2. Hydropower Basics
All Hydro is based on a simple formula:
P = hgrk
P = power output in kW
h = height in meters – in cross flow generally defined as distance from water surface to center of
r = flow rate in cubic meters per second – typically plants measure in MGD (millions of gallons
per day) so we convert
g = acceleration due to gravity of 9.8 m/s2
k = system efficiency – many ways to define this:
For a given system design g and k are fixed. Output is linear to both h (head) and r (flow rate).
Double the head = Double the output
Double the Flow = Double the output
This is why most hydro installations are at sites with max potential (head)
3. Overall System Efficiency
Also called Water to Wire Efficiency
A. Turbine Efficiency – Nozzle / Runner assembly – Most control
B. Drivetrain Efficiency – Belt Drive / Gear Box – Some control
C. Generator Efficiency – Control by component selection
D. Power Conditioning Components – Grid Tie Inverter – Little Control
Water to Wire Efficiency = A X B X C X D
5. Waterfall Development Design
We tried to develop a system that was:
2. Not overly complex
3. Reasonably easy to manufacture
4. Components can be swapped out easily to achieve
6. Development Strategy to date
Review and understand existing technology – ie: John Hinkey report referencing 100 technical papers
Select system components required for product – what is and isn’t required
Come up with preliminary general design
Build subscale working prototype
Test & Evaluate in house with waterfall test system
Verify results with CFD & make improvements
First Pilot Project – WSUD (Stickney Machine) – Output approx 1.4kW
No way to test in house
Built off of Nozzle 2.0 design and knowledge
Monitor system after installation – power output, RPM, Voltage, etc.
Second Pilot Project – Delta Diablo – Output approx. 12 – 14 kW
Scaled up from WSUD by using power spreadsheets
Verified output using CFD
7. System Main Components
From Top to Bottom
Intake Manifold – Captures and directs flow to Penstock
Penstock – Directs flow to nozzle / runner assembly
Nozzle Assembly – Compresses flow / includes flow control valve
Runner – Produces power from water – rotating member of system
Distributor Valve – Controls flow of water to nozzle and runner
Level Sensor – Monitors water level in Intake manifold
Belt Drive (current design) – transmits power to generator
8. Breakdown of system components – WSUD Model
Nozzle / Runner
9. WSUD System Prior to installation at Port Orchard, WA
(Currently Installed at Stickney)
10. CFD from Nozzle 2.0 (Half Scale of WSUD System)
Approx 1000 GPM Design Flow Rate
11. Turbine Flow Rate and Efficiency
Flow rate through system is determined by cross
sectional area of nozzle opening and jet velocity
Max system flow rate is at 100% gate setting (wide
Reasonable efficiencies can be maintained down to
about 50% gate setting.
Below 50% gate setting efficiency drops off rapidly
due to atomization and turbulence
12. Efficiency of Cross Flow Turbine
Overall System efficiencies in the range of 80 + %
Efficiency is shown for system with Flow Control (Distributor Valve)
Relatively flat down to about 50% of design flow rate
13. Sizing Procedure
Looking at hourly plant flow rates determine desired design flow rate for turbine. Plant flow rates
vary considerably throughout the day so care must be taken to choose the proper design flow rate.
There is a calculator built into the Springfield spreadsheet that can be used as a basis for a tool to help
with this task but it needs work.
Calculate approximate nozzle jet velocity using the following formula:
V = Velocity in m/s
η = Nozzle Coefficient (Assume .7)
g = Acceleration due to gravity (9.8 m/s sq)
h = design head
Jet velocity and volumetric flow rate increase by the square root of 2gh as head increases.
Nozzle coefficient is a function of design parameters – compression ratio, etc. A higher nozzle
coefficient will allow more flow through the same opening at the same head.
V = 𝜂 2𝑔ℎ
14. Sizing Procedure Continued
Using desired design flow rate and nozzle jet velocity you can deduce the required cross sectional area
for the nozzle.
There are spreadsheets (turbine models) that can be used for this purpose. This is really the only way
to do this. Changing the Jet 1 and Jet 2 width and length will change table parameters.
For any given flow rate a number of designs will achieve the same end result.
Spreadsheets have been updated to match both experimental and CFD data.
Example of Output from Springfield Spreadsheet
Gate Opening ( Q/Qo ) Flow Rate Flow Rate Available Power Q/Qo Correction Efficiency Output Power Output Power
at Effective Head
% MGD GPM Watts Watts HP
100 12.27 8522 11,952 1.0000 0.70 8,366.40 11.22
90 11.05 7670 10,757 1.0250 0.72 7,718.00 10.35
80 9.82 6818 9,562 1.0250 0.72 6,860.44 9.20
70 8.59 5966 8,366 1.0250 0.72 6,002.89 8.05
60 7.36 5113 7,171 1.0000 0.70 5,019.84 6.73
50 6.14 4261 5,976 0.9375 0.66 3,921.75 5.26
40 4.91 3409 4,781 0.8125 0.57 2,719.08 3.64
30 3.68 2557 3,586 0.6250 0.44 1,568.70 2.10
20 2.45 1704 2,390 0.3750 0.26 627.48 0.84
10 1.23 852 1,195 0.0000 0.00 0.00 0.00
15. Example of output from Springfield Model
y = 801.7x - 1130.9
0.00 2.00 4.00 6.00 8.00 10.00 12.00 14.00
Flow Rate (MGD)
Output Power (kW) vs Flow (MGD)
16. Comparison WSUD to Delta Diablo
LOCATION Port Orchard, WA
PROTOTYPE NUMBER WSUD-1
TURBINE TYPE Banki
DESIGN HEAD 98.0 In
HEAD LOSS COEFICIENT 0.95
EFFECTIVE HEAD 93.1 In
NOZZLE COEFICIENT 0.7
ESTIMATED JET VELOCITY 15.64 Ft/s
NOZZLE TYPE 2 Channel
FLOW CONTROL Distributor
JET 1 WIDTH 1.375 in
JET 1 LENGTH 11.5 In
JET 1 AREA 15.8125 Sq. In.
JET 2 WIDTH 1.375 in
JET 2 LENGTH 11.5 In
JET 2 AREA 15.8125 Sq. In.
TOTAL AREA 31.625 Sq. In.
FLOW RATE FULL GATE 2.22 MGD
FLOW RATE FULL GATE 1542 GPM
FLOW RATE 1/2 GATE 1.11 MGD
FLOW RATE 1/2 GATE 771 GPM
PROJECT DELTA DIABLO
PROTOTYPE NUMBER DD-1
TURBINE TYPE Banki
DESIGN HEAD 144.0 In
HEAD LOSS COEFICIENT 0.95
EFFECTIVE HEAD 136.8 In
NOZZLE COEFICIENT 0.7
ESTIMATED JET VELOCITY 18.96 Ft/s
NOZZLE TYPE 2 Channel
FLOW CONTROL Distributor
JET 1 WIDTH 2.125 in
JET 1 LENGTH 28 In
JET 1 AREA 59.5 Sq. In.
JET 2 WIDTH 2.125 in
JET 2 LENGTH 28 In
JET 2 AREA 59.5 Sq. In.
TOTAL AREA 119 Sq. In.
FLOW RATE FULL GATE 10.13 MGD
FLOW RATE FULL GATE 7032 GPM
FLOW RATE 1/2 GATE 5.06 MGD
FLOW RATE 1/2 GATE 3516 GPM
Flow Rate is function of Jet Velocity
and Total Area of Nozzle
Note - corrected for head Delta
area = Approx. 3.71 x WSUD
Inputs are in
17. Differences between WSUD and Delta Diablo
Delta Diablo has about half again as much usable head as WSUD
This means velocity will increase by square root of 2g(difference in head)
Corrected for head it was determined that Delta Diablo Area = approx 3.71 x WSUD to
accommodate the design flow rate of approximately 10 MGD
If we were just scaling the system in both X and Y dimensions we would use a scale factor
of the square root of 3.71 which is 1.926. This was used as guideline
However because of size constraints at Delta Diablo I chose not to use the same scale
factor for the jet width and length. I wanted a wider (which is defined as jet length)
Jet width was increased by a scale factor of only 1.55
While Jet Length was increased by a scale factor of 2.43
The actual numbers are arbitrary at this point and I chose actual dimensions that were
easy to work with. The target design flow rate was an estimate so the resulting flow rate
from the spreadsheet of 10.13 MGD is ok.
Note the jet length (inside dimension) is 28 inches but the runner length is 30 inches.
The runner needs to be slightly longer than the nozzle opening however this amount is
also slightly arbitrary – the runner could also be 36 inches long and the flow rate would
be the same. The runner would have more inertia and be more expensive to build and
the bearing support plates would have to be spaced farther apart to accommodate the
18. Selection of Drivetrain Components
Based on experimental data and CFD the spreadsheet will also attempt to
calculate the runner RPM at peak power using a Tip Speed Ratio.
This can be used to select the proper drivetrain components required to match
the output to the generator which normally has a peak power point.
In the case of Delta Diablo I selected a 1.06:1 Down belt drive from Gates. We
are actually slowing down the RPM because we were using a very low RPM
generator that we had on hand.
Normal loaded RPM of turbine runner = 125 RPM
Peak power and efficiency of generator = 120 RPM
19. General Design Guidelines
A lot of development work has been done to come up with the current full size design –
Delta Diablo – approx. 10 MGD and 10 – 12 kW output.
Current design has limited run time but built off of previous subscale prototypes and
verified with CFD. Output that we saw was approx. 14kW which indicates higher than
No need to change things like distributor valve shape (lots of development work to
minimize losses), shape of nozzle (lots of development work), runner blade geometry
(lots of development work), etc. unless head is drastically increased.
System can be scaled (X-Y) or just widened (with same cross section) to accommodate
different flow rates.
Flow rates can be verified by using the spreadsheets.
Current design incorporates flow control. This adds complexity to the system but allows
for a wider working range of flow rates at high efficiency.
20. Runner Design
Many parameters – shown on next page
Current design has reasonable efficiency – verified with CFD
Optimum # of runner blades can only be determined by experimentation or
CFD but is generally considered to be in the high 20’s to low 30’s count.
With limited development time we have tested runners with only 25 (WSUD)
and 29 (Delta Diablo) blades but we cannot compare output because of scale.
Data indicates 29 blade will offer higher performance.
Runner parameters based on head so should not be necessary to change things
like Blade Entry Angle / Blade Exit Angle, etc.
D2/D1 ratio is almost always .68.
Our objective with both the runner and nozzle assembly was to come up with a
system that offers a reasonable efficiency without an excessive amount of
Improvements can be made but will require experimentation and CFD.
21. 21Hydrovolts PROPRIETARY
Runner Geometry and Parameters – From John Hinkey Report
• D2/D1 = Runner Diameter Ratio
– Typically = 0.68
• B = Runner Length or Width
• W = Nozzle Length or Width
• H or h = Head From Shaft
• = Angle of Attack or Nozzle
– Typically 16-24 deg.
• = Nozzle Entry Arc Angle
– Typically 90-140 deg.
• 1 = Blade Entry Angle
– Typically ~25-30 deg.
• 2 = Blade Exit Angle
– Typically ~80-90 deg.
22. Example of work done with CFD
Velocity On Each
Water Leakage At
End of Nozzle
23. General Design Guidelines – From John Hinkey
• Nozzle: (Vertical Flow Better)
– Alpha Exit Angle : 16 deg.
– Nozzle Entry Arc : 90+ deg
– Width: Slightly More Narrow Than Runner (How Much? TBD): Tight Clearances May Negate
– Casing Profile: More Aggressive Than R* = Const
– Valve Type: Tear-Drop Or None Seem To Be About Equal At 100% Gate
+ Cylindrical Seems To Be Very Very Good At Less Than 100% Gate
– Width/Diameter : TBD, But Very Narrow Runners Appear To Have Lower Performance - B/D1
– Blade Number: 25-35, likely ~30
– Blade Angles: Inlet – 25-30 deg./Outlet 50-90 deg.
– Blade Thickness: Thinner Is Better
– Diameter Ratio: 0.68 (Blade “Solidity” Need Looking Into)
– Interior Guide Vanes: Not Worth It At This Point
– Smaller Is Better, Except At Higher Blade Counts Where There Is POTENTIALLY An Optimum
Very Small Gap
24. Design Considerations for further development –
future projects – final product
If possible generator should be moved up top to intake manifold assembly
Above will require 90 degree gearbox and driveline
Linear actuator for flow control will also be moved up to intake manifold
Need cost analysis for above changes. May be cost prohibitive.
Need cost analysis of entire system. What is target ballpark cost?
What does the final product look like?
What is included in the final product?
Does final product include power conditioning electronics?
Who is responsible for installation?
Who is responsible for monitoring of initial systems?
Who is responsible for issues with turbine? Part failures?
25. Additional Resources
Waterfall Development Plan.doc
Banki Flow Control Development Plan.pdf
Banki Turbine Review Task.ppt
Delta Diablo Power 18 x 30.xlsx
Stickney Turbine Repair Plan.docx
Stickney Trip Report.docx