A unified fractional flow framework for predicting the liquid holdup in two-phase pipe flows

Two-phase pipe flow occurs frequently in oil&gas industry,nuclear power plants,and CCUS.Reliable calculations of gas void fraction(or liquid holdup)play a central role in two-phase pipe flow models.In this paper we apply the fractional flow theory to multiphase flow in pipes and present a unified modeling framework for predicting the fluid phase volume fractions over a broad range of pipe flow conditions.Compared to existing methods and correlations,this new framework provides a simple,approximate,and efficient way to estimate the phase volume fraction in two-phase pipe flow without invoking flow patterns.Notably,existing correlations for estimating phase volume fraction can be transformed and expressed under this modeling framework.Different fractional flow models are applicable to different flow conditions,and they demonstrate good agreement against experimental data within 5%errors when compared with an experimental database comprising of 2754 data groups from 14literature sources,covering various pipe geometries,flow patterns,fluid properties and flow inclinations.The gas void fraction predicted by the framework developed in this work can be used as inputs to reliably model the hydraulic and thermal behaviors of two-phase pipe flows.

Diagnostic performance of intravascular ultrasound-based fractional flow reserve in evaluating of intermediate left main stenosis

BACKGROUND The recently introduced ultrasonic flow ratio(UFR),is a novel fast computational method to derive fractional flow reserve(FFR)from intravascular ultrasound(IVUS)images.In the present study,we evaluate the diagnostic performance of UFR in patients with intermediate left main(LM)stenosis.METHODS This is a prospective,single center study enrolling consecutive patients with presence of intermediated LM lesions(diameter stenosis of 30%-80%by visual estimation)underwent IVUS and FFR measurement.An independent core laboratory assessed offline UFR and IVUS-derived minimal lumen area(MLA)in a blinded fashion.RESULTS Both UFR and FFR were successfully achieved in 41 LM patients(mean age,62.0±9.9 years,46.3%diabetes).An acceptable correlation between UFR and FFR was identified(r=0.688,P<0.0001),with an absolute numerical difference of 0.03(standard difference:0.01).The area under the curve(AUC)in diagnosis of physiologically significant coronary stenosis for UFR was 0.94(95%CI:0.87-1.01),which was significantly higher than angiographic identified stenosis>50%(AUC=0.66,P<0.001)and numerically higher than IVUS-derived MLA(AUC=0.82;P=0.09).Patient level diagnostic accuracy,sensitivity and specificity for UFR to identify FFR≤0.80 was 82.9%(95%CI:70.2-95.7),93.1%(95%CI:82.2-100.0),58.3%(95%CI:26.3-90.4),respectively.CONCLUSION In patients with intermediate LM diseases,UFR was proved to be associated with acceptable correlation and high accuracy with pressure wire-based FFR as standard reference.The present study supports the use of UFR for functional evaluation of intermediate LM stenosis.

PIV analysis and high-speed photographic observation of cavitating flow field behind circular multi-orifice plates

Based on a self-developed hydrodynamic cavitation device with different geometric parameters for circular multi-orifice plates,turbulence characteristics of cavitating flow behind multi-orifice plates,including the effects of orifice number and orifice layout on longitudinal velocity,turbulence intensity,and Reynolds stress,were measured with the particle image velocimetry(PIV)technique.Flow regimes of the cavitating flow were also observed with high-speed photography.The experimental results showed the following:(1)high-velocity multiple cavitating jets occurred behind the multi-orifice plates,and the cavitating flow fields were characterized by topological structures;(2)the longitudinal velocity at each cross-section exhibited a sawtooth-like distribution close to the multi-orifice plate,and each sawtooth indicated one jet issuing from one orifice;(3)there were similar magnitudes and forms for the longitudinal and vertical turbulence intensities at the same cross-section;(4)the variation in amplitude of Reynolds stress increased with an increase in orifice number;and(5)the cavitation clouds in the flow fields became denser with the increase in orifice number,and the clouds generated by the staggered layout of orifices were greater in number than those generated by the checkerboard-type one for the same orifice number.The experimental results can be used to analyze the mechanism of killing pathogenic microorganisms through hydrodynamic cavitation.

A Model on the Void Fraction in Liquid Slugs for Vertical Slug Flow

Aim To develop a hydrodynamic model on the void fraction in liquid slugs for gas liquid slug flow in vertical tubes. Methods Developing the model by considering the gas exchange between the Taylor bubble and the following liquid slug. Results Some experimental data are obtained to check the model. In comparison with previous published results, the predictions from this model are better and in good agreement with the experimental data. The error is within ±20%. Conclusion The proposed model can correctly predict the void fraction in liquid slugs for gas liquid two phase slug flow in vertical tubes.

UNSTEADY FLOWS OF A GENERALIZED SECOND GRADE FLUID WITH THE FRACTIONAL DERIVATIVE MODEL BETWEEN TWO PARALLEL PLATES

The fractional calculus approach in the constitutive relationship model of a generalized second grade fluid is introduced.Exact analytical solutions are obtained for a class of unsteady flows for the generalized second grade fluid with the fractional derivative model between two parallel plates by using the Laplace transform and Fourier transform for fractional calculus.The unsteady flows are generated by the impulsive motion or periodic oscillation of one of the plates.In addition,the solutions of the shear stresses at the plates are also determined.

Unsteady rotating flows of a viscoelastic fluid with the fractional Maxwell model between coaxial cylinders

The fractional calculus is used in the constitutive relationship model of viscoelastic fluid. A generalized Maxwell model with fractional calculus is considered. Based on the flow conditions described, two flow cases are solved and the exact solutions are obtained by using the Weber transform and the Laplace transform for fractional calculus.

Fractional flow reserve: Current applications and overview of the available data

Flow fractional reserve(FFR) allows to evaluate the functional significance of coronary artery lesions, through the ratio of the mean coronary artery pressure after the stenosis to the mean aortic pressure duringmaximum hyperemia. The actual widely accepted cutoff value is 0.80. Below this value a coronary lesion is considered significant and therefore it requires invasive revascularization. Several studies [in particular Fractional Flow Reserve vs Angiography for Multivessel Evaluation 1(FAME-1) and FAME-2] have shown the relationship between FFR measurement and hard end-points(death, myocardial infarction, and urgent revascularization). Consequently, FFR evaluation represents the cornerstone in the decision-making in intermediate coronary lesions. Recent studies paved the way for further applications of FFR evaluation in complex and tricky clinical settings. In this paper, we perform an overview of the data regarding contemporary application of FFR. In particular, we review the use of FFR in: left main intermediate stenoses, serial stenoses, evaluation after stenting, guidance in coronary artery bypass surgery, and acute coronary syndrome. All the data presented in our overview confirm the essential role of FFR assessment in the daily clinical practice. The shift from "operator-dependent" to "FFR-dependent" evaluation in intermediate coronary artery stenosis is of paramount importance in order to improve the prognosis of our patients, through the discrimination of the functional role of every single coronary stenosis.

Investigation of oil-air two-phase mass flow rate measurement using Venturi and void fraction sensor

Oil-air two-phase flow measurement was investigated with a Venturi and void fraction meters in this work. This paper proposes a new flow rate measurement correlation in which the effect of the velocity ratio between gas and liquid was considered. With the pressure drop across the Venturi and the void fraction that was measured by electrical capacitance tomography apparatus, both mixture flow rate and oil flow rate could be obtained by the correlation. Experiments included bubble-, slug-, wave and annular flow with the void fraction ranging from 15% to 83%, the oil flow rate ranging from 0.97 kg/s to 1.78 kg/s, the gas flow rate ranging up to 0.018 kg/s and quality ranging nearly up to 2.0%. The root-mean-square errors of mixture mass flow rate and that of oil mass flow rate were less than 5%. Furthermore, coefficients of the correlation were modified based on flow regimes, with the results showing reduced root-mean-square errors.

Long-term outcomes after fractional flow reserve-guided percutaneous coronary intervention in patients with severe coronary stenosis

Objective To explore the safety and efficacy of FFR-guided percutaneous coronary intervention (PCI) in vessels with severe diameter stenosis. Methods & Results Of 1090 patients undergoing fractional flow reserve (FFR) assessment from 2002 to 2009,we identified 167 patients in whom FFR was measured in at least one 70%–89% stenotic lesion. These patients were subdivided into an FFR-defer group (n = 49) if PCI was deferred (FFR > 0.80),and an FFR-perform group (n = 118) if PCI was performed (FFR ≤ 0.80). Comparatively,an additional 1176 patients undergoing PCI in at least one lesion with 70%–89% stenosis but without measurement of FFR served as a control (angiography- guided) group. Clinical outcomes were compared during a median follow-up of 49.0 months. The 5-year Kaplan-Meier estimated revascularization rates were 16% in the FFR-defer group and 33% in the FFR-perform group (P = 0.046). The incidence of major adverse cardiac events were comparable in these two groups (HR = 0.82,95% CI: 0.37–1.82,P = 0.63). The number of stents placed was significantly lower in the FFR-guided group (0.9 ± 0.8 vs. 1.4 ± 0.8,P < 0.001). Conclusions Functional revascularization for lesions with visually severe stenosis is clinically safe and associated with fewer stents use. This study suggests that extending the use of FFR to more severe coronary lesions may be reasonable.

An Investigation on the Void Fraction for upward Gas-Liquid Slug Flow in Vertical Pipe

In order to investigate the influence of the entrance effect on the spatial distribution of phases, the experiments on gas-liquid two-phase slug flow in a vertical pipe of 0.03m ID were carried out by using optical probes and an EKTAPRO 1000 high speed motion analyzer. It demonstrates that the radial profile of slug flow void fraction is parabolic. Influenced by the falling liquid film, the radial profile curve of liquid slug void fraction in the wake region is also parabolic. Since fully turbulent velocity distribution is built up in the developed region,the void fraction profile in this region is the saddle type. At given superficial liquid velocity, the liquid slug void fraction increases with gas velocity. The radial profiles of liquid slug void fraction at different axial locations are all saddle curves, but void fraction is obviously high around the centerline in the entrance region. The nearer the measuring station is from the entrance, the farther the peak location is away from the wall.

Volumetric fraction measurement in oil-water-gas multiphase flow with dual energy gamma-ray system

Volumetric fraction distribution measurement is a constituent part of process tomography system in oil-water-gas multiphase flow. With the technological development of nuclear radial inspection, dual-energy γ-ray techniques make it possible to investigate the concentration of the different components on the cross-section of oil-water-gas multiphase pipe-flow. The dual-energy gamma-ray technique is based on materials attenuation coefficients measurement comprised of two radioactive isotopes of 241Am and 241Cs which have emission energies at 59.5 keV and 662 keV in this project. Nuclear instruments and data acquisition system were designed to measure the material’s attenuation dose rate and a number of static tests were conducted at the Multiphase Laboratory, Institute of Mechanics, Chinese Academy of Sciences. Three phases of oil-water-gas media were inves- tigated for their possible use to simulate different media volumetric fraction distributions in experimental vessels. Attenuation intensities were measured, and the arithmetic of linear attenuation coefficients and the equations of volumetric fractions were studied. Investigation of an unexpected measurement error from attenuation equations revealed that a modified arithmetic was involved and finally the system achieved acceptable accuracy in experimental research.

Clinical applications of fractional flow reserve in bifurcation lesions

Pereutaneous coronary intervention （PCI） for coronary bifurcation lesions has been associated with lower procedural success rates and worse clinical outcomes compared with PCI for simple coronary lesions. Angiographic evaluation alone is sometimes inaccurate and does not reflect the fimctional significance of bifurcation lesions. The fractional flow reserve （FFR） is an easily obtainable, reliable, and reproducible physiologic parameter. This parameter is epicardial lesion specific and reflects both degree of stenosis and the myocardial territory supplied by the specific artery. Recent studies have shown that FFR-guided provisional side branch intervention strategy for bifurcation lesions is feasible and effective and can reduce unnecessary complex interventions and related complications. However, an adequate understanding of coronary physiology and the pitfalls of FFR is essential to properly use FFR for PCI of complex bifurcation lesions.

Analysis of one-dimensional rheological consolidation of double-layered soil with fractional derivative Merchant model and non-Darcian flow described by non-Newtonian index

To further investigate the one-dimensional(1D)rheological consolidation mechanism of double-layered soil,the fractional derivative Merchant model(FDMM)and the non-Darcian flow model with the non-Newtonian index are respectively introduced to describe the deformation of viscoelastic soil and the flow of pore water in the process of consolidation.Accordingly,an 1D rheological consolidation equation of double-layered soil is obtained,and its numerical analysis is performed by the implicit finite difference method.In order to verify its validity,the numerical solutions by the present method for some simplified cases are compared with the results in the related literature.Then,the influence of the revelent parameters on the rheological consolidation of double-layered soil are investigated.Numerical results indicate that the parameters of non-Darcian flow and FDMM of the first soil layer greatly influence the consolidation rate of double-layered soil.As the decrease of relative compressibility or the increase of relative permeability between the lower soil and the upper soil,the dissipation rate of excess pore water pressure and the settlement rate of the ground will be accelerated.Increasing the relative thickness of soil layer with high permeability or low compressibility will also accelerate the consolidation rate of double-layered soil.

Void fraction measurement and calculation model of vertical upward co-current air-water slug flow

The focus of this paper is on the measurement and calculation model of void fraction for the vertical upward co-current air-water slug flow in a circular tube of 15 mm inner diameter. High-speed photography and optical probes were utilized, with water superficial velocity ranging from 0.089 to 0.65 m·s^(-1)and gas superficial velocity ranging from 0.049 to 0.65 m·s^(-1). A new void fraction model based on the local parameters was proposed, disposing the slug flow as a combination of Taylor bubbles and liquid slugs. In the Taylor bubble region, correction factors of liquid film thickness Cδand nose shape CZ*were proposed to calculate aTB. In the liquid slug region, the radial void fraction distribution profiles were obtained to calculate aLS, by employing the image processing technique based on supervised machine learning. Results showed that the void fraction proportion in Taylor bubbles occupied crucial contribution to the overall void fraction. Multiple types of void fraction predictive correlations were assessed using the present data. The performance of the Schmidt model was optimal, while some models for slug flow performed not outstanding. Additionally, a predictive correlation was correlated between the central local void fraction and the cross-sectional averaged void fraction, as a straightforward form of the void fraction calculation model. The predictive correlation showed a good agreement with the present experimental data, as well as the data of Olerni et al., indicating that the new model was effective and applicable under the slug flow conditions.

A Fast-Fractional Flow Reserve Simulation Method in A Patient with Coronary Stenosis Based on Resistance Boundary Conditions

Fractional flow reserve(FFR)is the gold standard to identify individual stenosis causing myocardial ischemia in catheter laboratory.The purpose of this study is to present a fast simulation method to estimate FFR value of a coronary artery,which can evaluate the performance of vascular stenosis,based on resistance boundary conditions.A patient-specific 3-dimensional(3D)model of the left coronary system with intermediate diameter stenosis was reconstructed based on the CTA images.The resistance boundary conditions used to simulate the coronary microcirculation were computed based on anatomical reconstruction of coronary 3D model.This study was performed by coupling the 3D coronary tree model with the lumped parameter model(0D model).The flow rate and pressure of coronary tree were calculated in twenty minutes.In addition,the effect of inlet pressure and myocardial mass on FFRss values has been investigated.The results showed that the effect of myocardial mass was greater than the effect of inlet pressure on FFRss.This FFRss simulation method can quickly and accurately assess the influence of coronary stenosis in aid clinical diagnosis.

An Experimental Study on the Void Fraction for Gas-Liquid Two-Phase Flows in a Horizontal Pipe

The flow patterns and the void fraction related to a gas-liquid two-phase flow in a small channel are experimentally studied.The test channel is a transparent quartz glass circular channel with an inner diameter of 6.68 mm.The working fluids are air and water and their superficial velocities range from 0.014 to 8.127 m/s and from 0.0238 to 0.556 m/s,respectively.The void fraction is determined using the flow pattern images captured by a high-speed camera,while quick closing valves are used for verification.Four flow patterns are analyzed in experiments:slug flow,bubbly flow,annular flow and stratified flow.For intermittent flows(bubbly flow and slug flow),the cross-sectional void fraction is in a borderline condition while its probability distribution function(PDF)image displays a bimodal structure.For continuous flows(annular flow and stratified flow)the cross-sectional void fraction behaves as a fluctuating continuous curve while the(PDF)image displays a single peak structure.The volumetric void fraction data are also compared with available predictive formulas,and the results show that the agreement is very good.An effort is also provided to improve the so-called Gregory and Scott model using the available data.

Electromagnetohydrodynamic (EMHD) flow of fractional viscoelastic fluids in a microchannel

This study investigates the electromagnetohydrodynamic(EMHD)flow of fractional viscoelastic fluids through a microchannel under the Navier slip boundary condition.The flow is driven by the pressure gradient and electromagnetic force where the electric field is applied horizontally,and the magnetic field is vertically(upward or downward).When the electric field direction is consistent with the pressure gradient direction,the changes of the steady flow rate and velocity with the Hartmann number Ha are irrelevant to the direction of the magnetic field(upward or downward).The steady flow rate decreases monotonically to zero with the increase in Ha.In contrast,when the direction of the electric field differs from the pressure gradient direction,the flow behavior depends on the direction of the magnetic field,i.e.,symmetry breaking occurs.Specifically,when the magnetic field is vertically upward,the steady flow rate increases first and then decreases with Ha.When the magnetic field is reversed,the steady flow rate first reduces to zero as Ha increases from zero.As Ha continues to increase,the steady flow rate(velocity)increases in the opposite direction and then decreases,and finally drops to zero for larger Ha.The increase in the fractional calculus parameterαor Deborah number De makes it take longer for the flow rate(velocity)to reach the steady state.In addition,the increase in the strength of the magnetic field or electric field,or in the pressure gradient tends to accelerate the slip velocity at the walls.On the other hand,the increase in the thickness of the electric double-layer tends to reduce it.

Measurement of oil volume fraction and velocity distributions in vertical oil-in-water flows using ERT and a local probe

This paper presents the use of a high performance dual-plane electrical resistance tomography (ERT) system and a local dual-sensor conductance probe to measure the vertical upward oil-in-water pipe flows in which the mean oil volume fraction is up to 23.1%. A sensitivity coefficient back-projection (SBP) algorithm was adopted to reconstruct the flow distributions and a cross correlation method was applied to obtain the oil velocity distributions. The oil volume fraction and velocity distributions obtained from both measurement techniques were compared and good agreement was found, which indicates that the ERT tech- nique can be used to measure the low fraction oil-water flows. Finally, the factors affecting measurement precision were discussed.

Gamma-ray attenuation technique for measuring void fraction in horizontal gas-liquid two-phase flow

The measurement of void fraction is of importance to the oil industry and chemical industry. In this article, the principle and mathematical method of determining the void fraction of horizontal gas-liquid flow by using a sin- gle-energy γ-ray system is described. The γ-ray source is the radioactive isotope of 241Am with γ-ray energy of 59.5 keV. The time-averaged value of the void fraction in a 50.0-mm i.d. transparent horizontal pipeline is measured under various combinations of the liquid flow and gas flow. It is found that increasing the gas flow rate at a fixed liquid flow rate would increase the void fraction. Test data are compared with the predictions of the correlations and a good agreement is found. The result shows that the designed γ-ray system can be used for measuring the void fraction in a horizontal gas-liquid two-phase flow with high accuracy.

Linear Plus Linear Fractional Capacitated Transportation Problem with Restricted Flow

In this paper, a transportation problem with an objective function as the sum of a linear and fractional function is considered. The linear function represents the total transportation cost incurred when the goods are shipped from various sources to the destinations and the fractional function gives the ratio of sales tax to the total public expenditure. Our objective is to determine the transportation schedule which minimizes the sum of total transportation cost and ratio of total sales tax paid to the total public expenditure. Sometimes, situations arise where either reserve stocks have to be kept at the supply points, for emergencies or there may be extra demand in the markets. In such situations, the total flow needs to be controlled or enhanced. In this paper, a special class of transportation problems is studied where in the total transportation flow is restricted to a known specified level. A related transportation problem is formulated and it is shown that to each basic feasible solution which is called corner feasible solution to related transportation problem, there is a corresponding feasible solution to this restricted flow problem. The optimal solution to restricted flow problem may be obtained from the optimal solution to related transportation problem. An algorithm is presented to solve a capacitated linear plus linear fractional transportation problem with restricted flow. The algorithm is supported by a real life example of a manufacturing company.