IN
DEGREE PROJECT VEHICLE ENGINEERING, SECOND CYCLE, 30 CREDITS
STOCKHOLM SWEDEN 2017,
Layout of spillway aerator air vents and its effect on air supply
GUSTAV DAGGENFELT
KTH ROYAL INSTITUTE OF TECHNOLOGY
Layout of spillway aerator air vents and its effect on air supply
Gustav Daggenfelt June 12, 2017
Abstract
Chute aerators are constructed to protect spillways from cavitation dam- age. They function by launching the water flow as a jet and supplying air underneath since having air entrained into the water is an effective way to mitigate cavitation. This report looks at Bergeforsen, a dam in northern Sweden, and its spillway as a basis for investigating how altering the aer- ator’s outlet alters its performance. Five different designs are tested using CFD with ANSYS Fluent 17. The designs are evaluated with regard to total air flow, air flow distribution, duct pressure distribution, cavity length, and air concentration in water jet.
It was found that designs with more even duct pressure distribution, that transported air further toward the spillway center, had somewhat reduced total air supply compared to designs that released more of its air in the early part of the duct. Consequently there appear to be a trade off between effectively distributing the air and providing more air flow. The current design used by Bergeforsen strikes this balance quite well, better than the other tested designs.
Luftinblandare byggs f¨or att skydda utskov fr˚an kavitationsskador. De fungerar genom att l˚ata vattenstr¨ommen bli en str˚ale under vilken luft tills¨atts eftersom att blanda in luft i vattenstr¨ommen ¨ar ett effektivt s¨att att motverka kavitation. Den h¨ar rapporten unders¨oker Bergeforsen, en damm i norra Sverige, och dess utskov f¨or att unders¨oka hur luftinblandarens utsl¨app p˚averkar dess prestanda. Fem olika designer testas med hj¨alp av CFD i ANSYS Fluent 17. Designerna utv¨arderas med avsikt p˚atotalt luftfl¨ode, f¨ordelning av luftfl¨ode, tryckf¨ordelning i luftg˚angen, l¨angd p˚alufth˚alrum, samt luftkoncentration i vattenstr˚alen.
Det uppt¨acktes att designer med mer j¨amn tryckf¨ordelning i luftg˚angen, som transporterade mer luft till utskovets mitt, hade n˚agot mindre total lufttillf¨orsel j¨amf¨ort med designer som sl¨appte ut mer av luften tidigare ur luftg˚angen. Det ser d¨arf¨or ut att kr¨avas en kompromiss mellan effektiv f¨ordelning och totalt luft fl¨ode. Den design som anv¨ands i Bergeforsen idag uppfyller den kompromissen ganska v¨al, b¨attre ¨an de andra som testades.
Acknowledgements
This work was done at the department for Hydraulic Engineering at Kung- liga Tekniska H¨ogskolan on behalf of Vattenfall AB and supervised by James Yang. Particular thanks to Penghua Teng for providing grids for CFD and for plenty of help and advice along the way.
Contents
1 Background 3
2 Theory 5
2.1 Spillway . . . 5
2.2 Cavitation . . . 5
2.3 Aeration . . . 6
2.4 Bergeforsen . . . 7
3 Method 9 3.1 Numerical model . . . 9
3.2 Air vent designs . . . 10
4 Results 12 4.1 Duct pressure . . . 12
4.2 Air Volume Flow . . . 13
4.3 Air Cavity . . . 14
5 Conclusion & Discussion 17 6 Appendix 18 6.1 Graphics . . . 18
Chapter 1
Background
Spillways are important structures serving as outlets for excess water from hydroelectric dams. In steeper and longer spillways, so more commonly in large dams, the streaming water can reach high velocities that cause cavitation damage which erode the concrete along the spillway floor and walls.
Cavitation damage has been ob- served in spillways world wide through- out the 20th century. A dam fail- ure at the Madden Dam in Panama 1935 first prompted research into the phenomenon [2]. Some of the most standout cases have been in pipe spill- ways such as Glen Canyon Dam 1983 [1] where initial cavitiation damage is less likely to be spotted early. In that case the erosion eventually led to vi- brations breaking apart large pieces of concrete and pulling out metal bars, opening up an 11 m deep hole.
Cavitation in spillways can be mit- igated in several ways; redesigning the spillway for reduced flow veloci- ties, smoothing out the concrete sur- face and removing edges or other ir- regularities, and installing an aerator upstream of the critical region.
Aerators are devices that mix air into the water, most importantly the
parts of the flow adjacent to the walls or bottom. A chute aerator is a de- sign that use a ramp deflector to launch the water into a jet underneath which there is an air duct outlet. The free surface of the jet then has air en- trained into it [2].
Bergeforsen power station is lo- cated on Indals¨alven outside Timr˚a.
The dam began its service in 1955 and is currently under ongoing main- tenance and modernization for future use. Primarily a new spillway was constructed in 2014 [8]. The new spill- way has an aerator to reduce erosion caused by cavitation. The aerator has 13 square outlets along a ramp spanning the width of the spillway.
Potentially the aerator could be im- proved by changing the design of the outlet, and as a result improve the protection against erosion.
Due to the spillway’s unusually large width the flow characteristics differ somewhat compared to other smaller Swedish dams. The size also make experiments with small scale models less reliable. Therefor CFD- simulation will be the method used to investigate.
Figure 1.1: Bergeforsen’s new spillway, air vents from the aerator can been seen along the bottom.
Chapter 2
Theory
2.1 Spillway
A spillway is an essential part of dam construction as it is the outlet for ex- cess water from the reservoir to the river beneath. Typically it can be separated into three sections; a gate, a channel or chute, and an energy dis- sipator. The gate regulates the water flow from the reservoir into the chute where it flows down into the dissipa- tor where the water has its kinetic en- ergy reduced before it’s released into the river.
2.2 Cavitation
In high velocity water flow over an ir- regular or rough surface there will be pockets of flow separation resulting in low pressure areas. If these pres- sure drops are large enough the wa- ter will start to transition into vapor, essentially a boiling phenomenon due to decreased pressure rather than in- creased temperature. The formation of these vapor bubbles in the water is called cavitation.
As the vapor returns to the higher pressure levels of the surrounding flow the bubbles will collapse back into water. As they do so the collapsing
process will cause small shock waves and micro jets of water that can cre- ate large pressure spikes on nearby surfaces such as the concrete floor or walls resulting in erosion and mate- rial fatigue.[1, chapter 1] In hydro- engineering this entire chain of events is usually included in the term cav- itation due to the temporary nature of the vapor bubbles.
The collapse of a vapor bubble is cyclical; the bubble is first com- pressed before it collapses into two smaller bubbles and releases a wa- ter micro jet, the two then combine back into a single bubble and the cy- cle begins again. After each cycle the resulting bubble is smaller than it was at the start.[1, page 8-10] If the collapse happens in the vicinity of a boundary the microjet tends to be directed towards it, as shown in figure 2.1.
When the two bubbles recombine they generate shock waves and it is these and the micro jets that cause cavitation damage. Which factor is more important is hard to determine, partially because the shock waves from one bubble collapse can trigger a chain reaction in other nearby bubbles. Such a chain reaction can result in an ultra
Figure 2.1: Bubble collapse and re- bound cycle close to a boundary. [1, page 9]
jet when multiple micro jets from dif- ferent bubbles combine into a larger single jet with velocity in the order of about half the sonic velocity of the liquid.[1, page 9-10]
Cavitation damage is progressive, which means that erosion of a sur- face is going to increase the inten- sity of cavitation on that surface, and it’s therefore important to use pre- ventive measures as damage can go from being unnoticed to being dan- gerous quickly.[3, page 95]
The risk of cavitation can be esti- mated using the cavitation index K
K = hp+ ha− hv
V2/2g (2.1) where hpis the bottom pressure head, ha is the atmospheric pressure head, hv is the vapor pressure head, V is the water flow velocity and g is grav- itational acceleration. A K-value at 0.2 or less indicates critical risk of cavitation requiring aeration.[7]
Aeration reduces cavition by hav- ing air entrained in the flow. The main reason for this appears to be the fact that an air-water mixture with more than 1% undissolved air, some- what counter-intuitively, can have a much lower sonic velocity than either fluid has on its own. This reduces the pressure spikes generated by both the
shock waves and the jets during bub- ble collapse.[1, pages 11-12 & 34]
2.3 Aeration
As early as 1953 it was found that cavitation damage can be effectively mitigated if there is between 6-8%
air entrainment in the water[5]. In truth the air concentration required is poorly understood as it is difficult to measure air concentration at the area where damage occurs. It also depends on surface roughness, flow velocity, depth and other unknown factors. The findings from several studies however agree that only small amounts of air are needed to signif- icantly reduce cavitation damage[2].
In order to increase the air entrain- ment, particularly in the crucial parts of the flow close to the spillway floor, aerators are commonly installed. Aer- ators are airducts that suck in out- side air and distribute it from under- neath the water flow.
Figure 2.2: Example of a general aer- ator design. Sideview crossection.
Aerators typically use an offset and a deflector or ramp in order achieve a water jet with an air cavity under- neath in which air can be supplied,
Figure 2.3: Water flow over an aera- tor with P and L defined.
as shown in figure 2.2. The flow can therefor be said to have three general flow zones; the jet zone, the reattach- ment and spray zone, and the far- field zone.[6] The jet reattachment point is denoted P and its distance from the deflector and/or offset is the jet length L. The flow zones can then be defined as jet zone at 0 < x/L <
1, reattachment and spray zone at 1 < x/L < 3, and far-field zone at x/L > 3. The reattachment point P can be defined in various ways but in this report is defined by the point of peak pressure on the spillway bot- tom. Figure 2.3 shows a possible ex- ample based on one of the CFD sim- ulations.
Very little of the air entrained in the jet zone remain in the lower parts of the flow after reattachment point P , instead most of the air is detrained by being transported up and released from the water surface. Aerators con- sequently have only a small effect on the bottom air concentration in the far-field zone [6]. Luckily not much air is required.
A common ratio used to evaluate the effectiveness of an aerator is the
air entrainment coefficient:
β = QA QW
(2.2) where QAand QW are the respective volume flows of air and water at the aerator.
Another similar parameter is the local average air concentration at the aerator defined as
Ca= QA/(QA+ QW) (2.3) however both of these parameters have the weakness of not considering the bottom air concentration in the down- stream region.[7]
When doing initial design of a vent aerator there are several important steps to take, the dimensions of the ramp and offset are of primary im- portance but those will not be cov- ered in this report. Instead focus is on the vent and duct design.
The air duct should be designed to avoid so called choked flow which is where a sonic flow regime is reached.
A duct flow velocity limited to under 100 m/s is therefor recommended as well as a maximum pressure drop in the duct of roughly 2-6% depending on the amount of friction losses in the duct. The vent outlet area is recom- mended to be less than the area of the duct intake.[1, page 70]
2.4 Bergeforsen
The spillway at Bergeforsen dam, shown in figure 1.1, has an opening width of 25 m which makes it the largest spill- way in Sweden. It’s crest is at an el- evation 112.75 m and the aerator is located 24.72 m downstream, more measurements are given in table 2.1.
Width at opening 25 m
Width at aerator 35 m
Chute slope, θ 32◦
Crest elevation above aerator 14.73 m
Offset height 1.5 m
Aerator intake area 20.43 m2 Aerator outlet area 13 m2
Table 2.1: Relevant data from the spillway [9, page 7]
Chapter 3
Method
In order to test a few variations on air vent design they are modeled in 3D for Ansys Fluent 17. The flow through the spillway is then simu- lated until the flow through the mod- eled section has reached a relatively stable level. The results from the dif- ferent design are then compared to each other with focus on a few key parameters to determine what improve- ments have been made.
The key parameters are as follows:
total air volume flow through the aer- ator, pressure distribution through the horizontal duct, spanwise volume flow distribution across the vent outlet, jet length and air concentration in lower jet surface.
3.1 Numerical model
A symmetrical half of the chute spill- way is modeled with an inlet flow that was in accordance with previous ex- periments made by James Yang and Penghua Teng [9], this was done to reduce the calculation time that would be required by modeling the entire reservoir and spillway system. An initial calculation using the Volume of Fluid Method (VOF) was done but was deemed to provide insufficient ac-
Figure 3.1: View of the CFD model
curacy so instead the Eulerian mul- tiphase model in ANSYS Fluent 17 was used.
Simulations like this overestimate the air concentration in the lower part of the flow downstream of the jet reat- tachment point P . In other words the detrainment of air is not accu- rately modeled. However the flow be- fore that point, in the duct and cav- ity, has been found sufficiently accu- rate for these tests with regards to airflow and jet length [4].
The Eulerian model is used for flows consisting of multiple interact- ing phases, in our case water and air.
It assumes pressure is shared between
phases and then solves momentum and continuity equations separately for each phase.
The mass continuity equation in this case for phase i is
∂
∂t(αiρi) + ∇ · (αiρi−→vi) = 0 (3.1) where α is the volume fraction, ρ is the density, −→v is the velocity vector.
The momentum balance equation for phase i is
∂
∂t(αiρi−→vi) + ∇ · (αiρi−→vi−→vi) =
− αi∇p + ∇ · ¯¯τi+ αiρi−→g +
n
X
j=1
−
→Rij +−→ Fi+−→
Flif t,i +−→
Fwl,i+−→
Fvm,i+−→
Ftd,i (3.2) where p is pressure, ¯τ is the stress¯ strain tensor, g is gravitational ac- celeration and the five force vectors are
−
→F - external body force
−
→Flif t - lift force
−
→Fwl - wall lubrication force
−
→Fvm - virtual mass force
−
→Ftd- turbulent dispersion force.
There is also the term that describes interaction between faces, where−→
Rij
is the phase interaction force.
Realizable k − is used as the viscosity model and the constructed grids use approximately 390 000 cells.
Bubble diameter was selected to be 1 mm.
The boundary conditions are shown in table 3.1. A closer look at the up-
Upstream water Water velocity flow boundary inlet, 9.5 m/s Spillway top surface Air pressure inlet Aerator top duct Air pressure inlet Downstream boundary Pressure Outlet
Centerplane Symmetry
Other boundaries Wall
Table 3.1: Boundary conditions stream boundary conditions can be seen in the appendix.
To ensure a good grid size three different grids; a course (∼230 000 cells), medium and fine (∼490 000 cells) grid were tested for the rect- angular aerator design. The medium size was found to provide sufficient grid independence and was used for the rest of the calculations.
3.2 Air vent designs
Five different air vent designs, all with the same total area of 13 m2 (6.5 m2 for each symmetrical half) are tested:
the current design using square open- ings and four other simple designs with rectangular, tapered, and stepped openings.
The original design uses 1.0x1.0 m square openings with 7 of them placed 1 m apart towards the middle.
All other designs use a single 35 m long opening with the rectangu- lar option being 0.37 m wide. The tapered design goes from 0.5 m at the middle to 0.25 m at the walls.
The single step design has a 0.59 × 17.5 m midsection with a 0.15 × 8.75 m section on each side. The multi step design uses a total of seven 5
m sections with the middle one be- ing 0.9 m wide followed by 0.55 m, 0.2 m and 0.1 m as you go towards the walls.
See appendix for more detailed figures.
Chapter 4
Results
4.1 Duct pressure
The pressure drop in the air-duct is directly related the air velocity in this non-compressible model. It was sampled along a horizontal line that was placed as far away from any of the walls as possible with visual approxima- tion.
Figure 4.1: Pressure distribution in horizontal air duct, relative atmospheric pressure
Figure 4.1 shows that as we reduce the vent size towards the wall and increase the size closer to the middle we significantly reduce the maximum
pressure drop but maintain a more even pressure drop which indicates that a larger part of the flow is transported towards the center of the spillway.
See appendix for cross sections that visualize the air flow in the air duct.
4.2 Air Volume Flow
The total air volume flow through the air duct is shown in table 4.1.
Vent design QA(m3/s) β
Squares 117.2 0.329
Rectangle 118.1 0.332
Tapered 119.0 0.334
Single Step 106.7 0.300 Multi-Step 99.50 0.278
Table 4.1: Air volume flow rates and air entrainment coefficients.
The spanwise distribution of the air entrainment coefficient β is shown in figure 4.2, calculated just outside the vent outlets (which is why we have some flow in between the square openings). Clearly, as more of the airflow is moved further along the duct there is a price to pay in terms of total amount of air supplied.
Figure 4.2: Air flow distribution, calculated as β/m
4.3 Air Cavity
The jet length L, previously mentioned in chapter 2.3, can be defined in a few different ways but in this case it’s defined by the location of the highest pressure on the bottom surface of the spillway. The spanwise change in jet length L can be seen in figure 4.3. As we can see the jet length varies quite a lot with the different designs. The multi step design has the shortest jet lengths, particularly close to the wall. The original design with square openings on the other hand the longest jet lengths at the wall and then gets shorter relative to other designs at the centerline.
Figure 4.3: Jet length across the spillway chute.
The air becomes entrained into the lower side of the jet, inside the cavity, so in attempt to evaluate the air concentration it is good to look at this boundary region between the water jet and the air. Figure 4.4, 4.5 and 4.6 shows the air concentration close to the jet at L/2 at three different positions.
The concentration is measured from the jet center which is defined as the point of minimum air concentration. In figure 4.4 we can clearly see how the air volume fraction is close to or at 0 at the origin and that after that the design with square openings appear to provide the best air entrainment, followed by the multi stepped design.
In figure 4.5 we instead see the best result from tapered design. We also begin to see that the minimum air volume fraction is slightly above 0. This is even more clear in figure 4.6, where we see several designs never dip below
Figure 4.4: Air concentration at L/2, at the spillway center.
5% air concentration. The two designs with lower minimum improve greatly as we move away from the jet center so all designs are likely to be sufficient for this slower part of the flow.
For an example cross section visualizing the flow in the cavity see ap- pendix.
Figure 4.5: Air concentration at L/2, 8.5 m from the spillway center.
Figure 4.6: Air concentration at L/2, 17 m from the spillway center.
Chapter 5
Conclusion & Discussion
As shown in figure 4.1 and 4.2 the multi step design succeeds quite well at moving air further into the duct, but it does so at a cost to the total air supply.
While the good air distribution from the multi step design can be seen in the air concentration in figure 4.4 it still does not appear to outperform the current design. This is despite the fact that the current design releases most of its air supply from the duct long before reaching the center of the spillway, as can be seen in figure 4.2. One possible explanation for this is that the air cavity still allows for significant lateral transportation of air which reduces the influence of the duct design somewhat.
There appear to be a strong correlation between air volume flow and jet length, with the rectangular and tapered designs performing the best.
The choice of bubble diameter could affect the results. Experimental data suggests that the air concentration in the water jet’s lower surface is most accurately calculated by a small bubble diameter, which the selected 1 mm should be sufficient for, but the air flow rate appear to be better cal- culated by bubble diameters closer to 4 mm [4]. However since this analysis is focusing on comparing different designs the overall evaluation is unlikely to change.
To sum up the current design provide good overall performance despite its somewhat unbalanced pressure distribution. The rectangular and tapered designs supplied the most air. The multi step design had the least air supply but distributed it effectively.
The central vents in the current design does not appear to be very effec- tively used. A potential marginal improvement could be to move the fourth vent, counted from the wall (see figure 6.6 in the appendix), a meter or two out toward to the wall as that appear to be a part of the duct that is effective at releasing air without losing out with regard total air supply or distribution. However, to confirm that would require further experiments.
Chapter 6
Appendix
6.1 Graphics
Figure 6.1: Upstream and aerator boundary conditions. Wall shown in gray, symmetry in green, pressure inlet in yellow, and water velocity inlet in blue.
Figure 6.2: Rectangular layout
Figure 6.3: Tapered layout
Figure 6.4: Single step layout
Figure 6.5: Multi step layout
Figure 6.6: Current layout
Figure 6.7: Duct sub-pressure in color and arrows marking flow direction.
Rectangular design.
Figure 6.8: Duct sub-pressure in color and arrows marking flow direction.
Tapered design.
Figure 6.9: Duct sub-pressure in color and arrows marking flow direction.
Single step design.
Figure 6.10: Duct sub-pressure in color and arrows marking flow direction.
Multi step design.
Figure 6.11: Duct sub-pressure in color and arrows marking flow direction.
Current design.
Figure 6.12: Air concentration and air flow direction in the cavity region.
Figure shows the tapered design at the symmetry plane.
Bibliography
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[2] Kristian Kramer. Development of aerated chute flow, 2004.
[3] International Comission on Large Dams. Spillways, shockwaves and air entrainment, 1992.
[4] James Yang Penghua Teng and Michael Pfister. Studies of two-phase flow at a chute aerator and cfd modelling, 2016.
[5] A.J. Peterka. The effect of entrained air on cavitation pitting, 1955.
[6] Michael Pfister and Willi H. Hager. Chutes aerators i: Transport char- acteristics, 2010.
[7] Michael Pfister and Willi H. Hager. Chutes aerators ii: Hydraulic design, 2010.
[8] Vattenfall. Bergeforsen. http://kraftverk.vattenfall.se/bergeforsen, Ok- tober 2016.
[9] James Yang and Penghua Teng. Cfd modeling of two-phase flow of a spillway chute aerator of large width, 2015.
