scholarly journals The Analysis of Nonlinear Vibrations of Top Tensioned Cantilever Pipes Conveying Pressurized Steady Two-Phase Flow under Thermal Loading

2017 ◽  
Author(s):  
Adeshina Adegoke ◽  
Ayo Oyediran
Keyword(s):  
Transverse Vibration ◽  
Thermal Loading ◽  
Nonlinear Vibrations ◽  
Two Phase Flow ◽  
Equations Of Motion ◽  
Multiple Scale ◽  
Phase Flow ◽  
Vibration Frequencies ◽  
Two Phase ◽  
Void Fractions

This paper studied the nonlinear vibrations of top tensioned cantilevered pipes conveying pressurized steady two-phase flow under thermal loading. The coupled axial and transverse governing partial differential equations of motion of the system were derived based on Hamilton’s mechanics with the centreline assumed to be extensible. Multiple scale perturbation method was used to resolve the governing equations, which resulted to an analytical approach for assessing the natural frequency, mode shape and the nonlinear coupled axial and transverse steady state response of the pipe. The analytical assessment reveals that at some frequencies the system is uncoupled, while at some frequencies a 1:2 coupling exists between the axial and the transverse frequencies of the pipe. Nonlinear frequencies versus the amplitude displacement of the cantilever pipe conveying two-phase flow at super critical mixture velocity for the uncoupled scenario exhibit a nonlinear hardening behaviour, an increment in the void fractions of the two-phase flow resulted to a reduction in the pipe’s transverse vibration frequencies and the coupled amplitude of the system. However, increasing the temperature difference, pressure and the presence of top tension were observed to increase the pipe’s transverse vibration frequencies without a significant change in the coupled amplitude of the system.

Prediction of Pump Performance Under Air-Water Two-Phase Flow Based on a Bubbly Flow Model

1993 ◽  
Vol 115 (4) ◽  
pp. 781-783 ◽  
Author(s):  
Kiyoshi Minemura ◽  
Tomomi Uchiyama
Keyword(s):  
Two Phase Flow ◽  
Bubbly Flow ◽  
Phase Flow ◽  
Centrifugal Pumps ◽  
Flow Conditions ◽  
Two Phase ◽  
Performance Change ◽  
Void Fractions ◽  
Two Phases

This paper is concerned with the determination of the performance change in centrifugal pumps operating under two-phase flow conditions using the velocities and void fractions calculated under the assumption of an inviscid bubbly flow with slippage between the two phases. The estimated changes in the theoretical head are confirmed with experiments within the range of bubbly flow regime.

New Experimental Data and Analysis for Two-Phase Flow-Induced Vibration of Tube Bundles: Preliminary Results

2003 ◽  
Author(s):  
Deepanjan Mitra ◽  
Vijay K. Dhir ◽  
Ivan Catton
Keyword(s):  
Two Phase Flow ◽  
Structural Parameters ◽  
Cross Flow ◽  
Instability Criterion ◽  
Phase Flow ◽  
Flow Induced Vibration ◽  
Two Phase ◽  
Void Fractions ◽  
Comparison Of The Results ◽  
Square Array

In the past, fluid-elastic instability in two-phase flow has been largely investigated with air-water flow. In this work, new experiments are conducted in air-water cross-flow with a fully flexible 5 × 3 normal square array having pitch-to-diameter ratio of 1.4. The tubes have a diameter of 0.016 m and a length of 0.21 m. The vibrations are measured using strain gages installed on piano wires used to suspend the tubes. Experiments are carried out for void fractions from 0%–30%. A comparison of the results of the current tests with previous experiments conducted in air-water cross-flow shows that instability occurs earlier in a fully flexible array as compared to a flexible tube surrounded by rigid tubes in an array. An attempt is made to separate out the effects of structural parameters of three different experimental datasets by replotting the instability criterion by incorporating the instability constant K, in the reduced velocity parameter.

Void Fractions in Two-Phase Flow: A Correlation Based upon an Equal Velocity Head Model

1969 ◽  
Vol 184 (1) ◽  
pp. 647-664 ◽  
Author(s):  
S. L. Smith
Keyword(s):  
Two Phase Flow ◽  
Head Model ◽  
Phase Flow ◽  
Excellent Correlation ◽  
Two Phase ◽  
Void Fractions ◽  
Dynamic Head ◽  
Wide Range ◽  
Mixture Phase ◽  
Simple Physical Model

An expression is obtained for void fraction in two-phase flow based upon a simple physical model. The model assumes an annular flow regime with a liquid phase and a homogeneous mixture phase flowing with equal dynamic head. Excellent correlation is obtained with a wide range of experimental data, indicating a significant improvement over current methods.

Estimation of Average Void Fraction for Gas-Liquid, Two-Phase Flow in an Industrial Nozzle Assembly Using a Quick-Closing-Valve

2008 ◽  
Author(s):  
Mohammad A. Rahman ◽  
Johana Gomez ◽  
Ted Heidrick ◽  
Brian A. Fleck ◽  
Jennifer McMillan
Keyword(s):  
Void Fraction ◽  
High Speed ◽  
Two Phase Flow ◽  
Video Camera ◽  
Synchronization Error ◽  
Phase Flow ◽  
Closing Time ◽  
Two Phase ◽  
Void Fractions ◽  
Atomization Performance

Experimentally accurate void fraction measurements are a challenge in an air/water, two-phase flows through an industrial nozzle assembly, as a highly non-uniform void fraction exists in the feeding conduit prior to the nozzle. In this study, average void fractions were measured by isolating a section in the feeding conduit of a horizontal nozzle assembly, termed as the quick-closing-valve (QCV) technique. A high-speed video camera was utilized to capture the asynchronization closing time, tac. The average closing time and asynchronization for the pneumatically controlled valves were 200 ms and 2 ms, respectively. Based on the equation of 100umtac (1−α)/αlc, the synchronization error between the two valves was 1.12%, 1.26%, and 1.79% for the 1%, 2% and 4% ALR cases, respectively; here um is the mixture velocity, α is the void faction, and lc is the closing length. Higher synchronization error at 4% ALR occurs due to enhanced momentum in the flow regime. Experimental results indicate that the average α over the 33.4 cm feeding conduit (6.25 mm ID) was 76% (αtheoretical = 75%) for the 2% ALR, and 85% (αtheoretical = 83%) for the 3.3% ALR. In the two-phase, two-component flow the α affects the drop size and stability of the spray produced from an industrial nozzle assembly. Learning from this study will yield insights and conceptual understanding of two-phase flow phenomena in conduit, which would affect stability, pulsation tendency, and possibly atomization performance of the nozzle downstream. Two-phase flow nozzles have wide applications in the industries, e.g. petrochemical, pharmaceutical, and others.

Fluidelastic Instability and Periodic Fluid Forces in a Normal Triangular Tube Bundle Subjected to Air-Water Flow

2010 ◽  
Author(s):  
G. Ricciardi ◽  
M. J. Pettigrew ◽  
N. W. Mureithi
Keyword(s):  
Two Phase Flow ◽  
Tube Bundle ◽  
Fatigue Cracks ◽  
Cross Flow ◽  
Fretting Wear ◽  
Phase Flow ◽  
Steam Generators ◽  
Two Phase ◽  
Fluid Forces ◽  
Void Fractions

Two-phase flow in power plant steam generators can induce tube vibrations, which may cause fretting-wear and even fatigue cracks. It is therefore important to understand the relevant two-phase flow-induced vibration mechanisms. Fluidelastic instabilities in cross-flow are known to cause the most severe vibration response in the U-bend region of steam generators. This paper presents test results of the vibration of a normal triangular tube bundle subjected to air-water cross-flow. The test section presents 31 flexible tubes. The pitch-to-diameter ratio of the bundle is 1.5, and the tube diameter is 38 mm. Tubes were flexible in the lift direction. Seven tubes were instrumented with strain gauges to measure their displacements. A broad range of void fractions (from 10% to 90%) and fluid velocities (up to 13 m/s) were tested. Fluidelastic instabilities were observed for void fractions between 10% and 60%. Periodic fluid forces were also observed. The results are compared with those obtained with the rotated triangular tube bundle, showing that the normal triangular configuration is more stable than the rotated triangular configuration.

A Method for Extracting the Time Delay From the Unsteady and Quasi-Steady Fluidelastic Forces in Two-Phase Flow

2013 ◽  
Author(s):  
Teguewinde Sawadogo ◽  
Njuki Mureithi
Keyword(s):  
Time Delay ◽  
Two Phase Flow ◽  
Phase Flow ◽  
Two Phase ◽  
Fluid Forces ◽  
Void Fractions ◽  
Fluidelastic Instability ◽  
Measured Time ◽  
Unsteady Fluid ◽  
Theoretical Results

The time delay is a key parameter for modeling fluidelastic instability, especially the damping controlled mechanism. It can be determined experimentally by measuring directly the time lag between the tube motion and the induced fluid forces. The fluid forces may be obtained by integrating the pressure field around the moving tube. However, this method faces certain difficulties in two-phase flow since the high turbulence and the non-uniformity of the flow may increase the randomness of the measured force. To overcome this difficulty, an innovative method for extracting the time delay inherent to the quasi-steady model for fluidelastic instability is proposed in this study. Firstly, experimental measurements of unsteady and quasi-static fluid forces (in the lift direction) acting on a tube subject to two-phase flow were conducted. The unsteady fluid forces were measured by exciting the tube using a linear motor. These forces were measured for a wide range of void fraction, flow velocities and excitation frequencies. The experimental results showed that the unsteady fluid forces could be represented as single valued function of the reduced velocity (flow velocity reduced by the excitation frequency and the tube diameter). The time delay was determined by equating the unsteady fluid forces with the quasi-static forces. The results given by this innovative method of measuring the time delay in two-phase flow were consistent with theoretical expectations. The time delay could be expressed as a linear function of the convection time and the time delay parameter was determined for void fractions ranging from 60% to 90%. Fluidelastic instability calculations were also performed using the quasi-steady model with the newly measured time delay parameter. Previously conducted stability tests provided the experimental data necessary to validate the theoretical results of the quasi-steady model. The validity of the quasi-steady model for two-phase flow was confirmed by the good agreement between its results and the experimental data. The newly measured time delay parameter has improved significantly the theoretical results, especially for high void fractions (90%). However, the model could not be verified for void fractions lower or equal to 50% due to the limitation of the current experimental setup. Further studies are consequently required to clarify this point. Nevertheless, this model can be used to simulate the flow induced vibrations in steam generators’ tube bundles as their most critical parts operate at high void fractions (≥ 60%).

Towards Understanding Two-Phase Flow Induced Vibration of Piping Structure With a U-Bend

2019 ◽  
Author(s):  
Olufemi E. Bamidele ◽  
Wael H. Ahmed ◽  
Marwan Hassan
Keyword(s):  
Void Fraction ◽  
Vibration Amplitude ◽  
Two Phase Flow ◽  
Bubbly Flow ◽  
Phase Flow ◽  
Flow Conditions ◽  
Flow Induced Vibration ◽  
Two Phase ◽  
Void Fractions ◽  
Flow Induced Vibrations

Abstract The current work investigates two-phase flow induced vibrations in 90° U-bend. The two-phase induced vibration of the structure was investigated in the vertical, horizontal and axial directions for various flow patterns from bubbly flow to wavy and annular-dispersed flow. The void fractions at various locations along the piping including the fully developed void fraction and the void fraction at the entrance of the U-bend were fully investigated and correlated with the vibration amplitude. The results show that the excitation forces of the two-phase flow in a piping structure are highly dependent on the flow pattern and the flow conditions upstream of the bend. The fully developed void fraction and slip between phases are important in modelling of forces in U-bends and elbows.

Vibration of a Tube Bundle in Two-Phase Freon Cross-Flow

1995 ◽  
Vol 117 (4) ◽  
pp. 321-329 ◽  
Author(s):  
M. J. Pettigrew ◽  
C. E. Taylor ◽  
J. H. Jong ◽  
I. G. Currie
Keyword(s):  
Two Phase Flow ◽  
Tube Bundle ◽  
Density Ratio ◽  
Cross Flow ◽  
Flow Regimes ◽  
Phase Flow ◽  
Two Phase ◽  
Void Fractions ◽  
Fluidelastic Instability ◽  
First Results

Two-phase cross-flow exists in many shell-and-tube heat exchangers. The U-bend region of nuclear steam generators is a prime example. Testing in two-phase flow simulated by air-water provides useful results inexpensively. However, two-phase flow parameters, in particular surface tension and density ratio, are considerably different in air-water than in steam-water. A reasonable compromise is testing in liquid-vapor Freon, which is much closer to steam-water while much simpler experimentally. This paper presents the first results of a series of tests on the vibration behavior of tube bundles subjected to two-phase Freon cross-flow. A rotated triangular tube bundle of tube-to-diameter ratio of 1.5 was tested over a broad range of void fractions and mass fluxes. Fluidelastic instability, random turbulence excitation, and damping were investigated. Well-defined fluidelastic instabilities were observed in continuous two-phase flow regimes. However, intermittent two-phase flow regimes had a dramatic effect on fluidelastic instability. Generally, random turbulence excitation forces are much lower in Freon than in air-water. Damping is very dependent on void fraction, as expected.

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