Analytical calculation of DNB-superheating by a postulated thermo-mechanical effect of nucleate boiling

Observations of stationary subcooled nucleate boiling with forced convection in a glass-pipe at a pressure of 0.1 MPa lead to a new interpretation of the wall. This interpretation applied to the rules of linear non-equilibrium thermodynamics results in framework equations with non-linear heat transfer as indicated by several empirical correlations. Momentum balances at the singular surfaces of a bubble have been combined with a sonic limit for the mass transfer through the interfaces serving as a maximum condition with respect to heat transfer (DNB). The calculation predicts the corresponding wall temperature from properties of state without using empirical coefficients and therefore must be valid independent of coolants' geometries and surface conditions. Documented measurements at pool boiling, forced and free convection with cryogenic liquids, water and liquid metals emphasize this if data are properly selected corresponding to the precondition that void fraction remains low.     

Observations on braided thin wire nucleate boiling in microgravity

A microgravity experiment was conducted on the Space Shuttle Endeavor (STS-108) to observe sustained nucleate boiling of water. Subcooled water was boiled with a single strand and a braid of three 0.16 mm diameter and 80 mm long Nichrome resistive wires. A CCD video camera recorded the experiment while six thermistors recorded the temperature of the fluid at various distances from the heating element. This paper reports experimental results in observations, measurements, and data analysis. Bubble explosions were found to take place shortly after the onset of boiling for both the single and braid of wires. The explosion may produce a high heat transfer rate, as it generates a cloud of microbubbles. The number, size, and departure rate of the bubbles from the heater wire were measured and compared with theoretical models as a function of time. The temperature measurements revealed a complex temperature distribution in the fluid chamber due to bubbles ejected from the wire that carried thermal energy close to the temperature sensors. Drag forces on departing bubbles were calculated based on bubble movement and used to predict bubble propagation. Results from this experiment provided further understanding of nucleate boiling dynamics in microgravity for the eventual design and implementation of two-phase heat transfer systems in space applications.     

Direct numerical simulation of bubble dynamics in subcooled and near-saturated convective nucleate boiling

With the long-term objective of Critical Heat Flux (CHF) prediction, bubble dynamics in convective nucleate boiling flows has been studied using a Direct Numerical Simulation (DNS). A sharp-interface phase change model which was originally developed for pool boiling flows is extended to convective boiling flows. For physical scales smaller than the smallest flow scales (smaller than the grid size), a micro-scale model was used. After a grid dependency study and a parametric study for the contact angle, four cases of simulation were carried out with different wall superheat and degree of subcooling. The flow structures around the growing bubble were investigated together with the accompanying physics. The relation between the heat flux evolution and the bubble growth was studied, along with investigations of bubble diameter and bubble base diameter evolutions across the four cases. As a validation, the evolutions of bubble diameter and bubble base diameter were compared to experimental observations. The bubble departure period and the bubble shapes show good agreement between the experiment and the simulation, although the Reynolds number of the simulation cases is relatively low.     

Experimental study of pool temperature effects on nucleate pool boiling

Nucleate pool boiling experiments with constant wall temperature were performed using pure R113 for subcooled, saturated, and superheated pool conditions. A microscale heater array and Wheatstone bridge circuits were used to maintain the constant wall temperature and to measure the instantaneous heat flow rate accurately with high temporal and spatial resolutions. Images of bubble growth were taken at 5000 frames per second using a high-speed CCD camera synchronized with the heat flow rate measurements. The bubble geometry was obtained from the captured bubble images. The effect of the pool conditions on the bubble growth behavior was analyzed using dimensionless parameters for the initial and thermal growth regions. The effect of the pool conditions on the heat flow rate behavior was also examined. The bubble growth behaviors during subcooled, saturated, and superheated pool boiling were analyzed using a modified Jakob number that we newly defined. Dimensionless time and bubble radius parameters with the modified Jakob number characterized the bubble growth behavior well. These phenomena require further analysis for various pool temperature conditions, and this study will provide good experimental data with precise constant wall temperature boundary condition for such works.     

A survey of experimental heat transfer data for nucleate pool boiling of liquid metals and a new correlation

The experimental data for heat transfer during nucleate pool boiling of saturated liquid metals on plain surfaces are surveyed and a new correlation is presented. The correlation is h = Cq^0.7p_r^m, where C and m are, respectively, 13.7 and 0.22 p_r < 0.001 and 6.9 and 0.12 for p_r > 0.001 (h is in W/m² K and q in W/m²). This correlation has been verified with data for K, Na, Cs, Li, and Hg from 17 sources over the reduced pressure (p_r) range of 4.3 × 10⁻⁶ to 1.8 × 10⁻². The correlation of Subbotin et al. was found unsatisfactory, but a modified correlation was developed that also gives good agreement with most of the data.     

Subcooled flow boiling of R-134a in vertical channels of small diameter

Subcooled flow boiling heat transfer for refrigerant R-134a in vertical cylindrical tubes with 0.83, 1.22 and 1.70 mm internal diameter was experimentally investigated. The effects of the heat flux, q″ = 1–26 kW/m², mass flux, G = 300–700 kg/m² s, inlet subcooling, ΔT_sub,i = 5–15 °C, system pressure, P = 7.70–10.17 bar, and channel diameter, D, on the subcooled boiling heat transfer were explored in detail. The results are presented in the form of boiling curves and heat transfer coefficients. The boiling curves evidenced the existence of hysteresis when increasing the heat flux until the onset of nucleate boiling, ONB. The wall superheat at ONB was found to be essentially higher than that predicted with correlations for larger tubes. An increase of the mass flux leads, for early subcooled boiling, to an increase in the heat transfer coefficient. However, for fully developed subcooled boiling, increases of the mass flux only result in a slight improvement of the heat transfer. Higher inlet subcooling, higher system pressure and smaller channel diameter lead to better boiling heat transfer. Experimental heat transfer coefficients are compared to predictions from classical correlations available in the literature. None of them predicts the experimental data for all tested conditions.     

Stability of nucleation sites in pool boiling

A study was carried out to observe bubble nucleation and site deactivation mechanisms under equilibrium pool boiling of liquids on single sites. The experiments were conducted with benzene, ethanol, and their mixtures on single sites made of glass. These mechanisms were filmed using a cine camera as the temperature of the boiling liquid was decreased in programmed steps. The experiments showed that the deactivation of a bubble nucleation site in the surface occurred by progressive condensation of vapor within it until the volume of vapor became equal to or smaller than the volume of a spherical bubble of diameter equal to that of the site. Based upon these experimental observations, a site deactivation mechanism is proposed for heterogeneous pool boiling and stability criteria are developed for single cylindrical cavities. The effect of relevant parameters on depth-to-diameter ratio of the sites is also determined.     

Simulation of size effects by a phase field model for fracture

In phase field fracture models the value of the order parameter distinguishes between broken and undamaged material. At crack faces the order parameter interpolates smoothly between these two states of the material, which can be regarded as phases. The crack evolution follows implicitly from the time integration of an evolution equation of the order parameter, which is coupled to the mechanical field equations. Among other phenomena phase field fracture models are able to reproduce crack nucleation in initially sound materials. For a 1D setting it has been shown that crack nucleation is triggered by the loss of stability of the unfractured, spatially homogeneous solution, and that the stability point depends on the size of the considered structure. This work numerically investigates to which extend size effects are reproduced by the 2D phase field model. Exemplarily, a finite element study of the hole size effect is performed and the simulation results are compared to experimental data.     

Film boiling of an electrically insulating fluid in the presence of an electric field

This paper deals with the experimental and theoretical investigation of the influence of an electric field on the heat transfer rate during stable film boiling of the electrically insulating fluid FC-72. In particular the case of stable saturated film boiling from a horizontal plate is studied. The experiments show that the heat transfer rate increases ±50 when an electric field of 27.3 kV/cm is applied. A new correlation for the heat transfer rate in the presence of an electric field based on the heat transfer model of Klimenko is derived in this paper. Therefore the behavior of the liquid-vapor interface is studied in more detail. This study shows that the electric field has a two fold effect on the interface. On the one hand the distance between adjacent bubbles decreases and on the other hand the bubbles elongate in the presence of the electric field. The new correlation is in good agreement with the experiments. Received on 20 October 1998     

交变电场作用下骨表面温升的实验研究

骨具有力电性质,这一性质可促进骨组织生长。骨既是生理器官又是介电材料,在交变电场作用下,其表现行为可能有生理作用。为此,本文测量了骨悬臂梁试样在交变电场下的表面温升与顶端挠度。发现在电压70V,频率为10~70kHz的交流电场下,最大表面温升达到2~4℃,最大挠度变化为9.0~78.7μm;在频率10kHz,电压为70~175V的交流电场下,最大表面温升达到4~6℃,最大挠度变化为13.0~114.3μm。同时测量了两种经典介电材料有机玻璃和聚乙烯在交变电场下的温升与顶端挠度,最大温升低于0.5℃,但是挠度与骨试样相当,所以相对高温升是骨特有的性质。将交流电压有效值替换成相同幅值的直流电压时,最大温升也低于0.5℃,基本没有挠度变化,所以相对的高温升反映了骨的交流性质。分析后认为,骨在交变电场作用下的温升由胶原的介电损耗引起。实验数据显示,骨在交变电场下,表面温度变化与加载电压的平方成正比,且在实验加载的10~70kHz频段内,骨的介电常数随频率的变化明显。     

Drop and Bubble Deformation in an Electric Field

A steady problem of drop (bubble) shape in a uniform electric field is considered when the drop and the surrounding medium are immiscible. The electric-charge transport includes both the ohmic current across the interphase boundary and convective transport over the interface. If there is no convective transport, the drop (bubble) may be transformed into either an elongated or a flattened spheroid. Under these conditions, the sign of the deformation remains unchanged for arbitrary values of the problem parameters. Convective charge transport along the surface initiates additional motion in both the drop and the surrounding medium. However, with increase in the convective-transport intensity the deformed drops display different behavior. The compression of a flattened drop slows and, under certain conditions, compression is replaced by extension. However, an elongated spheroid cannot be transformed into a flattened spheroid. The calculations were performed under the assumption that the drop is convex. It was found that, for both an elongated and a flattened drop, the maximum ratio of the major and minor spheroid axes is 2:1. In experiments with oils, the possibility of both a decrease in the drop compression rate and deformation sign reversal was demonstrated.     

Flow pattern and boiling heat transfer of CO2 in horizontal small-bore tubes

Increasing attention has been focused on carbon dioxide (CO₂) heat pump system where the temperature level is rather low, while the operating pressure is rather high. In this system, the density difference between vapor and liquid becomes rather small, which significantly affects flow patterns. Low surface tension and latent heat also have significant influence on two-phase flow patterns and heat transfer. This paper describes experimental and numerical investigation on flow patterns and heat transfer characteristics of boiling flow CO₂ at high pressure in horizontal small-bore tubes ranging from 1.0 mm to 3.0 mm I.D. Even though the density difference is rather small at high pressure, phase stratification takes place, which leads to the intermittent dryout at the upper wall. So far developed discrete bubble model by the authors for vertical flows is modified so as to include horizontal flow mechanisms. The predicted flow patterns with this new model agree on the whole with the experimental observation.     

Effects of external electric field on pool boiling: Comparison of terrestrial and microgravity data in the ARIEL experiment

Pool boiling in microgravity, in the presence of an electric field or less, was investigated in ARIEL test setup, integrated in Fluidpac facility, on Foton-M2 orbital mission. The nucleate boiling curve with FC-72 was measured in terrestrial and reduced gravity conditions, on a heated surface whose size was relevant from a technical point of view, for various degrees of fluid subcooling and high heat rates. An external electrostatic field was also added to investigate its use as a possible replacement of buoyancy. Counterpart tests were carried out in the same apparatus in normal gravity, before the mission. The present paper deals in particular with the comparison between boiling performance in normal and reduced gravity in the entire experimental range.     

Electrohydrodynamic stability of poorly conducting parallel fluid flow in the presence of transverse electric field

In this paper we study electrohydrodynamic instability (EHDI) in a poorly conducting parallel inviscid fluid in the presence of an electric field and space variation of electrical conductivity. It is shown that EHDI causes inhomogeniety in the material science processing. This inhomogeniety can be controlled by understanding the nature of EHDI in the presence of an electric field and a shear due to horizontal basic velocity. The condition for EHDI is determined in terms of the electric number rather than the point of inflexion of the basic velocity profile using both moment and energy methods combined with Galerkin expansion technique. From this analysis, it is shown that a proper choice of electric number controls inhomogeniety by controlling instability of a parallel poorly conducting inviscid fluid. For unstable motion it is shown that the growth rate, C_i, is confined in a semi circle region

     

裸露地表土壤风蚀及其电场数值模拟

土壤风蚀及电场机理研究是认识其灾害本质,进而实现有效防治的基础。采用颗粒流体动力学方法,建立裸露地表土壤风蚀的气-固耦合模型,并基于水的电离理论,建立了运动土壤颗粒碰撞带电模型。数值计算结果不仅从理论上再现了裸露地表土壤风蚀的发生、发展及达到动态稳定的过程,而且定量分析了土壤风蚀过程颗粒的带电特性及其产生的风蚀电场。在风-颗粒相互耦合作用下,裸露地表土壤颗粒的风蚀过程最终达到动态稳定,土壤风蚀量随高度呈指数规律递减,且贴近地表层风蚀量较大。土壤颗粒在运动中的碰撞使得颗粒发生带电现象,粒径较大颗粒带正电,粒径较小颗粒带负电;由带电土壤颗粒产生的风蚀电场强度随高度减小,且在风蚀过程中逐渐增强,在风蚀达到动态平衡时风蚀电场趋于稳定。本文综合考虑了风-土壤-电场的土壤风蚀过程,这将为建立更加符合实际、较为全面的土壤风蚀模型提供理论基础。     

An experimental investigation of flow boiling in an asymmetrically heated rectangular microchannel

By using unique experimental techniques and carefully constructed experimental apparatus, the characteristics of flow boiling of water in microscale were investigated using a single horizontal rectangular microchannel. A polydimethylsiloxane rectangular microchannel (D_h = 103.5 and 133 μm) was fabricated by using the replica molding technique, a kind of soft lithography. A piecewise serpentine platinum microheater array on a Pyrex substrate was fabricated with the surface micromachining MEMS technique. Real time flow visualization of the phase change phenomena inside the microchannel was performed using a high speed CCD camera with microscope. The experimental local boiling heat transfer coefficients were studied, and single bubble inception, growth, and departure, as well as elongated bubble behavior were analyzed to elucidate the microscale heat transfer mechanisms. Tests were performed for mass fluxes of 77.5, 154.9, and 309.8 kg/m² s and heat fluxes of 180–500 kW/m². The effects of mass flux, heat flux, and vapor qualities on flow boiling heat transfer in a microchannel were studied.     

内压对电场下晶内微裂纹演化的影响

基于表面扩散的经典理论及其弱解描述,建立曲率、内压和电场共同作用下的有限单元法,分析了金属材料内部晶内微裂纹的演化过程。对于形态比为β的微裂纹,存在一临界电场值χc,当χ<χc时,微裂纹逐渐圆柱化;当χ>χc时,微裂纹分节为上下或左右两个较小的微裂纹。内压加速有助于微裂纹分节。对于β>1的微裂纹,当β和χ一定时存在一临界内压值qc,当q>qc时,随着电场和内压的增大会率先在裂纹的右端发生裂纹扩展。     

Tuning of non-uniform switch toughening in ferroelectric composites by an electric field

This paper deals with a mode III interfacial crack subject to anti-plane stress and in-plane electric fields. The analysis concentrates on the tuning of fracture toughness from non-uniform ferroelectric-ferroelastic domain switch-ing by an electric field. The electric loading changes the size of the asymmetric switching zone. Employing the weight function method, we obtain the electrically-dependent switch toughening for stationary and quasi-static growing interfacial cracks, respectively. Multi-domain solutions are derived for non-poled and fully-poled ferroelectric composites. Numer-ical results are presented on the electric field tuning of the critical applied stress intensity factor. The research provides ways to optimize fracture properties of ferroelectric compos-ites by altering the electric field.     

Experimental investigation of vapor bubble growth during flow boiling in a microchannel

Experiments were conducted to analyze flow boiling characteristics of water in a single brass microchannel of 25 mm length, 201 μm width, and 266 μm depth. Different heat flux conditions were tested for each of two different mass flow rates over three different values of inlet fluid temperature. Temporal and spatial surface temperature profiles were analyzed to show the relative effect of axial heat conduction on temperature rise along the channel length and the effect of flow regime transition on local surface temperature oscillation. Vapor bubble growth rate increased with increasing wall superheat. The slower a bubble grew, the further it was carried downstream by the moving liquid. Bubble growth was suppressed for increased mass flux while the vapor bubble was less than the channel diameter. The pressure spike of an elongating vapor bubble was shown to suppress the growth of a neighboring bubble by more than 50% of its volume. An upstream progression of the Onset of Bubble Elongation (OBE) was observed that began at the channel exit and progressed upstream. The effects of conjugate heat transfer were observed when different flow regime transitions produced different rates of progression for the elongation sequence. Instability was observed at lower heat fluxes for this single channel experiment than for similar studies with multiple channels.