Carderock Division

Measurements of Biofouling Drag Using a 2-D Channel

Flow Apparatus with Models of Bio-fouled Panels

International Congress on Marine

Corrosion and Fouling 2018

Scott Gowing (1) presenting

Peter Chang (2), Scott Storms (3)

(1) CSRA

(2) NSWC Carderock

(3) NSWC Philadelphia

Sponsored by the Carderock Division Naval Innovative Science and Engineering (NISE) program

Distribution Statement A: Approved for Public Release1

Carderock Division

Goal

Provide Equivalent Roughness of

Biofouling for Numerical Drag Predictions

• Measure drag on model biofouled panels

• Determine size of uniform sandgrain roughness that causes same

drag as model biofouling

• Use sandgrain sizes as input to CFD codes to predict hull drag

caused by biofouling modeled in panels

• Provide quantitative assessments for:

- Hull maintenance decisions

- Evaluations of biofouling mitigation schemes

Hydraulically Smooth Heavy Slime

(Vargas 2018) 2

Carderock Division

Channel Flow Facility

View of basin end

• Bulk velocity from flowmeter

• Pressure gradient along channel

yields friction factor

• Vary speed with pump3

Carderock Division

Channel Flow Facility

Turbine

Flow

Meter

Variable

Speed

Pump

Pressure Control

ChannelPressure

Transducers(4 ranges)

Data

Acquisition

4

Constant

area

transition

Carderock Division

Channel Cross Section

Model Biofouler Plates

8

1

Smooth Calibration Plates

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Carderock Division

Sample Plates

Metal backplate

with dovetails

Printed biofouler

plates with dovetailsSmooth plastic or

polished metal plates

for calibration

Backplate and printed panel mesh to

create biofouler plate assembly(assembly insures constant channel height)

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Carderock Division

Model Fouler Plates

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Carderock Division

Smooth Plates

mirror plates - top view mirror plates - end view

Channel overview

• Polished metal or acrylic plates provide smooth surface8

Carderock Division

Channel Flow Friction

• Friction based on streamwise pressure gradient, channel

height, and bulk flow rate

• Pressure gradient measured over multiple taps

Measured Skin Friction

𝑪𝒇 =𝒅𝑷

𝒅𝒙

𝒉

𝝆 𝒖𝟐

0.00

0.10

0.20

0.30

0.40

0.50

0.60

0.70

0 20 40 60 80

Pre

ssu

re d

rop

re

tap

#1

(p

sid

)

x/h

8.67E+047.12E+045.56E+043.83E+042.17E+04

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Carderock Division

Channel Flow Friction

• Integrate log-law with modified B relation for channel flow

• Integration yields analytic equation (some rounding involved)

Prandtl’s Equation for Smooth Channel Friction

Equation for Smooth or Rough Channel Friction

• Equation can be solved (implicitly with Excel Goal Seek) to relate

Cf and relative roughness (k/h)

𝟏

𝟒𝑪𝒇≈ 𝟐. 𝟎𝟑𝟓 𝒍𝒐𝒈 𝑹𝒆𝒉 𝟒𝑪𝒇 − 𝟎. 𝟒𝟕𝟏

𝟏

𝟒𝑪𝒇≈ 𝟐. 𝟎𝟑𝟓 𝒍𝒐𝒈

𝑹𝒆𝒉 𝟒𝑪𝒇

𝟏+𝟎.𝟎𝟓( 𝒌 𝒉)𝑹𝒆𝒉 𝟒𝑪𝒇− 𝟎. 𝟒𝟕𝟏

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Carderock Division

Smooth Plate Data

Smooth plastic and mirror plates

• Smooth plastic and mirror plate data match Prandtl predictions

• Schultz & Flack data a little higher

• Lee & Moser data are in-between

0.000

0.002

0.004

0.006

0.008

0.010

1.00E+04 3.00E+04 5.00E+04 7.00E+04 9.00E+04 1.10E+05

Cf

Re channel

all smooth data

Prandtl

Schultz & Flack 2013

Lee & Moser 2015

smooth mirror

smooth plastic

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Carderock Division

Roughness Effects

Add Roughness Effects

• Roughness shifts velocities lower by constant value in log layer

• Adjust DB constant in log law to represent roughness (typical

approach)

𝒖

𝒖∗= 𝟓. 𝟕𝟓 𝒍𝒐𝒈

𝒖∗𝒚

𝝊

+ 𝟓. 𝟓 − 𝚫𝑩

DB=7.63

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Carderock Division

• CFD calculations use uniform sandgrain to model roughness effects

• Derive equivalent sandgrain roughness for coated or biofouled surfaces from

channel flow experiments measuring friction via pressure drop

• Allows CFD calculations for biofouled surfaces

CFD Roughness

Calculations

0

5

10

15

20

0.0 1.0 2.0 3.0 4.0

DB

log 𝒌_𝒔^+

Uniform sandgrain roughness (Nikuradse)

𝒖∗𝒌

𝝊= 𝒌𝒔

+

𝐥𝐨𝐠 𝒌𝒔+

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Carderock Division

• CFD calculations use uniform

sandgrain roughness (Vargas)

• Derive equivalent sandgrain

roughness for biofouled

surfaces from channel flow

experiments

• Enables CFD calculations for

fouled surfaces

• Experiments validate CFD

predictions

CFD Roughness

Calculations

(uniform roughness)

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Schultz

Carderock Division

Biofouler Plate Data

• Drag values up to 2X or more of smooth values

• Some panels show “fully rough” drag behavior

- friction no longer dependent on Re channel

0.000

0.002

0.004

0.006

0.008

0.010

0.012

0.014

1.00E+04 3.00E+04 5.00E+04 7.00E+04 9.00E+04 1.10E+05

Cf

Re channel

all smooth data 5 pts

panel 8

panel 7

panel 9

panel 1

panel 1X0.5

panel 1X3

panel HPX0.5

panel HPX1.0

panel oyster

panel half oyster

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Carderock Division

Results

• Plot Re*sqrt(Cf) product vs sqrt (2/Cf)

• Fit data with linear fits

• For each plate, calculate DB at each data point

- difference of sqrt(2/Cf)rough - sqrt(2/Cf)smooth (from linear fit)

• Determine equivalent sand grain size that yields measured DB

y = 2.745x - 1.6309

y = 1.3966x + 5.9334

y = 1.0021x + 7.9931

y = 0.7618x + 8.7233

y = 0.1831x + 11.575

10

12

14

16

18

20

22

24

26

28

30

7.00 7.50 8.00 8.50 9.00 9.50 10.00

sqrt

(2/C

f)

ln (Re*sqrt(Cf))

all plastic plates

panel #8

panel #9

panel #1

panel #7

DB

Derivation for DB shift

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Carderock Division

Roughness Forms

Roughness Functions

• Different roughness functions

(sandgrain-type, Colebrook-type)

possible for fitting if panels are not

characterized by single size scale

• Adjust size scale to force conformity

with selected function (DB determined

by DCf)

Granville - 1978

Schultz - 2003

DB

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Carderock Division

0

2

4

6

8

10

12

14

16

18

20

0.01 0.1 1 10 100 1000 10000

de

lta

Bk+

Sandgrain sizes (tested at scale)

Colebrook

sandgrain

panel #8

panel HPX0.5

panel #9

panel HPX1.0

0

2

4

6

8

10

12

14

16

18

20

0.01 0.1 1 10 100 1000 10000

de

lta

B

k+

Colebrook sizes (tested at scale)

Colebrook

panel #8

panel HPX0.5

panel #9

panel HPX1.0

Sandgrain Type Fits

Sandgrain Roughness Function Sizes

• Data slopes match Colebrook sizes better than sandgrain sizes but

CFD uses sandgrain sizes in roughness function

-> sizes must be defined using sandgrain scales

DB

𝒌𝒔+𝒌𝒔

+D

B

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Carderock Division

Comparisons

• Panels #1 and #7 (barnacle data)

have similar form to barnacle fouling

measured by Schultz 2004

Comparison to Other Biofouler Data

0

5

10

15

20

0.01 0.1 1 10 100 1000

del

ta B

ks+

Colebrook type

panel #7

panel #1

DB

Schultz 2004

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Carderock Division

Roughness Scaling

• Modeled roughness scale = 1/l * actual roughness scale

• Correct DB using Colebrook function

• DBFS = DBMS + dDB/dks+ * dks

+ and dks+ = (l * ks+)

• Works well if fully rough

Some Panels are Scaled (l = scale ratio)

0

2

4

6

8

10

12

14

16

18

20

0.01 0.1 1 10 100 1000

DB

ks+

Colebrook type

panel #7

scaled values

scaled DB

value

10X

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Carderock Division

0 2 4 6 8 10

Deteriorated Coating/Light Slime*

Incipient Fouling 1 (3%, 0.6 mm)

Incipient Fouling 2 (3%, 0.7 mm)

Tubeworm (7%, 0.9 mm)

Heavy Slime*

Tubeworm#

Tubeworm (18%, 0.9 mm)

Small Calcareous Fouling/Weed*

Barnacle 1 (4%, 6.6 mm)

Barnacle 1 (6%, 6.6 mm)

Medium Calcareous Fouling*

Barnacle 1 (19%, 6.6 mm)

Barnacle 2 (13%, 8.7 mm)

Heavy Calcareous Fouling*

EQUIVALENT SANDGRAIN SIZES (mm)

Comparisons

Channel data show fouler ranking similar to other data:

slime tubeworms small calcareous heavy calcareous fouling

increasing sandgrain sizes

Present data

Other data

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Carderock Division

0 2 4 6 8 10

Deteriorated Coating/Light Slime*

Incipient Fouling 1 (3%, 0.6 mm)

Incipient Fouling 2 (3%, 0.7 mm)

Tubeworm (7%, 0.9 mm)

Heavy Slime*

Tubeworm#

Tubeworm (18%, 0.9 mm)

Small Calcareous Fouling/Weed*

Barnacle 1 (4%, 6.6 mm)

Barnacle 1 (6%, 6.6 mm)

Medium Calcareous Fouling*

Barnacle 1 (19%, 6.6 mm)

Barnacle 2 (13%, 8.7 mm)

Heavy Calcareous Fouling*

EQUIVALENT SANDGRAIN SIZES (MM)

4.5X coverage

Comparisons

• Variations in spatial density show increases in relative sandgrain sizes

• Sandgrain size increase not proportional to increased coverage

Present data

Other data

2.5X coverage

1.5X coverage

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Carderock Division

Project sponsored by the NSWCCD 219 program

Jack Price, Krista Michalis - Program managers

Eric Holm - Project manager

Abel Vargas - Fluid dynamic modeling

Christina Dehn - Panel preparation

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Credits

Carderock Division

END

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