Evaluations of Closure Correlations for the Simulation of Two-Phase Flows in Condensers

The effects of different closure correlations on numerical simulations of vapor-liquid two-phase flow and heat transfer in steam surface condensers are critically assessed in this study. A modified k-? turbulence model for two-phase flows is used in the simulation. The closure correlations are those for condensation vapor shear, interphase drag forces, non-condensable air, tube-side fluid flow, inundation, and hydraulic resistance due to the tube bundle. Numerical simulations of a steam surface condenser are carried out using different closure correlations, and the numerical results are compared with the experimental data. Recommendations are given for different closure correlations.     

A modified k–ε turbulence model for the simulation of two-phase flow and heat transfer in condensers

A modified k–ε turbulence model is developed in this study to simulate the gas–liquid two-phase flow and heat transfer in steam surface condensers. A quasi-three-dimensional algorithm is used to simulate the fluid flow and heat transfer in steam surface condensers. The numerical method is based on the conservation equations of mass and momentum for both gas-phase and liquid-phase, and mass fraction conservation equation for non-condensable gases. The numerical simulation of an experimental steam surface condenser has been conducted using the proposed modified k–ε turbulence model. The results obtained from the proposed model agree well with the experimental results and the results also show an obvious improvement in the prediction accuracy comparing with previous results where a constant value for the turbulent viscosity was used.     

Local heat transfer during reflux condensation mode in a U-tube with and without noncondensible gases

A series of experiments was performed to investigate the local heat transfer phenomenon inside a U-tube in a reflux condensation mode. A total of 477 data (108 for pure steam flow conditions and 369 for steam–air flow conditions) for the local heat transfer coefficients were obtained for various inlet flow rates of steam and air under atmospheric conditions. Based on the steam–air experimental results, a new correlation applicable to the reflux condensation mode is developed using the degradation factor. The new correlation includes the effects of the flow rates of the condensate and the noncondensible gases (air) on the heat transfer coefficient. Most of our data agree with the predicted values with a RMS error of 27.4%.     

A kinetic model for air-steam reforming of bio-oil over Rh–Ni/γ-Al2O3 catalyst: Acetol as a model compound

A new kinetic model is proposed for catalytic reforming of acetol to synthesis gas over a Rh–Ni/γ-Al₂O₃ catalyst. Acetol is one of the most important bio-oil model compounds formed under reactive flash volatilization reaction conditions. The model was implemented in the Aspen Plus simulation package and used to predict the product gas composition at different reaction temperatures and steam and oxygen ratios. The contributions of the reactions both in the reactor freeboard and the catalytic bed were assessed using CSTR and PFR reactor models, respectively. The reaction scheme included decomposition, steam reforming, and water-gas shift reactions. The results from the model predicted the product distribution within an acceptable degree of tolerance. This study confirms that thermal decomposition and partial oxidation of acetol precede the catalytic reactions involving steam. The effects of temperature, oxygen concentration in the feed, the volume of the freeboard, and the catalyst bed height can all be evaluated with this new kinetic model. This work suggests that bio-oil decomposed into different fractions of molecules like acetol can be successfully modelled by a series of decomposition reactions followed by partial oxidation and catalytic steam conversion. The heat transfer within the catalyst bed is found to be critical for achieving a good match with the experimental results.     

Robust modelling development for optimisation of hydrogen production from biomass gasification process using bootstrap aggregated neural network

In this study, a robust model using bootstrapped aggregated neural network (BANN) was developed for optimising operating conditions of a two-stage gasification for high carbon conversion, high hydrogen yield and low CO₂. The developed BAAN model predicted accurately (R² of 0.999) the gas composition and the 95% confidence bounds for model predictions on unseen validation data indicated good prediction reliability for various feedstock. The BANN was also used to predict the optimum operating condition for hydrogen production from waste wood (1st stage temperature of 900 °C, 2nd stage temperature of 1000 °C, steam/carbon molar ratio of 5.7) to achieve high hydrogen (71–72 mol%), gas yield (98–99 wt%) and low CO₂ (17–18 mol%). The optimal conditions were tested in the laboratory and the experimental results agreed well with the predicted data with an error of 0.01–0.05. Sensitivity analysis revealed that an increase in temperatures for both stages and high steam/carbon ratio favoured the H₂ production and carbon conversion.     

Estimation of design parameters for thermal performance evaluation of box-type solar cooker

The paper presents a simple test procedure for determination of design parameters to predict the thermal performance of a box-type solar cooker. A series of out-door experiments were performed on the double-glazed solar cooker of aperture area 0.245 m² with a fibre body to obtain two figures of merit, F₁ and F₂. The necessary design parameters—optical efficiency, F′η_o and heat capacity, (MC)′ of the cooker are calculated using the linear regression analysis of experimental F₂ data for different load of water. Based on the experimental results, a correlation for F₂ as a function of quantity of water (load) is proposed. The close agreement between experimental and calculated F₂ indicates the validity of the correlation. The proposed procedure is then applied to predict the heating characteristic curves of the solar cooker for different load of water. The predicted heating characteristic curves are validated by comparing with the experimental data from a series of cooker testing experiments. The results of present study reveal that F′η_o and (MC)′ are the critical design parameters required for the prediction of thermal performance of the solar cooker.     

Heat Transfer Correlation for Two-Phase Flow in Vertical Pipes Using Support Vector Machines

It has been shown by Tam and his coworkers [7] that the support vector machines (SVM) have excellent capability of handling complicated single-phase heat transfer problems. Therefore, it would be logical to extend the investigation to other flow situations, such as two-phase flow or flow in microtubes. In this study, SVM is used to correlate the two-phase, two-component flow data. Four sets of experimental data (a total of 255 data points) for vertical pipes used in this study were from Kim et al. [3]. They proposed a heat transfer correlation for turbulent gas–liquid flow in vertical pipes with different flow patterns and fluid combinations. Their correlation predicted the experimental data with a deviation range of –64.7% and 39.6%. Majority of the experimental data (245 data points or 96% of the data) were predicted within the ±30% range. A new correlation using SVM is developed in this study. The new correlation outperforms the traditional least-squares correlation and predicts the experimental data within the ±15% range.     

Biomass steam gasification in bubbling fluidized bed for higher-H2 syngas: CFD simulation with coarse grain model

A comprehensive coarse grain model (CGM) is applied to simulation of biomass steam gasification in bubbling fluidized bed reactor. The CGM was evaluated by comparing the hydrodynamic behavior and heat transfer prediction with the results predicted using the discrete element method (DEM) and experimental data in a lab-scale fluidized bed furnace. CGM shows good performance and the computational time is significantly shorter than the DEM approach. The CGM is used to study the effects of different operating temperature and steam/biomass (S/B) ratio on the gasification process and product gas composition. The results show that higher temperature enhances the production of CO, and higher S/B ratio improves the production of H₂, while it suppresses the production of CO. For the main product H₂, the minimum relative error of CGM in comparison with experiment is 1%, the maximum relative error is less than 4%. For the total gas yield and H₂ gas yield, the maximum relative errors are less than 7%. The predicted concentration of different product gases is in good agreement with experimental data. CGM is shown to provide reliable prediction of the gasification process in fluidized bed furnace with considerably reduced computational time.     

Studying the effect of convergence parameter of CUSP’s scheme in 2D modeling of novel combination of two schemes in nucleating steam flow in cascade blades

In the present research, considering the importance of appropriate design of steam turbines, a combination of scalar and convective upwind split pressure (CUSP) with known value of z schemes is used for numerically modeling condensation of the 2D nucleating steam flow. Considering the importance of z parameter in the CUSP scheme, effects of several different values of this parameter on the modeling of steam flows are subjected to sensitivity analysis using the combination method. Results of the improved numerical method across sensitive nucleation condensation shock zone are in good agreement with experimental data. Furthermore, numerical errors are lower than those conventional methods by up to about 80% with the mass flow rate being well stable, which indicates better satisfaction of conservation laws, and revealing efficiency of the proposed novel combination method.     

Numerical investigation of turbulent natural convection in an inclined square cavity with a hot wavy wall

The turbulent natural convection of air flow in a confined cavity with two differentially heated side walls is investigated numerically up to Rayleigh number of 10¹². The objective of the present work is to study the effect of the inclination angle and the amplitude of the undulation on turbulent heat transfer. The low-Reynolds-number k–ε, k–ω, k–ω–SST RANS models and a coarse DNS are used and compared to the experimental benchmark data of Ampofo and Karayiannis [F. Ampofo, T.G. Karayiannis, Experimental benchmark data for turbulent natural convection in an air filled square cavity, Int. J. Heat Mass Transfer 46 (2003) 3551–3572]. The k–ω–SST model is then used for the following test-cases as it gives the closest results to experimental data and coarse DNS for this case. The mean flow quantities and temperature field show good agreement with coarse DNS and measurements, but there are some slight discrepancies in the prediction of the turbulent statistics. Also, the numerical results of the heat flux at the hot wall are over predicted. The strong influence of the undulation of the cavity and its orientation is well shown. The trend of the local heat transfer is wavy with different frequencies for each undulation. The turbulence causes an increase in the convective heat transfer on the wavy wall surface compared to the square cavity for high Rayleigh numbers. A correlation of the mean Nusselt number function of the Rayleigh number is also proposed for the range of Rayleigh numbers of 10⁹–10¹².     

Optimization of hydrogen production by photocatalytic steam methane reforming over lanthanum modified Titanium (IV) oxide using response surface methodology

In this study, the optimization of hydrogen production by photocatalytic steam methane reforming over Lanthanum modified TiO₂ has been investigated using response surface methodology. The La/TiO₂ photocatalysts were synthesized using wet impregnation method and characterized for physicochemical and photocatalytic properties by N₂ physisorption, X-ray powder diffraction (XRD), Scanning electron microscopy (SEM), Energy dispersive X-ray (EDX), and ultraviolet-visible (UV-vis) spectroscopy. The characterization shows that the La/TiO₂ possesses appropriate properties to be used as photocatalysts. The photocatalysts were employed in the optimization studies of hydrogen production by photocatalytic steam methane reforming. The effects of irradiation time (10–150 min), metal loading (1–3%), methane concentration (10–50%), and steam concentration (0.5–1.5%) on the rate of hydrogen production were determined employing Box-Behnken experimental design. The application of the RSM resulted in the formulation of four models out which the quadratic model was adjudged to adequately fit the experimental data. A further statistical analysis of the quadratic model established the significance of the model with p-value far less than 0.05 and coefficient of determination (R²) of 0.975. A non-significant lack of fit obtained for the model further confirm the suitability of the quadratic model in fitting the experimental data. At the desirability function of 1, optimum conditions of 146.15 min, 2.94%, 22.83% and 1.24% for irradiation time, metal loading, methane concentration, and steam concentration, respectively resulted in the production of 2.42 μmol of hydrogen/min.     

Neural network based correlation for critical heat flux in steam-water flows in pipes

This paper presents a new approach using artificial neural networks (ANN) to predict the critical heat flux (CHF) for a steam–water mixture through pipes. A large number of experimental measurements are used for training and testing the developed network. The Levenberg–Marquardt algorithm was used to train the developed feed forward ANN. The training and validation are performed with good accuracy. The correlation coefficient obtained with unknown data applied to the network is 0.998 which is satisfactory and verifying the fidelity of the developed network. The present methodology proved to be much better than the traditional table and best-fit methods. Using the weights and biases obtained from the trained network, a new formulation is proposed for determination of the CHF Q_cr. Experimental results of Q_cr are compared with both the results obtained by the developed ANN based correlation and the results obtained by a best-fit correlation. Deviations between the results are found to be less than 5.5% and 30%, respectively. The developed ANN based correlation may make use of the dedicated ANN software unnecessary to use for each calculation time. As seen from the results obtained, the calculated Q_cr is obviously within acceptable uncertainties. This ANN based correlation can be employed with any programming language or spreadsheet program for estimating the CHF Q_cr. If the validity range changes, the ANN based correlation can be updated in terms of new sets of weights and biases using the same network architecture (same no. of hidden layers and no. of neurons).     

Prediction of silica carry-over and solubility in steam of boilers using simple correlation

Silica content of the boiler water is critical for steam turbines and scaling of boiler heat transfer surfaces. Silica (SiO₂) can volatilize with the steam in sufficient concentrations to deposit in steam turbines leading to scale formation on boiler surfaces. In this work, a simple correlation is presented to predict silica (SiO₂) solubility in steam of boilers as a function of pressure and water silica content. The solubility of silica in steam directly depends on both the density and temperature of steam. With decreasing temperature and density, solubility of silica reduces. As the pressure affects steam density which has a strong bearing on steam temperature, it has an important effect on the solubility of silica in steam. The proposed correlation predicts the solubility of silica (SiO₂) in steam for pressure up to 22,000 kPa and boiler water silica contents up to 500 mg/kg. The predictions from the proposed correlation have been compared with reported data and found good agreement with average absolute deviation being around 4%. This simple-to-use correlation can be of immense practical value for the engineers to have a quick check on silica (SiO₂) solubility in steam of boilers as a function of pressure and water silica content at various conditions without performing any experimental measurements. In particular, personnel dealing with the utility boilers would find the proposed approach to be user friendly involving no complex expressions with transparent calculations.     

Effects of water vapor addition on the laminar burning velocity of oxygen-enriched methane flames

The effects of steam addition on the laminar burning velocity of premixed oxygen-enriched methane flames are investigated at atmospheric pressure. Experiments are carried out with an axisymmetric burner on which laminar conical flames are stabilized. A newly devised steam production system is used to dilute the reactants with water vapor. The oxygen-enrichment ratio in the oxidizer, defined as O₂/(O₂ + N₂) (mol.), is varied from 0.21 (air) to 1.0 (pure oxygen). The equivalence ratio ranges from 0.5 to 1.5 and the steam molar fraction in the reactive mixture is varied from 0 to 0.50. For all compositions examined, the reactive mixture is preheated to a temperature T_u = 373 K. Laminar flame speeds are determined with the flame area method using a Schlieren apparatus. The deviations induced by stretch effects due to aerodynamic strain and flame curvature are assessed using Particle Imaging Velocimetry measurements and flame images, and these data are used to estimate the uncertainty of the flame speed measurements. The experiments are completed by numerical simulations conducted with the PREMIX code using different detailed kinetic mechanisms. It is shown that the laminar flame speed of CH₄/O₂/N₂/H₂O_(v) mixtures features a quasi-linear decrease with increasing steam molar fraction, even at high steam dilution rates. Numerical predictions are in good agreement with experimental data for all compositions explored, except for low dilution rates X_H2O<0.10 in methane–oxygen mixtures, where the flame speed is slightly underestimated by the calculations. It is also shown that steam addition has a non-negligible chemical impact on the flame speed for methane–air flames, mainly due to water vapor high chaperon efficiency in third-body reactions. This effect is however strongly attenuated when the oxygen concentration is increased in the reactive mixture. For highly oxygen-enriched flames, steam can be considered as an inert diluent.     

Convective boiling heat transfer and two-phase flow characteristics inside a small horizontal helically coiled tubing once-through steam generator

The pressure drop and boiling heat transfer characteristics of steam-water two-phase flow were studied in a small horizontal helically coiled tubing once-through steam generator. The generator was constructed of a 9-mm ID 1Cr18Ni9Ti stainless steel tube with 292-mm coil diameter and 30-mm pitch. Experiments were performed in a range of steam qualities up to 0.95, system pressure 0.5-3.5 MPa, mass flux 236-943 kg/m²s and heat flux 0-900 kW/m². A new two-phase frictional pressure drop correlation was obtained from the experimental data using Chisholm’s B-coefficient method. The boiling heat transfer was found to be dependent on both of mass flux and heat flux. This implies that both the nucleation mechanism and the convection mechanism have the same importance to forced convective boiling heat transfer in a small horizontal helically coiled tube over the full range of steam qualities (pre-critical heat flux qualities of 0.1-0.9), which is different from the situations in larger helically coiled tube where the convection mechanism dominates at qualities typically >0.1. Traditional single parameter Lockhart-Martinelli type correlations failed to satisfactorily correlate present experimental data, and in this paper a new flow boiling heat transfer correlation was proposed to better correlate the experimental data.     

Numerical modeling of a steam-assisted tubular coal gasifier

Understanding the heat and mass transfer phenomena in a coal gasifier is very useful for the assessment of gasifier performance and optimization of the design and operating parameters. In this paper, performance of an entrained flow air blown laboratory scale gasifier is numerically simulated with Fluent software. In the model, the continuous phase conservation equations are solved in an Eulerian frame, while those of particle phase are solved in a Lagrangian frame, with coupling between the two phases carried out through interactive source terms. The dispersion of the particles due to turbulence is predicted using a stochastic tracking model, in conjunction with the k–ε equations for the gas phase. The coal gasification model adopted includes devolatilization, combustion of volatiles, char combustion and gasification. The gasification performance inside the gasifier has been predicted for different air ratios as well as for different air and steam inlet temperatures. The overall temperature inside the gasifier is found to increase when the degree of air/steam pre-heating is increased, resulting in acceleration of the different reaction steps in the gasifier. The overall gasification performance indices such as carbon conversion, heating value of the exit gas and cold gas efficiency have been predicted. The predicted results show good agreement with available experimental data in literature.     

Microkinetic modelling and reaction pathway analysis of the steam reforming of ethanol over Ni/SiO2

Hydrogen production via the steam reforming of biomass-derived ethanol is a promising environmental alternative to the use of fossil fuels and a means of clean power generation. A microkinetic modelling study of ethanol steam reforming (ESR) on Nickel is presented for the first time and validated with minimal parameter fitting against experimental data collected over a Ni/SiO₂ catalyst. The thermodynamically consistent model utilises Transition State Theory and the UBI-QEP method for the determination of kinetic parameters and is able to describe correctly experimental trends across a wide range of conditions. The kinetically controlling reaction steps are predicted to occur in the dehydrogenation pathway of ethanol, with the latter found to proceed primarily via the formation of 1-hydroxyethyl. C-C bond cleavage is predicted to take place at the ketene intermediate leading to the formation of CH₂ and CO surface species. The latter intermediates proceed to react according to methane steam reforming and water-gas shift pathways that are enhanced by the presence of water derived OH species. The experimentally observed negative reaction order for water is explained by the model predictions via surface saturation effects of adsorbed water species. The model results highlight a possible distinction between ethanol decomposition pathways as predicted by DFT calculations on Ni close-packed surfaces and ethanol steam reforming pathways at the broad range of experimental conditions considered.     

The behaviour of ferritic weldments in thick section 12Cr12Mo14V pipe at elevated temperature

A major collaborative research programme is being carried out within the CEGB to examine the correlation between data, produced from a range of test methods, which are currently used in the design of welded steam pipes. In the part of the programme reported here, the elastic and creep deformation occurring in low alloy ferritic steel pipe-to-pipe weldments has been studied in pressure vessel experiments conducted at 565°C and 455 bar internal steam pressure. The welds were made in $\text{1}\text{2}\text{Cr}\text{1}\text{2}\text{Mo}\text{1}\text{4}\text{V}$ parent pipe using mild steel and low alloy 1CrMo, 2CrMo and $\text{1}\text{2}\text{CrMoV}$ weld metals. All the weldments were post-weld heat treated for 3 h at 700°C prior to testing. In addition, the weldments, represented as parent material, heat affected zone and weld metal, have been analysed to determine stresses and strains using a finite element three-material model.The main features of the macro- and micro-structures of the four weldments are briefly described. Results are then presented for the elastic and creep deformations observed in both the hoop and axial directions in the weldments. The experimental creep strain data are then used as a basis for calculating the stationary state stresses present on the surface of the weldments. The surface stationary state stress distribution and corresponding steady state strain rates, determined using the finite element model, are then presented.The pressure vessel experimental results and the data from the finite element analysis are discussed in terms of the hoop and axial deformation in the weldments. An assessment is then made of the correlation between the results from the experimental and analytical approaches. Finally, the practical implications of the present results are considered with respect to the design of operating plant.     

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.     

Development of a new drying correlation for practical applications

This paper deals with the development of a new Biot number–drying coefficient (Bi–S) correlation. The developed correlation is used to determine the moisture transfer parameters in terms of moisture diffusivity and moisture transfer coefficient involved in the solids drying process. In the development of this correlation, a large number of experimental data taken from various sources in the literature are employed. In order to verify the validity of the present correlation, three sets of experimental moisture content variations for three different products such as potato, apple and yam are compared with the moisture profiles calculated using the correlations results and a good agreement is found. Thus, it is believed that the developed correlation will be helpful to design engineers and workers in the drying industries, in calculating the parameters affecting the drying process in a simple and accurate manner and optimizing the process. Copyright © 2002 John Wiley & Sons, Ltd.