Heat Transfer In He Research Articles

Boiling and cavitation caused by transient heat transfer in superfluid helium-4

Superfluid helium-4 (He II) has been widely utilized as a coolant in various scientific and engineering applications due to its superior heat transfer capability. An important parameter required in the design of many He II based cooling systems is the peak heat flux ${q}^{*}$, which refers to the threshold heat flux above which boiling spontaneously occurs in He II. Past experimental and numerical studies showed that ${q}^{*}$ increases when the heating time ${t}_{h}$ is reduced, which leads to an intuitive expectation that very high ${q}^{*}$ may be achievable at sufficiently small ${t}_{h}$. Knowledge on how ${q}^{*}$ actually behaves at small ${t}_{h}$ is important for applications such as laser ablation in He II. Here we present a numerical study on the evolution of the thermodynamic state of the He II in front of a planar heater by solving the He II two-fluid equations of motion. For an applied heat flux, we determine the heating time beyond which the He II near the heater transits to the vapor phase. As such, a curve correlating ${q}^{*}$ and ${t}_{h}$ can be obtained, which nicely reproduces some relevant experimental data. Surprisingly, we find that there exists a critical peak heat flux ${q}_{c}^{*}$, above which boiling occurs nearly instantaneously regardless of ${t}_{h}$. We reveal that the boiling in this regime is essentially cavitation caused by the combined effects of the first-sound and the second-sound waves in He II. Based on this physical picture, an analytical model for ${q}_{c}^{*}$ is developed, which reproduces the simulated ${q}_{c}^{*}$ values at various He II bath temperatures and hydrostatic head pressures. This work represents a major progress in our understanding of transient heat transfer in He II.

Comparative Study of Heat Transfer Performance and Visualization Images of Superfluid Helium Boiling in Narrow Two-dimensional channel

In a narrow channel, boiling heat transfer in He II is much different from that in the case of an open bath. Even under saturated pressure condition, rapid temperature rise due to the onset of film boiling is not seen when the temperature reaches the lambda temperature, but only the temperature oscillation is detected. The behaviour of this state looks like the nucleate boiling, though it is known the steady nucleate boiling state is absent in He II in open bath. The high heat transfer coefficient in this quasi-nucleation boiling state above the lambda temperature suggests the range where this advantage in heat transfer appears is wider than that based on simple prediction of He II heat transfer. The appearance of metastable states of superheated He II and superheated He I should be considered in the case of a narrow channel. In this study, the visualization experiment result using a transparent heater and the transient temperature measurement data on a copper heater surface had been compared with each other. In the case of rather high heat flux, several film boiling modes were observed in a narrow two-dimensional channel. The peak of the heat transfer coefficient appeared around the lambda pressure. In the case of low heat flux, the heat transfer coefficient variation with the pressure shows sudden rise around the lambda point. The heat transfer coefficient under nearly saturated pressure condition below the lambda pressure is larger than that above the lambda pressure.

Quench-Spot Detection for Superconducting Accelerator Cavities Via Flow Visualization in Superfluid Helium-4

Superconducting ratio-frequency (SRF) cavities, cooled by superfluid helium-4 (He II), are key components in modern particle accelerators. Quenches in SRF cavities caused by Joule heating from local surface defects can severely limit the maximum achievable accelerating field. Existing methods for quench spot detection include temperature mapping and second-sound triangulation. These methods are useful but all have known limitations. Here we describe a new method for surface quench spot detection by visualizing the heat transfer in He II via tracking He$_2^*$ molecular tracer lines. A proof-of-concept experiment has been conducted, in which a miniature heater mounted on a plate was pulsed on to simulate a surface quench spot. A He$_2^*$ tracer line created nearby the heater deforms due to the counterflow heat transfer in He II. By analyzing the tracer-line deformation, we can well reproduce the heater location within a few hundred microns, which clearly demonstrates the feasibility of this new technology. Our analysis also reveals that the heat content transported in He II is only a small fraction of the total input heat energy. We show that the remaining energy is essentially consumed in the formation of a cavitation zone near the heater. By estimating the size of this cavitation zone, we discuss how the existence of the cavitation zone may explain a decades-long puzzle observed in many second-sound triangulation experiments.

The numerical boundary conditions of the wrapping pattern of thin insulation

The wrapping pattern of thin insulation is an important issue in cryogenic installations because it can significantly affect heat transport. The major objective of this study is to develop the numerical boundary conditions (BC) needed to model the wrapping pattern of thin insulation. An example of the practical application of the proposed BC includes the heat transfer of Rutherford NbTi cables immersed in superfluid helium (He II) across thin layers of electrical insulation. The proposed BC and a mathematical model of heat transfer in He II are implemented in the open source CFD toolbox OpenFOAM. The implemented mathematical model and the BC are compared with experiments. The study confirms that the thermal resistance of electrical insulation can be lowered by implementing the proper wrapping pattern. The proposed BC can be useful in the study of new patterns for wrapping schemes. Further possible improvements of the tool are indicated in the paper.

Visualization Study of Growth of Spherical Bubble in He II Boiling under Microgravity Condition

Under microgravityconditions, the heat transfer is considered to bedifferent from that in normal gravity becauseof zero subcooling due to zero hydrodynamic pressure in saturated He II. Thus the heat transfer in He II under microgravity is an interesting research target. Microgravity experiment is expected to reveal some hidden mechanism of boiling heat transfer acrossthe vapor-liquid interface because stable large-scale vapor bubblesare formed. In the present study, the behavior of a single spherical bubble generated by a micro heater was observed under microgravity conditionduring free fall in a drop tower for about 1.3 second. The visualized images taken by a high-speed camera were analyzed to examine the time variation of a large vapor bubble ofthe order of 10mm. It was seen that the sizes of a single bubble increased with decreasing He II temperature for fixed heat input. The bubble size near the lambda temperature was smaller than that at 1.9K though the effective thermal conductivity is quite small. The magnitude of the saturated vapor pressure seems to be a dominant factor to determine the bubble size. For the case of He I, the vapor bubble growth can be predicted by a simple consideration in terms of the latent heat and the gas density in film boiling state.

Stability Analysis of the LHC Cables for Transient Heat Depositions

<para xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> The commissioning and the exploitation of the LHC require a good knowledge of the stability margins of the superconducting magnets with respect to beam induced heat depositions. Previous studies showed that simple numerical models are suitable to carry out stability calculations of multi-strands cables, and highlighted the relevance of the heat transfer model with the surrounding helium. In this paper we present a systematic scan of the stability margin of all types of LHC cables working at 1.9 K against transient heat depositions. We specifically discuss the dependence of the stability margin on the parameters of the model, which provide an estimate of the uncertainty of the values quoted. The stability margin calculations have been performed using a zero-dimensional (0-D) numerical model, and a cooling model taking into account the relevant helium phases which may appear during a stability experiment: it includes Kapitza thermal resistance in superfluid He, boundary layer formation and heat transfer in He I, and considers the transition from nucleating boiling to film boiling during He gas formation. </para>

Numerical Study of the Transient Heat Transfer in He II for Superconducting Device Cooling: A Comparison to Gorter-Mellink Equation

Superfluid helium (He II) is frequently used for the cooling of the superconducting magnet. The prediction of the heat transfer characteristics of He II is very essential to guarantee the stable work of the devices cooled by He II. In the present study, the heat transfer process is analyzed numerically by using Gorter-Mellink equation and Landau's two-fluid model with Vinen's vortex line density equation, respectively. The analysis results obtained from both methods are compared and it is concluded that the numerical analysis should be carried out in the case of the transient heat transfer process

Study of the transient thermal wave heat transfer in a channel immersed in a bath of superfluid helium

Thermal wave is a very interesting phenomenon in which heat is transported in the wave mode. It is different from the ordinary Fourier heat transfer discipline in which heat is transported in the diffusive mode. In the present study, transient thermal wave (second sound wave) heat transfer in He II (superfluid helium) is numerically studied. Quantized vortices in He II, a phenomenon related to the superfluid nature, which is an important factor affecting the behavior of the thermal wave has been taken into account. The present results show that the shape of the thermal wave does not deform seriously and the amount of the heat contained in and transported by the thermal wave does not decrease as the thermal wave transmits along the channel when it is free from the quantized vortices; while the shape of the thermal wave starts to deform at the moment of the emission of the thermal wave and the amount of the heat transported by the thermal wave decreases when it is subject to the quantized vortices. The deformation is in stronger magnitude in the case of the larger heat flux. The surplus amount of the heat which cannot be carried away by the thermal wave accumulates in the thermal boundary layer formed by the dense quantized vortices and then is transferred in a diffusion-like mode. It is found that Gorter–Mellink equation is not suitable to describe the transient heat transfer process in He II.

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.

Steady-state pressure drop and heat transfer in He II forced flow at high Reynolds number

An experiment to study forced flow superfluid helium (He II) at high Reynolds number has been recently developed at the national high magnetic field laboratory (NHMFL). The liquid is pushed from a bellows pump through a 1 m long, 9.8 mm inside diameter smooth tube test section to attain a maximum velocity of 18 m/s and a Reynolds number up to 2×10 7. The test section is instrumented with eight bare chip thermometers, a heater and a differential pressure transducer. Measurements of pressure drop have been performed to determine the friction factor for Reynolds number exceeding 10 7. These are compared to results from previous forced flow experiments at lower velocities and to some existing correlations. The temperature rise in He II forced flow, due to the isenthalpic expansion in the test section, has also been measured for velocities between 0.5 and 16 m/s. These temperature profiles are related to the Joule–Thomson coefficient. The heater, positioned in the middle of the test section, allows heat transfer measurements and can be used as a thermal flow meter.

98/04150 A numerical model on transient, two-dimensional flow and heat transfer in He II

98/04150 A numerical model on transient, two-dimensional flow and heat transfer in He II

簡易モデルと二流体モデルによるＨｅ ＩＩの二次元熱流動特性解析

The two-fluid model explains the unique features of flow and heat transfer in superfluid helium, of He II. In the multidimensional analysis with a two-fluid model, much CPU time will be necessary because this model consists of four complicated equations. Thus we propose a new numerical model, called the simplified model, which is derived from the two-fluid model. It consists of a conventional continuity equation, a momentum equation for total fluid in the form of a modified Navier-Stokes equation, and an energy equation in the form of a conventional temperature-based energy equation in which the heat flux resulting from the Gorter-Mellink internal convection is properly incorporated. To verify the validity of the simplified model, its results are compared with results of the two-fluid model in the analysis of one-dimensional heat transfer in a vertical He II duct heated at the bottom boundary. To demonstrate the capability of the present model to deal with multidimensional problems, a two-deimensional analysis is performed for internal-convection heat transfer in an He II pool with one wall partially heated. Our purpose was to verify the validity of the simplified model in multidimensional analysis, so we compared the analytical results obtained by use of the simplified model with those obtained by the two-fluid model in a two-dimensional analysis. The validity of the analytical method, which obtained was adopted by Ramadan and Witt, is also discussed.

A numerical model on transient, two-dimensional flow and heat transfer in He II

A new numerical model is developed to study the unique features of flow and heat transfer in superfluid helium or He II. The model, called the simplified model, is derived from the original two-fluid model. It consists of a conventional continuity equation, a momentum equation for the total fluid in the form of a modified Navier-Stokes equation, and an energy equation in the form of the conventional temperature-based energy equation, in which the heat flux due to Gorter-Mellink internal convection is properly incorporated. To verify the validity of the simplified model, the analytical results by the simplified model are compared with those by the original two-fluid model in the analysis of one-dimensional heat transfer in a vertical He II duct heated at the bottom boundary. To demonstrate the capability of the present model for multi-dimensional problems, two-dimensional analysis is performed for internal-convection heat transfer in an He II pool with one of the walls partially heated. The two-dimensional results obtained by the present model are also compared with that by the modified two-dimensional model by Ramadan and Witt.

Estimation of Kapitza conductance effect on steady and transient boiling heat transfer in He I based on Kapitza conductance results in He II

Kapitza conductance in steady and transient boiling heat transfer on a horizontal 0.2-mm diameter test wire was estimated based on the measured Kapitza conductance value for the same surface in He II. The He II experiments performed are for liquid temperatures ranging from 1.8 to 2.1 K under atmospheric pressure, and the He I experiments of the steady and transient heat transfer caused by exponential heat inputs are for the periods ranging from 0.2 ms to 10s under saturated conditions at liquid temperatures ranging from 2.2 to 4.2 K, and subcooled conditions for the subcooling of 1.0 and 2.0 K at atmospheric pressure. The Kapitza conductance in He I is higher for higher saturation temperatures but little dependent upon heat flux, liquid subcooling, and heat input increasing rate. The temperature drop due to the Kapitza conductance for the wall superheat becomes more significant with the increase in heat flux and in saturation temperature. It was confirmed that the Kapitza conductance in He I can be estimated correctly based on the Kapitza conductance value for the same surface in He II.

Unsteady heat transfer in He II with cylindrical geometry

Heat transfer in He II with cylindrical geometry, involving stepwise switching on of a heater which forms an internal cylinder, is investigated in this paper using numerical methods. The problem is solved within the framework of the hydrodynamics of superfluid turbulence (HST), in which the density of the vortex tangle L reaches its equilibrium value with respect to the value of the velocity of the normal component (the so-called adiabatic approximation). In this paper we consider two different cases: the adiabatic one, which corresponds to an isolated system; and the isothermal one, which corresponds to a system immersed in a bath filled with He II at a given temperature. The results obtained and those evolved from Dresner's approach are compared using a newly introduced parameter, the Dr number.

Heat transfer in He II with stepwise switching on of heater

The problem of the dynamics of temperature and normal velocity fields in He II with stepwise switching on of a plane heater is investigated in this paper using numerical methods. The problem is solved in the framework of the hydrodynamics of superfluid turbulence in which the density of vortex tangle, L, reaches its equilibrium value with respect to the value of the relative velocity, v ns = ( v n - v s). Such an approximation, the so-called adiabatic approximation, is valid at times much larger than the time for development of turbulence, τ v. The results obtained are compared with other known solutions of similar problems and with experimental data.

Geometry dependence of steady-state heat flow in He II

The Gorter-Mellink equation of steady-state heat transfer in He II is used to develop a method of calculating the peak heat flux for a magnet cooled in a bath of He II. It is shown that the equivalent thermal resistance of a series or parallel arrangement of linear cooling channesl is given by R eq = f(T) 1 3 g eq where f( T) is the inverse of the heat conductivity function and g eq is the equivalent geometry factor respectively defined for series or parallel channels as g s = (Σg 3 i) 1 3 and p = [ Σ(1)/ g i )] −1. Here g i = L 1 3 i/A i where L and A are the channel length and cross-sectional area respectively. The peak heat flux is given by q ∗ = Z(T b )/(A o g en ) where Z( T b) is the integrated heat conductivity function. Specific forms of the peak heat flux are developed for three different winding geometries: a simple pancake-wound magnet, a layer-wound magnet, and a multiply connected coil pack.

Effect of channel geometry on heat transfer in He II chamber

Heat transfer from a horizontal surface to superfluid helium contained in a chamber has been measured. A test channel 13 mm in length was connected to the chamber at one end and opened to a helium bath at the other. Eleven kinds of channel with nearly equal void areas and six kinds of round tube channel with inner diameters ranging from 1.9 to 13 mm were used. Channels packed with wire were adopted as capillary channels. The equivalent diameter was used to characterize the wire-packed channels and non-round tubes. The limiting heat flux, defined as the flux at the start of film boiling on the heat transfer surface, showed a maximum at an equivalent diameter of 1.94 mm and decreased steeply with any further increase in equivalent diameter. The single tube channel proved to have a poor heat transport capability compared with the channel of an equally divided tube.

Thermal counterflow in a diverging channel: a study of radial heat transfer in He II

Heat transfer in superfluid helium is studied in a channel which imposes a radial 1/ r divergence in the heat flux density, q( r). A very sensitive AuFe thermocouple/SQUID system is employed to measure the temperature difference between various radial positions along the channel. Both laminar and turbulent dissipation are observed. The Gorter-Mellink mutual friction model, used to describe the turbulent thermal dissipation in channels of uniform cross-section, is applied locally to this diverging flow. Comparison of the turbulent dissipation measured over two sections of the channel shows that the Gorter-Mellink model alone is inadequate to describe the thermal resistance of He II in this non-uniform flow. Effects such as a suppression of the turbulence at the channel entrance or a transition to turbulence at some position within the channel may contribute to the discrepancy. Until these effects are carefully understood, use of the Gorter-Mellink model alone to characterize radial heat transfer in He II is highly suspect, even at high heat flux densities.

Stability of superconductors cooled internally by He II heat transfer

He II (superfluid helium) is a unique fluid which offers substantial advantages when utilized as a coolant for large superconducting magnets. One of the principal advantages of He II is its extremely high heat conductivity which allows rapid diffusion of localized transient heating. The present paper reviews the processes involved in transient heat transfer in He II. Emphasis is placed on those processes which are particularly relevant to the stability of superconducting magnets. The implications that these processes have on predicting the performance of actual magnet systems are also discussed. A recent experiment involving composite superconductors cooled with He II demonstrates the importance of transient heat transfer for obtaining stability in these systems.