This document provides an overview of hydropower basics and Hydro Holdings LLC's water turbine system. It discusses the basic formula for hydropower production and key system components. Hydro Holdings has developed a modular cross-flow turbine design that has been piloted at two wastewater treatment plants. The design aims to be reasonably easy to manufacture and have components that can be swapped out. Charts and equations show how turbine output is determined by flow rate and head, with overall efficiencies around 80% at design flow rates.

1. Jason Rota, Hydro Holdings LLC
Jan 10, 2014

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
runner shaft.
 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
Consists of:
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

4. Waterfall Matrix
Table representation of the above formula for Sales & Marketing Use.
System efficiency can be changed in lower right corner which changes all table values
WTP & WWTP: ESTIMATED POWER IN KILOWATTS BASED ON FLOW RATE AND HEIGHT OF DROP
AVERAGE VOLUMETRIC FLOW RATE IN MILLIONS OF GALLONS PER DAY (MGD)
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25
HEIGHTOFVERTICALDROPINFEET(FT)
1 0.09 0.18 0.27 0.37 0.46 0.55 0.64 0.73 0.82 0.92 1.01 1.10 1.19 1.28 1.37 1.47 1.56 1.65 1.74 1.83 1.92 2.02 2.11 2.20 2.29
2 0.18 0.37 0.55 0.73 0.92 1.10 1.28 1.47 1.65 1.83 2.02 2.20 2.38 2.56 2.75 2.93 3.11 3.30 3.48 3.66 3.85 4.03 4.21 4.40 4.58
3 0.27 0.55 0.82 1.10 1.37 1.65 1.92 2.20 2.47 2.75 3.02 3.30 3.57 3.85 4.12 4.40 4.67 4.95 5.22 5.50 5.77 6.05 6.32 6.60 6.87
4 0.37 0.73 1.10 1.47 1.83 2.20 2.56 2.93 3.30 3.66 4.03 4.40 4.76 5.13 5.50 5.86 6.23 6.60 6.96 7.33 7.69 8.06 8.43 8.79 9.16
5 0.46 0.92 1.37 1.83 2.29 2.75 3.21 3.66 4.12 4.58 5.04 5.50 5.95 6.41 6.87 7.33 7.79 8.24 8.70 9.16 9.62 10.08 10.53 10.99 11.45
6 0.55 1.10 1.65 2.20 2.75 3.30 3.85 4.40 4.95 5.50 6.05 6.60 7.15 7.69 8.24 8.79 9.34 9.89 10.44 10.99 11.54 12.09 12.64 13.19 13.74
7 0.64 1.28 1.92 2.56 3.21 3.85 4.49 5.13 5.77 6.41 7.05 7.69 8.34 8.98 9.62 10.26 10.90 11.54 12.18 12.82 13.47 14.11 14.75 15.39 16.03
8 0.73 1.47 2.20 2.93 3.66 4.40 5.13 5.86 6.60 7.33 8.06 8.79 9.53 10.26 10.99 11.73 12.46 13.19 13.92 14.66 15.39 16.12 16.86 17.59 18.32
9 0.82 1.65 2.47 3.30 4.12 4.95 5.77 6.60 7.42 8.24 9.07 9.89 10.72 11.54 12.37 13.19 14.02 14.84 15.66 16.49 17.31 18.14 18.96 19.79 20.61
10 0.92 1.83 2.75 3.66 4.58 5.50 6.41 7.33 8.24 9.16 10.08 10.99 11.91 12.82 13.74 14.66 15.57 16.49 17.40 18.32 19.24 20.15 21.07 21.98 22.90
11 1.01 2.02 3.02 4.03 5.04 6.05 7.05 8.06 9.07 10.08 11.08 12.09 13.10 14.11 15.11 16.12 17.13 18.14 19.15 20.15 21.16 22.17 23.18 24.18 25.19
12 1.10 2.20 3.30 4.40 5.50 6.60 7.69 8.79 9.89 10.99 12.09 13.19 14.29 15.39 16.49 17.59 18.69 19.79 20.89 21.98 23.08 24.18 25.28 26.38 27.48
13 1.19 2.38 3.57 4.76 5.95 7.15 8.34 9.53 10.72 11.91 13.10 14.29 15.48 16.67 17.86 19.05 20.24 21.44 22.63 23.82 25.01 26.20 27.39 28.58 29.77
14 1.28 2.56 3.85 5.13 6.41 7.69 8.98 10.26 11.54 12.82 14.11 15.39 16.67 17.95 19.24 20.52 21.80 23.08 24.37 25.65 26.93 28.21 29.50 30.78 32.06
15 1.37 2.75 4.12 5.50 6.87 8.24 9.62 10.99 12.37 13.74 15.11 16.49 17.86 19.24 20.61 21.98 23.36 24.73 26.11 27.48 28.86 30.23 31.60 32.98 34.35
** Only consider projects with usable vertical drops over 6 Feet and average flows above 5MGD. Above Values based on System Efficiency of: 0.7

5. Waterfall Development Design
Objectives
We tried to develop a system that was:
1. Modular
2. Not overly complex
3. Reasonably easy to manufacture
4. Components can be swapped out easily to achieve
different configurations

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
 CFD Verification
 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
Intake Manifold
Penstock
Nozzle / Runner
Assembly
Level Sensor
Generator
Enclosure
Weir Blocks
Distributor
Valve

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
open)
 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:
Where
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
-1,000.00
0.00
1,000.00
2,000.00
3,000.00
4,000.00
5,000.00
6,000.00
7,000.00
8,000.00
9,000.00
10,000.00
0.00 2.00 4.00 6.00 8.00 10.00 12.00 14.00
OutputPower(kW)
Flow Rate (MGD)
Output Power (kW) vs Flow (MGD)
Series1
Linear (Series1)

16. Comparison WSUD to Delta Diablo
PROJECT WSUD
LOCATION Port Orchard, WA
PROTOTYPE NUMBER WSUD-1
TURBINE TYPE Banki
INTAKE Penstock
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
LOCATION CA
PROTOTYPE NUMBER DD-1
TURBINE TYPE Banki
INTAKE Penstock
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
Jet Velocity
Calculated
using formula
Flow Rate is function of Jet Velocity
and Total Area of Nozzle
Note - corrected for head Delta
Diablo
area = Approx. 3.71 x WSUD
Inputs are in
RED

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)
turbine.
 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
wider runner.

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
expected efficiency.
 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
development.
 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
Center
•  = Angle of Attack or Nozzle
Entry Angle
– 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.
D1
D2 

Head H
Guide
Vane
&
Valve
Nozzle
1
2
Draft
Tube
(If Any)
Runner
Inlet

22. Example of work done with CFD
Un-Even Flow
Velocity On Each
Side Of
Valve/Distributor
Water Leakage At
End of Nozzle
Separated Flow
In Distributor

23. General Design Guidelines – From John Hinkey
Report
• 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
This Effect
– 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
• Runner
– Width/Diameter : TBD, But Very Narrow Runners Appear To Have Lower Performance - B/D1
NOT <<1
– 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
• Clearances
– 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
assembly
 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
 WSUD Task.ppt
 DeltaDiabloTask.ppt
 WSUD Power.xlsx
 Delta Diablo Power 18 x 30.xlsx
 Springfield 10kW.xlsx
 Stickney Turbine Repair Plan.docx
 Stickney Trip Report.docx