Aircraft and missiles moving in the atmosphere with supersonic velocities form air flows of a complicated spatial structure, in which compression shocks of different configurations and intensities arise. Since an air flow is strongly spatially inhomogeneous, the air density in the flow experiences random pulsations much exceeding turbulent pulsations of the air density in the atmosphere. Mean characteristics of supersonic flows are investigated rather well both theoretically and experimentally, but characteristic properties of turbulence in a supersonic flow are studied insufficiently.
To study turbulence in supersonic flows, the real-time measurements of the value and spectral composition of pulsations are required. Currently used sensors distort the flow structure and often have the low response rate. The dynamics of fluid or gas flows can also be studied and the turbulent velocity field in fluid and gas flows can be visualized with the use of noncontact optical methods. Among these are speckle photography and speckle interferometry methods (Fomin, 1998), in which the source of information is represented by intensity fluctuations of the laser radiation passed through the flow and a diffuse plate, as well as Doppler methods (laser Doppler anemometers (LDA)) (Abbrecht et al, 2003) and Particle Image Velocimetry (PIV) methods (Raffel et al, 2007) based on the measurement of velocities of microparticles suspended in a flow. LDA and PIV devices are very expensive and difficult in use. They are successfully used mostly for the investigation of fluid flows and subsonic gas flows. In the supersonic gas dynamics, their application is limited owing to such factors as increased requirements to the instrumentation (laser pulse energy, operation rate and sensitivity of recording instruments) and still open problems of velocity relaxation of tracing particles. In the seeding process, the tracing particle sizes are not identical and their concentration is not always uniform in a flow and this inevitably leads to the loss in accuracy of measurements.
The widely used methods of shadow visualization (Schlieren photography) do not allow the spatial spectrum of refractive index fluctuations to be determined from the obtained images. Shadow images are integral characteristics of the refractive index in the entire radiation propagation path, and the spatial distribution of the refractive index in different flow layers cannot be reconstructed from them. In this connection, it is interesting to study possibilities of the remote diagnostics of gas flow turbulence from the intensity fluctuations of the optical radiation crossing a flow. This method does not require the presence of scattering particles and diffusors and allows the spatial structure of pulsations in a flow to be studied at dimensions of the probing beam much smaller than the flow transverse size.
In this research field, intensity fluctuations of the laser beam passed through a model plane layer of a turbulent flow and the beam propagating through a jet of a jet engine have been studied experimentally ((Joia et al, 1997, 1995) and (Dmitriev et al, 2004, Sirazetdinov et al, 2001), respectively). However, these results (Joia et al, 1997, 1995, Dmitriev et al, 2004, Sirazetdinov et al, 2001) correspond to subsonic velocities of studied flows, and for their interpretation it is sufficient to use the results of the theory of incompressible fluid mechanics (Monin & Yaglom, 1971, 1975 ) and optical radiation propagation in such turbulent media (Gurvich et al,1976, Zuev et al, 1988). In case of supersonic flows, for the interpretation of measured results, it is necessary to take into account not only temperature fluctuations, but also pressure fluctuations, as well as the strong spatial inhomogeneity of the flow. In recent years, the theoretical papers were published, in which the authors undertook attempts to construct an electrooptical model of parameter fluctuations in compressible gas flows (Offer Pade, 2001, 2003, 2004, 2005). However, the results obtained can be considered only as an initial stage of the study of radiation propagation in supersonic flows. In (Offer Pade, 2001, 2003, 2004, 2005), only the variance of phase fluctuations of an optical wave passed through a supersonic flow was calculated and the variance of gas density fluctuations in a flow was estimated. The calculations were based on the Fluent Dynamic 6 turbulence model.
The existing theoretical models of turbulence of compressible flows can be found, in particular, in (Yoshizawa, 1995, Smits & Dussauge, 1996, Canuto, 1997). However, in this field there is no versatile model similar to the case of developed turbulence of incompressible flows (Monin & Yaglom, 1971, 1975 ).
This chapter presents the results of both experimental and theoretical studies of optical turbulence in supersonic flows. The experiments on laser beam propagation through supersonic flows were conducted in T-326 and T-313 wind tunnels of the Institute of Theoretical and Applied Mechanics of the Siberian Branch of the Russian Academy of Sciences (ITAM SB RAS). The theory of laser beam propagation through a supersonic flow was based on dynamical models of the Fluent 6.0 software. The transport equations for calculation of turbulent parameters were selected according to the
2. T-313 and T-326 wind tunnels
The batch-operated T-313 and T-326 wind tunnels use compressed air for their operation. Air is compressed by high- and medium-pressure compressors at a turbocompressor station. After pre-drying, air enters high- (up to 200 bar, volume of 96 m3) and medium-pressure (up to 18 bar, volume of 5600 m3) cylinders. The modern automated control system provides the trouble-proof operation of the station, gathering of information about the equipment functioning and volumes of generated compressed air and circulated water (Garkucha et al., 2009).
2.1. T-313 supersonic wind tunnel
The batch-operated T-313 supersonic wind tunnel is operated since 1965 and has the closed working part with the rectangular 0.6 0.6 2 m cross section (Fig. 1). The range of Mach numbers, which can be obtained in this tunnel, is 1.75 - 7. The discrete variation of the Mach number
A gas-cylinder station with the maximal air pressure up to 18 bar allows the working conditions to be maintained for about 10 min with the extreme Reynolds number Re 8 107 m-1 at the direct-flow operation and the Mach number of the flow
The setup is equipped with two pressure regulation systems to maintain the preset pressure in the settling chamber at the operation in the cold or hot channel. The regulation systems are based on the application of specialized chokes moved by hydraulic actuators, which are controlled by a pneumatic hydraulic control. The air exits the gas-dynamic channel of the setup through the silencing chamber installed beyond the aerodynamic hall. Each of the two ejectors has individual regulation systems.
The setup is equipped with 4-component aerodynamic mechanic external-type weighting scales, which allow the measurement of aerodynamic characteristics of models such as resistance force, lift, pitching moment, and rolling moment. The angle of attack of the model during the test can be changed manually or automatically by a preset program in a range from 5 to +22. The application of intramodel strain-gage weighter is possible.
To visualize the flow field near the model, the working part of the tunnel is equipped with optical windows and the coaxial IAB-451 Maksutov-system optical shadow device with the observation field 230 mm in diameter. The methods of colored oil visualization of limiting flow lines on the surface and the laser knife method are also used.
The experiments have determined that the degree of nonuniformity of the Mach number distribution in the zone of models was 1% in the supersonic velocity range and 1.5% at hypersonic velocities. The level of mass-flow pulsations varied depending on Mach numbers from 0.27% to 0.86%.
The automation system ensures the real-time acquisition of experimental data simultaneously from a large number of channels, the graphic presentation of measured results, and the primary data processing. The multiprocessor automation system for supersonic and hypersonic periodic wind tunnels is developed in accordance with the following principles: unification of the automatic data acquisition at the level of hardware and software interfaces and the possibility of fast setting for particular experimental conditions.
The T-313 supersonic wind tunnel allows the following experimental investigations of the gas-dynamic structure of complex turbulent supersonic flows:
Study of stationary aerodynamic characteristics of aircraft models;
Study of the structure of detached supersonic flows with the measurement of the distribution of the average pressure and pressure pulsations on the model surface;
Measurement of the pressure distribution in the boundary layer of the model;
Study of the structure of supersonic flows with the use of optical visualization methods (shlieren visualization of optical inhomogeneities of the flow, laser knife method, colored oil visualization of limiting flow streamlines as a model surface is approached);
Study of the problem of sonic boom level decrease at the flow of an aircraft flying with supersonic velocity;
Study of interference of shock waves;
Study of the mechanism of interaction of an intense tip vortex with a shock wave;
Study of the interaction of supersonic jets with a supersonic wake flow;
Study of flows in internal channels of super- and hypersonic aerojet engines, as well as study of problems of the integration of a planer and an engine of promising aircraft.
2.2. T-326 hypersonic wind tunnel
The batch-operated T-326 hypersonic wind tunnel (Fig. 2) is in work since 1971. Its working part is made as an Eiffel’s test chamber.
The setup is equipped with profiled axisymmetric nozzles with a section diameter of 200 mm. The range of feasible Mach numbers is
in the settling chamber is
The tunnel is equipped with a slit ejector with the high degree of compression, which ensures the setup operation at rather small Reynolds numbers. The ejector is connected to a medium-pressure system, and the main flow comes from a high-pressure gasgolder chamber through the heater. In this setup, the hypersonic flow with the Mach number
these conditions, to prevent the nitrogen and oxygen condensation in the flow, the air should be heated to the Pitot temperature no less than 400 K according to Daum recommendations.
The working part of the wind tunnel is equipped with optical windows. In addition, the wind tunnel is equipped with the IAB-451 Maksutov-system optical shadow device. The automatic data acquisition system allows one to record gas-dynamic flow parameters and readouts of pressure and temperature sensors set on the model surface.
The setup design allows one to study the shock-wave structure of supersonic anisobaric jets with the use of a specialized jet unit installed in place of the supersonic nozzle. The settling chamber of the jet unit is a tube with an inner diameter of 113 mm and has a mounting seat for changeable nozzles. The jet flows into the working chamber. The nozzle section falls within the field of view of optical windows with a diameter of 200 mm. The pointing device allows the total-pressure sensor (or other probe) to be moved in the jet flow field with the high positioning accuracy. The supersonic jet flows into the pressure chamber and is emitted into the silencing shaft through the supersonic diffusor of the exhaust line of the wind tunnel.
The T-326 hypersonic wind tunnel of the ITAM SB RAS allows the following types of experiments to be conducted: study of the laminar-turbulent transition at the hypersonic flow speed; study of heat exchange characteristics, study of flow pulsations in the anterior detachment zone; study of the structure of detached flows at the high supersonic flow speed with the measurement of the distribution of the average pressure and pressure pulsations on the model surface, as well as study of the shock-wave structure of the flow at the initial part of supersonic anisobaric jets.
3. Experimental setup for laser beam transmission through supersonic flow and acoustic measurements
3.1 Experimental setup based on T-326
Experimental investigations on the T-326 wind tunnel were conducted with the use of the jet unit with the convergent nozzle, whose section diameter was
In the experiments, the laser radiation passed through the jet in the transverse direction at different distances
The acoustic measurements were conducted in the frequency range 20 Hz-100 kHz with the use of 5 microphones 6 mm in diameter for three different configurations of microphone arrangement with respect to the jet (Fig. 3):
in parallel to the jet at a distance
around the circle 140 mm in radius (with an interval of 45) at a distance
horizontally across the jet along the axis
The measured results were used to calculate the value and spectral density of the sonic pressure, as well as mutual correlation functions of the sonic wave between the fixed microphone and each of 4 movable microphones.
In some experiments, the convergent nozzle with chevrons, which changed the flow structure and, consequently, the turbulence strength and the acoustic field, were used.
3.2. Experimental setup based on T-313
In the experiments with the T-313 wind tunnel, the supersonic flow (SF) above a model of an aircraft element was studied by passing the laser beam through the flow. A plane wing model was used. The angle of attack of the wing (slope with respect to the SF axis) varied from -4.7 to 19.7 toward the flow. Three lasers were used. The data recording started once the steady-state regime was established in the flow. The schematic of the optical experiments is shown in Fig.4.
The following parameters were recorded:
Intensity fluctuations of the laser radiation in the part of the laser beam separated by the mirror M (PMT 1 with a diaphragm d4 = 0.2 mm and laser L1 with a beam D1 = 90 mm in diameter).
Fluctuations of displacements of the laser beam image (system tracing the image centroid based on a dissector tube and laser L1) at the focus of an objective with a focal length of 450 mm and a diaphragm d1 = 10 mm. The signal digitization rate was 100 kHz, and the frequency range of the system was 0-1.5 kHz along every coordinate.
Fluctuations of the laser beam direction (four-quadrant coordinate photodiode CD and laser L2 with the beam D2 = 40 mm in diameter). The digitization rate of a signal from each element was 250 kHz. A diaphragm d2 = 2 mm in diameter was set at a distance of 700 mm in front of CD.
The data recorded were used to calculate spectral functions and relative variances of signal fluctuations.
4. Model of optical turbulence of supersonic flow
To develop a model of optical turbulence in a supersonic flow, it is necessary to know the spatial distribution of the gas density and the gas flow velocity. In addition to average values of the density and flow velocity, we also should know the characteristics of turbulent pulsations of these parameters, such as the variance and spectra of the density and the velocity components.
Average values of the flow parameters are usually determined with the system of averaged Navier—Stokes equations. The system is closed through the introduction of additional equations for the variance and the mutual correlation of fluctuations of medium parameters. There are several semiempiric models of turbulence, which allow the parameters
Within the framework of these models, we have derived the transport equation for the variance of fluctuations of the gas density from the equations proposed in (Yoshizawa, 1995). The equation derived looks as
where ρ is the mean gas density, the convective transfer of the density variance has the velocity equal to the average flow velocity vector u, and the turbulent kinematic viscosity serves as the diffusion coefficient. The sources in the right-hand side of Eq. (1) show that density fluctuations are generated by the inhomogeneity of the average density and gas velocity components, and the dissipation processes are determined by the dissipation of the kinetic energy of turbulent vortices (/
In flows with velocities ~10 M and lower, the effects associated with the gas compressibility are significant for the calculation of average jet parameters, but in the turbulent component they manifest themselves only slightly (Smits & Dussauge, 1996). Therefore, the spectral distribution of density fluctuations correspond to the Kolmogorov—Obukhov model. The main parameters of the model, namely, the structure characteristic of the refractive index fluctuations and the inner scale of turbulence
where is the air kinematic viscosity,
In the jet in the jet module of the T326, we can see elements (barrels) formed by the characteristic configuration of density and velocity stepwise changes (hanging and reflected), the Mach disk, where the flow velocity decreases down to subsonic values, and the outer boundary of the jet. This repeated structure can be seen over several tens of centimeters from the nozzle (4 to 5 barrels). At longer distances, the jet structure blurs due to the flow turbulization, generation of acoustic noise, and decrease of the mean flow speed down to subsonic values. The internal structure of barrels is shown in Fig. 5a. We can separate the following elements:
Along the outer surface of the jet, there is a gradually widening mixing zone (zone 5), in which the velocity and the velocity gradient achieve their maximal values. Over the jet cross section, the mean velocity and pressure vary depending on the distance of the cross section plane from the nozzle (zones 1-3).
Along the jet axis, the barrel-like structures repeat, their number is determined by the initial velocity of the flow. In the mean, the turbulence strength is minimal in the first barrel and grows up in the following barrels.
The third region is the near-axis area 30-40 mm in diameter with the supersonic velocity of the flow, high pressure and density and their gradients (zones 1, 4).
To estimate perturbations induced by the supersonic flow in the optical wave propagating through it, we have simulated numerically air flows arising in the jet unit of the wind tunnel with the convergent nozzle having a diameter
5. Methods of computer simulation of laser beam propagation through supersonic flow and retrieval of the parameters of the flow optical turbulence
Laser radiation distortions caused by regular and random inhomogeneities of air density in the supersonic flow can be used as a source of information on optical parameters of the flow. In the general case, the problem of reconstruction of optical model parameters is a complex mathematical problem. However, for certain flow configurations it can be solved rigorously. In particular, it is possible for axially symmetric flows.
Let an axisymmetric supersonic jet propagate in the positive direction of the axis
which depends mostly on the distribution of the mean gas density ρ(r,
Assuming that the beam radius is small compared to characteristic scales of variation of jet parameters, we can consider the dependence of measured parameters (3, 4) on the impact parameter
where is the distance to the jet axis. The mean air density in a flow is directly proportional to the mean refractive index.
For the regime of weak intensity fluctuations (Zuev et al., 1988) wich realized for the laser beam passed through the jet, we can obtain the equation analogous to Eq. (5) for the structure characteristic of the refractive index fluctuations in the axisymmetric flow
Thus, if a narrow laser beam propagates repeatedly through the jet in some cross section
The algorithms of reconstruction of flow parameters have been tested in a series of closed numerical experiments. The geometry of the experiments corresponded to the Т-326 jet unit. We considered the flow of the supersonic air jet into a half-space filled with air at an atmospheric pressure and temperature of 300 K, as well as the airflow of a conic model of an aircraft nose cone. For the simulation of the laser beam propagation, we used the method of splitting by physical factors (Kandidov, 1996). For each given cross section
Figure 6 shows the results of reconstruction of parameters of the optical model for the free jet (a) and the jet flowing over the conic model (b). The good agreement between the reconstructed values and initial data of the optical model of the flow both in the region of the turbulent decomposition of the jet and at the initial part of the jet with pronounced stepwise changes of averaged parameters demonstrate the possibility of the contactless determination of supersonic jet characteristics by optical methods.
6. Experimental and theoretical study of optical turbulence in supersonic flow of the T-313 and T-326 wind tunnels
6.1. T-326 wind tunnel
The propagation of laser radiation through a supersonic jet differs significantly from the case of atmospheric propagation. In the atmosphere, mean characteristics and turbulence on the path vary quite smoothly. In the jet, to the contrary, we observe strong gradients of the mean pressure and velocity (Fig. 5), and, consequently, the density and the refractive index of air. We should also take into account the propagation of probing beam outside the jet, where the sonic waves generated by the jet can affect significantly the beam.
6.1.1. Laser radiation intensity fluctuations
First experiments on the laser beam propagation through the jet used the scheme with reflection. The laser radiation passed through the Eiffel’s test chamber below the jet, reflected from a mirror 300 mm in diameter, and came back to a photodetector through the jet. The FFT method was used to calculate the spectral function
The spectra of intensity fluctuations measured at
In the further experiments, the beam path length beyond the jet was much shorter to minimize the effect of acoustic noise on intensity fluctuations of the probing beam.
Spectral functions of intensity fluctuations of the probing beam without influence of acoustic waves at different
At a distance
For the nozzle with chevrons, the behavior of the intensity spectrum of the probing beam remains the same as for the nozzle without chevrons.
Figure 8a shows the dependence of the relative variance of intensity fluctuations of the probing beam 2 on the distance
Assuming that turbulent intensity fluctuations of the probing laser beam can be described based on the Kolmogorov model of turbulence and using for the intensity relative variance
the increase of
The dependence of the variance of the beam intensity measured at different distances from the jet axis was then used to reconstruct the radial dependence of the structure characteristic of the refractive index in the jet without chevrons with the use of the reconstruction algorithm (6) modified for a quickly divergent beam. The results of the reconstruction shown in Fig. 9 are in a good agreement with the dependences drawn based on the optical model of the jet.
6.1.2. Acoustic measurements
The acoustic measurements on the jet unit of the T-326 wind tunnel with the use of microphones (Fig. 3) have shown that at
If a nozzle with chevrons is used in the jet unit (Fig.10b), then the separate harmonic at the frequency
To determine the form of the acoustic wave, we calculated the mutual correlation of acoustic signals measured by microphones М0, …, М4. As an example, Fig. 11 shows the coefficients of mutual temporal correlation of acoustic signals between the microphones in configuration 1 (Section 3.1, Fig. 3).
It can be seen from Fig. 11 that the mutual correlation coefficients at
Phase shift of the acoustic wave
The phase shift of the acoustic wave was determined from the position of the maxima of the correlation functions of М0, М1, М2, М3, М4 on the time scale, as shown in Fig. 11. The results of the determination of the phase shift at different configurations of the microphones (Fig. 3) are shown in Fig. 12.
For configuration 1, the phase shifts were determined with respect to the microphone installed at a distance of 135 mm from the nozzle. It follows from the data presented that the phase shift increases linearly as the distance to the nozzle shortens and has a minimum at a distance of 225 mm. To interpret experimental data, we have estimated the phase shift between the microphones on the assumption that the generated acoustic wave is spherical. The phase shift was calculated from the difference in distances
It can be seen from Fig. 12 a that the calculated data are close to the experimental dependence. This suggests that the sound source is at a distance of about 225 mm from the nozzle, and at a distance of 135 mm from the jet axis the acoustic wave is close to a spherical one. The phase shift between the microphones set at distances of 225 and 25 mm from the nozzle is 2.75 or 1.4.
The measurements with configuration 2 show that the phase shifts between microphone M0 and the others are close and range within 0.7–0.9. The conclusion about the close phase shifts between the microphones is also valid for configuration 3 at measurements at a distance
Figure 13 shows the results of numerical simulation of the acoustic field generated by the supersonic jet (Bodony, 2005). It can be seen that the source of the acoustic wave is near the area of the transition from supersonic flow velocities to subsonic ones. At some distance from the source, the acoustic wave becomes close to a spherical one and the phase shift is observed in the wave front above and below the jet. This is in a qualitative agreement with the experimental data in Fig. 12.
For the more detailed comparison, Fig. 13 shows the approximate (with respect to the simulated acoustic field) arrangement of the microphones along the jet in accordance with configuration 1 (Section 3.1) and the estimated phase of the simulated acoustic field at different distances along the jet. One can see that the phase of the acoustic wave near the beginning of the jet = 2.7 is close to the experimental value = 2.75 at a distance of 25 mm from the nozzle. The arrangement of the microphones was determined with respect to the nozzle diameter
6.2. T-313 wind tunnel
6.2.1. Laser radiation intensity fluctuations
Figure 14 shows the spectra of intensity fluctuations
Low-frequency fluctuations are caused by the effect of acoustic noise generated by the supersonic flow above the model. The wavelength of the generated sound can be estimated as
The dependence of the relative variance of intensity fluctuations in the probing laser beam on the angle of attack is shown in Fig. 15. In this figure, the vertical axis is divided into two sections having different scales for the presentation of significantly different values. It can be seen from the figure that incoming flow is actually laminar, and the relative variance of intensity fluctuations is only 2 3 10 5 in this case. Above the wing, the relative variance is four orders of magnitude higher, thus indicating the significant turbulization of the flow above the model.
6.2.2. Fluctuations of the laser beam propagation direction
The spectra of fluctuations of the laser beam propagation direction in the supersonic flow in T-313 above the model were measured by a quadrant detector (QD) by the scheme shown in Fig. 4.
It follows from the analysis of the measurement results that the spectra of beam propagation direction fluctuations along the
In the high-frequency region
The frequency of the maximum in the spectrum of laser beam image jitter recorded by the dissector tube (Fig. 4) is 250-300 Hz along the horizontal axis and 200-270 Hz along the vertical axis at angles of attack 15 and increases sharply up to 500 Hz at an angle of attack of 19.7. These fluctuations are possibly caused by the vibration of the wing under the effect of the incoming flow. The standard deviation of the image jitter is 12-17 arc sec. and is maximal at an angle of attack of 15.
Thus, the experimental results obtained show that the spectra of intensity fluctuations of the probing laser beam has roughly the same form both in the case of the supersonic jet generated by the T-326 jet unit and in the case of a model wing blown by a supersonic flow in T-313. The maximum of turbulent intensity fluctuations in the both cases falls on frequencies in the region of 50 kHz and higher. The estimates based on the Kolmogorov—Obukhov model of developed turbulence show that the structure characteristic of the refractive index in the studied supersonic flows is several orders of magnitude higher than in the atmosphere.
The optical model of turbulence developed on the basis of Fluent-6 allows one to simulate the propagation of a probing laser beam in supersonic flows with arbitrary geometric and thermodynamic parameters. The results of simulation and reconstruction of optical model parameters from simulated data on the probing of a supersonic jet in T-326 are close to the experimental findings.
From the results of acoustic measurements as well as from the probing laser beam intensity fluctuations, it follows that the supersonic jet generates sound. The source of sound lies in the region of the transition from the supersonic flow speed to the subsonic one. For the jet unit of the T-326 wind tunnel, the sound source is on the jet axis at a distance of 225 mm from the nozzle. With the distance from the source, the generated acoustic wave becomes close to a spherical one.
The work was financially supported in part by the Russian Foundation for Basic Research, grant 11-08-01059.