experiments and numerical simulations of the flow within a … · 2011. 6. 3. · experiments and...

Experiments and Numerical Simulations of the Flow Within a Simplified Model of a

Surge Chamberby

Alexandre Massé*‡1,3, Maryse Page2 and Laurent Mydlarski3

1 Groupe-Conseil LaSalle, LaSalle (Qc), H8R 1R8, Canada2 Hydro-Québec Research Institute, Varennes (Qc), J3X 1S1, Canada

3 McGill University, Dept. of Mechanical Engineering, Montréal (Qc), H3A 2K6, Canada

June 2011

‡ Corresponding Author: Alexandre Massé ([email protected])

Outline1) Introduction

Surge chamber, objectives, flow structures

2) Physical BackgroundOscillating mass phenomenon, self-induced sloshing, estimation of head losses

3) Experimental MethodApparatus, instrumentation, measurements

4) Numerical MethodLiterature review, governing equations, MULES, algorithm summary, numerical

simulations

5) ResultsVelocity field, reduced pressure profiles, free-surface profiles, self-induced

sloshing, characteristic frequencies, head losses, simulation parameters

6) Conclusions2

What is a Surge Chamber?

➔ Hydraulic damper: ↓ "water hammer" effect

under opening/closing of turbines

➔ Extra losses during normal operation (no opening/closing)

Schematic of a surge chamber

Simplified model of a surge chamber

Introduction Physical Background Expt. Method Num. Method Results Conclusions

from turbine

to river

Turbine/Generator Surge chamber

3


Research Objectives

1- UNSTEADY PHENOMENA: To understand and characterize the unsteady phemomena in a surge chamber under constant inflow (no opening/closing).

2- CODE VALIDATION: To obtain experimental data on a simplified model of a surge chamber and to compare the results with numerical simulations using OpenFOAM-1.5-dev.

➔ Identify the major flow structures➔ Select key local and global quantities describing the flow features➔ Estimate the confidence level in numerical simulations of such a flow

4

Reference

A. Massé, Experiments and Numerical Simulations of the Flow Within a Model of a Hydraulic Turbine Surge Chamber. M.Eng. Thesis, Department of Mechanical Engineering, McGill University, 2010.


Flow Structures

OpenFOAM results: P2, Q ~45 l/s, H ~550 mm

3D, unsteady, incompressible, swirling, two-phase flow

5

InletOutlet


Oscillating Mass Phenomenon

Simplifications:➔ Geometry➔ No inlet/outlet pipe losses➔ Fully-developed flow in pipes➔ Neglect flow topology in surge chamber

Analysis:➔ Newton's 2nd law in two pipes➔ Conservation of mass in surge chamber➔ Solve system of ODEs with numerical methods using non-equilibrium ICs

Solution:➔ ~ Constant input flow rate: ΔH

1 >> ΔH

2

➔ Stabilizes by oscillating around steady state values: inertia of pipe 2

Schematic of the hydraulic circuit of the simplified model of a surge chamber

sgD

ALP chambersurge

massoscil 70.64 22

_2_ ==

πHzF massoscil 149.0_ =

6


Self-Induced Sloshing Phenomenon

Self-induced sloshing:➔ Saeki et al., 2001: “the natural oscillation of fluid in a tank excited by the

flow in the absence of other external forces”

Fluid-dynamic (direct) feedback:➔ Reorganization of the flow in the shear layer into large coherent vortex

structures➔ Dominant frequency varies linearly with the inlet velocity (U

0)

Experiments of Chua & Shuy, 2006

Fluid-resonant (indirect) feedback:➔ Resonator: U-tube➔ Resonance: jet shear layer fluctuating

frequency close to the natural frequency of the resonator

➔ Resonance mode dominant for a range of flow rates

In this experiment:➔ Case: aligned inlet pipe under operation➔ Impingement point: downstream wall➔ Resonator: natural free-surface

oscillations

=

Lhn

Lgnn ππω tanh1

sPsloshing 25.1= HzFsloshing 80.0=

7


Estimation of Head Losses

Schematic of the control volume for the estimation of the head losses in the simplified model of a surge chamber

8

xgpp staticd

⋅−= ρReduced pressure:➔ at different elevations physically correspond to

energy differencesdp

( ) ( )[ ]3,32,21,13,32,21,1

~~~~~~tottottottottottotloss HmHmHmHmHmHmgPower −++−+=

Average power loss:➔ Applying 1st law of Thermodynamics to CV surrounding the chamber → time averaging → removing

vanishing terms➔ : instantaneous mass flow rate at section "i"➔ : instantaneous sum of the dynamic and reduced pressure heads at section "i", averaged by the

mass flow rates

im

itotH ,

Mean contribution Correlation between fluctuating quantities


Apparatus

Maximum flow rate:➔ One inlet pipe under operation: 70 L/s➔ Two inlet pipes under operation: 2*45 = 90 L/s

Surge chamber height:➔ Controlled by downstream reservoir, height adjustable weir

Schematic of the apparatus and dimensions of the surge chamber model (units: mm).

Three measurement sections:➔ Circumferential average➔ 48 hole cavity

9


InstrumentationADV:

➔ 3D instantaneous velocity in a remote sampling volume➔ Pulse-to-pulse coherent Doppler sonar: phase difference between

two consecutive pulses = velocity➔ Bad correlation for: large mean velocity gradients, high turbulence

intensity, air bubbles in the flow.

Schematic of the ADV head

( ) ( )( ) ( )

( ) ( ) ( )

( ) ( )( ) ( )

( ) ( )

+×

×+=

−

+−

−

+−

tiCtVtVi

tiCtVtVi

etBetStS

etBtSetSavgtR

rt

rt

γτ ω

γτ ω

11

1

2

12

( ) ( )[ ] ( )CVVtStS rt τ ωφ +−=×= *

21arg

One particle in the sampling volume

Many particles in the sampling volume

time lag

signal frequency

speed of soundphase difference

coherent motion incoherent motion

( ) 0=tBτ ω

+−=

C

trVt

tV

φ

( ) 12 =tR

( ) 0≠tBbiasedφ =

( ) 12 <tR

(good)

(bad)10


Instrumentation (cont)

∝ ∝

Schematic of the capacitive water level probe

Capacitive water level probes:➔ Instantaneous water level➔ Two electrodes: copper & water / One

dielectric: wire insulation➔ Output voltage capacitance water level

Reduced pressures:➔ Time-averaged readings➔ Cylindrical container linked to pressure hole➔ Break free-surface with a sharp-ended rod mounted on a vernier scale

xgpp staticd

⋅−= ρ

11


Measurements

Summary of measurements

Top view of the measurement locations for the mean free-surface profiles (40 "+" symbols), the free-surface oscillations of Cases #1 to #3 (5 "○" symbols), the free-surface oscillations of Case #4 (5 "□" symbols) and the losses (grey rings around each pipe). (L = 1114, l = 413, units: mm)

Operating Input Pipes Flow Rates [l/s] Water Level [mm] Measurements

Case #1 P2 45 550 Free-surface profilesVelocity fieldPressure profilesFree-surface oscillationsLosses

Case #2 P2 55 550

Case #3 P1 & P2 45 & 45 (90) 550

Case #4 P1 variable 550 Free-surface oscillations

Losses 3 permutations variable variable Losses

Locations of the reduced pressure taps at the downstream wall of the surge chamber model (looking downstream). (units: mm) 12


Review of Numerical Methodologies for Two-Phase Flows

Representation of (a) point-force and (b) resolved-surface treatment for Euler-Lagrange methods.

13

Lagrangian, Point-Force (a)➔Continuous flow, properties defined at the particles'

centroids➔Surface forces: empirical/theoretical treatment of the

particle/continuous phase relative velocity➔Grid cells > particles

Lagrangian, Resolved-Surface (b)➔Surface forces: integration of the fully resolved continuous

phase pressure and shear stresses over the particle surface➔More realistic surface forces➔High grid resolution over the particle➔Few particles in the flow domain

Eulerian, Mixed-Fluid ("one-fluid")➔Kinetic and thermal equilibrium between the two phases

within each cell➔Homogenous mixture within each cell➔Fluid properties depend on the phase concentration➔One set of momentum equations

Eulerian, Point-Force ("two-fluid")➔The two phases are treated as two separate continua,

interpenetrating each other➔Extra terms in the momentum equations account for the

momentum transfer between the two phases➔The relative phase velocities and temperatures are required

rasInterFoam


Review of Numerical Methodologies for Resolving the Interface

Free-surface methodologies: (a) moving grid, (b) front-tracking method and (c) volume of fluid method.

14

Surface Methods

➔The interface is marked or tracked

explicitly➔Moving grid (a), front-tracking (b), level-

set➔Exact position of the interface➔Special treatment for its breakup and

coalescence

Volume Methods

➔The two phases are marked by massless

particles or by an indicator function➔The exact position of the interface is

reconstructed from the markers➔Marker and cell, volume of fluid (c)➔"Interface-reconstruction" or "interface-

capturing"

rasInterFoam

aw

w

VVV+

=γVolume fraction


Governing Equations

Volume fraction transport equation:

( ) ( )[ ] 01 * =−⋅∇+⋅∇+∂∂

γγγγγrmix uV

t

extra artificial compression

Mixture continuity:

( ) 0=⋅∇+∂

∂mixmix

mix Vt

ρρ

Mixture momentum equations:

( ) ( )( )( ) ( ) ( ) ∫ −+∇⋅−∇⋅∇+∇−

=∇⋅∇−⋅∇+∂

∂

)(

'''

,

,

)(tS

mixmixmixeffmix

mixmixeffmixmixmixmixmix

dSxxnKxgVpd

VVVtV

δσρµ

µρρ

surface tension

➔ Solved explicitly with MULES: keep the phase fraction between 0 and 1

➔ Update the mixture physical properties

➔ Coupling through PISO

15

γσ ∇≈

K

∇∇⋅∇=

γγ

K

0=⋅∇ mixu

or ,

continuum surface force (CSF) model of Brackbill et al. (1992)

( )

−−⋅∇=⋅∇ γρρργγ r

mix

awmix uV

1

( ) γρρργγ r

mix

awmixmix uuV −−+= 1

mass velocity volume velocity phase relative velocity


Solving the Volume Fraction Transport Equation

16

( ) ( )[ ] 01 * =−⋅∇+⋅∇+∂∂

γγγγγrmix uV

t

( )[ ] ( ) ( ) 0max,min1 0

000

00000

=∑

+∇∇⋅

⋅⋅−+∑ ⋅+

∆−

f

f

f

f

f

ff

f

ff

fff

fffPP

n

P

StabiliserS

SSV

SSV

CSVVt γ

γγγγγγγ

( ) ( ) ( ) ( )[ ]0

,

0

,

0

,

0

, UDfCompffUDfLimitedf QQQQ γγλγγ −⋅+=

( ) ( )00 maxmin nb

n

Pnb γγγ ≤≤

Volume fraction transport equation:

Multidimensional Universal Limiter for Explicit Solution (MULES) in OpenFOAM:

implicit Euler scheme

explicit γ flux explicit γ flux, artificial compression

correction fluxlimiting factor

bounded, but diffusive

limited flux

"multidimensional universal limiter"

compressive, but unbounded

➔ Advect the interface without diffusing, dispersing or wrinkling it


Algorithm Summary

1. Initial fields: , , , , .

Compute , and .

2. Compute the new time step.

3. Using and , solve the transport equation (MULES).

Get and .

4. From , compute the interface curvature.

5. From and ,compute and at the CV centres.

6. Solve (PISO) for , , and .

7. Solve the k-ε turbulence model equations and get .

8. Set the newly computed field as the old values and return to step 2.

17

( )0

fSV

⋅

0

Pρ 0

,PTurbν

0

Pγ

0

PV

0

Ppd 0

Pκ 0

Pε

n

Pγ

0

Pγ

γ

( )0

fSV

⋅ρ

n

Pγ

n

Pγ 0

,PTurbν n

Peff ,µn

Pρ

n

PV n

Ppd ( )nfSV

⋅

n

PTurb ,ν

( )0

fSV

⋅

OpenFOAM-1.5-dev


Numerical Simulations

Aligned pipe, P1:➔ 11 different flow rates➔ Amplitude/frequency of free-surface oscillations➔ Frequency of shear layer

Self-induced

sloshing

Code input

parameters

18

Offset pipe, P2:➔ 5 meshes (interface &

entire domain refinement)➔ 2 levels of residuals➔ 2 time steps➔ 3 convection schemes

(momentum eqns.)

Two pipes, P1 & P2:➔ Case #3


Average Velocities

➔ Overall good agreement of

magnitudes and directions

between experiments and

simulations: ➔ Major structures simulated

7-8-10: impingement & deflection

11-12: direct to P3

13-14: close to bottom

3-4-9: upward & swirling

1-2-6: downward, air entrainement

5: vortex centre, low velocity

Velocity vectors from the experimental Case #1 (red arrows) and the base case of the numerical simulations (blue arrows). P2 in operation at 45 l/s and with a water level of 550 mm. 19

Case #1: P2-Q45-H550


Reduced Pressure Profiles

Case #1: P2-Q45-H550

➔ Shape is well simulated➔ Num: stagnation point

close to P2 axis➔ Expt: jet deflected

upward and toward P3

(a) Horizontal (z = 151 mm) and (b) vertical (y = 917 mm) reduced pressure profiles on the downstream wall of the surge chamber model for the cases of P2, and P1 & P2.

Case #3: P1&P2-Q45-H550

➔ Increase in reduced

pressures / water level

20


Free-Surface Profiles

Case #1, #2 and #3: ➔ Error bar: ±1 standard deviation➔ Overall good agreement➔ P1 does not affect much the time-

averaged profiles➔ Larger KE in P2: higher bump,

steeper profiles and more air

entrainment

21(a) Time-averaged free-surface profiles on five vertical planes. (b) Contour plot of the free-surface height for the numerical base case (Case #1).


Free-Surface Profiles (cont)

Case #1: P2-Q45-H550

➔ Expt.: air entrainement in the corner of the chamber defined by the intersection of the

upstream wall and the side wall closest to the output pipe➔ Num: Vertical diffusion of the free-surface over many cells➔ Diffusion believed to be related to the nature of the flow, rather than to unwanted

numerical diffusion

22

Numerical results of the base case. (a) Instantaneous screenshot of the cells having a volume fraction between 0.1 and 0.9. (b) Contour plot of the time-averaged heights of the cells with a volume fraction between 0.1 and 0.9.


Self-Induced Sloshing

Experimental and numerical (b) amplitudes and (a) frequencies of free-surface and shear layer oscillations

Free-surface profiles obtained in the experiments and with OpenFOAM, for a flow rate of 45 l/s

23

Case #4: P1-Qvariable-H550

➔ Amplitude increases, reaches a

maximum value and then decreases➔ Predicted peak in amplitude 34% lower

than that obtained in the experiments➔ Fluid-dynamic feedback for low flow

rates➔ Fluid-resonant feedback (1st or 2nd

mode) for other flow rates


Self-Induced Sloshing (cont)

2D velocity magnitudes and streamlines on vertical and horizontal planes passing through the axis of pipe P1 (Q = 45 l/s). 24


Characteristic Frequencies

25

Energy spectra of the free-surface at five different locations for the case of P2 in operation at 45 l/s with a downstream reservoir water level of 550 mm. The experimental Case #1 is shown in red and the numerical base case in blue.

Case #1: ➔ P2-Q45-H550➔ Expt: 2 characteristic frequencies

(1% agreement)i) Oscillating mass phenomenon

ii) Self-induced sloshing phenomenon➔ Num: 1 characteristic frequency

(10% agreement)i) Oscillating mass phenomenon

➔ Similar observations for Cases #2 & #3➔ Hypothesis: existence of flow

structures oscillating at frequencies

close to those associated with i) and ii)

Self-induced sloshing

Oscillating mass


Head Losses

Head losses: single inlet pipe

Head losses: two inlet pipes

P1:➔ Least-Square Fit (expt. Q): 0.422➔ Variations from L-S Fit:

Expt-Q: 7%Expt-H: 10%Num: 4%

P1 & P2:➔ Variations from Expts.:

Num: 12% (P1) & 20% (P2)

26

P2:➔ Least-Square Fit (expt. Q): 1.536➔ Variations from L-S Fit:

Expt-Q: 5%Expt-H: 1%Num: 13%

Head loss coefficients vs Q:➔ P1: Peak corresponds to maximum f-s sloshing amplitude➔ P2: Oscillating mass ???


Validation of the Simulation Parameters (Case #1: P2-Q45-H550)

Variation of the dominant period of oscillation of the flow with respect to the βm coefficent

Tested parameters of the base case:➔ βm (div. scheme of mom. Eqns.) = 0.5 - 0.3 – 0.1➔ Mesh size = 0.97*106 - 1.73*106 - 4.20*106 cells➔ Height of cells @ f-s = 3 - 1.5 - 0.75 mm➔ Max Co # = 0.8 - 0.2➔ Residuals = 10-7(reduced pressure), 10-6(velocity components), and 10-8(k and ε) – reduced by 102

27

Results:➔ Time-averaged quantities converged for the base case simulation parameters➔ Significant effects on flow periodic oscillations


Conclusions

28

1- UNSTEADY PHENOMENA:

➔ Constant input flow rate: i) oscillating mass & ii) self-induced sloshing phenomena➔ Unsteady phenomena simulated by OpenFOAM-1.5➔ Resonance = larger head loss coefficients

2- CODE VALIDATION:

➔ Global quantities: head losses➔ Local quantities: velocity fields, reduced pressure profiles, free-surface profiles➔ Overall good agreement / larger discrepancies for some flow structures


Acknowledgements

29

1- Groupe-Conseil LaSalle:➔ Experimental facilities

2- Hydro-Québec Research Institute:➔ Funding➔ Computational facilities and support

3- McGill University:➔ Scientific support

4- NSERC:➔ Funding

Reference

A. Massé, Experiments and Numerical Simulations of the Flow Within a Model of a Hydraulic Turbine Surge Chamber. M.Eng. Thesis, Department of Mechanical Engineering, McGill University, 2010.

experiments and numerical simulations of the flow within a … · 2011. 6. 3. · experiments and...

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