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