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.     

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.     

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.     

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.     

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.     

Visualization study of the interface between superheated He II and superheated He I in a two-dimensional narrow channel by using the shadowgraph method

Dynamic behavior of superheated He II-superheated He I interface as a result of heating in a narrow channel between parallel walls that simulates cooling channels of superconducting magnets was investigated using a shadowgraph visualization method. It was confirmed that a superheated state could be created in the narrow channel without preparing a special calm environment. A superheated He II-superheated He I interface transiently appeared between 2.0 K and lambda temperature when applying a small heat flux. The boiling state accompanying the superheated He II-superheated He I interface was repeatedly generated and collapsed. This boiling mode was anticipated to have a high heat transfer coefficient.     

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.     

Experimental investigation of heat transfer through porous media in superfluid helium

An experimental investigation of heat transfer through porous media in superfluid helium has been conducted in the framework of the development of porous electrical insulations for superconducting magnet cables cooled by superfluid helium. Several types of porous media with different characteristics were tested and, in particular, samples with pore size diameters of 0.1 μm, 1 μm, 2 μm, 10 μm and 20 μm. Temperature and pressure were measured between an insulating inner bath and the cryostat bath, communicating only through the porous medium. The cryostat bath is held constant all along the measurement and, for each sample, the tests are performed for bath temperature from 1.4 K to 2.1 K with 0.1 K increment. Depending on the porous medium average pore size diameter, different flow regimes are observed: for porous media with a pore diameter of 0.1 and 1 μm, only the Landau regime is observed whereas for porous media with a pore diameter of 2 μm, we observed the Landau regime and the Gorter-Mellink regime. For samples with a pore diameter of 10 and 20 μm, measurements only permitted to detect the Gorter-Mellink regime. In the laminar regime, the permeability of the samples was determined and it was found that the permeability is constant for bath temperature above 1.9 K whereas it increases as the bath temperature decreases from 1.8 K to 1.4 K. For samples with a pore size diameter of 10 and 20 μm, measurement permits only to observe the turbulent regime and the analysis exhibits a constant average tortuosity for each samples, independently of the bath temperature.     

He II heat transfer through random packed spheres: Pressure drop

Heat flow induced pressure drop through superfluid helium (He II) contained in porous media is examined. In this experiment, heat was applied to one side of a He II column containing a random pack of uniform size polyethylene spheres. Measured results include steady state pressure drops across the random packs of spheres (nominally 35 μm, 49 μm, and 98 μm diameter) for different heat inputs. Laminar, turbulent, and transition fluid flow regimes are examined. The laminar permeability and equivalent channel shape factor are compared to our past studies of the temperature drop through He II in the same porous media of packed spheres. Results from the pressure drop experiments are more accurate than temperature drop experiments due to reduced measurement errors achieved with the pressure transducer. Turbulent results are fitted to models with empirically derived friction factors. A turbulent model considering only dynamic pressure losses in the normal fluid yields the most consistent friction factors. The addition of the laminar and turbulent heat flow equations into a unifying prediction fits all regimes to within 10%.     

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.     

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.     

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.     

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.     

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.     

Film boiling on a vertical plate in subcooled helium II

Film boiling heat transfer coefficients were measured on 10, 30 and 50 mm long vertical plates in subcooled He II for bulk liquid temperatures from 1.8 to 2.1 K. A film boiling model on a vertical plate in subcooled He II was presented based on convection heat transport in the vapor film, radiation heat transport, and heat transport in He II. The numerical solutions of the model were obtained and an equation which can express the numerical solutions within ±5% difference was derived. The equation predicted well the experimental data for lower ΔT range but significantly under-predicted the data for higher ΔT. A correlation of film boiling heat transfer including radiation contribution was presented by modifying the equation based the experimental data. This correlation can describe the experimental data within ±20% difference.     

Dynamic quench of NbTi in pressurized He4: 1. dual lambda transition during transient heat transfer

New transient phase transition phenomena are reported for near-isobaric temperature excursions caused by a step input in heating power supplied from a composite conductor NbTi/Cu to superfluid He II above its thermodynamic critical pressure P_c. Transient triple — phase phenomena are found not only below P_c but also above P_c during dual-lambda transitions from He II to He I and from pseudo-liquid to pseudo-vapour of He I. Consequences are presented for stabilization of superconducting magnets.     

Light induced enhancement of transient heat transfer from a solid into liquid helium I

We report preliminary studies of a new effect: enhancement of transient heat transfer from a bismuth crystal into liquid helium by a light pulse. We found that when a single crystal of bismuth is rapidly heated above a certain threshold temperature in a bath of liquid helium by a step-function electric current, the application of a light pulse of intensity 1 to 200 mW cm^?2 and duration 2 μs to 1 ms causes a decrease of up to 75% in the total crystal superheat temperature within 3 ms. The threshold temperature is less than the homogeneous nucleation temperature of liquid helium. The marked increase in heat transfer across the solid-liquid interface, associated with the observed rapid cooling, is believed to be caused by increased bubble activity due to the light induced rapid nucleation of bubbles near the interface. Although the exact nature of the interaction mechanism involved is unclear at this time, several hypotheses are presented and discussed.     

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.     

Transient solid-liquid He heat transfer and onset of film boiling

The transient heat transfer between single-crystalline Ge chips and liquid helium is investigated during the application of light pulses with different optical power to the Ge sample. The strong temperature dependence of the electrical conductivity of Ge conveniently serves for monitoring the temporal behaviour of the sample temperature during the input of optical energy. After a certain time interval following the beginning of the light pulse an abrupt rise of the sample temperature is observed. This time interval is much longer than the thermal time constant expected for the sample. This abrupt rise of the sample temperature can be understood in terms of the onset of film boiling. The observed onset time of film boiling and its dependence upon the heat transfer power density agrees reasonably with earlier results by Steward.