Prediction Of Pressure Drop Research Articles

Direct-coupled desorption for small capacity ammonia-water absorption systems

An investigation of direct gas-coupled desorption for small capacity ammonia-water absorption is presented. Some applications favor or require the use of direct-coupling of the heat source for desorption; therefore, a systematic treatment of this topic is needed for the optimal design of small-capacity absorption systems. Gas-coupled desorption is accomplished through diabatic distillation, and an optimal gas side geometry is established. Gas side optimization considers pressure drop minimization as well as geometric constraints such as column diameter and number of gas tubes. A heat and mass transfer model is developed and validated with experiments. Excellent internal vapor purification is achieved and the results agree well with the heat transfer and pressure drop predictions. These results demonstrate the applicability of direct-coupled desorption to small-capacity ammonia-water absorption systems. A comparative assessment with indirect-coupled desorption components is also made.

Two-Phase Flow Pressure Drop in PEM Fuel Cell Flow Channels, Model Comparison and Improvement

Proton exchange membrane (PEM) fuel cell liquid water management remains a topic of research as these technologies continue to penetrate commercial markets. Two-phase flow pressure drop may be considered an in-situ diagnostic tool that can reveal the amount of liquid water accumulating in a reactant flow channel. While the topic of two-phase flow has been studied extensively, having a reliable two-phase flow pressure drop model that can accurately predict the pressure drop in PEM fuel cell flow channels is still an issue. In this study, in-situ and ex-situ two-phase flow pressure drops in PEM fuel cell flow channels are measured and compared with existing models. The objectives of the current study are to compare experimentally measured two-phase flow pressure drops with existing models as well as to improve the two-phase flow pressure drop model for an accurate pressure drop prediction for the application of PEM fuel cell. In-situ and ex-situ experiments were conducted and analyzed for this purpose. The models focused on in this work are all based on experimentally determined two-phase flow pressure drop for channel hydraulic diameters ranging from 0.15 mm to 12 mm. These models were developed for various applications and fluid/gas combinations. For this study’s ex-situ experiments, liquid-gas two-phase flow pressure drops were measured over 20 cm of a 2 mm x 1 mm flow channel machined from an aluminum plate. Water was injected through a Toray (TGP-060) gas diffusion layer (GDL) and emerged on its surface within the flow channel supplied with air flow. Fig. 1 compares 108 experimentally measured ex-situ two-phase flow pressure drops with nine two-phase flow pressure drop models. Figures a-g are based on the separated flow model and figures h-i are based on the homogeneous equilibrium model. The general trend observed in Fig. 1 suggests that although separated flow models outperform homogeneous equilibrium models, they mostly under-predict the two-phase flow pressure drop, especially at lower pressure drops. The seven separated flow model shown in Fig. 1a-g are further compared with each other by defining the mean absolute error (MAE), shown by λ in Fig. 1, (insert Equation 1 from JPG file) In addition, ω, θ, and ε are defined as the percentage of data points predicted within ±10%, ±30%, and ±50%, respectively. It can be observed from Fig. 1 that the model proposed by Mishima and Hibiki [2], shown in Fig. 1c, reflects the best prediction capability with the lowest MAE value. The MAE was further studied at different mass flow qualities and superficial air velocities as shown in Fig. 2. The numbers shown in parentheses indicate the number of experiment runs considered to calculate the MAE at each mass flow quality or superficial air velocity. Fig 2a shows the MAE at different mass flow qualities for each of the separated flow models. Other than mass flow qualities x = 0.87 and x = 0.97, the model proposed by Mishima and Hibiki [2] resulted in the lowest MAE compared to the other six models. However, the model proposed by Saisorn and Wongwises [1] showed a smaller MAE in these two mass flow qualities. Fig. 2b shows the MAE calculated at different superficial air velocities and air flow rates in the flow channel. For superficial air velocities of less than 2 m/s, the model proposed by Saisorn showed a superior performance. However, for superficial air velocities greater than 2 m/s, Mishima and Hibiki's model [2] outperformed. In addition to ex-situ results, experimental in-situ liquid-gas two-phase flow pressure drops are also being measured in an operating PEM fuel cell as shown in Fig. 3. The PEM fuel cell used in this study has seven parallel flow channels, each with 1 mm x 1 mm cross section, machined through stainless steel bipolar plates backed with clear polycarbonate sheets to visualize water. Two high-precision pressure transducers measure pressure drop along 80 mm of two flow channels. In addition to pressure drop measurement, liquid water accumulation and transport with the flow channels is also recorded with a CCD camera mounted directly above the cathode. A combination of ex-situ and in-situ results will cover a large range of liquid/gas flow rates which will be useful for model validation.

Validation of CTF pressure drop and void predictions for the NUPEC BWR database

Abstract A quantified validation of CTF pressure drop, equilibrium quality, and void fraction predictions is performed using the Japanese Nuclear Power Engineering Corporation boiling water reactor database. Four quantities of interest are compared between the experiments and the code predictions: pressure drop, average exit equilibrium quality, average exit void fraction, and subchannel exit void fraction. These four quantities of interest have root-mean-squared errors of 0.124, 0.005, 0.065, and 0.089, respectively. Pressure drop predictions are generally underpredicted for single phase cases and overpredicted for two phase cases. The equilibrium quality predictions are mostly within 0.01 of the designed experimental values, which indicates proper energy conservation. The void fraction results tend to be overpredicted by about 0.06, which is attributed to the interfacial modeling in the code. By splitting the subchannels into different groups, it is shown that those near unheated surfaces are the least accurately modeled, especially for cases that have a high concentration of unheated surfaces. The results are consistent with past validation analyses using a variety of subchannel codes. Unlike past studies with CTF, this work incorporates all 69 pressure drop experiments and 392 steady state void experiments from the database. A new method for quantification of asymmetries is proposed and applied, but the interpretation of the results depends on the definition of the measurement error.

Significance of gas-liquid interfaces for two-phase flows in micro-channels

Investigation was designed to clarify the difference in resistance for single-phase and two-phase flows in constricted capillaries, to define the effective pore throat, and at what pore size of a micro-channel the capillary resistance to gas-liquid interfaces starts taking effect. The experimental results indicate that the pressure drop profile for two-phase flows is significantly different from that for single-phase flows in constricted capillaries. For the same capillary, the resistance to a single-phase flow keeps constant after initial increase due to the fluid acceleration, but for two-phase flows, the resistance increases sharply when the two-phase interface enters the channel with a diameter smaller than a certain size. We defined this ‘certain size’ as the ‘effective pore throat’. For a flow channel with a diameter larger than the effective pore throat, the capillary resistance to the interface is almost zero. When the flow channel has a size less than the effective pore throat, capillary force to two-phase interfaces takes effect, and the resistance to two-phase flows increases suddenly. The ‘effective pore throat’ is a critical point to determine whether the capillary resistance to the interface takes effect in a confined flow channel. It is between 150 and 650 µm depending on capillary tip size and is very different from the geometrical throat of a channel. To predict pressure drops for a two-phase flow in constricted capillaries, a new equation is derived based on Darcy-Weisbach equation to calculate the frictional pressure drop in constricted capillaries. Young-Laplace equation is used to calculate the capillary pressure drop. The results show that after the interface enters the channel with a diameter less than the ‘effective pore throat’, the combination of our newly derived equation and Young-Laplace equation can predict the pressure drop with a deviation of ±20%. However, theories in literature cannot explain the sudden increase in the pressure drop and simulations cannot predict the effective pore throat.

Modeling of pressure drop in two-phase flow of mono-sized spherical particle beds

To reduce the uncertainty in predicting pressure drop for two-phase flow through spherical particle beds, especially composed of small-sized particles that adversely affect the cooling, an experimental study was performed. A series of experiments were performed to measure the pressure drop of upward two-phase flow through well-packed spherical particle beds with 2, 3.5, and 5 mm diameter particles under isothermal conditions varying the gas flow rates with no water inflow at the bottom. Based on the experimental results and the results of our previous study related to the modification of Ergun constants, a new improved model for prediction of the two-phase flow pressure drop through porous media was proposed. The adequacy of the proposed model was verified by comparison with various existing experimental data for particle diameters of 3.18–6.35 mm and the superficial air velocity of 0–0.8 m/s.

Study and characterization of gas-liquid slug flow in an annular duct, using high speed video camera, wire-mesh sensor and PIV

An experimental study is presented on air-water two-phase flow in a 10.5-m-long annular duct with an external diameter of 155 mm and an inner diameter of 60 mm. Particle image velocimetry (PIV) is applied to obtain instantaneous velocity measurements of the flow field. The annular duct inclination is of 5° from the horizontal. A CCD camera (2448 pixel × 2050 pixel, 5 Mpixel,12-bit) was positioned in the test section to record the seeding particles. The illumination was provided by a double pulsed PIV laser (Nd:YAG, frequency doubled to 532 nm) with a measured pulse intensity of 70 mJ/pulse. It was used at 15 Hz (resulting in the independence of the velocity samples). Based on the instantaneous local velocities, Probability Density Functions (PDF) and mean velocities are calculated. Two-phase flow arranged in the slug-flow pattern is observed, at superficial velocities of jw = 0.154 m/s and ja = 0.044 m/s. 3000 samples per case are processed using cross-correlation procedure, for the PIV analysis. A home-made Annular Wire-Mesh Sensor (AWMS) was applied to obtain time-signal-measured void-fraction data as a function of the electrical permittivity. The average bubble velocity is estimated by two techniques, (i) High-Speed Video Recording and (ii) Particle Image Velocimetry (PIV) together with the AWMS. A comparison of the two techniques is presented. A new technique based on AWMS for the measurement of bubble-passage frequency, bubble length and slug length is proposed. It was observed: (i) deceleration of the water phase beneath the bubble as it passes, shown by velocity profiles at different bubble locations, (ii) an increase in bubble velocity as air superficial velocity is increased and (iii) the complexity of the flow pattern, shown in details by AWMS cross-sectional images. The new experimental results are of great value for comparison with CFD models and for the development of more refined pressure-drop prediction tools in two-phase annular-duct flows.

Assessment of the CUPID Code for Bubbly Flows in Horizontal Pipes

Two-phase flow in a horizontal pipe has a pronounced feature; that is, two-phase-flow parameters are highly nonsymmetric because gravity is perpendicular to the mean flow direction. Thus, three-dimensional analysis is necessary for the accurate prediction of two-phase flow in a horizontal pipe, such as the hot leg and cold leg of a pressurized water reactor and the pressure tubes in a CANDU reactor. In this study, we simulated bubbly flows in horizontal pipes using the CUPID code, which adopts a two-fluid, three-field model for two-phase flow. In the preliminary calculations, it was found that the particle-averaged two-fluid momentum equation, rather than the standard two-fluid momentum equation, predicts a physically reasonable slip ratio and nondrag forces, except turbulent dispersion forces have negligible effects on the radial void distribution when the particle-averaged two-fluid momentum equation is used. Based on the results, we selected the physical models and computational mesh for subsequent code assessment using various bubbly flow experiments in horizontal pipes. The turbulent dispersion force model was improved to take into account the large void fraction change at the top. The results of the code assessment show good predictions for the axial pressure drop, liquid velocity, and turbulent kinetic energy profile and predict reasonably well the effects of jl and jg on two-phase-flow parameters. However, additional studies are needed for more accurate prediction of the nonsymmetric distribution of gas velocity and turbulent kinetic energy.

Pressure drop of two-phase liquid-liquid slug flow in square microchannels

Networks of microdevices can be used to form, sort, split and recombine droplets by varying the fluidic resistance of the channels. To facilitate design of such systems we propose two models to calculate pressure drop of liquid-liquid slug flow in square microchannels. By approximating a droplet surrounded by liquid film as annular flow, the moving film model includes the velocity profile in the lubricating layer. In the no-film model, the presence of liquid film is neglected. Pressure drop measurements of water-toluene and water-silicone oil slug flow generated in glass/silicon devices of 200 and 400 μm width serve to validate these two models. We found that the droplet viscosity influences the applicability of the models. Good agreement is obtained for water-toluene slug flow, with the average error of 15–20% between the measured and calculated values for both models, proving that the presence of the lubricating film may be neglected for flows with similar viscosities of both phases. On the contrary, both predictions agree poorly with experiments for silicon oil-water flow which we attribute to the lower than expected liquid film thickness around the silicon oil droplets. Therefore we use the moving film model to estimate the thickness of the lubricating layer which we find to lie between 0.5% and 0.75% of the channel width, lower than the assumed 2%. Finally we compare the performance of our models against two correlations adapted from literature. We thus demonstrate that our approach allows reliable pressure drop prediction for liquids with similar viscosities and delivers important information on flow hydrodynamics.

A re-evaluation of design equations for the established flow region of vertical dilute-phase pneumatic conveyors

An analysis of data sets from the literature was completed for particle velocities of granular material in vertical, dilute-phase pneumatic conveyors. The generally accepted equation of motion used to describe such velocity data incorporates the solids friction factor, a variable term based on the additional pressure drop due to solids. The analysis determines that rather being a variable, the term is a constant related to the physical properties of the particle that influence its bouncing behaviour as it progresses along the pipeline. In addition, the analysis reveals that particle drag coefficients determined from the particle velocity data differ significantly from values taken from the standard drag coefficient curve. This observation was confirmed by drag coefficient measurements reported in the literature and made using particle-elutriating equipment. The drag coefficients from the pneumatic conveying experiments and the test equipment were determined under turbulent conditions, which is considered to account for the difference in values from the standard curve determined under quiescent conditions. Relationships are presented that predict the turbulence-influenced drag coefficients and the particle velocity data with good accuracy. These relationships are used to predict pressure drops for two data sets presented with the particle velocity data. The single-term pressure drop equation is used and predicts with good accuracy as well as producing the trough-shaped curve characteristic of the measured pressure drops.

A simple methodology to incorporate flashing and variation of thermophysical properties for flow boiling pressure drop in a microchannel

This paper proposes a simple approach to model the complex interplay among the various thermophysical phenomena occurring in flow boiling. In order to assess the need for such a model, flow boiling pressure drop of FC-72 in a single trapezoidal microchannel with a hydraulic diameter of 111 μm is measured by varying heat flux and mass flux. The pressure drop obtained is in the range of 10–45 kPa, which does not compare well with the existing models based on constant properties. Therefore, a new predictive approach is developed for meticulous evaluation of pressure drop across a microchannel with flow boiling. It uses the separated flow model with evaluation of thermophysical properties at local pressure, thus incorporating the effect of flashing on thermodynamic quality, and the effect of heat flux on the two-phase multiplier. Relations based on a modified form of Clausius-Clapeyron equation are employed for evaluation of local thermophysical properties for fluids. This methodology is combined with different empirical correlations from the literature to predict pressure drop. The proposed predictive methodology, comprising close form equations, is physically sound and yet easy to implement, and reproduces large pressure drop experimental data better than the existing methods.

Experimental investigation of the frictional pressure drop of steam-water two-phase flow in AP1000 surge line

The Steam-Water Co-Current Flow (SWCOCF) in the AP1000 Pressurizer Surge Line (PZR SL) are important phenomena during the depressurization stage of the Small Break Loss-of-Coolant Accidents (SB-LOCAs), which affect the predictions of SWCOCF pressure drop in PZR SL and safety analyses. To investigate the pressure drop characteristics of SWCOCF in the PZR SL of AP1000, a PZR SL test model made of stainless steel is designed and a test loop is also established. The test section is mainly composed of a long inclined tube with a short acrylic visual section, a whole surge line tube and a vertical section. Two experiments were conducted: the single phase water experiment and the SWCOCF experiment. The total friction factor and the full-liquid two-phase friction multiplier as well as the liquid-only two-phase friction multiplier of the PZR SL tube were obtained, separately. The research results show that: the whole surge line two-phase friction multiplier increases with the increasing of mass quality, and decreases with the increasing of pressure. Two prediction models of two-phase friction multiplier for the surge line were developed based on the Martinelli-Nelson and Lockhart-Martinelli method, respectively. The fitted full-liquid two-phase friction multiplier model and the liquid-only two-phase friction multiplier model can predict the two-phase friction pressure drop in PZR SL very well. This paper may provide contributions to the design and safety analysis of AP1000 surge line.

Droplet flux measurements in two-phase, low liquid loading, horizontal pipe flow using a high-density gas

Entrained fraction is one of the essential parameters needed for the prediction of frictional pressure drop and efficient design of downstream facilities. In the literature, there are very few entrained fraction datasets focused on low liquid loading flows, and even less datasets obtained from high pressure systems. This paper provides experimental entrained fraction data for low liquid loading gas-oil flows in a 100-mm diameter horizontal PVC and carbon steel pipe. High-density sulphur hexafluoride (SF6) gas and Exxsol D60 oil are used as the fluid phases to mimic actual field conditions. Superficial gas and oil velocities are varied between 5 m/s to 15 m/s and 1 mm/s to 7 mm/s, respectively. Local drop flux along the vertical diameter of the pipe cross-section is measured using the isokinetic sampling approach. Effects of several parameters such as system pressure (gas density), gas and liquid flow rates, and pipe material on the entrained fraction are studied. As expected, the entrained fraction increases with either the gas density or the gas velocity. The effect of liquid flow rate on the entrainment is not obvious; results show either a constant level or a decrease in entrainment with an increase in liquid flow rate, depending on the gas flow rate. The measurements conducted using two different pipe materials (PVC and carbon steel) demonstrated that surface material can cause significant differences in the entrainment. Therefore, the near-wall film behavior will have considerable influence on the entrainment mechanism, especially when the thickness of the liquid film becomes very thin. Finally, this paper also provides an evaluation of the existing correlations and/or models available in the literature against the acquired entrainment data using the high-density gas test facility.

Effect of geometrical parameters on slug behaviour and two phase pressure drop in microchannel T-junctions

Geometric parameters of a microchannel such as cross-sectional area, shape and aspect ratio are important factors in determining the two phase flow characteristics. Two phase flow analyses were carried out experimentally for microchannel T-junction geometries at low values of capillary number. Three hydraulic diameters were used, namely 250, 400 and 550 μm, while the aspect ratio was varied between 0.1 to 1. Experiments were performed for the gas volume flow rate ranging from 2 to 30 ml/min while the liquid volume flow rate ranged between 0.1 to 10 ml/min. Slug length was estimated from the processing of high speed images of slug flow and pressure drop was simultaneously recorded. For constant mass flux in rectangular channels, an increase in the aspect ratio leads to an entrapment of continuous phase at the corner. This influences the transport characteristic of such channels. The effects of aspect ratio on slug length and pressure drop are reported. A simplified scaling model based on the geometric parameters of microchannels as well as gas and liquid flux is proposed which agrees reasonably well (within ±15%) with the present experimental data as well as data available in literature. A flow based pressure drop prediction model was developed which agrees well (within ±10%) with the experimentally measured two phase pressure drop. It is believed that a priori information on slug length and pressure drop in a given flow through a microchannel will help to design the flowing system better.

Effect of local thermophysical properties and flashing on flow boiling pressure drop in microchannels

Pressure drop in microchannels can be considerably high, which can cause significant changes in thermophysical properties. Thus, the existing pressure drop modelling approach for flow boiling in microchannels, which neglects the effects of property gradients and flashing, suffers from large errors in case of high pressure drop. To mitigate this, a new modelling approach has been developed for comprehensive evaluation of pressure drop along a microchannel with flow boiling. It is based on the separated flow model, incorporating the evaluation of thermophysical properties at local pressure, the effect of flashing on thermodynamic quality, and the effect of heat flux on the two-phase multiplier. Relations based on the Clausius–Clapeyron Equation were employed for evaluation of local thermophysical properties. This approach was applied along with different empirical correlations from the literature to predict flow boiling pressure drop. Experiments were conducted on flow boiling of DI water in a single microchannel of hydraulic diameter 111 µm, with mass fluxes of 205–410 kg/ m2s and heat fluxes of 7.5–19.5 W/cm2, and the pressure drop recorded was 10–36 kPa. It was found that the new modelling approach improves the accuracy of pressure drop predictions significantly in case of high pressure drop.

Interfacial area transport models for horizontal air-water bubbly flow in different pipe sizes

The current work seeks to develop the interfacial area transport models for horizontal bubbly flow applicable to various pipe sizes. A steady-state one-dimensional, one-group interfacial area transport equation (IATE) for horizontal adiabatic air-water bubbly flow is presented. The models discussed include: (a) frictional pressure drop prediction based on Lockhart–Martinelli approach; (b) drift-flux based closure relations for void-weighted bubble velocity and void fraction; (c) bubble interaction mechanisms; and (d) local void fraction reconstruction to calculate covariance parameters associated with asymmetric bubble distribution in horizontal bubbly flow. To develop these models, experiments are performed to establish local databases in bubbly flow using the four-sensor conductivity probe in horizontal test facilities with three different inner diameters (38.1 mm, 50.8 mm, and 101.6 mm). In total, 23 test conditions with superficial liquid and gas velocities in the ranges of 3.00–6.00 m/s and 0.08–1.00 m/s, respectively, are employed in the current work. The range of void fraction for the established database is 0.017–0.193. It is demonstrated that, the void weighted bubbly velocity (<<vg>>), void fraction (<α>), and frictional pressure loss can be predicted very well with an averaged percent difference of ±4.8%, ±4.7%, and ±2.1%, respectively. The covariance parameters can be predicted generally within ±30% using the current approach for void fraction reconstruction. As a result, the IATE can predict the measured interfacial area concentration with an averaged percent difference of ±5.9%, except for the test conditions with large bubbles generated as flow develops. Meanwhile, it is found that decreasing liquid velocity decreases the contributions to the total change of interfacial area concentration by random collision induced bubble coalescence, and turbulent impact induced bubble breakup.

Pressure drop modelling in sand filters in micro-irrigation using gradient boosted regression trees

Filters are essential for guaranteeing the good performance of microirrigation systems. Pressure losses across filters should be known for the proper design and management of this irrigation equipment. Pressure losses produced by filtering media in sand filters can be computed using Ergun or Kozeny–Karman equations, which require knowledge, among other parameters, of the sphericity of the filter medium. As this parameter is not easy to determine, it is useful to explore the performance of alternative computing methods that can avoid requiring knowledge of sphericity. In this paper, taking as starting point the nonparametric machine learning approach known as the gradient boosted regression tree (GBRT) approach and hybridising it with the differential evolution (DE) technique, the pressure drop in sand filters used in microirrigation has been modelled. For different filtering materials such as modified glass, crushed glass, silica sand and glass microspheres, experimental data of pressure drop for velocities between 0.004 and 0.025 m s−1 was collected and the model built. The results demonstrated that DE–GBRT–based model was able to accurately predict pressure drop. The model also allowed ranking of the importance of the independent variables examined within the model. Taking into account this ranking, and using only the main variables, a simplified method with an improved coefficient of determination was constructed.

Assessment of Forces in Intradermal Injection Devices: Hydrodynamic Versus Human Factors

The force that has to be exerted on the plunger for administering a given amount of fluid in a given time, has an important influence on comfort for the subject and usability for the administrator in intradermal drug delivery. The purpose of this study is to model those forces that are subject-independent, by linking needle and syringe geometry to the force required for ejecting a given fluid at a given ejection rate. We extend the well-known Hagen-Poiseuille formula to predict pressure drop induced by a fluid passing through a cylindrical body. The model investigates the relation between the pressure drop in needles and the theoretic Hagen-Poiseuille prediction and is validated in fifteen needles from 26G up to 33G suited for intradermal drug delivery. We also provide a method to assess forces exerted by operators in real world conditions. The model is highly linear in each individual needle with R-square values ranging from 75% up to 99.9%. Ten out of fifteen needles exhibit R-square values above 99%. A proof-of-concept for force assessment is provided by logging forces in operators in real life conditions. The force assessment method and the model can be used to pinpoint needle geometry for intradermal injection devices, tuning comfort for subjects and usability for operators.

Prediction of heat transfer, pressure drop and entropy generation in shell and helically coiled finned tube heat exchangers

In this study, the heat transfer, pressure drop and entropy generation in shell and helically coiled tube heat exchangers, are numerically investigated. The heat transfer rate is intensified by installing the annular fins on the outer surface of the coiled tube. The fluid of coil side is the hot water which flows through the coiled tube at temperature of 70°C and velocity of 1m/s. While, on the shell side, the cooling dry air flows through the shell side at temperature of 10°C and velocity of 1–4m/s. The height and number of the fins change, as well as the velocity of the shell side fluid. The main results of this study are some correlations which are suggested for the estimation of the Nusselt number and friction factor of the shell side. Furthermore, the relationship between the NTU, the entropy generation rate and the thermal effectiveness are obtained. The model is validated by comparing the numerical values of the Nusselt numbers of both side and the friction factor of the coil side, with the predicted values based on the previous empirical correlations. In the last section of this study; as a guide for the designer of these types of heat exchangers; a sample problem is defined and solved.

A layered model for inclined pipe flow of settling slurry

The paper deals with mathematical and physical modelling of flow of partially-stratified settling slurry in inclined pipes. Experimental results are presented of flows of aqueous slurries of four fractions of sand and gravel in two laboratory loops of different pipe diameters. They show a considerable variation in pressure drop and distribution of solids with the pipe slope. The degree of flow stratification and frictional pressure drop decrease with the increasing angle of inclination in the ascending pipe while the opposite applies in the descending pipe. A predictive mathematical model is presented which is based on a description of a layered structure of partially stratified slurry flow and takes flow inclination into account. The experimentally observed effects of pipe inclination are well reproduced by model predictions. Predicted pressure drops and solids distributions are in a very reasonable agreement with the experimental results and indicate suitability of the model for engineering practise.

Prediction and optimization of condensation heat transfer coefficients and pressure drops of R134a inside an inclined smooth tube

In this study, an adaptive neuro-fuzzy inference system (ANFIS) is proposed for the prediction and optimization of condensation heat transfer coefficient and pressure drops along an inclined smooth tube. The performance of three ANFIS structure identification methods, grid partitioning (GP), a subtractive clustering method (SCM), and fuzzy C-means (FCM) clustering, were examined. For training the proposed ANFIS model, an in-house experimental database was utilised. Three statistical criteria, the mean absolute error (MAE), mean relative error and root mean square error were used to evaluate the accuracy of each method. The results indicate that the GP structure identification method has the lowest number of training errors for both the pressure drop, i.e., MAE = 6.4%, and condensation heat transfer coefficient, i.e., MAE = 2.3%, models. In addition to the ANFIS model, numerical simulations were also conducted to assess the accuracy and capability of the proposed model. The comparison shows that the CFD simulation results have better accuracy for the specified operating conditions. However, the errors of both the CFD and ANFIS methods were within the uncertainties of the experimental data. It was therefore concluded that the ANFIS model is useful in obtaining faster and reliable results. Finally, the optimization results showed a possible optimum point at a mass flux of 100 kg/m2 s, saturation temperature of 36.2 °C, downward inclination angle of −15° and a vapour quality of 0.48. At this condition the pressure drop is almost zero.