Using intrinsic coordinates, the slip flow in a minute meandering channel is studied by perturbation about the small ratio of curvature to inverse half gap width. The exact solution for an annulus shows this ratio can be as large as 0.5 with less than 1% error. Velocity slip on the walls and the pressure drop depend on the slip factor. Formula for the pressure drop in a channel with a single bend is derived.

Phase separation has been proven to increase performance of condensers of energy conversion systems (in vapor compression systems). Instead of conventional design, the inlet to a microchannel condenser prototype is in the middle of the height. After the first pass, in the vertical second header of the condenser, vapor phase separates from liquid phase due to gravity and sometimes other effects. In ideal case vapor should go to the top and liquid to the bottom, resulting in increased heat transfer. Due to interaction between vapor and liquid, separation is not perfect, expressed through the separation efficiency. A mechanistic model presented in the paper is built to predict the phase separation efficiency based on force balance analysis for the liquid phase and correlations for the two-phase pressure drop. For the force balance criteria, liquid phase is divided into droplets and film and treated separately. Initial agreement with experiment is achieved to be within ±15%. For a second header at one inlet condition of the flow, the liquid separation efficiency is a function of the vapor separation efficiency. Liquid separation efficiency decreases with increasing inlet mass flux.

Static mixers (SM) have become standard equipment in the process industries. They are widely used in applications that involve chemical reactions, heat transfer, blending of fluids, or a combination of these. Compared to mechanically agitated vessels, SMs consume less energy, require less maintenance, and can provide mixing with shorter residence time. Assessment of the performance of SM provides a means to categorize and rank the available devices and new designs, which in turn facilitates selection for specific applications. Applying the second law efficiency (SLE) principle, we derived and proposed a novel mixing parameter, the M number, which is a dimensionless ratio of mixing level to energy loss. The parameter is compared to an industry-standard method of mixing evaluation that relies on the coefficient of variation (CoV) change across the mixer. Both CoV and the M number are used to evaluate mixing performance from computational fluid dynamics (CFD) results for a static mixer for various inlet conditions. Unlike the CoV-based parameters considered, the M number offers the advantages of accounting for energy loss and the natural mixing effects of the system. In addition, an empirical relationship is obtained that relates the M number to the Reynolds number (Re). Potential applications for the M number are discussed and its limitations are noted. Work in progress includes investigation with other SM.

The flow of oil/water mixtures in a pipe can occur under different flow patterns. Additionally, being able to predict adequately pressure drop in such systems is of relevant importance to adequately design the conveying system. In this work, an experimental and numerical study of the fully dispersed flow regime of an oil/water mixture (liquid paraffin and water) in a horizontal pipe, with concentrations of the oil of 0.01, 0.13, and 0.22 v/v were developed. Experimentally, the values of pressure drop, flow photographs, and radial volumetric concentrations of the oil in the vertical diameter of the pipe cross section were collected. In addition, normalized conductivity values were obtained, in this case, for a cross section of the pipe where an electrical impedance tomography (EIT) ring was installed. Numerical studies were carried out in the comsol multiphysics platform, using the Euler–Euler approach, coupled with the k– ε turbulence model. In the simulations, two equations for the calculation of the drag coefficient, Schiller–Neumann and Haider–Levenspiel, and three equations for mixture viscosity, Guth and Simba (1936), Brinkman (1952), and Pal (2000), were studied. The simulated data were validated with the experimental results of the pressure drop, good results having been obtained. The best fit occurred for the simulations that used the Schiller–Neumann equation for the calculation of the drag coefficient and the Pal (2000) equation for the mixture viscosity.

Based on a novel control scheme, where a steady modification of the streamwise velocity profile leads to complete relaminarization of initially fully turbulent pipe flow, we investigate the applicability and usefulness of custom-shaped honeycombs for such control. The custom-shaped honeycombs are used as stationary flow management devices which generate specific modifications of the streamwise velocity profile. Stereoscopic particle image velocimetry and pressure drop measurements are used to investigate and capture the development of the relaminarizing flow downstream these devices. We compare the performance of straight (constant length across the radius of the pipe) honeycombs with custom-shaped ones (variable length across the radius) and try to determine the optimal shape for maximal relaminarization at minimal pressure loss. The optimally modified streamwise velocity profile is found to be M-shaped, and the maximum attainable Reynolds number for total relaminarization is found to be of the order of 10,000. Consequently, the respective reduction in skin friction downstream of the device is almost by a factor of 5. The break-even point, where the additional pressure drop caused by the device is balanced by the savings due to relaminarization and a net gain is obtained, corresponds to a downstream stretch of distances as low as approximately 100 pipe diameters of laminar flow.

The pressure drop in 90 deg elbows under the operating conditions of geothermal power plants in Mexico is studied using the computational fluid dynamics model. The elbow resistance coefficient was calculated for a steam flow with high Reynolds numbers (1.66–5.81 × 10 6 ) and different curvature ratios (1, 1.5, and 2). The simulations were carried out with the commercial software ANSYS cfx , which considered the Reynolds-averaged Navier–Stokes (RANS) compressible equations and the renormalization group (RNG) k– ε turbulence model. First, the methodology was validated by comparing the numerical results (velocity and pressure) with published data of airflow (25 °C, 0.1 MPa) with high Reynolds numbers. Then, scenarios with different diameters (0.3–1.0 m) and conditions of the working fluid (0.8–1.2 MPa) were simulated to obtain velocity, pressure, density, and temperature profiles along the pipeline. The temperature and density gradients combined with the compressible effects achieved in the 90 deg elbows modified the flow separation, pressure drop, and resistance coefficient. Based on the resistance coefficient, factors were generated for a new equation, which was integrated into Geosteam.Net to calculate the pressure drop in a pipeline at the Los Azufres geothermal power plant. The difference with the data measured by a pressure transducer was 7.59%, while the equations developed for water or air showed differences between 11.23% and 45.22%.

This study uses novel methods, combining discrete element method (DEM) simulations for packing and computational fluid dynamics (CFD) modeling of fluid flow, to simulate the pressure drop across rigid, randomly packed beds of spheres ranging from 1 to 3 mm in diameter, with porosities between 0.34 and 0.45. This modeling approach enables the combined effect of void fraction and particle size to be studied in more depth than that has been previously possible and is used to give insight into the ability of the well-established Ergun equation to predict the pressure drop behavior. The resulting predictions for pressure drop as a function of superficial velocity were processed to yield coefficients α and β in the Ergun equation and were found to be in keeping with equivalent data in the literature. Although the scatter in α with structural variations was very small, the scatter in β was large (±20%), leading to inaccuracies when used to predict pressure drop data at velocities beyond the Darcy regime. Evaluation of the packed particle structures showed that regions of poor packing, in samples with high porosity and large particle sizes, lead to lower β values. The findings bring strong support to the belief that a generalized model, such as that by Ergun, cannot yield a unique value for β , even for identical spheres.

High cavitating or supercavitating flows in fuel injector systems are crucial since they improve the mixing and the fuel atomization into combustion chambers, decreasing both fuel consumption and pollutant emissions. However, there is a lack of information regarding the required time to obtain high cavitating flows at the nozzle outlet, from the start of the injection pulse. In this work, a new method to quantify the time to get supercavitating flows at the nozzle outlet is developed. In particular, the delay in the inception of a supercavitating flow through a micronozzle is numerically analyzed for different pressure drops in a well-studied benchmark for fuel injectors. The three-dimensional simulations show that a delay higher than 100 μ s is necessary for moderate pressure drops. Nevertheless, the delay tends to decay by rising amplitudes of the pressure pulse, reaching a saturation value of around 65 μ s.

The hydrodynamic cavitation in a Venturi tube is studied both theoretically and experimentally. A lumped parameter model was developed to describe the accumulation and dissipation of energy in the biphasic flow as a function of the bubble population characteristics (mean volume, standard deviation, and void fraction). Resistance, capacitance, inductance, and frequency lumped-parameters were identified applying the fluid conservation equations (mass and momentum) along with electrical/hydraulic analogies. Experiments with 1,2-propanediol were carried out in a hydraulic circuit composed of valves, a pump, and a Venturi nozzle. The acoustic noise generated (at different cavitation regimes) by the passage of the fluid through the tube was acquired with a piezoelectric sensor. After processing the experimental signals, the system frequency at each operation condition was determined. Plausible estimations of the void fraction were obtained at different experimental frequencies by evaluating a theoretical expression of the frequency lumped-parameter. This semi-empirical technique might be a low-cost alternative when the void fraction of a flow needs to be determined and tomography devices are not available.

This paper presents computational simulations of flows in packed beds and compares the computational pressure-drop results with those given by the Ergun correlation. The computational methodology used in this work follows the combined discrete element method (DEM) and computational fluid dynamics (CFD) technique. DEM is used to predict the locations and packing structure of the particles in the bed, while CFD is used to predict the flow field in the void space surrounding the packed particles. The computational results obtained for irregular packed beds show that the local packing-structure parameters have significant effects not only on the local velocity and pressure fields but also on macroscopic quantities, such as the average pressure gradient along the length of the packed column. The computational results also show that classical correlations based on averaged values, such as the Ergun correlation, have poor predictive accuracy for macroscopic variations along a packed column, and this is mainly because such correlations do not account for local packing-structure parameters. The computational results confirm the existence of sections with linear variation of macroscopic parameters along the length of the packed column, and this leads to the conclusion that accurate results from DEM-CFD methods on shortened columns can be extrapolated to full-length columns. Moreover, it was found that unlike regularly packed beds, the predicted pressure for randomly packed beds experiences an apparent strong recovery near the downstream end of the packed bed, and then experiences a strong dip down to the plateau leading to the exit pressure.

Stratified gas–liquid flow is a flow regime typically encountered in multiphase pipelines. The understanding and modeling of this regime is of engineering importance especially for the oil and gas industry. In this work, simulations have been conducted for stratified air–water flow in pipes. We solved the Reynolds-averaged Navier–Stokes (RANS) equations with the volume of fluid (VOF) method. The aim of this work was to evaluate the performance of the k–ω shear stress transport (SST) turbulence model with and without damping of the turbulence at the gas–liquid interface. Simulation results were compared with some of the latest experimental results found in the literature. A comparison between the simulated velocity and kinetic energy profiles and the experimental results obtained with the particle image velocimetry (PIV) technique was conducted. The characteristics of the interfacial waves were also extracted and compared with the experiments. It is shown that a proper damping of the turbulence close to the interface is needed to obtain agreement with the experimental pressure drop and liquid hold-up. In its current form, however, RANS with the k –ω turbulence model is still not able to give an accurate prediction of the velocity profiles and of the interface waves.

Large eddy simulation (LES) is conducted for the flow over the shell side of a helical coil steam generator (HCSG) heat exchanger. Simulations are conducted on a simplified experimental test section that represents a one-column region of the helical coils using half-rods. Although the rods are wall-bounded, the flow still exhibits the turbulent characteristics and fluctuations from vortex shedding that one would expect from crossflow around a cylinder. The spectral element, computational fluid dynamics (CFD) code Nek5000, is used to capture the physics, and the results are compared with particle image velocimetry (PIV) measurements. In order to ensure that the turbulence is resolved, analysis is conducted by using the Taylor length scales and normalized wall distance. Sensitivity to the inlet boundary conditions (BCs) and the spatial discretization for different polynomial order solutions are also studied, finding only minor differences between each case. Pressure drop and velocity statistics show reasonable agreement with PIV. Proper orthogonal decomposition (POD) analysis reveals that the primary modes are similar between experiment and simulation, although the LES predicts higher turbulent kinetic energy than does PIV. Overall, the study establishes the resolution and resources required in order to conduct a high-fidelity simulation over 12 helical rods.

In this study, a qualitative assessment of transitional velocity engineering models for predicting non-Newtonian slurry flows in a horizontal pipe was performed using data from a wide range of pipe diameters (25–268 mm). In addition, the gamma theta transition model was used to compute selected flow conditions. These models were used to predict transitional velocities in large pipe diameters (up to 420 mm) for slurries. In general, it was observed that most of the current engineering models predict transitional velocities conservatively. Based on the gamma theta transition model results, for large Hedström numbers (He ≳ 10 5 ), other methods should be used to predict transitional velocities if a change in the pipe diameter (scale-up) results in an order of magnitude increase in the He value. It was also found that the gamma theta transition model predicted a laminar flow condition in the fully developed region for flow conditions with a small plug region (low-yield stress-to-wall shear stress ratio), which is contrary to what has been observed in some experiments. This is attributed to the local fluid rheological parameters values, which might be different from those reported. However, the gamma theta transition model results are in good agreement with the experimental data for flow conditions that have a large plug region (high-yield stress-to-wall shear stress ratio).

The hydrodynamic entrance length, pressure drop analysis, viscosity, and fully developed velocity profile in horizontal pipe for crude oil with and without water and surfactant were studied in a 2 in ID horizontal pipe of length 2.5 m experimentally. Hydrodynamic entry length and fluid characteristics have been examined by varying temperature, water fraction, and flow rates. Temperature was varied by 25–40 °C, flow rates 40–60 LPM, and water 0–15% v/v and Madhuca longifolia from 500 to 2000 ppm. Triton X-100 was mixed with water to increase the emulsion capability during crude oil–water flows. The results showed significant influence of water, flow rate, and temperature on the hydrodynamic entry region length, pressure drop, viscosity, and velocity profiles along with natural surfactant. Pressure drop was reduced by 93.75%, 94.18%, and 93.02% with 15% water and 2000 ppm surfactant at 40 °C for 40 LPM, 50 LPM, and 60 LPM, respectively. Viscosity of the crude oil during flowing is greatly influenced by water and addition of surfactant. After addition of 2000 ppm surfactant and 15% water at 40 °C, viscosity reduced by about 94%. Hydrodynamic entry region length increased from 0.0354 to 0.2014 m, 0.0368 to 0.2336 m, and 0.0384 to 0.2641 m during transportation of crude oil after addition of 2000 ppm surfactant and 15% water at 40 °C for 40 LPM, 50 LPM, and 60 LPM flow, respectively.

The pressure drop across 90 deg sharp-angled miter elbows connecting straight circular pipes is studied in a bespoke experimental facility by using water and air as working fluids flowing in the range of bulk Reynolds number 500 < Re < 60 , 000 . To the best of our knowledge, the dependence on the Reynolds number of the pressure drop across the miter elbow scaled by the dynamic pressure, i.e., the pressure-loss coefficient K , is reported herein for the first time. The coefficient is shown to decrease sharply with the Reynolds number up to about Re = 20 , 000 and, at higher Reynolds numbers, to approach mildly a constant K = 0.9 , which is about 20% lower than the currently reported value in the literature. We quantify this relation and the dependence between K and the straight-pipe friction factor at the same Reynolds number through two new empirical correlations, which will be useful for the design of piping systems fitted with these sharp elbows. The pressure drop is also expressed in terms of the scaled equivalent length, i.e., the length of a straight pipe that would produce the same pressure drop as the elbow at the same Reynolds number.

This paper proposes a novel orifice flow model for non-Newtonian fluids. The orifice model is developed for sharp orifices with small apertures (orifice to pipe diameter ratio: 0.04 ≤ β ≤ 0.16) for which predictive models are not present in the literature. The orifice flow experiment is conducted with three different orifices and three different fluids. From the experimental data, a correlation is developed that relates Euler number to Reynolds number and orifice diameter ratio. It also accounts for elastic effects of the fluid on orifice flow by including Weissenberg number in the model. The developed model predicts the experimental data within reasonable accuracy.

To achieve longer-life liquid-metal fast reactor cores, designers are considering to increase the wall gap of the wire-wrapped hexagonal fuel bundles to account for volumetric void swelling and radiation creep. A new wire-wrapped hexagonal test bundle has been constructed, with a wall gap larger than prior experiments, and experimental pressure drop data have been generated under laminar, transition, and turbulent flow regimes (corresponding to Re of 250–19,000), to complement the existing database of small wall gap experimental bundles. The comparison of the experimental data set with the predictions of four existing correlations (Baxi and Dalle Donne, Cheng and Todreas detailed (CTD), Kirillov, and Rehme) showed general agreement between data and the selected correlations. However, the CTD correlation most accurately predicted the experimental trend and the transition between flow regimes. The analysis of the experimental data also revealed that the larger wall gap size caused a lower bundle pressure drop due to the increased bypass flow area.

In this paper, a theoretical study of ball valves is carried out for investigating the local resistance and pressure drop of ball valves in operating process. An equivalent model of ball valves is proposed based on the inherent mechanism of the resistance loss, which can be divided into three equivalent throttling components: a thick orifice, two variable-opening eccentric orifice plates, and a Z type elbow. Through analysis of the flow resistance of the three components, a general parametric modeling of ball valves is presented for the flow resistance analysis, and then an analytical formula of pressure drop is demonstrated. The results obtained from the presented model are compared with the prior test data to validate this model, and good agreement is observed. Indicate that the presented model has high accuracy in predicting the resistance and pressure loss in various openings. The results show that the influences of thin orifice plates play an important role in the total flow resistance coefficient and pressure drop, especially in the small opening. The effects of thick orifice plates and the Z type elbow gradually increased as the valve opening rises and becomes significant when the opening is more than 70%.

Hybrid low pressure air extractors are an economic way to enhance indoor air quality. The evaluation of their energetic performances needs the analysis of flow parameters that is typically done with wind tunnel data and numerical simulations. The purpose of this study is to analyze, numerically and experimentally, the flow and the energetic performances of a hybrid rooftop extractor. This innovative extractor has two main features: it works at low difference of pressure, below 50 Pa, and its fan is placed far above the duct outlet, out of the fluid flow. The hybrid extractor works following three modes of operation: stack effect, Venturi effect, and fan rotation. The two first modes of operation allow large energy saving. To analyze the three modes of operation, three sets of corresponding Reynolds-averaged Navier–Stokes (RANS) simulations are developed. The first one allows us to estimate the pressure drop due to the geometry of the air extractor. The second one is used to check the ability of the extractor to generate a suction into the duct in the presence of wind. The final one involves multiple reference frame (MRF) modeling in order to study the flow when the electric motor drives the fan. The numerical simulation configurations are validated with experimental data. A good behavior of the extractor is found for simulations of stack effect mode and Venturi effect mode. The stack effect and the Venturi effect allows the hybrid extractor to work most of the time without electric power. Finally, energetic comparisons are given.

Foam structures are a class of modern microporous media that possesses high thermal conductivity, large accessible specific surface area, and high porosities. Nowadays, industrial applications, such as filtration, heat exchange and chemical reaction, etc., utilize porous media such as open-cell foams. Knowledge of pressure drop induced by these foam matrices is essential for successful design and operation of high-performance industrial systems. The homogenized pressure drop data in the literature are widely dispersed (up two orders of magnitude) despite numerous researches has been conducted since two decades. Most of the empirical pressure drop correlations were derived using Ergun-like approach. In this view, a careful evaluation of empirical correlations as well as the relationship of intrinsic flow law characteristics (permeability and inertia coefficient) with morphological parameters is imperative. This paper presents the start-of-the-art of various pressure drop correlations as well as highlights the ambiguities and inconsistencies in various definitions of several key parameters. The applicability of the empirical correlations presented in the literature was examined by comparing them against numerically calculated pressure drop data of open-cell foams (metal and ceramic) for the porosities ranging from 0.60 up to 0.95. A comprehensive study has been conducted to identify the reasons of dispersed pressure drop data in the literature. Although substantial progress has been made in the field of fluid flow in open-cell foams, it is yet difficult to predict pressure drop data from a given set of morphological parameters.