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Effect of an interfacial shear stress on steam condensation in the presence of a noncondensable gas in a vertical tube
Abstract
Experimental and analytical studies were performed to examine local condensation heat transfer coefficients in the presence of a noncondensable gas inside a vertical tube. The experimental data for pure steam and steam/nitrogen mixture bypass modes were compared to study the effects of noncondensable nitrogen gas on annular film condensation phenomena. The condenser tube had a relatively small inner diameter of 13 mm. The experimental results demonstrated that the local heat transfer coefficients increased as the inlet steam flow rate increased and the inlet nitrogen mass fraction decreased. The results obtained using steam/nitrogen mixtures with a low inlet nitrogen mass fraction were similar to those obtained using pure steam. Therefore, the effects of noncondensable gas on steam condensation were weak in the small-diameter condenser tube because of interfacial shear stress. A new correlation based on dimensionless shear stress and noncondensable gas mass fraction variables was developed to evaluate the condensation heat transfer coefficient inside a vertical tube with noncondensable gas, irrespective of the condenser tube diameter. A theoretical model using a heat and mass transfer analogy and simple models using four empirical correlations were developed and compared with the experimental data obtained under various experimental conditions. The predictions of the theoretical model and the simple model based on a new correlation were in good agreement with the experimental results.
... Classical and modified HMTA condensation models were built in this work. The classical model referred to the conventional diffusion layer model 16,19,21,23 in predicting water vapor condensation, where the total HTC consists of liquid film HTC, sensible HTC, and latent HTC, in terms of the effects of NCG on condensation. The modified model was developed considering the dimerization of NO 2 in the diffusion layer on the basis of the classical model. ...
... The friction factor f r is a degradation factor, the ratio of experimental HTC to the original predicted HTC, which can be used to improve the accuracy of water−NCG condensation model prediction. 21,22 The f r for film roughness of water is as follows f Re 1.375 10 1 21.544 (100/ ) ...
Pure nitrogen dioxide (NO2) has significant economic value and is widely used in many fields, for which condensation technology plays an important role in separation and purification. However, developing cost-effective NO2 condensers remains challenging due to the lack of precise theoretical guidelines and comprehensive understanding of NO2 condensation process. In this work, NO2 condensation at various inlet surface subcoolings, mole fractions of noncondensable gas (NCG), and Re numbers was studied with a visualization experimental system. The influential rules of each parameter on heat transfer coefficients (HTCs) and the NO2 condensate state as the coexistence of droplet, streamlet and film were revealed. A substantial underestimation of experimental data by the classical heat and mass transfer analogy (HMTA) model was quantified. The large discrepancy was found to originate from the uniqueness in heat transfer, mass transfer, and condensate state caused by NO2 dimerization during condensation. A modified HMTA model was developed considering the release heat of dimerization reaction and the promotion of mass transfer by an increased NO2 concentration gradient within the diffusion layer which contribute to improvements of HTCs by ∼6 and ∼49%, respectively. The correction of liquid film roughness regarding potential heterogeneity of dimerization was proposed as a function of the key parameters, contributing to the improvement of HTCs by ∼150%. An accurate theoretical formula for HTCs prediction within an error of ±25% was finally derived, providing the key step for success in practical applications.
... It is obvious that as the air mass fraction increases, the condensation HTC of the three test tubes decreases. Compared to the steam condition, the existence of air had a theatrical deterioration effect on heat transfer, and this phenomenon was fully studied in the previous study (Kageyama et al., 1993;Lee and Kim, 2008). The steam needs to be diffused from the mainstream to the steam-liquid interface to condese. ...
In this article, a series of steam condensation experiments were performed on the outer surface of chrome-plated tube and polished tube under steam and steam–air mixed conditions to study their heat transfer characteristics and whether they could be used to optimize Passive Containment Cooling System in advanced nuclear reactors. The effects of total pressure, air mass fraction and subcooling on condensation heat transfer of the chrome-plated tube and polished tube were analyzed. Moreover, basing on the existing experiment, a smooth tube that has the same size as the polished tube and chrome-plated tube was tested under the same conditions. The experimental phenomena indicated that filmwise condensation and dropwise condensation co-exist on the tube exterior surface, and more droplets were observed on the exterior surface of the chrome-plated tube. Under the steam condition, with the fixed wall subcooling, condensation heat transfer coefficient of the polished tube and chrome-plated tube shows different change rules under different pressure: the condensation heat transfer coefficient of the polished tube increases with the increase of pressure, while the chrome-plated tube decreases with the increase of pressure. Compared with the smooth tube, the heat transfer performance can be improved by using the chrome-plated tube and polished tube. Under the steam–air condition, the existence of air deteriorates heat transfer performance seriously. The heat transfer performance of the chrome-plated tube and the polished tube are both improved compared with the smooth tube when the air mass fraction is below 60℃. When the air mass fraction is over 60℃, the heat transfer ability of these tubes are similar to the smooth tube. Besides, within the measurement parameters of our experiment, the increase in total pressure has a positive effect on steam condensation with air.
... Lee et al. [118] conducted a series of experimental and theoretical studies based on previous studies using the degradation factor method. Then they further improved the model associating the degradation factor and found that the condensation heat transfer coefficient of mixture gas acted as the same as the condensation heat transfer coefficient of pure steam when the inlet nitrogen content was 3% [119]. ...
With social development and economic enhancement, energy is facing significant worldwide demand, and fossil fuels are the prime energy sources for various energy systems over past decades. Furthermore, among fuel-consumed applications, power plants are the primary source of energy consumption. There is a lot of waste heat and steam accompanied by the latent heat produced in the exhaust flue gas. Therefore, the latent heat recovery from the flue gas plays an important role in increasing the efficiency of the system and saving water. To recover the heat and mass in power plants, three primary methods are proposed to condense the vapor based on previous studies: (1) flue gas condensation technology, (2) liquid desiccant-based dehydration (LDD) technology and (3) membrane technology. This paper mainly reviews and summaries the indirect cooling technology in flue gas condensation technology. The numerical simulation and theory of flue gas condensation are introduced. Different heat exchanger types and conducted experiments are also summarized. The performance of the indirect cooling technology is affected not only by its own configuration and design but also by the flue gas inlet temperature, velocity, water vapor mass fraction, etc. The major concerns and outlook of practical applications for further study are attributed to the heat exchanger size and cost, acid corrosion, ash accumulation in flue gas, etc.
... where f is the friction coefficient, which can be calculated using Equation (15), derived by Kim and Lee [32], or graphically read from the literature [33]: ...
This paper deals with the intensification of water vapour condensation in vertical pipes. Two configurations of vertical condensers are compared. A standard configuration and a novel configuration with cooling water at the inner pipe wall in direct contact with the condensing vapour. For this configuration, a detailed mathematical model of heat transfer is made using empirical relationships to describe the behaviour of the liquid film and vapour. The focus is placed on a detailed description of the processes at the vapour-liquid interface. The results of the mathematical model are compared with an experimental study in which the real condensing power was assessed depending on the vapour mass flow rate, the cooling water temperature at the pipe inlet, and the volumetric flow rate of the cooling water. This paper presents specific mean heat transfer coefficients useable for design calculations. The results show that the heat transfer coefficient is proportional to the liquid film temperature as well as the vapour flow rate. The condensers are compared with the same vapour flow rate and cooling water temperature. The novel configuration rejects the same amount of condensation heat as the standard configuration, but only requires a third of the amount of cooling water.
... According to the calculation based on [21], the calculated improvement of the HTC was lower than 2 % for the all measurements. This is in a good agreement with the equation introduced in [22], where the theoretical and experimental analysis of the local HTC during the condensation of water vapour in the presence of a NCG in a vertical tube condenser was conducted. This study focused on the effect of the shear stress and created a new empirical factor which incorporates the influence of the shear stress on the heat transfer. ...
This paper deals with the condensation of water vapour possessing a content of noncondensable gas in vertical tubes. The condensation of pure steam on a vertical surface is introduced by the Nusselt condensation model. However, the condensation of water vapour in a mixture with non-condensable gas differs from pure vapour condensation and is a much more complex process. The differences for the condensation of water vapour in a mixture containing a high concentration were theoretically analysed and evaluated. In order to investigate these effects, an experimental stand was built. Experiments were carried out in regards to the case of pure steam condensation and the condensation of water vapour with a non-condensable gas mixture to evaluate the influence of the variable non-condensable gas content during the process. A non-condensable gas in a mixture with steam decreases the intensity of the condensation and the condensation heat transfer coefficient. A gradual reduction of the volume and partial pressure of steam in the mixture causes a decrease in the condensation temperature of steam, and the temperature difference between steam and cooling water. The increasing non-condensable gas concentration restrains the transportation of steam towards the tube wall and this has a significant effect on the decrease in the condensation rate.
... Oh et al. [ 7 ] used an iterative method to calculate the heat and mass characteristics of vapor/NCG mixtures based on the heat and mass [ 8 ] proposed an iterative calculation procedure to calculate the local heat transfer coefficient based on the diffusion layer model and the results were in good agreement with the experimental data. Lee and Kim [ 9 ] developed a numerical model based on the degradation factor method using different em pirical correlations and proposed a new correlation of heat transfer coefficient considering the interfacial shear stress and NCG mass fraction. Qiu et al. [ 10 ] proposed a combinational numerical model using the CFD method to predict the condensation characteristics of hydrocarbon mixtures in the coilwound heat exchangers. ...
The condensation process of pure propane and propane/methane mixture on the vertical plate were experimentally and numerically researched to clarify the condensation characteristics at the first stage of natural gas liquification. In this work, a visualization experimental system was designed to study the flow pattern and heat transfer characteristics of propane vapor condensation on the vertical plate. The condensate film on the plate is wave laminar flow on the experimental conditions of liquid film Reynolds number from 59 to 321. With the increase of the liquid film Reynolds number, the flow patterns turn from straight isolated waves (about 8-10 mm length) to dense and short waves, which enhances the condensation heat transfer coefficient. At the same time, a 2-D numerical model was proposed to reveal the condensation mechanism of propane and propane/methane mixture with different wall subcooled temperature (5-40 K) and methane mole fraction (80%-95%). The numerical results agree well with the experimental data. And the results show that 80% methane reduces the liquid film thickness approximately by half comparing with the pure propane. The increase of methane mole fraction could reduce the liquid film thickness, but its contribution to the heat transfer is negligible compared with the mass diffusion resistance caused by the gas boundary layer. The heat transfer coefficient decreases beyond ninety percent compared with pure propane at the methane mole fraction of 80–95%.
... Highly turbulent pattern may be achieved by proper selection of the tube diameter and specific flow load. In this case, there is a large similarity with steam condensation in the presence of noncondensables, for which a large experimental material is available in the recent years, namely in the field of nuclear industry (Lee and Kim, 2008). Mean HTC values of about 4000e6000 W/m 2 K and 8000e11,000 W/m 2 K were reported by steam condensation with inert gas in horizontal and vertical tubes, respectively (Papini and Cammi, 2010). ...
... Highly turbulent pattern may be achieved by proper selection of the tube diameter and specific flow load. In this case, there is a large similarity with steam condensation in the presence of non-condensables, for which a large experimental material is available in the recent years, namely in the field of nuclear industry (Lee and Kim, 2008). Mean HTC values of about 4000-6000, and 8000-11,000 W/m 2 K were reported by steam condensation with inert gas in horizontal and vertical tubes, respectively (Papini and Cammi, 2010). ...
This paper deals with the conceptual design of an energy efficient and cost-effective methanol-to-olefin (MTO) process. The innovative solution consists in full recovery of the energy generated by reaction. The reactor effluent enthalpy can cover feed preheating, evaporation and superheating in a sequence of three feed-effluent-heat exchanger units. The novel method employs mechanical vapour compression for upgrading the temperature/enthalpy profile of the condensing water/hydrocarbon mixture, recovering a considerable amount of energy, otherwise lost by water quenching. Saved energy may pay back the compressor cost in about one year. The energy released in the reactor is used for running a combined heat and power cycle. The power is sufficient for driving the compressors, while the low-pressure steam may run an ammonia-absorption refrigeration plant that supplies most of the cold utilities in separations. The olefin separation and purification is handled in a compact scheme of five columns, energetically integrated with the reaction and preliminary separation sections. The ethylene/propylene splitter is designed for high recovery and flexible operation. Heat pump is implemented for propylene purification. Rigorous sizing is performed for the key units. Operation and capital costs are minimised since the design is almost neutral regarding energy requirements and employs a minimum number of units.
... The correlation includes the effects of the flow rates of the condensate and the mass fraction of NCG on the heat transfer coefficient. Then they further improved the model [95,108], associating the degradation factor with the function of the mass fraction of NCG and shear-force of the mixture, and pointed out that when the inlet nitrogen content was 3%, the condensation heat transfer coefficient of steam/nitrogen equaled the condensation heat transfer coefficient of pure steam. Meanwhile, the data indicated that the steam in a small tube had a larger interfacial shear force, and that the condensation heat transfer coefficient decreased with the increase of tube diameter. ...
In 1929, Donald Othmer discovered that a small amount of non-condensable gases (NCG) in pure vapor had a great effect on condensation heat transfer coefficient (HTC), reducing the efficiency of heat transfer equipment. Since then, a large amount of research has been performed. This paper reviews experimental, mechanism and model research progresses in condensation in the presence of NCG. Particular attention is given to research on physical models of heat transfer for filmwise condensation (FWC) with NCG, with a brief review of dropwise condensation (DWC). The models for FWC heat transfer in the presence of NCG can be divided into two categories: semi-theoretical models and theoretical models. The semi-theoretical models are based on hydraulics and thermodynamics, use some specific parameters of the correlation which determined by experiments, and are suitable for engineering design. The theoretical models are based on mass, momentum, and energy conservation equations, and divided into boundary layer models and diffusion layer models. Through research of experiments and models people found that, condensate film thickness, surface waves, interfacial shear strength and suction effect play an important role in the FWC heat transfer in presence of NCG.
... But under the long-term stable condition of the PCCS, the temperature of the cooling water will get close to 100 • C with flow fluctuations which is had to forecast by the result from forced circulation with high subcooling. So the study of condensation of steam in the presence of noncondensable gases under low wall subcooling degree is necessary to be investigated (Su et al., 2013;Ganguli et al., 2008;Rosa et al., 2009;A1-Shammaria et al., 2004;Lee and Kim, 2008;Chen et al., 1998;Seungmin et al., 2005;Kang and Park, 2001;Tagami, 1965;Kageyama et al., 1993). Since Nusselt proposed the pure steam condensate model in 1916 (Nusselt, 1916), numbers experimental investigations have been conducted to study the steam condensation heat transfer with noncondensable gases. ...
... The maximum relative uncertainty of 36% was obtained with the lowest value of DT LM . The large uncertainty is clearly due to the small temperature difference between the steam gas mixture and the cooling water as shown by Uhia et al. [25], Lee and Kim [26] and Lee et al. [27]. Table 1 shows the uncertainties for different parameters involved in the measurements. ...
... The thickness of the condensate film depends on the surface geometry, hydrodynamic boundary condition at the solid surface and the condition of vapour i.e., presence of noncondensable species in the bulk mixture at free stream. Starting from the pioneering work of Nusselt [1], a large number of investigations [2][3][4][5][6][7][8][9][10][11][12][13][14][15][16][17][18][19] have been reported on film condensation heat transfer over non-circular geometries with and without non-condensable gases in the condensing vapours. All these studies typically focus on the role of surface geometry in enhancing the rate of heat transfer during condensation vis-à-vis the reduction in heat transfer and condensation rates due to the existence of non-condensable gases in the bulk mixture. ...
A theoretical study has been executed to investigate the implications of interfacial slip in presence of non-condensable species in the bulk mixture of vapour on heat transfer characteristics in film condensation over horizontal tubes with varying radius of curvature. A polar surface comprising a segment of an equiangular spiral in the form of Rp = aemθ (a and m being parametric constants), generated symmetrically on a vertical chord, has been considered. We reveal that there is a substantial enhancement in the rate of condensation heat transfer due to an effective interfacial slip at the solid–liquid interface. The enhancement in condensation heat transfer due to solid–liquid interfacial slip is more pronounced in the case of vapour with non-condensable species, but less pronounced for higher values of m (a surface profile parameter).
... We used two models in our calculations. The first model is called a diffusion one [20][21][22]. Central to this model is the approach proposed in [23], according to which the mass flow is limited by the diffusion resistance of the layer with increased concentration of air near the phase bound ary. ...
Specific features pertinent to the flow of steam–gas mixture are discussed as applied to the inclined tubes of air-cooled condensers used in steam turbine units, and the condensate film annular flow and “streamlet” models are analyzed. The calculated results are compared with the data obtained by other researchers. It is shown that with relatively small flow rates of steam–gas mixture typical for air-cooled condensers, the restoration of pressure along the channel may exceed the losses connected with hydraulic resistance. Data on the influence of cooling air temperature on the condensation process are also presented.
... The results showed that the condensation heat transfer coefficient decreased along the tube but increases at high gas mixture Reynolds number. Lee and Kim [18] performed experimental and analytical studies to investigate the effect of non-condensable gas (nitrogen), ranging from 0 to 40%, to water vapor condensation in a small tube diameter of 13 mm and 2.8 m long. The effects included in their model were the same as in Ref. [15]. ...
Experimental and theoretical studies were conducted to study the water vapor condensation in the presence of air, simulated for flue gas from natural gas fired boiler system. A vertical annulus tube of 2 m length was used for the study. The inlet water vapor mass fraction ranged from 3 to 12% and the gas mixture Reynolds number was between 4600 and 14,000. A theoretical model was developed from heat and mass analogy to study the heat and mass transfer characteristics when water vapor condensed in the presence of air at low inlet water vapor mass fraction. The predicted results compared to the experimental observations showed that the gas mixture at high Reynolds number could cause waviness at the interface, and the suction effect from vapor condensation can enhance heat and mass transfer rate even at low rate of condensation. The sensible and condensation heat transfer coefficient both influence the overall heat transfer coefficient at low (inlet) water vapor mass fraction, but the condensation heat transfer coefficient is more influenced when Reynolds number and inlet water vapor mass fraction are increased. A correlation of condensation heat transfer coefficient has been proposed from the analogy model.
... What's more, when a LOCA happens, the steam that injected into the containment will be mixed with air and other non-condensable gases (hydrogen, air, etc.) which have a bad effect on the steam condensation heat transfer. So the study of condensation of steam in the presence of non-condensable gases is necessary to be investigated (Ganguli et al., 2008;A1-Shammaria et al., 2004;Lee and Kim, 2008;Chen et al., 1998;Seungmin et al., 2005;Kang and Park, 2001;Kageyama et al., 1993). ...
Condensation in the presence of noncondensable gas is of interest to the passive containment cooling system in the nuclear power plant. Most researches focus on the heat transfer characteristics of condensation in an individual vertical tube or a parallel tube bundle. However, the influence of the condenser structure on condensation heat transfer is rarely considered in previous works. Thus, a numerical simulation was conducted for condensation in the presence of NCG in a condenser composed of two headers and 158 condenser tubes. A steady three-dimensional model was developed to predict the NCG distribution and the heat transfer performance of the condenser when the PCCS loop was stably running. The fluid inside the condenser was regarded as a single-phase mixture composed of steam and air, and the liquid film was evaluated by the Eulerian Wall Film model. The results indicated that the air tends to accumulate in the middle of the condenser tubes rather than the headers. The fluid flow in most of the tubes was blocked, so the heat transfer coefficients of pure steam and the steam-air mixture were lower than expected. An orifice plate was further designed to optimize the pressure and flow field in the PCCS condenser. The effect of the optimization was quantitatively evaluated. The results showed that the heat transfer performance of the condenser was improved by up to 87.8% with the orifice plate.
Various methods have been proposed to reduce the performance degradation effects of non-condensable gases (NCG) on condensation heat transfer. Among the papers that can reduce the negative effects of NCG, the paper about comparing passive and active methods is insufficient. In this study, to overcome the performance degradation effects of NCG, super-hydrophobic surface modification (passive method) and the steam jet injection method (active method) were applied to horizontal aluminum tubes, which were evaluated experimentally. The test variables were the initial pressure and total pressure for adjusting the NCG mass fraction. The overall and condensation heat transfer coefficients were derived according to the NCG mass faction. In surface modification experiments, super-hydrophobic tubes exhibited better overall heat transfer coefficients up to three times that of filmwise condensation in bare tubes. By reducing the NCG mass fraction from a high level to a low level, the condensation phenomena of the super-hydrophobic tubes transformed in the order of dropwise condensation, flooded condensation, and attached filmwise condensation, resulting in the degradation of heat flux efficiency. In particular, attached filmwise condensation resulted in worse condensation performance than normal filmwise condensation, so no performance improvements can be expected based on surface modification under these circumstances. In contrast, the steam jet injection method provided a noteworthy heat transfer enhancement ratio of 1.18 to 1.77 times for a broad range of NCG mass fractions.
In this study, the use of the steam jet method to destroy the mixed boundary layer of steam and non-condensable gas (NCG) was researched in order to enhance the condensation heat transfer performance. An experimental facility was designed and manufactured in which steam was injected vertically into a single aluminum tube. Both the initial chamber pressure related to the amount of NCG and the bulk chamber pressure after the normal steam injection were tested. The time and enhancement parameters were obtained, including the steam jet continuance time, the maximum heat transfer enhancement ratio, the average heat transfer enhancement ratio and the average overall heat transfer coefficient. The results of the experiment indicate that after the steam jet injection, the maximum heat transfer enhancement ratio increased by at least 137%, and the average heat transfer enhancement ratio increased by at least 118%. In addition, as the NCG mass fraction increased, the values of the continuance time, maximum heat transfer enhancement ratio, average heat transfer enhancement ratio, and average overall heat transfer coefficient improved. Thus, it was confirmed that the steam jet injection method, under the conditions of an accident in which a large amount of NCG flows into the condenser, can effectively improve the condensation performance. Finally, the idea of a bundle-type condenser which is applied by the steam jet method was proposed.
Water formation test loop was constructed with a scale ratio of 1:1 to investigate the condensation and analogous U-shaped tube water seal in front of pressurizer safety valve. The water seal features were investigated under different pressure and various concentrations of non-condensable gases. The test data reveals that water seal can completely formed even in the presence of non-condensable gases in high content. Water formation time reduced when increased system pressure and refilling of the pipe is much more rapid than the initial one due to a lower content of non-condensable gases remaining in the steam phase. A simple criterion to determine the water seal starting point has been put forward in this paper. The strong natural convection in the water seal keeps the temperature difference lower than 20K.
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An experimental investigation on condensation heat transfer characteristics of steam in the presence of multicomponent noncondensable gases in a horizontal tube is conducted in the present research. The experimental runs are carried out at a volume ratio of helium and noncondensable gases varying from 0% to 90%, the mixture gases pressure between 0.13 and 0.2 MPa, over the mixture gases velocity changing from 8 to 34 m/s, covering all the major flow patterns inside a pipe. The effects of inner wall subcooling, mixture gases velocity and pressure on local heat transfer coefficient have been analyzed for annular, wavy and stratified flow. The change of the condensation heat transfer capacity for different volume ratios of helium in the noncondensable gases have been studied at the same time. The results indicate that the local heat transfer coefficient increases with the increasing wall subcooling for annular and wavy flow but decreases for stratified flow. With the flow regime transforming from annular to stratified flow, the active influence of the gases velocity is gradually weakened and the local heat transfer coefficient even starts to decrease when it reaches stratified flow. For all flow patterns, the increases of helium volume fraction and mixture gases pressure always enhance the condensation heat transfer. Based on the experimental analysis, an empirical correlation for predicting the local heat transfer coefficient is proposed. The comparison of the calculated results and the experimental data shows that the present correlation can give satisfactory engineering accuracy.
Steam condensation in the presence of nitrogen is experimentally performed in a horizontal rectangular channel with cross sectional dimension of 5×6 mm. Steam mass flux varies from 203.7 to 431.3 kg·m-2·s-1, while the nitrogen mass fraction from is 0 to 15 %. Coolant water flows countercurrent in a rectangular channel as well, which is the same size with the steam side. The steam channel is on top of the coolant channel, and the released heat from the steam is transferred to the coolant water by heat conduction only through the connecting part of each channel, the thickness of which is 3 mm. The coolant mass flow rate is from 500 to 1100 kg·h-1, while the corresponding coolant side Reynolds number is from 2.2×104 to 5.1×104 and the coolant side heat transfer coefficient is from 20.2 to 40.1 kW·m-2·K-1. The results show that higher coolant Reynolds number results in significant promotion of the overall heat transfer coefficient, while the condensation heat transfer coefficient is reduced. In addition, larger steam mass flux leads to greater overall heat transfer coefficient and condensation heat transfer coefficient. However, the influence of nitrogen on condensation is not significant, especially for condensation with higher steam mass flux.
Reflux condensation heat transfer of steam–air flow has been studied experimentally and theoretically. Effect reflux and co-current flow configurations and flow pressure on condensation heat transfer are investigated. Particular attention was paid to phenomena occurring at the interface and produced by the high steam velocity when the system runs at very low pressure. A total of 200 data points were used to analyze the average condensation heat transfer. An analytical model based on diffusion layer theory, momentum balance and combination of heat and mass transfer, has been developed. A good accuracy was obtained between model predictions and measurements at low pressure. The heat transfer coefficient for the reflux condensation is lower than the co-current flows, because of a thicker condensate film. Comparison between experimental results and predictions shows that the wavy film and non-condensable gas effects are very pronounced for condensation at low pressure. A new equation of the Fwave factor is proposed.
The effect of a non-condensable gas on steam condensation has been studied. From experimental and theoretical studies to date, clear evidence of significant heat transfer deterioration by the non-condensable gas can be seen. The deterioration varies with the concentration of the non-condensable gas, geometric parameters, system pressure, etc. However, these data and correlations may be unreliable due to the high concentration of CO2 in the vapor mixture and lack of verification through experiments. In this paper, a systematic investigation has been conducted for film-wise condensation using a vapor mixture of steam and a high concentration of CO2. Some data were obtained on a vertical plate, with the average vapor velocity of 1.2 m/s, CO2 mass fraction of 20%—94% and a pressure of 1 atm. The effects of CO2 concentration and surface sub-cooling on heat transfer characteristics have been investigated. Moreover, the relevant parameters such as gas/liquid film resistance were included in the description of the condensation phenomenon. The developed correlation for steam and a high concentration of CO2, based on experimental results, has a standard deviation of less than ±20%.
To have a better understanding on forced convection condensation with noncondensable gas inside a horizontal tube, an experimental research and theoretical investigation were conducted under annular and wavy flow. The effects of noncondensable gas mass concentration, mixture gases velocity, pressure and inner wall sub-cooling on the condensation heat transfer have been analyzed. The results indicate that the local heat transfer coefficient increases with the increase of the mixture inlet velocity and pressure while decreases with the increase of the noncondensable mass fraction and wall sub-cooling. Based on the above conclusions, an empirical correlation for predicting the local heat transfer coefficient was proposed which showed a good agreement with the experimental data with an error of ±20%. Furthermore, a theoretical model using the heat and mass transfer (HMT) analogy method was developed including the suction effect. The heat transfer capacity for the film, gaseous boundary and convective heat transfer of the bulk gases were compared along the tube. Besides, the axial distribution of the bulk gases and liquid–gas interface temperatures inside the tube were analyzed. The present theoretical model fits better with the experimental data compared with Lee's and Caruso's models for stratified flow.
The paper presents a feedwater preheater for a zero-emission steam cycle used for electricity generation from fossil fuels. The objective was to study an effectiveness of the preheater to separate a steam-gas mixture by condensation and utilize the latent heat for regenerative heating of the feedwater. Set of experimental regimes was carried out for three different modifications of the preheater. Experiments were conducted in order to investigate an impact of the presence of a non-condensable gas in the mixture on the intensity of heat transfer in the preheater..
The condensation heat transfer occurring in containment atmospheres during the loss of coolant accident (LOCA), is one of the most important areas in research related to the safety of nuclear reactors. In the advanced Generation III and III+ nuclear reactors, decay heat is removed by passive containment cooling system (PCCS). For the system, the study of condensation of steam in the presence of non-condensable gases is prior to be investigated because when LOCA happens steam flashes into the containment which contains air and other non-condensable gases (helium, argon, etc.). An experimental investigation has been conducted to evaluate the steam heat removal capacity over a vertical tube external surface with air. Condensation heat transfer coefficients have been obtained under the total pressure ranging from 0.4MPa to 0.6MPa, the wall subcooling ranging from13 to 257deg;C and air mass fraction ranging from 0.07 to 0.52. The influence of the wall subcooling on the steam condensation heat transfer with the fixed pressure and air mass fraction have been researched. The effect of wall subcooling on condensation heat transfer coefficient with air is negative. The developed empirical correlation for the heat transfer coefficient covered all data points within 15%.
A method was presented to predict phase change behavior and liquid film evolution on specimens by combining the Eulerian wall film (EWF) model of two-phase flow with the self-defined formula of dew amount. Firstly, a self-built environmental test chamber was used to carry out condensation physical tests, and simulated tests were respectively performed based on the EWF model and the single-phase flow model. It is found that the EWF model is more accurate than the single-phase flow model due to necessary consideration of the phase change process. Then, a self-defined formula was established to calculate the dew amount and it was verified by the physical tests. Finally, under the premise that simulated and tested temperatures, relatively humidity curves and dew amounts show good agreement, the changing process of liquid films on specimen surfaces was predicted, and the simulation prediction of liquid film shape on specimen surfaces is in consistent with in-situ video imaging morphology during the physical tests.
Based on the volume of fluid (VOF) method, a steady three-dimensional numerical simulation of laminar film condensation of water vapor in a horizontal minitube, with and without non-condensable gas, has been conducted. A user-defined function defining the phase change is interpreted and the interface temperature is correspondingly assumed to be the saturation temperature. An annular flow pattern is to be expected according to a generally accepted flow regime map. The heat-transfer coefficient increases with higher saturation temperature and a smaller temperature difference between the saturation and wall temperatures, but varies little with different mass flux and degree of superheat. The existence of a non-condensable gas will lead to the generation of a gas layer between vapor and liquid, resulting in a lower mass-transfer rate near the interface and higher vapor quality at the outlet. In consequence, the heat-transfer coefficient of condensation with a non-condensable gas drops sharply compared with that of pure vapor condensation. Meanwhile, the non-condensable gas with a smaller thermal conductivity would cause a stronger negative effect on heat flux as a result of a higher thermal resistance of heat conduction in the non-condensable gas layer.
An experimental and theoretical investigation on condensation from steam/air mixture was carried out in a horizontal tube with a large range of noncondensable gas fractions and inlet gas Reynolds number. A theoretical model is developed based on Liao’s modified diffusion layer theory including the roughness and suction effect. The model predictions were compared with experiment and literature data. The effect of noncondensable gas on overall heat transfer performance was studied. Moreover, the local parameters such as temperatures, gas concentrations and heat transfer coefficients were analyzed along the tube. The predicted values agree well with the experiment and literature data, showing the validation of theoretical model. The average heat transfer coefficient decreases with the increase of inlet noncondensable gas fraction and the decrease of inlet mass flux. The heat transfer rate increases with the increase of inlet pressure, while the heat transfer coefficient shows an opposite trend. The variation tendency of bulk temperature is consistent with that of bulk noncondensable gas fraction. For stratified flow, the heat transfer coefficients at the top part are higher than that at the bottom. But the difference is gradually closing especially at higher inlet noncondensable gas fractions due to the different distributions of thermal resistances. The heat flux decreases along the tube especially near the outlet. Meanwhile, increasing the inlet mass flux could significantly enhance the heat flux.
Based on the double boundary layer theory, a generalized mathematical model was developed to study the distributions of gas film, liquid film, and heat transfer coefficient along the tube surface with different geometries and curvatures for film condensation in the presence of a noncondensable gas. The results show that: (i) for tubes with the same geometry, gas film thickness, and liquid film thickness near the top of the tube decrease with the increasing of curvature and the heat transfer rate increases with it. (ii) For tubes with different geometries, one need to take into account all factors to compare their overall heat transfer rate including gas film thickness, liquid film thickness and the separating area. Besides, the mechanism of the drainage and separation of gas film and liquid film was analyzed in detail. One can make a conclusion that for free convection, gas film never separate since parameter A is always positive, whereas liquid film can separate if parameter B becomes negative. The separating angle of liquid film decreases with the increasing of curvature. Journal of Thermal Science and Engineering.
Noncondensable gases deteriorate heat transfer in the condensation process. It is therefore necessary to study vapor-gas condensation heat transfer process and analyze main factors influencing the process. Based on the double-film theory and the Prandtl boundary layer theory, this investigation developed a mathematical model of gas-liquid film thicknesses and local heat transfer coefficient for studying laminar film condensation in the presence of noncondensable gas over a horizontal tube. Induced velocity in the gas film, gas-liquid interfacial shear stress, and pressure gradient were considered in the study. Importantly, gas-liquid film separations were analyzed in depth in this paper. It obtained the distributions of gas-liquid film thicknesses, local heat transfer coefficient, condensate mass flux, and gas-liquid interfacial temperature along the tube surface, and analyzed the influences of bulk velocity, total pressure, bulk mass concentration of noncondensable gas and wall temperature on them, providing a theoretical guidance for understanding and enhancing vapor-gas condensation heat transfer. Gas film thickness and gas-liquid film separations have certain effects on vapor-gas condensation heat transfer. The average dimensionless heat transfer coefficients are in agreement with the data from related literatures.
This paper presents a study of flushing non-condensable (NC) gases out of a chamber by a saturated steam flow. During the flushing and mixing process, significant heat transfer occurs among the NC gases, steam and the chamber wall, with a coupled steam condensation. The flushing effectiveness hence is strongly dependent upon the mixing, condensation characteristics, the steam feeding rate as well as the thermal capacity of wall. The objective of this study is to explore modeling approaches on such a process which would be applied to assist the optimization of the process design and operation. An experimental system has been developed to provide a set of data for model validations. A simple mechanistic model based has also been developed to show the “equilibrium-based” flushing characteristics. However, to account for finite rate of heat and mass transfer and non-uniform mixing, a more complicated full-field computational fluid dynamics modeling and simulation must be involved. The typical boundary conditions in most commercial CFD codes (such as FLUENT) cannot be directly applied to the flushing processes due to the coupled surface condensation. Hence, in this paper, we have also proposed the condensation-based boundary conditions for the CFD simulations. Full-field CFD simulations with those boundary conditions are being investigated.
The passive containment cooling system (PCCS) is widely used in the advanced Generation III and III+ nuclear reactor systems to maintain the integrity of the containment under long term post utmost accidents like the loss of coolant accident (LOCA) and the main steam line break accident (MSLB). In the steam condensation process, the presence of large amounts of noncondensable gases (mainly air) will lead to the serious deterioration of heat transfer. Further research on steam condensation in the presence of air must be conducted. Condensation process of steam in the presence of air has been successfully modeled by applying a user defined function (UDF) added to the commercial computational fluid dynamics (CFD) package. Calculated profiles of temperature, air concentration, velocity components and condensation heat transfer coefficient (HTC) are compared to experimental results. The simulation results indicate that there is a good agreement between the experimental results and the model predictions. It also shows that both the latent and the sensible HTCs decreased with the increase of the air mass fraction, and the latent heat transfer is the dominant factor of the total condensation heat transfer when the air mass fraction less than 50%. Local latent HTC shows an upward tendency along the height direction of the heat transfer tube from bottom to top, with sensible HTC taking on an opposite trend.
Pressurized Entrained Flow High Temperature Black Liquor Gasification (PEHT-BLG) is a new technology not yet commercialized. The technology has the potential to improve the efficiency of energy and chemical recovery in the pulping industry. It also enables new processes, i.e. production of renewable motor-fuels from the syngas. The technology is not yet fully developed and interest in computer models for scale-up and optimization of the process in combination with experiments is favourable in the development process. A demonstration plant has been in operation since late 2005, in Pitea, Sweden. At Lulea University of Technology (LTU), a CFD model of a vertical tube in the counter current condenser has been developed using the commercial code FLUENT 6. The geometry is consistent with the demonstration plant and input data of the design has been used as boundary conditions for the model. The objective is to create a CFD model that can be used as a designing tool for the technology developer in future scale-up and for commercialized units. The model predicts the condensation process very well and shows that the major part of the condensation takes place in the first quarter of the tube under the given conditions. The heat transfer through the tube wall has been modeled based on results from the literature. The results show the importance of accurate heat transfer coefficients. Compared to designing data, the heat transfer through the wall and the condensate rate show good agreement. However, these results need to be validated against experimental data for different conditions.
A theoretical model using a heat and mass transfer analogy and a simple model using Lee and Kim's [Lee, K.-Y., Kim, M.H., 2008a. Experimental and empirical study of steam condensation heat transfer with a noncondensable gas in a small-diameter vertical tube. Nucl. Eng. Des. 238, 207–216] correlation were developed to investigate steam condensation in the presence of a noncondensable gas inside a vertical tube submerged in pool water. Rohsenow's correlation was used to consider the secondary pool-boiling heat transfer. Both models were assessed with the experimental data of Oh and Revankar [Oh, S., Revankar, S.T., 2005a. Investigation of the noncondensable effect and the operational modes of the passive condenser system. Nucl. Technol. 152, 71–86; Oh, S., Revankar, S.T., 2005b. Effect of noncondensable gas in a vertical tube condenser. Nucl. Eng. Des. 235, 1699–1712; Oh, S., Revankar, S.T., 2005c. Complete condensation in a vertical tube passive condenser. Int. Commun. Heat Mass Trans. 32, 593–602; Oh, S., Revankar, S.T., 2005d. Analysis of the complete condensation in a vertical tube passive condenser. Int. Commun. Heat Mass Trans. 32, 716–727; Oh, S., Revankar, S.T., 2006. Experimental and theoretical investigation of film condensation with noncondensable gas. Int. J. Heat Mass Trans. 49, 2523–2534; Oh, S., Gao, H., Revankar, S.T., 2007. Investigation of a passive condenser system of an advanced boiling water reactor. Nucl. Technol. 158, 208–218] for low pressure and Kim [Kim, S.J., 2000. Turbulent film condensation of high pressure steam in a vertical tube of passive secondary condensation system. Ph.D. dissertation, Korea Advanced Institute of Science and Technology] for high pressure, which were obtained from in-tube steam condensation with air in the pool water. These models predicted the data of Oh and Revankar well, but they slightly underestimated the data of Kim. The design of the Passive Residual Heat Removal System (PRHRS) condensation heat exchanger was evaluated with the theoretical model at real operating conditions (e.g., secondary pool-boiling, high system pressure). The PRHRS condensation heat exchanger designed was estimated to remove sufficiently the remaining heat in a reactor during a major accident.
A comprehensive survey of the literature in the area of numerical heat transfer (NHT) published between 2000 and 2009 was conducted. An objective of this survey is in an attempt to narrow the gap between the education and research communities. In the system of a channel flow, there are generally inlets and outlets. The flow is confined by the surrounding walls, and the fluid flows are predominantly in one direction. The pressure drop is significant in comparison with the momentum changes. The streamwise heat conduction is much less than the transverse counterpart. When combustion takes place in the system, source or sink terms will appear in the energy equation or species equations. In external flows, the fluid generally moves over a solid object (or objects), and is unbounded away from the object. Considerable effort has been devoted to inverse problems. Much attention has been paid to numerical methods handling the moving interface between two phases.
Degradation of condensation HTC (Heat Transfer Coefficient) under an air presence in a vertical tube was explored both experimentally and analytically, with the aim of developing evaluation methods for the design of passive containment cooling systems in the next generation reactors. Measurements were done using a stainless steel tube of 49.5mm I. D. and 2.0m length, enclosed by a cooling jacket. Flow rates of steam, air and cooling water, and the system pressure were varied as the experimental parameters. First, condensation HTC was correlated to a function of mixture Reynolds number and air partial pressure ratio, in which thermal resistance of the condensate film was excluded. Secondly, an analogy between heat and mass transfer was applied. The calculated values agreed well with the measured values of condensation HTCs in turbulent flow, while an obvious underestimation was observed for the flow in which mixture Reynolds number was lower than 2, 300. Finally, ratios of calculated to experimental HTCs, which include thermal resistances of the condensate film, averaged 1.01 for turbulent steam flow.
A condensation experiment in the presence of non-condensable gas in a vertical tube of the passive containment cooling system of the CP-1300 is performed. The experimental results show that the heat transfer coefficients (HTCs) increase as the inlet air mass fraction decreases and the inlet saturated steam temperature decreases. However, the dependence of the inlet mixture Reynolds number on the HTC is small for the operating range. An empirical correlation is developed, and its predictions are compared with experimental data to show good agreement with the standard deviation of 22.3%. The experimental HTCs are also compared with the predictions from the default and the alternative models used in RELAP5/MOD3.2. The experimental apparatus is modeled with two wall-film condensation models in RELAP5/MOD3.2 and the present model, and simulations are performed for several subtests to be compared with the experimental results. Overall, the simulation results show that the default model of RELAP5/MOD3.2 underpredicts the HTCs, and the alternative model over-predicts them, while the present model predicts them well throughout the condensing tube.
Degradation of condensation HTC (Heat Transfer Coefficient) under an air presence in a vertical tube was explored both experimentally and analytically, with the aim of developing evaluation methods for the design of passive containment cooling systems in the next generation reactors. Measurements were done using a stainless steel tube of 49.5 mm I. D. and 2.0 m length, enclosed by a cooling jacket. Flow rates of steam, air and cooling water, and the system pressure were varied as the experimental parameters. First, condensation HTC was correlated to a function of mixture Reynolds number and air partial pressure ratio, in which thermal resistance of the condensate film was excluded. Secondly, an analogy between heat and mass transfer was applied. The calculated values agreed well with the measured values of condensation HTCs in turbulent flow, while an obvious underestimation was observed for the flow in which mixture Reynolds number was lower than 2.300. Finally, ratios of calculated to experimental HTCs. which include thermal resistances of the condensate film, averaged 1.01 for turbulent steam flow.
This research investigates experimentally local heat transfer from condensation in the presence of noncondensable gases inside a vertical tube. Using a novel experimental apparatus for accurately measuring local heat fluxes, an extensive data base has been obtained for the condensation of pure steam, steam–air mixtures and steam–helium mixtures. Three different correlations, implementing the degradation factor method, diffusion layer theory, and mass transfer conductance model, are presented. The correlation using the simple degradation factor method has been shown to give satisfactory engineering accuracy. However, this method is based on very simplified arguments that do not fully represent the complex physical phenomena involved. Based on diffusion layer theory and a mass transfer conductance model, more physically based correlations were developed for the heat transfer of vapor-gas side. The total heat transfer coefficient predicted by the correlations from these two mechanistic models are in close agreement with experimental values.
An experimental investigation has been conducted to determine the local condensation heat transfer coefficient (HTC) of steam in the presence of air or helium flowing downward inside a 46-mm-i.d. vertical tube. The gas-steam mixture flow rate was measured with a calibrated vortex flowmeter before it entered the 2.54-m-long test condenser. Cooling water flow rate in an annulus around the tube was measure with a calibrated rotameter. Temperatures of the cooling water, the gas-steam mixture, and the tube inside and outside surfaces were measured at 0.3-m intervals in the test condenser. Inlet and exit pressures and temperatures of the gas-steam mixture and of the cooling water were also measured. The local heat flux was obtained from the slope of the coolant axial temperature profile and the coolant mass flow rate. It was found that for the same mass fraction of the noncondensable gas, compared with air, helium has a more inhibiting effect on the heat transfer, but for the same molar ratio, air was found to be more inhibiting. An application where there is important is the proposed advanced passive boiling water reactor design (Simplified Boiling Water Reactor), which utilizes the isolation condenser as a main component of the passive containment cooling system (PCCS).
A theoretical model has been developed to study the local heat transfer coefficient of a condensing vapour in the presence of a noncondensable gas, where the gas/vapour mixture is flowing downward inside a vertical tube. The two-phase heat transfer is analysed using an annular flow pattern with a liquid film at the tube wall and a turbulent gas/vapour core. The gas/vapour core is modeled using the analogy between heat and mass transfer. The model incorporates Nusselt equation with McAdams modifier and Blangetti model for calculating the film heat transfer coefficient, Moody and Wallis correlations to account for film waviness effect on gas/vapour boundary layer. The suction effect due to condensation, developing flow and property variation of the gas phase is also considered. A comparative study of heat transfer coefficient and vapour mass flow rate has been made with various models to account for condensate film resistance and condensate film roughness. Results show that for very high Reynolds number, the condensation heat transfer coefficient is higher than the film heat transfer coefficient.
This paper develops a theory to reveal the effect of small amounts of non-condensable gas on laminar filmwise condensation of a vapour-gas mixture flowing turbulently in a vertical tube. The reductions in heat transfer due to the non-condensable gas are found to be more significant at low pressures and at low Reynolds numbers of the mixture. Comparisons of the theory with some experimental data reported in the literature are in good agreement.RésuméOn développe une théorie pour révéler l'effet de petites quantités de gaz incondensables sur la condensation en film laminaire d'un mélange vapeur-gaz qui s'écoule de façon turbulente dans un tube vertical. La réduction du transfert thermique par le gaz incondensable est plus marquée aux faibles pressions et aux faibles nombres de Reynolds. Des comparaisons de la théorie avec quelques données expérimentales dans la littérature sont en bon accord.ZusammenfassungIn diesem Artikel wird eine Theorie entwickelt, die den Einfluß kleiner Mengen nicht kondensierbarer Gase auf die laminare Filmkondensation von turbulent strömenden Dampf-Gas-Gemischen in einem senkrechten Rohr aufzeigt. Eine deutliche Verringerung des Wärmetransports durch das nicht kondensierbare Gas zeigt sich bei kleinen Drücken und niedrigen Reynolds-Zahlen des Gemisches. Vergleiche zwischen dieser Theorie und einigen experimentellen Werten aus der Literatur zeigen gute Übereinstimmung.РефератПpeдлoжeнa тeopия, oбьяcняющaя влияниe нeбoльщoгo кoличecтвa нeкoндeнcиpyeмoгo гaзa нa лaминapнyю плeнoчнyю кoндeнcaцию пapoгaзoвoй cмecи пpи тypбyлeнтнoм тeчeни в вepтикaльнoй тpyбe. Haйдeнo, чтo в зтoм cлyчae интeнcивнocть тeплoпepeнoca зиaчитeльиo cнижaeтcя пpи низкич дaвлeнияч и чиcлaч peйнoльдca для cмecи. Cpaвнeниe тeopии c нeкoтopыми пpeдcтaвлeнньыми в литepaтype зкcпepимeнтaльными дaнными дaeт чopoщee cooтвeтcтвиe.
This paper proposes a set of condensation models for forced and natural convection in the presence of a noncondensable gas. A simple model is derived by using the analogy between mass, momentum and energy transfer. The effects of a wavy interface are implemented in this model by using correlations for a rough wall surface. A two—dimensional condensation model using a κ-ϵ model for the turbulent vapor-air flow was also developed to investigate the effect of two—dimensional flow and to provide a sound theoretical basis for the simple model. Each model is compared with the available ‘eparate’ effects' experimental data. The forced convection model is then compared to the Carolinas Virginia Tube Reactor (CVTR) integral test by using the vapor-air velocity predicted by a separate two—dimensional fluid dynamics model. The effect of countercurrent flow is also considered in this comparison. The natural convection model is also compared to the steady-state integral data of Tagami. The comparison shows good agreement with both sets of experimental data.
This study reviews experimental local heat-transfer data for laminar and turbulent film heat transfer for downward condensing films, under the influence of interfacial-waviness and shear–stress effects. Local laminar-wavy-film heat transfer and transition to turbulence are significantly influenced by local wave characteristics, which depend not only on the film developing length, but also on the film-formation method. The results demonstrate that the dimensionless film thickness, incorporating shear stress, provides a more appropriate length scale to estimate laminar-wavy-film heat transfer, as well as transition to turbulence. For turbulent films, a phenomenologically-based local heat-transfer correlation has been proposed, treating the near-wall and near-interface regions in series, to derive a `two-layer resistance model', based on the investigation of turbulence structure across sheared gas–liquid interfaces.
Based on a heat and mass transfer analogy, an iterative condensation model for steam condensation in the presence of a non-condensable gas in a vertical tube is proposed including the high mass transfer effect, entrance effect, and interfacial waviness effect on condensation. A non-iterative condensation model is proposed for easy engineering application using the iterative condensation model and the assumption of the same profile of the steam mass fraction as that of the gas temperature in the gas film boundary layer. It turns out that the Nusselt number for condensation heat transfer is expressed in terms of air mass fraction, Jakob number, Stanton number for mass transfer, gas mixture Reynolds number, gas Prandtl number and condensate film Nusselt number. The comparison shows that the non-iterative condensation model reasonably well predicts the experimental data of Park, Siddique, and Kuhn.
Noncondensable gases significantly modify the mechanism of condensation for cocurrent downward flow in vertical tubes. Two-dimensional experimental measurements presented here show similarity between gas concentration distributions and the temperature distributions encountered in laminar and turbulent heat transfer. Thus the analogy between heat and mass transfer, coupled with a reasonable condensate film model, can provide predictions of the local condensation rate. This work presents a simple 9-step iterative calculation procedure for calculating the local heat flux. The empirical model, based on a modified Dittus-Boelter formulation and utilizing an effective condensation thermal conductivity, converges with 2 to 10 iterations at each axial location. Experimental results from several investigators are compared with the predictions of the model, with good agreement.
Results are presented from an experimental investigation of the relation between heat transfer and friction in smooth and rough tubes. Three rough tubes and one smooth tube were formed from electroplated nickel. The rough tubes contained a close-packed, granular type of surface with roughness-height-to-diameter ratios ranging from 0.0024 to 0.049. Measurements of the heat-transfer coefficients (CH) and the friction coefficients (CF) were obtained with distilled water flowing through electrically heated tubes. A Prandtl number range of 1.20-5.94 was investigated by adjusting the bulk temperature of the water. Results were obtained for Reynolds numbers from 6 × 104 to 5 × 106 and from 1.4 × 104 to 1.2 × 105 at the lowest and highest Prandtl numbers respectively. A similarity rule for heat transfer was used to correlate, interpret, and extend the experimental results. The results were compared with previously existing results, both theoretical and experimental. Increases in CH due to roughness of as high as 270 per cent were obtained. These increases were, in general, accompanied by even larger increases in CF. An exception to this general behavior occurs at high Prandtl number in the region of transition between the "smooth" and the "fully rough" CF characteristic.
An experimental study is performed to investigate the high pressure steam condensation heat transfer in a large diameter condenser tube which is adapted for passive systems in Advanced Nuclear Power Plants. Experiments are conducted with high pressure steam in a single vertical tube with an inner diameter of 46 mm at a maximum pressure of 7.5 MPa. The film condensation heat transfer coefficients in the vertical tube are calculated by the difference of measured tube wall temperatures, and the two-phase pressure drops in the condenser tube are also measured. A new turbulent annular film condensation model is developed on the basis of the similarity of pipe flow and annular film flow. The present model gives better results than those of the Shah model in comparison with the experimental data.
An experimental study is performed to investigate the effects of noncondensable (NC) gas in the steam condensing system. A vertical condenser tube is submerged in a water pool where the heat from the condenser tube is removed by boiling heat transfer. The design of the test section is based on the passive condenser system in an advanced boiling water nuclear power reactor. Data are obtained for various process parameters, such as inlet steam flow rate, noncondensable gas concentration, and system pressure. Degradation of the condensing performance with increasing noncondensable gas is investigated. The condensation heat transfer coefficient and heat transfer rate decrease with noncondensable gas. The condensation heat transfer rate is enhanced by increasing the inlet steam flow rate and the pressure. The condensation heat transfer coefficient increases with the inlet steam flow rate, however, decreases with the system pressure. For the condenser submerged in a water pool with saturated condition, the strong primary pressure dependency is observed.
Experimental and theoretical investigations were conducted for the film condensation with noncondensable gas in a vertical tube. Condensation experiments were performed for a steam–air mixture in a vertical tube submerged in a water pool where the heat from the condenser tube was removed through a boiling heat transfer. Degradation of the condensation with noncondensable gas was investigated. A heat and mass analogy model for the annular filmwise condensation with noncondensable gas was developed. In the steam–air mixture region, general momentum, heat and mass transport relations derived by analytic method were used with the consideration of surface suction effect. The predictions from the model were compared with the experimental data and the agreement was satisfactory.
This paper develops a theory for turbulent vapor condensation in vertical tubes when non-condensable gases are present. The local heat transfer coefficient is calculated and the results are compared with experimental data. Approximate methods to calculate the condensate film thickness with good precision are developed without need to iterate to solve the transcendental equation which obeys the film thickness. A comparison of the theory predictions with some experimental data resulted in a good agreement.
Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Nuclear Engineering, 1992. Includes bibliographical references (leaves 124-128).
The thermal entrance problem for low Reynolds number, turbulent flow of gases in circular tubes is solved analytically by the method of Sparrow, Hallman, and Siegel. Fluid properties are considered constant. The solution is based on a Reynolds-number-dependent velocity profile developed, in a companion paper, by modifying Reichardt’s wall and middle law eddy diffusivity expressions. Tabular values of the eigenvalues and normalized Nusselt numbers are presented for a range of Reynolds numbers from 3,000 to 50,000. The axial variation of Nusselt number is found to be correlated by NuNu∞=1+0.8(1+70,000Re−3/2)xD−1 to within ±5 percent for x/D ≥ 2. The fully developed value agrees with the Dittus-Boelter correlation. For the eigenvalues, λn2, and the associated constants, An, correlations of the form λn2=a1,nRe−b1,n+c1,nRe−d1,nAn=a2,nRe−b2,n+c2,nRe−d2,n are obtained. Heat transfer data are presented, primarily for helium, for the conditions of the analysis. In the low Reynolds number turbulent regime, these data clearly support the present analytical solution.
Investigation of heat transfer from condensing steam–gas mixtures
- S Z Kuhn
S.Z. Kuhn, Investigation of heat transfer from condensing steam–gas mixtures
The correlation of liquid entrainment fraction and entrainment rate in annular two phase flow
- Whalley
P.B. Whalley, G.F. Hewitt, The correlation of liquid entrainment fraction and
entrainment rate in annular two phase flow, AERE-R-878 (1978).
Investigation of heat transfer from condensing steam-gas mixtures and turbulent films flowing downward inside a vertical tube
- S Z Kuhn