in hydraulic engineeringhani/ofgbg19/slides_silje.pdf · 2019-12-23 · air entrainment stepped...

Air entrainment Stepped Spillway Hydraulic Jump Conclusion References

Numerical modelling of air entrainmentIn hydraulic engineering

Silje Kreken Almeland

Department of Civil and Environmental Engineering,NTNU, Trondheim, Norway

Gothenburg Region OpenFOAM User Group MeetingNovember 20, 2019

Silje Kreken Almeland Numerical modelling of air entrainment 2019-11-20 1 / 35


Numerical modelling of air entrainment

Develop a sub-grid model for air entrainment based on interFoam

(a) Stepped Spillway1 (b) Hydraulic Jump2

1Photo taken from [2]2Photo taken from [1]



Numerical modelling of air entrainment

Develop a sub-grid model for air entrainment based on interFoam

Testing airInterFoam[4]





Defining the concept

1 Air entrainmentDefining the conceptState of the artairInterFoam

2 Stepped SpillwayInception point and surface elevationDependence on inputvariablesVoid fraction

3 Hydraulic JumpFeaturesResults

4 Conclusion

5 ReferencesSilje Kreken Almeland Numerical modelling of air entrainment 2019-11-20 4 / 35


Defining the concept

Air entrainment in free surface flow



State of the art

State of the art

Euler-Euler two fluid modeltwoPhaseEulerFoam

. Numerical diffusion at the interface for stratified flow

Interface capturing methodsinterFoam

. Challenging to capture the processes at the surface

Hybrid models



State of the art

Subgrid models based on VoF

Existing subgrid models basedon VoF

Hirt (2003)[3] ⇒

Lopes (2017)[4] ⇒airInterFoam

https://openfoamwiki.net/index.php/Contrib/airInterFoam



State of the art

interFoam

Solves a single set of mass- and momentum equations

∇U = 0

∂ρU

∂t+∇· (ρUU ) = −∇p∗ + g·x∇ρ+∇· τ + f

interFoam uses a VOF method with a compression term tocapture the interface

∂α

∂t+∇· (αU) +∇· [U rα(1− α)] = 0

where U r = U 1 −U 2 is the relative velocity



airInterFoam

airInterFoam

∂αg∂t

+∇ · (ugαg)− b · ∇ · (νt∇αg) = Sg



airInterFoam

airInterFoam

∂αg∂t

+∇ · (ugαg)− b · ∇ · (νt∇αg) = Sg

Sg =a

φent

⟨∂un∂n

⟩δfs



airInterFoam

airInterFoam

∂αg∂t

+∇ · (ugαg)− b · ∇ · (νt∇αg) = Sg

Sg =a

φent

⟨∂un∂n

⟩δfs

k > kc, u > uc



airInterFoam

airInterFoam

∂αg∂t

+∇ · (ugαg)− b · ∇ · (νt∇αg) = Sg

Sg =a

φent

⟨∂un∂n

⟩δfs

k > kc, u > uc

ug = ul + ur



airInterFoam

airInterFoam

αg is calculated

αl is calculated independent of αg

α2 = 1− αl − αg



airInterFoam

airInterFoam

Interacts with the αl-equation by reducing thecompression

fvc::flux

(

-fvc::flux(-phir, alpha2, alpharScheme),

alpha1,

alpharScheme

)



airInterFoam

Test cases

. Stepped spillway

. Hydraulic jump





Stepped Spillway

Sketch taken from [6]



Stepped Spillway

(a) Step 3 (b) Step 4 (c) Step 5 (IP)

(d) Step 6 (e) Step 7 (f) Step 8

Photos taken from [6]



Stepped Spillway



Inception point and surface elevation


airInterFoam, kc = 0.2

a

aSketch taken from [6]





a




Dependence on inputvariables

Dependent on inputvariables

(a) kc = 0.2, ∆x = 0.005 (b) kc = 0.2, ∆x = 0.0025

(c) kc = 0, ∆x = 0.005 (d) ∆x = 0.005, ug = ul + ur





a




Void fraction

Void fraction

(a) Step 5

(b) Step 6

(c) Step 7Photos taken from [6]



Features

Hydraulic Jump

Froude number, Fr = u√gh

Figure: Hydraulic jump




Features

Hydraulic Jump

Void fraction profiles

Velocity profiles

Free surface contour



Features

Test Case

Froude number 4.8Physical experiments by Murzyn[5], reproduced byWitt[7] using interFoam





Results

interFoam – reproduction

(a) Current work , realizableKE

(b) Witt (2015)[7]

Figure: Mean flow field for αair.



Results

interFoam – realizableKE vs k-ε

realizableKE

k-ε



Results

interFoam – k-ε

∆x = 0.005

∆x = 0.0025



Results

interFoam – airInterFoam – k-ε

∆x = 0.005, interFoam

∆x = 0.0025, interFoam

∆x = 0.005, airInterFoam



Results

Dependence on parameters

ug = ul + ur, kc = 0.2

ug = ul, kc = 0.2

ug = ul, kc = 0.8

ug = ul, kc = 2



Conclusion

Using a local reduction in interface compression gavesome air entrained into the flowGave results close to the experimental for prediction of

Inception pointSurface elevation curveVoid fraction (at lower parts of the spillway)

Sensitive toGrid refinementInput parameters

Behavior of hydraulic jump sensitive to choice ofturbulence model

too little air transported in lower parts and towards the end of the jump



References I

[1] J. Ball.Hydraulic Jump.Available at https://www.flickr.com/photos/jball359/6998692825, 2019-11-20.

[2] C. Gonzalez.International symposium on hydraulic structures ciudad guayana, venezuela, october 2006 air entrainment and energydissipation on embankment spillways.11 2019.

[3] C. Hirt.Modeling turbulent entrainment of air at a free surface.Flow Science, Inc, 2003.

[4] P. Lopes, J. Leandro, and R. F. Carvalho.Self-aeration modelling using a sub-grid volume-of-fluid model.International Journal of Nonlinear Sciences and Numerical Simulation, 18(7-8), dec 2017.

[5] F. Murzyn, D. Mouaze, and J. Chaplin.Optical fibre probe measurements of bubbly flow in hydraulic jumps.International Journal of Multiphase Flow, 31(1):141–154, jan 2005.

[6] D. Valero and D. Bung.Hybrid investigation of air transport processes in moderately sloped stepped spillway flows.In E-proceedings of the 36th IAHR World Congress 28 June - 3 July, 2015, The Hague, the Netherlands, pages 1 – 10, 2015.

[7] A. Witt, J. Gulliver, and L. Shen.Simulating air entrainment and vortex dynamics in a hydraulic jump.International Journal of Multiphase Flow, 72:165 – 180, 2015.


https://www.flickr.com/photos/jball359/6998692825

in hydraulic engineeringhani/ofgbg19/slides_silje.pdf · 2019-12-23 · air entrainment stepped...

Documents