Heat transfer and flow of He II in narrow channels

Heat transfer and fluid flow of He II in a long, narrow channel connected to a bath that supplies a constant supply of heat have been investigated by numerical simulations by using the simplified model of Kitamura et al. [Cryogenics 37 (1) (1997) 1]. Such channels are used to cool compact, stable, low-temperature magnets. The fluid flow is driven by natural convection and the mutual friction between the normal fluid and the superfluid.In this model, the thermomechanical effect and the Goter-Mellink mutual friction balance each other. A consequence of this balance is that the velocity and temperature distributions of He II can be characterized by a dimensionless, dependent parameter equal to the ratio of the fluid speeds of internal convection to the total fluid flow. After a sudden application of heat flux, the internal convection dominates over the total fluid flow until the establishment of steady-state temperature gradients. This predicts that the time required to set up the steady-state total fluid flow is proportional to the total heat capacity in the channel.     

Numerical analysis for two-dimensional transient heat transfer from a flat plate at one-side of a duct containing pressurized He II

A numerical analysis of two-dimensional transient heat transfer produced by step heat inputs to a flat plate located at one end of a rectangular duct containing pressurized He II was performed. The computer code, SUPER-2D, that is the two-dimensional heat transfer code for He II developed by Tatsumoto et al. [1] based on the two fluid model and the theory of the mutual friction was used for the calculation. The time lag from the application of the step heat input to the occurrence of the λ transition, which is called a lifetime, was obtained for various values of step heat flux for bulk liquid temperatures ranging from 1.8 to 2.0 K. The calculations were made for three rectangular ducts having different cross-sectional area. The ratios of the cross-sectional area of the duct to the heated surface area, A_d/A_h, were 1.0, 1.6 and 2.0. Effect of the A_d/A_h on the lifetime was clarified. The solutions agreed with the experimental data by Shiotsu et al. [2] for the ducts with the same structures and the corresponding conditions. It was confirmed that the computer code, SUPER-2D, can describe transient heat transport in He II as well as steady-state one [1].     

Numerical analysis for steady-state two-dimensional heat transfer from a flat plate at one side of a duct containing pressurized He II

A computer code of two-dimensional heat transfer in superfluid helium named SUPER-2D was developed based on the two fluid model and the theory of the mutual friction. Critical heat fluxes (CHFs) on a flat plate located at one end of six rectangular ducts having different cross-sectional areas were calculated by using the SUPER-2D for temperatures ranging from 1.8 to 2.07 K in pressurized He II. The ratios of the cross-sectional area to heated area, A_d/A_h, were varied from 1.0 to 3.5. As the ratio increased, the CHFs rapidly increased and approached a constant value. The solutions agreed with the experimental data by Tatsumoto et al. [Adv. Cryog. Eng. 45 (1999) 1073] for the same structures of the ducts and corresponding experimental conditions. It was found from the analysis that several vortices are generated around the heated surface and play an important role in determining the CHF.     

Experimental investigation of the film boiling heat transfer in He II: Heat transfer coefficient

He II film boiling is of both academic and applied interests. However, information about He II film boiling is still inadequate and further study is needed from both the technical application and the scientific aspects. In the present study, a thin stainless steel foil heater (10 μm thick) is employed to induce boiling in He II. The average heater surface temperature is measured to evaluate the heat transfer performance of He II film boiling under different thermal conditions. And meanwhile, the pressure and the temperature oscillations induced by the film boiling are also measured. It is found that the pressure oscillation and the temperature oscillation highly correlate with each other, which indicates that the vapor bubble is vibrating on the heater surface during film boiling. The heat transfer coefficient of the film boiling depends on both the pressure over the heater surface and the He II bath temperature. The heat transfer coefficients of three kinds of boiling states: noisy film boiling, transition boiling and silent film boiling, are measured in the present study. The visualization of the boiling process is also carried out.     

Heat and mass transfer processes in two phase He II/vapor

Modeling heat and mass transfer characteristics of two phase He II is discussed. The case considered assumes that the channel flow is one-dimensional and stratified, with mass exchange between the two phases. Two specific examples are considered in some detail. The first is the heat and mass transfer characteristics for small liquid flow rate. Use of several simplifying assumptions allows the problem to be reduced to solution of a one-dimensional ordinary differential equation. The result is a non-dimensional expression for the liquid level or void fraction along the channel. A set of dimensionless parameters are defined that establish the relative contributions of vapor mass transport and counterflow in the He II. The model also predicts the temperature profile and vapor mass flow rate. The second case concerns the flow of liquid under nearly isothermal conditions with relatively small vapor mass flow rate. Under these conditions, the flow may be modeled using classical hydrodynamics taking into consideration the unique characteristics of the He II. Results of these models are compared to experimental data for heat and mass transfer in a two phase He II/vapor flow.     

Numerical analysis of two-dimensional steady-state and transient heat transfer in a parallel duct filled with pressurized He II

Analysis on steady-state and transient heat transfer on a flat plate at the middle of a parallel duct immersed in He II was performed for bath temperatures from 1.8 to 2.1 K at 101.3 kPa. Two-dimensional computer code named SUPER-2D developed by the authors based on the two-fluid model and the theory of mutual friction was used. Steady-state critical heat flux (CHF) and the time lag from the application of a step heat input to λ transition, that is called a lifetime, were obtained numerically for various step heat fluxes and for the channel gaps from 2 to 20 mm. Effect of the gap restriction on the CHF and the lifetime were clarified. The solutions were compared with the experimental data for the ducts with the same structures and the corresponding conditions. They agreed well with the experimental data. The heat transport mechanism in the parallel duct was clarified.     

Influence of the steady background turbulence level on second sound dynamics in He II - II

We report complementary results to our previous publication [Dalban-Canassy M, Hilton DK, Van Sciver SW. Influence of the steady background turbulence level on second sound dynamics in He II. Adv Cryo Eng 2006;51:371-8], both of which are aimed at determining the influence of background turbulence on the breakpoint energy of second sound pulses in He II. The apparatus consists of a channel 175 mm long and 242 mm² in cross section immersed in a saturated bath of He II at 1.7 K. A heater at the bottom end generates both background turbulence, through a low level steady heat flux (up to q_s = 2.6 kW/m²), and high intensity square second sound pulses (q_p = 100 or 200 kW/m²) of variable duration Δt₀ (up to 1 ms). Two superconducting filament sensors, located 25.4 mm and 127 mm above the heater, measure the temperature profiles of the traveling pulses. We present here an analysis of the measurements gathered on the top sensor, and compare them to similar results for the bottom sensor [1]. The strong dependence of the breakpoint energy on the background heat flux previously illustrated is also observed on the top sensor. The present work shows that the ratio of energy received at the top sensor to that at the bottom sensor diminishes with increasing background heat flux.     

Comparison of cavitation flows in He I and He II

This paper describes some of the results of an experimental study on the cavitation phenomena in He II and He I by the visualization and the measurements of the pressure and the temperature. The cavitation flow is generated in liquid helium driven by a bellows pump in the downstream region of the throat in a Venturi channel with a rectangular cross section. It is found that there are some definite differences in the appearance of cavitation between He I and He II flows, and that the λ-phase transition from He I to He II is sometimes induced because of the temperature drop in cavitating He I flow. In addition, the expression for the relation between the amount of the temperature drop induced by cavitation and the void fraction was described, which was found to be qualitatively in good agreement with the experimental result.     

Analysis of helium II thermal links for instrument cooling in low gravity

The Low Temperature Microgravity Physics Facility (LTMPF) is a reusable, cryogenic facility that will accommodate a series of low temperature experiments to be conducted at the International Space Station. The facility will use a He II cryostat to cool the instruments. Some configurations of the science instruments in the cryostat will require an enhanced thermal link between the He II bath and parts of the instruments. Such an enhanced link can be made with plumbing filled with He II. This paper reports the results of analysis that was performed using the BATC proprietary helium flow software called SUPERFLO, on four different concepts for this link. The four concepts analyzed were: a simple tube with the heated end closed, a closed end tube with a porous plug at its entrance, a closed end tube filled with capillary tubes, and a porous plug driven flow loop. It was found that the concepts that used a porous plug were more robust since they were much less prone to boiling. This is due to the low gravity which causes all of the liquid in helium tank and plumbing to be very close to saturated conditions unless a porous plug is used to create a thermomechanical pressure. The effects of varying system parameters such as a acceleration, heat flux, pore size and tube size were also investigated and the results are reported.     

Fast Mode in Dense Aerogel Filled with Superfluid He II and Dilute Mixture of 3He in 4He

Longitudinal sound wave propagation in 90% porous silica aerogel filled with superfluid He II and dilute mixture of ³He in ⁴He has been studied using a low frequency resonance method. The observed fast mode was identified as a mode intermediate between the sound in the aerogel matrix and first sound. It was shown that the behavior of the fast mode in dense aerogel differs from both high porosity aerogel and rigid porous medium. We discuss the obtained results within the framework of theoretical models available.      

Application of particle image velocimetry for measuring He II thermal counterflow jets

The particle image velocimetry (PIV) technique was successfully applied for measuring the velocity of a He II thermal counterflow jet. Neutrally buoyant hydrogen-deuterium solid particles were used as tracer particles for PIV measurement. In the application, the normal component velocity was measured. The jet velocity profile and spatial decay of the jet velocity were compared with those of turbulent round jets of ordinary viscous fluids. The velocity measured near the jet nozzle exit was compared with the theoretical prediction for the normal component flow velocity.     

Thermo-fluid dynamics of several film boiling modes in He II in the pressure range between atmospheric pressure and saturated vapor pressure

Four film boiling modes including the silent film boiling and the noisy film boiling were discriminated experimentally. Each mode was classified through visual observation and transient pressure and temperature measurements near the heater. It was found that in subcooled He II there were two film boiling modes, which are the strongly subcooled and weakly subcooled film boiling modes. The variation of boiling state between these two modes could be visually observed well by use of a transparent heater. All mode of film boiling is clearly mapped in diagrams as a function of pressure, temperature and heat flux. It is elucidated that the existence of He I layer influences the development of the vapor layer.     

Effect of superheating on heat transfer from a good thermal conductor in a two-dimensional channel to He II below the λ-point pressure

Heat transfer characteristics in He II have been investigated in relation to superheating. When a good thermal conductor in a narrow two-dimensional channel is heated above the critical heat flux of the λ-transition, superheated He I nucleates in the hottest area of the conductor covered with superheated He II. The spread of superheated He I, which has a low thermal conductivity, forms an intermediate state in which superheated He I coexists with superheated He II. Superheated He I together with superheated He II is apparently stabilized since part of the heat cut off by superheated He I tends to flow in the conductor. Higher heat input turns the intermediate state into a mixed state where superheating and boiling alternate irregularly.     

Boiling phenomena in pressurized He II confined to a channel

Results from an experiment to study boiling phenomena in a channel containing pressurized He II are presented as a function of temperature, pressure and orientation with respect to gravity. The experimental apparatus is made of glass to allow visual observations and high-speed motion pictures to be made of boiling events. Visual data are combined with temperature and pressure measurements to characterize the boiling behaviour and to group the phenomena into boiling regimes. Results are presented in the form of heat transfer regime maps, temperature and pressure traces during boiling, and sketches of the helium vapour and liquid in the channel. One unexpected result is the observation of a macroscopic region of He I with He II below and vapour above. The two interfaces are clearly visible. Another unanticipated result is that the boiling phenomena are often characterized by the periodic production, growth and collapse of vapour even though the heat input is constant.     

An experimental and numerical study of He II two-phase flow in the TESLA test facility

We report on measurements of the liquid level and temperature corresponding to different local heat loads at several sections of the He II two-phase flow channel in the TESLA (Tera-eV Energy Superconducting Linear Accelerator) Test Facility phase I (TTF1) during its operation. The measurements show that under normal operating conditions saturation between He II and its vapor can be maintained even in the transient process of heat transfer. A computer code for He II stratified two-phase flow analysis has been developed for the numerical simulation of the He II and vapor flow in the configuration of the cryogenic cooling channel in TTF1. Comparison with the measurement shows the prediction by the code agrees well with the experimental results. The code also predicts the maximum heat load under which the two-phase tube in TTF1 would locally dry out. In its application, the code is helpful to evaluate the impact on the flow behaviour resulting from changes to the TTF1 configuration.     

Photographic studies of light induced nucleation of boiling at the interface of a solid and superheated liquid helium I

We report the results of photographic studies which show that light induces the nucleation of vapour bubbles in superheated liquid helium I. We believe that these bubbles are associated with the cooling that we have previously observed to result from a flash of visible light applied to the surface of a bismuth crystal heater-thermometer immersed in the superheated liquid. We have used this photographic technique to study vapour bubble growth dynamics and compare our results with the theory.     

Light induced nucleation of vapour bubbles at the interface of a solid and superheated liquid helium i: test of the photoelectron hypothesis

We report further studies of light induced enhancement of heat transfer from a solid into liquid helium 1. We have previously found that a flash of visible light applied to a solid surface immersed in the superheated liquid results in the production of vapour bubbles and a subsequent decrease in liquid layer superheat. Because there appeared to be a long wavelength cut-off we felt that this effect could be due to a mechanism involving photoemission of electrons into the liquid helium. In this hypothesis, electrons are first detached from the solid by the action of light and second, serve as bubble nuclei in the superheated liquid helium. The results reported in this paper fail to support this explanation.     

Heat transfer through subcooled He I layer from distributed heat source in a pressurized He II channel

The subcooled He I layer, in contact with a large heated surface in a channel filled with the pressurized superfluid He II (He II_p), expands the non-boiling region above the Kapitza region up to q_n, above which nucleate boiling sets in. As the bath temperature decreases, q_n is increased more rapidly than q_λ at which the superfluidity is broken at the centre of the heated surface. The value of q_n is increased as the channel gap increases, and is independent of the channel orientation as well as q_λ. Metastabilization of superconducting coils may be enhanced by taking the non-boiling limit q_n into account.     

Critical heat flux on a flat plate heater located at the middle of a duct in forced flow of pressurized He II

Critical heat fluxes (CHFs) were measured for two types of rectangular ducts containing horizontal flat plate heaters. One has the flat plate heater of 6 mm wide and 20 mm long located on the inner lower wall at 50 mm from the inlet. The other duct has two horizontal flat plates of 6 mm wide and 20 mm long on inner upper and lower walls at 50 mm from the inlet. The equation of CHF for the forced convection containing a new nondimensional-parameter m introduced in order to calculate cross-sectionally averaged liquid temperature at the center of the duct was derived based on two fluid model, ordinary convection theorem and experimental results. It was confirmed that this correlation can describe not only the author's data on the duct but also other worker's data for channels with different shapes and sizes.     

Thermodynamic analysis of processes in refrigerators using superfluid helium (He II) by means of T − q diagram

A T − q diagram is presented for superfluid helium (He II) by means of which a technique for thermodynamic analysis of processes in refrigerators using He II is worked out. With large pressure drops it is necessary to use p, T, q diagrams, i.e. three-dimensional space. The mathematical basis for using either method is presented and explained.