8 drag and lift coefficients

Short course for UNIVERSIDAD NACIONAL DE INGENIERIA January 26-29, 2016

Planning and Design for Rehabilitation of Rivers Using Large Wood Metodología para Reforestar Ríos Degradados por Actividades Humanas usando Técnicas de Bioingeniería

8.0 Drag and lift coefficients

Course overview Day I (Jan 26)—Foundational topics

• Three design approaches • Key issues for large wood design

Day 2 (Jan 27)—Designing large wood structures • Case study I—Little Topashaw Creek, Mississippi • Design life for wood structures/selection of design event or condition

Day 3 (Jan 28)—Risk, uncertainty and construction • Sensitivity and Monte Carlo analyses

• Constructability assessment • Case study II—Trinity River, California • Monitoring

Day 4 (Jan 29)--Field trip

Shields Engineering LLC

• Introductions • Review of information resources (design handbooks and spreadsheets) for large wood • Is wood appropriate for your site?—criteria for screening (Planning)

• Types of wood structures • Findings of recent research on drag and lift coefficients

• “Road testing” selected design spreadsheets

2

Ratio of Net Buoyant Force to Drag Force

 Fb   dVd   wVw 

1000

Assuming d/w = 0.45

100

Just a reminder…

1

0.1 0

1

2

3

Stream velocity, m/s

Buoyant force Easy(?) to compute, but don’t overlook!

4

5

Doug Shields, Jr. www.friendofrivers.com

10

CD A wU Fd  2g

2 o

C A U FL  2g

2 o First, let’s focusLon dragwforces

Drag and lift vary based on LW geometry and flow velocity 10

Things to keep in mind Textbook curves represent temporal means for objects submerged in steady flows with nearly uniform approach velocity distributions. Isolated objects with essentially two-dimensional geometries.

Flat plate D

1 1 U 2 LD 2

D

Ellipse

FD

CD

CD 

Circle

D

Airfoil

0.1

D 0.5D

Flat plate

0.01

0.001 1.E+03

D

D

1.E+04

1.E+05 Re 

UD v

1.E+06

1.E+07

0.18D

Ideal v. actual

Effect of surface roughness increasing surface roughness 1.2

0.8

Cd

U

k/b = 0.02

b

k/b = 0.007

0.4

k/b = 0.002

104

2

4

8 105

Sanded surface

2

4

8 106 2

4

8

107

Re

Smooth surface

Increasing surface roughness : decreases critical Re (turbulent crisis) - increases minimum Cd

FD 1 U 2 LD 2

Lab range

10

Prototype range

Flat

1

CD

CD 

D D

Circle

D D

Ellipse

0.

5D

0.1 Airfoil

0.01

D

Flat plate

D

0.001 1.E+03

1.E+04

1.E+05

UD Re  v

1.E+06

1.E+07

0.1 8D

Measure forces in larger channel

Range for our experiments in grassed channel

Tests Conducted in Stillwater, OK, Grassed Channel Alonso et al. (2009), Shields and Alonso (2012)

Testing program • Vertical (lift) and horizontal (drag) forces measured at 1 Hz for steady and unsteady flows.

• Two flow rates, one producing velocity of ~0.74 m/s and the other ~1.2 m/s.

• LW of increasing geometric complexity • Smooth cylinder (PVC) • Rough cylinder (logs with bark) • Log with short branches • Log with long branches • Rootwad

3

2

Approach velocity ~ 1.2 m3 s-1

Effect of LW complexity on CD

All LW held at angle of 30o with flow

1 0 PVC

Hackberry

Oak

Short branchesLong branches

Rootwad

Error bars indicate temporal variability based on 1Hz force measurements—equivalent to 0.12 to 0.15, or 9% to 34%.

3

Effect of LW Drag Coefficients Mean and + 1 std dev complexity on CD

2

All LW held at angle of 30o with flow

1

Approach velocity ~ 1.2 m3 s-1

0 PVC

Hackberry

Oak

Short branchesLong branches

Rootwad

For branched LW, error bars indicate temporal variability based on 1Hz force measurements—equivalent to 0.05 to 0.20, or less than 23%

Manners and Doyle conceptual model Manners, R. B. and Doyle, M. W. 2008. A mechanistic model of woody debris jam evolution and its application to wood-based restoration and management. Riv Res Applic 24:1104-1123.

CD

CD as a function of blockage • Knutson and Fealko (2014) suggest use of an “envelope curve” based on Fr and B from work by Parola that gives CD between 0.1 and 1.8.

• Note these data are for actual LW, not just cylinders. But how were A and U determined?

Some approaches‌.

Shields Engineering, LLC

Include differential hydrostatic force as a driving force—requires hydraulics from 1D or 2D simulation

16

CD as a function of blockage Gippel approach attempts to include differential hydrostatic force in drag coefficient

Comparison of approaches 4.5 4.0 3.5 3.0 2.5 2.0 1.5 1.0 0.5 0.0

Gippel

0

0.2

0.4 0.6 Blockage Ratio, B

0.8

Parola

1

Shields Engineering, LLC

Applied Drag Coefficient, CD

18

Standing wave formation

Wave drag important when flow barely overtops LW 1.00 0.75

Equation 7 Hackberry log Oak log PVC log

z

0.50

Cw 0.25 0.00

Cw max inversely proportional to -0.25 surface (bark) 0 roughness

1

2 z/D

3

• In the absence of better information, CD may be assumed = 0.9 for fully submerged conditions and = 1.5 for conditions where the water surface is within one (typical) log diameter of the top of the structure.

• Drag forces rapidly diminish with time during the first few high flow events as patterns of scour and deposition reshape the local topography (Wallerstein et al. 2001).

• When computing A, a large wood structure may be treated as a single body rather than as individual cylinders if the upstream face of the structure is only slightly porous due to ballast, racked debris, or trash (Gippel et al. 1996).

• For structures located on the outside of bends, the approach flow velocity may be assumed equal to 1.5 times the cross-sectional mean velocity (U.S. Army Corps of Engineers 1994).

Doug Shields, Jr. www.friendofrivers.com

What to use for CD in design?

What about lift forces?

CD A wU Fd  2g

2 o

CL A wU FL  2g

2 o

For cylinders normal to flow

D

Lift important only when log is submerged and very close to bed.

D is log diameter

For branched logs at various angles to flow

5 4 3

Lift Coefficients, CL

Effect of LW complexity on CL

All LW held at angle of 30o with flow

2 1 0 -1

PVC

Hackberry

Oak

Short branches

Long branches

Rootwad

Error bars indicate temporal variability based on 1Hz force measurements—equivalent to 0.08 to 0.69, or 9% to ~3000%.

• Knutson and Fealko (2014) note lift forces typically ignored in LW design • In the absence of better information, CL may be assumed = 1.0 for complex large wood structures that are submerged.

Lift may be assumed = 0 for large wood that is not fully submerged.

Doug Shields, Jr. www.friendofrivers.com

What to use for CL in design?

Smooth Log (PVC)

Moderately Rough Log (Hackberry)

1.4

Velocity, m/s and Depth, m

Temporal variation of forces on cylindrical logs during hydrograph Flow depth, m Velocity, m/s

1.2

1.0 0.8 0.6 0.4 0.2 0.0

Vertical force (lift + buoyancy), N

Force, N

600

300

0

Force, N

600

Horizontal force (drag), N

300

0 00:00

05:00

10:00

Time from start of run, mm:ss

15:00

00:00

10:00

20:00

Time from start of run, mm:ss

30:00

Forces on LW during hydrograph Log with long branches, rotation 2

Rootwad, rotation 2

1.0

Flow depth, m

Flow Depth, m

0.8

0.6

0.4

Top of LW

0.2

0.0

Force, N

Vertical force (lift + buoyancy), N 1000

500

0

Horizontal force (drag), N

Force, N

1000

500

0 00:00

05:00

10:00

Time from start of run, mm:ss

15:00

00:00

10:00

20:00

Time from start of run, mm:ss

30:00

Forces during unsteady flow (a storm event) • Buoyant forces vary with wood density and submergence • Lift and drag vary with • • • • •

Incident velocity LW geometry/orientation Skin roughness Turbulent fluctuations Submergence (wave drag not included in textbook CD values)

Doug Shields, Jr.

www.friendofrivers.com