Theoretical modelling of miniature loop heat pipe

Development in the design and thermal performance of the loop heat pipes (LHPs) demands the corresponding improvement in the theoretical modeling capabilities of these devices. In this paper, mathematical model for assessing the thermal performance of the miniature LHPs (mLHPs) on the basis of the operating temperature and thermal resistance of the loop has been discussed in detail. In order to validate the theoretical model, a mLHP with the flat disk shaped evaporator, 30 mm in diameter and 10 mm thick, was developed and tested with nickel and copper wick structure. By comparison with experimental results, it was found that the theoretical model was able to predict the evaporator temperature and loop thermal resistance very well and within the uncertainties imposed by the underlying assumptions. The mathematical model can be used to validate the design of the mLHP and verify whether the proposed design is consistent with the maximum heat load capacity required for the intended application. In addition to this, the model can assists in understanding and refining the outcomes of the experimental studies.     

微型热驱动回路的脉动及位差对热性能的影响

以甲醇为工质，采用高速数据采集系统测定了微型热驱动回路在不同运行参数下的压力 及温度脉动，其脉动周期及脉动幅度随蒸发段热流密度的增加而减小. 实验发现，在蒸发段 热流密度较低的情况下，蒸气管中是泡状流或弹状流交替存在，而在蒸发段热流密度较高时， 蒸气管中为环状流. 就位差对热性能的影响进行了详细的实验研究，并在冷凝器空气自 然对流和强迫对流情况下，以加热块温度90${^\circ}$C为上限，得出微通道蒸发器和冷凝 器在不同位差下的最大蒸发段热流密度. 通过对实验现象的观察及分析，以期开发出适用于 未来电子产品高功率需求的微型化电子冷却器.     

Heat transfer mechanism of miniature loop heat pipe with water-copper nanofluid: thermodynamics model and experimental study

In order to ensure the normal work of electronic product, the thermal management is of key importance. Miniature loop heat pipe (mLHP) is a promising device of heat transfer for electronic products. Cu-water nanofluid with different concentration is used as working material in mLHP. Experiments are conducted to investigate its heat transfer performance. The heat flux owing to thermal diffusion is calculated. It is found that this heat flux and the boiling temperature are non-monotonic function of concentration of nanoparticle. Turning concentration appears at about 1.5 wt%. Differential equation of thermal diffusion produced by micro movement of nanoparticle is established in this paper. Average speed formula for nanoparticles is derived and slope of the curve of phase equilibrium is obtained. Based on the theoretical research in this paper, enhanced heat transfer mechanism of nanofluid is analyzed. The facts that heat flux owing to thermal diffusion and boiling temperature are all associated with nanoparticle concentration are also well explained with the aid of the derived theory in this paper.     

Non-linear effects in a natural circulation evaporator: geysering coupled with manometer oscillations

Investigations at ambient pressure and water for working fluid using a steam-heated single tube natural circulation evaporator revealed a novel type of geysering. This mode appears during start-up of the evaporator and changes to density wave oscillation type I with rising heating steam pressure and decreasing subcooling of the working fluid. The observed operational state is dominated by two interacting phenomena: geysering and manometer oscillations. The periodically appearing geyser feeds kinetic energy into the system whereby the damped manometer oscillation is maintained. Due to manometer oscillations backflow occurs during the incubation phase. Hence, preheated liquid is stored in the feeding line with temperatures greater than the saturation temperature at ambient pressure. This leads to an extreme violent vapour generation and expulsion after onset of the geyser as a result of flashing with maximum mass fluxes 20–60 times higher than the average value. By a moderate increase in pressure drop coefficient of the feeding line, the operational behaviour changes from geysering coupled with manometer oscillation to density wave oscillation type I respectively to a steady mode.     

Start-up investigation on a dual-evaporator MPCL system

This paper describes the start-up process of a space activate thermal control system, two-phase mechanically pumped cooling loop (MPCL) with two evaporators, in ground-based testing. Each evaporator has an outer diameter of 3 mm and a length of 10 m and the total loop of the system is about 40 m. In this paper, the system design and work principle as well as the test setup of an MPCL are presented and the start-up processes of the MPCL are studied. The experiments on the start-up processes under different evaporative temperatures were carried out. Tests attention has been paid to the system performance characteristics such as differential pressure, absolute pressure, mass flow rate, main components temperatures and so on. During the start-up processes, the system presents a good stability and each part of the system performs a reasonable temperature wave, except some superheat phenomena in the evaporator which cause a pressure shock to the system. The superheat is mainly related to evaporative temperature and the initial liquid distribution in the evaporator. In general, the lower the evaporative temperature is the higher superheat occurs. When set-point evaporative temperature is ?15 °C, the differential pressure shock can reach 6.23 bar which is as 7.5 times as the stable state. In conclusion, the MPCL with dual-evaporators can be started up successfully and is an effective kind of thermal control technology for future space applications.     

Thermodynamic analytical model of a loop heat pipe

A thermodynamics analytical model is developed to explore different parameters effects on a loop heat pipe (LHP). The LHP is a two-phase device with extremely high effective thermal conductivity that utilizes the thermodynamic pressure difference to circulate a cooling fluid. The effects of pipe length, pipe diameter, condenser temperature, and heat load are reported. As pipe length increases and/or pipe diameter decreases, a higher temperature is expected in the evaporator.     

Two phase flow and heat transfer characteristics of a separate-type heat pipe

Two phase flow and heat transfer characteristics of a separate-type heat pipe have been studied experimentally and theoretically. The experimental apparatus have the same geometry for the evaporator and the condenser which consist of 5-tube-banks, with working temperature ranges of 80–125°C. The experimental working fluid is dual-distilled water with corrosion-resistant agents. Heat transfer coefficients for boiling and condensation along with heat flux and working temperature are measured at different filling ratio. According to the results of the experiments, the optimized filling ratio ranges from 16 to 36%. Fitted correlations of average heat transfer coefficients of the evaporator and Nusselt numbers of the condenser at the proposed filling ratio are obtained. Two phase flow characteristics of the evaporator and the condenser as well as their influence on heat transfer are described on the basis of simplified analysis. Reasons for the pulse-boiling process remain to be studied.     

Heat-transfer characteristics of the top heat mode closed-loop oscillating heat pipe with a check valve (THMCLOHP/CV)

The aim of this study is to investigate the heat-transfer characteristics of a top heat mode closed-loop oscillating heat pipe with a check valve (THMCLOHP/CV). Water and ethanol are used as the working fluids at various working temperatures. The results show that the specific heat flux increases significantly when the working temperature increases and when the aspect ratio of the evaporator length L _e to the pipe diameter d decreases for the pipe filling ratio varying from 30 to 80%. The maximum specific heat flux equal to 786.34 W/m² is reached with the use of ethanol as the working fluid at L _e /d = 25, angle of inclination to the horizontal axis 90°, and filling ratio of 80%.     

Two-phase flow patterns of a top heat mode closed loop oscillating heat pipe with check valves (THMCLOHP/CV)

This research is aimed at studying the two-phase flow pattern of a top heat mode closed loop oscillating heat pipe with check valves. The working fluids used are ethanol and R141b and R11 coolants with a filling ratio of 50% of the total volume. It is found that the maximum heat flux occurs for the R11 coolant used as the working fluid in the case with the inner diameter of 1.8 mm, inclination angle of ?90?, evaporator temperature of 125?C, and evaporator length of 50 mm. The internal flow patterns are found to be slug flow/disperse bubble flow/annular flow, slug flow/disperse bubble flow/churn flow, slug flow/bubble flow/annular flow, slug flow/disperse bubble flow, bubble flow/annular flow, and slug flow/annular flow.     

Start-up and steady thermal oscillation of a pulsating heat pipe

As a novel electronic cooling device, pulsating heat pipes (PHPs) have been received attention in recent years. However, literature survey shows that no studies were carried out on the start-up and steady thermal oscillation of the PHPs. In the present paper, the copper capillary tube was being bended to form the snake-shaped PHP. Heating power was applied on the heating section, and transferred to the condensation section and dissipated to the environment by the pure natural convection. The inside diameter of the capillary tube is 2.0 mm and the working fluid is selected as FC-72. A high speed data acquisition system was used to detect the start-up and steady thermal oscillation of the PHP. Two types of the start-up process were observed: a sensible heat receiving start-up process accompanying an apparent temperature overshoot followed by the steady thermal oscillation at low heating power, and a smooth sensible heat receiving start-up process incorporating a smooth oscillation period at high heating power. For the steady thermal oscillation, also two types were found: the random thermal oscillation with a wide frequency range, indicating the random distribution of the vapor plug and liquid slug inside the capillary tube at low heating power, and the quasi periodic thermal oscillation with the same characteristic frequency for both heating section and condensation section, indicating the uniform distribution of the vapor plug and liquid slug inside the capillary tube at high heating power. The power spectral density (PSD) was used to analyze the thermal oscillation waves. The frequency corresponds to the time that a couple of adjacent vapor plug and liquid slug passing through a specific wall surface.     

Heat transfer characteristics of rotating triangular thermosyphon

An experimental investigation is carried out to study heat transfer characteristics of a rotating triangular thermosyphon, using R-134a refrigerant as the working fluid. The tested thermosyphon is an equilateral triangular tube made from copper material of 11?mm triangular length, 2?mm thickness, and a total length of 1,500?mm. The length of the evaporator section is 600?mm, adiabatic section is 300?mm, and condenser section is 600?mm. The effects of the rotational speed, filling ratio, and the evaporator heat flux on each of the evaporator heat transfer coefficient, h_e, condenser heat transfer coefficient, h_c, and the overall effective thermal conductance, C_t are studied. Experiments are performed with a vertical position of thermosyphon within heat flux ranges from 11 to 23?W/m² for the three selected filling ratios of 10, 30 and 50?% of the evaporator section volume. The results indicated that the maximum values of the tested heat transfer parameters of the rotational equilateral triangular thermosyphon are obtained at the filling ratio of 30?%. Also, it is found that the heat transfer coefficient of the condensation is increased with increasing the rotational speed. The tested heat transfer parameters of the thermosyphon are correlated as a function of the evaporator heat flux and angular velocity.     

On heat transfer in screw compressors

Heat transfer between the working fluid and machine parts within a screw compressor does not affect its performance significantly because the thermal energy dissipation is usually less than 1% of the compressor power input. However, it can be detrimental to the machine reliability because the fluid compression creates a non-uniform three dimensional temperature field leading to local distortions, which may be larger than the clearances between the machine parts. This phenomenon is widely known and special control procedures are required to allow for start-up and shut down, as well as for steady running operation. These measures are usually derived only from test-bench data and may result in larger clearances than necessary, thereby reducing the optimum performance.This paper gives an outline of two methods of computing heat transfer in a screw compressor; namely: by means of a quasi-one dimensional differential model and by three dimensional computational fluid dynamics (CFD). Both methods enable the clearance size for start-up and steady running conditions to be determined. The 3D CFD procedure is more accurate but requires a far longer running time. Two cases are considered: heat transfer in a dry screw compressor where fluid temperatures are high, and an oil-flooded screw compressor where fluid temperatures are relatively low but the convective heat transfer coefficient is substantially higher.     

Full-Core Test Method for Experimental Determination of Convective Boiling Heat Transfer Coefficients in Tubes of Crossflow Compact Evaporators

An experimental methodology is proposed in which localized convective boiling heat transfer coefficients inside the tubes of compact evaporators are determined by testing of full evaporator cores. The proposed technique makes use of a special test system having two main flow circuits. One of these flow loops is a conventional vapor compression system, which provides a steady, low-quality, two-phase flow of refrigerant to the tube side of the evaporator. The second primary flow loop provides a steady flow of the vapor of a second working fluid, which condenses on the finned side of the evaporator. Measured data from this system are analyzed using an iterative scheme. Trends in the variation of the refrigerant-side heat transfer coefficient determined by this method throughout a typical evaporator core are described, and the differences and similarities relative to previously published results for single round tubes are discussed.     

Heat transfer characteristics of a two-phase closed thermosyphon using de ionized water mixed with silver nano

Effect of using silver nanofluid (De Ionize water mixed with silver nano and particles less than 100 nm.) on heat transfer characteristics of a two-phase closed thermosyphon at normal operating condition was investigated in this research. The thermosyphon made by copper tube with 7.5, 11.1 and 25.4 mm ID. The filling ratios of 30, 50 and 80% by evaporator length and aspect ratios of 5, 10, and 20 (Le/d _i ) with vertical position. Pure water and DI water mixed with silver nanofluid of us as working fluid to compare. The working temperatures were 40, 50 and 60°C. It was found that, the maximum hat transfer rate of 750.81 W, with aspect ratio of 20(diameter of 25.4 mm ID) and working temperature of 60°C. The DI water mixed silver nanofluids more than approximate 70% to compare with pure water.     

Performance test of a shell-and-plate type evaporator for OTEC

The performance test of a shell-and-plate type evaporator (total surface area 21.95 m², length 1450 mm, width 235 mm, 100 plates) for ocean thermal energy conversion (OTEC) plants is reported. Freon 22 (R22) and ammonia (NH₃) were used as the working fluid. Empirical correlations are proposed for predicting the boiling heat transfer and the heat transfer coefficients on the water side. The water-side pressure drop is about 2.9 × 10⁴ N/m² when the warm water velocity is 0.7 m/s. The water-side friction factor is obtained.     

Comparative study on heat pipe performance using aqueous solutions of alcohols

This paper deals with the performance characterization of heat pipes using an aqueous solution of long chain alcohols like n-Butanol, n-Pentanol, n-Hexanol and n-Heptanol as working mediums. These solutions are called as self-rewetting fluids, since these fluid mixtures possess a non-linear dependence of the surface tension with temperature. A cylindrical heat pipe made up of copper with two layers of wrapped screen is used as a wick material and partially filled with the self-rewetting fluid water mixture and tested for its heat transport capability like thermal efficiency and thermal resistance at different inclinations and input power levels. A number of tests have been performed with heat pipes, filled with various aqueous solutions of alcohols with a concentration of 2?ml/l in de-ionized water (DI water) on volume basis. The results obtained for heat pipes using self rewetting fluids show improved performances, when compared to DI water heat pipes.     

The analysis of two-phase flow instability in a vertical U-tube evaporator

This paper describes both the experimental and theoretical analysis of two-phase flow instability in a vertical U-tube evaporator. In the experiment investigation the effects of various parameters on flow instability are studied by using Freon-12 as working medium and the influence of flow oscillations on heat transfer deterioration is obtained. The mathematical model to describe flow oscillations occurring in the vertical U-tube with flow stagnation and upward movement of bubbles due to buoyancy in the heated downcomer is developed. The finite differential equations are solved by using a modified two-step iteration technique. The calculated results are in good agreement with the experimental data.     

Effect of pore size distribution in bidisperse wick on heat transfer in a loop heat pipe

The purpose of this article is to experimentally investigate the effect of different pore size distributions in bidisperse wicks upon the heat transfer performance in a LHP. Three bidisperse wicks and one monoporous wick were tested in a loop heat pipe. The pore size distributions of the bidisperse wicks were measured, and the results reflected the three different large/small pore size ratios. The experiments showed that the maximum heat load of the monoporous wick reached about 400 W; and the three bidisperse wicks showed improvements on the maximum heat load up to 570 W. For the monoporous wick, the evaporator heat transfer coefficients of 10 kW/m² K and total thermal resistance of 0.19°C/W were achieved at a high heat load of 400 W. For the better bidisperse wick, the evaporator heat transfer coefficients could attain about 23 kW/m² K and total thermal resistance of 0.13°C/W. The results also indicated that a smaller cluster size in a bidisperse structure created a small pore size ratio. It was also found that the bidisperse wick with smaller clusters had a better enhancement in terms of the evaporator heat transfer coefficient.     

An experimental investigation of thermally induced flow instabilities in a convective boiling upflow system

The two-phase flow instabilities in a single channel, forced convection, open loop, up-flow system have been investigated experimentally using R-11 as the working fluid. The effects of mass flow rate, heat input, inlet liquid temperature and upstream compressible volume on two-phase flow instabilities have been investigated. Two heater surfaces were tested at five different heat inputs with constant inlet temperature, and four different inlet temperatures with constant heat input. For each case, the mass flow rate was varied over a wide range covering the entire scope for boiling two-phase flows. Experiments were also conducted at different compressible volumes, with constant heat input, inlet fluid temperature, and average mass flow rate. The oscillations of inlet mass flow rate, heater inlet pressure, and heater wall temperature were recorded. The effects of mass flow rate, inlet liquid temperature and heat input on the amplitudes and periods of inlet pressure and thermal oscillations are presented in tabular and graphical forms.

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Experimentelle Untersuchung der thermisch bedingten Strömungsinstabilitäten bei konvektiven Sieden in einer Aufwärtsströmung

Zusammenfassung Mit R-11 als Arbeitsfluid werden Zweiphasen-Strömungsinstabilitäten im Einzelkanal bei erzwungener Aufwärtsströmung ohne Rückführung experimentell untersucht, und zwar besonders im Hinblick auf den Einfluß der Massenstromdichte, der Wärmezufuhr, der Eintrittstemperatur und des in Strömungsrichtung zunehmenden kompressiblen Volumenanteils. Zwei Heizflächen wurden einmal mit fünf verschiedenen Heizflächenbelastungen und konstanter Eintrittstemperatur getestet und dann bei vier verschiedenen Wärmeeinträgen und konstanter Eintrittstemperatur. In jedem der Fälle erfolgte die Variation der Massenstromdichte in einem so weiten Bereich, daß das gesamte Feld der Zweiphasen-Siedeströmungen durchfahren werden konnte. Es wurden auch Experimente mit verschiedenen kompressiblen Volumenanteilen bei konstanter Wärmezufuhr, Fluideintrittstemperatur und mittlerer Massenstromdichte durchgeführt. Die Oszillationen der Massenstromdichte und des Druckes am Eintritt in die Heizstrecke sowie deren Wandtemperatur wurden aufgezeichnet. Die Enflüsse der Massenstromdichte, der Fluideintrittstemperatur und der Wärmezufuhr auf Amplituden und Perioden der Druck- und Temperaturoszillationen sind tabellarisch und in Diagrammform dargestellt.

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Dedicated to Prof. Dr.-Ing. F. Mayinger's 60th birthday     

Forced convection heat transfer of Giesekus viscoelastic fluid in pipes and channels

A theoretical solution is presented for the convective heat transfer of Giesekus viscoelastic fluid in pipes and channels, under fully developed thermal and hydrodynamic flow conditions, for an imposed constant heat flux at the wall. The fluid properties are taken as constant and axial conduction is negligible. The effect of Weissenberg number (We), mobility parameter (α) and Brinkman number (Br) on the temperature profile and Nusselt number are investigated. The results emphasize the significant effect of viscous dissipation and fluid elasticity on the Nusselt number in all circumstances. For wall cooling and the Brinkman number exceeds a critical value (Br ₁), the heat generated by viscous dissipation overcomes the heat removed at the wall and fluid heats up longitudinally. Fluid elasticity shifts this critical Brinkman number to higher values.