Pressure Drop Model Research Articles

A FRACTAL PRESSURE DROP MODEL FOR CABLE-IN-CONDUIT CONDUCTORS BASED ON POROUS MEDIA ANALOGY

Assessment of the pressure drop that occurs in cable-in-conduit conductors (CICCs) requires a reliable predictive model. In this paper, a fractal model to predict the pressure drop of helium flows in CICCs is proposed based on the porous media analogy and fractal theory. A fractal friction factor correlation is also derived using the proposed pressure drop model. The good agreement between the predictions and the experimental data for conductors with [Formula: see text] verifies the validity of both the fractal pressure drop model and the friction factor correlation for such configuration conductors. The fractal correlation indicates that the friction factor of the cable bundle in a CICC is related not only to the void fraction but also to the average hydraulic diameter, the tortuosity of the fluid flow paths, the maximum pore size and the fractal dimension of the cable cross-section. This theoretical correlation does not contain any fitting constants and each parameter has a clear physical meaning.

An improved reduced-order model for pressure drop across arterial stenoses.

Quantification of pressure drop across stenotic arteries is a major element in the functional assessment of occlusive arterial disease. Accurate estimation of the pressure drop with a numerical model allows the calculation of Fractional Flow Reserve (FFR), which is a haemodynamic index employed for guiding coronary revascularisation. Its non-invasive evaluation would contribute to safer and cost-effective diseases management. In this work, we propose a new formulation of a reduced-order model of trans-stenotic pressure drop, based on a consistent theoretical analysis of the Navier-Stokes equation. The new formulation features a novel term that characterises the contribution of turbulence effect to pressure loss. Results from three-dimensional computational fluid dynamics (CFD) showed that the proposed model produces predictions that are significantly more accurate than the existing reduced-order models, for large and small symmetric and eccentric stenoses, covering mild to severe area reductions. FFR calculations based on the proposed model produced zero classification error for three classes comprising positive (≤ 0.75), negative (≥ 0.8) and intermediate (0.75 - 0.8) classes.

Recent advances in condensation heat transfer in mini and micro channels: A comprehensive review

Condensation in mini and microchannels has been investigated to improve utilization of thermal energy and heat transfer in various disciplines and applications. The high heat transfer coefficients accomplished by two-phase condensing flows in microchannels has prompted the use of compact heat transfer equipment and utilization of environmentally friendly heat transfer fluids. This work presents a comprehensive review of condensation studies in microchannels that have been carried out in the last two decades. The review includes experimental investigations, theoretical predictive models of two-phase heat transfer coefficients and pressure drop, as well as computational predictions of condensation in mini and microchannels. A wide range of operating conditions, channel geometries, heat transfer fluids, methods of investigation, and advancements in condensation heat transfer in mini and microchannels are presented. As condensation at the microscale presents a promising path towards heat transfer enhancement for numerous applications, this paper is intended to be a reference for future research targeting advancements in mini and microchannel condensation.

Hydrodynamics of Liquid-Liquid Flows in Micro Channels and Its Influence on Transport Properties: A Review

Hydrodynamics plays a major role in transport of heat and mass transfer in microchannels. This includes flow patterns and flow regimes in which the micro-channels are operated. The flow patterns have a major impact the transport properties. Another important aspect is the pressure drop in micro-channels. In the present review, the experimental and Computational Fluid Dynamics (CFD) studies covering all the above aspects have been covered. The effect of geometrical parameters like shape of channel, channel size, material of construction of channels; operating parameters like flow velocity, flow ratio and fluid properties have been presented and analyzed. Experimental and analytical work of different pressure drop models has also been presented. All the literature related to influence of flow patterns on transport properties like volumetric mass transfer coefficients (VMTC) and heat transfer coefficients (HTC) have been presented and analyzed. It is found that most works in Liquid-Liquid Extraction (LLE) systems have been carried out in slug flow and T-junctions. Models for coupled systems of flow and mass transfer have been presented and works carried out for different coupled systems have been listed. CFD simulations match experimental results within 20% deviations in quantitative and qualitative predictions of flow phenomena for most research articles referred in this review. There is a disparity in prediction of a generalized regime map and a generalized regime map for prediction of flow patterns for various systems would need the help of Artificial Intelligence.

Using Symbolic Regression Models to Predict the Pressure Loss of Non-Newtonian Polymer-Melt Flows through Melt-Filtration Systems with Woven Screens

Abstract When selecting a melt-filtration system, the initial pressure drop is a critical parameter. We used heuristic optimization algorithms to develop general analytical equations for estimating the dimensionless pressure loss of square and Dutch woven screens in polymer processing and recycling. We present a mathematical description – without the need for further numerical methods – of the dimensionless pressure loss of non-Newtonian polymer melt-flows through woven screens. Applying the theory of similarity, we first simplified, and then transformed into dimensionless form, the governing equations. By varying the characteristic independent dimensionless influencing parameters, we created a comprehensive parameter set. For each design point, the nonlinear governing equations were solved numerically. We subsequently applied symbolic regression based on genetic programming to develop models for the dimensionless pressure drop. Finally, we validated our models against experiments using both virgin and slightly contaminated in-house and post-industrial recycling materials. Our regression models predict the experimental data accurately, yielding a mean relative error of MRE = 13.7%. Our modeling approach, the accuracy of which we have proven, allows fast and stable prediction of the initial pressure drop of polymer-melt flows through square woven and Dutch weave screens, rendering further numerical simulations unnecessary.

Experimental Study on the Ventilation Resistance Characteristics of Paddy Grain Layer Modelled with Response Surface Methodology

The ventilation resistance of air flow through rice grain layers is one of the key parameters affecting drying uniformity as well as the energy consumption of the drying process. In order to reveal the variation of characteristics of the ventilation resistance with paddy grain moisture content, the air velocity and the bed layer depth are needed. A second order model was fitted to pressure drop using the response surface methodology and the results are compared with those of the Ergun model. The results showed that the pressure drop increases with the increase of paddy grain moisture content, air velocity and the bed layer depth, and the interactions between the air velocity and the bed layer depth have the most significant influence on the pressure drop. Moreover, a second-order polynomial pressure drop model based on RSM was established and compared with the Ergun model. The results showed that the pressure drop model established by RSM is similar to that of the Ergun model.

Wet gas pressure drop across multi-orifice plate in horizontal pipe in low gas-phase Froude number region

In comparison with the traditional single-orifice plate, as a throttling element, multi-orifice plates exhibit a low pressure loss, low flow-induced noise, and stable pressure difference response, which are advantageous in wet gas measurements. In this study, the pressure drop of wet gas across two multi-orifice plates (one with circular holes and another with slotted holes) in a horizontal pipe was experimentally investigated in the stratified flow region and intermittent flow region. The two regions are different from the flow pattern but can be collectively referred to as a low gas-phase Froude number (FrG) region. At the same porosity, there is no significant difference between circular and slotted multi-orifice plates in pressure drop characteristics. As the flow pattern transitions from stratified to intermittent, ΦG increases considerably with a decrease in FrG and an increase in liquid-phase Froude number (FrL); this differs from the well-known wet gas pressure drop characteristics of orifice plates as obtained from common wet gas with annular-mist flow. The prediction accuracies of the available pressure drop models for the gas–liquid flow across the orifice plate were analyzed based on the experimental results. The findings indicate that none of the models can provide accurate predictions in the two low-FrG subregions simultaneously. With the modified models, in which FrG and FrL are correlated simultaneously, new correlations are proposed for the low-FrG region. Among these models, the modified Murdock model exhibits the best prediction accuracies, i.e., 15% and 6%, when the upstream is in the flow pattern transition region and stratified flow region, respectively. These results elucidate the mechanism and prediction methods for the application of multi-orifice plates to wet gases as a measuring sensor.

Experimentally investigating bubble dynamics and pressure drop for bubbly upflow in a vertical annular channel

This paper experimentally investigates the bubble characteristics for a bubbly upflow in an annular channel using two-sensor probes and the high-speed camera. The measured parameters include the radial distributions of void fraction, interfacial area concentration, and bubble size. The present measured results are also compared with those from the previous work, confirming the reasonability of present data for the bubbly flow. A simplified two-phase frictional pressure-drop model is proposed to estimate the frictional pressure-drop across the annular channel for the bubbly upflow. Based on comparison with the measured data, the deviation in the two-phase frictional pressure-drop predicted by this simplified model is within 40%. In addition to providing the understanding of bubble dynamics in an annular geometry, the present measured data can also help develop and assess the CFD two-phase model.

Pressure drop characteristics of airlift in transporting particles

In this paper, the airlift process is divided into liquid-solid two-phase section and gas-liquid-solid three-phase section with the air inlet as the interface, and the corresponding pressure drop models are established based on the energy conservation and the phase hold-up equations. The results show that the pressure drop decreases rapidly first and then tends to be constant with the increase of pipe diameter in both two-phase and three-phase sections. The pressure drop in the two-phase section is less affected by the air superficial velocity and the immersion rate, while the pressure drop in the three-phase section decreases with the increase of the air superficial velocity and increases with the increase of the immersion rate. In addition, whether in the two-phase or three-phase sections, the measured pressure drop results are in good agreement with the calculated values, especially under the conditions of low air superficial velocity and high immersion rate.

Flow boiling heat transfer and two-phase flow phenomena of CO2 in macro- and micro-channel evaporators: Fundamentals, applications and engineering design

• Comprehensive review of fundamentals and applications of CO 2 flow boiling. • Analysis of flow boiling heat transfer data and physical mechanisms. • General CO 2 flow pattern maps, mechanistic model for heat transfer and pressure drop. • CO 2 flow boiling and two phase flow in enhanced tubes and mechanisms. • Analysis of the oil effect on CO 2 flow boiling and two phase pressure drop. • Engineering applications of CO 2 flow boiling and two phase flow. • Discussion of CO 2 evaporator simulation and engineering design. • Future research needs in CO 2 flow boiling and potential practical applications. The paper presents a comprehensive review of fundamentals and engineering applications of CO 2 flow boiling heat transfer, flow patterns and two-phase pressure drops in macro- and micro-channel evaporators. First, distinctions of macro- and micro-channels are discussed. Second, the review addresses the extensive experimental studies on CO 2 flow boiling heat transfer and two-phase flow in macro- and micro-channels. The effects of the physical properties on flow boiling heat transfer, flow patterns and pressure drops are analysed by simulations using various physical property packages. Furthermore, analysis of the existing experimental studies of flow boiling heat transfer is presented and the physical mechanisms are discussed. Next, generalized CO 2 flow pattern map and flow pattern based mechanistic flow boiling heat transfer and two phase pressure drop models specially developed for CO 2 are discussed. New experimental database of flow boiling heat transfer and diabatic two phase frictional pressure drop have been set up to evaluate the models. Comparative results of the flow pattern map, heat transfer and pressure drop models to the experimental database are analysed. In addition, studies of CO 2 flow boiling in enhanced channels are summarized. The oil effects on the flow boiling heat transfer and two phase frictional pressure drop are analyzed and simulated as well. According to the extensive analysis, the physical mechanisms and prediction models of the CO 2 flow boiling heat transfer and two phase flow phenomena in evaportaors have been well understood. In the aspect of engineering application, comparisons of simulation results and the experimental data in the real thermal systems are discuseed. Furthermore, research need of CO 2 evaporators is discussed. Some practical design methods of CO 2 evaporators are recommended according to the analysis. Finally, the potential application of CO 2 for high heat flux cooling, thermal and power systems are also discussed. Future research needs in flow boiling heat transfer and two phase flow of CO 2 in evaporators and engineering applications are discussed and recommended according to this comprehensive review.

Two-phase flow pressure drop in PEM fuel cell flow channel bends

During the operation of a proton exchange membrane (PEM) fuel cell water is produced as a byproduct of electrochemical reactions. As the produced water passes through the porous structure of the electrodes and enters the flow channels, liquid–gas two-phase flow forms within the flow channels. If a reliable model that can accurately predict the pressure drop is available, then the two-phase flow pressure drop can be used as an in-situ diagnostic tool to quantify the water content within the flow channels. While the two-phase flow pressure drop is investigated for straight sections of PEM fuel cell flow channels, few attention has been paid to evaluate the pressure drop across flow channel bends. In this study, liquid–gas two-phase flow across a flow channel bend is investigated with an ex-situ approach. A 90∘ flow channel bend was fabricated across a channel with a hydraulic diameter of 1 mm. Experiments were conducted by supplying air and hydrogen as the gas phase and injecting liquid water into the flow channel in order to represent the two-phase flow condition in the cathode and anode flow channels, respectively. The two-phase flow across the bend was visualized with a CCD camera and the pressure drop values were measured for the PEM fuel cell flow conditions. A comparison between the experimental data and predictions from some of the existing models prompted the need for a model that can accurately predict the two-phase flow pressure drop across PEM fuel cell flow channel bends. In this study, a new model to predict the frictional two-phase flow pressure drop across flow channel bends was developed based on the separated flow model. Because the two-phase flow in PEM fuel cell flow channels is dominated by the gas phase, the new model incorporated the gas minor loss which was defined as the pressure drop caused by the flow channel bend. In order to predict the gas minor loss, a correlation for the loss coefficient was obtained based on the gas single-phase pressure drop. In addition, a correlation was proposed for the C parameter as the two-phase flow across the flow channel bend featured an enhanced interaction between the two phases of liquid and gas. Results indicated that the proposed two-phase flow pressure drop model along with the proposed C correlation were able to predict the pressure drop with mean absolute error values of 7.74% for air–water runs and 10.77% for hydrogen–water runs.

Universal condensation heat transfer and pressure drop model and the role of machine learning techniques to improve predictive capabilities

A novel, universal model is proposed to predict the condensation frictional pressure drop and heat transfer coefficient for horizontal microchannel and macrochannel flows. Over 4000 data points across the entire vapor quality range are collected with mass fluxes ranging from 50 – 800 kg m−2 s−1, reduced pressures from 0.03 – 0.96, and hydraulic diameters from 0.1 – 14.45 mm. The working fluids include synthetic refrigerants (R1234ze(E), R134a, R245fa, R404A, R410A), hydrocarbons (pentane and propane), and natural refrigerants (ammonia and carbon dioxide). Several models, including flow-regime based correlations and machine learning regression models (support vector regression, random forest, and artificial neural networks) are developed and compared with each other. Overall, machine learning algorithms, especially the random forest model, predict the data best for the pressure drop and heat transfer, with an absolute average deviation of about 4% for both models.

An Assessment on Average Pressure Drop and Dust-Holding Capacity of Hollow-Fiber Membranes in Air Filtration.

In this work, we tried to analyze dust loading behavior of polypropylene hollow fiber membranes using average pressure drop models. Hollow fiber membranes varying in fiber diameter were loaded with a standardized test dust to simulate particle-polluted air. We measured pressure drop development of the membranes at different flowrates and dust concentrations, and, after each experiment, the dust deposited on the membrane fibers was weighed to obtain dust holding capacity (DHC). The obtained experimental data was analyzed using various average pressure drop models and compared with average pressure drop obtained from pressure drop/dust load dependence using a curve fit. Exponential and polynomial fitting was used and compared. Pressure drop in relation to the dust load followed different trends depending on the experimental conditions and inner fiber diameter. At higher flowrate, the dependence was polynomial no matter what the fiber diameter. However, with higher fiber diameter at lower permeate velocities, the dependence was close to exponential curve and followed similar trends as observed in planar filter media. Dust-holding capacity of the membranes depended on the experimental conditions and was up to 21.4 g. However, higher dust holding capacity was impossible to reach no matter the experiment duration due to self-cleaning ability of the tested membranes.

Experimental Investigation on Adiabatic Two-Phase Frictional Pressure Drop of R1234ze(E) and R134a in a Horizontal Minichannel

Abstract R1234ze(E) has been created as an environmentally friendly substitution of R134a. An experimental investigation on adiabatic two-phase frictional pressure drop inside a 1.88 mm horizontal minichannel with R1234ze(E) and R134a was conducted. The saturation pressure and mass flux ranged within 0.6–0.9 MPa and 450–900 kg/(m2 s). Based on the 299 measured data points, the influences of various factors, including saturation pressure, mass flux, and the like, are examined detailedly. Larger mass flux brings about larger frictional pressure drop, and vapor quality performs the same function, but saturation pressure works inversely. The frictional pressure drops between R1234ze(E) and R134a present no significant differences. The experimental data are compared against 23 predictive models, among which the one from Xu and Fang (2013, “A New Correlation of Two-Phase Frictional Pressure Drop for Condensing Flow in Pipes,” Nucl. Eng. Des., 263, pp. 87–96) gives the best accuracy. In addition, a database including 3150 experimental adiabatic two-phase frictional pressure drop data points is derived from the current study and 29 published literature. Based on the database, the 23 models are assessed, and the most effective one is from Müller-Steinhagen and Heck (1986, “A Simple Friction Pressure Drop Correlation for Two-Phase Flow in Pipes,” Chem. Eng. Process., 20(6), pp. 297–308). This work can provide guidance for choosing appropriate two-phase frictional pressure drop models under adiabatic conditions.

Personalized Pre- and Post-Operative Hemodynamic Assessment of Aortic Coarctation from 3D Rotational Angiography.

Coarctation of Aorta (CoA) is a congenital disease consisting of a narrowing that obstructs the systemic blood flow. This proof-of-concept study aimed to develop a framework for automatically and robustly personalizing aortic hemodynamic computations for the assessment of pre- and post-intervention CoA patients from 3D rotational angiography (3DRA) data. We propose a framework that combines hemodynamic modelling and machine learning (ML) based techniques, and rely on 3DRA data for non-invasive pressure computation in CoA patients. The key features of our framework are a parameter estimation method for calibrating inlet and outlet boundary conditions, and regional mechanical wall properties, to ensure that the computational results match the patient-specific measurements, and an improved ML based pressure drop model capable of predicting the instantaneous pressure drop for a wide range of flow conditions and anatomical CoA variations. We evaluated the framework by investigating 6 patient datasets, under pre- and post-operative setting, and, since all calibration procedures converged successfully, the proposed approach is deemed robust. We compared the peak-to-peak and the cycle-averaged pressure drop computed using the reduced-order hemodynamic model with the catheter based measurements, before and after virtual and actual stenting. The mean absolute error for the peak-to-peak pressure drop, which is the most relevant measure for clinical decision making, was 2.98 mmHg for the pre- and 2.11 mmHg for the post-operative setting. Moreover, the proposed method is computationally efficient: the average execution time was of only [Formula: see text] minutes on a standard hardware configuration. The use of 3DRA for hemodynamic modelling could allow for a complete hemodynamic assessment, as well as virtual interventions or surgeries and predictive modeling. However, before such an approach can be used routinely, significant advancements are required for automating the workflow.

Pressure drop model for fibrous media in depth filtration: Coupling simulation of microstructure and CFD porous media during dust loading

The micro-scale model of fibrous media was simulated to obtain viscous resistance in clean state, which was provided to the CFD porous media. A macro-scale model for predicting the pressure drop during dust loading was established based on the Euler-Lagrangian method by implementing the UDF in ANSYS-Fluent. The trapping mechanism programs were developed to realize different distribution forms of particles in the porous media. The macro-empirical model was used to calibrate the macro-scale model under different SVFs. The 592*592*292-4 V–F9 filter was simplified to CFD porous media and the numerical simulation was carried out during dust loading. The results show that the pressure drop shows different growth trends under different trapping mechanism programs. Very good agreement was found between the experimental and simulated pressure drop during dust loading. Thus, the macro-scale model broadens the way of studying the pressure drop of fibrous media in depth filtration.

Dynamic Performance Analysis of a Compact Annular-Radial-Orifice Flow Magnetorheological Valve and Its Application in the Valve Controlled Cylinder System

A compact annular-radial-orifice flow magnetorheological (MR) valve with variable radial damping gaps was proposed, and its structure and working principle were also described. Firstly, a mathematical model of pressure drop was established as well to evaluate the dynamic performance of the proposed MR valve. Sequentially, the pressure drop distribution of the MR valve in each flow channel was simulated and analyzed based on the average magnetic flux densities and yield stress along the damping gaps through finite element method. Further, the experimental test rig was setup to explore the pressure drop performance and the response characteristic of the MR valve and to investigate dynamic performance of the valve controlled cylinder system under different radial damping gaps. The experimental results revealed that the pressure drop and response time of the MR valve augment significantly with the increase of applied current and decrease of the radial damping gap. In addition, the damping force of the proposed MR valve controlled cylinder system decrease with the increase of the radial damping gap. The maximum damping force can reach about 4.72 kN at the applied current of 2 A and the radial damping gap of 0.5 mm. Meanwhile, the minimum damping force can reach about 0.67 kN at the applied current of 0 A and the radial damping gap of 1.5 mm. This study clearly demonstrates that the radial damping gap of the MR valve is the key parameter which directly affects the dynamic characteristics of the valve controlled cylinder system, and the proposed MR valve can meet the requirements of different working conditions by changing the radial damping gaps.

Optimization of pressure drop model for shale gas wells in area X based on correlation coefficient method

The bottom hole pressure is an important parameter in the production process of a gas well, and it is of great significance to many aspects such as gas well productivity evaluation, dynamic analysis and production allocation. A large number of shale gas wells in area X were lack of the bottom hole pressure data. In order to solve this problem, based on extensive research in many articles, this paper selected eight kinds of calculation models as candidate objects, such as Hagadorn-Brown and Beggs-Brill. Different models were used to calculate the bottom hole pressure of only two shale gas wells with measured pressure data in this area, and the calculated results were compared with the measured data to select the best model for calculating the bottom hole pressure of shale gas wells in area X. In the optimization analysis, it was found that the conventional average relative error comparison method or the graph comparison method could not reflect the application situation of the calculation models well in this area. Therefore, on the basis of the two comparison methods, the correlation coefficient method was introduced to quantify the overall difference between the calculated pressure and the measured pressure. The results showed that the calculated result of Orkiszewski model fitted the measured pressure best.

Development and Validation of an Accurate 1D Model for Pressure Drop in Complex Coolant Piping Systems of Hybrid and Electric Vehicles

<div class="section abstract"><div class="htmlview paragraph">The development of efficient, reliable, and affordable Hybrid and Electric Vehicles (xEVs) relies on optimized Vehicle Thermal Management System (VTMS) architecture and control strategies. Compared to conventional vehicles, xEVs have more complex VTMS due to additional powertrain components and cooling circuits to meet distinct thermal requirements. The cooling circuits comprise a combination of hoses, straight, and bent pipes to route coolant flow around obstacles between powertrain components at distinct locations in the vehicle. The increased length and geometrical complexity of these piping systems, compared to conventional vehicles, results in increased pressure losses. Thus, accurate predictions of pressure drop within these piping systems is critical for component selection for an optimized VTMS. Numerical simulations are often used to study interactions between components from a system-level perspective allowing early stage rapid assessment of performance. In this work, an accurate 1D model for pressure drop in piping systems is developed based on literature review and validated using 3D Computational Fluid Dynamics (CFD) predictions. The 1D model is implemented in the software tool GT-SUITE which is used for integrated 0D/1D/3D multi-physics system simulation of the entire VTMS. The CFD calculations are performed using GT-CONVERGE. Overall, the pressure drop predictions of the 1D model are in good agreement with the 3D CFD for a range of Reynolds numbers including laminar, transition, and turbulent regimes and even when significant losses are present due to flow redevelopment after bends. Typically, commercial tools often ignore flow redevelopment and were originally developed for high Reynolds number flows. A typical battery electric vehicle is constructed in GT-SUITE and results indicate that deviations on pressure drop predictions lead to significant deviations on pump operating conditions and isentropic efficiency. The 1D model allows fast and accurate simulations over a broad range of complex piping configurations for an optimized VTMS.</div></div>

Effect of moisture content on flow behavior and resistance characteristics of dense-phase pneumatic conveying

The flow characteristic of high pressure dense-phase pneumatic conveying of pulverized coal is essential to the safe and stable operation of the gasifier. In this paper, the effects of coal moisture content on conveying behavior and resistance characteristics of dense-phase pneumatic conveying were explored. Meanwhile, a model of the additional pressure drop of particles was proposed and compared with the experimental data. The results show that though the resistance and cohesiveness increase with increasing moisture content, its influence is different in dense and dilute phase. In the dense-phase region, the coal with lower moisture content shows a larger solid mass flow rate and solid concentration; while in the dilute-phase region, the moisture content has minor effect on conveying characteristics. For the coal with lower moisture content in dense-phase region, the solid mass flow rate and solid concentration are larger, and the gas velocity has a small effect on solid friction factor, due to its smaller cohesiveness and resistance, which is showed in our experiments and inferred from our model. The additional pressure drop model was proposed for straight pipes and bends, whose parameters are probably effective than the existing parameters in this kind of model, as the deviation in the vertical rise pipe, horizontal pipe and bend pipe is controlled within ±30%, and the corresponding vertical down pipe are controlled within ±40%.