Cryogenic sloshing investigation by means of non-intrusive

18th International Symposium on the Application of Laser and Imaging Techniques to Fluid Mechanics・LISBON | PORTUGAL ・JULY 4 – 7, 2016

Cryogenic sloshing investigation by means of non-intrusive measurement techniques

Alessia Simonini1,2, Maria Rosaria Vetrano1, Laura Peveroni1, Pierre Colinet2

1: Dept. of EA, von Karman Institute for Fluid Dynamics, Belgium 2: Dept. of TIPs, Université Libre de Bruxelles, Belgium

* Correspondent author: [email protected]

Keywords: Cryogenics, Sloshing, PIV, LeDaR, Free Surface

ABSTRACT

The motion of a free liquid surface inside its container is called sloshing and it is strongly affected by external excitations applied to the partially filled container. It can refer to embarked containers filled of fluid, motion of cooling liquids in systems subjected to earthquake or motion of propellant inside a tank, which can influence the trajectory of vehicles. The understanding and the prediction of this particular motion is of special importance in space vehicles which are powered by cryogenic propellant. This is the case of the cryogenic upper stage where the dynamic response to sloshing can also interfere on the thermodynamics of the stored fuel. The scope of this paper is to investigate cryogenic sloshing by means of non-intrusive optical techniques and to evaluate their performances. Liquid nitrogen is used as substitute fluid of a real cryogenic propellant (LH2/LO2). Two techniques will be applied to a container partially filled with liquid nitrogen and subjected to a lateral harmonic excitation. Both techniques need the use of tracers into the flow: Level Detection and Recording, LeDaR and Particle Image Velocimetry, PIV. In this paper the techniques are detailed and preliminary results of the liquid/gas interface shape and of the fluid velocity during LN2 sloshing will be presented.

1. Introduction The motion of the free liquid surface is called “sloshing” (Ibrahim, 2005). This phenomenon is particularly important during the management of conventional and cryogenic propellants on spacecraft: it can affect the normal operating condition, compromising the full space mission (Abramson, 1966). Being able to understand the behavior of the propellant subjected to extreme environmental conditions means being able to predict its position and topology inside the tank, for a given external and gravitational acceleration and a determined thermodynamic condition. The prediction and control of this motion is far from being understood due to the different parameters that play a role in the dynamic system such as the geometry of the container, the type of external excitation (shape, frequency content and amplitude), the level of the liquid and finally the kind of liquid. In this context, the possibility to investigate directly cryogenic liquids allows to study the behavior of a cryogenic propellant. In particular, the creation of a reliable and consistent experimental database is crucial for assessing the accuracy and the range of validity of


existing numerical models for cryogenics. The main goal of this work is to present the possibility to characterize the free surface shape and the velocity field of liquid nitrogen contained in a partially filled transparent vessel. In both cases, particles are added to liquid nitrogen: in the first case lighter particles are floating at the free surface, giving the possibility to apply LeDaR (Level Detection and Recording) (Tóth, 2008); in the second case, particles which are matching the density of the fluid are inserted in the liquid to perform PIV (Particle Image Velocimetry) in liquid nitrogen. The latter is a cryogenic liquid used as replacement fluid for cryogenic propellants (Liquid oxygen and liquid hydrogen). PIV is a well-establish technique which, when applied to cryogenic liquids, is still in development regarding the seeding selection and procedures (Fonda E. a., 2012). Indeed, even if liquid nitrogen is a good replacement fluid for cryogenic propellant, its particular density range at cryogenic temperature (~807Kg/m3) is a challenge for the density of the particles. Moreover, the extreme low temperature environment is influencing the seeding procedure due to possible entrainment of humidity between particles, bringing to agglomeration of particles. Finally, the use of laser light to illuminate the seeded liquid nitrogen can affect the thermal equilibrium of the system. Regarding sloshing in general, one of the major problems, encountered performing PIV on this kind of flows, is the presence of a liquid gas interface that has a complex shape evolving in time. An example of cryo-sloshing can be seen in fig. 1.

Fig. 1 Example of cryo-sloshing (image acquired using a high speed camera at 90 fps).

In this paper an experimental test case of liquid nitrogen sloshing will be presented and the procedures followed in order to detect the free surface and to apply PIV to a cryogenic fluid will be outlined. 2. Analysis of the problem Under certain assumptions, such as incompressible, non-viscous and irrational flow, the natural frequencies and the response to various forced excitations can be analytically calculated for


various container geometries, even considering the effect of capillary-gravity waves. For a liquid in an upright circular cylindrical tank, the well-developed potential theory, gives a first approximation of the natural frequencies and an approximated formula for the fluid oscillations. Let’s consider a system composed by an upright cylindrical tank of radius R partially filled with a liquid till a level L (see fig. 2). Considering the effect of capillary-gravity waves, the natural frequencies can be express by: 𝜔"#$ = &'()

*1 + -

.&*/𝜉"# tanh '()5

* (1)

Fig. 2 Reference system.

where ρ and σ are respectively the density and the surface tension of the fluid. The index m refers to the diametric nodes and the index n to the circumferential nodes for the different kind of vibration. The quantities ξmn corresponds to the roots of the equation𝑑𝐽9 ξ"#𝑟 𝑅 𝑑𝑟|>?* = 0 , where J1 is the Bessel function of first order and first kind (Abramson, 1966). Two kind of modes are then observable. The asymmetric modes, which are associated to horizontal oscillations of the center of mass (Fig. 3) and symmetrical modes along the vertical axis, which are possible but generally difficult to excite and, therefore, rarely observed (Institute, T.S.C., 2007).

Fig. 3 Schematic of the asymmetrical modes (Dodge, 2000).


In the case of a lateral excitation of the system, the first asymmetric mode (m=1, n=1) is the predominant (Lance, 1966) and it is related to the lowest natural frequency of the system. For the first mode, m=1, we have a nodal diameter perpendicular to the direction of motion. Frictionless liquid, however, exhibits an oscillatory behavior for any disturbance and, for a forced excitation at the resonances, unbounded levels in the response. The effect of capillary hysteresis at the contact line can be neglected considering a tank with a radius much bigger than the capillary length of the fluid. For larger liquid height ratios, L/R > 1, the contribution of the container bottom will decrease as the height ratio L/R increases. Moreover, it can be observed that the wave motion penetrates only to about a depth of the order of one wave length, while the lower part of the liquid follows the container motion like a rigid body. Considering a case for which L/R > 1, and making the hypothesis of small oscillations and velocities, Bauer reports the dependence of the natural frequencies from two important dimensionless parameters, the Bond number, Bo, and the Ohnesorge number, Oh (Bauer & Eidel, 1999) :

Bo = .&*/

- (2)

Oh = .D/

-* (3)

The Bond number describes the relative importance of gravity forces respect to surface tension forces while the Ohnesorge number measures how easy the free surface breaks, and it is important since it affects the natural frequencies of the system (Royon-Lebeaud, 2005) and damping behavior.3. Experimental set-up In order to perform optical techniques during liquid nitrogen sloshing the main three hardware components are:

1. the transparent sloshing cell; 2. the cryostat, a device able to maintain the sloshing cell at cryogenic temperature along

time; 3. the sloshing table.

The principal element of the experimental setup consists in a cylindrical cell, so called sloshing cell. This cell is mainly composed by a quartz module. It is made by a square bar of 100 mm2 and 134 mm of height with a cylindrical hole drilled inside till a depth of 104 mm and a diameter of 80 mm. This design allows to minimized image distortion due to the curved walls by means of refractive index matching (nquartz = 1.45; nLN2 = 1.205 (Fonda E. , 2012)). Since the cell has to be leak-tight and gas-tight the hole is closed by an upper flange with a cryogenic o-ring as connection.


The upper flange is pushed against the o-ring by means of a system of invar bars and a bottom flange. The upper flange is provided by a feeding line and an evacuation line. Between the quartz and the bottom flange a Teflon joint is used to compensate the different thermal contractions of quartz and metallic parts. The assembled cell is shown in fig. 4a.

(a)

(b)

Fig. 4 (a) Drawing of the cryogenic sloshing cell and its picture. (b) Drawing of the cryostat.

The cell is inserted inside the sample area of the cryostat (see fig. 4b). The latter is a system constituted by a liquid nitrogen reservoir and a sample space, both surrounded by a volume kept in vacuum (≈10-4 Pa) in order to minimize heat transfer with the external environment. A supplementary shield is limiting also radiation from the environment. The liquid nitrogen reservoir is used to cool down the sample space by means of a heat exchanger on which liquid nitrogen flows. The heat exchanger is provided by an RTD sensor in order to set the desired temperature. The cell is placed inside the sample space with its upper flange in contact with the heat exchanger. Gas helium is inserted inside the sample space in order to enhance the heat exchange inside the sample space itself. The bottom part of the cryostat is provided with 5 windows in order to optically access the inner part where the cryogenic sloshing cell is placed. The latter is filled with liquid nitrogen coming from the reservoir of the cryostat. The sample space is provided with a cryogenic temperature sensor (RTD) which assesses its temperature. The sloshing cell is considered in thermal equilibrium when temperature variations in time are of the order of one Kelvin per hour. As above mentioned, the temperature in the sample space can be regulated by the heat exchanger. On the contrary, the cryogenic sloshing cell has no control on pressure with the consequence that the working conditions follow the saturation line of liquid nitrogen, as shown in fig. 5a. Finally, the full equipment is mounted on a shaking table where all the PIV equipment can be mounted. The shaking table used for this experiment is Shakespeare (acronymous of SHaking


Apparatus for Kinetic Experiments of Sloshing Project with Earthquake REproduction). Shakespeare can provide customized excitations. It is provided by an optical displacement sensor (ODS) to track the history of the motion (Accuracy 1µm - 250Hz resolution). The setup to perform both, LeDaR and PIV, it is composed by a CW laser and a camera. Depending on the technique the kind of camera is different. The sketch of the general experimental setup for non-intrusive measurement technique applied to cryogenic sloshing is shown in fig. 5b.

(a)

(b)

Fig. 5 (a) P-T diagram for nitrogen. (b) Sketch of the LeDaR and PIV setup.

4. LeDaR (Level Detection and Recording) 4.1. Experimental conditions

The LeDaR technique has been defined for the first time at von Karman Institute (Tóth, 2008) to characterize surface flows in rectangular reservoirs at ambient temperature. During the LeDaR measurements, a reservoir filled with seeded liquid is illuminated by a laser sheet. The liquid can be seeded with: • a dye, which can be excited by the laser light and emits in a spectral region far away from the exciting one. • low density particles which accumulates on the liquid/gas interface and scatter the laser light. A video camera, equipped of appropriate cut-off optical filters, is used to acquire images of the interface. A schematic of a LeDaR experimental set-up is presented in fig. 6a. At the best author knowledge, there exists no fluorescent dye which is soluble in liquid nitrogen. For this reason, floating particles have been chosen as scattering media in order to detect the liquid/gas interface. The particles used are 3M K46 glass bubbles (density 460 Kg/m3 and peak size [10%, 50%, 90%] = [15, 40, 70] µm). Their density is almost half of that one of liquid nitrogen at ambient pressure (807 Kg/m3 at 106 kPa). The amount of particles inserted is ~10mg/l which


gives a volume ratio between the fluid and the particles of ~40000. The low amount of particles used (the technique should be the less intrusive as possible) is insufficient to cover the whole liquid/gas interface as it can be seen in fig. 6b. Therefore, in order to overcome this problem, 200 phase locked images have been acquired and averaged to retrieve the full liquid/gas interface profile. The phase locked acquisition procedure is performed by selecting a specific phase of the motion (i. e. correspondent to the 30% of the sinusoidal period) and then 200 images of the liquid gas interfaces are acquired, when the excitation corresponds to that phase.

(a)

(b)

Fig. 6 (a) Schematic of LeDaR technique; (b) Example of an image of LeDaR in LN2.

These images are processed and the interface shapes obtained are then averaged. Three different phase locked positions have been used for each excitation frequency, as reported in fig.7 and in table1.

Fig. 7 Phase locked acquisition scheme.

Table 1 Test condition matrix for LeDaR

Test D [mm]

L [mm]

A [mm]

f [Hz]

Phase locked pos. (%)

1

80 >D 1.5

2

18.8

2 47.3

3 78.8

4

2.5

21.4

5 47.1

6 75.8

4.2. Data processing

The image post processing used for the LeDaR technique is done with a VKI code based on Matlab and consists in the following steps:


• For each image an intensity filter is applied in order to remove less intense structures which do not belong to the liquid gas interface

• A rough mask is applied to select the ROI in which the liquid/gas interface is present. • The maxima of each image pixel column are computed and an “instantaneous” profile of

the liquid/gas interface is determined. • The images corresponding to profiles which differ from each other of maximum +/- 3 px

(+/- 0.2 mm with the used calibration) are selected. • These profiles are averaged. • The maxima of the average image are computed and the final “average” liquid/gas

interface profile is computed. The same procedure is also made for the reference liquid/gas interface position, i.e. the position of the interface when the liquid is at rest.

4.3. Results In this section the liquid gas interface measured by LeDaR for the tests Test4, Test5 and Test6 are presented. It is possible to observe that the reconstruction of the liquid/gas interface profiles does not allow having relevant information about the contact angle. This is due to two main reasons. First the LeDar technique has not a sufficient spatial resolution to be capable to evaluate an apparent contact angle close enough to the solid wall to be representative of the process. Secondly, since particles have been added to the fluid interface, the contact angle is most probably affected and will not represent the one associated to the sloshing phenomenon. A way to overcome these two problems would be to perform LeDaR visualizations zoomed on the contact line position using a different way to optically distinguish between the fluid and the gas phase.

Fig. 8 Phase locked interface shape in LN2, A=1.5 mm, F=2.5 Hz.

5. PIV (Particle Image Velocimetry) 5.1. Experimental conditions

In literature few works regarding PIV in cryogenics are present (Raffel, 2007; Fonda E. , 2012). Both of them underline the difficulty to find classic PIV particles which are neutrally buoyant for liquid nitrogen and moreover, difficulty to seed the fluid. Indeed, during the seeding procedure


humidity could be trapped between particles with a consequent clustering due to formation of ice crystals. Commercial particles respecting the density matching of liquid nitrogen are not easily available since they are normally manufactured to match water density. In this work it has been chosen to use Cospheric hollow glass sphere (density 830 Kg/m3 and diameter [5-15] µm) and to set the liquid nitrogen temperature in order to have neutral buoyancy. For the specific case a temperature of 72K (see fig. 9aError! Reference source not found.) and the relative saturation pressure of P=0.05 MPa have been chosen. The amount of PIV particles used as tracer is of the order of 60mg/l. An example of PIV image in LN2 is presented in fig. 9bError! Reference source not found..

(a)

(b)

Fig. 9 (a) T-ρ diagram for nitrogen; (b) Example of an image of PIV in LN2.

5.2. Data processing 5.2.1. PIV

The following steps compose the image processing procedure: • Masking of the images in order to isolate the Region of Interest (ROI). • Vector calculation of the PIV images. Different parameters are tested and the cross

correlation peak ratio is kept for all cases above a threshold of 2. • Vector post-processing of the velocity vector field

The dynamic masking of the images is done in order to limit the PIV processing to the ROI. The masking is performed taking advantage of the lighter particles (particle density is not uniform) which are floating on the surface of the liquid/gas interface and that, being illuminated by the laser sheet, generate a quasi-continuous line, which can be found using standard filtering algorithms. An example of PIV image and relative mask is shown in fig. 10.


The Particle Image Velocimetry analysis has been conducted in time series mode, meaning that the image “i+1” is cross correlated with the image “i” giving rise to an instantaneous velocity field. The PIV processing has been done using the parameter listed in table 2Table . Even if a minimal cross-correlation peak of 2 has been set for the vector calculations, in the vicinity of the contact line (between the fluid and the solid reservoir), due to the presence of low signal to noise ratio, in some cases, unphysical values of the velocities are present. The post processing aims to eliminate these values using the following two filters:

• The Allowed vector range filter restricts the vectors to a user specified range in units of particle separation [pixel]

• The median filter computes a median vector from a group of neighboring vectors and compares the middle vector with this median vector ± deviation of the neighboring vectors. The center vector is rejected when it is outside the allowed range of the average vector ± deviation of the neighbor vectors.

(a)

(b)

(c)

Fig. 10 Example of masking procedure. (a) Raw image, (b) mask computed by image processing, (c) mask applied to the image.

Table 2: Vector calculation parameters

Quantity Value

Iteration type Sequential cross-correlation

Initial window size 128x128 pixels

Final window size 96x96 pixels

Initial overlap 50%

Final overlap 75%


Number of passes 2

Minimal cross correlation peak ratio 2

The vector eliminated could be replaced by interpolation (median filter) but this has not been done during this post-processing. Therefore, the velocity maps would contain some “holes”, i.e. zones in which the fluid velocity is not determined. A more aggressive post processing can be done if needed but then precautions should be taken about the results obtained. Another important point to take into account is the use of a mesh composed by rectangular elements in order to compute cross correlation in PIV. This kind of mesh is not adapted to the region in which the liquid/gas interface is curved or oblique due to the inevitable truncation of the squared elements.

5.2.2. PTV

The PTV method here combines PIV+PTV method. First standard PIV is made to determine a velocity field. The velocity vectors are then used as estimators of the displacement of each particle contained in the related cross-correlation window allowing used to decrease the number of possible particle partners and therefore to reduce the number of false measurements. The detection and tracking of individual particles (PTV) then is performed. The detection of particle is based on intensity threshold and pairing of particles between the frames. The velocity of each particle is then computed from its displacement. The PTV post processing uses a filter which corrects the velocity values using the velocity information in the neighborhood. It first searches all valid vector positions and check for vectors in the neighborhood than, based on the velocity values of these vectors, it interpolates the velocity field. The result of this filter is a smoothed velocity field where spurious vectors have been replaced by the interpolation of the neighboring vectors.

5.3. Results In this section two examples of results are reported. The first one aims to show vector maps, which presents a low number of invalid vectors and the relative effect of post processing. The other one would, on the contrary, show the effect of post processing in presence of a higher number of invalid vectors. It is possible to notice, referring to Fig. 11, that the impact of the post-processing is marginal for both PIV and PTV results. Indeed, for PIV only the vectors in the upper-left corner of the ROI are affected while for PTV, which suffers less of the meshing effect, the post-processing effect is barely visible. When the interface presence affects strongly the


image quality (wrong masking, brighter spots, disperse scattered light presence …), the velocity vectors, especially for PIV, are strongly disturbed and, sometimes, unphysical even after post-processing (see fig. 11Error! Reference source not found.). On the contrary, also in this case, PTV results are less affected since the technique is based on the pairing of isolated particles therefore it is less affected by noise present in the images.

(a) PIV raw

(b) PIV post processed

(c) PTV raw

(d) PTV post processed

Fig. 11 Example of PIV and PTV velocity maps and effect of post-processing in case of low number of invalid vectors.

Therefore, it is possible to conclude, that, for the test cases analyzed in this work, the Particle Tracking Velocimetry seems more adapted to the determination of the velocity field, even in the presence of additional noise generate by the liquid/gas interface itself.

6. Conclusions


In this work, the liquid gas interface profile and the velocity field of LN2 during sloshing have been determined using two optical measurement techniques. The LeDaR technique, used to determine the 2D position of the liquid/gas interface has given satisfactory results but it fails in the vicinity of the reservoir wall, where the contact line position is perturbed by the presence of the particles used as seeding. The determination of the contact angle would need the use of a different seeding which could keep the contact angle unperturbed.

(a) PIV raw

(b) PIV post processed

(c) PTV raw

(d) PTV post processed

Fig. 12 Example of PIV and PTV results with the different post-processing where the effect of the post processing is strong

The fluid velocity field has been determined by means of both PIV and PTV. It has been showed that, if the liquid/gas interface is enough flat and horizontal, the number of invalid vector computed by PIV is low and therefore both PIV and PTV can satisfactory determine the velocity field. Contrarily, when the liquid gas interface is not anymore flat and horizontal, the rectangular mesh used for the PIV cross correlations and the presence of additional noise close to


the wall perturb strongly the PIV velocity field, while the PTV remains undisturbed. It should be remembered that, the PIV measurement presented here, are all instantaneous flow field, therefore more affected by the noise and the quality of the images. It is possible therefore to conclude that the use of optical techniques can allow the characterization of the sloshing phenomenon in cryogenic fluids. Nevertheless, some improvements are needed and they are part of the future work planned for this research activity. In the case of LeDaR, it is clear that the presence of the particles on the surface disturbs strongly the contact angle, therefore other techniques should be considered. A possibility would be to use techniques based on the deflection of light due to the curvature of the liquid meniscus or to find a luminescent material which can be dissolved in LN2. As future work the PIV technique will definitely need the development of unstructured meshes which could dynamically be adapted to the liquid/gas interface shape. This development has already started at VKI in collaboration with the University of Bristol. Acknowledgments This work was supported by the National Fund for Scientific Research in Belgium, FRS–FNRS (FRIA).

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Cryogenic sloshing investigation by means of non-intrusive