Calculation of the Theoretical Critical Flow Rate of Saturated Steam

1982 ◽  
Vol 104 (1) ◽  
pp. 211-214
Author(s):  
J. W. Murdock
Keyword(s):  
Flow Rate ◽  
Critical Pressure ◽  
Theoretical Method ◽  
Ideal Gas ◽  
Saturated Steam ◽  
Critical Flow ◽  
Maximum Deviation ◽  
Average Deviation ◽  
Flow Rates ◽  
Critical Flow Rate

This paper is concerned with the computation of the theoretical critical flow of dry saturated steam through passages over a range of 1 psia (7 kPa) to the critical pressure of 3208.2 psia (22.12 MPa). Two computational methods are used: a theoretical method using ideal gas relations, and a flow maximization method using actual saturated steam properties. An equation is developed and based on the theoretical equation that yields flow rates that have an average deviation of 0.1 percent and a maximum deviation of 0.3 percent from the flow rate found by flow maximization. It is also demonstrated that Napier’s equation currently recommended by PTC 25.3-1976 “Safety and Relief Valves” is unsatisfactory for the calculation of theoretical critical flow rates.

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

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%.

Part Load Instability and Rotating Stall in a Multistage Low Specific Speed Pump

2020 ◽  
Author(s):  
E. M. A. Vermunt ◽  
K. A. J. Bruurs ◽  
M. S. van der Schoot ◽  
B. P. M. van Esch
Keyword(s):  
Flow Rate ◽  
Head Loss ◽  
Rotating Stall ◽  
Critical Flow ◽  
Flow Rates ◽  
Critical Flow Rate ◽  
Lower Flow ◽  
Low Specific Speed ◽  
Saddle Type ◽  
Specific Speed

Abstract A new diffuser design is developed for a low specific speed, multistage pump. In this design the diffuser and the de-swirl vanes are integrated into single vanes. This creates diffuser channels that extend from behind the impeller exit through the cross-over, up to the eye of the next stage impeller. Experiments show the occurrence of a saddle type instability in the head curve. At a critical flow rate of close to 50% of the flow rate at Best Efficiency Point (BEP), the head drops by 7% of the head at BEP. In this study Computational Fluid Dynamics (CFD) are used in an effort to understand the underlying flow phenomena. The head curve that is obtained with the transient CFD simulations contains a saddle type instability at a flow rate that is approximately the same as in the experiments, but with a lower magnitude. At flow rates higher than the critical flow rate, the predicted head and power are in very good agreement with the experimental data. At flow rates lower than the critical flow rate, the head and power are slightly over-predicted. An analysis of the pressure distribution in the pump reveals that the head loss at different flow rates in the diffuser shows a discontinuity at the critical flow rate. Since both the impeller head and the head loss in the vaneless gap increase continuously for decreasing flow rate, this is an indication that the cause of the head instability lies in the diffuser. Moreover, a strong increase in the variability of head and power at flow rates below the critical flow suggests that the phenomenon is unsteady. Flow patterns in the impeller and in the diffuser, as calculated by CFD, show a high degree of periodicity and are very similar for flow rates down to the critical flow rate. However, for lower flow rates the flow pattern changes completely. A single rotating stall cell is observed that causes two or three neighboring diffuser channels to stall, leading to a significantly lower flow rate or even a reversed flow. This stall pattern rotates in the direction of impeller rotation at a very low frequency of approximately 3.3% of the impeller rotation frequency.

Superflow of helium II through narrow slits

1952 ◽  
Vol 213 (1113) ◽  
pp. 158-175 ◽  
Keyword(s):  
Flow Rate ◽  
Critical Flow ◽  
Heat Current ◽  
Normal Flow ◽  
Critical Rate ◽  
Intermediate Point ◽  
Flow Rates ◽  
Critical Flow Rate ◽  
Helium Ii ◽  
Frictional Dissipation

The flow of liquid helium II has been investigated under gradients of pressure and temperature in slits of 1 μ diameter. Besides the flow rate, the heat current and the pressure difference at the ends of the slit, the pressure at an intermediate point within the slit has been determined. It was found that for superflow the entire drop in pressure and temperature occurs at the narrowest place in the slit. In the remainder of the slit mass flow takes place under effectively zero gradient of pressure or temperature. The experiments also indicate the existence of a critical flow rate beyond which frictional dissipation makes its appearance. The critical rate was determined by four different criteria which yielded consistent results. The temperature dependence of the critical rate is similar to that observed in the helium II film. With flow under a temperature gradient and for higher flow rates the hydrostatic pressure within the slit was found to drop below that at the ends and an explanation for this effect has been suggested. Some experiments with wider slits have shown that in these even for small velocities the transport is a mixture of superflow and normal flow which renders the phenomena very complex.

A Model To Calculate the Theoretical Critical Flow Rate Through Venturi Gas Lift Valves

SPE Journal ◽  
2010 ◽  
Vol 16 (01) ◽  
pp. 134-147 ◽  
Author(s):  
Alcino R. Almeida
Keyword(s):  
Heat Capacity ◽  
Natural Gas ◽  
Flow Rate ◽  
Ideal Gas ◽  
Isobaric Heat Capacity ◽  
Critical Conditions ◽  
Critical Flow ◽  
Critical Flow Rate ◽  
Gas Lift ◽  
The Ideal

Summary A model to calculate the theoretical critical flow rate of nitrogen (N2) or natural gas through a Venturi gas lift valve is described herein. This new model considers real-gas effects not only in density calculations but also in other thermodynamic properties that are relevant during gas isentropic evolution. For the properties of N2, the Bennedict, Webb, and Rubin (BWR) equation of state and an accurate correlation for the ideal-gas isobaric heat capacity were used. For natural gas, the Dranchuk and Abou-Kassem equation, which reproduces the well-known Standing and Katz chart, was used, and, for the ideal-gas isobaric heat capacity, it was assumed that the natural gas was a mixture of methane and ethane only, their individual ideal-gas heat capacity being calculated by updated correlations. To validate the use of the proposed equations of state, a comparison of calculated with experimental or reference data on properties of N2 and natural gas (including pure methane and some relevant mixtures) was performed with very good results for N2 and for natural-gas compositions usual in gas lift operations (dry gas with very small amounts of contaminants). For natural gas with moderate amounts of N2 and carbon dioxide (CO2), accurate results were obtained after correction of critical conditions and of ideal heat capacity. The model was also compared with other theoretical models found in the literature, which use compositional approaches for natural gas, with excellent results. Some experimental results obtained with commercial Venturi valves manufactured in Brazil are also presented.

Effect of Sand Bed Deposits on the Characteristics of Turbulent Flow of Water in Horizontal Annuli

2018 ◽  
Vol 141 (5) ◽  
Author(s):  
Majid Bizhani ◽  
Ergun Kuru
Keyword(s):  
Turbulent Flow ◽  
Reynolds Stress ◽  
Flow Rate ◽  
Velocity Profiles ◽  
Experimental Program ◽  
Critical Flow ◽  
Local Velocity ◽  
Flow Rates ◽  
Critical Flow Rate ◽  
Horizontal Annuli

An experimental program was conducted to investigate turbulent flow of water over the stationary sand bed deposited in horizontal annuli. A large-scale horizontal flow loop equipped with the state-of-the-art particle image velocimetry (PIV) system has been used for the experiments. Experiments were conducted to measure the instantaneous local velocity profiles during turbulent flow and examine the impact of the presence of a stationary sand bed deposits on the local velocity profiles, Reynolds shear stresses and turbulence intensities. Results have shown that the existence of a stationary sand bed causes the volumetric flow to be diverted away from the lower annular gap. Increasing the sand bed height causes further reduction of the volumetric flow rate in the lower annulus. Velocity profiles near the surface of the bed deposits showed a downward shift from the universal law in wall units indicating that the flow is hydraulically rough near the sand bed. The equivalent roughness height varied with flow rates. At flow rates less than the critical flow rate, the Reynolds stress profile near the bed interface had slightly higher peak values than that of the case with no sand bed. At the critical flow rate, however, the peak Reynolds stress values for the flow over the sand bed was lower than that of the case with no bed. This behavior is attributed to the bed load transport of sand particles at the critical flow rate.

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

Energies ◽  
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.

Numerical Simulation of Vibration of Composite Pipelines Conveying Pulsating Fluid

2019 ◽  
Vol 11 (09) ◽  
pp. 1950090 ◽  
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.

Critical flow rate of anode fuel exhaust in a PEM fuel cell system

2006 ◽  
Vol 156 (2) ◽  
pp. 512-519 ◽  
Author(s):  
Wenhua H. Zhu ◽  
Robert U. Payne ◽  
Bruce J. Tatarchuk
Keyword(s):  
Fuel Cell ◽  
Flow Rate ◽  
Pem Fuel Cell ◽  
Cell System ◽  
Critical Flow ◽  
Fuel Cell System ◽  
Critical Flow Rate

Hydraulic Characteristics of Pipelines Transporting Hot Waxy Crudes

2006 ◽  
Author(s):  
Jun Chen ◽  
Jinjun Zhang ◽  
Hongying Li
Keyword(s):  
Flow Rate ◽  
Pour Point ◽  
Friction Loss ◽  
Low Flow ◽  
Critical Flow ◽  
Outlet Temperature ◽  
Hydraulic Characteristics ◽  
Critical Flow Rate ◽  
Waxy Crude ◽  
Oil Pipeline

Waxy crudes are generally pipelined by means of heating. In general, the friction loss of a pipeline decreases with decreasing flow rate. This is the case of isothermal pipeline. However, a hot oil pipeline operated at low flow rate might show a contrary case, i.e. friction-loss increases with decreasing flow rate. This is an unstable operation state and may result in disastrous consequence of flow ceasing if tackled improperly. For a waxy crude pipeline, this may also be exaggerated by the non-Newtonian flow characteristics at temperatures near the pour point. That is to say, there may exist a critical flow rate for pipelines transporting heated waxy crude, and in order to ensure safe operation, the flow rate of a pipeline transporting hot oil should be no less than this critical flow rate. Based on theoretical analysis and can study, the hydraulic characteristics of pipelines transporting hot waxy crudes was investigated, and an empirical model was developed correlating the critical flow rate QC and the pipelining parameters, such as the average overall heat transfer coefficient, the ground temperature, the heating temperature, etc. Another relationship was found between TZC, the outlet temperature of the pipeline corresponding to the critical flow rate, and the critical flow rate. This TZC is also the lowest pipeline outlet temperature that ensures the normal pipelining operation state. Case study on a 720mm O.D. pipeline transporting heated Daqing waxy crude with a pour point of 36 °C showed that the TZC was in a range of 31∼34.2°C.

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