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Development of the Pressure-Time Method for Flow Rate Measurement in Hydropower Plants by Numerical Simulation
Luleå University of Technology, Department of Engineering Sciences and Mathematics, Fluid and Experimental Mechanics.
2019 (English)Doctoral thesis, comprehensive summary (Other academic)
Abstract [en]

Hydropower is a clean and sustainable energy resource developed since the late 19th century. To specify the hydraulic performance characteristics of hydraulic turbines, the volumetric flow rate as one of the few basic quantities should be determined. Discharge represents the most difficult quantity to measure. A good measurement accuracy and estimation is difficult to estimate compared to the power and head, especially in low head machines. Despite the developments in discharge measurement techniques, this part of the hydraulic machine performance tests is often a major challenge. The pressure-time method is one of the discharge measurement techniques, which is studied in this PhD thesis. Most of the researches, to improve the accuracy of this method, are performed experimentally, whilst limited one-dimensional numerical simulations are done on this method. Therefore, detailed investigation of this method has been difficult. The studies conducted in this thesis are divided in two experimental and numerical parts. Because the flow physics in the pressure-time method is a combination of decelerating flow with variable rate and water hammer phenomenon, at the first experimental studies are performed considering unsteady constant rate decelerating and accelerating flows. The results helped to better understanding the studies in the second part concerned with numerical simulations. In the second part, the physical phenomenon behind the water hammer and constant rate decelerating and accelerating flows is studied. Then the physical characteristics of the flow in the pressure-time method is investigated in detail based on the time variation of the wall shear stress and the γ parameter. The γ parameter represents the difference between the turbulence structure in a transient accelerating or decelerating flow and the one in the quasi-steady condition. It is demonstrated that for the pressure-time method, part of the flow decrease excursion can be characterized as quasi-steady and the rest is unsteady. The dominance of inertia and turbulence dynamics is investigated to evaluate the wall shear stress in the part of the excursion with the unsteady assumption. It is found that the inertia has a dominant effect during the excursion. The evaluation of the effective forces in the flow rate calculation in a straight pipe showed that the wall shear stress is a good approximation of the losses calculation and the other terms can be neglected. To extend the applicability of this method outside the limitations of the IEC41 standard, variable pipe cross-section and different friction loss calculation are also studied. A new method for the loss calculation in the penstocks with variable cross section is proposed.  The errors induced by the proposed method are in an acceptable range provided that the contraction angle is less than ϴ=10°. The evaluation of the important forces showed that the variation of the momentum flux is the most significant term in the flow rate estimation in a pipe with a contraction. Then, the wall shear stress is the second most significant. 

Place, publisher, year, edition, pages
Luleå: Luleå University of Technology, 2019.
Series
Doctoral thesis / Luleå University of Technology 1 jan 1997 → …, ISSN 1402-1544
National Category
Fluid Mechanics and Acoustics
Research subject
Fluid Mechanics
Identifiers
URN: urn:nbn:se:ltu:diva-72001ISBN: 978-91-7790-284-3 (print)ISBN: 978-91-7790-285-0 (electronic)OAI: oai:DiVA.org:ltu-72001DiVA, id: diva2:1269971
Public defence
2019-05-10, E1024, Lulea university of Technology, Lulea, 13:00 (English)
Opponent
Supervisors
Available from: 2018-12-12 Created: 2018-12-11 Last updated: 2020-04-22Bibliographically approved
List of papers
1. Numerical Investigation of the Pressure-Time Method
Open this publication in new window or tab >>Numerical Investigation of the Pressure-Time Method
2017 (English)In: Flow Measurement and Instrumentation, ISSN 0955-5986, E-ISSN 1873-6998, Vol. 55, p. 44-58Article in journal (Refereed) Published
Abstract [en]

The pressure-time method is a discharge measurement technique commonly used to estimate the flow rate in hydro-power plants to assess the turbine hydraulic efficiency. In this paper two-dimensional Reynolds-averaged Navier-Stokes equations with the low-Reynolds k-ω SST turbulence model are used to model and evaluate the pressure-time method. The flow rate decrease is modeled by valve closure and use of the dynamic mesh technique. The results are compared with experimental data showing the close trend. Moreover, the affecting parameters in the pressure-time method including compressibility, calculation of the losses and finding the upper time limit of integration of the pressure-time diagram are studied in detail. Furthermore, the flow characteristics with both compressible and incompressible assumptions are investigated. The obtained results demonstrated the compressibility effect even before the complete valve closure. The physics of the flow, in the closed conduit in the pressure-time method, before the complete valve closure is studied based on the time variation of the wall shear stress and the γγ parameter. The γγ parameter represents the difference between the turbulence structure in a transient accelerating or decelerating flow and the one in the quasi-steady condition. It is demonstrated that for the pressure-time method, some part of the flow decrease excursion can be characterized as quasi-steady and the rest is unsteady. The dominance of inertia and turbulence dynamics is investigated to evaluate the wall shear stress in the part of the excursion with the unsteady assumption. It is found that the inertia has a dominant effect during the excursion. The flow rate is calculated by evaluating all the terms of losses, e.g., wall shear stress, normal stresses, Reynolds stresses and density variation. Based on the relative magnitude of each term the results indicate that the wall shear stress is a good approximation of the losses for the flow rate calculation and the other terms can be neglected. Due to the primary role of losses in the flow rate calculation other methods in losses calculation are also considered for comparison (e.g., quasi-steady friction or steady-state friction factor). The available methods to find the upper time limit of the flow rate approximation integral still have significant errors. The flow rate reduction is calculated at each time step before complete valve closure using CFD methods.

Place, publisher, year, edition, pages
Elsevier, 2017
National Category
Fluid Mechanics and Acoustics
Research subject
Fluid Mechanics
Identifiers
urn:nbn:se:ltu:diva-63250 (URN)10.1016/j.flowmeasinst.2017.05.003 (DOI)000403861200005 ()2-s2.0-85019139193 (Scopus ID)
Note

Validerad; 2017; Nivå 2; 2017-05-16 (andbra)

Available from: 2017-05-05 Created: 2017-05-05 Last updated: 2019-01-11Bibliographically approved
2. Computation of two- and three-dimensional water hammer flows
Open this publication in new window or tab >>Computation of two- and three-dimensional water hammer flows
2019 (English)In: Journal of Hydraulic Research, ISSN 0022-1686, E-ISSN 1814-2079, Vol. 57, no 3, p. 386-404Article in journal (Refereed) Published
Abstract [en]

This paper investigates water hammer flows using two- and three-dimensional (2D and 3D) numerical simulations. The unsteady Reynolds-averaged Navier–Stokes (URANS) equations in conjunction with the k–ω SST turbulence model are employed for the computations. The valve modelling approach is used for 3D simulations, with superior agreement with the experiments. Similar predictions are obtained by 2D simulations and the flow rate reduction curve obtained from the 3D computations. The asymmetric flow patterns induced by the valve are confined within approximately one pipe diameter upstream of the valve. The contributions of inertia and pressure gradient terms are dominant at the instance of pressure wave passage, leading to abrupt changes in the fluid flow parameters. However, the effects of inertia and viscous shear stress terms are significant after the pressure wave passage, resulting in the flow tendency to approach a new steady condition. The viscous and turbulent dissipations are dominant close to and away from the wall, respectively.

Place, publisher, year, edition, pages
Taylor & Francis, 2019
Keywords
Ball valve modelling, fluid dynamics, laminar flow, three-dimensional numerical simulation, turbulent flow, two-dimensional numerical simulation, water hammer
National Category
Fluid Mechanics and Acoustics
Research subject
Fluid Mechanics
Identifiers
urn:nbn:se:ltu:diva-70075 (URN)10.1080/00221686.2018.1459892 (DOI)000465125300009 ()2-s2.0-85049567988 (Scopus ID)
Note

Validerad;2019;Nivå 2;2019-04-23 (oliekm)

Available from: 2018-07-05 Created: 2018-07-05 Last updated: 2022-06-29Bibliographically approved
3. Numerical Investigation of the Pressure-Time Method Considering Pipe with Variable Cross Section
Open this publication in new window or tab >>Numerical Investigation of the Pressure-Time Method Considering Pipe with Variable Cross Section
2018 (English)In: Journal of Fluids Engineering, ISSN 0098-2202, E-ISSN 1528-901X, Vol. 140, no 10, article id 101401Article in journal (Refereed) Published
Abstract [en]

A common method to calculate the flow rate and consequently hydraulic efficiency in hydropower plants is the pressure-time method. In the present work, the pressure-time method is studied numerically by three-dimensional (3D) simulations and considering the change in the pipe cross section (a contraction). Four different contraction angles are selected for the investigations. The unsteady Reynolds-averaged Navier-Stokes (URANS) equations and the low-Reynolds k-ω shear stress transport (SST) turbulence model are used to simulate the turbulent flow. The flow physics in the presence of the contraction, and during the deceleration period, is studied. The flow rate is calculated considering all the losses: wall shear stress, normal stresses, and also flux of momentum in the flow. The importance of each term is evaluated showing that the flux of momentum plays a most important role in the flow rate estimation while the viscous losses term is the second important factor. To extend the viscous losses calculations applicability to real systems, the quasi-steady friction approach is employed. The results showed that considering all the losses, the increase in the contraction angle does not influence the calculated errors significantly. However, the use of the quasi-steady friction factor introduces a larger error, and the results are reliable approximately up to a contraction angle of Θ = 10 deg. The reason imparts to the formation of a local recirculation zone upstream and inside the contraction, which appears earlier as the contraction angle increases. This feature cannot be captured by the quasi-steady friction models, which are derived based on the fully developed flow assumption.

Place, publisher, year, edition, pages
The American Society of Mechanical Engineers (ASME), 2018
National Category
Fluid Mechanics and Acoustics
Research subject
Fluid Mechanics
Identifiers
urn:nbn:se:ltu:diva-70582 (URN)10.1115/1.4040718 (DOI)000442422900014 ()2-s2.0-85051402544 (Scopus ID)
Note

Validerad;2018;Nivå 2;2018-08-24 (svasva)

Available from: 2018-08-24 Created: 2018-08-24 Last updated: 2022-02-10Bibliographically approved
4. Evaluation of transient effects in the pressure-time method
Open this publication in new window or tab >>Evaluation of transient effects in the pressure-time method
2019 (English)In: Flow Measurement and Instrumentation, ISSN 0955-5986, E-ISSN 1873-6998, Vol. 68, article id 101581Article in journal (Refereed) Published
Abstract [en]

The pressure-time is a method for measuring the flow rate in closed conduits and is typically used in hydropower applications. The scope of the present paper is to examine the flow physics in the pressure-time method using experimental measurements and two-dimensional numerical simulations. The Unsteady Reynolds-averaged Navier–Stokes (URANS) equations and the low-Re k-ω SST turbulence model are employed for the simulations. The contributions of inertia, pressure gradient, viscous and turbulent shear stresses are investigated in the flow during a pressure-time measurement. It is shown that away from the wall and at the first times, the turbulent shear stress balances with the pressure gradient. By increasing the time, the inertia effect becomes dominant and balances with the pressure gradient and turbulent shear stress. Close to the wall, both viscous and turbulent shear stresses are the dominant terms which are decreasing by increasing the time. It is also shown that the prediction of the friction losses can be improved by modeling the dependence of the friction factor on the dimensionless parameter instead of the Reynolds number.

Place, publisher, year, edition, pages
Elsevier, 2019
Keywords
Pressure-time method, Flow rate measurement, Transient flow, CFD, Experiments
National Category
Fluid Mechanics and Acoustics
Research subject
Fluid Mechanics
Identifiers
urn:nbn:se:ltu:diva-71997 (URN)10.1016/j.flowmeasinst.2019.101581 (DOI)000483649300016 ()2-s2.0-85068409096 (Scopus ID)
Note

Validerad;2019;Nivå 2;2019-07-08 (johcin)

Available from: 2018-12-11 Created: 2018-12-11 Last updated: 2020-08-26Bibliographically approved
5. Improved frictional modeling for the pressure-time method
Open this publication in new window or tab >>Improved frictional modeling for the pressure-time method
2019 (English)In: Flow Measurement and Instrumentation, ISSN 0955-5986, E-ISSN 1873-6998, Vol. 69, article id 101604Article in journal (Refereed) Published
Abstract [en]

The pressure-time method is classified as a primary method for measuring discharge in hydraulic machinery. The uncertainty in the discharge determined using the pressure-time method is typically around ±1.5 %; however, despite dating back almost one hundred years in time, there still exists potential to reduce this uncertainty. In this paper, an improvement of the pressure-time method is suggested by implementing a novel formulation to model the frictional losses arising in the evaluation procedure. By analyzing previously obtained data from CFD, laboratory and full-scale pressure-time measurements it is shown that the new friction model improves the accuracy of the flow rate calculation by approximately 0.1–0.2% points, compared to currently utilized friction models. Despite being a small absolute improvement, the new friction model presents an important development of the pressure-time method because the relative improvement is significant.

Place, publisher, year, edition, pages
Elsevier, 2019
Keywords
Pressure-time method, Transient friction modeling, Pipe flow
National Category
Fluid Mechanics and Acoustics
Research subject
Fluid Mechanics
Identifiers
urn:nbn:se:ltu:diva-75599 (URN)10.1016/j.flowmeasinst.2019.101604 (DOI)000496341600005 ()2-s2.0-85070506497 (Scopus ID)
Note

Validerad;2019;Nivå 2;2019-08-20 (svasva)

Available from: 2019-08-20 Created: 2019-08-20 Last updated: 2020-04-22Bibliographically approved

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Saemi, Simindokht

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Citation style
  • apa
  • ieee
  • modern-language-association-8th-edition
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  • de-DE
  • en-GB
  • en-US
  • fi-FI
  • nn-NO
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  • Other locale
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Output format
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