release.Second,the injectors allocated near the pressure node and velocity antinode were mainly impacted by the transverse acoustic velocity,rather than acoustic pressure.Third,there was only one single acoustic oscillation of approximate 4200 Hz frequency at which the first transverse resonance occurred.Referring to previous studies,4,13a specific injector con figuration under a specific working condition features a certain limited frequency range in which the combustion instability occurs.For this reason,it is not sure that whether the frequency of 4200 Hz is appropriate to the injectors used in Hardi et al.’s experiment12to trigger combustion instabilities.Hence,it is difficult to determine whether the injection and atomization are periodic during a real combustion instability process through Hardi et al.’s experiment.

Among all the component processes in rocket engines,the injection and atomization processes dominate other subsequent processes to a great extent and they are relatively convenient for measurement.A characteristic time analysis was performed by Anderson et al.13to identify which component contributes to instability.It was found that atomization processes,such as a jet breakup,had similar time scales to the acoustic time scales associated with resonant frequencies of representative combustion chambers.However,this similarity always exists but does not always lead to combustion instabilities.Besides,there are two obvious differences between the primary atomization frequencies and the acoustic resonance frequencies.First,the primary atomization frequencies are acquired by measuring the distances between two adjacent ligaments ranging from d to 10d,where d is the injector’s orifice diameter.Thus,to the primary atomization,there were not strict frequencies or periodicities which could be identified by FFT analysis.So those primary atomization frequencies could only be regarded as some kind of ‘mean frequency’.Second,this‘mean frequency’of primary atomization was about twice the maximum combustion instability frequency predicted by the Hewitt Stability Correlation,14although the two frequencies had the similar varying trend with respect to U/d,where U is the jet velocity.Nevertheless,the primary atomization can present strict periodicities if some driver periodically forces it as that is suggested in Santoro et al.’s study.15It was also showed that the periodic primary atomization at 5500 Hz frequency which is equal to the maximum combustion instability frequency.This frequency is much lower than the free primary atomization frequency leading to the oscillating chamber pressure of the peak-to-peak 0.138 MPa amplitude.It means that the primary atomization in the unstable combustion chamber features utterly different state from the free primary atomization.Those differences could attribute to injection pressure oscillations of large amplitude.The injection pressure oscillations accompany the flow oscillations that modulate the velocities of the liquid particles with time.Then a large proportion of fluid particles are superposed together at certain point where the liquid particles with high velocities overtake those with low velocities.This phenomenon called the klystron effect was reported in impinging jet injectors1,16and swirl injectors.17,18Besides,the back pressure oscillation,with the frequency approximating the fundamental frequency of sheet waves,enhances the wave amplitude and the atomization angle,which accelerates the sheet’s breakup and decreases the mean size of the droplets downstream of the impingement point.19

The stochastic characteristics of the primary atomization frequency are based on the case of unforced turbulent impinging jets.For combustion instability cases,the state of atomization is possibly unusual,since the amplitude of back pressure fluctuations in combustion chambers is always the same order of magnitude as the pressure drop of injectors.4In that case,the effect of back pressure fluctuations on injection and atomization should not be neglected.Nevertheless,this effect has not been investigated systematically.

In some particular cases,injection and atomization could present periodic characteristics due to self-pulsations that might originate from the feed lines or the hydraulic and aerodynamic instabilities.Bazarov and Yang18studied the effect of pressure fluctuations excited by self-pulsations between the feed lines and the injectors on the atomization of the swirl injectors.The self-pulsation characteristics of a gas/liquid swirl coaxial injector were investigated by measuring spray patterns,acoustic characteristics,spray oscillation characteristics,and the self-pulsation boundary under ordinary20and high21back pressure respectively.However,combustion instabilities caused by self-pulsations can generally be avoided by changing dynamic characteristics of the feed system(such as adding a restrictor ring in the feed line)or limiting working range.Besides,frequencies of combustion instabilities are not always equal to those of self-pulsations just right.Hence,the injection and atomization under extrinsic fluctuations rather than self-pulsations should be paid more attention to.

In comparison to back pressure oscillations with large amplitudes,pressure oscillations at supply pipes are relatively easy to generate.Wilson et al.22at the University of Alabama in Huntsville(UAH)designed and built a hydro-mechanical pulsator to simulate the effects of high-frequency combustion instability in liquid rocket engines.Ahn et al.developed mechanical pulsators that differed from those made in Russia and at UAH.23They also obtained the periodically changing air core diameters inside the transparent vortex chamber and the nozzle,as well as the spray near the exit nozzle using the high-speed camera.Khil et al.17developed a method to transiently measure the mass flow rate fluctuation of a simplex swirl injector produced by a hydrodynamic mechanical pulsator on the feed line in front of the injector inlet.

Most of these works mentioned above mainly concentrated on the pressure and mass flow rate fluctuations in the injectors rather than in atomization fields.Atomization fluctuations,however,directly influence the subsequent component combustion processes.Besides,atomization fluctuations are different from the fluctuations in the injectors due to the klystron effect,viscosity,surface tension and aerodynamic force.For this reason,this paper presented the atomization dynamic characteristics of a simplex swirl injector with fluctuated pressure drop generated by a hydrodynamic mechanical pulsator.

2.Experimental method and procedures

2.1.Schematic of experimental system

A schematic of experimental system is shown in Fig.1.Tap water was used as the working fluid.The experimental system consists of a pressurized water supply system,a simplex swirl injector,pressure sensors,a data acquisition system and a high-speed camera system.Fig.2 shows a schematic of the simplex open-end swirl injector,which has six tangential entries.The average injection pressure drops of all tests were approximately identical,2.2 MPa.The injector unit was instrumented by piezoeresistive and piezoelectric sensors which monitored the static and high-frequency pressure,respectively.

The piezoeresistive sensor has data acquisition rates of 1000 Hz with pressure measuring in the range of 0–6 MPa and measuring error of 0.5%.The piezoelectric sensor is capable of acquisition rates up to 100 kHz with pressure measuring in the range of 0–25 MPa and measuring error of 0.15%.

The shadow photography technique was used to acquire spray and atomization patterns of the simplex swirl injector and a 500 W steady Light-Emitting Diode(LED)lamp was used as the light source.The patterns were captured by a high-speed video camera.The frame resolution was set at 800 × 504 pixels.The shutter speed was set at 10 μs and the frame rate of 13,000 frame/s(frames per second)was selected.

2.2.Hydrodynamic mechanical pulsator

As shown in Fig.3,the hydrodynamic rotating-disk mechanical pulsator was designed to generate flow-line pressure fluctuations in feeding pipes.The pulsator can generate pressure fluctuations of which fluctuation frequency range is 1–4600 Hz.This device is theoretically similar to that mentioned by Bazarov and Yang.18An example of pressure pulsation produced by the hydro-mechanical pulsator with a peak frequency of 274 Hz and amplitude of 1.05 MPa is shown in Fig.4.In our experiments,amplitudes of pressure fluctuations remained 1±0.2 MPa at all fluctuation frequencies.In the atomization experiment of the simplex swirl injector,the pressure fluctuations of 80 different frequencies varying from 6.6 to 848.8 Hz were generated in the feeding pipe.

2.3.Analysis methodology of image

In present research,all the experimental results and analysis are based on the temporal shadow images of atomization and the assumption of the axisymmetric simplex swirl injector.

2.3.1.Capture of liquid film edges

In order to analyze the correlation of the fluctuations between the liquid film and the injection pressure drop,an in-house code of image-processing based on MATLAB was developed to capture the edges of temporal liquid films.As shown in Fig.5,the temporal liquid film edges generated by the simplex swirl injector were captured automatically by using an image processing program.The procedure is:(A)the edge points of liquid films were scanned along the red dash lines in the area between the light blue and dark blue solid lines;(B)all the edge points were linked together to form a liquid film edge(the green line).As shown in Figs.5 and 6,the temporal positions of the edge points induced by a pressure pulsation at frequency of 184 Hz were recorded at two different heights from the injector plate(H1=10.3 mm and H2=20.9 mm).It is found that liquid film fluctuations increase with the liquid film movement since the liquid film fluctuation amplitude at H1is obviously larger than that at H2.The result could attribute to klystron effect,which is able to amplify the effect of an initial small velocity discrepancy of fluid mass particles on atomization fluctuations.

2.3.2.Capture of atomization zone

Fig.7(a)and(b)show the procedure of atomization ‘density’calculation in two different regions at the same time.Both of them have liquid mass gather in two different interrogation regions.However,the liquid mass had been broken into many small droplets in the region shown in Fig.7(a),whereas the liquid still remained the film state in the interrogation region of Fig.7(b).The procedure of determining the atomization zone and semi-quantifying the number density of droplets is listed below.

First,the original gray values of atomization shadow images g0(x，y)are reversed to g(x，y)(The range of gray is from 0 to 1.),as shown in the following equation:

where(x，y)is the coordinates of images.

where(X，Y)is the center location of the interrogation region,2m+1 and 2n+1 are the dimensions of the interrogation region in the x direction and y direction,respectively.

Second,as shown in Eq.(2),the average valuesˉg(X，Y)of gray-reversed images were 0.205 and 0.297 in the interrogation regions of Figs.7(a)and(b),respectively.Furthermore,the gradients of these gray-reversed images were calculated and then binarized and eventually averaged.The gradient G(x，y)and its averageare given by the following equations:

where g is reversed gray value,and x and y are the pixel x-coordinate and y-coordinate,respectively.

According to the procedure for calculatingof the single interrogation region,temporal shadow images of the entire atomization fields were meshed to multiple interrogation regions,of whichwere obtained using an in-house code of image processing based on MATLAB.The temporal average value ofis given by the following equation:

where N is the frame number of the shadow images,and Δt is the time interval between two time-adjacent images.

Fig.8 shows the distribution offields using color contour.Based onfields,the center of atomization was targeted using iterative calculation.First,an original location(X0，Y0)was designated manually as shown in Fig.8(a).Second,(X0，Y0),as(Xn-1，Yn-1),was substituted into the following iterative equations:

3.Results and discussion

3.1.FFT analysis

In order to analyze the frequency response characteristics of the fluid film and atomization fluctuations,FFT was adopted to calculate the maximum amplitudes of the two kinds of fluctuations and their dominant frequencies.

Fig.9(a)shows the FFT maximum amplitudes of the fluid film fluctuations at four different H(5.0,10.1,15.1 and 20.0 mm)which is the vertical distance from the injector outlet as shown in Fig.5.Compared with the amplitudes at different vertical distances,increase of fluid film fluctuations along the injection direction was found apparently.As shown in Figs.5 and 6,it is indicated that there is an obvious klystron effect on the fluid film leading to the superposition of the fluid film eventually.The klystron effect ampli fies the effect of injection pressure drop fluctuations on atomization fluctuations.However,the klystron effect does not necessarily occur for the simplex swirl injector at any frequency.It is shown that the amplitudes increase with the growing fluctuated frequency in the region from 0 to 100 Hz and then decrease from 100 to 300 Hz approximately.

Furthermore,corresponding to the maximum amplitudes,the relative FFT dominant frequencies of fluid film fluctuations are shown in Fig.9(b).The dominant frequency of the fluid film fluctuation is strictly equal to that of the pressure fluctuation if the fluctuated pressure frequency is lower than about 250 Hz,and it is obviously lower than the fluctuated pressure frequency remaining between 70 and 170 Hz if the fluctuated pressure frequency is higher than about 250 Hz.It is further illustrated that the atomization of the simplex swirl injector can only respond to the pressure fluctuation under a limited frequency range from about 0 to 300 Hz.

Similarly,Fig.10(a)shows the FFT maximum amplitude of the atomization fluctuation(represented byGˉ(X，Y，t)shown in Section 2.3.2 in central region(targeted in Fig.8).Compared with the fluid film fluctuation,the amplitude of the atomization fluctuation features the similar varying tendency with the pressure fluctuation frequency.It is indicated that the forced fluctuation of the fluid film does lead to the forced atomization fluctuation with the klystron effect.

Uniformly,the FFT dominant frequency of the atomization is shown in Fig.10(b).Slightly differing from the fluid film fluctuation,the responsive frequency of the atomization is further narrowed to the range from 0 to 230 Hz.Besides,the atomization frequency does not always conform to the fluctuated pressure frequency in the low-frequency range.If the fluctuated pressure frequency is lower than 30 Hz,the dominant atomization frequency could be higher than the fluctuated pressure frequency sometimes.

According to the results shown in Figs.9 and 10,both liquid film and atomization fluctuations are sensitive to fluctuated frequencies.There is no response of liquid film and atomization to pressure fluctuations if fluctuated frequencies are larger than about 250 Hz,even though pressure fluctuation amplitudes are of the same order magnitude as the average injection pressure drop.These dramatic dynamic characteristics of simplex swirl injectors could attribute to the specific liquid film con figuration which directly influences the primary atomization process.

3.2.Breakup length

The pressure fluctuation not only forces the atomization of the simplex swirl injector to be periodic,but also changes the breakup length of the simplex swirl injector.In this study,the breakup length is defined as the vertical distance between the central location of atomization(Xc，Yc)(mentioned in Section 2.3.2)and the injector outlet.As shown in Fig.11,the breakup length is reduced significantly in the frequency range from 100 to 200 Hz.At the fluctuated pressure frequency 145 Hz,the breakup length reaches to the minimum,which is approximately 60%of the ordinary breakup length without pressure fluctuation.The breakup length is not affected if the fluctuated pressure frequency is higher than about 250 Hz.As mentioned above,the breakup length features the fairly similar varying tendency to the fluid film fluctuation and the atomization fluctuation.It is illustrated that the klystron effect could lead to the advanced breakup of the liquid film and its intensity determined the reduced magnitude of the breakup length.

The advanced breakup of the liquid film results in the advanced and more concentrated primary atomization process,causing the advanced and more concentrated collective heat release.Conversely,this heat release could lead to more obvious influences on the injection and atomization processes,since it is closer to injectors.This interaction between atomization and heat release could result in occurrence of combustion instabilities.

3.3.Correlation analysis

In order to analyze the response of atomization to pressure fluctuations,correlation analysis was used.Correlation value is given by the following equation:

where Cor is the correlation value of A and B,T is the period of the pressure fluctuation,t is the phase difference between A and B,and Ntis the number of sampling.

For the sake of assessing the dependency of the atomization on the pressure fluctuation,the correlations between the pressure fluctuation and the liquid film and atomization fluctuations were calculated.

Fig.12 shows three correlations,between the pressure fluctuation and sine function that has the same frequency as the pressure fluctuation,between the liquid film fluctuation and sine function,and between the pressure fluctuation and the liquid film fluctuation.The pressure fluctuation has a favorable periodicity,since the correlation between the pressure fluctuation and sine function remains above 0.7.It is certified that periodic pressure fluctuations are available for all frequencies from 0 to 800 Hz.The other two correlations are larger than 0.6 in the frequency range from 0 to about 200 Hz and drop rapidly if the fluctuated pressure frequency is higher than 200 Hz.The two correlations both decrease to about 0.2 if the fluctuated frequency is higher than about 250 Hz.That means that the liquid film fluctuation has a strong correlation(＞0.6)with the pressure fluctuation and a favorable periodicity merely in the frequency range from 0 to about 200 Hz and the liquid film has no response to pressure fluctuations if fluctuated frequencies are larger than 250 Hz.The liquid films ejected from simplex swirl injectors could be considered to be low-pass filtering elements.Fig.13 shows three correlations,between the pressure fluctuation and sine function,between the atomization fluctuation and sine function,and between the pressure fluctuation and the atomization fluctuation.Being similar to liquid film fluctuation,the atomization fluctuation also has a strong correlation(＞0.6)with the pressure fluctuation and a favorable periodicity but in a more narrow frequency range approximately from 80 to 200 Hz.Higher frequency fluctuations could be suppressed further during liquid film fluctuation process and it could lead to a more narrow frequency range for periodic primary atomization.By and large,the correlation between the atomization fluctuation and the pressure fluctuation increases with the fluctuated frequency from 0 to 100 Hz and remains above 0.7 from 100 to 200 Hz.The atomization fluctuation and the pressure fluctuation lose their correlation rapidly if the fluctuated pressure frequency is higher than 200 Hz.

According to Figs.12 and 13,liquid film and atomization fluctuations have similar correlation relation with pressure fluctuations.It is apparent that periodic atomization fluctuations rely on periodic liquid film fluctuations.Due to the low-pass filtering effect of liquid films,atomization could only respond to pressure fluctuations in a certain low-frequency range.Atomization and pressure fluctuations have no stable phase relation in frequency ranges larger than 300 Hz.The primary atomization processes remain their intrinsic stochasticity under high-frequency pressure fluctuations.It is possible that the stochastic atomization process hinders periodic heat release and positive Rayleigh index between pressure fluctuations and heat release rates.It is known that positive Rayleigh index is the necessary condition to combustion instabilities.It is worth noting that the frequency limitation of periodic primary atomization just corresponds to hot fire tests of combustion instabilities in previous studies.4,13

In order to demonstrate that the frequency limitations of these correlations are ascribed to the atomization dynamic characteristics of the simplex swirl injector itself rather than the dissipative effect of the pipe line system on high frequency pressure fluctuations,a contrast atomization experiment of a like-on-like impinging jet injector element was conducted.The injector element has two orifices of 1 mm diameter and an impingement angle of 60°.In the atomization experiment of the impinging injector,the pressure fluctuations of 10 different frequencies from 223 to 2230 Hz were generated in the feed line.The average injection pressure drop of all tests for the impinging jet injector element was 1 MPa.

As shown in Fig.14,the atomization of the impinging jet injector element has obvious periodicity.The klystron effect leads to periodic dense droplet clusters.Compared with the simplex swirl injector,the impinging jet injector element is able to respond to the pressure fluctuations of much higher frequencies.

Fig.15 shows that the atomization of the impinging jet injector element is able to response to the pressure fluctuation in a wide fluctuated frequency range from 223 to 2230 Hz.The correlation between the atomization and the pressure fluctuation has no decreasing tendency with increasing frequency,which reveals huge differences between the impinging jet injector element and the simplex swirl injector in respect of dynamic responsive properties using the same supply system.

4.Conclusions

The dynamic characteristics of the atomization of simplex swirl injector were studied experimentally.A hydrodynamic mechanical pulsator was used to create pressure fluctuation of a wide range through the injector.The shadow photography technique was used to acquire temporal spray and atomization images.An in-house code of image processing based on MATLAB was developed to capture the edges of fluctuated liquid films and to locate the atomization zone and semiquantify droplet number densities automatically.The fluctuated value of each parameter,including the pressure,liquid film positions,atomization in the central region,could be obtained when the pressure fluctuation was generated in the pipe line of the injector.The frequency response characteristics of the fluid film and atomization fluctuations were obtained.The correlations between the pressure fluctuation and the fluid film and atomization fluctuations were analyzed.

First of all,the FFT maximum amplitudes and dominant frequency of the fluid film and atomization fluctuations at different distances from the injector outlet were calculated as a function of the fluctuated pressure frequency.A responsive frequency cut-off phenomenon was obviously found for the atomization of simplex swirl injector.The most sensitive frequency range is about from 100 to 200 Hz.The cut-off frequency is about250 Hz,for the fluid film and the atomization.A slight discrepancy of cut-off frequency between fluid film and atomization could attribute to the depression effect of liquid film on high-frequency vibration.

Moreover,the breakup length defined as the vertical distance from the central location of atomization to the injector outlet was examined as a function of the fluctuated pressure frequency.The reduction of the breakup length was quantified and analyzed.The advanced breakup results from the klystron effect,whose intensity determines the reduced length.

Finally,the cross-correlation calculation was adopted to investigate the atomization periodicity of the simplex swirl injector and its dependency on the pressure fluctuation.Also,the frequency cut-off phenomenon was obvious and similar to the responsive frequency for the simplex injector.The effects of the fluctuated pressure amplitude and pipe line system on the cut-off phenomenon were excluded via the contrast experiment of the impinging jet injector element.For the simplex swirl injector,the question whether the atomization responds to the pressure fluctuation merely relies on the fluctuated pressure frequency if the fluctuated pressure amplitude is high enough.It is an intrinsic property of injectors.This result corresponds to low-frequency combustion instabilities that ever occurred in pre-combustors of LOx/kerosene rocket engines in the development stage.Compared to impinging injectors,it is possible that other simplex liquid swirl injectors also feature similar atomization dynamic characteristics as a low-pass filtering element in rocket engines to suppress high-frequency combustion instabilities.

Acknowledgments

This work was supported by the National Natural Science Foundation of China(Nos.11502186 and 51606138);the National Key Basic Research Program of China(973 Program)and National Key Scienti fic Instrument;the Equipment Development Projects of China (No.2012YQ04016408).

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