Pressure Drop Correlations Research Articles

Development of a thermal-hydraulic analysis code for helically coiled once-through steam generator

Helically coiled once-through steam generators being compact in size and most efficient for heat transfer have been widely used in many SMRs (Small and Medium-size Reactor). It is very imperative to study the hydraulic characteristics of the helically coiled once-through steam generator prior to their integration with SMRs. In this study a thermal hydraulics code that uses a two-fluid two-phase flow model with the consideration of thermal non-equilibrium is developed for thermal-hydraulic characteristics analyses of helically coiled steam generators. A pressure-velocity coupling algorithm is applied to solve equations and a set of heat transfer correlations and frictional pressure drop correlations are embedded into the code.Validation of the code is done using experimental data of pressure drop and heat transfer for helical coil tubes. The code is also tested for simulation of the transient as well as steady state thermal-hydraulic characteristics of OTSG (Once-Through Steam Generator) of IRIS (International Reactor Innovative and Secure) and results are compared with the design data and the RELAP5’s result, the simulation results are found in close agreement with these available results.

Experimental characterization of random packed spheres, cylinders and rings, and their influence on pressure drop

The reliable prediction of the pressure drop of packed-beds requires an accurate understanding of the packing characteristics. Therefore, packings of spheres, cylinders and hollow cylinders are studied: firstly, developing a reproducible and easily achievable packing generation method by single particle dropping; secondly, evaluating and correlating the average bed porosity as a function of the tube-to-particle diameter ratio λ, the diameter-to-height aspect ratio and the inner-to-outer diameter aspect ratio. The packed-bed pressure drop was measured, thoroughly evaluating the influence of particle filling speed, the error propagation from porosity deviations resulting in a multiplication factor of 3.1–3.9 for spheres and 2.4–3.0 for cylinders depending on material characteristics, and the influence of particle surface roughness, with rough particles increasing the packing friction by 17.5%. A novel Carman-type pressure drop correlation for smooth equilateral cylinder packings valid for Rep = 10–3000 is described.

An Experimental Investigation of Pressure Drop During Partial Condensation of Low Pressure Steam

Abstract As direct dry-cooling systems are becoming more popular for thermal power plants, there is a demand to increase the flexibility of the application and performance of these cooling systems. A novel hybrid (dry/wet) dephlegmator (HDWD) cooling system is being developed, and at this stage in the development of the HDWD, the performance analysis and optimization of the HDWD is currently subject to uncertainties in a number of parameters. One of the parameters is the confidence in the correlations to predict the steam-side pressure drop over the wide range of full to partial condensation conditions expected in the system as a result of the design. This study makes use of an experimental apparatus to measure steam pressure drop over a range of partial to full condensation inside a circular horizontal tube. The experiment is conducted by measuring the steam flow and steam pressure drop in a horizontal primary condenser tube with the presence of a secondary condenser tube. The primary condenser has a tube length of 2.5 m and an inside tube diameter of 19.3 mm similar to the proposed HDWD design. Existing correlations for pressure drop in condensing flow are compared with the results to assess the applicability of the correlations for the HDWD case. It was found that the correlation of Lockhart and Martinelli’s with the Chisholm parameter fits the experimental data the best with a mean error of ±15.6%. A parametric study also indicated that there is a prominent increase in the frictional pressure drop at low partial condensation ratios (i.e., high steam through flow) as expected with wave drag at the vapor and condensate interface due to the difference in velocity.

Numerical study on porosity distribution and hydrodynamics of packed bed in narrow square channels

Recently square-channel packed bed reactors with micro to milli dimensions are often found in the literature on process intensification. However, its porosity profiles and resultant flow behaviors have been overlooked. Therefore, this study proposes two new CFD approaches to model such reactors relying on the accurate local porosity profiles in the square bed. Discrete element method was employed to model random packed beds of monodisperse spherical particles in square channels with channel-to-particle size ratio of 3 to 10. The obtained lateral porosity profiles were axially averaged and expressed as a function of distance from the wall in three defined zones. Momentum source term to be added in the momentum conservation equation was calculated based on the local porosity profile functions in Correlations-based Continuum (CC) approach, while on the axially-averaged porosity profiles in Pseudo-Particle Resolved (PPR) approach. The square beds’ hydrodynamic behaviors were investigated using CC and PPR approaches, which were validated with Particle Resolved approach in terms of velocity profile, and with empirical correlations for pressure drop.

Sub‐channel‐based multiscale thermal‐hydraulic analysis of a medium‐power, lead‐cooled fast reactor

The lead-cooled fast reactor (LFR) offers enhanced safety and reliability with the fine properties of liquid lead and lead alloy. To study accurately the thermal characteristics of fast reactors, the multiscale thermal-hydraulic coupling simulation is an effective way. Multiscale coupling based on the sub-channel code has evident advantages on the analysis of fuel assemblies. In this study, a multiscale thermal-hydraulic analysis of a forced-circulation, medium-power LFR under steady-state and transient conditions is performed with the system code ATHLET and sub-channel code KMC-SUBtraC which was developed based on the previous version by modifying the pressure drop correlations and adding the assembly-level calculation. The codes are one-way-coupled, with good efficiency and precision. Transient verification of the sub-channel code is conducted with the CFD code. In the steady-state analysis of M2LFR-1000, mass flow and temperature distributions of the assemblies, sub-channels, and fuel rods in the hottest assembly are analyzed and the safety performance is investigated. In the transient analysis, two typical DECs (unprotected overpower transient and ULOF+ULOHS) are simulated and the multiscale thermal-hydraulic characteristics are analyzed. With the negative reactivity feedback, the variations of the temperatures of the coolant and fuel rods are within the safe limits, which shows the inherent safety of the reactor. And the results indicate that the loss of primary flow could increase the risk of cladding corrosion.

The modelling and design of an MRI-compatible cryosurgical probe

Cryo-ablation is a breast cancer treatment method that utilizes a small probe in precise locations within the body to freeze and destroy unwanted cancer tissue. Recently, there has been a growing interest in combining cryo-ablation with magnetic resonance imaging (MRI). The challenge of combining these two technologies is that MRI devices require the absence of metals, and traditional heat exchangers used in cryoprobes are typically composed of thermally conductive metals that tend to disrupt the image produced by an MRI, impairing its functionality. Subsequently, it becomes of interest to develop a heat exchanger composed of thermally conductive MRI-compatible materials such as zirconium. This report presents the results of a thermal modelling effort to characterize and design a non-metallic Joule-Thomson cryoprobe for cryo-ablation. The model is comprised of a Joule-Thomson valve, as well as a discretized recuperative heat exchanger that includes the effects of axial conduction, pressure drop, two-phase and single-phase convection correlations, and fluid properties for single-components and mixtures. The device operates at 170 K with a heat load of 10 W, which is a viable temperature and heat load for cryo-ablation.

A Study on Thermal-Hydraulics Characteristics for Designing a Shell and Tube Conderser for a 1200 MWe Nuclear Power Plant

The study explores the thermal-hydraulics parameters of a condenser of a nuclear power plant with 1200MWe net electric output and 37% thermal efficiency using empirical correlations of pressure drop and heat transfer coefficient both for the tube and shell sides. Considering a two-phase fluid system, a shell and tube condenser with coolant water on the tube side and condensing steam on the shell side has been selected. For designing a condenser with a thermal load of 2060MWth, the input temperature data of cold fluid inlet and outlet temperatures are taken as 29.4ºC and 40ºC while the condensation temperature is taken as 53.97oC. Transverse, two-pass condenser with 4 shell tanks has been considered in this study and the length of each shell tank is taken as 14m. Based on these input data, this work finds heat transfer area, logarithmic mean temperature difference (LMTD), and convection heat transfer coefficient inside the tubes as 549536m2, 18.74°C, and 2869.85W/m2.ºC respectively for 20mm tube outer diameter. Hydrodynamic parameters relating to the friction factors and pressure drops on tube side are found as 0.031 and 14.86kPa respectively. Similar design data have been generated for varying coolant inlet temperatures and tube inner diameters. Results reveal that velocity of flow inside the tubes as well as the number of tubes in a bundle decrease with the increase in tube diameter. Finally, the thermal-hydraulic data may be used to design a large scale commercial condenser to be applicable for a large scale nuclear plant since limited design data are available in the literature.
 Journal of Bangladesh Academy of Sciences, Vol. 43, No. 2, 181-189, 2019

Prediction of Pressure Drop in Subsea Pipeline Using Pipesim Software

The number of offshore developments for which long-distance tie-back is usually implemented has increased recently, leading to increasing pressure loss concerns from such systems. In the literature, it revealed that pressure drop in multi-phase transport is quite complex to compute manually. Hence the need for multi-phase flow simulation software. PIPESIM is a leading industry software currently used in the oil and gas industry for multiphase flow simulation. In this study, a 64km subsea pipeline system comprising two sections; 23km, 22.064in ID and 41km, 24inch ID, coated with 3mm (0.003m) polyethene insulation and transporting multiphase hydrocarbon fluid in an ultra-deep-water field was modelled in PIPESIM. Network simulation for the base case was carried out at 114barg (114MPa) inlet pressure and 18.7MMSCfd gas flowrate. The observed system pressure drop was dependent on pipeline inlet pressure, flowrates, and internal pipe diameter. 13.8barg (13.8MPa) was lost from the system for the base case simulation. Sensitivity analysis carried out using Gas volumetric flowrates of 3, 12 and 18.7 MMSCFd. The inlet pressures of 57, 114 and 171barg combined with six different pipe diameters generated a unique combination of 81 data points that were used in the development of a pressure drop correlation using the LINEST regression analysis tool in Microsoft Excel. At high flowrate and high inlet pressure, the pressure-drop observed was minimal and vice versa. Also, at constant flowrates and inlet pressures, the pressure drop was observed to increase with increasing pipe sizes. An R 2 value of 0.9226 was obtained from the analysis. The plot of Predicted Pressure-drop against Calculated pressure-drop similarly gave an R 2 value of 0.8025. Both results showed usefully, and hence the developed correlation can be used as an estimate in the absence of PIPESIM software for pressure drop prediction purposes. Keywords: Pressure drop prediction, Multi-flow Simulation, PIPESIM, Pipe sizing, Regression Analysis DOI: 10.7176/IEL/10-2-06 Publication date: March 31 st 2020

New Correlations for Two Phase Flow Pressure Drop in Homogeneous Flows Model

The calculation of pressure drop in pipes two-phase flow is essential in different areas. Even though several studies concerning this issue have been conducted, an accurate correlation is still required. The objective of the paper is to develop correlations for two-phase friction pressure drop and mixture viscosity. The new correlation can be used to compute the friction pressure drop for two phase flow in homogenous approach modeling. The original equation is generated from a similitude between the mixture viscosity for two-phase flows and the thermal conductivity of the porous structure. The new correlation is evaluated against 846 experimental data of friction pressure drop collected from literature on circular pipes; the experimental data including different working fluids such as R1234ze (E), R32, R-600a R717, R134a, R410A and carbon dioxide (CO2) at different hydraulic inner diameters and mass flux. Models are assessed based on the relative percentage error and the probability density function (PDF). The predictions by the new correlation and other correlations from the literature are compared based on some experimental data. It is found that new correlation has a mean absolute relative deviation (MARD) of 30%. It is proved that these new correlations of two-phase flow pressure drop can be used to predict the experiment measurements of pressure drop, on circular pipes, minichannels and microchannels.

Experimental and Computational Fluid Dynamics Validation of Correlations for Dry Pressure Drop in Trays without Downcomer

AbstractThe dry tray pressure drop (ΔPd) is a design parameter that provides preliminary information about the total pressure drop. This work aimed to assess correlations for ΔPd prediction for different types of trays without downcomer and to evaluate the effects of the free area ratio (φ) and the hole diameter (d) on ΔPd. Assessment was performed by comparing results of several correlations with those from an experimentally validated computational fluid dynamics simulation. The study shows that the correlations of Červenka and Kolář, Bennett, Agrawal and Cook, and Stichlmair and Mersmann predicted the dry pressure drop satisfactorily. The correlation of Bennett, Agrawal and Cook can be recommended for the prediction of ΔPd for a wide range of geometries and operation conditions. Also, φ has a higher influence on ΔPd than d.

Comparison of Experimental and Computational Heat Transfer Characterization of Water Jet Impingement Array with Interspersed Fluid Extraction

A jet impingement cooling device was designed with jet-adjacent fluid extraction ports distributed throughout the impingement array. The device was fabricated from a photopolymer material using a three-dimensional printing technique and tested for flow resistance and cooling performance using water as the working fluid. Parallel to physical experiments, computational simulations were performed using a quarter-jet repeating unit cell consistent with the physical device geometry, but independent of the manifold architecture. Pressure drop and heat transfer results from both methods were evaluated and compared. It was found that the computational and experimental pressure drop results showed excellent agreement after manifold pressure drops were properly accounted for using a reduced-order analytical model. Heat transfer results were shown to have reasonable agreement with differing trends. A discussion on possible causes for the difference is presented and suggestions are made for future accommodation. Finally, this work proposes a strategy for development of broadly applicable thermal and pressure drop correlations which span a wide range of geometries, fluid properties, heat fluxes, and flow parameters.

Modelling of condensation pressure drop for R134a and R134a-lubricant-mixtures in multiport flat tubes

This paper presents the results of an experimental investigation on pressure drop characteristics for R134a and R134a-lubricant mixtures in multiport flat tubes (MPFT). An experimental facility has been set up, carefully validated and used to determine the pressure drop value in the two-phase flow regime inside extruded MPFT with hydraulic diameters from 0.91 mm to 0.53 mm with either triangular or rectangular channel cross sections with and without an axial fin structure. Based on the investigation published in Knipper et al. (2019), the operating parameters have been varied within a broad range to ensure a high degree of reliability and comparability to pressure drop correlations. In addition, the nominal oil content has been varied between 0 and 7% by weight. A good agreement of the pressure drop data with several correlations can again be confirmed for most of the flat tubes. With respect to the urgent need for reliable correlations regarding low liquid only Reynolds numbers (Relo=800−5000), the authors present an approach based on the Cavallini et al. (2006) correlation that is also considering the surface roughness of the tube. For both, pure R134a and R134a-PAG-oil-mixtures, a good agreement with the newly determined data can be achieved and, thus, an enlarged range of applicability can be stated.

Development of heat transfer and pressure drop correlations in twisted tube heat exchangers

Heat transfer in concentric twisted tubes exchangers has several applications in the chemical and food industry mainly due to its compact structure and high transport coefficients, however, its use has been limited as a consequence of drop pressure. This study reports Nusselt number and friction factor correlations as a function of the dimensionless Dean number as well as Prandtl number, and a torsional step parameter. Simulations were carried out using ANSYS CFX® V16.0 software at workstations belonging to Grupo de Investigación en Materiales Avanzados y Energía of Instituto Tecnológico Metropolitano. Six geometries were developed with SolidEdge® ST9 academic license. Geometry modification, cleanup, and repair were made although DesignModeler® 2019 academic license. Finally Meshing® for discretization. The mesh size independence, and incidence of the turbulence model, and twisting step validated the computational tools use. Correlation numerically showed an increase of 60% average respect to smooth bending tube.

A CORRELATION FOR PRESSURE DROP PREDICTION FOR SOLID-LIQUID SLURRY FLOWS THROUGH HORIZONTAL PIPELINES

This paper has shown a correlation of pressure drop for pseudohomogeneous or mildly heterogeneous solid-liquid slurry flows through horizontal pipelines derived using a curve-fitting technique applied on exhaustive simulation data. These data are attained using a properly validated Eulerian model for multiphase flows whose applicability is confirmed for the selected range of slurry flows. The spread of geometric and working input parameters of solid-liquid slurry flows targeted during the present research work has been quite inclusive and widespread. This increases the applicability realm of the derived correlation.

Experimental Investigation of Heat Transfer and Flow Characteristics in Different Inlet Subcooled Flow Boiling in Microchannel

The current experimental study considered the heat transfer and pressure drop for subcooled flow boiling of deionized water in a microchannel heat sink. The heat sink consisted of a single microchannel, 300μm wide and 300μm in height with a hydraulic diameter of 300μm. The heat sink was formed of oxygen-free cooper with 72mm length and 12mm width. Experimental operation conditions spanned the heat flux 78-800 kW/m2, mass flux 1700 and 2100kg/m2.s and at 21, 31 K subcooled inlet temperature. Boiling heat transfer coefficient was measured and compared with existing correlations. Also, the experimental pressure drop was measured and compared with micro scale pressure drop correlations. The results show that higher mass flux leads to a higher boiling heat transfer coefficient and the dominant mechanism is convective boiling. Also, the experimental pressure drop decreases with increasing heat flux in a single phase region, while it increases in a two-phase region. The heat transfer coefficient increase with increasing the inlet subcooled. When compared the experimental results in the experimental condition range, it was found that an existing correlation provides satisfactory prediction of heat transfer coefficient and pressure drop.

Additive manufacturing of interpenetrating periodic open cellular structures (interPOCS) with in operando adjustable flow characteristics

Structured catalyst supports and structured reactors offer interesting features to address heat and mass transport challenges in catalytic processes. The present work addresses the unique role of so-called interpenetrating periodic open cellular structures (interPOCS) as a geometrically flexible system enabling in operando adjustment of fluid flow characteristics. The interPOCS studied in this work consist of an interwoven structure of two POCS with a defined offset, each based on a diamond unit cell. The specific surface area and porosity, as the structures’ influential morphology parameters, were derived as a function of cell size and strut thickness, respectively. Both, POCS and interPOCS of different geometrical parameters were designed via computer-aided design, fabricated by fused deposition modeling and geometrically characterized. The influence of the structure offset and the geometrical dimension on the pressure drop was investigated in detail. From experimental data, the coefficients of an Ergun-type pressure drop correlation were fitted and a two cavity channel model was established to describe the dependency of the pressure drop on the offset position. The possibility of the structure shift in interPOCS represents a highly interesting and versatile option for in operando adjustment in catalytic processes.

Numerical Investigation of Air-Side Heat Transfer and Pressure Drop Characteristics of a New Triangular Finned Microchannel Evaporator with Water Drainage Slits

The present study investigated a new microchannel profile design encompassing condensate drainage slits for improved moisture removal with use of triangular shaped plain fins. Heat transfer and pressure drop correlations were developed using computational fluid dynamics (CFD) and defined in terms of Colburn j-factor and Fanning f-factor. The microchannels were square 2.00 × 2.00 mm and placed with 4.50 mm longitudinal tube pitch. The transverse tube pitch and the triangular fin pitch were varied from 9.00 to 21.00 mm and 2.50 to 10.00 mm, respectively. Frontal velocity ranged from 1.47 to 4.40 m·s−1. The chosen evaporator geometry corresponds to evaporators for industrial refrigeration systems with long frosting periods. Furthermore, the CFD simulations covered the complete thermal entrance and developed regions, and made it possible to extract virtually infinite longitudinal heat transfer and pressure drop characteristics. The developed Colburn j-factor and Fanning f-factor correlations are able to predict the numerical results with 3.41% and 3.95% deviation, respectively.

A new method for scale-up of solvent-based post-combustion carbon capture process with packed columns

Solvent-based post-combustion carbon capture (PCC) with packed column is the most commercially ready CO2 capture technology. To study commercial-scale PCC processes, validated pilot scale models are often scaled up to commercial-scale using the generalized pressure drop correlation (GPDC) chart which requires assuming the column pressure drop. The GPDC method may lead to either over-estimation or under-estimation of the column diameter. In this paper, a new method for estimating the packed column diameter without assuming the pressure drop has been proposed and used for model scale-up. The method was validated by scaling between two existing pilot plant sizes. The CO2 capture process was simulated in Aspen Plus® and validated at pilot scale. The validated model was scaled up to commercial CO2 capture plant capable of serving a 250 MWe combined cycle gas turbine power plant using the new method proposed in this study. The results obtained from the scale-up study were compared to those obtained when the GPDC method was used to design the same commercial CO2 capture plant. The results showed that the GPDC method overestimated the absorber and stripper diameter by 1.6 % and 8.5 % respectively. Process simulation results for the commercial-scale plant showed about 2.12 % and 5.63 % lower solvent flow rate and reboiler duty with the proposed method. Therefore, the capital and operating costs for the process using the newly proposed scale-up method could be lower based on our estimates of the column dimensions, solvent flow rate and specific reboiler duty.

Hydraulic resistance and heat transfer augmentation in pipes with inner helical micro-ribs: Review, data generalisation, and technical recommendations

The paper presents the data generalization and development of general correlations for heat transfer and pressure drop in pipes with inner helical micro-ribs. Heat transfer and friction coefficient data were gathered from related investigations on single-phase turbulent flow of Newtonian fluid in pipes with various shape inner helically-ribbed surfaces

Air-side heat transfer and pressure drop characteristics of microchannel evaporators for household refrigerators

Microchannels are likely to be the next heat transfer technology for household refrigerating applications, especially due to their compact design and high heat transfer rate per unit of volume. In contrast to the conventional tube-fin evaporators, the available heat transfer and pressure drop correlations are not well-stablished yet. This study introduces a new microchannel evaporator design to be used in ‘no-frost’ household refrigerators. The performance of sixteen evaporators prototypes with distinct geometric characteristics were evaluated experimentally in an open-loop wind-tunnel calorimeter facility coming up with data for the overall thermal conductance and the air-side pressure drop data as a function of the air flow rate. Empirical correlations for Colburn j-factor and friction f-factor were devised in terms of the Reynolds number and key compact heat exchanger parameters, being able to predict 90% of the experimental counterparts within ±10% and ±20% error bands, respectively. Furthermore, comparisons against a typical no-frost tube-fin evaporator was carried out with respect to air-side pressure drop and overall thermal conductance, which indicated a promising potentiality of application in household refrigeration appliances.