Experiments in Fluids 37 (2004) 438–454 DOI 10.1007/s00348-004-0828-9
Quantitative visualization of compressible turbulent shear flows using condensate-enhanced Rayleigh scattering J. Poggie, P. J. Erbland, A. J. Smits, R. B. Miles
438 Abstract This paper describes several flow visualization experiments carried out in Mach 3 and Mach 8 turbulent shear flows. The experimental technique was based on laser scattering from particles of H2O or CO2 condensate that form in the wind tunnel nozzle expansion process. The condensate particles vaporize extremely rapidly on entering the relatively hot fluid within a turbulent structure, so that a sharp vaporization interface marks the outer edge of the rotational shear layer fluid. Calculations indicate that the observed thin interface corresponds to a particle size of 10 nm or less, which is consistent with optical measurements, and that particles of this size track the fluid motions well. Further, calculations and experiments show that the freestream concentration of condensate required for flow visualization has only a small effect on the wind tunnel pressure distribution. Statistics based on the image data were compared to corresponding results from probe measurements and agreement was obtained in statistical measures of speed, scale, and orientation of the large-scale structures in the shear layer turbulence. The condensateenhanced Rayleigh scattering technique is judged to be a useful tool for quantitative studies of shear layer structure, particularly for identifying the instantaneous boundary layer edge and for extracting comparative information on the large-scale structures represented there.
Received: 9 February 2004 / Accepted: 2 May 2004 Published online: 2 July 2004 Springer-Verlag 2004 J. Poggie (&), P. J. Erbland Aeronautical Sciences Division, Air Vehicles Directorate, Air Force Research Laboratory, Wright-Patterson AFB, Ohio 45433, USA E-mail:
[email protected] A. J. Smits, R. B. Miles Department of Mechanical and Aerospace Engineering, Princeton University, Princeton, New Jersey 08544, USA
We would like to acknowledge the work of several collaborators who do not appear in the list of authors: D. R. Smith carried out the shock generator experiments and the single-pulse Mach 3 boundary layer visualizations, S. Cogne and J. Forkey obtained the double-pulse images of the Mach 3 boundary layer, and W. Konrad and T. Nau performed the simultaneous hotwire/laser scattering experiments. Technical support was provided by R. Bogart, W. Stokes, and P. Howard. This work was funded in part by grants from the Air Force Office of Scientific Research and the National Aeronautics and Space Administration Langley Research Center. This paper is a work of the U.S. Government and is not subject to copyright protection in the United States.
1 Introduction A striking feature of many high Reynolds number, turbulent flows is the sharp boundary that exists between the irrotational freestream fluid and the vortical flow within a turbulent shear layer (Corrsin and Kistler 1954). Largescale turbulence structures (of the order of the boundary layer thickness, d) distort this interface, engulfing irrotational freestream fluid, and stretching it into thin sheets between turbulent regions. Enhanced by the concomitant increase in the surface area of the interface, viscous diffusion acts at the Kolmogorov length scale to spread vorticity, and, thus, cause the growth of the shear layer. Due to this role in the process of shear layer growth, d-scale turbulence structures have received considerable attention in both subsonic (Robinson 1991) and supersonic flow (Spina and Smits 1994; Smits and Dussauge 1996). A variety of experimental techniques have been successfully applied to such work, but the present paper will focus on a flow visualization method based on Rayleigh scattering from nm-scale particles of condensate. In this technique, a small quantity (parts per million concentration) of a condensable vapor (here, water or carbon dioxide) is introduced into the air supply of a supersonic or hypersonic wind tunnel. As this vapor undergoes the nozzle expansion process, it condenses into solid-phase clusters of several molecules. A laser is focused into a sheet in the wind tunnel test section and the flow is imaged by recording the light scattered by the particles of condensate. The condensate particles vaporize again when the temperature is sufficiently high, such as downstream of a shock wave or within a shear layer. Because the particles are extremely small, they vaporize rapidly, and the region of vaporization appears as a sharp interface in flow images. In initial work, the particles and the vaporization process were considered an impediment to direct measurements of air density (Smith et al. 1989; Shirinzadeh et al. 1991), but have since proved to be an excellent way to increase scattering signal levels and to mark the outer edge of a boundary layer or shear layer (Smith and Smits 1995). Here, this technique will be called condensate-enhanced Rayleigh scattering. The condensate-enhanced Rayleigh scattering technique is related to the traditional ‘‘vapor screen’’ method of flow visualization (Settles 2001), but differs from it in several ways important to our work on turbulent shear layer structure. The term ‘‘vapor screen method’’ is typically used to describe a technique in which relatively large quantities of water vapor are introduced into the
For the experiments in the Mach 3 tunnel, the scattering particles formed ‘‘naturally’’ in the nozzle expansion process due to condensation of residual water vapor. (Other constituents of air, such as O2 or CO2, may also contribute to these particles.) The water vapor content of the air in the storage tanks was about 14 ppm for these experiments. Additional seeding with CO2 was required for laser scattering experiments in the Mach 8 tunnel. A supply cylinder, containing liquid CO2 and pressurized using He, was connected to the tunnel air supply upstream of the heater. A liquid flow meter, in conjunction with pressure and temperature transducers, allowed continuous monitoring of the seed flow rate. The source of illumination for the scattering experiments were Nd:YAG lasers manufactured by Continuum, Inc. Experiments were carried out both in the green range (wavelength k=532 nm) and in the ultraviolet range (k=266 nm). Typical energy outputs were 220 mJ–290 mJ per pulse in the green range and 20 mJ–50 mJ per pulse in the ultraviolet range, at a repetition rate of 10 Hz, and with a pulse duration of several ns. The beam was typically focused into a sheet in the wind tunnel using long focal length cylindrical lenses. In some of the experiments, a molecular iodine filter was used to suppress background scattering and reflections in favor of the Doppler-shifted signal from the flow. This device consisted of a small cell containing iodine crystals and gas, maintained at a fixed temperature and pressure. Scattered light was viewed through windows in 2 the cell by an intensified camera. For further information Experimental facilities Experimental studies of a turbulent boundary layer and a on the iodine cell, see Forkey (1996), which describes its development and characterization. free shear layer were carried out in the Princeton UniThe video signal was usually recorded on VHS video versity’s 8 in·8 in Mach 3 blow-down wind tunnel (Bogtape, and later digitized using a computer frame-grabber donoff 1983; Vas and Bogdonoff 1971). This facility has three 902mm-long test sections, each with a square cross- card. section of 203 mm·203 mm. The pressure in the settling chamber was maintained at 0.689 MPa ±1% for all of the 3 experiments described in this paper. In a typical twoInteraction of condensate and flow minute run, the stagnation temperature was initially 290 K and dropped by about 8% over the run. Data were typically 3.1 acquired in a 20 s–40 s window within the run (20 s at Qualitative results 10 Hz imaging rate gives 200 images), for a 1%–2% drop As part of an early experimental program in the Mach 3 in stagnation temperature. The stagnation temperature wind tunnel (Smith et al. 1991), tests were conducted with was recorded during each run and the average value was an oblique shock generator with an adjustable flow turning used to reduce the data. Details of the boundary layer and angle. The shock generator was mounted on the wind shear layer experiments will be described later. tunnel ceiling, forming a planar oblique shock wave which Additional experiments were carried out in a flat-plate impinged onto the turbulent boundary layer on the tunnel boundary layer flow in the Princeton Mach 8 wind tunnel floor. Images from these tests provide an overview of the facility (Baumgartner 1997). The test section in this tunnel kind of results that have been obtained with the condenis cylindrical, 229 mm in diameter, and 2.0 m long. Tunnel sate-enhanced Rayleigh scattering technique. stagnation temperature is maintained during a run by a Examples of side-view Rayleigh scattering images obstorage heater consisting of coiled stainless steel pipe. This tained in this flow are shown in Fig. 1, and are labeled 1 device is preheated electrically before a run and delivers through 4 in order of increasing strength of the incident thermal energy to the flow while the tunnel is running. shock wave. The freestream flow direction is from left to Sub-atmospheric back pressures are provided by an ejec- right in each image. The (high-temperature) boundary tor system operating from the same high-pressure air layer on the wind tunnel floor is visible at the bottom of supply as the tunnels. Typical test conditions for the the field of view as a dark region with a convoluted edge, boundary layer experiments reported here were a stagna- whereas the freestream flow appears brighter. The incident tion pressure of 6.89 MPa (±2.5%) and a stagnation tem- shock is visible as a bright line extending from the top left perature of 825 K (±2.5%). to the bottom right of each image. The dark spot present in freestream flow by bypassing the wind tunnel drying system. This results in a higher density of condensate particles downstream of the nozzle and a much larger particle size than in the condensate-enhanced Rayleigh scattering technique, which introduces only parts per million of water vapor or carbon dioxide vapor. The particles resulting from the vapor screen method are typically of the order of the wavelength of the incident illumination, and, thus, are in the Mie scattering regime. Although larger particles produce more scattered light, they do not track the flow as well, nor do they vaporize as quickly. Both flow tracking and vaporization rate are key issues in the study of turbulent boundary layer structures, and will be examined quantitatively later. The present paper will review some of the work that has been done with the condensate-enhanced Rayleigh scattering technique. The experiments described here were carried out at the Princeton Gas Dynamics Laboratory between 1990 and 2000 in both supersonic (Mach 3) and hypersonic (Mach 8) wind tunnel facilities. Much of this work has previously been presented only in the form of theses, dissertations, or conference papers, and, thus, has not been available in an archival reference. This paper summarizes a large body of data and analysis, and, based on the collected results, makes the case that flow visualization based on condensate vaporization can be used for quantitative studies of large-scale structures in supersonic turbulent shear flows.
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Fig. 1. Experiments with obli-
que shock generator. Flow is from left to right. Images (1) through (4) show increasing incident shock strength
local temperature and flow velocity. The suitability of the condensate vaporization technique for a given flow condition depends on rapid vaporization, particle tracking of the flow, and minimal deviation from normal test conditions with the presence of condensation. These issues were modeled carefully in a study of the feasibility of seeding the Mach 8 tunnel with CO2 in order to carry out condensate-enhanced Rayleigh scattering visualizations (Erbland 2000). In this study, quasi-one-dimensional computations of the non-equilibrium condensation process were carried out and compared to experimental measurements of the wall pressure in the tunnel nozzle. The wall pressure taps were 0.81 mm in diameter and seven taps were located between the nozzle throat at x=0 m and the nozzle exit plane at x=1.2 m. The taps were sampled using a Scanivalve mechanical multiplexer system and MKS Baratron pressure transducers, with an overall measurement uncertainty of 1%. The computational model included the quasi-onedimensional forms of the mass, momentum, and energy conservation equations, as well as appropriate forms of the equations of state. The nucleation rate was computed using the Lothe-Pound model (Abraham 1974). The particles of condensed phase were assumed to have a uniform temperature equal to that of the local gas flow and their growth rate was determined from a free molecular flow model (Wegener et al. 1972), since the Knudsen number is typically Kn>10 for these particles. The resulting system of ordinary differential equations was solved using a fourth3.2 order Runge-Kutta algorithm. An effective area distribuQuantitative results The results from the shock generator experiments indicate tion, based on the wall pressure distribution predicted by that the distance between the onset of vaporization and the axisymmetric parabolized Navier-Stokes (PNS) computadisappearance of the condensate particles depends on the tions of the baseline nozzle flow, was interpolated to all the images is due to a defect in the image intensifier array (a burn mark), and the horizontal line present in some of the images is an artifact caused by a camera synchronization problem that was present in these early experiments. In the freestream flow, there is, in each case, an initial rise in scattering intensity across the incident shock, followed by a decrease in the scattering intensity further downstream. It appears that the density of scattering particles initially rises sharply due to the density jump across the shock, and then falls off more gradually as particles vaporize due to the increased temperature downstream of the shock. In images 2 through 4 of Fig. 1, an induced separation shock appears, produced by the interaction of the incident shock with the boundary layer on the wind tunnel floor. Images of this shock also show the pattern of a sharp increase in scattering intensity followed by a gradual dropoff, although the separation shock is sometimes obscured by particle-free fluid originating in the turbulent boundary layer. The region downstream of the shock appears darker as the shock strength increases, presumably because of the increased temperature and more complete particle vaporization in that region. In image 4, for example, the region downstream of the intersection of the incident shock and the induced separation shock appears quite dark relative to the flow upstream.
fourth-order accuracy in the calculations. A grid resolution study indicated that a 2,001-point grid correctly resolved the peak nucleation rate. Thermodynamic properties, such as enthalpy of sublimation and cluster surface free energy, were evaluated from curve fits available in the literature (Erbland 2000). Figure 2 presents some of the results, comparing measured nozzle wall pressures to values computed with the quasi-one-dimensional model for different seeding rates. Relatively good agreement is obtained between theory and experiment for seeding mass fractions of x0=0.0, 0.007 and x0=0.0157. Both pressure levels and onset of condensation are well predicted. The effect of the condensation on the flow is analogous to that of heat addition in the classical Rayleigh flow problem: the Mach number is driven down and the local pressure rises. The computations predicted a mean cluster radius of 2 nm– 3 nm, consistent with optical measurements that bounded the radius at less than 10 nm. The computations predicted a pressure rise of no more than 8% for the two lower seed mass fractions and a corresponding decrease in Mach number of no more than 7%. Thus, only a relatively small flow perturbation is introduced by seeding levels sufficient for flow visualization. Another important consideration is the cluster dynamic response. The clusters are expected to move in a rarefied, viscosity-dominated flow, as shown by the data in Table 1. For a nominal cluster diameter of dp=10 nm, the Reynolds number and Knudsen number based on diameter and freestream conditions are Re=0.13 and Kn=92, respectively. For a diameter an order of magnitude larger (100 nm), the corresponding numbers are Re=1.3 and Kn=9.2. Under such conditions, it is possible to show (Erbland 2000) that the particles have an exponential time response to a sudden change in flow velocity, with the following time constant:
sv ¼
qp dp2 18l
½1 þ Knð2:492 þ 0:84 exp ð0:435=KnÞÞ
ð1Þ
where qp is the particle density and l is the gas viscosity. Some example values of sv are shown in Table 1. Clusters of diameter less than 50 nm meet the Stokes number criterion of Samimy and Lele (1991), and, thus, are expected to follow the flow closely. (The Stokes number criterion is S=0.2u¥sv/d
