Waterfall Turbine Development Primer

Jason Rota, Hydro Holdings LLCJan 10, 2014

Hydropower BasicsAll 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 outputDouble the Flow = Double the output

This is why most hydro installations are at sites with max potential (head)

Overall System EfficiencyAlso called Water to Wire Efficiency

Consists of:

A. Turbine Efficiency – Nozzle / Runner assembly – Most control

B. Drivetrain Efficiency – Belt Drive / Gear Box – Some controlC. Generator Efficiency – Control by component selectionD. Power Conditioning Components – Grid Tie Inverter – Little

Control

Water to Wire Efficiency = A X B X C X D

Waterfall MatrixTable 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

HEIGHT OF

VERTICAL

DROP IN

FEET (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

Waterfall Development Design ObjectivesWe tried to develop a system that was:

1. Modular2. Not overly complex3. Reasonably easy to manufacture4. Components can be swapped out easily to

achieve different configurations

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

System Main ComponentsFrom Top to Bottom

Intake Manifold – Captures and directs flow to PenstockPenstock – Directs flow to nozzle / runner assemblyNozzle Assembly – Compresses flow / includes flow control

valve Runner – Produces power from water – rotating member of

systemDistributor Valve – Controls flow of water to nozzle and

runnerLevel Sensor – Monitors water level in Intake manifoldBelt Drive (current design) – transmits power to generator

Breakdown of system components – WSUD Model

Intake Manifold

Penstock

Nozzle / Runner Assembly

Level Sensor

Generator Enclosure

Weir Blocks

Distributor Valve

WSUD System Prior to installation at Port Orchard, WA(Currently Installed at Stickney)

CFD from Nozzle 2.0 (Half Scale of WSUD System) Approx 1000 GPM Design Flow Rate

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

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

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/sη = 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 =

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

Example of output from Springfield Model

0.00 2.00 4.00 6.00 8.00 10.00 12.00 14.000.00

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

f(x) = 801.69685431788 x − 1130.85780990697

Output Power (kW) vs Flow (MGD)

Series1Linear (Series1)

Flow Rate (MGD)

Out

put P

ower

(kW

)

Comparison WSUD to Delta DiabloPROJECT WSUDLOCATION Port Orchard, WAPROTOTYPE NUMBER WSUD-1TURBINE TYPE BankiINTAKE Penstock

DESIGN HEAD 98.0 InHEAD LOSS COEFICIENT 0.95EFFECTIVE HEAD 93.1 InNOZZLE COEFICIENT 0.7

ESTIMATED JET VELOCITY 15.64 Ft/s

NOZZLE TYPE 2 ChannelFLOW CONTROL DistributorJET 1 WIDTH 1.375 inJET 1 LENGTH 11.5 InJET 1 AREA 15.8125 Sq. In.JET 2 WIDTH 1.375 inJET 2 LENGTH 11.5 InJET 2 AREA 15.8125 Sq. In.TOTAL AREA 31.625 Sq. In.

FLOW RATE FULL GATE 2.22 MGDFLOW RATE FULL GATE 1542 GPMFLOW RATE 1/2 GATE 1.11 MGDFLOW RATE 1/2 GATE 771 GPM

PROJECT DELTA DIABLOLOCATION CAPROTOTYPE NUMBER DD-1TURBINE TYPE BankiINTAKE Penstock

DESIGN HEAD 144.0 InHEAD LOSS COEFICIENT 0.95EFFECTIVE HEAD 136.8 InNOZZLE COEFICIENT 0.7ESTIMATED JET VELOCITY 18.96 Ft/s

NOZZLE TYPE 2 ChannelFLOW CONTROL DistributorJET 1 WIDTH 2.125 inJET 1 LENGTH 28 InJET 1 AREA 59.5 Sq. In.JET 2 WIDTH 2.125 inJET 2 LENGTH 28 InJET 2 AREA 59.5 Sq. In.TOTAL AREA 119 Sq. In.

FLOW RATE FULL GATE 10.13 MGDFLOW RATE FULL GATE 7032 GPMFLOW RATE 1/2 GATE 5.06 MGDFLOW 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

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.

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

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.

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.

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 HGuideVane

&Valve

Nozzle

1

2DraftTube

(If Any)

RunnerInlet

Example of work done with CFDUn-Even Flow

Velocity On Each Side Of

Valve/Distributor

Water Leakage At End of Nozzle

Separated FlowIn Distributor

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

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?

Additional ResourcesWaterfall Development Plan.docBanki Flow Control Development Plan.pdfBanki Turbine Review Task.pptWSUD Task.pptDeltaDiabloTask.pptWSUD Power.xlsxDelta Diablo Power 18 x 30.xlsxSpringfield 10kW.xlsxStickney Turbine Repair Plan.docxStickney Trip Report.docx