# Experimental study of liquid injection under supercritical conditions

Téodor Chazelle¹, Florian Lespinasse¹, Saïd Idlahcen¹, Jean-Bernard Blaisot¹, Benoît Barviau¹, Guillaume Ribert*¹

¹INSA Rouen Normandie, Université Rouen Normandie, CNRS, Normandie Université, CORIA UMR 6614, F-76000 Rouen, France

*Corresponding author: guillaume.ribert@insa-rouen.fr

## Abstract

Injecting fuel under high-pressure and high-temperature conditions compexifies considerably the physical understanding of the involved phenomena. The challenges faced when collecting data within such extreme conditions induce a lack of reliable experimental results in the literature, which critically hinders the modeling of these phenomena. The measurements presented here aim to reduce this gap by providing experimental quantitative data on an ethane jet in a high-pressure chamber filled with nitrogen at rest from 4 MPa up to 6 MPa. Firstly, shadowgraphy is used both to study the jet topology and to compute its spreading angle, from subcritical to supercritical conditions, varying also the liquid mass flow rate, hence enabling a close study of a whole range of injection regimes. Then the Image Correlation Velocimetry (ICV) technique is applied to the same configuration, through a double-frame Diffuse Background Illumination (DBI) system. It results in complete velocity fields and velocity profiles for a broad range of conditions.

## Introduction

The growing interest in supercritical fluids in recent years have been driven by two major domains: on one hand, applications that seek the supercritical fluids' characteristics, in particular the ability to pass from liquid-like to gas-like properties without phase change, to improve their processes, such as the use of supercritical CO₂ as a solvent in chemistry; on the other hand, applications that, while operating at high-pressure for efficiency improvement, ended up crossing the critical pressure and temperature of their working fluids. The latter includes propulsion applications such as liquid rocket engines, diesel engines, and gas turbines, like turbojets at take-off [1]. Thus, there is a need to better understand fluid injection in thermodynamic conditions over the critical point, since it significantly modifies the behavior of the injection, with an impact on the definition of an interface. Indeed, over a certain value of pressure and temperature, discontinuities between the liquid and the gas phases of a species cease to exist and the properties of the fluid rather present a continuum between a liquid-like and a gas-like state. The problem is all the more complex for the multispecies configurations often encountered in practice. Therefore, the theoretical aspects of high-pressure injection and the fundamental mechanisms that control the transition from an atomizing spray behavior to a dense-gas mixing one are still discussed [2]. The modeling and computation of high-pressure flows also raises specific issues from a numerical point of view. In particular, the computation of kinematic viscosity leads to a higher Reynolds number when pressure increases with consequences on mesh requirements [3]. Recent works [4, 5, 6] give an overview of the different requirements and challenges that such high-pressure conditions can create. The development such models and numerical simulations requires validation on experimental quantitative data, which are not sufficiently available in the literature.

As a matter of fact, obtaining valuable information on injections under such extreme conditions is a real challenge [7]. The development of non-intrusive measurement techniques in recent decades has enabled better general knowledge of reactive and non-reactive flows. Nevertheless, wide variations of refractive index, due to the large density gradients present at high-pressure [8], are an obstacle to collecting quantitative information. Transmission measurement techniques, such as shadowgraphy, schlieren, or diffuse background illumination (DBI) [9, 10, 11, 12] are mainly used to obtain the shape of the flow structure, to discern interfaces and observe the resulting mixing layer. From these measurement techniques, it is possible to obtain geometric information such as the length or the angle of penetration, and the size of drops and of the flow disturbances. These techniques are limited by the performance of the camera in terms of spatial and temporal resolution and they can't give local thermodynamic information. Mie scattering can be used to detect the presence of liquid [2]. Density fields can be obtained either by PLIF [13, 14, 15] or by Raman scattering [16, 17]. Oschwald et al. [16] show a degradation of the measurement performances of the Raman scattering technique in some parts of the flow. Such signal deviations have also been observed by Cessou et al. [18] with PLIF on an injection of cryogenic liquid oxygen (LOx) in an environment of hydrogen (H₂) at 6 MPa. This deviation has been attributed to strong refractive index gradients due to high pressures, and it is a great challenge to evaluate and quantify the deviations of light rays.

In this perspective, a high-pressure bench was designed at CORIA laboratory to study the injection of liquid within controlled ambient conditions. Aiming at obtaining various quantitative data, different optical diagnostics are used, providing visualizations of the jet in both classical shadowgraphy and DBI, spreading angle values, velocity fields and velocity profiles for subcritical and supercritical ambient pressure, subcritical and supercritical ambient temperature and for a whole range of injection regimes.
<figure><img src="image_1.png" /><figcaption>**Figure 1.** Schematic view of the test bench with a DBI optical setup and a close-up on the injector's exit.</figcaption></figure>

## Material and methods

The main elements and monitoring instruments of the test bench are presented in Fig. 1. The test bench consists of a high-pressure chamber, an injection fluid circuit (ethane), and a nitrogen gas circuit to fill the chamber with pressure and temperature-controlled inert gas (referred to as ambient gas). The chamber is equipped with one pressure transducer, two thermocouples, and a heating system. The ambient gas circuit is served by tanks of nitrogen stored at 12 MPa and equipped with a pressure controller, a series of valves, and a heating system. The injection fluid circuit consists of two pumps, which operate in parallel, the corresponding valves, and a simple round injector, which is a hollow cylinder with a 2 mm internal diameter and a 4 mm external one. These devices are controlled and monitored via LabView. This system allows obtaining a continuous and extended injection of liquid (or liquid-like fluid) in a chamber that can be pressurized up to 7 MPa and heated to 150 °C, with fine control on flow rate, up to 760 mL/min, i.e. 4.04 m/s at the exit of the injector.

Two optical setups are implemented to collect data within the test chamber, which is equipped with four silica windows. The first one is a shadowgraphy setup, which is based on the measurement of optical refractive index and density gradients which deflect a collimated light beam during its propagation through the medium. The light source is a CaviLux (Cavitar), providing a low-coherence light beam of 640 nm wavelength and controllable pulse duration and inter-pulse delay. This light beam is then collimated by two convergent lenses (55 mm focal length, 40 mm diameter and 200 mm focal length, 50 mm diameter, respectively), resulting in a 50 mm diameter beam. The second optical setup, shown in Fig. 1, provides double-pulse Diffuse Background Illumination (DBI) to gather image-pairs for Image Correlation Velocimetry (ICV, detailed hereafter). The same illuminating source is chosen, but the two lenses are replaced by an optical diffuser. For both optical diagnostics, the information is collected by a LaVision Image ProX camera, equipped with a 105 mm Nikon lens and extension rings (32 mm). The main difference in the collection between the two diagnostics is that ICV uses the two-frame mode of the camera (controlled by LaVision's DaVis software). This system also triggers the light-source pulse, enabling full control of both the pulse duration and the inter-pulse delay, two key parameters for such a technique. Here, a pulse duration of 0.01 µs and delay varying between 50 and 100 µs were found to be adequate with the jet's motion, as the ICV technique assumes the inter-image displacement consists mostly of translation, with negligible deformation [19]. With this system, sets of hundreds of paired images are recorded for each test condition, with a 47 px/mm resolution.

Through adequate post-processing, three kinds of information can be obtained from these diagnostics. Normalizing the images from shadowgraphy and DBI enables topological and morphological analysis. To obtain a spreading angle value, the series of normalized shadowgraphy images (120 images per test condition) are binarized and the standard deviation of the series is computed. This standard deviation matrix corresponds to the local gray level fluctuations within the series [20]: to binarize the resulting image means choosing a perturbation level threshold that corresponds to the average external boundary of the drop cloud. Computing the resulting slope of this external boundary gives the spreading angle value. Since spreading angle is a widespread variable used to characterize jets in sub and supercritical conditions, determining this value enables quantitative comparisons with literature data [21] and with previous data obtained on the same test chamber [22]. In contrast, ICV analysis regarding supercritical conditions is not available in the literature to the authors' knowledge. The ICV is an adaption of correlations' methods from PIV to seedless flows, following fluid structures rather than particles. The correlation algorithm developed by Sedarsky et al. [19] for Diesel injection at atmospheric pressure was found to be effective with the high-pressure injection images, so it will be presented and then used in the following.
The main difference between ICV post-processing compared to PIV resides in the matching procedure since the intensity peaks from the seeding cannot be found. Therefore, the first step of the algorithm is to determine suitable areas for correlation. Areas with significant light intensity variations are preferable since more pronounced shapes lead to more reliable correlations. Hence a set of target points is defined by applying Canny edge detection to identify strong intensity gradient coordinates. Around each target point, a “Template” zone is defined and, in the second image, a 2 or 3 times bigger “Search field” is defined, as shown in Fig. 2. Then each template zone is matched with a “Result” zone of the same size by identifying the translation (dx, dy) which maximizes the normalized cross-correlation coefficient [19]:

$$R(dx, dy) = \frac{1}{n-1} \sum_{x,y} \frac{(S(x', y') - \bar{S})(T(x, y) - \bar{T})}{\sigma_S \sigma_T} \quad (1)$$

where x and y are the spatial coordinates of both images (horizontal and vertical respectively), T(x, y) is the grey level value of the (x, y) pixel in the template region, S(x', y') is the grey level value of the (x + dx, y + dy) pixel in the search field, T and S are the average of their respective region, σT and σS are the standard deviations of the said regions and n is the sum of the pixels from the search and template regions. Fig. 2 illustrates the result of the feature matching with the template and the result zones highlighted.

<figure><img src="image_2.png" /><figcaption>Figure 2. Example of the three regions used in the feature matching algorithm for a jet of ethane in nitrogen at 5 MPa, 293 K, and 760L mL/min.</figcaption></figure>

A validation procedure is then applied to eliminate correlations with low coefficients or aberrant vector magnitudes. Then, the series are averaged over time and binned within 5 × 5 pixels blocks. Blocks with less than a defined number of valid vectors are excluded, thus substantially filtering out the remaining false results. Statistical analysis was performed to determine the minimum number of paired images needed to properly describe the velocity profile. 1000 paired images were recorded and the convergence was obtained after processing 200 paired images. The following results are therefore obtained for 200 image pairs.

## Results and discussion

The test chamber conditions are chosen to be on either side of the ethane critical point, in pressure and temperature, to address subcritical and supercritical regimes. The critical point of ethane is $P_c = 4.9$ MPa and $T_c = 305$ K. The third key parameter, the injection flow rate, is also changed to cover a wide range of two-phase injection regimes (namely Rayleigh, 1st wind-induced, 2nd wind-induced, and atomization regimes [23]) and thus investigate the effects of critical point crossing on each regime. Pressure varies from 4 MPa to 6 MPa by 0.5 MPa increment. The chamber temperature is either at room temperature (around 293 K) or 333 K. For each of the $(P, T)_{ch}$ pairs, four injection flow rates are tested (50, 100, 200, and 380 mL/min). An additional flow rate (760 mL/min) is considered for DBI/ICV tests, after an improvement of the test bench. The pressure of the injected fluid is automatically adjusted by the pumps to meet the required flow rate; its temperature, monitored but not controlled, is equal to the room temperature when leaving the pumps.

As stated before, the topological analysis can be achieved by both shadowgraphy and DBI. Each diagnostic has its advantageous characteristics: in shadowgraphy, the refraction gradients, which correspond to the density gradients, can be observed within the gas phase but they partly cover the liquid (or liquid-like) core. For the DBI it is the other way around: liquid/liquid-like structures appear, even in the denser zone at the center of the downstream jet, but the information in the gas/gas-like phase is mostly lost. At constant subcritical temperature, crossing the critical pressure isobar results, for the same flow rate, in a more perturbed regime. For example, a 50 mL/min flow rate will belong to the Rayleigh regime at 4 MPa and to the 1st wind-induced regime at 6 MPa. Fig. 3 shows the jet in the atomization regime for the four conditions but more atomized at the higher pressure. One can also notice that while usual atomization regimes [23] are still observed for a chamber pressure above the critical pressure,
<figure><img src="image_3.png" /><figcaption>**Figure 3.** DBI visualization of the ethane jet at a given flow rate (760 mL/min) for four different conditions, highlighting separately the effect of pressure and temperature increase.</figcaption></figure>

<figure><img src="image_4.png" /><figcaption>**Figure 4.** Jet opening as a function of the density ratio, for each measurement point, plotted by flowrate, compared with results from a previous test campaign (N.Vallée [22], hollow symbols). Color red denotes warm conditions, color blue denotes cool conditions.</figcaption></figure>

features typical of supercritical injection [21] (e.g. behavior reminding dense-gas mixing) are not found for ambient temperature below the critical temperature. Crossing the critical isotherm at constant subcritical pressure induces strong thermal effects and a droplet size reduction through surface tension diminution, as can be seen in Fig. 3. Thorough efforts were made to obtain visually stable jets on the duration of a series but controlling the exact injected fluid temperature at the exit of the injector remains a challenge, that will be addressed in an upgraded version of the test bench. Finally, above critical pressure and temperature, the droplets are even more reduced in size, but still present, and finger-like structures and diffuse interfaces envelop the dark core near the injector exit. The similar topological conclusions can be drawn from the shadowgraphy visualizations but won't be presented here. Shadowgraphy was also used to obtain one quantitative data, the spreading angle measurement. Such angle measurements are essential to qualify and validate numerical codes. In the present experiment, the trend observed is in agreement with results coming from literature [21]. In addition to this, results were compared to the ones previously obtained by Vallée [22] in the same chamber. Note that Vallée [22] did not conduct angle measurements at 333 K, but at 323 K; however the “cool”/“warm” distinction remains relevant. On Vallée results, the same increasing value of jet angle with flow rate, density ratio, and temperature is observed. The same type of plateau with density ratio increase under supercritical conditions (here over $ρ_{ch}/ρ_{inj} = 0.14$) is retrieved. Although the values differ point-to-point, the same trends are present within two blocks corresponding to the “cool” conditions on the one hand and the “warm” conditions on the other hand.

As stated previously, Image Correlation Velocimetry provides local velocity data time-averaged over each series. Since target points are only located on areas showing strong intensity gradients, no information can be drawn from the dark core of the jet. This explains the lack of data near the injection axis for some of the test cases. Velocity data are processed to obtain either velocity fields or velocity profiles at a given axial position. Both velocity components are accessible from the data. The velocity magnitude fields are shown in Fig. 5 and 6 for five chamber pressures
and for minimum and maximum flow rates respectively.

<figure><img src="image_5.png" /><figcaption>**Figure 5.** Axial velocity fields averaged over the 200 image-pairs series for 50 mL/min, two chamber temperatures, and five chamber pressures. The color black represents zones with no or not enough values.</figcaption></figure>

They are representative of the other flow rates, as for in-between flow rates, in-between behaviors are observed. For both cool and warm conditions, the velocity globally decreases with the pressure increase, as well as the velocity gradients. This behavior was expected: as the chamber pressure increases, the density of the ambient gas increases and so does the aerodynamic stress. This increase in aerodynamic forces tends to slow down the penetration of the jet, ligaments and drops. For 50, 100, and 200 mL/min the velocity increases significantly with temperature, with a migration of the highest velocity zones from the downstream center to the upstream center and, more generally, a clear change of shape. This behavior is in agreement with the morphological analysis from the original DBI images. It should also be noted that, between the cool and the warm conditions, the nature of the observed structures differs substantially: at low temperatures, for these flow rates, the flow forms a mostly cylindrical jet in the Rayleigh regime, oscillating in the downstream region, which explains the high velocities observed here; whereas at high ambient temperature, since the injection temperature is not controlled and the flow rate is low enough, the ethane's flow seems to be, at large extent, vaporized: the tracked structures mostly correspond to strong gas-like density gradients. For the highest flow rates (380 and 760 mL/min), no clear increase in velocity with temperature is observed, but the velocity gradient slightly attenuates (see also the velocity profile analysis hereafter). At 760 mL/min and supercritical temperature, some fast structures in the jet periphery appear, which are noticeably absent elsewhere. Most of these effects are guessed to be directly linked to the morphological changes mentioned above, even if further analysis needs to be carried out.

Velocity profiles for the same two flow rates are presented in Fig. 7, at three different axial positions. They are in agreement with the velocity fields results. For both flow rates, velocity decrease with pressure is visible. At 50 mL/min, the pressure also flatten the curve, especially at $x/D = 10$ and $x/D = 15$. For the cold conditions, this effect can be linked to the jet oscillation, which are accentuated with pressure and cover a wider space around the axis. The velocity values at 4 MPa and 333 K tends to support the hypothesis of a vaporization within the injector. Indeed, for liquid ethane at such conditions, assuming a volumetric flow rate conservation between the pump and the injector exit, the spatially-averaged velocity within a cylinder would be around 0.27 m/s, which is not the case here, with values almost entirely over 0.3 m/s near the injector exit. It means the density has necessarily changed between the pump and the injector exit. However, the velocity profile analysis shows that, at downstream axial positions, increasing the temperature does not increase the velocity, but decreases it; once again, this can be an effect of the jet oscillations, which cease to exist at the higher temperature. For the faster flow rate, at 760 mL/min, the results are once again coherent with the velocity fields. For example, the velocity gradient attenuation with temperature increase is retrieved: the maximum and minimum velocities are close, but the slope from the minimum to the maximum shows an exponential growth at low temperature and a rather linear one at high temperature. At
<figure><img src="image_6.png" /><figcaption>**Figure 6.** Axial velocity fields averaged over the 200 image-pairs series for 760 mL/min, two chamber temperatures, and five chamber pressures. The color black represents zones with no or not enough values.</figcaption></figure>

supercritical pressure, the temperature increase does not seem to have any effect on the velocity, in trend as in values. It should however be noted that most of the information is lost at the center, which is one of the drawbacks of the ICV as explained before, and some effects may not be detected. Since no measurements of the velocity of a liquid-like jet under supercritical conditions were reported in the literature to the authors' knowledge, no comparison was possible with other experimental results, but a comparison with numerical simulation would be straightforward and would benefit both perspectives.

## Conclusions

An experimental bench has been set up as part of an integrative project aiming at investigating unresolved aspects of high-pressure liquid injection under supercritical conditions. Several optical diagnostics have been implemented to obtain complementary information. Topological analysis is achieved from both shadowgraphy and DBI images to check the effects of pressure and temperature increases on the injection regimes, highlighting the presence of a transcritical atomization regime. Out of the shadowgraphy results, spreading angle measurements are computed, enabling comparison with the extensive literature on the subject [21]. Finally, velocity measurements for a whole range of thermodynamic ambient conditions and injection flow rates are carried out through Image Correlation Velocityometry. If effects typical of supercritical conditions have yet to be properly characterized, several effects induced by the pressure increase and the temperature increase have been shown. In terms of perspectives, a few modifications are planned on the test bench to improve the overall chamber conditions control and stability over time and the injection temperature control. In addition to the further developments of topological and velocity analysis, in particular the investigation of higher ambient pressures effects, the use of spontaneous Raman scattering will enable species concentration and phase determination within the flow, opening the way to an actual thermodynamic analysis, which imaging does not permit. All this data will contribute to improve the numerical simulation currently implementing a new mathematical model, while the model will provide a deeper understanding of the experimental results.

## Acknowledgements

This work was funded by the ANR (Agence Nationale de la Recherche) research project INSIDE (Injection of supercritical fluids: simulations, diagnostics, and experiments), Grant No. ANR-19-CE05-0037.
<figure><img src="image_7.png" /><figcaption>**Figure 7.** Time-averaged velocity magnitude profiles comparisons for cool (blue) and warm (red) conditions, at three different axial position, at constant pressure (4 MPa) and at (a) 50 mL/min and (b) 760 mL/min.</figcaption></figure>

**Nomenclature**

* *D* diameter [mm]

* *P* pressure [MPa]

* *T* temperature [K]

* *x* axial position [mm]

* *ρ* density [kg/m³]

**Subscripts:**

* *c* critical point conditions

* *ch* chamber (ambient) conditions

* *inj* injected fluid upon entering the chamber conditions

* *r* relatively to the critical point conditions

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