Lecture 14
Energy dissipation
When water spills and flows over the spillways, then it
acquires a very high velocity, as the whole potential energy (due to potential
head) is transformed into kinetic energy. The process of destruction of this
kinetic energy is known as energy dissipation. Or,
When water flows over a spillway, it undergoes a transformation from potential energy to kinetic energy due to the drop in elevation (potential head). This results in water attaining a very high velocity as it moves downstream. However, this high-velocity flow can cause significant damage to the spillway structure, the downstream channel, and the surrounding environment if not properly managed. The process of reducing or destroying this kinetic energy to safe levels is known as energy dissipation. This process is critical in hydraulic engineering to ensure the stability and safety of hydraulic structures and their surroundings.
Why is Energy Dissipation Necessary?
High-velocity water flowing over a spillway possesses
immense kinetic energy. If this energy is not dissipated, it can lead to:
· Erosion:
Scouring of the downstream riverbed and banks, potentially undermining the
spillway structure.
· Structural
Damage: Damage to the spillway apron, stilling basin, or other downstream
structures.
· Environmental
Impact: Disruption of aquatic ecosystems due to turbulent flows and
sediment transport.
· Safety
Hazards: Risk to human life and property in downstream areas.
For the dissipation of the excessive kinetic energy
possessed by the water the following two methods are commonly adopted.
(1) By developing a hydraulic jump.
(2) By using different types of buckets.
Hydraulic Jump
A hydraulic jump is one of the most common and effective
methods of energy dissipation. It occurs when high-velocity, supercritical flow
(Fr > 1) transitions to low-velocity, subcritical flow (Fr < 1).
Hydraulic jumps are facilitated in stilling basins located at the base of
spillways.
Types of Jumps
Different types of hydraulic jumps are developed on a
horizontal floor. The jump form and its flow characteristics primarily depend
on the Froude number (F₁) of the incoming flow, expressed as:
F1=V1/√(g⋅y1)
where:
·
V1 = mean velocity of flow before the
jump,
·
g = acceleration due to gravity,
·
y1 = pre-jump (initial) depth of
flow.
Thus, hydraulic jumps may be classified according to the
values of F1 as follows.
1.
F₁ = 1: Flow is critical; no jump forms.
2.
F₁ = 1 to 1.7: Undular jump with surface
undulations; energy dissipation is low (~5%).
3.
F₁ = 1.7 to 2.5: Weak jump with small
surface rollers; energy dissipation is ~20%.
4.
F₁ = 2.5 to 4.5: Oscillating jump with
irregular jet oscillations; energy dissipation ranges from 20% to 45%.
5.
F₁ = 4.5 to 9: Steady jump, stable and
well-balanced; energy dissipation ranges from 45% to 70%.
6.
F₁ > 9: Strong jump with rough water
surface and high energy dissipation (up to 85%).
Hydraulic jump at
the toe of a spillway
Jump Height and Tail Water Rating Curves
For a hydraulic jump to be developed in a rectangular
channel the following equation must be satisfied,
Or,
Where,
·
y1 is prejump (or initial) depth;
·
y2 is post jump (or sequent) depth.
For a given discharge intensity q, the initial
depth y1 is determined by
y1=q/V1,
where
V1=√2gH1 (assuming
no head loss).
To form a hydraulic jump across all discharge intensities,
the sequent depth y2 must correspond to y1 based on the
jump equation. By calculating y2 for various q values,
a Jump Height Curve (J.H.C.) or Jump Rating Curve
(J.R.C.) can be plotted.
The actual tailwater depth y2′ depends on
downstream hydraulic conditions. Observing y2′ for
different q values allows plotting a Tailwater Rating Curve
(T.W.R.C.). These curves help analyze jump formation and tailwater
interactions.
Jump Location
For a given discharge intensity q (and
thus y1), the location of a hydraulic jump downstream of a spillway
depends on the relationship between the tailwater depth y2′ and the
sequent depth y2. Three cases arise:
1.
Case 1: y2′=y2
The jump forms precisely at the
spillway toe, providing ideal scour protection.
2.
Case 2: y2′<y2
The jump shifts downstream, causing
severe erosion between the spillway and the jump location. This scenario should
be avoided in design.
3.
Case 3: y2′>y2
The jump is drowned or submerged
near the spillway toe, reducing energy dissipation efficiency. This case is
also undesirable.
The location of the hydraulic jump depends on the discharge
intensity q and the corresponding tailwater depth y2′. Since
both q and y2′ vary, the relationship between the Jump
Height Curve (J.H.C.) and the Tailwater Rating Curve
(T.W.R.C.) must be analyzed. These curves are plotted together, and
their relative positions can result in five possible conditions given in Fig.
below. For each condition, specific
measures are required to ensure the jump forms close to the spillway toe for
effective energy dissipation and erosion control.
Fig: Tailwater
conditions for the design of scour protection works
Condition 1
The jump height curve and the tail water rating curve are
coinciding with each other for all the discharges. Thus, in this case for all
the discharges jump will develop close to the toe of the spillway. As such a
horizontal apron may be provided on the river bed downstream from the toe of
the spillway. In such a case, a simple concrete apron of length 5 (y2 - y1) is
generally sufficient to provide protection in the region of hydraulic jump, as
shown in Fig.
Condition 2
When the jump height curve exceeds the tailwater rating
curve for all discharge levels, the hydraulic jump will form further downstream
from the spillway toe. To ensure the jump occurs closer to the spillway toe,
the tailwater depth must be increased. This can be achieved through the
following methods:
1.
Depressed Apron: Excavate the riverbed
downstream of the spillway toe to create a horizontal or sloping depressed
apron. The apron's dimensions should ensure the jump remains within its
confines for all discharge levels.
2.
Stilling Basin: Construct a stilling
basin by installing a sill or baffle on the riverbed downstream of the spillway
toe. The basin's size and depth must be designed to contain the jump for all
discharge conditions.
Fig. (a)
Depressed horizontal floor; (b) Stilling basin for hydraulic jump
Condition 3
The jump height curve lies below the tailwater rating curve
for all discharges, indicating that higher tailwater depths will result in a
drowned jump, leading to minimal energy dissipation. To ensure the formation of
a clear hydraulic jump, the following measures can be implemented:
a.
Install a sloping apron on the riverbed,
extending from the spillway's downstream surface. The apron's slope should be
designed to facilitate jump formation across all discharge conditions.
b.
providing a roller bucket type of energy
dissipator. It consists of an apron, which is upturned sharply at ends.
(a)
(b)
Fig: Hydraulic
jump on a sloping apron (a) and roller bucket (b)
Condition 4
The jump height curve exceeds the tailwater rating curve at
low discharges but falls below it at high discharges. To ensure a hydraulic
jump formation near the spillway, the following measures can be implemented:
a.
Install a stilling basin to induce a jump at low
discharges, combined with a sloping apron to facilitate a jump at high
discharges (Fig. a).
b.
Use a sloping apron positioned partly above and
partly below the riverbed, allowing the jump to form on the lower section at
low discharges and on the upper section at high discharges (Fig. b).
Fig. (a) Sloping apron combined with a
stilling basin; (b) Sloping apron partly above and partly below the river bed
Condition 5
At low discharges, the jump height curve is below the
tailwater rating curve but exceeds it at high discharges. To ensure the
hydraulic jump forms near the spillway, the following measures can be
implemented:
a.
Install a sloping apron positioned partly above
and partly below the riverbed. This allows the jump to form higher on the apron
at low discharges and lower on the apron at high discharges.
b.
Construct a stilling basin with a sill or baffle
to increase tailwater depth, promoting jump formation at high discharges.
However, at low discharges, the stilling basin may further elevate the already
excessive tailwater depth, resulting in a drowned jump and reduced energy
dissipation. If this does not risk scour, the design can remain unmodified for
low discharges.
Fig: sloping apron positioned partly above and partly
below the riverbed
Stilling Basins
A stilling basin is a structure designed to contain a
hydraulic jump, either partially or fully, to dissipate energy. It typically
includes features such as chute blocks, baffle blocks, and end sills to shorten
the hydraulic jump, thereby reducing the basin's length and cost. These
components also enhance energy dissipation and stabilize the jump. The design
of the stilling basin depends on the type of hydraulic jump, which is
influenced by the Froude number (F₁) of the incoming flow.
U.S.B.R. Stilling Basins
Stilling basins for Froude number between 1.7 to
2.5
For Froude numbers between 1.7 and 2.5, a horizontal apron
is sufficient in stilling basins. Since the flow exhibits minimal turbulence,
additional accessories are generally unnecessary. However, the apron must be
adequately long to fully contain the hydraulic jump. The required length is
approximately 5 times the sequent depth (y2), ensuring the jump remains within
the apron.
Stilling basins for Froude numbers between 2.5 and
4.5
Type I stilling basin
Stilling basins for Froude numbers higher than 4.5
·
When the velocity of the incoming flow is less
than 15 m/s :
Type
II stilling basin.
·
When the velocity of the incoming flow exceeds
15 m/s :
Type III stilling basin
Bucket Type Energy Dissipators
A bucket-type energy dissipator, positioned at the spillway
toe, deflects overflow water to reduce energy. It is suitable only for overflow
spillways and is more cost-effective than stilling basins when the incoming
flow's Froude number (F₁) exceeds 10. This is because high F₁ values result in
significant differences between initial and sequent depths, necessitating
larger, deeper stilling basins. Bucket dissipators are adaptable to various
tailwater conditions but require a riverbed composed of solid rock for
implementation.
The bucket type energy dissipators are of the following
three types.
(i)
Solid roller bucket
(ii)
Slotted roller bucket
(iii)
Ski-jump (or flip or trajectory)
bucket.
