Experiments in Fluids

, Volume 39, Issue 1, pp 48–55

Optical density and velocity measurements in cryogenic gas flows

Authors

    • Institute of Fluid Dynamics (IFD)ETH Zurich
  • J. P. Kunsch
    • Institute of Fluid Dynamics (IFD)ETH Zurich
  • T. Rösgen
    • Institute of Fluid Dynamics (IFD)ETH Zurich
Originals

DOI: 10.1007/s00348-005-0966-8

Cite this article as:
Jensen, O.S., Kunsch, J.P. & Rösgen, T. Exp Fluids (2005) 39: 48. doi:10.1007/s00348-005-0966-8

Abstract

This paper presents the application of optical measurement techniques in dense-gas flows in a heavy-gas channel to determine planar two-component (2C) velocity profiles and two-dimensional (2D) temperature profiles. The experimental approach is rather new in this area, and represents progress compared with the traditional techniques based on thermocouple measurements. The dense-gas flows are generated by the evaporation of liquid nitrogen. The optical measurement of both the velocity and density profiles is accomplished by the implementation of particle image velocimetry (PIV) and background-oriented schlieren (BOS) systems. Supplemental thermocouple measurements are used as independent calibrations to derive temperatures from the density data measured with the BOS system. The results obtained with both systems are used to quantify the dilution behavior of the propagating cloud through a global entrainment parameter β. Its value agrees well with the results obtained by earlier studies.

1 Introduction

The widespread storage and transport of liquefied gases like propane can result in the accidental release into the environment of dense-gas clouds. Therefore, the spreading and dilution behavior of dense gases is always a major concern in current risk assessment studies. The spreading behavior of gases strongly depends on the density ratio of the gas to the ambient air. Due to the low temperature of the accidentally released clouds, their density is higher than the ambient value and their propagation dynamics depends on gravity. However, with a density sufficiently close to the one of the ambient air, the gas behaves passively, i.e., it moves with the prevailing flow conditions of the surrounding air. The spreading and dilution behavior of these so-called heavy-gas clouds is investigated here with particle image velocimetry (PIV) (Raffel et al. 1998; Scarano 2002; Willert and Gharib 1991). Additionally, measurements are carried out with the background-oriented schlieren (BOS) method (Dalziel et al. 2000; Meier 2002; Richard and Raffel 2001), which are supplemented by separate thermocouple reference measurements for the extraction of 2D temperature data. The purpose of this study is to assess the applicability of the present measurement techniques in cryogenic gas clouds and to support the modeling activities.

2 Experimental setup

The main experimental facility for this study is the heavy-gas channel at the Institute of Fluid Dynamics, ETH Zurich, Switzerland (Fig. 1). It was designed to investigate the propagation of dense clouds, i.e., clouds having densities larger than the ambient air. The density of the released clouds can exceed that of the ambient air by a factor of two, down to a factor close to one at the end of the cloud. This higher density causes the propagation along the floor of the channel. The current setup is chosen to create cryogenic gas clouds through the evaporation of liquid nitrogen under different conditions. The channel has a length of 12 m, is 1.2 meters wide, and has a height of 1 m. It consists of three distinct sections. The first section is the release chamber. Here, the liquid nitrogen is evaporated under controlled conditions to produce clouds with varying properties. The second section is, essentially, a horizontal surface. This section can be used to investigate the “undisturbed” propagation of the heavy-gas cloud and is suited for the installation of obstacles like fences or step-like features. The third section is composed of a series of consecutive steps that can be varied in height and length. This section can be compared to idealized topographic features and provides additional acceleration of the flow.
Fig. 1

Schematic view of the heavy-gas channel

Currently, two different release scenarios can be used to generate cryogenic heavy-gas clouds with variable properties. In the first scenario, the evaporated liquid nitrogen is suddenly released from the release chamber. With the second scenario, it is possible to continuously release a cryogenic gas cloud from a heated Dewar container filled with liquid nitrogen. The additional heating required in this case is provided by immersion heaters.

Only the setup for continuous release will be discussed here. Studies based on the configuration for sudden release are documented e.g., by Jensen et al. (2001) and Jensen (2003).

The continuous-release setup represents a generic configuration, allowing the extraction of well defined parameters of the flow. An electrical heating system is installed in a reservoir of liquid nitrogen large enough to create steady-state measuring conditions for the experiments. By varying the applied power, the amount of evaporated nitrogen can be varied continuously.

The setup for computerized BOS is rather simple, as shown in Fig. 2. For this technique, only few hardware components are necessary. The setup consists mainly of a structured background image (black-dot pattern on transparent background) placed behind the phase object, i.e., the heavy-gas channel, and a camera placed on the opposite side. The camera used here has a 1,000×1,000-pixel resolution. The background image is mounted in front of an electroluminescent sheet, which is used as the light source. This arrangement creates a very uniform illumination of the target pattern. To eliminate effects due to perspective distortions, the camera was placed as far away from the channel as possible. A telelens (focal length up to 200 mm) was used to provide a sufficient resolution of the background image. The two reference temperatures needed for the calculation of the temperature field from the index of refraction in the whole field of view (see Eq. 3) are determined by thermocouple measurements. Probe rakes with nine thermocouples each are placed at the left and right edges of the field of view of the camera. This provides the necessary temperature measurements as close as possible to the imaged area, but without disturbing it. Additionally, the redundant thermocouples can be used for verification purposes.
Fig. 2

Schematic view of the setup for background-oriented schlieren (BOS)

The experimental setup for the planar two-component (2C) velocity measurements is shown in Fig. 3. It consists of the light-sheet optics, a double-cavity Nd:YAG laser with a pair repetition rate of 15 Hz, and a 10-bit digital camera with 984×1,008-pixel resolution. The camera has a matching acquisition rate of 30 frames per second. The whole optical system is placed on a movable frame. In this way, the system can be positioned anywhere along the channel without changing the relative positions of the optical components. It is possible to generate a light sheet with a thickness of 2 mm and a width of 60 cm at its base while maintaining a high light intensity inside. This allows for a good contrast in the pictures captured with the CCD camera. The field of view normally observed with the camera is about 40-cm high by 40-cm wide. The reason for this fairly large window is the correlation of large structures related to density variations in the ice–particle distribution. These tracer particles are automatically generated during the evaporation process of the liquid nitrogen.
Fig. 3

Schematic view of the setup for particle image velocimetry (PIV)

3 Background-oriented schlieren measurements

The BOS technique (Meier 2002; Richard and Raffel 2001), which is similar to “synthetic” schlieren (Dalziel et al. 2000), is used to measure the index of refraction of the cryogenic gas cloud. In the present experiment, this technique provides the opportunity to deduce the 2D temperature field in a fairly straightforward manner. The technique is based on the distortion of one image, due to density changes, compared to an undistorted reference image. This approach can best be compared with laser speckle density photography, as described by Køpf (1972) and Wernekink and Merzkirch (1987). The processing of the images is shown in Fig. 4. First, an image pair is observed with and without a phase object placed between the background pattern and the camera, as depicted in Fig. 5. The phase object can be, for example, a heat source that changes the temperature and, therefore, the density or a compressible flow pattern. Here, the cold heavy-gas cloud is responsible for the density variations. A typical image pair of one such measurement is shown in Fig. 6. The correlation of both images results in a field of displacement vectors [Δx(xi, yi), Δy(xi, yi)]T in the observed area (Jensen 2003):
$$ \begin{aligned} \Delta x{\left( {x,y} \right)} = & \frac{1} {2}W{\left( {W + 2B} \right)}\frac{1} {{n_{0} }}\frac{{\partial n}} {{\partial x}} \\ \Delta y{\left( {x,y} \right)} = & \frac{1} {2}W{\left( {W + 2B} \right)}\frac{1} {{n_{0} }}\frac{{\partial n}} {{\partial y}} \\ \end{aligned} $$
(1)
with the undisturbed index of refraction n0 and the index of refraction n(x, y) of the phase object. The result is based on the assumption of a 2D index of refraction field with variations only in the x and y directions. This vector field, as shown in Fig. 7, represents the gradient of the index of refraction. Particularly large gradients can be observed in the mixing region between the lower layers of the cryogenic flow and the ambient air. The refractive index n(x, y) can then be calculated with different techniques. One way is to solve the Poisson equation Δn(x, y)=ρ in discrete form. Another approach is to directly solve for n(x, y) from the measured field ∇n(x, y) by using a finite-difference approximation scheme of high order. The latter scheme was used for the results presented here. The calculated index of refraction n(x, y) can be inserted into the Gladstone-Dale equation (Vasil’ev 1971) and, in combination with the equation for perfect gases, gives (for constant pressures):
$$ n = 1 + \frac{{{\text{const}}}} {T} \Rightarrow T = \frac{{{\text{const}}}} {{n - 1}} $$
(2)
Because the solution for n is determined up to another unknown (calibration) constant, Eq. 2 has to be modified to:
$$ T{\left( {x,y} \right)} = \frac{1} {{c_{1} \cdot n{\left( {x,y} \right)} + c_{2} }} $$
(3)
with two unknown constants c1 and c2, determined by:
$$ \begin{aligned} c_{1} = & \frac{{\frac{1} {{T_{{\text{a}}} }} - \frac{1} {{T_{{\text{W}}} }}}} {{n_{{\text{a}}} - n_{{\text{W}}} }} \\ c_{2} = & \frac{1} {{T_{{\text{W}}} }} - c_{1} n_{{\text{W}}} \\ \end{aligned} $$
(4)
The subscripts a stands for ambient air conditions and W for the conditions close to the wall. The refractive indexes na and nW are taken as the values of the solution n(x, y) at the locations where Ta and TW are known. The temperature measurements are taken at the same time as the corresponding images.
Fig. 4

Flow chart of the temperature calculation with BOS

Fig. 5

Sketch of influence of the phase object on rays of light for the y direction. The dashed line stands for the case without the phase object

Fig. 6

Typical image pair of a BOS measurement. The left picture is the calibration image without the cloud

Fig. 7

Displacement of the structured background image due to the phase object

The measurements presented here are carried out close to the first backward-facing step (Fig. 1) because of the best optical accessibility into the channel at this position. In Fig. 8, the resulting temperatures calibrated with the data from the thermocouple measurements are shown. This temperature field is averaged only over the width of the channel. In fact, all the BOS results presented here are obtained from single image pairs only, because the averaging of several correlation maps only has a very small effect on the quality of the data. The expected increase of the temperature along the x and y directions is clearly visible in Fig. 8, and even more clearly in Fig. 9. Here, the temperature is shown at the left and right edges of Fig. 8, together with the thermocouple measurements. The agreement between both methods is very good. This is more important for the right edge of the image, since both thermocouples used for the calibration are located on the left, upstream edge of the image. Therefore, a good agreement between both methods can be expected on the left hand side.
Fig. 8

2D temperature profile in the field of view

Fig. 9

Temperature distribution over the height at the left and right edges of Fig. 8, together with thermocouple measurements

The results presented here are, as stated before, averaged along the line-of-sight. This approach is best used with 2D flows. The correlation of measurements from thermocouples placed 66 cm apart at the same distance downstream from the source of the flow show correlation values of up to 0.8. This justifies the validity of the setup for the measurements presented in this section.

4 Particle image velocimetry measurements

The optical velocity measurements are carried out under the same experimental conditions as the BOS measurements, albeit at different positions due to better optical access into the facility with the setup implemented here. Two types of tracers for the flow visualization are used for the different regions of the flow. The lower layers of the flow are naturally visible due to the ice particles that are automatically generated during the evaporation process of the liquid nitrogen. The upper layers of the flow are visualized by the introduction of talcum powder into the facility where needed. A consequence of the ice particle seeding is the very high number density of the tracers in the flow, so that only the textures visible in the images can be correlated, as shown in Fig. 10.
Fig. 10

Snapshot of the flow illuminated with a light sheet

In Fig. 11, velocity profiles are shown for two positions in the channel. The profiles are computed by averaging three consecutive experimental runs, each generating 150 planar 2C velocity vector maps, i.e., every data point is the average of 450 velocity vector maps. The u velocity (in the x direction) has a nearly constant value above the height of 0.2 m. The height of the boundary between the dense-gas flow and the ambient air can be identified by temperature measurements. According to Fig. 15, this boundary lies approximately at 0.2 m, i.e., where room temperature prevails. The most likely explanation for the non-vanishing u velocity above this boundary is the movement of the talcum-powder seeding itself, and not simply the entrainment motion. Because the seeding is introduced into the flow upstream of the light sheet, its velocity has to be non-zero and, therefore, an additional horizontal momentum is observable in the velocity profiles. The measured velocity profiles depend on the flow conditions of the ambient air and on the way the talcum powder is introduced into the flow. Variations in the velocity profiles between measurements conducted under similar experimental conditions validate this assumption. The same explanation holds true for the y component of the velocity. The spraying process of the talcum powder is clearly the dominant factor in this case, since a global v velocity (in the y direction) should be very small in the density-driven flow. This assumption is supported by the observation of v velocities being sometimes below and sometimes well within the resolution of the PIV technique in this case. This variation observed under similar experimental conditions can only be caused by the manual introduction of the seeding and, because the talcum powder is introduced into the facility approximately 1 m above the floor of the channel, it should have a negative (downward-pointing) velocity in the chosen frame of reference.
Fig. 11

Velocity profile at two positions in the channel. Further details of the velocity profiles are shown in Fig. 12

Fig. 12

Averaged velocity profiles at the positions x1=2.9 m and x2=5.25 m

The behavior of the velocity and temperature at different distances from the source is shown in Figs. 13 and 14. These velocities and temperatures cover the lower layer of the dense-gas flow as shown in Fig. 10, which constitutes the more important part of the cloud. Each data point in Figs. 13 and 14 represents one experiment conducted under the same release conditions. The temperature of the cloud increases linearly with growing distance from the source. This can be explained easily by heat transfer from the floor and the entrainment of ambient air into the cloud. The behavior of the velocity as a function of distance from the source is not as obvious as the behavior of the temperature, although a small increase is indicated by the data.
Fig. 13

Velocity as a function of the distance from the release chamber

Fig. 14

Temperature measured with thermocouples as a function of the distance from the release chamber

5 Analysis

An objective of the present experiments was not only to generate a better insight into the basic physics of a dense-gas cloud, but also to extract and interpret the relevant parameters supporting the modeling activities. An important issue is the dilution behavior of a cryogenic dense-gas cloud, which can be described globally by an entrainment parameter.

This parameter can be deduced from a mass and a momentum balance, which are formulated for a generic differential “control volume.” This element is defined by a box delimited by an inlet and outlet vertical plane at two locations downstream of the release chamber and the top surface of the cloud propagating between both locations. The inlet and outlet planes are located at x1=2.9 m and x2=5.25 m, i.e., Fig. 11 represents the control volume. An expression for β is derived in detail in Appendix 1. This expression is evaluated with the experimental information available at both locations x1 and x2, as documented in Figs. 14 and 15, to obtain the value β=0.0026. This value of the entrainment parameter obtained with the present experimental data, is close to the range β=0.0028–0.0037 obtained by Ruff et al. (1988) for their experiments with cryogenic nitrogen. It should be observed that Ruff et al. (1988) used another heavy-gas channel with different release conditions and they evaluated β by means of an energy balance.
Fig. 15

Temperature profile measured with thermocouples at four positions in the channel

The temperature measurements yield almost constant temperatures over the height of the cloud, as documented by the temperature profiles in Fig. 15. The homogeneous temperature distribution is an indication for the intense mixing of the cloud and the dependence of β on heat transfer effects (Kunsch and Fanneløp 1995).

The definition of the entrainment parameter presented so far is simple, and several references making use of β are available for comparison and interpretation (Fanneløp 1994; Ruff et al. 1988). In addition, risk assessment studies, including heavy-gas dispersion in the chain of events, call for simple tools allowing rapid estimates of the propagation and dilution behavior. So, the shallow-layer models for dense-gas clouds require parameters accounting for the complex flow phenomena governing the frontal dynamics or the dilution behavior in a global manner. Hence, even nowadays, there are still good reasons for concentrating the information on the entrainment and dilution behavior of the present experiments in a single parameter. The easy way for extracting the corresponding information, as demonstrated in the present study, may be considered as an example. However, the optical methods presently used are suitable for a more detailed insight into the structure of a dense-gas cloud, e.g., regarding the frontal dynamics or the mixing zone on top of the dense-gas layer.

6 Summary and conclusions

The main goal of this study was to investigate the propagation of cryogenic dense-gas clouds with optical methods. Therefore, a particle image velocimetry (PIV) system and a background-oriented schlieren (BOS) system were set up to determine the two important properties; velocity and temperature.

The velocities presented are computed from the flow images obtained using PIV. Due to the properties of the “natural” seeding used, only the textures in the images can be correlated; no individual particles can be identified. As a benefit, this makes it possible to process comparatively large fields of view. Averaged planar two-component (2C) velocity profiles in a viewing area with a size of 40×40 cm could be computed for different positions in the facility.

The temperatures presented in 2D are measured with the BOS system. With a correlation algorithm, the apparent displacement of the image due to variations in the refractive index can be calculated. An in-situ calibration was performed based on discrete calibration temperatures acquired with thermocouples.

The modeling activities could be furthered by using the combined experimental results for velocity and temperature to extract a global parameter that quantifies the dilution of the cryogenic gas cloud during its propagation. An entrainment coefficient β can be derived from a mass balance and a horizontal momentum balance for a differential “control volume” in the heavy-gas channel. The coefficient is close to the values obtained in similar studies conducted by Ruff et al. (1988).

The results presented in this study show the general feasibility to investigate the spreading of cryogenic dense-gas clouds with optical methods. With the applied techniques, the two important distributions of velocity (planar 2C) and temperature (2D) of the propagating clouds could be measured. A PIV system and a BOS system were designed for this purpose. In the context of optical velocity measurements, the simultaneous visualization of the cryogenic gas flow and the ambient air was realized successfully, due to the large field of view employed. The velocimetry system and the schlieren system both allow to derive two-dimensional data. Small-scale structures in both the velocity and temperature, were, however not accessible with the optical methods chosen.

Copyright information

© Springer-Verlag 2005