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PIV application in He II forced flow research
Cryogenics 49 (2009) 535–542
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Cryogenics journal homepage: www.elsevier.com/locate/cryogenics
PIV application in He II forced flow research T. Xu a,*, S.W. Van Sciver a,b a b
National High Magnetic Field Laboratory, Florida State University, Tallahassee, FL, USA Mechanical Engineering Department, FAMU-FSU College of Engineering, Tallahasse, FL, USA
a r t i c l e
i n f o
Article history: Received 3 June 2008 Accepted 23 October 2008
Keywords: He II PIV Forced flow Solid hydrogen particles Particle seeding
a b s t r a c t We report an experimental approach for applying the PIV technique to measurements in He II forced flow. The forced flow of He II is created in a 3.5 m long experimental channel within the Liquid Helium Forced Flow Visualization Facility (LHFVF). We demonstrate that micron size solid hydrogen isotope particles are the best choice for tracing He II forced flow. A novel particle seeding device has been developed to form and seed such solid hydrogen isotope particles directly within He II flow. Velocity field measurements of forced flow He II subjected to a constant locally applied heat flux are presented. Results are compared to analysis based on the two-fluid model. Ó 2008 Elsevier Ltd. All rights reserved.
1. Introduction
2. Experimental approach to He II forced flow
Today, liquid helium is widely used as a coolant in cryogenic systems for space based experiments, high field superconducting magnets, and high energy particle accelerators [1–3]. He II forced flow is an important approach to cooling in such applications. Therefore, understanding the dynamics and heat transfer aspects of He II forced flow is of substantial importance. Besides its engineering application, He II forced flow is also of fundamental interest to the physics community because of the quantum mechanical behavior of He II. The coexistence and coupling between quantum turbulence in superfluid component and classical turbulence in normal fluid component in He II forced flow make it a rich field for the study. Here we use particle image velocimetry (PIV), a type of visualization technique, as the primary tool to study these flow phenomena. Detailed velocity field information obtained using the PIV technique should help to reveal the dynamic aspects of He II flows, which can not be thoroughly investigated by traditional instrumentation for the study of He II such as temperature, pressure, and second sound measurements. One of the primary aims of this research is to develop a universal protocol for applying the PIV technique to He II forced flow and to solve the technical hurdles raised by the cryogenic environment and the low density of He II. As an example of the kind of data that can be obtained from such measurements, velocity measurements of He II forced flow with a constant local heat flux are presented.
Shown in Fig. 1 is a schematic of the experimental setup used to generate forced flow for the present research. The experimental apparatus is contained in the Liquid Helium Forced Flow Visualization Facility (LHFVF), which is specifically designed to perform visualization studies in forced flow cryogenic fluids. This facility has the capability to do flow visualization experiments on single phase forced flow and two-phase flow of different cryogenic fluids in a horizontal orientation.
* Corresponding author. Tel.: +1 850 644 1059. E-mail address: [email protected] (T. Xu). 0011-2275/$ - see front matter Ó 2008 Elsevier Ltd. All rights reserved. doi:10.1016/j.cryogenics.2008.10.021
2.1. LHFVF The experimental space of the LHFVF, 0.2 m in diameter and 5.1 m in length, can be accessed on both ends of the facility. The large inner bore allows experiments of various sizes to be inserted. Multi-channel cold instrumentation is available for measuring temperature, pressure and liquid level. Two concentric radiation shields around the inner bore are actively cooled to 100 K and 10 K, respectively by natural circulation loops of LN2 and LHe. After the initial cool down, the facility consumes around 100 l of liquid helium in a 12 h period. The He II supply to the experimental loop is provided by the liquid reservoirs located in the vertical stacks at the ends of the LHFVF; the quantity supplied is manually controlled by the filling valves as shown in Fig. 1. In this configuration, the liquid in the experimental loop, which includes the experimental channel and two metal bellows pumps suspended below each reservoir, can be isolated from the stacks during the test. The two bellows, which have a 1.81 102 m2 effective area and 0.057 m stroke, provide a maximum volume displacement of approximately 1 l. These
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Fig. 1. Schematic of He II forced flow experimental setup.
bellows are driven by the linear stepper motors mounted at the top of the stack to create precisely controlled flows in the experimental loop. The stepper motors are slaved together to provide a constant volume forced flow process at a volume displacement rate up to 0.1 l/s. There are two visualization ports along the horizontal section of the LHFVF, one at the midpoint and one 1 m down stream to right in the schematic. Each port has three sets of optical windows aligned 90° apart from the top to the bottom on both the outside wall of the LHFVF and the thermal shields. The windows mounted on the LHe shield are coated with infrared reflecting film to minimize the radiation heat transfer through the visualization ports to the experimental space. The maximum viewing area provided is 50 mm in diameter. 2.2. He II forced flow channel design The forced flow channel developed for the present visualization research is constructed of stainless steel and has a 20 mm
20 mm square cross-section and is 3.35 m in length. The reason for having a square shape cross-section instead of a classical round tube is to allow the use flat glass windows without disturbing the flow. The channel has two sets of optical windows aligned with those on the LHFVF. The light source windows on the top and bottom of the channel are 14 mm in diameter. The camera windows located on the front side perpendicular to the light sheet are 24 mm in diameter, which is larger than the channel width. This design allows one to study the fluid motion in the vicinity of the wall as shown in Fig. 2. The sapphire view ports (model number: 17105-01-W and 17105-02-W) used on the channel are from CeramTec, Inc. and have proven to be reliable in the He II temperature region in our experiments. The particle injection port, designed to connect the seeding unit, is located 0.18 m upstream from the center visualization port. This location ensures that the seeded particles are able to flow past the center window section within the limited maximum volume displacement of the bellows pump (1 l). Detailed information of the seeding unit is given later in this paper.
Fig. 2. Schematic of He II forced flow experimental channel.
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The end reservoir is a large diameter tube, 80 mm in diameter and 0.2 m in length, equipped with a capacitive level gauge and a calibrated temperature sensor. The vapor line at the top of this reservoir is connected to the vapor line of the right side stack. In this way, the vapor phase in the experimental loop and the right side stack are linked, even though the liquid is separated by the filling valve. Therefore, the liquid in the experimental loop and the right side stack always have the same bath temperature during the tests. The channel is also capable of two-phase forced flow experiments, in which case the end reservoir serves as a phase separator. 2.3. Instrumentation and flow control The PIV system used in these experiments consists of a frequency doubled Nd:YAG pulse laser, CCD camera, light sheet forming optics, timing unit and PC based PIV control and analysis software as shown in Fig. 3. The laser emits green light with a wavelength of 532 nm and has a maximum repetition rate of 15 Hz. The dual-head configuration is capable of firing two laser pulses with adjustable time interval from less than 1 ls to 10 ms, when operated with the current timing unit. This allows one to measure the velocity field over a wide dynamics range. The CCD camera is a sharpVISIONTM 1300-DE from Integrated Design Tool, Inc. It is equipped with a progressive scan interline monochrome CCD chip (model number: Sony ICX205AL), which has a maximum resolution of 1300 1030 pixels with a pixel size of 6.7 lm. A 105 mm f/2.8D macro lens is connected to the camera through an F-mount to C-mount adapter. This combination provides a large reproduction ratio at long working distance. The f# is set at 2.8, which provides a depth of field of about 1 mm, matching the thickness of the laser sheet. The camera connects to the data acquisition computer through IEEE-1394 interface to achieve real time communication and high speed data transfer rate (400 Mb/s). The timing unit includes a timing box from Integrated Design Tools, Inc. and PCI-6602 board from National Instruments. The timing box provides TTL HIGH-TRUE signals to trigger and synchronize the pulse laser and the CCD camera. The image data is acquired and processed by proVISION-XS PIV software from integrated Design Tools, Inc. The whole PIV system is mounted on a mobile frame and can be easily switched between the two visualization ports as shown in Fig. 3. Three CernoxTM 1050 bare chip sensors from LakeShore Cryotronics are installed in the channel: two at the back side of the
Fig. 4. Flow control and DAQ system. Dashed line box is low temperature region.
channel wall of each optical port, and one at the side wall 12.5 mm downstream from the seeding port. The sensors are mounted on special flanges [4] with the sensing film facing the flow allowing direct measurement of the temperature of He II. These temperature sensors are calibrated in situ against a commercially calibrated germanium resistance sensor placed in the end reservoir. The temperature gradient along the channel is assumed negligible during the calibration process. The heating power is provided by the coiled wire heater at 0.64 m downstream from the entrance of the channel as shown in Fig. 2. The heater (96.7 X), 19 mm in length and 5 mm in diameter, is placed at the centerline of the cross-section. Since the distance between the heater and the center visualization port is 50 times the channel width, the disturbance to the flow structure caused by the heater can be neglected. The flow chart of the flow control and the DAQ system is shown in Fig. 4. The control commands are sent to the Compumotor 6200 two-axis indexer by the Mac based LabView program through the GPIB interface. The indexer interprets the commands and sends them to the chosen motor driver module and the displacements of the actuators are sent back to the computer by the indexer to achieve real-time monitoring. The voltage signals from the temperature sensors are amplified by a set of Preston 8300 XWB amplifiers and then converted to digital signals by the PCI-6071E National Instruments DAQ card, which has a full measuring range of ±10 V DC with 12-bit resolution. The coiled manganin wire heater is powered by a DC power supply (model number TENMAÒ 72-7245). The control system for the seeding unit is described in the next section. 3. Tracer particles and seeding in He II 3.1. Selection of tracer particles
Fig. 3. PIV setup of He II forced flow experiments.
The accuracy of PIV measurements mostly relies on the fidelity of tracer particles in the flow and the image quality of the light
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scattering pattern of tracer particles on CCD devices. Unfortunately, these two requirements are in conflict when used as the guidelines to determine the tracer particle size. The two important characteristic quantities describing the tracking ability of tracer particles are: (1) the characteristic response time of tracer particles sp to a flow change and (2) the slip velocity Vslip caused by the density difference between tracer particles and the fluid in a gravitational field. Both sp and Vslip are proportional to the square of the particle diameter dp as given below:
sp ¼ d2p ðqp þ qHe =2Þ=18gn 2 V slip ¼ dp ðqp qHe Þ g=18gn
ð1Þ ð2Þ
where subscript p and He represent particle and He II respectively, and gn is the viscosity of the normal fluid component of He II. This means that reducing particle size always improves the tracking ability of particles. In order to quantify the maximum particle size allowed, here we introduce the Stokes number St,
St ¼ sp =st
ð3Þ
where st is the characteristic time of the turbulent flow and can be written in the Kolmogorov time scale form,
st ¼
pffiffiffiffiffiffiffiffi t=e
ð4Þ
where t is the kinetic viscosity of He II and e is the average rate of energy dissipation per unit mass. Thus, the Stokes number can be rewritten as
St ¼
2 1 qp dp þ 0:5 18 qHe g
ð5Þ
where g is the Kolmogorov length scale. It is reasonable to assume that the smallest length scale of normal fluid turbulence is equal to the quantized vortex line spacing, which is 105 m for relative velocity of 1 m/s. Thus, neutrally buoyant particles less than 10 lm in diameter are generally acceptable as the criterion states that the particle response time needs to be at least one order magnitude smaller than the characteristic time of He II turbulent flows (St < 0.1). On the other hand, to achieve discernable image recording, the particles have to scatter enough light to be sensed by the CCD chip at a relatively high signal to noise ratio. In the micron size range, the scattering power is proportional to dp2 and the particle image diameter dt is dominated by the light diffraction limited minimum diameter and is almost independent of dp. This means that one
faces a trade-off between dp size and laser power input I0. Thus, the optimum particle size should be small enough to faithfully reveal the characteristic information of the target flow and have an image diameter not significantly greater than its physical diameter [5]. Fig. 5 plots dt and dt/dp as the function of particle size and f# with the PIV setting in the present research. For the present case with f# = 2.8, the optimum particle size is around 5 lm. In addition specific to He II research, minimizing the laser power is critical to reducing the error in the velocity measurements caused by the laser heating of the He II [6]. Possible sources of tracer particles for He II experiments can be divided into two categories: one is the commercially available synthetic spherical particles like hollow glass spheres and PMMA micro-spheres, and the other one is the solidified gas particles generated in the cryogenic environment during the experiments. More detailed information about these different particles is given in Zhang et al. [7]. Here, we have chosen solidified hydrogen isotope particles as the tracers for the following reasons. Although, only the right ratio mixture of solidified H2–D2 can be truly neutrally buoyant in He II (qHe 145 kg/m3), solid hydrogen (qp = 89 kg/m3) and solid deuterium (qp = 206 kg/m3) are also considered to be good candidates for tracer particle material because of small density differences between them and He II. The light weight provides these particles with better tracking ability compare to PMMA micro-spheres of the same size and keeps them in the flow longer, which is especially important to the horizontal orientated flow cases. In addition, these particles evaporate after the experiments are warmed above the normal boiling temperature (for example TNBP = 23.6 K for deuterium) and can be easily cleaned out by purging the system with pure helium gas. This feature avoids warming the experiment back to room temperature and the associated effort of disassembling the apparatus for cleaning. There are two disadvantages of solidified hydrogen particles: (1) the loss of control of particle shape and (2) the tendency of the particles to agglomerate. Solid hydrogen isotope particles generally have irregular shapes and rough surfaces because of the way of particles form. The spin caused by the unsymmetrical shape may result in some random motion of tracer particles in the flow. Also, change in the drag coefficient due to the non-spherical shape and rough surface may produce errors in the modeling work, which usually assumes a perfect spherical shape for tracer particles. Experiments [8,9] have shown that the particles tend to agglomerate after being generated. This reduces the lifetime of the seeded particles. Furthermore, the seeding process is more complicated compared to that for synthetic particles. 3.2. Particle seeding
Fig. 5. Particle image diameter dt and dt/dp as a function of particle size and f#.
Several different approaches have been developed to introduce solidified gas particles into He II. The first attempt to use solid H2– D2 as tracer particles in He II was attributed to Chopra and Brown in 1975 [10]. They obtained millimeter size solid particles by injecting a H2–D2 gas mixture above the free surface in a He II reservoir. Later, Nakano and Murakami reported generating 1 lm particles by this same method and used these particles as tracers in the LDV measurements in a thermal counterflow jet [11,12]. In this method, since the particles are formed in the vapor phase above the free surface, a large portion of them are pumped away with helium vapor before entering liquid phase as shown in Fig. 6a. Therefore, the seeding efficiency of this method is quite low. Another way to form solid particles has been reported recently by Celik et al. [8]. In this experiment, liquid neon was injected into He II directly through a plain orifice atomizer to form micron size particles, as shown in Fig. 6b. However, this process was not very successful in producing small, uniform solid hydrogen particles.
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Fig. 6. Schematic of the methods to seed solidified gas particles.
A more successful attempt at seeding micron scale solid hydrogen particles was made by Boltnev et al. in 2002 [13]. In their case, deuterium gas was first diluted with helium gas (1/20–1/1000) at room temperature. The gas mixture was then injected onto the free surface of He II through a nozzle placed 30 mm above it. Small angle X-ray scattering results showed that the solid deuterium particles formed in this way were in the submicron range. Injecting diluted seeding gas into liquid helium directly has been developed by our group and Bewley et al. independently [9,14]. This seeding method can be applied to the experiments which do not have the vapor phase close to the target flow visualization region. It also avoids the possible agglomeration at free surface due to the small settling velocities of solid hydrogen isotope particles. Bewley et al. reported creating 1–4 lm solid hydrogen particles by injected diluted seeding gas into He I. The experiment was then slowly pumped down to He II region. Because of particle agglomeration during pumping process, this experiment was restricted within the temperature range very close to the k point (Tk = 2.176 K). In the present research, we chose to inject diluted seeding gas into He II directly. Thus, the operating temperature is not limited. Furthermore, because of the rapid seeding process (generally a few seconds) and the very low mass diffusion rate of the seeded particles at He II temperatures, seeding can be made into He II locally near the visualization port provided the tracer particles do not need to occupy to the whole flow. The local seeding can also reduce the possibility of agglomeration and the heat input by seeding process. The seeding system for LHFVF includes three units: injection unit, seeding gas mixing and supply unit, and control unit. The injection unit is connected to the seeding port of experimental channel with the orifice contacting He II directly as shown in Fig. 7. The injection valve, a cryogenic miniature pulse valve made by the Parker Hannifin Corporation, is installed at the end of the seeding tube to achieve better control of the pressure and the temperature of seeding gas jet. A 120 X strain gauge (backing material: reinforced epoxy-phenolic) placed inside the valve is used as the heater to melt the solid hydrogen in case the orifice accidentally gets blocked. A silicon diode temperature sensor is mounted inside the seeding tube to measure the seeding gas temperature. Shown in Fig. 8 is the schematic of the seeding gas mixing and supply unit. The operation of this unit is relatively common. The
Fig. 7. Injection unit of hydrogen isotope particle seeding system.
whole unit is first evacuated by a roughing vacuum pump and purged with pure helium gas for more than ten times. The seeding gas section (brown path) is then evacuated and purged with the desired seeding gas (H2, D2 or H2–D2) for more than 20 times to remove any impurity in the system. After the purging process, the seeding gas section is charged back with seeding gas to around 0.2 MPa. Due to the high permeability of hydrogen isotopes, the 2 m long high pressure rubber hose between the needle valve VOUT and VT3 is saturated with the seeding gas within several hours. The section is then purged with helium gas for five or six times. Because of the seeding gas concentration difference between that absorbed in the rubber and the helium gas, the seeding gas slowly diffuses into the helium carrier gas. Thus, strongly diluted hydrogen gas is made and ready for the seeding process. Though we are not able to measure the exact dilution ratio in this case, it is reasonable to expect that it is much lower than 1%. The diluted seeding gas pressure is controlled and monitored by the BarocelÒ absolute pressure transducer. The gate valve VG is opened manually each time before the injection and closed immediately afterwards to avoid hydrogen molecules from accumulating around the orifice plate due to cryo-pumping. A DC power supply (model number TENMAÒ 72-7245) and a timing unit made in house are used to control and energize the solenoid pulse valve. The detailed test results of this seeding system were reported in our previous paper [6]. The optimum back pressure Pb of the diluted seeding gas and pulse valve opening time so, were obtained experimentally by trial and error and are 0.11 MPa and 1.1 s, respectively. The results also show that a strongly diluted seeding gas (helium gas >99% of the seeding mixture) is required to avoid
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Fig. 8. Schematic of the seeding gas mixing and supply unit.
large solid hydrogen clusters from forming during seeding process in a narrow channel. The slip velocity measurements showed that the solidified hydrogen isotope particles generated by this seeding system follow a continuous size distribution with 90% of the particles being less than 10 lm in diameter with the distribution peaked around 4.3 lm. Therefore, these tracer particles generally meet the criteria given in Section 3.1. 4. Results and discussion Here, we report PIV measurements of He II forced flow with constant heat flux using the experimental setup described above. A constant heat flux up to 6.6 kW/m2 was applied to a steady state forced flow of He II through the channel using the heater shown in Fig. 2. Generally speaking, the heat can be transported by both thermal counterflow and forced convection of He II in this case. The portion of the heat qic conducted by thermal counterflow induces a velocity difference between normal fluid component and bulk fluid, which can be expressed as
qic ¼ qsTðU n UÞ
ð6Þ
In order to compare the velocity field of He II, normal fluid and tracer particles, in this case the mean forced flow velocity is maintained at 23 mm/s, which is the same order as the normal fluid velocity according to the heat flux range used. Shown in Fig. 9 are the steady state temperature profiles measured at different heat fluxes along the flow direction. The dash lines in the figure are the theoretical calculations using Eq. (7), which represent the case that all the applied heat is transferred by thermal countflow:
1=3 1 dT q¼ f ðTÞ dx
ð7Þ
where f(T) is the heat conductivity function for He II and is equal to Aqn =ðq3s s4 T 3 Þ. The results show that the measured values are in rea-
Fig. 9. Temperature profiles along the channels as a function of heat flux with a constant forced flow velocity Umean = 23.0 mm/s. Heater is located at x = 2.71 m. x = 0 represents the end reservoir. The dash lines are calculated values based on one-dimensional thermal counterflow heat transfer equation using measured bath temperature at x = 0 as the boundary condition.
sonable agreement with the calculations. Thus, we can assume that the heat transferred by forced convection can be neglected and essentially all the heat is transferred by thermal counterflow in the same direction with the flow in this specific case. This result is quite understandable because of the high efficiency of thermal counterflow and the low forced flow velocity in the present experiments. Therefore, the normal fluid velocity should be written in one-dimensional form as a function of total heat flux q,
U n ¼ U þ q=qsT
ð8Þ
Fig. 10 shows the averaged velocity field of the solid deuterium particles in He II forced flow with a constant heat flux, q = 5.8 kW/ m2 as a typical example of these measurements. The y-axis is in
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Fig. 12. Velocity profiles of deuterium particles in forced flow along the channel width for different heat flux at 1.95 K. y = 1 represents the center of the channel.
Fig. 10. Averaged velocity field of the deuterium particles in forced flow He II with a constant heat flux: q = 5.8 kW/m2, Umean = 23.0 mm/s, and Tb = 1.95 K.
the vertical direction and parallel to the cross-section plane with y = 0 representing the center line of the channel and the x-axis is in the flow direction. The streamlines of the measured velocity field are generally parallel to the direction of the flow and the heat flux. The horizontal velocity component of the tracer particles are general greater than the averaged forced flow velocity Umean, 23 mm/s, however, much lower than the averaged normal fluid velocity using Eq. (8), which is 44.3 mm/s for the case in Fig. 10. We believe that the particle velocity is the result of the force balance on the particle between the viscous drag of the normal fluid component and the interaction force from the quantized vortex line of the superfluid component, which was discussed in the literature [7,14,15]. For better comparison, we averaged the velocity vectors along the flow direction and plotted the particle velocity profiles along the channel width W at two different bath temperatures 1.80 K and 1.95 K, see Figs. 11 and 12. The data show that the velocity increase caused by the thermal counterflow is approxi-
mately equal over the channel width. The presence of the thermal counterflow does not change the shape of the velocity profile including the turbulent boundary layer, which was reported in our previous work [16]. Since thermal counterflow is the only heat transfer mechanism in this case, the heat flux can be considered uniform over the channel width due to the high effective thermal conductivity of He II. The relative velocity of the normal fluid component with respect to the forced flow velocity, which is a function of the heat flux only, should be the same along the channel width according to Eq. (8) except for the region very close to the wall, which must satisfy the viscous boundary condition. Therefore, it is reasonable to have uniform shifts in the particle velocity profiles. The averaged velocity profiles in Figs. 11 and 12 were integrated to obtain Umean, the mean particle velocity in the horizontal direction. As shown in Fig. 13, Umean increases approximately linearly with normal fluid velocity in the flow within the heat flux and temperature range tested. The slope of the linear fit is around 0.38, which is slight lower than the value obtained in the pure thermal counterflow experiment by Zhang [7] (slope between 0.4 and
Fig. 11. Velocity profiles of deuterium particles in forced flow along the channel width for different heat flux at 1.80 K. y = 1 represents the center of the channel.
Fig. 13. Mean velocity of deuterium particles in He II forced flow as a function of relative normal fluid velocity predicted by the two-fluid model.
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0.6). In forced flow, the quantized vortex line density is not only a function of temperature but also the function of flow velocity. This may affect the interaction between tracer particles and superfluid component. Although these results are still quite preliminary, they represent the first PIV measurements of the combined forced flow and counterflow in He II. In the future, we plan to repeat this experiment at higher forced flow velocities, which increases the quantized vortex line density without increasing the relative velocity of the normal fluid component in the flow. 5. Summary An experimental system focusing on PIV applications to He II forced flow research has been designed, built and tested. The unique design of the window section of the experimental channel allows one to study the fluid motion in the vicinity of wall. To enable these measurements, a novel seeding system has been developed to generate and seed solid hydrogen isotope particles into the He II flow field. The slip measurements confirm that the generated particles follow a certain statistical distribution and range in diameter from one to ten microns. We do not see a noticeable change in the performance of the seeding system for the range of temperature studied (1.65–2.10 K). Therefore, this seeding scheme can be applied to different He II experiments regardless of system scale or the existence of free surface. The preliminary results of He II forced flow with constant heat flux demonstrate that the behavior of tracer particles is similar to that in the pure thermal counterflow case. Acknowledgement This work is supported by the US Department of Energy-Division of High Energy Physics under Grant FG02-96ER-40952.
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Cryogenics journal homepage: www.elsevier.com/locate/cryogenics
PIV application in He II forced flow research T. Xu a,*, S.W. Van Sciver a,b a b
National High Magnetic Field Laboratory, Florida State University, Tallahassee, FL, USA Mechanical Engineering Department, FAMU-FSU College of Engineering, Tallahasse, FL, USA
a r t i c l e
i n f o
Article history: Received 3 June 2008 Accepted 23 October 2008
Keywords: He II PIV Forced flow Solid hydrogen particles Particle seeding
a b s t r a c t We report an experimental approach for applying the PIV technique to measurements in He II forced flow. The forced flow of He II is created in a 3.5 m long experimental channel within the Liquid Helium Forced Flow Visualization Facility (LHFVF). We demonstrate that micron size solid hydrogen isotope particles are the best choice for tracing He II forced flow. A novel particle seeding device has been developed to form and seed such solid hydrogen isotope particles directly within He II flow. Velocity field measurements of forced flow He II subjected to a constant locally applied heat flux are presented. Results are compared to analysis based on the two-fluid model. Ó 2008 Elsevier Ltd. All rights reserved.
1. Introduction
2. Experimental approach to He II forced flow
Today, liquid helium is widely used as a coolant in cryogenic systems for space based experiments, high field superconducting magnets, and high energy particle accelerators [1–3]. He II forced flow is an important approach to cooling in such applications. Therefore, understanding the dynamics and heat transfer aspects of He II forced flow is of substantial importance. Besides its engineering application, He II forced flow is also of fundamental interest to the physics community because of the quantum mechanical behavior of He II. The coexistence and coupling between quantum turbulence in superfluid component and classical turbulence in normal fluid component in He II forced flow make it a rich field for the study. Here we use particle image velocimetry (PIV), a type of visualization technique, as the primary tool to study these flow phenomena. Detailed velocity field information obtained using the PIV technique should help to reveal the dynamic aspects of He II flows, which can not be thoroughly investigated by traditional instrumentation for the study of He II such as temperature, pressure, and second sound measurements. One of the primary aims of this research is to develop a universal protocol for applying the PIV technique to He II forced flow and to solve the technical hurdles raised by the cryogenic environment and the low density of He II. As an example of the kind of data that can be obtained from such measurements, velocity measurements of He II forced flow with a constant local heat flux are presented.
Shown in Fig. 1 is a schematic of the experimental setup used to generate forced flow for the present research. The experimental apparatus is contained in the Liquid Helium Forced Flow Visualization Facility (LHFVF), which is specifically designed to perform visualization studies in forced flow cryogenic fluids. This facility has the capability to do flow visualization experiments on single phase forced flow and two-phase flow of different cryogenic fluids in a horizontal orientation.
* Corresponding author. Tel.: +1 850 644 1059. E-mail address: [email protected] (T. Xu). 0011-2275/$ - see front matter Ó 2008 Elsevier Ltd. All rights reserved. doi:10.1016/j.cryogenics.2008.10.021
2.1. LHFVF The experimental space of the LHFVF, 0.2 m in diameter and 5.1 m in length, can be accessed on both ends of the facility. The large inner bore allows experiments of various sizes to be inserted. Multi-channel cold instrumentation is available for measuring temperature, pressure and liquid level. Two concentric radiation shields around the inner bore are actively cooled to 100 K and 10 K, respectively by natural circulation loops of LN2 and LHe. After the initial cool down, the facility consumes around 100 l of liquid helium in a 12 h period. The He II supply to the experimental loop is provided by the liquid reservoirs located in the vertical stacks at the ends of the LHFVF; the quantity supplied is manually controlled by the filling valves as shown in Fig. 1. In this configuration, the liquid in the experimental loop, which includes the experimental channel and two metal bellows pumps suspended below each reservoir, can be isolated from the stacks during the test. The two bellows, which have a 1.81 102 m2 effective area and 0.057 m stroke, provide a maximum volume displacement of approximately 1 l. These
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Fig. 1. Schematic of He II forced flow experimental setup.
bellows are driven by the linear stepper motors mounted at the top of the stack to create precisely controlled flows in the experimental loop. The stepper motors are slaved together to provide a constant volume forced flow process at a volume displacement rate up to 0.1 l/s. There are two visualization ports along the horizontal section of the LHFVF, one at the midpoint and one 1 m down stream to right in the schematic. Each port has three sets of optical windows aligned 90° apart from the top to the bottom on both the outside wall of the LHFVF and the thermal shields. The windows mounted on the LHe shield are coated with infrared reflecting film to minimize the radiation heat transfer through the visualization ports to the experimental space. The maximum viewing area provided is 50 mm in diameter. 2.2. He II forced flow channel design The forced flow channel developed for the present visualization research is constructed of stainless steel and has a 20 mm
20 mm square cross-section and is 3.35 m in length. The reason for having a square shape cross-section instead of a classical round tube is to allow the use flat glass windows without disturbing the flow. The channel has two sets of optical windows aligned with those on the LHFVF. The light source windows on the top and bottom of the channel are 14 mm in diameter. The camera windows located on the front side perpendicular to the light sheet are 24 mm in diameter, which is larger than the channel width. This design allows one to study the fluid motion in the vicinity of the wall as shown in Fig. 2. The sapphire view ports (model number: 17105-01-W and 17105-02-W) used on the channel are from CeramTec, Inc. and have proven to be reliable in the He II temperature region in our experiments. The particle injection port, designed to connect the seeding unit, is located 0.18 m upstream from the center visualization port. This location ensures that the seeded particles are able to flow past the center window section within the limited maximum volume displacement of the bellows pump (1 l). Detailed information of the seeding unit is given later in this paper.
Fig. 2. Schematic of He II forced flow experimental channel.
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The end reservoir is a large diameter tube, 80 mm in diameter and 0.2 m in length, equipped with a capacitive level gauge and a calibrated temperature sensor. The vapor line at the top of this reservoir is connected to the vapor line of the right side stack. In this way, the vapor phase in the experimental loop and the right side stack are linked, even though the liquid is separated by the filling valve. Therefore, the liquid in the experimental loop and the right side stack always have the same bath temperature during the tests. The channel is also capable of two-phase forced flow experiments, in which case the end reservoir serves as a phase separator. 2.3. Instrumentation and flow control The PIV system used in these experiments consists of a frequency doubled Nd:YAG pulse laser, CCD camera, light sheet forming optics, timing unit and PC based PIV control and analysis software as shown in Fig. 3. The laser emits green light with a wavelength of 532 nm and has a maximum repetition rate of 15 Hz. The dual-head configuration is capable of firing two laser pulses with adjustable time interval from less than 1 ls to 10 ms, when operated with the current timing unit. This allows one to measure the velocity field over a wide dynamics range. The CCD camera is a sharpVISIONTM 1300-DE from Integrated Design Tool, Inc. It is equipped with a progressive scan interline monochrome CCD chip (model number: Sony ICX205AL), which has a maximum resolution of 1300 1030 pixels with a pixel size of 6.7 lm. A 105 mm f/2.8D macro lens is connected to the camera through an F-mount to C-mount adapter. This combination provides a large reproduction ratio at long working distance. The f# is set at 2.8, which provides a depth of field of about 1 mm, matching the thickness of the laser sheet. The camera connects to the data acquisition computer through IEEE-1394 interface to achieve real time communication and high speed data transfer rate (400 Mb/s). The timing unit includes a timing box from Integrated Design Tools, Inc. and PCI-6602 board from National Instruments. The timing box provides TTL HIGH-TRUE signals to trigger and synchronize the pulse laser and the CCD camera. The image data is acquired and processed by proVISION-XS PIV software from integrated Design Tools, Inc. The whole PIV system is mounted on a mobile frame and can be easily switched between the two visualization ports as shown in Fig. 3. Three CernoxTM 1050 bare chip sensors from LakeShore Cryotronics are installed in the channel: two at the back side of the
Fig. 4. Flow control and DAQ system. Dashed line box is low temperature region.
channel wall of each optical port, and one at the side wall 12.5 mm downstream from the seeding port. The sensors are mounted on special flanges [4] with the sensing film facing the flow allowing direct measurement of the temperature of He II. These temperature sensors are calibrated in situ against a commercially calibrated germanium resistance sensor placed in the end reservoir. The temperature gradient along the channel is assumed negligible during the calibration process. The heating power is provided by the coiled wire heater at 0.64 m downstream from the entrance of the channel as shown in Fig. 2. The heater (96.7 X), 19 mm in length and 5 mm in diameter, is placed at the centerline of the cross-section. Since the distance between the heater and the center visualization port is 50 times the channel width, the disturbance to the flow structure caused by the heater can be neglected. The flow chart of the flow control and the DAQ system is shown in Fig. 4. The control commands are sent to the Compumotor 6200 two-axis indexer by the Mac based LabView program through the GPIB interface. The indexer interprets the commands and sends them to the chosen motor driver module and the displacements of the actuators are sent back to the computer by the indexer to achieve real-time monitoring. The voltage signals from the temperature sensors are amplified by a set of Preston 8300 XWB amplifiers and then converted to digital signals by the PCI-6071E National Instruments DAQ card, which has a full measuring range of ±10 V DC with 12-bit resolution. The coiled manganin wire heater is powered by a DC power supply (model number TENMAÒ 72-7245). The control system for the seeding unit is described in the next section. 3. Tracer particles and seeding in He II 3.1. Selection of tracer particles
Fig. 3. PIV setup of He II forced flow experiments.
The accuracy of PIV measurements mostly relies on the fidelity of tracer particles in the flow and the image quality of the light
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scattering pattern of tracer particles on CCD devices. Unfortunately, these two requirements are in conflict when used as the guidelines to determine the tracer particle size. The two important characteristic quantities describing the tracking ability of tracer particles are: (1) the characteristic response time of tracer particles sp to a flow change and (2) the slip velocity Vslip caused by the density difference between tracer particles and the fluid in a gravitational field. Both sp and Vslip are proportional to the square of the particle diameter dp as given below:
sp ¼ d2p ðqp þ qHe =2Þ=18gn 2 V slip ¼ dp ðqp qHe Þ g=18gn
ð1Þ ð2Þ
where subscript p and He represent particle and He II respectively, and gn is the viscosity of the normal fluid component of He II. This means that reducing particle size always improves the tracking ability of particles. In order to quantify the maximum particle size allowed, here we introduce the Stokes number St,
St ¼ sp =st
ð3Þ
where st is the characteristic time of the turbulent flow and can be written in the Kolmogorov time scale form,
st ¼
pffiffiffiffiffiffiffiffi t=e
ð4Þ
where t is the kinetic viscosity of He II and e is the average rate of energy dissipation per unit mass. Thus, the Stokes number can be rewritten as
St ¼
2 1 qp dp þ 0:5 18 qHe g
ð5Þ
where g is the Kolmogorov length scale. It is reasonable to assume that the smallest length scale of normal fluid turbulence is equal to the quantized vortex line spacing, which is 105 m for relative velocity of 1 m/s. Thus, neutrally buoyant particles less than 10 lm in diameter are generally acceptable as the criterion states that the particle response time needs to be at least one order magnitude smaller than the characteristic time of He II turbulent flows (St < 0.1). On the other hand, to achieve discernable image recording, the particles have to scatter enough light to be sensed by the CCD chip at a relatively high signal to noise ratio. In the micron size range, the scattering power is proportional to dp2 and the particle image diameter dt is dominated by the light diffraction limited minimum diameter and is almost independent of dp. This means that one
faces a trade-off between dp size and laser power input I0. Thus, the optimum particle size should be small enough to faithfully reveal the characteristic information of the target flow and have an image diameter not significantly greater than its physical diameter [5]. Fig. 5 plots dt and dt/dp as the function of particle size and f# with the PIV setting in the present research. For the present case with f# = 2.8, the optimum particle size is around 5 lm. In addition specific to He II research, minimizing the laser power is critical to reducing the error in the velocity measurements caused by the laser heating of the He II [6]. Possible sources of tracer particles for He II experiments can be divided into two categories: one is the commercially available synthetic spherical particles like hollow glass spheres and PMMA micro-spheres, and the other one is the solidified gas particles generated in the cryogenic environment during the experiments. More detailed information about these different particles is given in Zhang et al. [7]. Here, we have chosen solidified hydrogen isotope particles as the tracers for the following reasons. Although, only the right ratio mixture of solidified H2–D2 can be truly neutrally buoyant in He II (qHe 145 kg/m3), solid hydrogen (qp = 89 kg/m3) and solid deuterium (qp = 206 kg/m3) are also considered to be good candidates for tracer particle material because of small density differences between them and He II. The light weight provides these particles with better tracking ability compare to PMMA micro-spheres of the same size and keeps them in the flow longer, which is especially important to the horizontal orientated flow cases. In addition, these particles evaporate after the experiments are warmed above the normal boiling temperature (for example TNBP = 23.6 K for deuterium) and can be easily cleaned out by purging the system with pure helium gas. This feature avoids warming the experiment back to room temperature and the associated effort of disassembling the apparatus for cleaning. There are two disadvantages of solidified hydrogen particles: (1) the loss of control of particle shape and (2) the tendency of the particles to agglomerate. Solid hydrogen isotope particles generally have irregular shapes and rough surfaces because of the way of particles form. The spin caused by the unsymmetrical shape may result in some random motion of tracer particles in the flow. Also, change in the drag coefficient due to the non-spherical shape and rough surface may produce errors in the modeling work, which usually assumes a perfect spherical shape for tracer particles. Experiments [8,9] have shown that the particles tend to agglomerate after being generated. This reduces the lifetime of the seeded particles. Furthermore, the seeding process is more complicated compared to that for synthetic particles. 3.2. Particle seeding
Fig. 5. Particle image diameter dt and dt/dp as a function of particle size and f#.
Several different approaches have been developed to introduce solidified gas particles into He II. The first attempt to use solid H2– D2 as tracer particles in He II was attributed to Chopra and Brown in 1975 [10]. They obtained millimeter size solid particles by injecting a H2–D2 gas mixture above the free surface in a He II reservoir. Later, Nakano and Murakami reported generating 1 lm particles by this same method and used these particles as tracers in the LDV measurements in a thermal counterflow jet [11,12]. In this method, since the particles are formed in the vapor phase above the free surface, a large portion of them are pumped away with helium vapor before entering liquid phase as shown in Fig. 6a. Therefore, the seeding efficiency of this method is quite low. Another way to form solid particles has been reported recently by Celik et al. [8]. In this experiment, liquid neon was injected into He II directly through a plain orifice atomizer to form micron size particles, as shown in Fig. 6b. However, this process was not very successful in producing small, uniform solid hydrogen particles.
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Fig. 6. Schematic of the methods to seed solidified gas particles.
A more successful attempt at seeding micron scale solid hydrogen particles was made by Boltnev et al. in 2002 [13]. In their case, deuterium gas was first diluted with helium gas (1/20–1/1000) at room temperature. The gas mixture was then injected onto the free surface of He II through a nozzle placed 30 mm above it. Small angle X-ray scattering results showed that the solid deuterium particles formed in this way were in the submicron range. Injecting diluted seeding gas into liquid helium directly has been developed by our group and Bewley et al. independently [9,14]. This seeding method can be applied to the experiments which do not have the vapor phase close to the target flow visualization region. It also avoids the possible agglomeration at free surface due to the small settling velocities of solid hydrogen isotope particles. Bewley et al. reported creating 1–4 lm solid hydrogen particles by injected diluted seeding gas into He I. The experiment was then slowly pumped down to He II region. Because of particle agglomeration during pumping process, this experiment was restricted within the temperature range very close to the k point (Tk = 2.176 K). In the present research, we chose to inject diluted seeding gas into He II directly. Thus, the operating temperature is not limited. Furthermore, because of the rapid seeding process (generally a few seconds) and the very low mass diffusion rate of the seeded particles at He II temperatures, seeding can be made into He II locally near the visualization port provided the tracer particles do not need to occupy to the whole flow. The local seeding can also reduce the possibility of agglomeration and the heat input by seeding process. The seeding system for LHFVF includes three units: injection unit, seeding gas mixing and supply unit, and control unit. The injection unit is connected to the seeding port of experimental channel with the orifice contacting He II directly as shown in Fig. 7. The injection valve, a cryogenic miniature pulse valve made by the Parker Hannifin Corporation, is installed at the end of the seeding tube to achieve better control of the pressure and the temperature of seeding gas jet. A 120 X strain gauge (backing material: reinforced epoxy-phenolic) placed inside the valve is used as the heater to melt the solid hydrogen in case the orifice accidentally gets blocked. A silicon diode temperature sensor is mounted inside the seeding tube to measure the seeding gas temperature. Shown in Fig. 8 is the schematic of the seeding gas mixing and supply unit. The operation of this unit is relatively common. The
Fig. 7. Injection unit of hydrogen isotope particle seeding system.
whole unit is first evacuated by a roughing vacuum pump and purged with pure helium gas for more than ten times. The seeding gas section (brown path) is then evacuated and purged with the desired seeding gas (H2, D2 or H2–D2) for more than 20 times to remove any impurity in the system. After the purging process, the seeding gas section is charged back with seeding gas to around 0.2 MPa. Due to the high permeability of hydrogen isotopes, the 2 m long high pressure rubber hose between the needle valve VOUT and VT3 is saturated with the seeding gas within several hours. The section is then purged with helium gas for five or six times. Because of the seeding gas concentration difference between that absorbed in the rubber and the helium gas, the seeding gas slowly diffuses into the helium carrier gas. Thus, strongly diluted hydrogen gas is made and ready for the seeding process. Though we are not able to measure the exact dilution ratio in this case, it is reasonable to expect that it is much lower than 1%. The diluted seeding gas pressure is controlled and monitored by the BarocelÒ absolute pressure transducer. The gate valve VG is opened manually each time before the injection and closed immediately afterwards to avoid hydrogen molecules from accumulating around the orifice plate due to cryo-pumping. A DC power supply (model number TENMAÒ 72-7245) and a timing unit made in house are used to control and energize the solenoid pulse valve. The detailed test results of this seeding system were reported in our previous paper [6]. The optimum back pressure Pb of the diluted seeding gas and pulse valve opening time so, were obtained experimentally by trial and error and are 0.11 MPa and 1.1 s, respectively. The results also show that a strongly diluted seeding gas (helium gas >99% of the seeding mixture) is required to avoid
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Fig. 8. Schematic of the seeding gas mixing and supply unit.
large solid hydrogen clusters from forming during seeding process in a narrow channel. The slip velocity measurements showed that the solidified hydrogen isotope particles generated by this seeding system follow a continuous size distribution with 90% of the particles being less than 10 lm in diameter with the distribution peaked around 4.3 lm. Therefore, these tracer particles generally meet the criteria given in Section 3.1. 4. Results and discussion Here, we report PIV measurements of He II forced flow with constant heat flux using the experimental setup described above. A constant heat flux up to 6.6 kW/m2 was applied to a steady state forced flow of He II through the channel using the heater shown in Fig. 2. Generally speaking, the heat can be transported by both thermal counterflow and forced convection of He II in this case. The portion of the heat qic conducted by thermal counterflow induces a velocity difference between normal fluid component and bulk fluid, which can be expressed as
qic ¼ qsTðU n UÞ
ð6Þ
In order to compare the velocity field of He II, normal fluid and tracer particles, in this case the mean forced flow velocity is maintained at 23 mm/s, which is the same order as the normal fluid velocity according to the heat flux range used. Shown in Fig. 9 are the steady state temperature profiles measured at different heat fluxes along the flow direction. The dash lines in the figure are the theoretical calculations using Eq. (7), which represent the case that all the applied heat is transferred by thermal countflow:
1=3 1 dT q¼ f ðTÞ dx
ð7Þ
where f(T) is the heat conductivity function for He II and is equal to Aqn =ðq3s s4 T 3 Þ. The results show that the measured values are in rea-
Fig. 9. Temperature profiles along the channels as a function of heat flux with a constant forced flow velocity Umean = 23.0 mm/s. Heater is located at x = 2.71 m. x = 0 represents the end reservoir. The dash lines are calculated values based on one-dimensional thermal counterflow heat transfer equation using measured bath temperature at x = 0 as the boundary condition.
sonable agreement with the calculations. Thus, we can assume that the heat transferred by forced convection can be neglected and essentially all the heat is transferred by thermal counterflow in the same direction with the flow in this specific case. This result is quite understandable because of the high efficiency of thermal counterflow and the low forced flow velocity in the present experiments. Therefore, the normal fluid velocity should be written in one-dimensional form as a function of total heat flux q,
U n ¼ U þ q=qsT
ð8Þ
Fig. 10 shows the averaged velocity field of the solid deuterium particles in He II forced flow with a constant heat flux, q = 5.8 kW/ m2 as a typical example of these measurements. The y-axis is in
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Fig. 12. Velocity profiles of deuterium particles in forced flow along the channel width for different heat flux at 1.95 K. y = 1 represents the center of the channel.
Fig. 10. Averaged velocity field of the deuterium particles in forced flow He II with a constant heat flux: q = 5.8 kW/m2, Umean = 23.0 mm/s, and Tb = 1.95 K.
the vertical direction and parallel to the cross-section plane with y = 0 representing the center line of the channel and the x-axis is in the flow direction. The streamlines of the measured velocity field are generally parallel to the direction of the flow and the heat flux. The horizontal velocity component of the tracer particles are general greater than the averaged forced flow velocity Umean, 23 mm/s, however, much lower than the averaged normal fluid velocity using Eq. (8), which is 44.3 mm/s for the case in Fig. 10. We believe that the particle velocity is the result of the force balance on the particle between the viscous drag of the normal fluid component and the interaction force from the quantized vortex line of the superfluid component, which was discussed in the literature [7,14,15]. For better comparison, we averaged the velocity vectors along the flow direction and plotted the particle velocity profiles along the channel width W at two different bath temperatures 1.80 K and 1.95 K, see Figs. 11 and 12. The data show that the velocity increase caused by the thermal counterflow is approxi-
mately equal over the channel width. The presence of the thermal counterflow does not change the shape of the velocity profile including the turbulent boundary layer, which was reported in our previous work [16]. Since thermal counterflow is the only heat transfer mechanism in this case, the heat flux can be considered uniform over the channel width due to the high effective thermal conductivity of He II. The relative velocity of the normal fluid component with respect to the forced flow velocity, which is a function of the heat flux only, should be the same along the channel width according to Eq. (8) except for the region very close to the wall, which must satisfy the viscous boundary condition. Therefore, it is reasonable to have uniform shifts in the particle velocity profiles. The averaged velocity profiles in Figs. 11 and 12 were integrated to obtain Umean, the mean particle velocity in the horizontal direction. As shown in Fig. 13, Umean increases approximately linearly with normal fluid velocity in the flow within the heat flux and temperature range tested. The slope of the linear fit is around 0.38, which is slight lower than the value obtained in the pure thermal counterflow experiment by Zhang [7] (slope between 0.4 and
Fig. 11. Velocity profiles of deuterium particles in forced flow along the channel width for different heat flux at 1.80 K. y = 1 represents the center of the channel.
Fig. 13. Mean velocity of deuterium particles in He II forced flow as a function of relative normal fluid velocity predicted by the two-fluid model.
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0.6). In forced flow, the quantized vortex line density is not only a function of temperature but also the function of flow velocity. This may affect the interaction between tracer particles and superfluid component. Although these results are still quite preliminary, they represent the first PIV measurements of the combined forced flow and counterflow in He II. In the future, we plan to repeat this experiment at higher forced flow velocities, which increases the quantized vortex line density without increasing the relative velocity of the normal fluid component in the flow. 5. Summary An experimental system focusing on PIV applications to He II forced flow research has been designed, built and tested. The unique design of the window section of the experimental channel allows one to study the fluid motion in the vicinity of wall. To enable these measurements, a novel seeding system has been developed to generate and seed solid hydrogen isotope particles into the He II flow field. The slip measurements confirm that the generated particles follow a certain statistical distribution and range in diameter from one to ten microns. We do not see a noticeable change in the performance of the seeding system for the range of temperature studied (1.65–2.10 K). Therefore, this seeding scheme can be applied to different He II experiments regardless of system scale or the existence of free surface. The preliminary results of He II forced flow with constant heat flux demonstrate that the behavior of tracer particles is similar to that in the pure thermal counterflow case. Acknowledgement This work is supported by the US Department of Energy-Division of High Energy Physics under Grant FG02-96ER-40952.
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