numerical investigation of the flow around a naca0015 near

HES-SO Valais-Wallis

Numerical investigation of the flow

around a NACA0015 near cavitation

inception

Journées SHF/AFM : Machines Hydrauliques et Cavitation, 8 et 9 Novembre 2017, Paris, France

Dr. J. Decaix* and Pr. Dr. C. Münch, Univ. of Applied Sciences and Arts – Western Switzerland Valais, Sion, Switzerland

Dr. G. Balarac, Univ. Grenoble Alpes, LEGI, CNRS, F38000, Grenoble, France

*[email protected]

HES-SO Valais-Wallis Journées SHF/AFM : Machines Hydrauliques et Cavitation, 8 et 9 Novembre 2017, Paris, France

CONTEXT OF THE STUDY

Cavitation inception and cavitation modelling are challenging problems

J.P. Franc, Advanced School on CAVITATION INSTABILITIES AND ROTORDYNAMIC EFFECTS IN

TURBOPUMPS AND HYDROTURBINES Udine July 7 - 11 2014

Acosta, A. J., & Parkin, B. R. (1975). Cavitation Inception - A

Selective Review. Journal of Ship Research, 19(4), 193–205.

NACA 16012



𝜎𝑖 = −𝐶𝑝𝑚𝑖𝑛=

𝑝0 − 𝑝𝑐

0.5 𝜌𝑈2

𝑝𝑐 = 𝑝𝑣

Simplest :

Cavitation index Cavitation modelling

J.P. Franc, Advanced School on CAVITATION INSTABILITIES

AND ROTORDYNAMIC EFFECTS IN TURBOPUMPS AND

HYDROTURBINES Udine July 7 - 11 2014

NACA 16012

NACA 16012



More realistic cavitation index

Cavitation inception is influenced by:

The water quality (nuclei content)

Interaction of bubble dynamics and vortical structures

Turbulence

Surface roughness

𝜎𝑖 =𝑝0 − 𝑝𝑣

0.5 𝜌𝑈2+ 𝐾

𝑝′2

0.5 𝜌𝑈2−

𝑇

0.5 𝜌𝑈2

𝑇 = 𝑝𝑣 − 𝑝𝑐 −𝐶𝑝𝑚𝑖𝑛

T : Tensile strength of the liquid


0.5 𝜌𝑈2+

𝛼𝛽

0.5 𝜌𝑈2

α : concentration of dissolved gas

β : Henry’s constant −𝐶𝑝𝑚𝑖𝑛

Holl (1960) Vortex cavitation

Arndt (2002)


SIMULATION REQUIREMENTS


0.5 𝜌𝑈2+ 𝐾

𝑝′2

0.5 𝜌𝑈2−

𝑇

0.5 𝜌𝑈2

The pressure field has to be captured accurately

The dynamics of the flow has to be captured accurately

The gas/vapour content has to be taken into account

RANS

LES

Two-phase flow model

Thermodynamics


TEST CASE

NACA 0015

Incidence : 5 degrees

Chord length : 10 mm

Inlet velocity : 10.7 m/s

Reynolds number : 105

Kjeldsen et. al (2000). Spectral Characteristics of Sheet / Cloud

Cavitation. Journal of Fluids Engineering, 122, 481–487.


NUMERICAL SET UP (RANS)

Computational domain: 15c x 10c x 0.5c

Boundary conditions

• Uniform inlet velocity, Uin = 10.7 m3/s

• Average pressure, Pout = 105 Pa

• NACA, no slip wall

• SIDE, symmetry (2D) or periodic (3D)

• TOP and BOTTOM, free slip wall

Turbulence model: SST k-ω, RNG k-ε, Spalart-

Allmaras, SST k- ω TM, kklOmega, SAS SST k-ω

Solver: CFX 17.2 and OpenFOAM 3.0.1

Mesh: Structured mesh

138 000 nodes


NUMERICAL SET UP (LES)

Computational domain: 15c x 10c x 0.5c

Boundary conditions

• Uniform inlet velocity, Uin = 10.7 m3/s

• Average pressure, Pout = 105 Pa

• NACA, no slip wall

• SIDE, periodic

• TOP and BOTTOM, free slip wall

Turbulence model: LES-WALE and dynamic

Smagorinsky

Solver: CFX 17.2, OpenFOAM 3.0.1 and Yales2

Mesh: Structured mesh and unstructured mesh

43 106 elements


RESULTS: Influence of the mesh

Solver Mesh Y+

[-]

Cl

[-]

Cf

[-]

Pmin

[Pa]

σinlet

[-]

CFX

Coarse v2 67 0.499 0.0166 9’294

1.72 Medium v2 22 0.511 0.0176 8’519

Medium v1 4.7 0.490 0.0206 9’996

Fine v2 1 0.490 0.0203 13’137

OpenFOAM

Coarse v2 34 0.302 0.0254 33’671

1.72 Medium v2 11 0.448 0.0199 14’873

Medium v1 3 0.481 0.0214 14’377

Fine v2 0.5 0.487 0.0204 11’641

2D RANS, SST k-ω

Targeted lift coefficient ≈ 0.62


RESULTS: Influence of the turbulence model

2D RANS, fine Mesh v2

Solver Turbulence

model

Y+

[-]

Cl

[-]

Cf

[-]

Pmin

[Pa]

σinlet

[-]

CFX

SST k-ω 1 0.490 0.0203 13’137

1.72 SST k-ω TM 0.8 0.612 0.0189 3’287

RNG k-ε 0.9 0.536 0.0178 1’624

Spalart-Allmaras 1.1 0.490 0.0262 15’142

OpenFOAM

SST k-ω 0.5 0.487 0.0204 11’641

1.72 kklOmega 0.5 0.613 0.0249 5’154

RNG k-ε 0.8 0.428 0.0821 35’521

Spalart-Allmaras 0.6 0.496 0.0231 11’127



RESULTS: Influence of the turbulence model

SST k-ω SST k-ω TM RNG k-ε

2D RANS, fine Mesh v2, CFX


RESULTS: RANS vs LES

3D unsteady simulations

Solver Turbulence model Number of

elements

Y+

[-]

Cl

[-]

Cf

[-]

Pmin

[Pa]

σinlet

[-]

CFX

SST k-ω

4 106

1 0.491 0.0202 13’249

1.72

SST k-ω TM 0.8 0.614 0.0187 3’239

SST SAS k-ω 1 0.490 0.0177 13’125

SST SAS k-ω TM 1 0.550 0.0177 7’203

WALE 1 0.555 0.0173 6’350

OF 3.0

SST k-ω

4 106

0.5 0.493 0.0197 10’187

1.72 SST SAS k-ω 0.5 0.479 0.0212 12’341

WALE 0.6 0.559 0.0178 4’985

YALES2 Smagorinsky Dynamic 43 106 0.7 0.639 0.0207 276 1.72



RESULTS: RANS vs LES

SST SAS k-ω

OpenFOAM

WALE

OpenFOAM

Smagorinsky dynamic

YALES2

Iso-value of the Q-criterion


RESULTS: Pressure

Smagorinsky dynamic

YALES2


RESULTS: Cavitation criterion

Cavitation if p < pv

pv = 2 kPa pv = 2 kPa

𝐵𝑖𝑖 = 𝜏𝑖𝑖 − 𝑝 + 𝑝𝑣

Cavitation if

B11 > 0 ; B22 > 0 ; B33 > 0

Joseph (1998)

Smagorinsky dynamic

YALES2





Cavitation if

B11 > 0 ; B22 > 0 ; B33 > 0

Joseph (1998)


Smagorinsky dynamic

YALES2


CONCLUSION

Standard RANS models are not able to capture accurately the pressure

field around the NACA profile for Re ≈ 105

Laminar-turbulent transition models are required to capture the pressure

field around the NACA profile for Re ≈ 105

LES required a sufficient refined mesh (around 40 million of elements) to

resolved the pressure around the NACA profile

LES shows large pressure fluctuations in the transition region

Cavitation inception seems to depend on the criterion used

numerical investigation of the flow around a naca0015 near

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