URANS computations of an unstable

cavitating vortex rope.

Platform for Advanced Scientific Computing Conference 2016.08-10 June 2016, Lausanne, Switzerland

Dr. Jean Decaix* and Pr. Cecile Munch, Univ. of Applied Sciences and Arts - WesternSwitzerland Valais, Sion, Switzerland.Dr. Andres Muller and Pr. Francois Avellan, Ecole Polytechnique Federale de Lausanne,Laboratory for Hydraulic Machines, Lausanne, Switzerland.

*jean.decaix@hevs.ch

J. Decaix PASC16, Lausanne, 08-10 June 2016 1

CONTEXTFP7 ENERGY no: 608532 HYPERBOLE

HYdropower plants PERformance and flexiBle Operation towards Lean integration of new renewable Energies

https://hyperbole.epfl.ch

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NEW CHALLENGES

The energy production and market are strongly

variable

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NEW CHALLENGES

The energy production and market are strongly

variable

The electrical network requires stabilityJ. Decaix PASC16, Lausanne, 08-10 June 2016 3

SOLUTION

To use hydropower plants for stabilizing the grid

⊲ Fast response.

⊲ Renewable energy.

⊲ Reversible energy using pump-storage power plants.

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SOLUTION

To use hydropower plants for stabilizing the grid

⊲ Fast response.

⊲ Renewable energy.

⊲ Reversible energy using pump-storage power plants.

Challenge: how to make the power plant moreflexible

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FLEXIBILITY

⇒ RUNNING AT OFF DESIGN OPERATING POINT

Vortex rope

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CAVITATING VORTEX ROPE

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CAVITATING VORTEX ROPE

RUNNER

DRAFT TUBE

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TEST CASE

Q > Q BEP

Inlet

Outlet

Vortex rope

Parameter H (m) T (N m) E (J kg−1) N (rpm) Q (m3s−1)Value 26.8 1’400 263 800 0.515

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FLOW MODELLING

Homogeneous URANS Equations

∂ρ

∂t+∇ ·

(

ρ ~C)

= 0

∂ρ ~C

∂t+∇ ·

(

ρ ~C ⊗ ~C)

= −∇p +∇ · (¯τ + ¯τt)

Viscous and turbulent stresses 1

¯τ = µ(

∇ ~C +∇t ~C)

¯τt = µt

(

∇ ~C +∇t ~C)

−2

3ρ k tr

(

¯I)

µt =ρa1k

max (a1ω; SF2)

1F.R. Menter. Zonal two equation k − ω turbulence models for aerodynamic flows. In AIAA 93-2906, 24th Fluid Dynamics

Conference Orlando, Florida, 1993.

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CAVITATION MODELLINGTransport equation for the vapour volume fraction rg

∂rg

∂t+

(

~C · ∇)

rg =1

ρg(Sv + Sc)

Source terms

Sv = Fv3rnuc (1− rg ) ρg

Rnuc

√

2

3

|pv − p|

ρfsgn (pv − p) if p < pv

Sc = Fc3rgρgRnuc

√

2

3

|pv − p|

ρfsgn (pv − p) if p > pv

Parameters

Fv = 50 Fc = 0.01 rnuc = 510−4Rnuc = 10−6

m

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MESH

Sub-Domain Number of nodes(in million)

Spiral Case 1.69

Stay Vanesand 3.17

Guide Vanes

Runner 2.63

Draft Tube 3.10

Total 10.59

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NUMERICAL SET UP

ANSYS CFX set up

⋄ Time step: ∆ t = 2e−4 s ⇔ 1 degree of runner revolution per time step.

⋄ Second order scheme for time discretization.

⋄ Transient rotor/stator interface with GGI interpolation.

⋄ High order scheme for spatial discretization.

Boundary conditions

⋄ Inlet: flow discharge.

⋄ Outlet: opening pressure condition.

⋄ Solid wall: no slip wall with wall law.

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SIMULATIONS

σ = 0.38 σ = 0.20 σ = 0.11

Section 1

Operating point Head [m] Torque [N m]

σ = 0.38 26.10 (26.75) 1441 (1409)σ = 0.20 26.33 (26.80) 1443 (1428)σ = 0.11 24.37 (26.75) 1322 (1426)

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σ = 0.38

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σ = 0.2

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σ = 0.11

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PRESSURE COEFFICIENT

SECTION 1

CFD results Experimental results

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CONCLUSION

⊲ The use of hydraulic power plants to stabilize the electrical networkrequires to extend the range of operating points of the turbines.

⊲ Such an extension requires to better understand the behavior of thecavitating vortex rope.

⊲ Two-phase URANS simulations are useful and accurate tools toinvestigate cavitating flow in hydraulic turbines.

⊲ CFD results allow to improve our knowledge of the transition betweenstable and unstable vortex rope.

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RUNNER CAVITATION

σ = 0.38 σ = 0.20 σ = 0.11

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