DROPLET SIZING AND INFRARED TEMPERATURE MEASUREMENTS IN SUPERHEATED SPRAYS

G. Lamanna (1), P. Rack(1), Y. Khafir(1), H. Fulge(2), S. Fasoulas(2), G. Gréhan(3), S. Saengkaew(3), B. Weigand(1), J. Steelant(4)

(1) Institut für Thermodynamik der Luft- und Raumfahrt (ITLR), Universität Stuttgart, Pfaffenwaldring 31, 70569 Stuttgart, Germany, Email: Grazia.Lamanna@itlr.uni-stuttgart.de

(2) Institut für Raumfahrtsysteme (IRS), Universität Stuttgart, Pfaffenwaldring 29, D-70569 Stuttgart, Germany, Email: fulge@irs.uni-stuttgart.de

(3) CNRS UMR 6614 – CORIA, Université de Rouen, 675, avenue de l’Université, 76801 Saint Etienne du Rouvray Cedex, Email: gerard.grehan@coria.fr

(4) Propulsion and Aerothermodynamics Division, ESA-ESTEC, Keplerlaan 1, 2200 AG Noordwijk, The Netherlands, Email: Johan.Steelant@esa.int

ABSTRACT

The present paper discusses some preliminary experi-mental results on the droplet size and temperature distri-butions in superheated sprays. Droplet size data show that liquid disintegration controlled by nucleate boiling is less efficient compared to aerodynamic-controlled atomization. In fact, it leads to larger SMD values. The size distribution evolves from a log-normal skewed curve in the transition regime to a more symmetric a broader distribution in the fully flashing mode. Its shape evolution can be best described by the Weibull function. Concerning the temperature evolution, a novel post-processing methodology is proposed to re-construct the local temperature profile from integral measurements. The algorithm is based on a double Abel inversion and was validated through a comparison with experimental and theoretical data. Application to real sprays requires the inclusion of scattering effects in the post-processing algorithm. 1. INTRODUCTION

Non-intrusive optical measurements in flashing sprays are challenging, since data must be mainly acquired in dense optical regions, where nucleate boiling is confined. In recent years, considerable advances have been made in the experimental characterization of both the temperature and drop size distribution within such sprays. For the thermal field, Zhang et al. [1] employed laser-induced exciplex fluorescence to determine the vapor concentration and liquid temperature in n-hexane. By using the Differential Infrared Thermography (DIT), Kamoun et al. [2] showed that, alike the velocity field, the temperature profiles exhibit very rapidly a self-similar behavior, while most of the relevant cooling is confined in the near-nozzle region (i.e. for axial distances x/D < 20). Similar results were obtained by Vetrano et al. [3] with laser induced fluorescence (LIF). Despite the noteworthy progress, the above data cannot be used yet for the validation of superheated evapo-

ration models, as some controversy still exists on which temperature is actually being measured. For LIF, Perrin et al. [4] have shown that, due to the focusing of laser light within the drop, the LIF temperature is somewhat intermediate between the surface and central value. Unfortunately, no theoretical expression is available that defines exactly the LIF mean temperature. Additional factors affecting the accuracy of LIF measurements in sprays are due to multiple-scattering effects [4] and to spurious fluorescence peaks caused by morphology-dependent-resonances (MDR) [5]. The inclusion of such effects in the LIF post-processing algorithms represents therefore a necessary step for improved temperature measurements in such turbid media. Similar conside-rations hold also for the DIT technique, which provides only an average, integral temperature value (TDIT) [6]. In this paper, we develop a theoretical definition for TDIT by solving formally the radiative heat transfer equation within the spray. The advantage of this theoretical model is twofold. First, it clarifies how numerical data should be averaged for a meaningful comparison with experiments. Second, it paves the way for the development of a radically new post-processing algorithm. The latter employs a double Abel-inversion algorithm to reconstruct the local spray temperature and is briefly described is section 3.2. Detailed information on the drop size distribution, instead, is required both for the assessment of eva-poration models and for the correct initialization of flow simulations. An important classification is provided in [7], where it is shown that the Sauter-mean diameter (SMD) decreases steadily with superheat and attains a minimum value at highly superheated conditions (i.e. in the fully flashing regime). Albeit very instructive, the database presented in [7] was acquired in the dilute region of he spray (i.e. for x/D > 100) and hence it gives only limited information on the atomization process, controlled by nucleate boiling. More recently, Kamoun et al. [8] employed global rainbow thermometry (GRT)

to measure droplet sizes in superheated ethanol jets. A major limitation of Kamoun’s analysis is that it considered only the variation of one representative mean diameter upon superheat. However, the use of a single average value can be very misleading. Indeed, two different size distributions may have the same value for one mean diameter (e.g. d10) and yet exhibit an entirely different statics for the remaining mean diameters. In this paper, we extend Kamoun’s analysis by evaluating the characteristics of the experimental size distribution with respect to both the differential and cumulative volume distribution and by including a comparative analysis among the different mean diame-ters. In addition, we revise several size-distribution formulas in order to identify which function provides the best fit with respect to all mentioned statistical parameters. Finally, we analyse the variation of the size distribution function both with superheat and along the spray axis in order to gain a better understanding on the effect of nucleate boiling on the disintegration process and on the interplay between nucleate boiling and super-heated evaporation. 2. EXPERIMENTAL FACILITIES

A schematic layout of the test bench for the GRT test-campaign is shown in Fig. 1. Its distinctive feature is the use of one, large circular window (φ = 200 mm) to capture back-scattered light over a solid angle of appro-ximately 20 degree. The injector is mounted vertically on top of the chamber and employs a single-hole nozzle with a diameter D = 150 µm and an aspect ratio L/D = 6.7. The test bench for DIT studies is almost a duplicate of the GRT setup: the main difference being the increased optical access through four lateral windows, placed 90 degree from each other (φ = 135 mm). More details on the DIT setup can be found in [6].

Figure 1. CAD drawing of the test facility

2.1. GRT Setup

The global rainbow setup is shown in Fig. 2. It can be

schematically divided in an emitting and receiving part. The former consists of an optical trap and a variable power cw-argon laser LWGL (up to 500 mW) with a diameter of 1 mm at a wavelength of λ = 532 nm. The receiving part consists of two convex lenses, a spatial filter and a semi-transparent screen. The first lens (f1 = 80 mm, φ = 160 mm) collects the scattered light within a solid angle of approximately 20°, the second lens (focal length f2 = 80 mm, φ = 160 mm) conjugates the image of the focal plane of the first lens on the semi-transparent screen. The image of the rainbow is acquired by a cooled, digital 14bit CCD camera system (PCO-4000). Both the emitting and receiving parts are mounted on a 2D traverse allowing the horizontal and vertical positioning of the measurement volume relative to the nozzle exit. The nominal resolution of the traverse is 10 µm. The correspondence between pixel position and the absolute angular location of scattered light is established through a calibration procedure, as descri-bed in [8].

Figure 2. Optical layout of the GRT setup. Courtesy of

Bonin [9].

2.2. DIT Setup

For thermographic visualization, the optical layout is schematically in Fig. 3. For the two temperature con-trolled backgrounds, an electrical heated foil and two Peltier elements are employed for heating and cooling operations, respectively. Both constructive elements are embedded in a MACOR frame to minimize thermal losses. A FLIR-Orion SC7000 camera, with a spectral sensitivity between 3 and 5 µm, is used for acquiring the thermograms. For the present experimental campaign, a macro-objective with a magnification factor of 1:1 is employed.

Figure 3. Optical layout of the DIT setup [6].

3. POST-PROCESSING

This section describes briefly the data reduction strategy adopted in the post-processing. The objective is two-fold: 1) to obtain a complete statistical description of the size distribution function and 2) to re-construct the three-dimensional temperature field from the integral infrared measurements. 3.1. GRT Data Reduction

For retrieving the size distribution function, the inversion method developed by Saengkaew [9-10] is employed. The inversion algorithm is based on Nussenzveig’s theory and employs a non-negative least square method to minimise the distance between the recorded and the computed global rainbow distribution. A detailed discussion on the inversion strategy for spray applications and its related accuracy can be found in [10]. Hereafter, we will describe the approach chosen to identify a proper statistical representation of the size distribution function.

(a) Differential Size Distribution

(b) Cumulative Undersize Distribution

Figure 4. Example of DSD (a) and CUD (b) data First, the discrete differential size distribution (DSD), as obtained from the inversion algorithm, is converted to a continuous function by simple geometric relations. This

step facilitates the comparison with analytical functions and enables the calculation of the cumulative size distribution (CUD), i.e. the distribution of liquid volume by size class. An example of both distributions is exem-plary shown in Fig. 4. Second, we revert to statistical theory to identify a model for the size distribution in superheated sprays. Different statistical functions are analysed in regard to their ability to capture the variation of the DSD and CUD functions with super-heat. As commonly done in statistics, one must first select a suitable scale and shape parameter for the stati-stical function. For the Weibull distribution, for exam-ple, the CUD assumes the following analytical expres-sion:

F x;k,λ( ) =1− e− x λ( )k (1)

where k > 0 is the shape parameter and λ > 0 is the scale parameter of the distribution. Typically, the scale para-meter λ is chosen among the different average diameters dqp. The subscript ‘qp’ indicates the order of the mean or the method of averaging [11] and are defined as

dqpp−q =

d p ∂n∂d∂d

dmin

dmax∫

dq ∂n∂d∂d

dmin

dmax∫ (2)

For q=3 and p=2, one recovers the definition of the Sauter mean diameter (SMD). A non-trivial issue is how to choose the scale parameter without introducing any loss of information in the statistical description of the size distribution function. To answer this question, we compare the different average diameters to the SMD, as illustrated in Fig. 5. Despite some scatter, a linear de-pendence can be observed for all average diameters. As a result, we can conveniently choose the SMD as scale parameter without any loss of generality, since any other dqp will simply result in a scale change by a con-stant factor. The choice of the shape factor is discussed in section 4 together with the selected analytical model for the size distribution function.

Figure 5. Comparison of average diameters with SMD

3.2. DIT Post-processing

The differential infrared thermography (DIT) is an ima-ge contrast technique that consists in imaging twice the spray in front of a temperature-controlled background [6]. By taking the difference between the two images, the local spray emissivity can be calculated as

εspray =1−ICam2 − ICam1IBack2 − IBack1( )

(3)

The spray temperature can then be obtained from [6]

TDIT =TCam4 − 1−εspray( )TBack4

εspray4 (4)

In this context, it is important to clarify the meaning of the measured quantity TDIT. For this purpose, we formally solved the radiation heat transfer equation through the spray. The result of this exercise gives:

I δ( ) = I0 exp −δ( )+ Iε,slab0

δ

∫ exp −δslab( )dδ (5)

where Iε,slab is the slab thermal emission and δ is the optical depth. The latter is defined as the integral of the local absorption coefficients along the line-of-sight

δ = βslab0

s

∫ ds (6)

Equation (5) states that the radiation recorded by the infrared camera is the sum of two contributions. The first term represents the amount of background radiation transmitted by the spray. The second term represents the total thermal radiation emitted by the spray. The latter can be expressed as the integral of each slab’s thermal radiation, multiplied by the attenuation, experienced du-ring its propagation within an absorbing media. After simple algebra, it follows

σεSprayTDIT4 = σεslabTslab

4 (δ)0

δ

∫ exp −δslab( )dδ (7)

Relation (7) indicates that TDIT represents an equivalent spray temperature. In other words, it is a fictive tempe-rature value, such that it reproduces the complete thermal radiation emitted by the spray when multiplied by its total emissivity εspray. Hereafter, we propose a me-thodology to reconstruct the local spray temperature. The key feature relies on a double inverse Abel trans-form. Taking into account Eq. (6), the first inversion

enables to retrieve the local distribution of the absor-ption coefficients from

δ = − ln 1−εspray( ) (8)

Once the absorption coefficients are known, it is possible to calculate the local slab attenuation and emissivity, respectively. The second inverse Abel transform enables to re-construct the slab thermal emission (see Eq. (7)). Finally, the local spray temperature can be obtained from

Tslab =fslab

σεslab exp −δslab[ ]4 (9)

The Abel inversion algorithm was developed by Fulge et al. [11]. It exploits the spline method to perform the inverse Abel transformation of measured data sets and does not require any a priori assumptions about the local distribution. 4. RESULTS

The present section is divided in two distinct parts. The first part focuses on the characterization of the atomization process in superheated sprays. The second part demonstrates the feasibility of the proposed methodology to reconstruct the local temperature distri-bution from integral measurements. 4.1. Disintegration in superheated sprays

Thanks to the linear dependence among the different average diameter (see Fig. 5 for reference), we can simply revert to the SMD data to analyse the efficiency of the atomization as function of superheat Rp. The latter is defined as the ratio between the equilibrium vapour pressure at the injection temperature and the ambient pressure (i.e. Rp = psat (Tinj) / pam). Note that, at large axial distances (i.e. x/D = 40), the SMD decreases with increasing superheat, in compliance with literature results [7].

Figure 6. SMD variation along the spray axis x/D

A reverse trend is, instead, observed in the near nozzle region (i.e. x/D < 13). This can be explained in light of the different physical mechanisms controlling the atomisation process. At low Rp values (i.e. in the transition regime), flow instabilities and aerodynamic forces are the dominating factors. As a result, the average drop size is of the same order of magnitude as the liquid ligaments. Hence, relative small drops are shed from the jet and result in a relative narrow size distribution. At high Rp values (i.e. in the fully flashing regime), instead, nucleate boiling is the controlling process for the jet disintegration. Following the random bursting of small bubbles, the resulting drop size distribution is relative broad and may entail a few relative large droplets, thus resulting in a larger SMD values. These considerations are indeed confirmed by the analysis of the drop size distribution, as shown in Fig. 7. As can be seen, the drop size distribution evolves from a almost log-normal function al low Rp values to a very broad and symmetrical distribution in the fully flashing regime. To highlight this effect, Fig. 8 shows the evolution of the half width of the size distribution with superheat.

Figure 7. Variation of the DSD with superheat

Figure 8. Variation of the half width with superheat

An important conclusion from this analysis is that the Weibull distribution is the only suitable choice to model effectively the shape variation in superheated sprays.

Figure 9, for example, demonstrates clearly how unsuited is the Rosin Rammler distribution for fitting the experimental data in the transition regime, inde-pendently from the choice of the shape and scale para-meter. On the contrary, an excellent agreement is found with Weibull distribution with respect to both the DSD and the CUD, as shown in Fig. 10.

Figure 9. Data fitting with different modifications of the Rosin Rammler distribution

Figure 10. Data fitting with the Weibull distribution 4.2. DIT Temperature Reconstruction

The feasibility of the temperature reconstruction algo-rithm is first demonstrates on a theoretical case. For this purpose, we consider a liquid drop with known emissivity and temperature distribution, as illustrated in Fig. 11. The theoretical example helps also to better comprehend the meaning of the temperature measured with the DIT technique. Two cases are considered with a constant temperature and a linear temperature decay, respectively. The constant temperature case is discussed in Fig. 12. In this case, the DIT temperature (green line)

and actual drop temperature (blue line) perfectly over-lap. This can be explained simply because the average of a constant distribution coincides with the actual constant physical temperature. For a uniformly heated droplet, the re-constructed temperature (TAbel) represents the trivial solution and is correctly recovered by the inversion algorithm.

Figure 11. Emissivity distribution within an acetone drop

Figure 12. Temperature reconstruction for a uniformly

heated acetone droplet

Figure 13. Temperature reconstruction for a non-uniformly heated acetone droplet

Figure 13 illustrates the comparison among the three

different temperatures for a non-uniformly heated dro-plet. Note that also in this case TAbel coincides almost exactly with the actual temperature distribution (TReal) within the liquid droplet. A large discrepancy is, in-stead, observed between TDIT and TReal. The difference between the two temperature is highest at the drop middle axis due to the higher optical depth (i.e. higher attenuation). As next step, we applied the reconstruction algorithm to an actual spray. The result of this exercise is shown in Fig. 14. For comparison, the temperature data obtained with the two-colour laser induced fluore-scence (2C-LIF) technique are also reported. The LIF-data have been obtained in the group of Prof. Vetrano (VKI), who employed our setup in the framework of the ESA-TRP project “Multi-Phase Aspects in Propulsion Systems”. Despite the good agreement, it should be noted that the analysis of the spray data revealed a strong influence of scattering, particularly in the near-nozzle region. For the present comparison, they have been estimated by employing a genetic algorithm. For future applications, scattering effects will be included by applying the Kubelka-Munk approach.

Figure 14. Axial temperature variation in an acetone superheated spray Rp = 4.

5. CONCLUSIONS

In this work, superheated sprays have been experi-mentally characterized by measuring droplet size and temperature distributions. Global Rainbow Thermo-metry (GRT) was used for drop sizing, while Diffe-rential Infrared Thermography (DIT) was employed for the temperature field. The major contribution of the paper lies in the introduction of a novel post-processing methodolology. Contrary to previous work that used only one repre-sentative mean diameter, here the characteristics of the size distribution are analyzed with respect to both the differential and cumulative volume distribution and

TLIF

TAbel

TDIT

include a comparative analysis among the different mean diameters. Furthermore, we revised several analytical models for the size distribution and found that the Weibull function provides the best fit with respect to all mentioned statistical parameters. We show that flashing is less efficient than aerodynamic-driven atomization, as it leads to larger Sauter Mean Diameters (SMD) immediately after disintegration. Thanks to the enhanced vaporization under superheated conditions, the picture is reversed in the dilute region of the spray, where SMD values in flash boiling sprays become significantly smaller and exhibits only a weak dependence upon the initial superheat, in compliance with literature data. A double Abel-inversion algorithm is employed to reconstruct the local spray temperature. We show that DIT data lead to a significant underestimation of the local spray temperature in the flashing zone, where steep gradients are expected. With increasing superheat, the temperature decay becomes more and more prominent in the near nozzle region, thus confirming the rapid vaporization rate observed in the droplet database. The reconstruction algorithm is validated against theo-retical and experimental data. Application to real sprays requires the inclusion of scattering effects in the post-processing algorithm. 6. ACKNOWLEDGEMENT

The financial support of ESA-ESTEC in the framework of the TRP project “Multi-phase aspects in propulsion systems - Contract No. 22985/09/NL/EM” is gratefully acknowledged. 7. REFERENCES

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