KTH ROYAL INSTITUTE

OF TECHNOLOGY

Water Hammer Phenomenon Analysis

using the Method of Characteristics

and Direct Measurements using a

"stripped" Electromagnetic Flow MeterMaster Degree Project in PhysicsBy Joel Carlsson

Wednesday, 2016 June 1

Direct Mass Flow Measurement

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Introduction

• The present thesis constitutes a part of Vattenfall'sThermal Hydraulic Loads program for development and experimental validation of RELAP5/MOD3 models for water hammer transients.

• Thesis work:

• (1) solve the classic water hammer equations, including fluid structure interaction (FSI) through a special wave speed calculation which are not included in RELAP5/MOD3

• (2) identify and implement a possible direct method to measure the transient mass flow rate in the experimental test rig

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Background Water Hammer Initiation

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• Any disturbances or change, in a

pipe system's mean flow e.g.

pump stop or valve closure will

initiate pressure waves

• As the pressure waves propagate,

they create transient pressure and

flow conditions transient load

on the structure, i.e. pipe system

The Method of Characteristics (MOC)

• The most popular numerical method for one dimensional, hydraulic transient problems.

• It got attributes of accuracy, simplicity, numerical efficiency, and programming simplicity

• What MOC basically does is that it eliminates the independent variable x and the partial differential equations gets converted into ordinary differential equations (ODE:s) in the dependent variable t.

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𝑑𝑉

𝑑𝑡+

1

𝜌𝑐∙𝑑𝑃

𝑑𝑡+𝑓 𝑉 𝑉

2𝐷= 0

𝑑𝑉

𝑑𝑡−

1

𝜌𝑐∙𝑑𝑃

𝑑𝑡+𝑓 𝑉 𝑉

2𝐷= 0

𝑑𝑥

𝑑𝑡= 𝑐

𝑑𝑥

𝑑𝑡= −𝑐

Direct Mass Flow Measurement

• The commercially available electromagnetic flow meters do not have a fast enough time resolution (0.1 s) to measure the present transient flow rate, (0.1 ms)

• By passing the signal processing and taking the original raw signal will increase the frequency response but also the uncertainty of the measurement (not clear how large the "noise“ level will be).

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Direct Mass Flow Measurement Results

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Direct Mass Flow Measurement Results

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Comparison between the RELAP5/MOD3 and the MOC codes

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The slope of the curve will give the force

acting on the pipe. The following equation is

used for calculating the force on the pipe: න0

𝐿 𝑑 ሶ𝑚

𝑑𝑡𝑑𝑥𝐹 =

Validation with Experimental data

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Validation with Experimental data

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Conclusion

• The direct mass flow measurement results indicate the possibility of measuring the mass flow at fast transients. The drawbacks will be the increased uncertainty produced by the "noise“, filtering of the signal is required and that a sufficient flow rate is required for detecting the transient.

• The produced results indicate that the implemented MOC code produces more accurate results compared to the experiments and that RELAP underestimates the mass flow gradient and thereby the loads.

• In the future, better models and more accurate results will lead to less conservative assumptions and less calculations will be needed. Consequently less time will be spent and in the end less money.

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References

• Figure at page 4: Allen R Inversin. Micro-hydropower sourcebook. 1986.

• Mohamed S Ghidaoui, Ming Zhao, Duncan A McInnis, and David H Axworthy.

A review of water hammer theory and practice. Applied Mechanics Reviews,

58(1):49-76, 2005

• M Hanif Chaudhry. Applied hydraulic transients. Technical report, Springer,

1979.

• Frederick J Moody and DE Winterbone. Introduction to unsteady

thermofluidmechanics, 1991.

Thank you for your attention!

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