A cryogenic-helium pipe flow facility with unique double-line molecular tagging velocimetry capability
Hamid Sanavandi, Shiran Bao, Yang Zhang, Ruben Keijzer, Wei Guo, Lou N. Cattafesta III
aa r X i v : . [ c ond - m a t . o t h e r] M a r A cryogenic-helium pipe flow facility with unique double-line moleculartagging velocimetry capability
H. Sanavandi,
1, 2
S. R. Bao,
1, 2
Y. Zhang,
1, 3
R. Keijzer, W. Guo,
1, 2, a) and L. N. Cattafesta III
1, 3 Department of Mechanical Engineering, Florida State University, Tallahassee, Florida 32310,USA National High Magnetic Field Laboratory (NHMFL), Florida State University, 1800 E Paul Dirac Dr., Tallahassee,Florida 32310, USA Florida Center for Advanced Aero-Propulsion (FCAAP), Florida State University, 2003 Levy Ave., Tallahassee, Florida 32310,USA
Cryogenic helium-4 has extremely small kinetic viscosity, which makes it a promising material forhigh Reynolds ( Re ) number turbulence research in compact laboratory apparatuses. In its superfluidphase (He II), helium has an extraordinary heat transfer capability and has been utilized in variousscientific and engineering applications. In order to unlock the full potential of helium in turbulenceresearch and to improve our understanding of the heat transfer mechanism in He II, a flow facility thatallows quantitative study of helium heat-and-mass transfer processes is needed. Here we report ourwork in assembling and testing a unique helium pipe flow facility that incorporates a novel double-linemolecular tracking velocimetry (DL-MTV) system. This flow facility allows us to generate turbulentpipe flows with Re above 10 , and it can also be adapted to produce heat-induced counterflow inHe II. The DL-MTV system, which is based on the generation and tracking of two parallel thinHe ∗ molecular tracer lines with an adjustable separation distance, allows us to measure not only thevelocity profile but also both the transverse and longitudinal spatial velocity structure functions. Wehave also installed a deferential pressure sensor to the flow pipe for pressure drop measurement. Thetesting results of the flow facility and the measurement devices are presented. We discuss how thisfacility will allow us to solve some outstanding problems in the helium heat-and-mass transfer topicarea. I. INTRODUCTION
Cryogenic helium-4 ( He) is known for its great potentialin fluid mechanics research and in thermal engineering appli-cations due to its unique mechanical and thermal properties .For instance, the kinematic viscosity ν of liquid He can belower than 10 − m /s, which is about three orders of magni-tudes smaller than that for ambient air . Therefore, it is fea-sible to generate turbulent flows in liquid helium with an ex-tremely high Reynolds ( Re ) number (defined as Re = DU / ν ,where D and U represent the characteristic length and veloc-ity of the flow). Understanding such high Re flows can ben-efit the design of transportation vehicles and defense vesselsfor better control and improved energy efficiency. Comparedto existing high Re flow facilities that utilize more conven-tional fluid materials, a cryogenic flow facility using liquid He has some unique advantages. For instance, the State-of-the-art Princeton Superpipe facility uses compressed air up to220 bar to achieve the desired low kinematic viscosity . Thishigh pressure makes it very challenging to incorporate viewports in the flow facility for visualization measurement of thevelocity field. On the other hand, quantitative flow visual-ization of liquid helium flows in compact cryostat has beendemonstrated . Especially, a powerful molecular tagging ve-locimetry (MTV) technique has been developed in our lab ,which allows us to measure both the instantaneous velocityprofile of the He flow in a channel and the spatial velocitystructure functions . Such measurements are largely im-practical for conventional high Re flow facilities that rely onsingle-point flow measurement tools. Nonetheless, our MTV a) Corresponding: [email protected] technique has not yet been implemented and demonstrated inany helium-based high Re flow equipment.Besides its small kinematic viscosity, helium is also knownfor its fascinating quantum hydrodynamics in the superfluidphase. Below about 2.17 K, ordinary liquid He (He I) tran-sits to the superfluid phase (He II), which consists of two fullymiscible components: an inviscid superfluid component withdensity ρ s (i.e., the condensate) and a viscous normal-fluidcomponent with density ρ n (i.e., the thermal excitations) .This two-fluid system has many interesting properties. Forinstance, instead of ordinary convective, heat transfer in HeII is via an extremely effective counterflow mode: the nor-mal fluid carries the heat away from the heat source, and thesuperfluid, which carries no entropy, flows in the opposite di-rection to compensate the fluid mass. Another unique featureof He II is that the rotational motion in the superfluid can oc-cur only with the formation of topological defects in the formof quantized vortex lines . These vortex lines all have iden-tical cores (about 1 Å in radius) and they each carry a singlequantum of circulation κ ≃ − cm/s. Turbulence in the su-perfluid therefore takes the form of an irregular tangle of vor-tex lines (quantum turbulence) . The normal fluid behavesmore like a classical fluid. But a force of mutual friction be-tween the two fluids , arising from the scattering of thermalexcitations by the vortex lines, can affect the flows in both flu-ids. This mutual friction can significantly alter the turbulencecharacteristics as well as the boundary-layer profile of He IIin various flows. Studying novel emergent behaviors of thistwo-fluid system often requires a flow facility with the capa-bility of measuring both the longitudinal and transverse spatialvelocity structure functions, which is lacking at present.In this paper, we discuss our work on assembling and test-ing a unique helium pipe flow facility that incorporates a noveldouble-line molecular tracking velocimetry (DL-MTV) mea- FIG. 1. A schematic diagram of the Liquid Helium Flow Visualization Facility (LHFVF). surement system. This flow facility is adapted from an exist-ing liquid helium flow visualization facility (LHFVF) that wasbuilt and utilized by Van Sciver and colleagues . Turbulentpipe flows in liquid He with Re above 10 can be produced,and it can also be adapted to produce thermal counterflow inHe II. The DL-MTV system, which is upgraded based on ourexisting MTV optics, allows the generation and tracking oftwo parallel thin He ∗ molecular tracer lines in liquid heliumwith an adjustable separation distance. With this DL-MTVsystem, the near-wall velocity profile and the velocity struc-ture functions in both the longitudinal and transverse direc-tions can be obtained. A deferential pressure sensor is alsoincorporated in the LHFVF for pressure drop measurementacross the flow pipe. In Sec II, we describe the experimen-tal apparatus which include the adapted LHFVF, the laser andimaging systems, and the pressure sensor. The testing resultsof these apparatus are presented in Sec III. In Sec. IV, we dis-cuss how this facility will allow us to solve some outstandingproblems in the helium heat-and-mass transfer topic area. Abrief summary is given in Sec. V. II. EXPERIMENTAL APPARATUSA. Liquid Helium Flow Visualization Facility
The Liquid Helium Flow Visualization Facility (LHFVF)is an cryostat designed for generating and visualizing liquid He pipe flows. This facility consists of a horizontal cylindri-cal experimental space (5 m long with an inner diameter of0.2 m) surrounded by two concentric radiation shields that arecooled by natural convection loops from the liquid helium andliquid nitrogen tanks (see the schematic diagram in Fig. 1).These shields and the tanks all sit inside the evacuated cryo-stat body. A flow pipe with a square cross-section (2 × )and a length of 3.35 m is installed at the center of the exper-imental space. This pipe is connected to two vertical heliumstorage stacks at the two ends of the LHFVF. The temperatureof the helium in the stacks can be controlled by regulating the vapor pressure. For flow visualization purpose, the LHFVFis equipped with two sets of view ports, one at the midpointand one about 1 m downstream. Each window set consists ofaligned windows (top, bottom, and front) installed in the flowpipe, the radiation shields, and the cryostat body. The win-dows mounted on the helium shield are coated with infraredreflective film to minimize the radiation heat leak to the ex-perimental space. The front window in the flow pipe has adiameter of 24 mm, greater than the inner side-width of pipe(see the inset in Fig. 1). This design allows us to examine theboundary layer flow in the vicinity of the pipe wall. In theexperiment, we pass the laser beams through the top and bot-tom windows and place the camera near the front window forimage acquisition.To generate the flow in the pipe, in the original LHFVFsetup , two bellows pumps were installed (one in each he-lium stack) and were welded to the flow pipe. These bellowspumps were supposed to move always oppositely such thatthe liquid He can be pushed to flow through the pipe fromone bellows to the other. However, during the last operationa few years ago these bellows pumps were severely damageddue to a malfunction of the control unit in coordinating themotions of the two bellows. This facility was since put instorage until we restored it recently. In the current LHFVFsetup, we removed the broken bellows and installed a singlebellows pump in the left stack (see Fig. 1). A superfluid leak-tight cryogenic filling valve is welded to the bellows, whichcontrols liquid He feeding into the bellows. The new bel-lows has an effective cross-section area 1.81 × − m and astroke length of 9.4 cm, which provides a maximum volumedisplacement of about 1.7 liter of liquid He. The bellows isconnected through a rod to a linear actuator (Parker ETS32)mounted coaxially on the top of the left stack. A computer-controlled stepper motor (Parker S57-102) is used to drive thelinear actuator. This stepper motor has a limiting thrust of 600N, which is more than enough to drive the low-viscosity liquid He through the pipe even at the highest speed we have tested.
FIG. 2. (a) A schematic diagram showing the typical experimentalsetup for creating and imaging He ∗ molecular tracer lines in helium.(b) A representative tracer-line image in He II upon its creation. (c)A schematic showing how the local velocity is calculated based onthe displacement of line segments. B. Double-line Molecular Tagging System
In order to make quantitative velocity measurement of the He flows in the LHFVF, we have implemented the MTVtechnique that was developed in our lab . The tracer particlesused in the MTV are He ∗ molecules in the excited electron-spin triplet state. These excimer molecules can be easily cre-ated in helium as a consequence of ionization or excitation ofthe ground state He atoms . They form tiny bubbles inliquid He (about 6 Å in radius ) and have an exceptionallylong lifetime (about 13 s ). Due to their small size and ef-fective mass, He ∗ molecules always follow the fluid motion ingaseous helium and He I, and they are entrained by the vis-cous normal-fluid component in He II since the Stokes drageasily dominates other forces .In our previous MTV experiments, a 5-kHz femtosecond(fs) laser system (wavelength λ : 780 nm, duration: 35 fs,pulse energy: up to 4 mJ) was used to generate thin lines ofHe ∗ tracers in helium via laser-field ionization . As shownschematically in Fig. 2 (a), the fs-laser beam is focused bya lens with a focal length f and is passed through an opti-cal cryostat that contains helium at a regulated pressure andtemperature. For an ideal Gaussian beam with a beam ra-dius ω at the focal plane, one can define a Rayleigh range z R = πω / λ , over which the laser intensity drops by 50%due to beam spreading . The He ∗ tracers are expected to beproduced essentially within the Rayleigh range. Our past testsshowed that a fs-laser pulse energy of about 60 µ J is sufficientto create He ∗ tracers. We then send in 3-5 pulses from a 1-kHzimaging laser at 905 nm to drive the He ∗ tracers to produce640 nm fluorescent light . The fluorescence is captured byan intensified CCD (ICCD) camera mounted perpendicular tothe tracer-line plane. Fig. 1 (b) shows a typical fluorescenceimage of the He ∗ tracer line taken right after its creation in HeII. The width of the tracer line is about 2 ω and its length isabout 2 Z R as expected. To extract velocity information, weallow an initially straight tracer line to move with the fluid bya drift time △ t (see Fig. 1 (c)). The deformed tracer line is di-vided into small segments and the center of each segment canbe determined by a Gaussian fit of its intensity profile. When △ t is small, the streamwise velocity u x ( z ) can be calculated as the displacement of the segment at z divided by △ t . ThisMTV method has been successfully applied to study varioustypes of turbulent flows in He II . He z x Focalregion Driftedtracerline u x (x,z)u x (x,z+∆z) u x (x+∆x,z)∆x∆z Sapphire windowWall
FIG. 3. A schematic diagram showing the concept of the double-linemolecular tagging velocimetry (DL-MTV).
Despite the usefulness of the MTV technique, by tracking asingle tracer line, we can only correlate the measured stream-wise velocities along the tracer line to determine the n -th ordertransverse velocity structure function S ⊥ n ( ~ r ) but cannot get anyinformation about the longitudinal velocity structure function S k n ( ~ r ) . These structure functions are defined as: S ⊥ n ( ~ r ) = | u x ( x , z + ∆ z ) − u x ( x , z ) | n S k n ( ~ r ) = | u x ( x + ∆ x , z ) − u x ( x , z ) | n (1)where x and z are, respectively, the coordinates in the stream-wise and the transverse directions, and the overline denotesensemble averaging. Knowing these structure functions, onecan extract quantitative information about the energy spec-trum and other statistical properties of the turbulent flows .In the case that the flows to be examined are boundary flows oranisotropic turbulent flows where the scalings of these struc-ture functions are very different, it is highly desirable to havethe capability of measuring both of them . To achieve thisgoal, a feasible solution is to create two parallel tracer lines inthe flow pipe with an adjustable separation distance, as shownschematically in Fig. 3. By tracking the displacement of thetwo tracer lines, one can determine the streamwise velocitiesalong both lines. Then, by correlating the velocities at twolocations in the streamwise direction and in the transverse di-rection, both S k n ( ~ r ) and S ⊥ n ( ~ r ) can be obtained.To implement this double-line MTV (DL-MTV) scheme,we have designed and assembled a unique optical system.First, a periscope device (i.e., a vertical post with two mirror-sets installed at its two ends) is used to guide both the fs-laser and the imaging laser beams from the optical table to abreadboard installed on top of the LHFVF. Then, the fs-laserbeam is divided into two orthogonal beams in parallel withthe breadboard using a beam splitter, as shown schematicallyin Fig. 4 (a). One of the two beams is reflected on a mirrorthat is mounted on a translation stage such that the separationdistance between the two fs-beams can be continuously ad-justed from zero to a maximum separation of about 10 mmwith a sub-micron resolution. The 905-nm imaging laser isfocused by a cylindrical lens into a laser sheet (thickness: 1mm, width: 10 mm) that covers the entire region traversed by a) b) FIG. 4. (a) A schematic diagram showing the optical setup for creating two tracer lines. (b) A picture of the assembled optical components. the two tracer lines. Finally, the two fs-beams are focused bytwo separate spherical lenses before they are combined withthe imaging laser sheet using a polarizer-based beam com-biner and reflected vertically down through the LHFVF. Notethat the two spherical lenses are mounted on optical rails suchthat they can be easily moved without affecting the parallelityor orientation of the fs-laser beams. The advantage of thesemovable lenses is that we can then control the creation of thetwo tracer lines at arbitrary distances from the bottom wall ofthe flow pipe. This feature is especially useful for examiningthe near-wall velocity profile. Fig. 4 (b) shows a picture of theoptical components that we have assembled.
C. Pressure Sensor
In pipe flow research and applications, a useful parameterfor evaluating the frictional lose is the friction factor f D . Foran impressible fluid, this factor is related to the pressure drop ∆ P along the flow pipe as ∆ P = f D · ( ρ ¯ u ) · L f / D h , where ρ is the fluid density, ¯ u is the mean velocity in the pipe, and D h and L f are the hydraulic diameter and the length of the pipe,respectively . To enable the measurement of f D for heliumpipe flows, we have installed a Validyne DP10-20 variable-reluctance deferential pressure transducer (DPT) to the flowpipe inside the LHFVF, as shown schematically in Fig. 5. Pressure sensor (DP10-20)View port
FIG. 5. A schematic diagram showing the locations where the pres-sure drop is measured by the pressure sensor.
This DPT sensor has a flat diaphragm sensing elementclamped between cases halves that are connected throughstainless-steel tubes (0.125-inch in diameter) to the bottomwall of the flow pipe at locations separated by L f = .
83 m. Special silver-coated indium-brazed stainless-steel gaskets areused to reliably seal the sensor to the tubes to prevent leakagein the He II runs. A Validyne CD19A carrier demodulatormodule is utilized to excite the sensor and to read the volt-age output. This voltage signal can be calibrated and con-verted to pressure readings. We choose DP10-20 becauseof its very good linearity in signal response. The nominalpressure-difference range of the DP10-20 sensor is 0 −
860 Pa.Nevertheless, it is specified that the sensor’s response can re-main linear up to 200% full pressure span with less that 0.5%zero shift, which nicely covers the range of the anticipatedpressure drop in our experiments. However, since these speci-fications are designated for operation temperatures above 220K, the sensor performance needs to be tested in helium.
III. TEST RESULTSA. Flow Facility Testing
We have developed a very effective procedure to cool downthe big LHFVF. First, the cryostat vacuum space is evacu-ated to below 10 − Pa. The nitrogen and the helium radia-tion shields are then cooled by introducing cryogenic liquidsinto the respective tanks. After that, cold helium vapor froma liquid helium storage dewar is forced to flow from the rightstack through the flow pipe to the left stack with the fillingvalve open. This procedure efficiently pre-cools both stacksand the flow pipe due to the maximal usage of the vapor en-thalpy. When the temperature of the stacks and the flow pipedrop to below 15 K, we start transferring liquid He into theright stack. After both stacks are fully filled, we then pump onthe stacks to cool the liquid helium to a desired temperatureby regulating the pressures in the stacks. We have successfullycooled down the LHFVF and achieved a helium temperatureas low as 1.4 K using this procedure.To generate flows in the pipe, we close the filling valve andthen push the bellows pump by controlling the stepper mo-tor using a LabVIEW computer program. This program sendscommands to an indexer (6200 Parker Automation) that con-trols three key parameters of the bellows motion: the steadybellows velocity V B , its transient acceleration a B , and the to-tal displacement ∆ h (which is always less than 9.4 cm). Totest the actual performance of the bellows pump and the con-trol system, we utilize a high-speed CCD camera (IDT XS-3)to take consecutive images of the linear actuator’s head. Aruler is placed nearby ro provide length scale calibration, asshown in Fig. 6 (a). The instantaneous velocity of the actuator(and hence the bellows) can be determined by analyzing theobtained images. FIG. 6. (a) A picture showing the linear actuator, the bellows hous-ing, and the ruler placed nearby for scale calibration. (b) Represen-tative curves showing the measured bellows velocity versus time.
Test runs with V B in the range of 0.025 cm/s to 12.7 cm/shave been conducted while the stacks and the flow pipe werefilled with He II at 1.8 K. The total displacement is set to ∆ h = .
6, and the acceleration up to a B =
127 cm/s is used.Representative velocity curves are shown in Fig. 6 (b). Allcases show a good agreement between the actual steady ve-locity and the programmed velocity between the transient ac-celeration and deceleration regions. Note that the ratio ofcross-section areas between the bellows pump and the flowpipe is about 45.3. Therefore, the bellows velocities that wehave tested correspond to mean flow velocities of He II in theflow pipe as ¯ u ∈ [0.01, 5.75] m/s. Using the known proper-ties of He II , one can work out that the pipe flow Reynoldsnumber Re D is in the range of 2 . × to 1 . × . Dueto the finite stroke length, there is a limited time window ∆ t W for flow measurements (i.e., approximated ∆ h / V B when a B ishigh). Nevertheless, even at the highest velocity that we havetested, ∆ t W is still long enough for the development of the tur-bulent flow and for us to make quantitative velocity field andpressure drop measurements. B. DL-MTV System Testing
Upon the completion of the DL-MTV optical setup, wehave carefully tuned the entire laser and imaging system andconducted tests to ensure that the DL-MTV scheme is indeedachieved. These tests include the alignment and overlappingof the fs-laser and imaging laser beams, visual examination
FIG. 7. (a) A picture showing the overlapping cross sections of thefs-laser and imaging laser beams on an IR card. (b) and (c) are rep-resentative images showing the cross-section intensity profiles of thetwo fs-laser beams and the imaging laser sheet taken with the IRcamera. (d) The measured diameter 2 ω ( z ) along one of the fs-laserbeams. The solid curve represents a fit using the ideal Gaussian beamequation as discussed in the text. of their beam profiles, and Rayleigh-range measurement ofthe fs-beams for controlling the thicknesses and lengths of thetracer lines. After that, the optical setup is tested for produc-ing and for position-control of the He ∗ tracer lines in the flowpipe filled with liquid helium.To ensure that the fs-laser and imaging laser beams havethe desired overlapping as they pass through the flow pipe,we fine tune their directions independently using mirror pairson the breadboard. An infrared (IR) card is then utilized toexamine the cross-section profiles and the relative positions ofthe laser beams at locations both above the top view port of theLHFVF and below the bottom view port. Beam collimation isachieved when the relative positions of the laser beams do notshift from the top view port to the bottom view port. A typicalbeam profile picture on the IR card is included in Fig. 7 (a),which clearly shows that the two fs-laser beams are coveredwithin the imaging laser sheet.In order to obtain more quantitative beam profile informa-tion, we remove the mirror that reflects the combined beamsdown into the LHFVF so that an IR camera (WinCamD-LCM4 from DataRay Inc.) can be placed at the focal regionof the laser beams for beam profile measurement. Typicalimages of the cross-section intensity profiles of the fs-laserbeams and the imaging-laser beam are shown in Fig. 7 (b)and (c), respectively. The two fs-laser beams have circularcross sections with nearly Gaussian intensity profiles. Theirseparation distance can be easily adjusted using the movablemirror on the breadboard in the range 0 to 10 mm with a sub-micron resolution. The imaging laser sheet has a thicknessof about 1 mm (measured at half the maximum intensity) anda width of 10.2 mm, close to our design specifications. Wehave also performed the beam width measurement along thetwo fs-laser beams in order to determine their Rayleigh rangein the focal region. Fig. 7 (d) shows an representative curveof the measured fs-beam diameter 2 ω ( z ) along one of the fs-laser beams that is focused by a lens with f =
75 cm. Themeasured beam diameter variation can be well fitted using theequation for ideal Gaussian beams : ω ( z ) = ω [ + ( z / z R ) ] .From this fit, both the beam waist at the focal plane ω andthe Rayleigh range z R can be determined. In the specific caseshown in Fig. 7 (d), ω = µ m and z R =
16 mm. Since2 z R =
32 mm is greater than the inner width of the flow pipe(20 mm), we expect that a tracer line with a diameter of about2 ω will be created through the entire width of the pipe. Notethat for a Gaussian beam, when the focal length f of the lensis much greater than z R , the beam waist ω is given by : ω = λ f / πω L , where λ is the fs-laser wavelength and ω L is the incident beam radius on the lens. Therefore, by usinglenses with different f , we can easily control the thicknessand length of the tracer lines. Tracer lines with ω as small as10-20 µ m has been readily created . FIG. 8. (a) A picture of the flow pipe illuminated with ambient lightfrom the top view port. (b1) and (b2) are representative images show-ing the two tracer lines created at different streamwise separationdistances using lenses with f =
75 cm. c) A representative imagedemonstrating the tunability of the vertical positions of the two tracerlines created using lenses with f =
50 cm.
Finally, we fill the flow pipe with liquid helium for tracer-line imaging test. Electronic shutters are used to allow 5 fs-laser pulses (at 5 kHz) to pass through the LHFVF to cre-ate the tracer lines which are then illuminated by a train of3 imaging-laser pulses (at 1 kHz). Typical fluorescence im-ages of two parallel tracer lines created in static He II at 1.8 K are shown in Fig. 8. For reference, an image of the flowpipe taken with ambient light illumination from the top viewport is included in Fig. 8 (a), where one can clearly see thetop and bottom walls of the pipe. The streamwise separationdistance between the two tracer lines can be easily adjusted,as demonstrated in Fig. 8 (b1) and (b1). We have also testedthe tunability of the vertical positions of the tracer lines. Inthis case, lenses with f =
50 cm are used so that the createdtracer lines are shorter. Then, by adjusting the positions ofthe lenses in the breadboard, we can shift one line close to thebottom wall and one line close to the top wall of the pipe, asshown in Fig. 8 (c). This tunability is important when we cre-ate very thin tracer lines for measuring the near-wall velocityfield.
C. Pressure Sensor Testing
Since the nominal specifications of the DP10-20 pressuresensor are not applicable for liquid helium temperatures, wehave performed calibration of the sensor immersed in liquidhelium in a test cryostat at a controlled bath temperature in therange 1.5–4.2 K. The sensing element of the pressure sensoris connected through pipes to helium gas reservoirs at con-trolled pressures. This way, the change in the voltage reading ∆ V can be correlated with the actual pressure difference ∆ P across the sensing element. Representative calibration data inHe II at 1.8 K are shown in Fig. 8. The sensor response re-mains linear to a maximum pressure difference of about 2500Pa. Through a linear fit to the data, the conversion factor be-tween the voltage change ∆ V and the pressure drop ∆ P can bedetermined. It turns out that this conversion factor only variesby a few percent from room temperature down to the lowesttemperature we have tested. P r e ss u r e d r op ( P a ) Voltage (mV)
He II T=1.8 KdP/dV =3.9 ± 0.1 Pa/mV
FIG. 9. Representative calibration data of the DP10-20 pressure sen-sor immersed in He II.
The calibrated pressure sensor is then installed to the flowpipe, and a test with flowing gaseous helium at 225 K isconducted to demonstrate the sensitivity of the sensor. Bycontrolling the speed of the bellows pump, we generate gasflows in the pipe at four different mean velocities: u = ρ = .
214 kg/m ) and its relatively large viscosity ( µ = . · s), the Reynolds number Re D = ρ uD h / µ at these veloc-ities are approximately 57, 130, 260 and 390. Fig. 10 (a)shows the pressure drop reading at u = FIG. 10. (a) A representative pressure-drop curve when a gaseoushelium flow is generated in the pipe. (b) The calculated friction factor f D versus the Reynolds number Re D for the gas flows. is clearly resolved. Based on the measured pressure dropdata, we can calculate the corresponding friction factor as f D = ∆ P ( D h / L f ) / ( ρ ¯ u ) . Fig. 10 (b) shows the obtained f D as a function of the Reynolds number Re D , which indeedagrees very well with the expected friction factor behavior f D = / Re D for laminar flows. This agreement confirms thatthe pressure sensor is functioning well. IV. DISCUSSIONS
The flow facility that we have assembled and tested has anumber of unique features: 1) it allows the generation of high Re pipe flows in both the classical fluid He I and in the quan-tum fluid He II; 2) the DL-MTV capability makes it possibleto measure not only the instantaneous velocity profile in thepipe but also the longitudinal and transverse velocity structurefunctions; and 3) the pressure drop (and hence the friction fac-tor) of the pipe flow can be measured. The combination of allthese features makes the facility one of its kind in classicaland quantum fluids research. In what follows, we outline afew interesting topics that can be studied using our facility. Law of the wall in classical pipe flow:
Turbulent pipeflow is a topic of great practical importance. In the tradi-tional view, the near-wall profile of the mean velocity ¯ u inpipe flow can be described by a logarithmic form known asthe “law of the wall”: ¯ u / u τ = ( / κ ) ln ( z / η ) + B , where u τ isthe friction velocity that can be evaluated based on the pres-sure drop measurement , η is the viscous scale, z denotes thewall-normal coordinate, and κ and B are the von Kármán co-efficient and the additive constant . Despite extensive experi-mental and numerical investigations, there are still unresolvedfundamental issues such as the extent of such a log law, thevalue of the log-law constants, and their Re dependence .So far, the state-of-the-art Princeton Superpipe experiments have observed the log law at z > η when Re is greaterthan 2.3 × . However, their reported Kármán coefficient κ = .
42 differs from typical values (i.e. 0 . − .
39) found inhigh Re boundary layer flows and channel flows , which castsdoubt on the universality of κ . On the other hand, Furuichi etal. reported κ = .
385 in their recent experiment using the“Hi-Redff” pipe flow facility , supporting the universality of κ . Since the accurate value of κ is crucial to modeling wall-bounded flows, more high- Re pipe-flow measurements usingindependent facilities like ours is needed.To resolve the near-wall velocity profile, it is crucial to havea fine dimensionless spatial resolution l + , defined as the ratioof the probe size l to the viscous scale η : l + = l / η . The l ofour DL-MTV system is limited by the minimum drift distanceof the tracer lines that can be resolved, which is about the halfthickness of the lines. As we have discussed in Sec. III, by us-ing appropriate lenses, it is possible to achieve 10-20 µ m for l . The viscous scale η can be estimated as η ≈ D · Re − . ,where D denotes the energy containing scale that roughlyequals the hydraulic diameter of the pipe . If we plug in l ∼ µ m and Re ∼ , a dimensionless resolution l + ofabout 30 is obtained, which is comparable to the typical l + values in the Superpipe experiments and should be sufficientto resolve the logarithmic velocity profile that is expected toappear at z + = z / η > Law of the wall in He II pipe flow:
Another interestingtopic is the near-wall velocity profile in He II pipe flow. Manylarge-scale cooling systems for particle accelerators and su-perconducting magnets involve pipelines for transporting HeII from the liquifiers or storage vessels to the equipment tobe cooled . The friction factor f D of He II in pipe flow isneeded in the design of these cooling systems. Despite somelimited measurements of f D in He II , a clear understandingof its behavior is difficult without detailed knowledge of thenear-wall velocity profile of the viscous normal fluid. Thisprofile could deviate from the classical law-of-the-wall due tothe mechanism as illustrated schematically in Fig. 11. FIG. 11. A schematic showing possible mismatch of the velocityprofiles of the two fluids in forced He II pipe flow.
In He II pipe flow, the two fluids can become strongly cou-pled by mutual friction in the bulk liquid at scales greater thanthe mean vortex-line spacing . However, the situation maychange near the pipe wall. Due to the no-slip boundary con-dition of the viscous normal fluid, there is a strong velocitygradient in a very thin boundary layer. There is no guaranteethat the mutual friction could be effective enough to maintaina similar velocity gradient in the superfluid. Such a velocityboundary layer in the super fluid would require highly nonuni-form distribution and polarization of the quantized vorticespinned to the wall , about which there is no existing knowl-edge. Therefore, the two fluids could have mismatched ve-locity profiles near the pipe wall. The relative velocity u ns inthe boundary layer then leads to a mutual friction f ns per unitvolume between the two fluids that modifies the classical log-arithmic velocity profile of the normal fluid. Measuring the re-vised law-of-the-wall of the normal fluid using our DL-MTVtechnique will not only enrich our knowledge of boundary-layer flows in general but also benefit various He II pipe-flowbased applications. He II counterflow turbulence:
In He II thermal coun-terflow, the velocity of the normal fluid u n is controlled bythe heat flux q as q = ρ sTu n , where ρ is the total densityof He II and s is the specific entropy . This heat transfermode is extremely efficient and can lead to an effective ther-mal conductivity of He II higher than that for pure metals .Therefore, He II has been widely utilized for cooling scien-tific and industrial equipment such as superconducting mag-nets, power transmission cables, superconducting acceleratorcavities, and satellites . However, it has been known thatwhen the heat flux exceeds a small critical value, turbulencecan appear spontaneously in the superfluid as a tangle of quan-tized vortices , which impairs the superior heat transfer ca-pability of He II. In the past, most of the experimental andnumerical studies have focused on the vortex-tangle dynam-ics in the superfluid . In recent years, by using ourMTV technique, we have revealed that the normal fluid canalso become turbulent and can exhibit non-classical scalingbehaviors . Indeed, due to the relative motion of thetwo fluids, the mutual friction sets in and dissipates the tur-bulent kinetic energy at all lengths scales, which is in markedcontrast to classical turbulence where the energy dissipationis important only below the viscous scale η . Understand-ing the novel normal-fluid turbulence and its influence on thevortex-tangle dynamics now becomes an outstanding chal-lenging problem in quantum fluids research.Interestingly, in a recent theoretical study, Biferale et al. suggested that counterflow turbulence should exhibit stronganisotropy at small scales , which differs strongly from clas-sical flows where better isotropy is expected at smaller scales.This intriguing property may be responsible for some unex-plained behaviors of counterflow turbulence. The only wayto experimentally study this anisotropy effect is by using theDL-MTV that we have implemented in the LHFVF. Instead ofpushing the bellows pump to generate pipe flows in the LH-FVF, it is straightforward to install a heater inside the bellowsto induce counterflow in the flow pipe. Then, by examiningthe displacement of two parallel tracer lines, we can comparethe scaling behaviors of the longitudinal and the transverse ve-locity structure functions and thereby evaluate the anisotropyquantitatively. This study will greatly improve our under-standing of the novel doubly turbulence in He II counterflow. V. SUMMARY
We have assembled and tested a unique LHFVF that in-corporates a novel DL-MTV measurement system. This flowfacility allows the generation of turbulent pipe flows with Re above 10 . The DL-MTV system allows us to measure notonly the instantaneous velocity profile of He I (or the nor-mal fluid in He II) but also the transverse and longitudinalspatial velocity structure functions. Besides, a pressure sen-sor has been installed and tested for pressure drop measure-ment. These measurement capabilities together with the vari-ous flows that can be generated make this facility an extremelyuseful equipment in classical and quantum fluids research. Inparticular, by studying the law of the wall in pipe flows of bothHe I and He II and by experimentally quantifying the novelanisotropy effect in He II thermal counterflow turbulence, newknowledge of cryogenic helium mass-and-heat transfer willbe obtained, which will benefit various practical applicationsinvolving cryogenic helium. ACKNOWLEDGEMENTS
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