The Relationship Between Standing Waves, Pressure Pulse Propagation, and Critical Flow Rate in Two-Phase Mixtures

A two-fluid model is presented that can be used to predict the celerity and attenuation of small-amplitude harmonic disturbances in bubbly two-phase flow. This frequency-dependent relationship is then used to predict the propagation of small-amplitude pressure perturbations through the use of Fourier decomposition techniques. Predictions of both standing waves and propagating pressure perturbations agree well with existing data. The low and high-frequency limits of the celerities predicted by the model are examined and their relationship to critical flow rate is demonstrated. Some limitations of the interfacial pressure model employed in conventional critical flow analysis are exposed and the implications to the prediction of critical flow rate are discussed.

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Prediction of Two-Phase Critical Flow Rate

Journal of Heat Transfer ◽

10.1115/1.3689050 ◽

1965 ◽

Vol 87 (1) ◽

pp. 53-57 ◽

Cited By ~ 28

Author(s):

S. Levy

Keyword(s):

Flow Rate ◽

Thermal Equilibrium ◽

Present Model ◽

Critical Flow ◽

Test Results ◽

Two Phase ◽

Mean Velocity ◽

Critical Flow Rate ◽

Pressure Losses ◽

Gas Void Fraction

An analytical model to predict two-phase critical flow rate is proposed. The model is based upon thermal equilibrium, a “lumped” treatment of the two-phase velocity (each phase is represented by a single mean velocity), and upon the neglect of frictional and hydrostatic pressure losses. A comparison of the proposed predictions with available test results and previous analyses shows that: (a) The present model agrees very well with the published test data; (b) In contrast to all other analyses, the model requires no assumption about the gas void fraction.

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Numerical Simulation of Liquid-Solid Two-Phase Flow Reflux in Particle Impact Drilling System

Advanced Materials Research ◽

10.4028/www.scientific.net/amr.402.824 ◽

2011 ◽

Vol 402 ◽

pp. 824-827

Author(s):

Hao Yu Sun ◽

Yang Zhang ◽

Bin Bin Wang

Keyword(s):

Flow Rate ◽

Critical Flow ◽

Particle Impact ◽

Multiphase Model ◽

Two Phase ◽

Economic Reason ◽

Critical Flow Rate ◽

Annular Gap ◽

Fluent Software ◽

Drilling System

In particle impact drilling system, the steel particles would be recycled for economic reason. Thus, whether particles can return to the ground under certain conditions is an important problem. In this paper, the relationship between critical flow rate and annular gap is numerically studied using the Eulerian multiphase model in FLUENT software. Both the numerical and the experiment results show that the critical flow rate decreases with the increasing annular gap, and the simulation results correspond well with experimental results.

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Investigation of Diameter Effect on Critical Flow

Volume 6: Thermal-Hydraulics ◽

10.1115/icone25-67076 ◽

2017 ◽

Author(s):

Zhao Minfu ◽

Lv Yufeng ◽

Zhang Dongxu ◽

Chen Yuzhou ◽

Bi Keming

Keyword(s):

Flow Rate ◽

Pressure Change ◽

Nozzle Diameter ◽

Critical Flow ◽

Actual Process ◽

Two Phase ◽

Critical Flow Rate ◽

System Pressure ◽

Flow Experiment ◽

Diameter Effect

Discrepancy has long existed about nozzle diameter effect on critical flow rate in two-phase critical flow analysis. The issue is of great importance because it involves whether the scaling test can accurately simulate the actual process during loss of coolant accident. A series of transient critical flow experiments has been performed in China Institute of Atomic Energy (CIAE), which aims to study the nozzle diameter effect. The diameter of adopted test nozzle is 5mm, 10mm and 15mm, respectively. The experiment result shows that the discharge mass flow rate decreases as nozzle diameter increases. This is contradictory with the results obtained from steady state critical flow experiment. Comprehensive analysis shows that the diameter effect observed in transient critical flow experiment is transient effect caused by system pressure change, and the mechanism is the dynamic unbalance in the transient period. It is presumed that for the same test section with a certain diameter, if the pressure change velocity is different, the measured critical flow rate will be different. The conclusion is validated in the pressurization and depressurization blowdown test. It| is arrived that nozzle diameter has no direct effect on critical flow rate, and thus the discrepancy on diameter effect is clarified.

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Discussion: “Prediction of Two-Phase Critical Flow Rate” (Levy, S., 1965, ASME J. Heat Transfer, 87, pp. 53–57)

Journal of Heat Transfer ◽

10.1115/1.3689051 ◽

1965 ◽

Vol 87 (1) ◽

pp. 57-58 ◽

Cited By ~ 1

Author(s):

V. E. Schrock

Keyword(s):

Heat Transfer ◽

Flow Rate ◽

Critical Flow ◽

Two Phase ◽

Critical Flow Rate

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Closure to “Discussion of ‘Prediction of Two-Phase Critical Flow Rate’” (1965, ASME J. Heat Transfer, 87, pp. 57–58)

Journal of Heat Transfer ◽

10.1115/1.3689052 ◽

1965 ◽

Vol 87 (1) ◽

pp. 58-58

Author(s):

S. Levy

Keyword(s):

Heat Transfer ◽

Flow Rate ◽

Critical Flow ◽

Two Phase ◽

Critical Flow Rate

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EXPERIMENTAL DATA SET NO. 26: THE DISPERSION AND ATTENUATION OF SMALL AMPLITUDE STANDING WAVES AND THE PROPAGATION OF ACOUSTIC PRESSURE PULSES IN BUBBLY AIR/WATER TWO-PHASE FLOWS

Multiphase Science and Technology ◽

10.1615/multscientechn.v6.i1-4.200 ◽

1992 ◽

Vol 6 (1-4) ◽

pp. 353-371

Author(s):

Arthur E. Ruggles

Keyword(s):

Experimental Data ◽

Small Amplitude ◽

Acoustic Pressure ◽

Standing Waves ◽

Two Phase Flows ◽

Two Phase ◽

Data Set ◽

Pressure Pulses ◽

Dispersion And Attenuation

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Role of Shearing Dispersion and Stripping in Wax Deposition in Crude Oil Pipelines

Energies ◽

10.3390/en12224325 ◽

2019 ◽

Vol 12 (22) ◽

pp. 4325

Author(s):

Zhihua Wang ◽

Yunfei Xu ◽

Yi Zhao ◽

Zhimin Li ◽

Yang Liu ◽

...

Keyword(s):

Crude Oil ◽

Flow Rate ◽

Critical Flow ◽

Wax Deposition ◽

Dominant Effect ◽

Critical Flow Rate ◽

Oil Pipelines ◽

Oil Flow ◽

Shearing Mechanism

Wax deposition during crude oil transmission can cause a series of negative effects and lead to problems associated with pipeline safety. A considerable number of previous works have investigated the wax deposition mechanism, inhibition technology, and remediation methods. However, studies on the shearing mechanism of wax deposition have focused largely on the characterization of this phenomena. The role of the shearing mechanism on wax deposition has not been completely clarified. This mechanism can be divided into the shearing dispersion effect caused by radial migration of wax particles and the shearing stripping effect caused by hydrodynamic scouring. From the perspective of energy analysis, a novel wax deposition model was proposed that considered the flow parameters of waxy crude oil in pipelines instead of its rheological parameters. Considering the two effects of shearing dispersion and shearing stripping coexist, with either one of them being the dominant mechanism, a shearing dispersion flux model and a shearing stripping model were established. Furthermore, a quantitative method to distinguish between the roles of shearing dispersion and shearing stripping in wax deposition was developed. The results indicated that the shearing mechanism can contribute an average of approximately 10% and a maximum of nearly 30% to the wax deposition process. With an increase in the oil flow rate, the effect of the shearing mechanism on wax deposition is enhanced, and its contribution was demonstrated to be negative; shear stripping was observed to be the dominant mechanism. A critical flow rate was observed when the dominant effect changes. When the oil flow rate is lower than the critical flow rate, the shearing dispersion effect is the dominant effect; its contribution rate increases with an increase in the oil flow temperature. When the oil flow rate is higher than the critical flow rate, the shearing stripping effect is the dominant effect; its contribution rate increases with an increase in the oil flow temperature. This understanding can be used to design operational parameters of the actual crude oil pipelines and address the potential flow assurance problems. The results of this study are of great significance for understanding the wax deposition theory of crude oil and accelerating the development of petroleum industry pipelines.

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Numerical Simulation of Vibration of Composite Pipelines Conveying Pulsating Fluid

International Journal of Applied Mechanics ◽

10.1142/s175882511950090x ◽

2019 ◽

Vol 11 (09) ◽

pp. 1950090 ◽

Cited By ~ 4

Author(s):

B. A. Khudayarov ◽

KH. M. Komilova ◽

F. ZH. Turaev

Keyword(s):

Internal Pressure ◽

Galerkin Method ◽

Flow Rate ◽

Pulsating Flow ◽

Integral Model ◽

Rheological Parameters ◽

Critical Flow ◽

Critical Flow Rate ◽

Weakly Singular ◽

Pulsating Fluid

Vibration problems of pipelines made of composite materials conveying pulsating flow of gas and fluid are investigated in the paper. A dynamic model of motion of pipelines conveying pulsating fluid flow supported by a Hetenyi’s base is developed taking into account the viscosity properties of the structure material, axial forces, internal pressure and Winkler’s viscoelastic base. To describe the processes of viscoelastic material strain, the Boltzmann–Volterra integral model with weakly singular hereditary kernels is used. Using the Bubnov–Galerkin method, the problem is reduced to the study of a system of ordinary integro-differential equations (IDE). A computational algorithm is developed based on the elimination of the features of IDE with weakly singular kernels, followed by the use of quadrature formulas. The effect of rheological parameters of the pipeline material, flow rate and base parameters on the vibration of a viscoelastic pipeline conveying pulsating fluid is analyzed. The convergence analysis of the approximate solution of the Bubnov–Galerkin method is carried out. It was revealed that the viscosity parameters of the material and the pipeline base lead to a significant change in the critical flow rate. It was stated that an increase in excitation coefficient of pulsating flow and the parameter of internal pressure leads to a decrease in the critical flow rate. It is shown that an increase in the singularity parameter, the Winkler base parameter, the rigidity parameter of the continuous base layer and the Reynolds number increases the critical flow rate.

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Effect of Non-Condensible Gas on the Subcooled Water Critical Flow in a Safety Valve

10th International Conference on Nuclear Engineering, Volume 3 ◽

10.1115/icone10-22559 ◽

2002 ◽

Author(s):

Se Won Kim ◽

Sang Kyoon Lee ◽

Hee Cheon No

Keyword(s):

Flow Rate ◽

Critical Pressure ◽

Safety Valve ◽

Pressure Ratio ◽

Water Flow Rate ◽

Critical Flow ◽

Inlet Temperature ◽

Nitrogen Gas ◽

Critical Flow Rate ◽

Subcooled Water

The effect of non-condensable gas on the subcooled water critical flow in a safety valve is investigated experimentally at various subcoolings with 3 different disk lifts. To evaluate its effect on the critical pressure ratio and critical flow rate, three parameters are considered: the ratios of outlet pressure to inlet pressure, the subcooling to inlet temperature, and the gas volumetric flow to water volumetric flow are 0.15–0.23, 0.07–0.12, and 0–0.8, respectively. It turns out that the critical pressure ratio is mainly dependent on the subcooling, and its dependency on the gas fraction and the pressure drop is relatively small. When the ratio of nitrogen gas volumetric flow to water volumetric flow becomes lower than 20%, the subcooled water critical flow rate is decreased about 10% compare to the water flow rate of without non-condensable gas. However, it maintains a constant value after the ratio of gas volumetric flow to water volumetric flow becomes higher than 20%. The subcooled water critical flow correlation, which considers subcooling, disc lift, backpressure, and non-condensable gas, shows good agreement with the total present experimental data with the root mean square error 8.17%.

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