Analysis of the complete condensation in a vertical tube passive condenser

A theoretical analysis on complete condensation in a vertical tube passive condenser was performed. The modified Nusselt model with a correction factor and the Blangetti model for film heat transfer were compared with the experimental data. For the interfacial shear, the effect of mass transfer at the interface was considered. For small film Reynolds number and small interfacial shear conditions, the modified Nusselt model agrees well with the experimental data. The condensation rate increases and the condensation heat transfer coefficient decreases as the system pressure increases. The overall trends of the analysis results are consistent with the classical Nusselt analysis for the pure steam condensation.     

Non-iterative condensation modeling for steam condensation with non-condensable gas in a vertical tube

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.     

Entropy generation of vapor condensation in the presence of a non-condensable gas in a shell and tube condenser

This article investigates the entropy production of condensation of a vapor in the presence of a non-condensable gas in a counter-current baffled shell and one-pass tube condenser. The non-dimensional entropy number is derived with respect to heat exchange between the bulk fluid and condensate, as well as heat exchange between the condensate and coolant. Numerical results show that heat transfer from the condensate to the coolant has a dominant role in generating entropy. For example, at an air mass flow rate of 330 kg/h, 93.4% of the total entropy generation is due to this source. The resultant profiles during the condensation process indicate that a higher air mass flow rate leads to a lower rate of entropy production. For example, as the air mass flow rate increases from 330 kg/h to 660 kg/h and 990 kg/h, the total entropy generation decreases from 976 J/s K to 904 and 857.2 J/s K, respectively. By introducing a new parameter called the condensation effectiveness, a correlation is also developed for predictions of the entropy number, and an illustrative example is presented.     

Research on convective condensation heat transfer for a gas mixture in a vertical tube

This paper discusses the convective condensation of a gas mixture in a vertical tube. A mathematical model was derived by combining a modified film model and Nusselt's condensation theory. The effect of wall temperature on film thickness and interfacial temperature was predicted and film thickness was calculated. When compared with the gas phase resistance method, the film model is better. The phenomenon of SO₂ absorption into condensate is illustrated and discussed. © 2004 Wiley Periodicals, Inc. Heat Trans Asian Res, 33(4): 219–228, 2004; Published online in Wiley InterScience ( www.interscience.wiley.com ). DOI 10.1002/htj.20011     

Laminar film condensation heat transfer of hydrogen and nitrogen inside a vertical tube

There have been a number of experimental investigations on condensing heat transfer to cryogenic fluids. The investigations with nitrogen and oxygen have shown reasonable agreement between experimental data and those predicted by Nusselt's theory. On the other hand, in the previous investigations with much colder fluids, such as hydrogen, deuterium, and helium, the experimental condensing heat transfer coefficients are smaller than those predicted by Nusselt's theory, and these differences become much larger when the film Reynolds number or decreasing temperature difference across the condensate film is decreased. In the present investigation, hydrogen and nitrogen were condensed inside a vertical tube (d = 15 mm, L = 30 mm) under steady‐state conditions, respectively, and condensing heat transfer coefficients were precisely measured. From the experimental results, the condensing heat transfer coefficients for saturated hydrogen and nitrogen vapors agree with those predicted by Nusselt's theory within ±20%. The results of the present study suggest that deuterium and helium might also behave as predicted by Nusselt's theory. © 2001 Scripta Technica, Heat Trans Asian Res 30(7): 542–560, 2001     

Numerical heat transfer analysis of laminar film condensation on a vertical fluted tube

The purpose of this study is to find a convenient and practical procedure for calculating heat transfer of laminar film condensation on a vertical fluted tube. The condensate film on the tube surface along the axial direction was divided into two portions: the initial portion and the developing portion. The developing portion was analyzed in details. The film thickness equation of condensate film over the crest and the momentum equation of condensate film in the trough were established respectively after some simplifications and coupled with two-dimensional thermal conduction equation. The relationship between the heat transfer rate and the length of the flute was obtained through solving the equations numerically. The present procedure was tested on a sinusoidal fluted tube. The amount of heat transfer rates Q_t of the tube were calculated at different temperature differences by using this procedure. The calculation was compared with the experimental data quoted. The results were in good agreement with a maximum deviation of 18%. So the present procedure is reliable and can be used in the parameter design of sinusoidal fluted tubes.     

Heat transfer research on vapor‐gas mixture with condensation in a vertical tube

The convection‐condensation heat transfer of vapor‐gas mixtures in a vertical tube was studied theoretically and experimentally. The effects of the condensation of a small amount of water vapor (8 to 20%) on heat transfer in a vertical tube were discussed. Comparisons show that theoretical solutions obtained through modified film model and experimental results are in good agreement. The results show that the condensation heat transfer of a small amount of water vapor and single‐phase convection heat transfer in the vapor‐gas mixtures are of the same order of magnitude, and these two modes of heat transfer could not be neglected. © 2002 Wiley Periodicals, Inc. Heat Trans Asian Res, 31(7): 531–539, 2002; Published online in Wiley InterScience ( www.interscience.wiley.com ). DOI 10.1002/htj.10055     

Film condensation on a vertical microchannel

In this paper, a two dimensional laminar liquid film which condenses on a vertical microchannel is investigated analytically. A liquid film thickness, condensation mass flux flow and the variation of the velocity through the liquid thickness were determined by modified Navier–Stockes and energy equations. The effect of some parameters on the liquid film thickness, condensation mass flow rate and velocity are investigated. These parameters include slipping in temperature, β, and velocity, α, due to microscale interaction. It was found that, the liquid film thickness, δ, decreases as the slipping factors increases, and diminishes as a value of slipping factors (α and β) become more than or equal to 0.1. Increasing the slip in temperature due to microscale interaction causes the condensation mass flow rate to increase as the value of slip in velocity increases. Additionally, the slip value in the channel was found to increase as the slip value in velocity, α, increases.     

Conjugated shear stress and Prandtl number effects on reflux condensation heat transfer inside a vertical tube

Local reflux condensation heat transfer coefficients have been measured inside a vertical tube with water (2.6 < Pr_liq < 4.5), ethanol (12.4 < Pr_liq < 18.4) and isopropanol (23 < Pr_liq < 55) as the test fluids. A counter current flow situation is established with the liquid film (0.68 < Re_film < 2000) and the vapour (1000 < Re_vap < 16,500) flowing downward and upward, respectively. The heat transfer has found to be impeded by the shear stress only in cases of a very thin film, i.e. in the smooth laminar range, and it can well be correlated by a simple analytical model. In the laminar-wavy range including developing turbulence the heat transfer coefficients are found to increase with the shear stress, an effect which proved to be enhanced with rising Pr_liq numbers. This has been correlated with very good agreement.     

Numerical study of a passive solar still with separate condenser

A passive solar still with separate condenser has been modeled and its performance evaluated. The system has one basin (basin 1) in the evaporation chamber and two other basins (2 and 3) in the condenser chamber, with a glass cover over the evaporator basin and an opaque condensing cover over basin 3. Basins 1, 2 and 3 yield the first, second and third effects respectively. The top part of the condensing cover is shielded from solar radiation to keep the cover relatively cool. Water vapor from the first effect condenses under the glass cover while the remainder of it flows into the condenser, by purging and diffusion, and condenses under the liner of basin 2. The performance of the system is evaluated and compared with that of a conventional solar still under the same meteorological conditions. Results show that the distillate productivity of the present still is 62% higher than that of the conventional type. Purging is the most significant mode of vapor transfer from the evaporator into the condenser chamber. The first, second and third effects contribute 60, 22 and 18% of the total distillate yield respectively. It is also found that the productivity of the solar still with separate condenser is sensitive to the absorptance of the liner of basin 1, and the mass of water in basins 1 and 2. The mass of water in basin 3 and wind speed have marginal effect on distillate production. Other results are presented and discussed in detail.     

Effect of an interfacial shear stress on steam condensation in the presence of a noncondensable gas in a vertical tube

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.     

The formation and behavior of fog in a tube bundle condenser

The formation and behavior of fog during partial condensation of humid air in a vertical tube bundle condenser has been investigated. For this purpose a special glass condenser has been constructed which allows to measure the aerosol parameters everywhere along the cooling tubes using an optical aerosol measurement system. At the operation conditions adjusted in the present work fog occurs only in the presence of foreign nuclei by heterogeneous nucleation. It is shown, that the total mass of fog being formed was not influenced by the number concentration of foreign nuclei. The formation of fog occurs immediately after the first contact of the humid air with the cooling wall due to local supersaturation. After the fog has been formed in the entry of the condenser, a strong decrease of fog particles has been observed further down with the total amount of fog being constant. The effect of various process settings on the resulting aerosol parameters has been investigated. Both simple and rigorous one-dimensional calculations and complex multi-dimensional simulations using CFD were carried out for the interpretation of experimental data. Although the multi-dimensional simulations showed strong local effects the one-dimensional models were suitable to predict the conditions for fog formation.     

Melting in a vertical tube rotating about a vertical,colinear axis

Experiments were performed in which melting of a phase-change medium occurred in a closed vertical tube which was rotated about a vertical axis colinear with that of the tube. The melting was initiated and maintained by a step-change increase in the wall temperature of the containment tube. During the course of the experiments, parametric variations were made in the rotational speed, in the temperature difference which drives the melting, and in the duration of the melting period. The phase-change medium was 99% pure n-eicosane paraffin with a melting temperature of 36.3°C. It was found that rotation gave rise to considerably more rapid melting than that for no rotation, with the time required to achieve a given amount of melting being halved due to rotation. The rate at which energy could be stored was also significantly increased by rotation. Furthermore, at any duration of the melting period, the shape of the unmelted solid differed markedly in the presence or absence of rotation, being either straight-sided or sloped-sided. The melted mass results for all of the investigated conditions were very tightly correlated in terms of the Froude, Stefan, Grashof, and Fourier numbers.     

Effect of void fraction models on the film thickness of R134a during downward condensation in a vertical smooth tube

In the present study, the void fraction and film thickness of pure R-134a flowing downwards in a vertical condenser tube are indirectly determined using relevant measured data together with an annular flow model and various void fraction models reported in the open literature. The vertical test section is a countercurrent flow double tube heat exchanger with refrigerant flowing down in the inner tube and cooling water flowing upward in the annulus. The inner tube is made from smooth copper tubing of 9.52 mm outer diameter with a length of 0.5 m. The experimental runs are carried out at average saturated condensing temperatures of 40 and 50 °C, and mass velocities are around 456 kg m^− 2 s^− 1, over the vapour quality range 0.82–0.93, while the heat fluxes are between 45.60 and 50.90 kW m^− 2. Analysis based on simple void fraction models of the annular flow pattern are presented for forced convection condensation of pure R134a, taking into account the effect of the different saturation temperatures at high mass flux conditions. The comparisons of calculated film thickness show that the void fraction models of Spedding and Chen, and Chisholm and Armand are the most accurate ones with the experimental data due to their low deviation with Whalley's annular flow model over 35 void fraction models presented in this paper.     

Experimental investigation of convective heat transfer coefficient during downward laminar flow condensation of R134a in a vertical smooth tube

This paper presents an experimental investigation of laminar film condensation of R134a in a vertical smooth tube having an inner diameter of 7–8.1 mm and a length of 500 mm. Condensation experiments were performed at mass fluxes of 29 and 263 kg m^?2 s^?1. The pressures were between 0.77 and 0.1 MPa. The heat transfer coefficient, film thickness and condensation rate during downward condensing film were determined. The results show that an interfacial shear effect is significant for the laminar condensation heat transfer of R134a under the given conditions. A new correlation for the condensation heat transfer coefficient is proposed for practical applications.     

Analysis of film condensation heat transfer inside a vertical micro tube with consideration of the meniscus draining effect

In this paper we report on a theoretical analysis of film condensation heat transfer in a vertical micro tube with a thin metal wire welded on its inner surface. Both the radial and the axial distributions of condensate liquid along the tube wall and over the meniscus zone, formed by the wire in contact with the tube inner surface, are determined based on the minimum energy principle over the liquid-vapor two-phase flow system. The influences of the contact angle between the condensate liquid and the channel wall as well as the wire diameter on the condensate distributions and the heat transfer characteristics are examined. It is found that an increase in the wire diameter results in significant enhancement of heat transfer in the channel. It is also demonstrated that the wettability between the wire and the condensate has a little influence on the overall heat transfer coefficients, although it affects the condensate liquid distribution. Compared to a round tube with the same inside diameter, significant enhancement of condensation heat transfer is found for the present configured microchannel.     

Optimum temperatures in a shell and tube condenser with respect to exergy

This paper focuses on evaluation of the optimum cooling water temperature during condensation of saturated water vapor within a shell and tube condenser, through minimization of exergy destruction. First, the relevant exergy destruction is mathematically derived and expressed as a function of operating temperatures and mass flow rates of both vapor and coolant. The optimization problem is defined subject to condensation of the entire vapor mass flow and it is solved based on the sequential quadratic programming (SQP) method. The optimization results are obtained at two different condensation temperatures of 46 °C and 54 °C for an industrial condenser. As the upstream steam mass flow rates increase, the optimal inlet cooling water temperature and exergy efficiency decrease, whereas exergy destruction increases. However, the results are higher for optimum values at a condensation temperature of 54 °C, compared to those when the condensation temperature is 46 °C. For example, when the steam mass flow rate is 1 kg/s and the condensation temperature increases from 46 °C to 54 °C, the optimal upstream coolant temperature increases from 16.78 °C to 25.17 °C. Also, assuming an ambient temperature of 15 °C, the exergy destruction decreases from 172.5 kW to 164.6 kW. A linear dependence of exergy efficiency on dimensionless temperature is described in terms of the ratio of the temperature difference between the inlet cooling water and the environment, to the temperature difference between condensation and environment.