Spillways Hoover dam

goal: deliver high discharge protecting dams from uncontrolled overtopping. Localized high velocity and large elevation range

design strategy for the concrete ogee spillway: keep atm. pressure on the spillway surface, as for a sharp crested weir. same hydrodynamics NOTE: the head H is differently evaluated H vs H’

L 2/3CLHQ

stronger structure

As compared to the lower nappe profile (no ogee), we may have a steeper (e.g for H<Hdesign) or a more shallow (e.g for H>Hdesign) profile

pressure is larger than atm. drag and lower Q flow separation

occurs low pressure at the surface cavitation

on the discharge coefficient....

for P/H>>1 (high spillways) we can consider the spillway as a sharp crested weir

gC

from

P

Hwith

LHCgQ

d

d

23

2C estimate we

CLHQ

728.0C

H'89.0Hfor

611.008.0611.0'C

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2

3/2

d

d

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QUALITATIVELY QUANTITATIVELY

Define L based on abutment and contractions: BB 3

note : lower H imposes a higher cd for the same discharge

upstream face slope and different geometries for the ogee

For low spillways Cd depends on pressure, total head, upstream face slope

P

H08.0611.0'C d

the lower nappe (sharp crested weir) change with the design head Hd

H>Hd

p<patm

cavit.

H<Hd

p>patm

drag

Therefore the discharge coefficient for each actual head values He will vary (while Hd and thus the ogee shape are fixed)

Example : given P/Hd=0.67 and He/Hd=1 we have C/C0~0.96 however if He/Hd=1.2 we have C/C0~0.99 3% more in discharge, but increased chance of cavitation damages How do we quantify the risk of cavitation ?

How do we quantify the risk of cavitation ? We accept a certain risk by tolerating a certain low pressure e.g. constraining hp/Hd > - 0.2 we must keep H/Hd < 1.33 This rule defines the design head Hd based on hydrologic prediction

low pressure peak at x/Hd=-0.2

Note that for Hd=He the pressure is ~ atmospheric

Given a design head Hd we obtain the constraint for the operational regime of the spillway: for larger design head, and limit cavitation zone (hp= p/ <-25ft), we have to be more careful He is the maximum head for a given design condition

EXAMPLE 4

Note that cavitation occurs for hp= p/ <-25 ft

Further reading:

spillway aeration avoid localized cavitation, increase discharge coeff. without smoothing surface

introducing air at atmospheric pressure , or making sure that the flow will entrain air (self-aeration for long spillways), reduces low pressure at the spillway surface and avoid cavitation

stepped versus smooth spillways http://www.flow3d.com/resources/news_12/spring/simulating-flow-over-stepped-spillways.html

En. dissipation estimates

N Number step, h step height: large N, low H >> smooth spillway

yc/h>0.8 skimming