Vapor Reynolds Number Research Articles

Vapor flow resistance characteristics in ultra-thin flat heat pipes

Miniaturization of electronic devices drives the development of ultra-thin flat heat pipes (UTFHPs). As the thickness of the heat pipe decreases, the microchannel effect of the vapor chamber exacerbates the deterioration of the vapor flow. The vapor flow resistance, which is often neglected in the conventional theory due to its extremely small effect compared to the liquid flow resistance, becomes a critical factor limiting the heat transfer performance of UTFHPs. To provide a theoretical basis for the design and performance evaluation of UTFHPs, this paper investigated the effect of the wicking structure and working fluid on the vapor flow resistance of UTFHPs based on theoretical derivations, numerical calculations, and experiments. The results indicate that conventional analytical theory is no longer applicable when the total thickness of the heat pipe is less than 1 mm. The vapor flow resistance obtained using the conventional equation is significantly smaller than the experimental results, which is caused by several factors: raised momentum loss at the wall and gas-liquid interface due to the growth of the velocity gradient in the boundary layer; exacerbated flow instability due to the mixing between the vapor and the working fluid; enhanced fluctuating effects on the flow channel due to the presence of the wicking structure. A dimensionless flow resistance coefficient equation was proposed with the vapor Reynolds number and the channel height ratio. An experiment was conducted to verify the accuracy of the flow resistance correlation. The difference between the experimental results and the calculated values is less than 15 %.

Saturated/subcooled flow boiling heat transfer inside micro/mini-channels: A new prediction correlation and experiment evaluation

In this study, a new general heat transfer correlation was developed for predicting the saturated/subcooled flow boiling heat transfer coefficient in micro/mini-channels. The collected database included 4250 data points, which covered eleven different working fluids. These included deionized water, new electronic fluorinated solutions, and refrigerants, among others. The temperature range of the experimental operation was from 0 to 100 °C with a saturated pressure of 101 to 775 kPa. The hydraulic diameter of micro/mini-channels varied from 0.1 to 3 mm, and the liquid sub-cooling was between 0 and 80 K. The database included various operation conditions, such as mass flux, heat flux, vapor quality, and reduced pressure. The liquid and vapor Reynolds numbers were calculated based on the hydraulic diameter. Six existing flow boiling heat transfer correlations were employed to evaluate the present data points in micro/mini-channels. However, it was observed that these correlations were unable to predict the present data points accurately due to high liquid sub-cooling and heat flux. Therefore, a new prediction correlation based on the present database was developed by dividing flow boiling into three stages, including subcooled boiling, developed nucleate boiling and nucleate boiling deterioration. This new prediction model can predict more than 80% of data points within ±30% error band.

Evaluation analysis of prediction methods for pressure drop of refrigerant-lubricant two-phase flow in compressor suction lines

Evaluation analysis on the approaches for predicting two-phase pressure drop of refrigerant-lubricant oil mixture in compressor suction line is presented in this study. A total of 274 pressure drop data for refrigerant-oil mixture in suction line were adopted to develop a novel consolidated database. These data were collected from the authors’ measurement and four published literatures. The working fluids included R410A, R134a and R32 with their relevant lubricant oils and the database covered the inner diameter, local quality, liquid and vapor Reynolds numbers with the ranges of 7.1–18.5 mm, 0.927–0.994, 0.32–19.1 and 2.59–20.4 × 104, respectively. Two analytical models namely annular flow model (AFM) and double-circle model (DCM) and four representative pressure drop correlations were introduced to conduct an assessment. The comparison result indicated that the analytical models tend to over predict the experimental data of annular flow pattern, while the DCM underestimates the data under stratified-wavy flow conditions. Among the four correlations, Hu correlation provided relatively satisfactory prediction and based on its format, an improved correlation was proposed. The proposed correlation incorporated the surface tension effect and it displayed the best agreement with the database, which yielded mean relative error of 18.16% and captured 85.40% of data within ±30% deviations.

Surfactant-enhanced ammonia-water bubble absorption

An investigation into the effect of surfactants on ammonia-water bubble absorption is presented. Heat and mass transfer in a 50–200 W bubble absorber are experimentally investigated at operating conditions spanning a wide range of working and coupling fluid conditions. The effect of surfactant is assessed by adding 50–2000 PPM of 1-octanol to the ammonia-water mixture. Absorber performance is enhanced by surfactants, with the highest enhancement of 35% observed at vapor Reynolds number > 1000. The effect of surfactant concentration on bubble absorption is also discussed. A segmental model for heat and mass transfer is developed and comparison with experimental data yields good agreement with an AAD of 8.3%. Temperature and mass flow rate profiles along the height of the absorber provide insights into the absorption enhancement mechanism in the presence of surfactants. The results from this study show the potential for these passive enhancement techniques to be implemented in ammonia–water absorption systems.

Bubble characteristics in subcooled flow boiling of seawater

Bubble characteristics are important to the two-phase flow dynamics and two-phase flow simulation. Different from the known slug flow in subcooled flow boiling of de-ionized water, fined bubbly flow and foam flow are found to be dominant in that of artificial seawater at high temperatures. Through image analysis, the present study conducts bubble characteristics measurements of such bubbly/foam flow of subcooled flow boiling in artificial seawater, including bubble Sauter mean diameters, bubble equivalent diameters and distributions of bubble sizes, bubble shapes and bubble orientations. The data set is compared with that in de-ionized water. The images for analysis are acquired from the high-speed camera with 4000 frame/s. The results indicate the Sauter mean diameters of de-ionized water could be larger than that of artificial seawater by 16–30%. Good agreements with two existing correlations prove the accuracy of current measurements and provide a way to predict the bubble characteristic in such fined bubble systems. Moreover, the results reveal the two-phase foam flow structure in artificial seawater is comparatively rigid and inflexible, compared to that in the de-ionized water. Increasing liquid temperature to 85℃ may keep the Sauter mean diameter of bubbles in artificial seawater at a stable value. The only peak of the unimodal bubble size distributions of artificial seawater is at 0.15–0.36 mm, while the possible other peak of bimodal bubble size distributions of de-ionized water is at 0.78–0.99 mm or 0.57–0.78 mm. Bubbles are mostly either nearly/perfectly parallel to the heated surface or perpendicular to the heated surface. Spherical shape for bubbles smaller than 0.2–0.25 mm, rigid ellipsoid shape for intermediate bubbles with diameter greater than 0.40 mm and less than 1.0 mm −2.7 mm, and distorted large bubbles, depending strongly on the liquid temperature, are observed. The data of bubble aspect ratio appear to be quite scattering due to the complicated nature of subcooled flow boiling. However, its general variation trend with Eötvös number or the product of Eötvös number and vapor Reynolds number agrees fairly well with some well-known correlations in the literature. Moreover, the bubble shape can also be predicted well with an extrapolated boundary of the Grace diagram on the plane of gas Reynolds number versus Eötvös number.

Machine learning algorithms to predict flow boiling pressure drop in mini/micro-channels based on universal consolidated data

Two-phase flow in mini/micro-channels can meet the high heat dissipation requirements of many state-of-the-art cooling solutions. However, there is lack of accurate universal methods for predicting parameters like pressure drop in these configurations. Conventional ways of predicting pressure drop employ either Homogeneous Equilibrium Model (HEM) or semi-empirical correlations. This current study leverages the availability of data collected over the past few decades to build several machine learning models to demonstrate the efficacy and ease of building and deploying such models. A consolidated database of 2787 data points for flow boiling pressure drop in mini/micro-channels is amassed from 21 sources that includes 10 working fluid, reduced pressures of 0.0006 –0.7766, hydraulic diameters of 0.15–5.35 mm, mass velocities of 33.1 < G < 2738 kg/m 2 s, liquid-only Reynolds numbers of 14–27,658, superficial vapor Reynolds number of 75.58–199,453 and flow qualities of 0 and 1. This consolidated database is utilized to develop four machine learning based regression models viz., Artificial Neural Networks (ANN), KNN regression, Extreme Gradient Boosting (XGBoost) and Light GBM. Both input parameters and hyperparameters are optimized for the individual models. The models with dimensionless input parameters: Bd, Bo, Frf, Frfo, Frg, Frgo, Frtp, Prf, Prg, Peg, Pef, Ref, Refo, Reg, Rego, Reeq, Suf, Sug, Wef, Wefo, Weg, Wego,Wetp predict the test data for ANN model, XGBoost model, KNN model, and LightGBM model with MAEs of 9.58%, 10.38%, 13.52%, and 14.49%, respectively. The optimized machine-learning models performed better than highly reliable generalized pressure drop correlations plus showed good performance across individual datasets, flow regimes, and channel configurations.

Indirect validation of fluid-to-fluid scaling criteria for modeling steam condensation based on empirical correlations and CFD simulations

Several nuclear reactor designs have adopted passive safety systems with condensation inside horizontal tubes, such as the Passive Auxiliary Feedwater System (PAFS) of the APR+, the new generation of the Korean-Standard Pressurized Water Reactors (PWR). Performing steam condensation experiments under high-pressure conditions is needed for the design and the realistic prediction of the condensation phenomena in such systems. To avoid the costs and technical complexities associated with experimentation at high-pressure conditions, a fluid-to-fluid scaling method to model high-pressure steam condensation with a simulant fluid, refrigerant for instance, had been developed. It was determined that the liquid-to-vapor density ratio, the Froude number, and the vapor Reynolds number should be preserved in order to guarantee the flow regime and heat transfer similarity between prototypes and models. The scope of the current work is to validate the developed scaling criteria. Due to the limitation of test data of different fluids with comparable test parameters, indirect validation is proposed based on two approaches. The first approach is based on empirical correlations, in which test data from one fluid are transferred to the equivalent conditions of the other fluid, the transferred data are then compared with condensation correlations to check the validity of the scaling method. The second approach is based on CFD calculations. A CFD model, using the commercial CFD code STAR-CCM+, for the simulation of condensation in hotizontal tubes is developed. The Fluid Film model is used for modeling the condensate film thickness and development. For modeling the phase change process, source and sink terms are introduced to the continuity, momentum, and energy equations at the interface between the vapor and the condensate film. The developed CFD model is then applied in the scaling criteria validation by using it to simulate the condensation phenomena of different models in one fluid and compare its results with the corresponding experimental data in other fluid. The validation results show good agreement between prototypes and their equivalent models, and show good feasibility and reasonable accuracy of the proposed scaling criteria.

On the scaling of convective boiling heat transfer coefficient

Flow boiling has been widely used during the last century, but the key mechanisms controlling the heat transfer process still remain elusive. In the particular case of convective flow boiling inside a heated pipe, most of the existing correlations have been proposed assuming an enhancement factor to the liquid Reynolds number. In this work, we show that during convective boiling heat transfer, the vapor Reynolds number plays a dominant role which has been overlooked. By comparing experimental data in this work and from the literature, we show that the enhancement factor to the liquid Reynolds number does not appropriately correlate the heat transfer coefficient. Further, it can be shown that most of the proposed enhancement factors can be re-written in terms of the explicit contribution of the ReV. In particular, at high qualities, the influence of ReL becomes negligible.

Machine learning algorithms to predict flow condensation heat transfer coefficient in mini/micro-channel utilizing universal data

Miniature condensers utilizing mini/micro-channel has been recognized as one effective technique for designing a compact heat rejection device. However, because of the complex behaviors in phase-change systems like flow condensation, accurately predicting heat transfer coefficients can be a challenging task. In this study, a large database is utilized to develop machine-learning based models for predicting condensation heat transfer coefficients in mini/micro-channels. A consolidated database of 4,882 data points for flow condensation heat transfer in mini/micro-channels is amassed from 37 sources that includes 17 working fluid, reduced pressures of 0.039 – 0.916, hydraulic diameters of 0.424 mm – 6.52 mm, mass velocities of 50 < G < 1403 kg/m2s, liquid-only Reynolds numbers of 285 – 89,797, superficial vapor Reynolds number of 44 – 389,298, and flow qualities of 0 – 1. This consolidated database is utilized to develop four machine learning based models viz., Artificial Neural Netoworks (ANN), Random Forest, AdaBoost and Extreme Gradient Boosting (XGBoost). A parametric optimization is conducted and ANN and XGBoost showed the best predicting accuracy. The models with dimensionless input parameters: Bd, Co, Frf, Frfo, Frg, Frgo, Ga, Ka, Prf, Prg, Ref, Refo, Reg, Rego, Suf, Sug, Sufo, Sugo, Wef, Wefo, Weg, and Wego predicted the test data for ANN and XGBoost models with MAEs of 6.8% and 9.1%, respectively. The optimal machine-learning models performed better than a highly reliable generalized flow condensation correlation. Models were also able to predict excluded datasheets with reasonable accuracy when data points including the specific working fluid were part of the training dataset of the remaining datasheets. The work shows that machine learning algorithms can become a robust new predicting tool for condensation heat transfer coefficients in mini/micro channels.

Modeling of Subcooled Flow Boiling with Nanoparticles under the Influence of a Magnetic Field

Subcooled flow boiling is one of the major issues in the nuclear and power generation industries. If the fluid inlet temperature in the boiling area is less than the boiling temperature, the boiling process is called subcooled boiling. The symmetry of a physical system is a constant property of the system and is fixed by deformation. Using magnetohydrodynamic (MHD) forces and broken symmetry induced by nanosized particles, fluid and thermal systems can be more controlled. In this study, the effect of a magnetic field and nanoparticles on subcooled flow boiling in a vertical tube was investigated. For this purpose, a one-dimensional numerical code was used to simulate the flow and variations of various parameters that have been investigated and evaluated. The results showed that as the flow entered the heated area, the vapor volume fraction, Froude number, fluid cross-sectional area forces, mixture velocity, fluid velocity, bubble departure diameter, liquid and vapor Reynolds numbers, squared ratio of the Froude number to the Weber number, and fluid cross-sectional area forces coefficient increased. In the same region, the Eötvös number, root mean square (RMS) of the fluid cross-sectional area force, sound velocity, liquid superficial velocity, critical tube diameter, bubble departure frequency, and density of the active nucleation site were reduced. It was also observed that after the heated area and under the influence of the magnetic field and the nanoparticles, the values of the vapor volume fraction, Froude number, fluid cross-sectional area force, mixture velocity, fluid velocity, vapor, liquid Reynolds number, and squared ratio of the Froude number to the Weber number were decreased. Moreover, there was no significant effect on the Eötvös number, liquid superficial velocity, Taylor bubble Sauter mean diameter, bubble departure diameter, critical tube diameter, bubble departure frequency, or density of the active nucleation site.

Heat Transfer in a Large, Inclined, Flattened-Tube Steam Condenser

Experimental results for capacity and heat transfer coefficient during steam condensation in a power-plant air-cooled condenser are presented. The condenser test section is a flattened steel tube with brazed aluminum fins. The tube is 5.7 m long with inner dimensions of 216 mm × 16 mm. The cooling air is in crossflow to the steam, with velocity at the fin inlet of 2.4–3.0 m s−1. Condensation pressures range from 70–105 kPa, with the tube inclined from 0–49° downwards. Adiabatic visualization sections at the tube inlet and outlet provide identification of annular flow at the inlet and stratified flow at the outlet. Steam-side heat transfer coefficient is found to depend on wall-steam temperature difference, with minimal dependence on quality or vapor Reynolds number. As a result, steam-side heat transfer coefficient does not decrease significantly along the condenser length, as is common for smaller condenser tubes with higher mass flux. There is a slight decrease in steam-side heat transfer coefficient near the condenser outlet due to a build-up of condensate at the tube bottom. Overall condenser heat transfer coefficient is found to decrease near the condenser outlet due to an increase in the thickness of the stratified condensate layer.

Fluid-to-fluid scaling criteria development for modeling high pressure steam condensation in horizontal tubes

Experimental investigations of high pressure steam condensation heat transfer are limited due to technical requirements and construction costs of experimental facilities. Applying fluid-to-fluid scaling methods is a possible way to overcome those difficulties. Performing experiments with simulant fluid, Freon for instance, allows testing at low pressure, low temperature and with low power requirements compared with the prototype. Fluid-to-fluid scaling criteria for modeling high pressure steam condensation have been developed based on two approaches, the Buckingham Pi theorem and the non-dimensionalization of the governing equations and the interface boundary conditions. Both criteria have been validated using eight benchmark problems and based on three different condensation models. The approach based on the non-dimensionalization of the governing equations and the interface boundary conditions showed a better method for modeling the high pressure steam condensation phenomena. It showed that, in order to guarantee the similarity between the prototype and the model, the liquid-to-vapor density ratio, the Froude number and the vapor Reynolds number should be preserved. In comparison with the prototype, by applying the scaling criteria to model steam condensation in secondary system passive decay heat removal system of a pressurized water nuclear reactor, the model's pressure can be reduced by six times. Therefore, reducing the cost of conducting experimental tests.

Experimental Study of Horizontal Flow Boiling Heat Transfer of R134a at a Saturation Temperature of 18.6 °C

In spite of the extensive work in flow boiling in small-diameter tubes, the general characteristics and dominant mechanisms remain elusive. In this study, flow boiling heat transfer of R134a inside a 5 mm I.D., smooth horizontal stainless steel pipe is experimentally studied. Local heat transfer coefficients (HTCs) were measured for heat fluxes from 3.9 to 47 kW/m2 and mass fluxes from 200 to 400 kg/m2 s at a saturation temperature of 18.6 °C. The studied cases have shown different behaviors at low and high heat fluxes. At low heat fluxes, the convective contribution looks to control the HTC, while at high heat fluxes the nucleation of vapor looks to be the dominant mechanism. Reducing the heat flux, the HTC approaches asymptotically a limit equivalent to the single-phase HTC defined in terms of the sum of the superficial liquid and vapor Reynolds numbers. A new correlation for dominant convective flow boiling is proposed and evaluated against experimental data from the literature.

Experimental study on flow condensation of mixture in a hydrophobic microchannel

The condensation flow patterns of ethanol–water mixture in a wide range of ethanol mass concentration inside a hydrophobic microchannel is experimentally studied via a high speed imaging system. The effects of channel surface wettability and ethanol concentration on flow condensation are compared and discussed. The experimental results indicate that the surface hydrophobic modification and ethanol concentration play a significant role in the flow condensation of mixture in a microchannel. The droplet condensation appears almost the whole two-phase flow region when the water steam is the main component, in which the droplet flow, droplet-streak flow, droplet-annular flow, droplet-injection flow and droplet-slug/bubble flow occur sequentially in a hydrophobic microchannel. With increasing ethanol concentration, the droplet-slug/bubble flow after droplet-injection flow disappears and is replaced by the pure slug/bubble flow. When the ethanol vapor is the main component, the droplet condensation almost disappears, and the annular-streak flow, annular flow, injection flow and slug/bubble flow appear sequentially along the flow direction. Both an increase in vapor Reynolds number and a decrease in ethanol concentration cause the injection location move toward the channel outlet. In addition, the surface hydrophobic modification introduces the droplet condensation, which is beneficial for the flow condensation heat transfer.

Void Fraction of Flow Boiling with Propane in Circular Horizontal Tube

An investigation into flow boiling void fraction was conducted to observe its characteristics and to develop a new correlation of void fraction based on the separated model. The study used a natural refrigerant of R-290, flowed in a horizontal tube of 7.6 mm inner diameter under experimental conditions of 3.7 to 9.6 o C saturation temperature, 10 to 25 kW/m 2 heat flux, and 185 to 445 kg/m 2 s mass flux. The void fraction, calculated by the present experimental data, was used for comparison with 31 existing correlations, including model types as follows: homogeneous, slip ratio, Kαh correlation, drift flux, and a model based on the LockhartMartinelli correlation (Xtt). A new void fraction correlation, as a function of liquid and vapor Reynolds numbers, was proposed, based on the data. The measured pressure drop was compared with some pressure drop correlations that use the newly developed void fraction combination. The best prediction was shown by the homogeneous model.

Analysis of laminar film condensation over vertical permeable hollow short fins

Laminar falling film condensation over vertical short fin is analyzed. The fin is considered to be hollow and permeable in order to account for condensate suction towards its inner core. The present work accounts for the shear stress at the interface caused by the large velocity of the saturated vapor. The continuity, momentum, and energy equations for the film condensate are solved using an iterative and implicit finite-difference method. The condensate flow rate inside the fin is obtained using the conservation of mass principle and the Poiseuille flow equations. The one-dimensional fin equation model is used to relate the fin temperature to the condensate flow convection heat transfer coefficient. Various computational and numerical methods techniques such as advanced linearization and generations of best-fit correlations are implemented. This is to reduce significantly the number of iterations required for solution convergence as all of the aforementioned equations are coupled. It is found that the dimensionless total mass transfer rate increases slightly as vapor Reynolds number increases. It increases apparently as both suction Reynolds number and dimensionless suction length increase. For both large suction Reynolds number and large dimensionless suction length, the flow rate of the condensate in the falling film can be neglected compared to the total suction condensate flow rate. The fin thermal length increases as Reynolds number, dimensionless suction length, and Grashof number increase. This study shows that significant condensation mass flow rate enhancement ratios are obtainable (can be 18 folds) due to suction through a hollow super conductive fin.

Reflux condensation of steam inside a short vertical large diameter tube

An experimental investigation of the reflux steam condensation inside a vertical tube at the atmospheric pressure is presented. The data were obtained for duralumin tube with the internal diameter of 200mm, length of 220mm and roughness height less than 0.05mm. The film and vapor Reynolds numbers were varied within the range of 1–25 and 790–3680, respectively. The data were lower than Nusselt theory prediction. In contrast to Nusselt theory according to which the modified Nusselt number decreases with the film Reynolds number, the obtained data show inverse dependence when the film Reynolds number is less than ten. For fixed vapor Reynolds numbers there are the maximum values of the Nusselt number for definite film Reynolds numbers. The correlations are suggested for the Nusselt number in the case of a constant and variable wall temperature along the tube. The general correlation based on the presented and earlier published experimental data for the tubes with different height and diameter ratio is suggested in addition.

Effect of vapor flow on the wetting behavior of unstable evaporating menisci in heated capillary tubes

The wicking height of a heated, evaporating meniscus formed by surface-wetting liquid in a vertical capillary tube with dynamic flow has been investigated. Previous experimental results and analytical models for measuring/predicting wicking heights in capillaries are also reviewed. An analytical model is presented that accounts for both major and minor vapor pressure losses along the vertical capillary tube. It is shown that during thermo-mechanical instability, vapor/meniscus interaction can become more prevalent due to increased vapor generation/pressure near the meniscus free surface. A relatively simple procedure for estimating onset of meniscus instability is presented and, when used with the vapor Reynolds number, can estimate whether vapor pressure loss is significant. By comparing the current model with the available experimental data, it is shown that the wicking height of an unstable, evaporating meniscus of n-pentane in a vertical, glass capillary tube is better estimated by considering vapor flow pressure losses – providing a 40% improvement over previous models that neglect vapor flow. In addition to vapor flow pressure loss, the dynamic contact angle and thin film profile must also be calculated to ensure accurate prediction of wicking height. Although the proposed model shows improvement, it is prone to under-predicting the actual meniscus wicking height for stable, evaporating menisci at lower relative heat loads. The proposed model can be used for predicting wicking behavior of heated, vertically-aligned liquid columns in capillary structures – which is relevant to the design of miniature heat transfer equipment/media such as wicked heat pipes, micro-channels and sintered/porous surfaces.

Film condensation in a large diameter tube with upward steam flow

Film condensation was considered for upward steam flow at the atmospheric pressure. The experimental data were obtained inside a vertical duralumin tube with the internal diameter of 200mm and roughness height of 0.14mm. The film Reynolds numbers and vapor Reynolds numbers were varied within the range of 1–16 and 280–3460, respectively. The obtained experimental data were lower than classical Nusselt prediction. The suggested correlation for the Nusselt number agrees the most of the data within 20%.

Visualization study of flow condensation in hydrophobic microchannels

A visualization study on flow condensation in hydrophobic rectangular silicon microchannels with hydraulic diameter of approximately 150 μm is conducted. Thin Au film with thickness of 200 nm is sputtered on channel surfaces to create a hydrophobic surface with an equilibrium contact angle of approximately 96°. In addition to traditional droplet flow, droplet‐annular compound flow, droplet‐injection compound flow, and droplet‐bubble/slug compound flow are also observed. The results indicate that injection location is postponed, and injection frequency increases with increasing inlet vapor Reynolds number and condensate Weber number. An empirical correlation of the injection location and injection frequency are presented and discussed. In particular, for a larger inlet vapor Reynolds number, the injection flow is closer to the channel outlet and the condensation heat transfer is enhanced. © 2014 American Institute of Chemical Engineers AIChE J, 60: 1182–1192, 2014