Vapor Boundary Layer Research Articles

Buoyancy effects on film boiling heat transfer from a sphere at low velocities

A theoretical model is developed for the forced convection film boiling phenomenon over a heated sphere moving vertically downwards in the water. Unprecedented compared with the previous analytical studies, this model accounts for the buoyancy effects while solving the momentum and energy equations in the vapour phase to obtain the velocity and the temperature distribution in terms of the vapour boundary layer thickness. To calculate the vapour boundary layer thickness, an energy balance is applied at the vapour–liquid interface. The flow of liquid around the sphere is considered to be governed by potential theory, and the energy equation in liquid is then solved for the known velocity distribution. We find that the vapour boundary layer thickness increases with an increase in the sphere temperature, the bulk water temperature and a decrease in the free stream velocity. This further results in a decrease in the film boiling heat transfer coefficient. The present study concludes that at low free stream velocities ( ${<}0.5\, {\rm m}\,{\rm s}^{-1}$ ) buoyancy becomes significant in delaying the separation, and when the velocity is further reduced the separation angle approaches $180^{\circ}$ .

Tomographic spectrometer for the temporally-resolved 2D reconstruction of gas phase parameters within a generic SCR test rig

We present a tomographic spectrometer for the measurement of gas phase species parameter distributions within the cross section of a generic exhaust gas test rig built for the investigation of the physico-chemical processes during exhaust gas aftertreatment with selective catalytic reduction (SCR). A urea-water solution (UWS) is injected into the hot gas flow to supply ammonia (NH3) through thermolysis and hydrolysis processes as the reducing agent of nitrous oxides (NOx) within the SCR catalyst. To achieve a full NOx conversion, the pre-catalyst distribution of the major exhaust gas species is of great importance. The injection leads to several desirable and undesired highly complex processes including spray breakup and film formation on the opposing wall. To further optimize the pre-catalyst distribution while maximizing the efficiency of the overall process, the knowledge of mole fraction and temperature distributions are crucial.The developed biaxial tomographic spectrometer utilizes a combined measurement method - laser absorption tomography by employing tunable diode laser absorption spectroscopy (TDLAS) data with the linear hyperspectral absorption tomography (LHAT) approach to achieve simultaneous multiparameter reconstructions. An image frame rate of 49 Hz was achieved following a phase averaging, and a tomographic signal-to-noise ratio limit was applied. Virtual experiments and measurements in homogeneous samples were performed to ensure the spectromter’s ability for qualitative and quantitative reconstructions. Measurements during water injection cycles into the hot gas flow have shown two main features within the distribution that can be linked to the presence of a vapor boundary layer at the channel bottom and an evaporated spray-induced cone feature. Temperature measurements of a thermocouple downstream of the measurement plane agree well with the reconstructed temperatures.The spectrometer is intended to further improve the understanding of the pre-catalyst flow in SCR systems and the results can be taken as reference for corresponding numerical calculations.

Rayleigh–Taylor unstable condensing liquid layers with nonlinear effects of interfacial convection and diffusion of vapour

Abstract

A new spatially scanning 2.7 µm laser hygrometer and new small-scale wind tunnel for direct analysis of the H2O boundary layer structure at single plant leaves

A new spatially scanning TDLAS in situ hygrometer based on a 2.7-µm DFB diode laser was constructed and used to analyse the water vapour concentration boundary layer structure at the surface of a single plant leaf. Using an absorption length of only 5.4 cm, the TDLAS hygrometer permits a H2O vapour concentration resolution of 31 ppmv. This corresponds to a normalized precision of 1.7 ppm m. In order to preserve and control the H2O boundary layer on an individual leaf and to study the boundary layer dependence on the wind speed to which the leaf might be exposed in nature, we also constructed a new, application specific, small-scale, wind tunnel for individual plant leaves. The rectangular, closed-loop tunnel has overall dimensions of 1.2 × 0.6 m and a measurement chamber dimension of 40 × 54 mm (H × W). It allows to generate a laminar flow with a precisely controlled wind speed at the plant leaf surface. Combining honeycombs and a miniaturized compression orifice, we could generate and control stable wind speeds from 0.1 to 0.9 m/s, and a highly laminar and homogeneous flow with an excellent relative spatial homogeneity of 0.969 ± 0.03. Combining the spectrometer and the wind tunnel, we analysed (for the first time) non-invasively the wind speed-dependent vertical structure of the H2O vapour distribution within the boundary layer of a single plant leaf. Using our time-lag-free data acquisition procedure for phase locked signal averaging, we achieved a temporal resolution of 0.2 s for an individual spatial point, while a complete vertical spatial scan at a spatial resolution of 0.18 mm took 77 s. The boundary layer thickness was found to decrease from 6.7 to 3.6 mm at increasing wind speeds of 0.1–0.9 m/s. According to our knowledge, this is the first experimental quantification of wind speed-dependent H2O vapour boundary layer concentration profiles of single plant leaves.

Flow and heat transfer characteristics of ambient air condensation on a horizontal cryogenic tube

Ambient air condensation on a cryogenic horizontal tube is investigated using a newly built mathematical model, in which the liquid film and the vapor boundary layer are coupled together with a major emphasis on the effect of buoyancy. Based on the model, the heat transfer coefficients and the film thickness as well as the interfacial shear are obtained under different conditions to investigate the effects on the flow and heat transfer characteristics of the superheating between vapor and film, the buoyancy in the boundary layer and the subcooling between wall and film. In addition to the flow and heat transfer characteristics of air, the other four different vapors, i.e. H2O, R134a, methane (CH4), argon (Ar), are also discussed. The results show that the superheating has a more significant contribution to the increase of heat transfer coefficient for air comparing to the other vapors, e.g. in the cases of superheating ΔT∞=100 and 200K the mean heat transfer coefficient increases by 10.3% and 24.3% for air, while it increases by only 1.8% and 3.9% for H2O. In contrast to superheating, the subcooling has a negative effect on the increase of heat transfer coefficient. Noteworthy, the buoyancy plays a non-negligible role on the flow and heat transfer characteristics of superheated air condensation. The analytical results are of great importance in the design and improvement of ambient-heated cryogenic vaporizer (AHCV).

A Semi-Empirical Model for Condensation Heat Transfer Coefficient of Mixed Ethanol-Water Vapors

A semi-empirical model describing the heat transfer characteristics of the pseudo-dropwise condensation of binary vapor on a cooled vertical tube has been formulated. By ignoring the thin film always present on the condensation surface and the intensification of mass transfer caused by the Marangoni effect, the heat transfer characteristics of pseudo-dropwise condensation are tentatively formulated. The model involved an analysis of the diffusion process in the vapor boundary layer along with the heat transfer process through the condensate drops. This model was applied to the condensation of the saturated binary vapor of ethanol and water, and was examined using experimental data at vapor pressure values of 101.33 kPa (provided by Utaka and Wang, 2004, “Characteristic Curves and the Promotion Effect of Ethanol Addition on Steam Condensation Heat Transfer,” Int. J. Heat Mass Transfer, 47, pp. 4507–4516), 84.52 kPa and 47.36 kPa. Calculations using the model show a similar trend to the experimental measurements. With the change of the vapor-to-surface temperature difference, the heat transfer coefficients revealed nonlinear characteristics, with the peak values under all ethanol mass fractions of binary vapor. The heat transfer coefficients increased with decreasing ethanol mass fraction.

The Dryline on 22 May 2002 during IHOP_2002: Convective-Scale Measurements at the Profiling Site

Abstract A detailed analysis of the structure of a double dryline observed over the Oklahoma panhandle during the first International H2O Project (IHOP_2002) convective initiation (CI) mission on 22 May 2002 is presented. A unique and unprecedented set of high temporal and spatial resolution measurements of water vapor mixing ratio, wind, and boundary layer structure parameters were acquired using the National Aeronautics and Space Administration (NASA) scanning Raman lidar (SRL), the Goddard Lidar Observatory for Winds (GLOW), and the Holographic Airborne Rotating Lidar Instrument Experiment (HARLIE), respectively. These measurements are combined with the vertical velocity measurements derived from the National Center for Atmospheric Research (NCAR) Multiple Antenna Profiler Radar (MAPR) and radar structure function from the high-resolution University of Massachusetts frequency-modulated continuous-wave (FMCW) radar to reveal the evolution and structure of the late afternoon double-dryline boundary layer. The eastern dryline advanced and then retreated over the Homestead profiling site in the Oklahoma panhandle, providing conditions ripe for a detailed observation of the small-scale variability within the boundary layer and the dryline. In situ aircraft data, dropsonde and radiosonde data, along with NCAR S-band dual-polarization Doppler radar (S-Pol) measurements, are also used to provide the larger-scale picture of the double-dryline environment. Moisture and temperature jumps of about 3 g kg−1 and 1–2 K, respectively, were observed across the eastern radar fine line (dryline), more than the moisture jumps (1–2 g kg−1) observed across the western radar fine line (secondary dryline). Most updraft plumes observed were located on the moist side of the eastern dryline with vertical velocities exceeding 3 m s−1 and variable horizontal widths of 2–5 km, although some were as wide as 7–8 km. These updrafts were up to 1.5 g kg−1 moister than the surrounding environment. Although models suggested deep convection over the Oklahoma panhandle and several cloud lines were observed near the dryline, the dryline itself did not initiate any storms over the intensive observation region (IOR). Possible reasons for this lack of convection are discussed. Strong capping inversion and moisture detrainment between the lifting condensation level and the level of free convection related to an overriding drier air, together with the relatively small near-surface moisture values (less than 10 g kg−1), were detrimental to CI in this case.

Prediction of Initial Emission Rates of 2-Butoxyethanol from Consumer Products Using Equilibrium Headspace Concentrations: An Application of the Vapor Pressure and Boundary Layer (VB) Model

The initial emission rate of volatile organic compounds (VOCs) from consumer products is important for assessing potential human exposure to VOCs in products. The vapor pressure and boundary layer (VB) model developed in the past was used to predict the emission rates of VOCs in the fast decaying phase from petroleum-based wet materials. This study has extended the model to largely water-based products. Study results have shown a good agreement (ratio = 1.01, r2 = 0.89) between model-predicted initial emission rates (ER0) of 2-butoxyethanol (2-BE) based on its equilibrium headspace concentration and experimentally measured ER0 in a small dynamic environmental chamber for 20 consumer products. These water-based products included wood surface treating stains, general cleaning agents, and degreasers with 2-BE concentrations over a wide range. The results also demonstrated a dependency between the headspace concentrations of the target analytes and the water content in the liquid. But dependency on water content had no effect on the use of headspace concentration to predict the ER0. The ER0 of 2-BE in the products ranged from 100 to 3000 mg m(-2) h(-1). In the majority of cases, the 2-BE concentration range in individual products indicated in the Material Safety Data Sheet agreed with the measured data.

Measuring and modeling vapor boundary layer growth during transient diffusion heat and moisture transfer in cellulose insulation

In this paper, an experimental test facility that permits continuous measurements of transient heat and moisture transfer in porous media is applied to study the vapor boundary layer in cellulose insulation. The experiment measures the relative humidity, temperature and moisture accumulation within the cellulose specimen with a fully developed flow of air at a controlled temperature and humidity provided above the surface. These experimental results are used to verify a mathematical model, which is used to develop an expression for moisture diffusivity ( α m) that is analogous to thermal diffusivity, and takes into consideration moisture storage. The moisture diffusivity is used to calculate the vapor density in the boundary layer and the size of vapor boundary layer in cellulose insulation. It is found that the moisture storage effect has a very significant effect on the vapor boundary layer and cannot be ignored. For cellulose insulation, the size of the vapor boundary layer may be over predicted by a factor of ten when moisture storage is neglected.

Laminar film condensation on an elliptical tube embedded in porous media

Laminar film condensation of saturated vapor flowing over an isothermal elliptical tube embedded in a porous medium is analyzed for conditions of free and forced convection. The flow field in the porous medium is described by the Darcy–Brinkman–Forchheimer model. The effect of vapor shear on condensation is determined by simultaneous solution of the two phase vapor boundary layer and condensate film momentum equations. The numerical results, which are presented in the form of local film thickness and local Nusselt number, show a dependence of these physical parameters on practical dimensionless parameters such as Reynolds number, Darcy number, Bond number and eccentricity.

Laminar boundary layer flow of saturated vapor and its condensate over a horizontal tube

The steady two-dimensional laminar flow of a stream of saturated vapor flowing over a tube that is kept at a uniform temperature, below the saturation temperature, is examined. Owing to the temperature difference between the vapor stream and the solid surface a film of condensate is generated that flows along the surface due to shear, pressure-drop, and gravity. In the limit as the boundary layer and film thickness remain smaller than the radius of curvature of the surface a simplified lubrication-type formulation describes the temperature and flow fields in the film, whereas the usual boundary layer formulation is applied in the vapor boundary layer. The case of flow past a horizontal cylinder of radius R is investigated numerically with the oncoming stream aligned with gravity. The parameters that control momentum and heat transfer in this problem are the viscosity ratio, μcs/μss, the density ratio, ρcs/ρss, the Prandtl number, Pr=cpcsμcs/kcs, the Froude number, Fr=U∞2/(gπR), and finally the thickness ratio between the condensate and the vapor boundary layer, ε, which is also a measure of the temperature difference between the vapor stream and the tube wall. Then, the Nusselt number and the skin friction coefficient, averaged over the upper half of the cylinder, are calculated for a wide parameter range. When Fr is very small and ε relatively large the flow remains attached until the trailing stagnation point of the cylinder. As the effect of adverse pressure drop becomes more pronounced (Fr increases or ε decreases) it is shown that the solution exhibits two different types of singularity in the rear part of the cylinder. The first one is a typical Goldstein singularity because it appears at the tube wall and it is associated with vanishing skin friction (wall shear) and rapidly increasing film thickness. The second one takes place near the interface between the vapor stream and the film of condensate in a region where very small velocities prevail in conjunction with vanishing shear rate. The latter has not been reported so far and it is expected to affect the flow locally, as opposed to the Goldstein singularity which is known to lead to massive separation in the case of a cylindrical surface. Upon proper rescaling of Fr and ε, Fr′=Fr ρss/ρcs, ε′=ε6(μss/μcs)7/2(ρcs/ρss)7/2, a critical curve is produced in the (Fr′,ε′) plane that marks the boundary curve separating the two types of singular behavior for most of the numerical data obtained herein for the steam–water system, irrespective of the saturation temperature.

Turbulent film boiling on a horizontal cylinder

The turbulent film boiling on a horizontal cylinder is formulated and solved giving due importance to thermal radiation. In the analysis the test surface is maintained under isothermal conditions and the thermophysical property variation of the vapor due to the steep temperature gradients in the vapor boundary layer is included in the formulation. The analysis is checked with some experimental data relevant to turbulent film boiling. The agreement between the two is found to be very satisfactory.

Forced Convection Laminar Film Condensation of Downward Flowing Vapor on a Single Horizontal Elliptic Cylinder or a Bank of Elliptical Tubes

A numerical study is performed on the laminar film condensation of pure saturated vapor flowing in the direction of gravity on a single horizontal elliptic cylinder or a bank of elliptical tubes. Temperature, velocity distribution, and heat transfer coefficient of the fully developed flow are carried out with a fully implicit finite difference scheme. The equality of shear stress at the liquid-vapor interface is used as the coupling condition between the two phases. The inertia and convection term are retained in the analysis. Outside of the vapor boundary layer, the vapor phase velocity is obtained from potential flow. The method of source density distribution on the body surface is used for determination of the external vapor velocity in elliptical tube banks. The effect of inundation produced by condensate on upper ellipses is taken into account by assuming that the vapor velocity field is not affected by the condensate flow from one elliptic cylinder to another. Based on the obtained solutions of flow field, the effect of surface tension, the interaction because of the ellipse spacing, and the inundation on the heat transfer coefficient and the boundary layer separation point have been evaluated. The results of this analysis are discussed especially in function of eccentricity e (effect of the surface tension). The heat transfer in interellipse space is analyzed and compared with the theoretical and experimental results of other authors. Good agreement is shown.

2708 水蒸気-空気混合気の細い鉛直管外面への自由対流層流膜状凝縮

An experimental study is presented on free convection laminar film condensation of steam-air mixture on a vertical tube. The test tube used is of about 220mm height and about 6mm outer diameter. The range of concentration of air is 0.1∿0.9. The average heat flux values or average heat transfer coefficients obtained have been about 2.5 times larger than the corresponding values from the two-phase boundary layer theory for a vertical flat surface. The enhanced values are quantitatively explained by the curvature effect upon the vapor boundary layer, which is analogically derived from single phase free convection heat transfer.

Numerical study of laminar condensation of downward flowing vapour on a single horizontal cylinder or a bank of tubes

AbstractThe results of numerical calculations for the downward flow of pure vapour condensing on horizontal tubes are presented. An implicit finite difference method is used. The equality of shear stress at the liquid—vapour interface is used as the coupling condition between the two phases. The inertia and convection terms are retained in the analysis. The vapour phase velocity is obtained from potential flow. The method of source density distribution on the body surface is used for the determination of the vapour flow in tube banks. The effect of flooding produced by condensation on upper tubes is taken into account by assuming that the vapour velocity field is not affected by the condensate flow from one tube to another. The results presented show that the vapour boundary layer separation depends on the Froude number. The heat transfer in the intertube space is analyzed and compared with the theoretical and experimental results of other authors. Good agreement is shown.

Various formulas and their accuracy concerning convective heat and mass transfer in the vapor boundary layer in the case of laminar film condensation of binary vapor mixtures

The equations of convective mass transfer are derived from the equations of convective heat transfer by replacing Nu c with Sh and Pr v with Sc and also (χ +/ω) Gr with (χ/ω) Gr for free- condensation. As for forced-convection condensation, the equations of Rose and Fujii el al. and the newly presented equation for mass transfer have almost the same accuracy, although their functional forms are quite different from each other. The accuracy of Rose's equation for heat transfer decreases as the effect of the enthalpy diffusion term increases. As for free-convection condensation, the newly presented equation for mass transfer is applicable in a wider range of W R or M in comparison with the previous equation of Fujii et al.

A numerical study of high-pressure droplet vaporization

The evaporation of single, spherical fuel droplets in a high-pressure, high-temperature environment has been studied numerically. The model is fully transient in both the liquid and the vapor phases. Transport properties are functions of temperature, pressure, and composition, and vary throughout the liquid droplet and the vapor boundary layer. Equilibrium at the liquid-vapor interface is calculated using the Peng-Robinson equation of state, and accounts for diffusion of the gas into the liquid droplet. The Peng-Robinson equation of state is also used to calculate the enthalpy of vaporization of the fuel species as well as the liquid and vapor mixture densities. The proposed model is compared with data obtained for a variety of liquids. The comparisons include the predictions of the critical mixing state, droplet vaporization rate, and droplet temperature. Transient effects in both the liquid and vapor phases are found to have a large effect on the droplet heatup and vaporization process. At very high temperature and pressure conditions the droplets were found to reach their thermodynamic critical mixing point in a totally transient process. Coupled diffusion processes were studied and found to be an important factor in high-pressure droplet vaporization. Anomalies in the transport properties of a fluid near its critical mixing point were studied and found to be insignificant in droplet vaporization under conditions similar to those in a diesel engine.

Theoretical Analysis for the Condensation Heat Transfer of a Binary Vapor Mixture under the Thermal Equilibrium Condition.

The condensation heat transfer of ethanol-water binary vapor mixture is theoretically examined with regard to the assumption of thermal equilibrium in the vapor boundary layer. If the vapor in the boundary layer is subcooled, liquid droplets appear. Under this condition, the effects of the temperature difference between the wall and ambient, and the ambient ethanol mole fraction, on the heat transfer process are investigated. The results show that the heat transfer coefficient under equilibrium conditions decreases from that obtained without droplet formation (nonequilibrium) according to the total amount of the generated liquid droplets.

Various Formulas and their Accuracy Concerning Convective Heat Transfer and Convective Mass Transfer in the Vapor Boundary Layer in the Case of Laminar Film Condensation of Binary Vapor Mixtures.

Various Formulas and their Accuracy Concerning Convective Heat Transfer and Convective Mass Transfer in the Vapor Boundary Layer in the Case of Laminar Film Condensation of Binary Vapor Mixtures.

Predictive modeling of high-temperature chemical system vaporization under atmospheric pressure

An improved numerical technique was evolved in order to stimulate the non-congruent vaporization of complex chemical systems under atmospheric pressure. It concerns a one-dimensional model of a liquid-gas transformation taking into account the connected concepts of interfacial chemical equilibrium and diffusion-regime mass transfer into a boundary layer of concentration. Such a model can be applied to a wide range of physicochemical and geometric configurations of vaporizing systems since the mass transfer coefficient can be estimated. The model has actually been applied to an oxide system at high temperature. It was underlined that the oxygen partial pressure acts strongly on the characteristics of the chemical equilibrium and mass transfer, and consequently on the selectivity of vaporization, in other words the separating power of a chemical species from the bulk. Experiments were also performed according to the physicochemical and geometric characteristics of the model, and their results analyzed and compared with theoretical ones. It was found as a relevant aspect of mass transfer that the oxygen concentration in the carrier gas has a great influence on the vapor boundary layer thickness in relation to the homogeneous nucleation process.