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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
5
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)
6
Carderock Division
Model Fouler Plates
7
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
9
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
10
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
11
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
12
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+
13
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)
14
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
15
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
16
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
17
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
18
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
19
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
20
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
21
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
22
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
23
Credits
Carderock Division
END
24