Lock Manifold Port Coefficients

ERDC/CHL CHETN-IX-30 October 2012

Lock Manifold Port Coefficients

by Richard L. Stockstill, E. Allen Hammack, and Jane M. Vaughan

INTRODUCTION: The U.S. Army Corps of Engineers (USACE) is responsible for the nation's inland navigation infrastructure. Navigation locks are an essential asset to the waterway system, and hydraulic design of new locks and extension of existing locks, as well as assessment of locks in operation, require evaluation of the locks' manifolds. Hydraulic evaluation of a lock manifold requires the calculation of flow rate and pressure distributions throughout the manifold. A set of energy equations (one written for flow through each port) and the continuity equation provide a means of calculating the flow distribution. Analytical solutions of lock manifold flow are given by Stockstill et al. (1991), Allen and Albinson (1955), Webster et al. (1946), Soucek and Zelnick (1945), and Zelnick (1942). One-dimensional (1-D) numerical flow solvers such as LOCKSIM (Schohl 1999) are also used to calculate the flow and pressures in lock manifolds. Each of these evaluation techniques requires knowledge of energy loss coefficients for multi-ported manifolds. The purpose of this technical note is to provide a single source of loss coefficient information for lock manifold ports. Coefficients have been gathered from technical reports, laboratory experiments, and computational models. The sizes and shapes of culverts and ports are described using dimensionless terms. This technical note includes loss coefficient information required for hydraulic analysis of manifold flow.

PORT HEAD LOSS: Hydraulic and geometric variables in the vicinity of a single port are defined in Figure 1. The head loss as flow passes from the culvert to the lock chamber through a port is shown as H' in Figure 1. The head loss for flow through individual ports of the manifold can be computed in terms of the culvert velocity head as:

H

'

=

K1

Q12 2g A12

(1)

where:

H ' = the head loss; K1 = the loss coefficient; g = the acceleration due to gravity; Q1 = the culvert discharge upstream from the port; and A1 = the culvert area upstream from the port.

This same head loss can be expressed in terms of the velocity head in the port as:

Approved for public release; distribution is unlimited.

ERDC/CHL CHETN-IX-30 October 2012

Figure 1. Definition sketch of hydraulic and geometric variables at a single port (lock filling).

H

'

=

K3

Q32 2g A32

(2)

where:

K3 = the loss coefficient; Q3 = the port discharge; and A3 = the port area.

The form losses computed using either Equation (1) or (2) require knowledge of the loss coefficient. Dimensional analysis shows that the loss coefficient is a function of the geometrical relations between the culvert parameters (W1 and D1) and those of the port (W3, D3, and L3), as illustrated in Figure 1. A two-dimensional potential flow solution of lateral flow reveals that the coefficient is also a function of the flow division at the port. This division is expressed as the

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ERDC/CHL CHETN-IX-30 October 2012

ratio of the port discharge (Q3) to the culvert discharge upstream from the port (Q1). The functional relation for a port loss coefficient, K, is:

K

=

fn

?????

Q3 Q1

,W3 W1

, D3 D1

, L3 W 1

??????

(3)

Other geometrical considerations, such as rounding of the port entrance and flaring of the port walls, roof, or invert, influence the loss coefficient. For a given manifold geometry, K becomes a function of Q3/Q1. Data required to define this function have been obtained in laboratory studies and computational models.

LOSS COEFFICIENTS FOR LOCK MANIFOLD PORTS: Graphs of loss coefficients for various lock manifold designs are provided in Figures 2-11. Each figure includes a sketch of the particular port shape and a graph of the head loss coefficient expressed both in terms of the velocity head of the main culvert upstream from the port, K1 as defined in Equation (1), and the port velocity head, K3 as defined in Equation (2). The values of K1 are more reliable for small discharge ratios whereas K3 values are more reliable for large ratios.

Square Ports. Zelnick (1942) presents discharge coefficients measured on a model representing lock manifold ports. The shapes tested included square-edged and round-edged ports. Each port cross section was square, but three port width-to-culvert width and port height-to-culvert height ratios were tested. The discharge coefficients are given as a function of the port discharge-toculvert discharge ratio. The actual laboratory data was included in the Zelnick (1942) report, so the head loss coefficients could be calculated in addition to the published discharge coefficients. The energy loss coefficients for the square ports are provided in Figures 2-7. The loss coefficients decreased as the relative port size increased. Lock manifold guidance suggests that the sum of the port areas should be about equal to the culvert cross sectional area (Headquarters, USACE 2006). So, the proper port size depends on the culvert size and the number of ports used to distribute flow along the length of the chamber. Figures 3, 5, and 7 illustrate that the round-edged ports are significantly more efficient than the square-edged ports (Figures 2, 4, and 6). The loss coefficients for the round-edge ports are about one-half as large as those for the square-edged ports.

ILCS Ports. Energy loss coefficients for generalized In-chamber Longitudinal Culvert System (ILCS) port shapes are provided in Hite and Stockstill (2004). The ILCS uses two ports at each ported station, one on either wall, as illustrated in Figures 8 and 9. Each port is located at the midheight of the culvert walls. Yanes (1951) studied the influence of two symmetrically placed ports. The basis of his analysis was the comparison of the two ports with a single port having an area equal to the two symmetrical ports. He concluded that, for port discharge-to-culvert discharge ratios less than 0.25, the results were identical. The symmetrical ports were as much as nine percent more efficient than the single port for discharge ratios between 0.25 and 0.70. However, the data for discharge ratios greater than 0.70 indicated that the symmetrical ports had a comparatively large loss. Yanes (1951) concluded that the pressure rise across divergent symmetrical ports at most of the ported stations along the manifold can be approximated from the results of a single port. So, the pair of ILCS ports is treated as a single port for head loss calculation.

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ERDC/CHL CHETN-IX-30 October 2012

FLOW

150

W1 0.333W1

PLAN

D1 W1

0.583W1 0.333D1

X-SECTION

125

100

K1

75

Q3 /Q1 K 1

0.1 3.53

0.2 8.64

50

0.3 15.9

0.4 25.5

0.5 37.5

0.6 52.1

0.7 69.3

25

0.8 89.4

0.9 113

1.0 139

0 0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0

Q3 / Q1

K3

45

40

35

30

Q3 /Q1 K 3

25

0.1 4.27 0.2 2.67

0.3 2.21

0.4 1.99

20

0.5 1.86

0.6 1.80

0.7 1.75

15

0.8 1.71 0.9 1.70

1.0 1.70

10

5

0 0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0

Q3 / Q1

Figure 2. Loss coefficients for a square port, W3/W1 = 0.333, D3/D1 = 0.333, square edges.

4

ERDC/CHL CHETN-IX-30 October 2012

85 80 75 70 65 60 55 50 45 40 35 30 25 20 15 10 5 0

0.0

8

FLOW

R0.355W3 W1

0.355W3

PLAN

0.333W1

D1 W1

0.583W1 R0.215D3

0.333D1

X-SECTION

Q3 /Q1 K 1

0.1 1.83

0.2 3.43 0.3 6.85 0.4 12.0 0.5 18.8 0.6 27.3 0.7 37.2 0.8 48.5 0.9 61.2 1.0 75.5

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1.0

Q3 / Q1

K1

7

6

K3

5

Q3 /Q1 K 3

4

0.1 2.41 0.2 1.08

0.3 0.949

0.4 0.946

3

0.5 0.942 0.6 0.938

0.7 0.934

0.8 0.930

2

0.9 0.927 1.0 0.923

1

0

0.0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1.0

Q3 / Q1

Figure 3. Loss coefficients for a square port, W3/W1 = 0.333, D3/D1 = 0.333, round edges.

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ERDC/CHL CHETN-IX-30 October 2012

0.583W1

FLOW

W1

0.458W1

PLAN

D1 W1

0.458D1

X-SECTION

K1

45

40

35

30

25

20

Q3 /Q1 K1

0.1 1.92

15

0.2 3.69 0.3 6.22

0.4 9.48

0.5 13.5

10

0.6 18.1

0.7 23.5

0.8 29.6

5

0.9 36.2 1.0 43.6

0 0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0

Q3 / Q1

40

35

K3

30

Q3 /Q1 K 3

25

0.1 8.33

0.2 4.03

0.3 3.03

0.4 2.58

20

0.5 2.38

0.6 2.20

0.7 2.13

15

0.8 2.03 0.9 1.98

1.0 1.92

10

5

0 0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0

Q3 / Q1

Figure 4. Loss coefficients for a square port, W3/W1 = 0.458, D3/D1 = 0.458, square edges.

6

ERDC/CHL CHETN-IX-30 October 2012

FLOW

R0.356W3 W1

0.356W3

PLAN

0.458W1

25

D1 W1

0.583W1 R0.215D3

0.458D1

X-SECTION

20

15

K1

Q3 /Q1 K 1

10

0.1 1.29

0.2 1.97

0.3 2.59

0.4 3.38

0.5 4.88

0.6 6.96

5

0.7 9.71

0.8 12.8

0.9 16.0

1.0 19.4

0 0.0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1.0

Q3 / Q1

8

7

6

Q3 /Q1 K3

0.1 5.73

5

0.2 2.24

0.3 1.32

0.4 0.938

0.5 0.879

4

0.6 0.857

0.7 0.851

0.8 0.851

3

0.9 0.851 1.0 0.850

K3

2

1

0

0.0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1.0

Q3 / Q1

Figure 5. Loss coefficients for a square port, W3/W1 = 0.458, D3/D1 = 0.458, round edges.

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ERDC/CHL CHETN-IX-30 October 2012

FLOW

W1

PLAN

0.583W1

25

0.583W1

D1 W1

0.583D1

X-SECTION

20

K1 K3

15

Q3 /Q1 K 1

0.1 1.44

10

0.2 2.26

0.3 3.44

0.4 4.97

0.5 6.84

0.6 9.04

0.7 11.6

5

0.8 14.4

0.9 17.6

1.0 21.1

0 0.0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1.0

Q3 / Q1

40

35

30

25

Q3 /Q1 K 3

0.1 16.5

0.2 6.65

20

0.3 4.46

0.4 3.64

0.5 3.14

0.6 2.93

15

0.7 2.77

0.8 2.63

0.9 2.52 1.0 2.44

10

5

0 0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0

Q3 / Q1 Figure 6. Loss coefficients for a square port, W3/W1 = 0.583, D3/D1 = 0.583,

square edges.

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