www.bhrgroup.co.uk 11 th international conference on pressure surges lisbon, portugal, 24 – 26...

www.bhrgroup.co.uk

11th International Conference on Pressure Surges

Lisbon, Portugal, 24 – 26 October 2012

Evaluation of flow resistance in unsteady pipe flow: numerical developments and

first experimental results



Contents Introduction

Data Collection and Analysis

Quasi-Two Dimensional Model

Numerical Results

Conclusions and Future Work



INTRODUCTION



Classic equations of unsteady flow through closed conduits

Continuity Equation

INTRODUCTION

𝑑𝐻𝑑𝑡

+ 𝑎2

𝑔𝐴𝜕𝑄𝜕𝑥

=0

𝑑𝑄𝑑𝑡

+𝑔𝐴𝜕𝐻𝜕𝑥

+𝑓

2𝐷𝐴𝑄|𝑄|=0

Dynamic Equation

Assumptions: Flow is one-dimensional and the velocity distribution is uniform over the cross

section Formulas for computing the steady-state friction losses are valid for transient

state conditions.

47.2

47.6

48.0

48.4

48.8

49.2

49.6

0 5 10 15 20time (s)H

ead

(m)

Classic Waterhammer

Unsteady Friction (Trika)Unsteady friction

Steady-stade friction



Classic equations of unsteady flow through closed conduitsINTRODUCTION

Flow Assumption: Flow is one-dimensional and the velocity distribution is uniform over the cross

section. Formulas for computing the steady-state friction losses are valid for transient

state conditions.

The flow reversal close to the pipe wall is responsable for energy dissipation that can not be described by steady state friction models.

QQ=0

𝑈>0

Viscous Forces

Inertial Forces

𝑈>0 𝑈=0𝑈=0

Velocity Profile – Classic ApproachReal Velocity Profile



Quasi two-dimensional analysis of unsteady flowsINTRODUCTION

Discretization of flow into a finite number of cylinders

Compute momentum and continuity equations to each cylinder

axial velocity

Uniforme pressure at each pipe cross-section (Assumption)

𝓊 𝑗𝜐 𝑗+1

𝜐 𝑗

𝜏 𝑗+1

𝜏 𝑗

lateral velocity

shear stress



DATA COLLECTION AND ANALYSIS



Data Collection and AnalysisExperimental facility

Steel pipeline with a 200 mm nominal diameter

(inner diameter 200 mm)

Centrifugal pump (nominal power PN = 15 kW)

QN = 20 l/s

HN = 38 m

Hydropneumatic vessel

Reversible pumping system

Total lenght 115 m

Volume = 1m3



Data Collection and AnalysisData Analysis

-20

-10

0

10

20

30

40

50

60

70

80

0 5 10 15 20

H (m

)

Time (s)

T1 T2 T3 1st ProblemHigh electric noise with a 20 m amplitude in steady state conditions

Pressure signal at three locations for Q = 5 l/sDay 3 (March 2012)

2nd ProblemPresence of air in the system

Filtered pressure signal at the downstream end of the pipeline (T3) in consecutives days for Q= 5l/s



Filtered pressure signal at the downstream end of the pipeline for different flow rates (Day 3 – March 2012)

Data Collection and AnalysisData Analysis

Effect due to the installation of a electric filterEffect due to the installation of air valves

The calculated wave speed increased from 900 m/s (Day 3 – March 2012) to 1050 m/s (May 2012).

The theoretical wave speed is 1300 m/s.



QUASI-TWO DIMENSIONAL MODEL



Quasi-Two-Dimensional ModelContinuity Equation

1D Model

2D Model

Mass fluxDiscretization of flow into a finite number of

cylinders

m j=2π r ρ𝓋 j



Quasi-Two-Dimensional ModelMomentum Equation

𝜕H𝜕 x

+𝜕𝓊𝑡

𝜕 t= 1𝑟 𝜌

𝜕𝜏𝜕𝑟

Forces considered in the momentum equation in 2-D Model

1D Model

2D Model



Quasi-Two-Dimensional Model

τ j=μ𝜕𝓊𝜕r

≈ μ𝓊 j−𝓊 j −1

r j−r j −1

Five – Layer Viscosity Distribution

{± gc d Hd t +d𝓊 j

d t= 1ρa j [m j−1( 12 (𝓊 j−1−𝓊 j )±c )−m j( 12 (𝓊 j−𝓊 j+1)±c )+( F j−1−F j ) ]

dxdt

=𝓊 j±c

Laminar Flow

Turbulent Flow

Numerical Solution

Shear stress calculation



NUMERICAL RESULTS



Numerical Analysis of laminar flow conditions

At mid-lenght of the pipeline The downstream end of the pipeline

The energy dissipation obtained with the 1D Model is approximately 0,36% of the initial pressure amplitude. On the other hand, for the same period, the Quasi - 2D Model leads to a 4.8% reduction of pressure amplitude.

Energy dissipation considering the 1D Model and Quasi - 2D Model (instantaneous valve closure)



Numerical analysis of laminar flow conditionsRadial distribution of axial velocity

t = ti t = ti+0,5L/c t = ti+L/c

t = ti+1,5 L/c t = ti+2 L/c

Axis of the conduit



Q = 10,8 l/s Q = 5,5 l/s

Flow(l/s)

Amplitude reduction of the pressure wave (1 cycle)

1D - Model Quasi - 2D Model

10,8 0,31% 5,47%

5,5 0,18% 2,58%

2,2 0,08% 1,40%

Q = 2,2 l/s

Numerical Analysis of turbulent flow conditionsEnergy dissipation considering the 1D Model and Quasi - 2D Model (valve closure time = 0,2 s)



1-D Model versus collected data 2-D Model versus collected data

The maximum pressure is reasonably described by both models.

None of the numerical models describes minimum pressures and pressure wave phase and shape.

Numerical analysis of turbulent flow conditionsNumerical versus experimental results



CONCLUSIONS AND FUTURE WORK



Conclusions and Future Work Results have shown that Quasi – 2D Models leads to a much higher energy

dissipation.

The next steps in experimental facility:

Instalation of air valves along the pipeline and a electric filter in the frequency converter;

Instalation of strains gauges, hot-films and a transparant box with PIV measurements;

The next steps in the numerical analysis are:

The comparasion of different turbulent flow models;

The analysis of the effect of gradually dampeded eddy viscosity distribution;

The comparison of the velocity profiles using the PIV equipment with the results obtained for different turbulent flow models;

The analysis if the real energy dissipation and the comparison with the model results.



Acknowledgments



Evaluation of flow resistance in unsteady pipe flow: numerical developments and first experimental results

Pedro Leite, Dídia I. C. Covas, Helena M. RamosInstituto Superior Técnico/Universidade Técnica de Lisboa

jhj

José Tentúgal Valente, Manuel Maria Pacheco FigueiredoFaculdade de Engenharia da Universidade do Porto

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analysis slide

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filtered pressure signal