View
8
Download
0
Category
Preview:
Citation preview
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
Air entrainment Stepped Spillway Hydraulic Jump Conclusion References
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]
Silje Kreken Almeland Numerical modelling of air entrainment 2019-11-20 2 / 35
Air entrainment Stepped Spillway Hydraulic Jump Conclusion References
Numerical modelling of air entrainment
Develop a sub-grid model for air entrainment based on interFoam
Testing airInterFoam[4]
(a) Stepped Spillway3 (b) Hydraulic Jump4
3Photo taken from [2]4Photo taken from [1]
Silje Kreken Almeland Numerical modelling of air entrainment 2019-11-20 3 / 35
Air entrainment Stepped Spillway Hydraulic Jump Conclusion References
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
Air entrainment Stepped Spillway Hydraulic Jump Conclusion References
Defining the concept
Air entrainment in free surface flow
Silje Kreken Almeland Numerical modelling of air entrainment 2019-11-20 4 / 35
Air entrainment Stepped Spillway Hydraulic Jump Conclusion References
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
Silje Kreken Almeland Numerical modelling of air entrainment 2019-11-20 5 / 35
Air entrainment Stepped Spillway Hydraulic Jump Conclusion References
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
Silje Kreken Almeland Numerical modelling of air entrainment 2019-11-20 6 / 35
Air entrainment Stepped Spillway Hydraulic Jump Conclusion References
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
Silje Kreken Almeland Numerical modelling of air entrainment 2019-11-20 7 / 35
Air entrainment Stepped Spillway Hydraulic Jump Conclusion References
airInterFoam
airInterFoam
∂αg∂t
+∇ · (ugαg)− b · ∇ · (νt∇αg) = Sg
Silje Kreken Almeland Numerical modelling of air entrainment 2019-11-20 8 / 35
Air entrainment Stepped Spillway Hydraulic Jump Conclusion References
airInterFoam
airInterFoam
∂αg∂t
+∇ · (ugαg)− b · ∇ · (νt∇αg) = Sg
Sg =a
φent
⟨∂un∂n
⟩δfs
Silje Kreken Almeland Numerical modelling of air entrainment 2019-11-20 9 / 35
Air entrainment Stepped Spillway Hydraulic Jump Conclusion References
airInterFoam
airInterFoam
∂αg∂t
+∇ · (ugαg)− b · ∇ · (νt∇αg) = Sg
Sg =a
φent
⟨∂un∂n
⟩δfs
k > kc, u > uc
Silje Kreken Almeland Numerical modelling of air entrainment 2019-11-20 10 / 35
Air entrainment Stepped Spillway Hydraulic Jump Conclusion References
airInterFoam
airInterFoam
∂αg∂t
+∇ · (ugαg)− b · ∇ · (νt∇αg) = Sg
Sg =a
φent
⟨∂un∂n
⟩δfs
k > kc, u > uc
ug = ul + ur
Silje Kreken Almeland Numerical modelling of air entrainment 2019-11-20 11 / 35
Air entrainment Stepped Spillway Hydraulic Jump Conclusion References
airInterFoam
airInterFoam
αg is calculated
αl is calculated independent of αg
α2 = 1− αl − αg
Silje Kreken Almeland Numerical modelling of air entrainment 2019-11-20 12 / 35
Air entrainment Stepped Spillway Hydraulic Jump Conclusion References
airInterFoam
airInterFoam
Interacts with the αl-equation by reducing thecompression
fvc::flux
(
-fvc::flux(-phir, alpha2, alpharScheme),
alpha1,
alpharScheme
)
Silje Kreken Almeland Numerical modelling of air entrainment 2019-11-20 13 / 35
Air entrainment Stepped Spillway Hydraulic Jump Conclusion References
airInterFoam
Test cases
. Stepped spillway
. Hydraulic jump
(a) Stepped Spillway5 (b) Hydraulic Jump6
5Photo taken from [2]6Photo taken from [1]
Silje Kreken Almeland Numerical modelling of air entrainment 2019-11-20 14 / 35
Air entrainment Stepped Spillway Hydraulic Jump Conclusion References
Stepped Spillway
Sketch taken from [6]
Silje Kreken Almeland Numerical modelling of air entrainment 2019-11-20 15 / 35
Air entrainment Stepped Spillway Hydraulic Jump Conclusion References
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]
Silje Kreken Almeland Numerical modelling of air entrainment 2019-11-20 16 / 35
Air entrainment Stepped Spillway Hydraulic Jump Conclusion References
Stepped Spillway
Silje Kreken Almeland Numerical modelling of air entrainment 2019-11-20 17 / 35
Air entrainment Stepped Spillway Hydraulic Jump Conclusion References
Inception point and surface elevation
Inception point and surface elevation
airInterFoam, kc = 0.2
a
aSketch taken from [6]
Silje Kreken Almeland Numerical modelling of air entrainment 2019-11-20 18 / 35
Air entrainment Stepped Spillway Hydraulic Jump Conclusion References
Inception point and surface elevation
Inception point and surface elevation
a
aSketch taken from [6]
Silje Kreken Almeland Numerical modelling of air entrainment 2019-11-20 19 / 35
Air entrainment Stepped Spillway Hydraulic Jump Conclusion References
Inception point and surface elevation
Inception point and surface elevation
a
aSketch taken from [6]
Silje Kreken Almeland Numerical modelling of air entrainment 2019-11-20 20 / 35
Air entrainment Stepped Spillway Hydraulic Jump Conclusion References
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
Silje Kreken Almeland Numerical modelling of air entrainment 2019-11-20 21 / 35
Air entrainment Stepped Spillway Hydraulic Jump Conclusion References
Dependence on inputvariables
Inception point and surface elevation
a
aSketch taken from [6]
Silje Kreken Almeland Numerical modelling of air entrainment 2019-11-20 22 / 35
Air entrainment Stepped Spillway Hydraulic Jump Conclusion References
Dependence on inputvariables
Inception point and surface elevation
a
aSketch taken from [6]
Silje Kreken Almeland Numerical modelling of air entrainment 2019-11-20 23 / 35
Air entrainment Stepped Spillway Hydraulic Jump Conclusion References
Void fraction
Void fraction
(a) Step 5
(b) Step 6
(c) Step 7Photos taken from [6]
Silje Kreken Almeland Numerical modelling of air entrainment 2019-11-20 24 / 35
Air entrainment Stepped Spillway Hydraulic Jump Conclusion References
Features
Hydraulic Jump
Froude number, Fr = u√gh
Figure: Hydraulic jump
Sketch taken from [7]
Silje Kreken Almeland Numerical modelling of air entrainment 2019-11-20 25 / 35
Air entrainment Stepped Spillway Hydraulic Jump Conclusion References
Features
Hydraulic Jump
Void fraction profiles
Velocity profiles
Free surface contour
Silje Kreken Almeland Numerical modelling of air entrainment 2019-11-20 26 / 35
Air entrainment Stepped Spillway Hydraulic Jump Conclusion References
Features
Hydraulic Jump
Void fraction profiles
Velocity profiles
Free surface contour
Figure: Hydraulic jump
Sketch taken from [7]
Silje Kreken Almeland Numerical modelling of air entrainment 2019-11-20 27 / 35
Air entrainment Stepped Spillway Hydraulic Jump Conclusion References
Features
Test Case
Froude number 4.8Physical experiments by Murzyn[5], reproduced byWitt[7] using interFoam
Figure: Hydraulic jump
Sketch taken from [7]
Silje Kreken Almeland Numerical modelling of air entrainment 2019-11-20 28 / 35
Air entrainment Stepped Spillway Hydraulic Jump Conclusion References
Results
interFoam – reproduction
(a) Current work , realizableKE
(b) Witt (2015)[7]
Figure: Mean flow field for αair.
Silje Kreken Almeland Numerical modelling of air entrainment 2019-11-20 29 / 35
Air entrainment Stepped Spillway Hydraulic Jump Conclusion References
Results
interFoam – realizableKE vs k-ε
realizableKE
k-ε
Silje Kreken Almeland Numerical modelling of air entrainment 2019-11-20 30 / 35
Air entrainment Stepped Spillway Hydraulic Jump Conclusion References
Results
interFoam – k-ε
∆x = 0.005
∆x = 0.0025
Silje Kreken Almeland Numerical modelling of air entrainment 2019-11-20 31 / 35
Air entrainment Stepped Spillway Hydraulic Jump Conclusion References
Results
interFoam – airInterFoam – k-ε
∆x = 0.005, interFoam
∆x = 0.0025, interFoam
∆x = 0.005, airInterFoam
Silje Kreken Almeland Numerical modelling of air entrainment 2019-11-20 32 / 35
Air entrainment Stepped Spillway Hydraulic Jump Conclusion References
Results
Dependence on parameters
ug = ul + ur, kc = 0.2
ug = ul, kc = 0.2
ug = ul, kc = 0.8
ug = ul, kc = 2
Silje Kreken Almeland Numerical modelling of air entrainment 2019-11-20 33 / 35
Air entrainment Stepped Spillway Hydraulic Jump Conclusion References
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
Silje Kreken Almeland Numerical modelling of air entrainment 2019-11-20 34 / 35
Air entrainment Stepped Spillway Hydraulic Jump Conclusion References
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.
Silje Kreken Almeland Numerical modelling of air entrainment 2019-11-20 35 / 35
Recommended