Prediction Of Pressure Drop Research Articles

Development and validation of the helically coiled steam generator model of RELAP5/MOD3.4 code

The flow field and heat transfer characteristics in a helical coil tube-type once-through steam generator (HCOTSG) are more complex than those in a straight pipe-type steam generator owing to the complex geometry of the former and the secondary flow induced by the centrifugal force. Straight tube heat transfer correlations and pressure correlations unapplicable for helical coils. System analysis codes used in design and safety analysis of HCOTSG are still missing. In this study, a code called RELAP5/MOD3.4-HCOTSG was developed for a numerical simulation of an HCOTSG based on the RELAP5/MOD3.4 code, and on suitable empirical correlations of the heat transfer coefficients and pressure drop chosen for HCOTSG. The code is first validated through a comparison with the IRIS HCOTSG design parameters, and the results indicate that the chosen models can accurately simulate the wall heat transfer and achieve a higher accuracy in the wall friction pressure drop prediction. Based on this, an analysis of typical transients is conducted to evaluate the transient characteristics of IRIS HCOTSG. The results indicate that the RELAP5/MOD3.4-HCOTSG code has the ability to calculate the transient flow and heat transfer characteristics of an HCOTSG and can serve as an analysis tool for the system calculation of a small modular reactor.

Pressure drop in converging flows in three-dimensional printing of concrete

The additive manufacturing technology of extrusion of concrete mixtures through a nozzle and deposition layer-by-layer is commonly called three-dimensional concrete printing (3DCP). Such materials are rheologically characterized by yield stress and viscosity. The Bingham model is a good approximation of their rheological behavior. We have developed approximate expressions for determination of pressure for flow through slightly tapered tubes and wedge-shaped extrusion dies, starting from the Buckingham–Reiner equation for flow of a Bingham fluid in a straight tube. The predictions are compared to numerical simulations for convergence half-angles (taper) from 0° to 30° and to analytical solutions available in the literature. Good comparison has been obtained for taper angles up to 15° but the agreement deteriorates as the angle increases. Some experimental data available in the literature have been analyzed, and the challenges for prediction of pressure drop in flow of concrete mixtures through tubes and dies, including entry flow losses, are discussed.

Experiment and Prediction of Pressure Drop in a Fiber–Powder Composite Material with Porous Structure for Energy Wheels and Air Cleaners

Energy wheels and air cleaners play crucial roles in building air conditioning systems. The former is essential for conserving energy in air conditioning systems, while the latter is necessary for ensuring the quality of indoor air. Pressure drop is a crucial parameter for both energy wheels and air cleaners, and it is essential to conduct theoretical and experimental investigations to aid in their design. In this study, we focused on the study of pressure drop in a fiber–powder composite material which can be used for both total heat exchange and air purification. Experimental tests were initially conducted to examine the impact of different parameters on the pressure drop in the material. Subsequently, based on the special fiber–powder structure of the material, two pressure drop prediction methods with different prediction strategies were proposed. The two prediction strategies were compared by analyzing the prediction accuracy of the two methods. As tested by experimental data, for both methods, the absolute prediction error was less than ±6 Pa when the pressure drop was below 50 Pa, and the relative prediction error was less than ±8% for most data sets when the pressure drop was greater than 50 Pa. Moreover, the root mean square error (RMSE) and mean absolute percentage error (MAPE) values of prediction for both methods were less than 4 Pa and 7% respectively. The test results show that although the prediction strategies are different, both prediction methods can obtain acceptable prediction results, and both methods are practical. This study is intended to serve as a valuable reference for the design of energy wheels and air cleaners.

Application of Lévêque Analogy to Open Cellular Porous Materials

Open-porous materials are used for thermal management applications, catalyst support, heat exchangers, and others owing to their enhanced heat transfer. Designing porous material for a specific heat transfer application requires quantifying effective thermal conductivity, pressure drop, and heat transfer as computed data or experimental correlations. This work extends the Lévêque analogy proposed for calculating heat transfer performance from pressure drop data for tube bundles and cross-rod matrices to porous materials. The current work shows the applicability of this analogy for periodic open-cellular porous materials. Seven unit cell geometries representing periodic cellular structures with 75% - 95% porosity are considered. Periodic flow and heat transfer simulation is performed in ANSYS Fluent for Reynolds numbers between 1 and 100 to provide pressure drop and heat transfer results. Permeability and inertial coefficient are estimated, and permeability is correlated successfully with the porosity and fiber diameter of the unit cell geometries. This correlation is validated using experimental data available in the literature, which allows for predicting pressure drops directly from the geometry. Lévêque’s analogy in the original form is explored using the pressure drop coefficient and Nusselt number, which provides a 44% frictional contribution to the total pressure drop. The correlation for the current geometries is further improved using a modified version of the Lévêque analogy, where the exponent is estimated using best fit instead of fixing at 1/3. The modified correlation is validated using experimental data from the literature, and a guideline to predict pressure drop and heat transfer from geometry is provided for periodic open-cellular porous materials.

Pressure drop characterization on cryogenic multiphase flow in spiral wounded heat exchanger under high mass flow conditions

In order to clarify the influence of dryness, working medium and mass flow rate on pressure drop characteristics in shell side of spiral wound heat exchanger, a simplified test section has been analyzed in this study. The model is with a coiled section under compact design: 1 mm layer spacing of and 2 mm tube spacing in the main structure. The mixed alkane composed of methane, ethane, propane and others are used as working fluid. The current study is focused on the pressure drop behaviors and the effects of multiphase flow in different stages of cooling process in the cryogenic heat exchanger. Systematic numerical model has been established in this study to investigate the pressure behaviors, which are also verified against newly constructed experimental system. Operating conditions range from vapor quality of 0.1–0.9, mass flux of 60–120 kg·(m2·s)−1, under the operation pressure of 0.25 MPa and temperature from −27 °C to −170.6 °C. The absolute error of pressure measurement is less than 1.5 kPa and the absolute error of pressure drop measurement is less than 25 Pa, and the relative error is 0.25 % for the current test. The experimental results show that the friction pressure drop increases with the increase of vapor quality from 0.1 to 0.9 and mass flux from 60 to 120 kg·(m2·s)−1, and the growth gradient of friction pressure drop decreases with the increase of vapor quality. A set of pressure drop correlation has been established to reflect the influence of factors such as vapor quality and mass flow rate, and the deviation between predicted pressure drop and experimental data was within ±20 %.

Pressure drop and bubble length prediction for gas-non-newtonian fluid two-phase flow in a curved microchannel

The control mechanism of the pressure drop and bubble size has a guiding significance for selecting the micropump, the pressure resistance design, and the precise control of the microfluidics. In this study, single-phase flows and gas-non-Newtonian fluid two-phase flows are studied in a microchannel containing curved structures. Sodium carboxymethyl cellulose solutions are used as the non-Newtonian fluids; water and nitrogen are used as Newtonian fluid and gas phases, respectively. The pressure drop and the bubble length are measured. The influences of operating conditions are discussed. The non-Newtonian properties of the solutions are found to affect the parameters measured significantly. The experimental results are compared with the existing models, and the fanning friction factor is used to evaluate the pressure drop. The two-phase flow pressure drop can be predicted by the Lockhart-Martinelli method with a newly developed C-coefficient as a function of the fluid characteristic parameters and microchannel structure parameters. The new correlation for two-phase pressure drop prediction has an error within 18%, smaller than existing models. A new prediction method for the dimensionless bubble length containing the two-phase friction multiplier is also given with an error of 16%.

Semi-empirical equation for determining the pressure drop of nanofibers

Air pollution, particularly the presence of particulate matter, has been linked to increased mortality rates. Air filtration is a widely used method to reduce exposure to airborne particles and protect public health. Nanofiber filter media has gained attention due to its ability to efficiently remove nanosized particles while minimizing pressure drop. However, accurately predicting the pressure drop in nanofiber media, which is influenced by the slip flow effect, remains a challenge. In this study, a simple semi-empirical equation was developed to calculate the pressure drop across nanofiber filter media. The model considers various filter parameters such as diameter, thickness, and solidity. Existing theoretical and empirical models were compared with experimental data, revealing limitations in accurately predicting pressure drop in nanofibers. To address this, a new empirical model, proposed by Bian, was examined. However, the Bian model demonstrated limited applicability due to its specific range of solidities. Numerical simulations were conducted to obtain additional pressure drop data, and a total of 107 cases were tested across various filter parameters. The simulations were performed using the Stokes equation to account for the low Reynolds numbers associated with nanofibers. The developed semi-empirical model provides a practical tool for analyzing the effect of filter parameters on nanofiber filter media's pressure drop, aiding in the design of efficient air filtration systems.

Simulation of circular pipe flow of thixotropic cemented tailings pastes

Cemented tailings pastes (CTPs) exhibit complex thixotropic behaviors, which considerably affect the accurate prediction of pressure drop in circular pipe transport. In this work, the thixotropy of CTPs is incorporated into the numerical simulation via a constitutive thixotropic model. The analytical solution of the velocity profile across the pipe based on the equilibrium rheological model is presented. Comparisons indicate that the Bingham model cannot accurately characterize the flow behaviors of CTPs. It also overestimates the pressure drop in the circular pipe. Moreover, the pressure drop predicted by the novel equilibrium model is overestimated because of thixotropy. A peak of the structural parameter can be observed near the edge of the plug region, which highly influences shear rate distribution. The effects of solids content and flow rate on pressure drop are analyzed. In summary, thixotropy should be considered in the circular pipe flow simulation of CTPs.

Solid friction coefficient in a horizontal straight pipe of pneumatic conveying

Pressure drop prediction model has been well concerned in pneumatic conveying system design. The Barth’s additional pressure drop prediction model is one of the most widely accepted and applied models, in which the solid friction coefficient in horizontal straight pipe is particularly important. In this work, a regression model of solid friction coefficient was addressed on the basis of two dimensionless numbers (the inlet Froude number and the solid-gas loading ratio), which were conducted based on fly ash pneumatic conveying experiment data in a 16 m length pipeline. Then, the prediction accuracy of the regressed model was verified by the pressure drop of other pneumatic conveying pipeline system, 123 m and 139 m pipelines, respectively. The results show that solid friction coefficient gradually decreases with inlet Froude number, conversely, it increases with solid-gas loading ratio. And the regressed solid friction coefficient maintained relatively high accuracy in the prediction of pressure drop, for both fly ash pneumatic conveying pipelines of 16 m length and 123 m length. However, a different prediction accuracy appeared for the different loading ratio of 139 m length pipeline complete pneumatic conveying system. The pressure drop prediction accuracy sharply declines when solid-gas loading ratio is larger than 85.

FRICTIONAL PRESSURE DROP DURING CONDENSING FLOW INSIDE MINI/MICRO-CHANNELS: PREDICTIVE TOOLS ASSESSMENT AND DATA TREATMENT

A total of 1210 new condensation friction pressure gradient points (database) is collected from 12 open articles on mini/micro-channels literature. The database covered a wide range of thermophysical properties associated with low-GWP refrigerants, physical dimension, mass velocity and vapor quality. A comparison of the experimental database against eleven two-phase flow frictional pressure drop prediction tools is carried out. Based on that, the mini/micro-channel developed by Xu and Fang exhibited the best ability to capture the tendency of the database with a mean absolute relative deviation of (36.59%) for all data. Keywords: Two-phase flow frictional pressure gradient; Mini/micro-channels; Condensing flow; New refrigerant fluid; Heat transfer; Collect database.

Pressure drop of structured packing in pilot column and comparison to common correlations

Packed columns are widely used in the chemical industry such as absorption, stripping, distillation, and extraction in the production of e.g. organic chemicals, and pharmaceuticals. Pressure loss and pressure drop correlations are of special interest when it comes to the hydrodynamic properties of a column. The pressure loss across the column is of interest in the design phase when the size of the blower to drive the gas stream through the column has to be decided. The loading point and flooding point are also influenced by the pressure loss and the area of operation is determined from these points. This work examines four different correlations on pressure drop. The correlations are (i) Ergun’s equation (1952), (ii) an improved version of Ergun’s equation by Stichlmair, Bravo, and Fair (1989), (iii) an equation developed by Billet and Schultes (1999), and (iv) an equation by Rocha, Bravo, and Fair (1993). The complexity of the correlations is increasing in the mentioned order, Ergun’s equation being the simplest one. This study investigates if the more complicated correlations give better predictions to pressure drop in packed columns. This is determined by comparing the correlations to experimental data for pressure drop in a packed column with 8.2 m of structured packing using water as the liquid and atmospheric air as the gas. Seven experiments were carried out for determining the pressure drop in the column with liquid flows varying from 0 to 500 kg·h−1. At constant liquid flow, the gas flow was varied from approximately 10 to 70 kg·h−1. The pressure drop across the non-wetted column was best described by the correlation by Rocha et al. while the pressure drop for liquid flows from 100 to 500 kg·h−1 was, in general, best described by Stichlmair’s equation. For an irrigated column, the highest deviation was a predicted pressure drop 69.6% lower than measured. The best prediction was 0.1% higher than the measured. This study shows, surprisingly, that for a system of water and atmospheric air, complicated correlations on pressure drop determination do not provide better estimates than simple equations.

Pressure drop model for rotating packed bed structural internals

Chemical industry remains in a constant need for new technologies providing increased production which is clean and energy-efficient. Rotating packed bed is a novel technology, which intensifies interfacial mass transfer with the use of centrifugal force. Similarly to column processes, pressure drop is one of the major bottlenecks in rotating packed bed processes. In this work, a universal dry pressure drop model for rotating packed bed baffle-based structured internals was developed and validated using experimental data. The model is based on Darcy-Weisbach equations, and takes into account linear pressure drop due to friction, local drops due to changes in gas flow direction, and pressure drop due to rotation. Nine packings of varying diameters, as well as baffle shapes and sizes, were tested experimentally at varying rotational speeds and gas flow rates. To include differences in baffle geometries, the unifying shape factor was implemented, taking into account the volume of solid material and the cross-sectional area of the packing. The stationary pressure drop model predictions fit with maximum relative error below 15%, while the relative errors of the overall pressure drop predictions were below 18%.

An Experimental Investigation of Two-Phase Frictional Pressure Drop in Straight-Tube Steam Generator Used in SFR

Due to the presence of sodium, it is a challenging task to achieve the reliable and safe operation of steam generators in a sodium-cooled fast reactor (SFR). Water flow oscillations in a two-phase flow system worsen the tube integrity. An accurate prediction of two-phase pressure drop is essential in designing steam generators to operate in a stable regime. Toward this, experiments have been carried out on an industrial-size 19-tube model sodium-heated steam generator of 5.5-MW capacity to understand two-phase pressure drop characteristics at various operating conditions. The measured data are used to estimate the two-phase frictional pressure drop. The concept of a two-phase friction multiplier has been used in the present study. A significant variation in the two-phase frictional multiplier is seen with steam quality, whereas the variation of the two-phase friction multiplier is insignificant at saturated steam condition. Based on the experiments, complemented by computational model, a correlation has been developed for the two-phase frictional multiplier as a function of steam quality for sodium-heated once-through straight-tube steam generators.

Design and optimisation of structural packings for rotating bed absorbers using computational fluid dynamics simulation

A method for pressure drop prediction using Computational fluid dynamics (CFD) was designed and validated experimentally with a set of baffle-based geometry types of Rotating Packed Bed’s packings. The methodology served as a foundation for a CFD optimisation tool of internal geometry based on minimal pressure drop. The baffles in the geometry were characterized by five parameters: bottom and top internal rounding, bottom and top external rounding, and baffle inclination angle. Based on the variables, 78 different geometry types were created and subjected to pressure drop optimisation with the CFD tool. The optimal geometry was manufactured, and the simulation results were verified experimentally. Up to 54% decrease in pressure drop was observed in comparison to the pre-optimisation packing. Mass transfer experiments were conducted with the use of CO2-NaOH absorption system, and results showed that the optimised packing, despite exhibiting less pressure drop, is capable of achieving up to 17% increase in effective mass transfer area.

Optimizing Pressure Prediction Models for Pneumatic Conveying of Biomass: A Comprehensive Approach to Minimize Trial Tests and Enhance Accuracy

This study investigates pneumatic conveying of four different biomass materials, namely cottonseeds, wood pellets, wood chips, and wheat straw. The performance of a previously proposed model for predicting pressure drop is evaluated using biomass materials. Results indicate that the model can predict pressure with an error range of 30 percent. To minimize the number of trial tests required, an optimization algorithm is proposed. The findings show that with a combination of three trial tests, there is a 60 percent probability of selecting the right subset for accurately predicting pressure drop for the entire range of tests. Further investigation of different training subsets suggests that increasing the number of tests from 3 to 7 can improve the probability from 60% to 90%. Moreover, thorough analysis of all three-element subsets in the entire series of tests reveals that when considering air mass flow rate as the input, having air mass flow rates that are not only closer in value but also lower increases the likelihood of selecting the correct subset for predicting pressure drop across the entire range. This advancement can help industries to design and optimize pneumatic conveying systems more effectively, leading to significant energy savings and improved operational performance.

Modelling of flow in backward erosion pipes

Backward erosion piping is an important failure mechanism that can affect the safety of water-retaining structure foundations, which results in the formation of shallow pipes at the interface of the cohesive layer and the sand layer. Pipe hydraulics provides a lot of valuable information about the erosion mechanism, but it had never been analysed systematically during equilibrium. This paper analyzes pipe hydraulics by combining the pipe flow model and numerical simulations of experiments. A single-phase pipe-flow model is presented that includes not only frictional and accelerational pressure drops, but also the pressure drop caused by inflow through the pipe wall. The pipe-flow model is included in pipe/aquifer coupling numerical models to achieve more accurate predictions of pressure drop and inflow distribution along the pipe. The predictions agree favourably with previously published experimental data. And the calculated pipe flow velocities, hydraulic regimes and gradients are analysed for different pipe lengths.

Bed filtration pressure drop prediction and accuracy evaluation using the Ergun equation with optimized dynamic parameters in industrial wastewater treatment

Industrial wastewater frequently contains suspended solid (SS) particles, which may be extremely harmful to human health and the environment. The bed filtration method offers clear benefits for treating wastewater contaminated with SS particles. An important technical indicator of the method is the bed pressure drop, but modeling of its development during bed filtration has been poorly studied. In this study, the Ergun equation is selected as the basis of the pressure drop model, and its parameters are optimized. To evaluate the model's accuracy at various flow rates and total bed depths, filtration experiments were carried out. The findings demonstrate that the model has a high prediction accuracy, with prediction errors for the bed pressure drop in the deep stage being less than 5 %. By the end of the deep stage, the accumulated masses of SS particles in the 5-cm layer below the bed surface in 15-cm and 25-cm depth beds accounted for about 85.1 % and 80.4 %, and were responsible for 51 % and 36 % of the pressure drop, respectively. And after the deep stage, less SS particles being retained as filter cake will benefit long-term operation. The optimization model provided in this study and the discovery of the pressure drop distribution within the bed can provide a theoretical basis for the design or improvement of the bed filtration process.

Experimental viscosity monitoring in complex pipe systems for flows of drilling muds based on the energy dissipation rate

This study aimed to measure the viscosity of non-Newtonian fluids (xanthan gum solution and drilling muds) in-situ during complex pipe flows using pressure drop and flow rate data without sampling. This method of viscometry can be applied to various inelastic non-Newtonian fluids and pipe systems of general geometries, including shear-thinning fluids (such as xanthan gum) and viscoplastic fluids with yield stress (drilling mud), as long as the flow rate and pressure drop within the system can be measured in-situ. The method employs two flow numbers (energy dissipation rate coefficient and effective shear rate coefficient) that are mainly determined by the flow geometry, nearly independent of the rheological behavior of a fluid. The representative effective shear rate for a given system is determined by the effective shear rate coefficient and flow rate; and the relationship between effective viscosity and material viscosity was found to be identical. The method was validated with three different non-Newtonian fluids in three different lab-scale complex pipe systems, including a straight circular pipe with connectors, a pipe system with an intermediate branch, and a 3D pipe system with height and slope variations. The accuracy assessment of viscosity measurement and pressure drop prediction showed no more than an 18.7% error in all the cases. The in-situ viscosity measurement method presented in this study can be used for process monitoring and process quantification of non-Newtonian fluid flows in various types of pipe flows used in industrial processes.

A black box based model for phase change heat exchanger in refrigeration system simulations using Kriging interpolation method

In the present study, a black box model for phase change heat exchangers is developed based on Kriging interpolation. The input and output of the heat exchanger black box model were established based on the mass-flow-guided method. Methods for the input domain determination of are established respectively for the application of system simulation and separate heat exchanger simulation. A training data set sampling method is established based on the Latin hypercube sampling method to achieve significant reduction in sample points while maintaining the integrity of the sample data characteristics. The heat exchanger calculation trend was determined by establishing a regression model; the accurate prediction of heat exchanger performance was achieved by making local corrections to the prediction results through a stochastic distribution process model. Validation results show that, for the condenser model, the average pressure drop prediction error is 0.25%, and the average heat transfer prediction error is 1.18%; for the evaporator model, the average pressure drop prediction error is 0.71%, and the average heat transfer prediction error is 0.80%. The model can achieve high prediction accuracy with a small amount of training data and has a good fitting performance in the range of general applications.

Pressure Drop Prediction Model of the Gas-Liquid Stratified Flow Development Section in the Horizontal Pipeline

Abstract The gas phase accelerating beyond the liquid phase caused by gas-liquid slippage cannot be ignored in short horizontal pipelines with undulation and inflow, and there is no method to calculate it. Therefore, a pressure drop prediction model for variable liquid holdup was developed in this paper. The theoretical model calculation results were validated using computational fluid dynamics. The effectiveness of the pressure drop prediction model has been demonstrated. The various pressure drop, liquid holdup, and development length laws were then examined. The findings indicate that: the pressure drop in the developed section of stratified flow is not only the friction pressure drop but also the acceleration pressure drop; the length of the stratified flow development section and pipeline pressure drop are more easily affected by the flowrate than the liquid holdup in the pipe inlet. Using the relevant data from coalbed methane horizontal wells as an example, the L/D of the development section is approximately 40–85 when the inlet flowrate is 0.8–1 m/s, and the inlet liquid holdup is 0.3–0.5. The pressure drop characteristics in the gas-liquid stratified flow development section are obviously different from those in the stable section. The development of a pressure drop prediction model for the stratified flow development section lays the theoretical groundwork for the investigation of gas-liquid two-phase flow in horizontal pipelines with short or undulating and inflow conditions.