EXPERIMENTAL STUDY OF SUBMERGED SINGLE-PORT
THERMAL DISCHARGES
by
GAROLD EUGENE KOESTER
AB,
University of Idaho
(1968)
SB, University of Utah
(1972)
Submitted in partial fulfillment of the
Requirements for the Degree of
Master of Science in Civil Engineering
at the
Massachusetts Institute of Technology
May 1974
Signature of Author..,
Dep drtment of Civil Engineering,
May 10,
1974
Certified by
Thesis Supervisor
.................
Accepted by.
Chairman, Departmen*(d'l Committee on Graduate Students
of the Department of Civil Engineering
ARCHIVES
AUG 1 1974
4-IRARIF-9
ACKNOWLEDGEMENTS
To E.
Eric Adams,
Graduate Research Assistant, whose guidance
and constructive counsel were of inestimable help,
gratefully give my most sincere thanks.
Rosenson,
undergraduate student,
I owe and
The assistance of Joseph
is acknowledged.
Supervision was
provided by Prof. D. R. F. Harleman, Professor of Civil Engineering,
and the manuscript was typed by S.
Demeris.
-2-
ABSTRACT
EXPERIMENTAL STUDY OF SUBMERGED
SINGLE-PORT THERMAL DISCHARGES
by
GAROLD EUGENE KOESTER
Submitted to the Department of Civil Engineering on May 10, 1974 in
partial fulfillment of the requirements for the degree of Master of
Science in Civil Engineering
An experimental investigation of the temperature field
induced by the heated effluent from a submerged single-port discharge is conducted. Primary emphasis is directed to the study of
the interaction of a shallow water jet with the bottom and the
free surface. The parametric Froude number Foranged between 4.9
and 15.7, the relative water depth H/D0 ranged between 1.9 and 6.3,
the relative crossflow v/uo ranged between 0.020 and 0.074, and the
relative discharge submergence z/H ranged between near surface
(z/H = 0) and near bottom (z/H ~ 1).
Graphic dimensionless
relationships among the pertinent parameters are presented to
illustrate the jet's behavior and for use in the preliminary design
of shallow water thermal outfalls.
Reasonable correlation has been found at large relative
water depths with the analytical prediction of Stolzcnbach et al
(1972). The non-dimensional relative jet penetration depth
parameter hmax/H is introduced to define a discharge configuration
as a hydrodynamically deep water or shallow water situation.
Thesis Supervisor:
Donald R. F.
Title:
Harleman
Professor of Civil Engineering
-3-
TABLE OF CONTENTS
1'11TLE PAGE
1
ABSTRACT
2
ACKNOWLEDGEMENTS
3
TABLE OF CONTENTS
4
I
INTRODUCTION
5
II
THEORETICAL BACKGROUND
8
2.1
2.2
General Characteristics
Mathematical Analysis
2.2.1
2.2.2
III
EXPERIMENTAL EQUIPMENT AND PROCEDURES
3.1
3.2
3.3
3.4
IV
Experimental Program
Experimental Limitations
Experimental Set-up
Procedure and Data Acquisition
10
17
27
27
30
31
33
EXPERIMENTAL RESULTS
35
4.1
4.2
Introduction
Single-port Discharge Without Crossflow
35
39
4.2.1
4.2.2
4.2.3
39
55
66
4.3
V
Round Buoyant Jet
Buoyant Near-Surface Discharge
8
10
Near-Surface Discharge
Discharges with Variable Submergence
Summary
Single-port Discharge with Crossflow
73
4.3.1
4.3.2
73
83
Near-Surface Discharge
Near-Bottom Discharge
88
SUMMARY AND CONCLUSIONS
NOMENCLATURE
92
LIST OF FIGURES
96
100
REFERENCES
-4-
I
iNTRODUCTION
The large quantities of waste-heat discharged from steam
electric power plants is a consequence of the low efficiency at
which they operate. Present levels of efficiency are about 40%
for fossil fuel plants and about 33% for nuclear-plants.
Water,
being the only economic cooling fluid for steam condensers,
is
the medium by which this heat is rejected to the environment.
High concentrations of heat in natural bodies of water can be
detrimental to the
aquatic life and natural chemical processes.
For this reason, governmental agencies have imposed criteria
regulating thermal discharges.
A usual criterion of temperature
regulations is that large induced temperature rises are restricted
to a mixing (dilution) zone, defined as the area in the immediate
vicinity of the point of discharge where the heated effluent is
diluted with the receiving water.
In this respect, the type of hydraulic structure used for
the discharge of heated effluent has an important effect on the
temperature
distribution in the water environment;
it
determines
the hydraulic characteristics of the discharge which govern the
rate of dilution.
In general, the rate of dilution is a function
of the existing turbulence and velocity of the receiving water,
the turbulence induced by the kinetic energy of the effluent,
and the density difference between the effluent and receiving
water.
The areal extent of the temperature distribution is a
function of the dilution rate plus the number and orientation of
ports in the discharge structure.
-5-
__
......
..........
Heated effluents are often discharged into water bodies
which are shallow relative to the characteristic size of the
discharge port.
This occurs because the large quantities of
heated effluent require discharge sources of large dimension.
It
is possible to construct hydraulic structures that induce surface
spreading with minimal mixing.
Consider a surface discharge
characterized by surface spreading at low Froude numbers.
The
region of temperature increase tends to be localized because the
rate of heat transfer to the atmosphere is great.
total mixing,
temperature
By avoiding
the volume of water which has a higher than normal
is minimized.
On the other hand, hydraulic structures can be constructed
to achieve complete mixing with possible storage of waste heat
below thermoclines.
In shallow water, surface and submerged
discharges at high Froude number exhibit similar temperature
distributions.
The general feature is that the mixing zone
extends from the water surface to the bottom of the receiving
body over long distances.
With the extensive mixing,
the tem-
perature rise above the ambient is minimized, although the
volume of water affected by a temperature rise is greatly increased.
Heat dissipation to the atmosphere is reduced by the
lower surface temperature.
When mixing devices are used to keep
temperature rise within allowable limits, there is likely to be
a corresponding reduction in the heat flux from the water to
the atmosphere by all processes:
conduction.
radiation, evaporation and
The alternatives elected should depend on the
-6-
predicted ecological effects of the heated effluent.
With this engineering decision in mind, this study is
presented as part of the continuing research effort to understand
and predict the behavior of thermal discharges at the Ralph M.
Parsons Laboratory.
Due to the complicated flow pattern which
results from the interaction of a shallow water jet with the
bottom and the free surface, a quantitative analysis of either
surface or submerged bouyant jets in shallow water is beyond the
scope of this study.
The nature of this investigation is ex-
perimental and addresses the problem of predicting temperature
concentrations in a large body of water induced by the heat flow
from a single port discharge structure.
The objective is to
present graphic dimensionless relationships of the pertinent
parameters describing the heat flow with emphasis on the near
surface configuration in a shallow body of water.
Application of
this study is anticipated to aid in the preliminary design of
shallow water thermal outfalls.
-7-
11
THEORETICAL BACKGROUND
2.1
General Characteristics
A single-port discharge is in essence a round-buoyant jet.
The physical processes that dominate its hydrodynamic behavior
under unconfined conditions are generally grouped into three
separate regions, see Figure 2-1.
The NEAR FIELD processes are
governed by the dynamic and buoyant characteristics of the discharge and of the ambient water in the immediate vicinity.
Very
near the outfall the fluid motion is dominated by inertia forces
arising from the initial
flux of momentum and is characterized
by shear-generated free turbulence which induces entrainment flow
of the ambient water into the jet.
The increasing flow of the
jet is diffused with a simultaneous reduction of velocities and
temperature.
Entrainment continues until the jet velocity is
reduced to a velocity comparable with that of the ambient water.
The buoyancy forces tend to deflect the axis of the jet toward
the free surface or, as in the case of a near-surface jet, resist
its vertical penetration.
The second region is the TRANSITION between the near field
and the far field.
Further dilution of temperature due to en-
trainment effectively ceases at this point.
A stable region is
achieved that is characterized by vertical stability of the
surface layer of mixed water.
currents,
Buoyancy forces,
generating density
and the ambient currents convect the mixed water away
from the near field.
-8-
Far
Field
Transition
Near Field-
Ix
4
z
H
D
0/
/
/
Figure 2-1:
/
/~
77
/~/
/
/
/
/
/
/
/
/
Region of Physical Processes that Govern a Single-port Thermal Discharge
/
In the FAR FIELD the convection of the mixed water continues
to be dominated by the ambient currents.
Additional temperature
decrease occurs through diffusion which is generated by ambient
turbulence and through surface heat loss to the atmosphere
which is the ultimate heat sink.
This study pertains primarily to
the near field phenomena.
2.2
Mathematical Analysis
The mathematical analysis of a buoyant jet aims
at a
description of the jet flow field, temperature field and trajectory
as a function of ambient flow parameters, initial jet parameters,
and experimentally determined coefficients, see Figure 2-2.
2.2.1
Round Buoyant Jet
For a round buoyant jet the governing equations of fluid
motion and heat conservation are formulated under the following
assumptions:
a)
The flow is steady:
b)
Fluctuating turbulent quantities are small compared
a/Dt
=
0.
to the mean.
c)
Turbulent eddy velocities are the dominant transport
mechanism.
d)
Viscous effects are neglected:
e)
The Baussinesq approximation is applied:
Large Reynolds number.
P
-10-
<< 1
y
x
Ta 'a
s
AT
0r
T op ,u 0
u
Vb
E)
C
D
e
Figure 2-2:
Definition Diagram for Round Buoyant Jet
-11-
The time-average equations of motion are:
Continuity
(2-1)
(rv) + Du = 0
as
r Dr
Axial Momentum:
P
a
U~u +
as
pvu
a ar
_P + pg sine s
a D (ru'v')
r ar
- p
a
v
as
(2-2)
Radf.al Momentum:
u3v
Pa as +a
-,2
a a
r ara
aP
r
vav
ar
au'v'
as
(2-3)
Heat Conservation
BT aT
+ v
UT
1D
__a-U'T'
-r
sT
_
(rT'v')
(2-4)
in which
s,r
-
cylindrical coordinates, D/a4 = V
u,v - mean velocities in s,r directions
u' ,v' - velocity fluctuations in s, r directions
p - mean local density
pa - constant ambient density
T = mean temperature
T'
= temperature fluctuations
6 = angle between x axis and a axis
The main properties of the jet flow field make simplification
of the governing equations possible.
-12-
They are:
a)
The pressure around the jet is hydrostatic.
b)
The increase of mass flow rate is equal to the entrainment
of ambient fluid per unit length of jet.
c)
The boundary layer approximation is utilized.
Convection
by transverse velocities are small compared to convection
by axial velocities.
Diffusion in the axial direction is
small compared to diffusion in the transverse direction.
d)
A consequence of the first assumption is that horizontal
momentum of the jet is conserved.
e)
There is a similarity of flow.
Velocities, temperature
and density can be described very closely by Gaussian
distributions, i.e., by equations of the form
u(r,s)
= uc(s)exp[-K(r/s) 2
AT(r,s)
=
(2-5)
uc
(s)exp[-KX(r/s) ]
(2-6)
Ap(r,s) -Apc
(s)exp[-KA(r/s) 2]
(2-7)
where
u(r,s)
-
the local velocity
u C(s)
-
the velocity at the centerline
AT(r,s)
=
the local temperatur e rise;
ATc (s)
=
temperature rise at the centerline; AT =(T
O-T a
Ap(r,s)
Ap c(s)
the local density de ficit; Ap
=
AT
=
(T-Ta
(pa
-
p)
density deficit at the centerline; Apc =(pc-po)
K and A = experimentally determined dimensionless
coefficients describing the gross effects of
the turbulent mixing process.
-13-
The density of the water is assumed to vary linearly
f)
with temperature
p(T)
pa
-
a(T-Ta)]
where S is the coefficient of thermal expansion.
(2-8)
The
concentration of the heat, ch, in the jet water is formulated in terms of density as
P
ch
-p
(2-9)
hp a - p O
Due to the entrainment of ambient water, the degree of dilution,
D,
is commonly defined as
D
C
h
p - p
a
0
P -p
(2-10)
a
where
the local density
p
P
= the density of the ambient fluid
p -
the density of the jet fluid
Substituting Equation (2-8) into Equation (2-10) the temperature dilution is obtained
T
D
-T
T a
T -T a
(2-11)
where
T
= the local temperature
Ta = the ambient temperature
T
= the jet temperature at the jet exit
The simplified governing equations become:
-14-
Continuity:
r (rv) +
au
0
as-
(2-12)
Momentum:
uau+ vu
o
pg sine - 1a(r-uv-)
r Dr
ar
s
I ; -F2
(ra- 2
pg cosO rr (rv )
-
(2-13)
(2-14)
Conservation of Heat:
U
sT
+ v
ar-T
-
L(rT'v')
r ar
(2-15)
With the boundary conditions:
=0
v
0
u'vi
as r
AT
=0
T'v'
-
W
0
The continuity equation, assuming small variation in density,
can be expressed as
d
where
2u(s,r)rdr - Q'(
(2-16)
Q' is the rate of entrainment of the ambient water per unit
length of the jet.
The equation for the conservation of heat is
d
2Tu(s,r)T(s,r)rdr
ds TO
si /~
=
(2-17)
0
-15-
fL
The conservation of momentum equation in the horizontal direction
is
21pu2 s,r)rdr
cose
-0
(2-18)
o2
The conservation in the vertical direction is expressed by
the equation
2Tpu 2 (s,r)rdr - g
sinO
f
ds
f
27T[p
- p(s,r) rdr
(2-19)
where
(2-8)
p(T) - pa[1-(T-Ta)]
Temperature, density and velocity along the trajectory of
the jet are usually obtained as follows:
1)
The assumed profiles, Equations (2-5) to (2-7), are
substituted into the conservation equations.
2)
Q1 in the conservation of mass equation is approximated
by
Q-
-2nbv
(2-20)
-(Iu
(2-21)
where
v
-
and hence
(2-22)
Q= 2nbauc
where a is an experimentally determined entrainment
coefficient and b is a local width of the jet, usually
taken as
b
-
(2-23)
s
-16-
3)
The resulting ordinary differential equations are then
solved
Ap , and uC using the initial
for ATc)
conditions AT
2.2.2
discharge
Apo, and u.
,
Buoyant Near Surface Discharge
The engineering importance of the submerged jet as a means of
dilution and disposal of heated water in large bodies of water
has motivated numerous analytical and experimental studies.
Of particular interest is a numerical model for determining
jet
properties at various distances from a buoyant near surface
discharge in unconfined and unstratified water by Stolzenbach
et al (1972).
Their model considers a discharge Q
water at temperature T
of heated
and density p0 from a rectangular open
channel of depth h0 , width 2b0 , and initial horizontal angle
0
at the surface of a receiving body of water at temperature
Ta, density pa and of large extent.
A non-uniform current V
may be present and it is assumed that the bottom of the receiving
water does not interfere with the vertical development of the
With the assumptions presented in Section 2.2.1
surface jet.
the basic equations of mass, momentum and heat conservation
may be simplified in rectangular coordinates:
Continuity:
S+
ax
Dy
+
az
= 0
(2-24)
x-Momentum:
2
+
ax
+
ay
u
9z
g
ax
-17-
dz - au'v'
y
Du'w'
az
(2-25)
y-Momentum:
+
+
-
g
dz + u2
3z
yax
x
Cs
(2-26)
Heat Conservation:
r)uT + kvT + wT _
3x
y
az
- Dw'T'
5z
5y
(2-27)
The technique used to develop the solution of these equations
is to assume a structure for the velocity and temperature within
the aiocharge and boundary conditions at the outer edges.
The
structure of the discharge is shown in Figures 2-3 and 2-4.
The longitudinal velocity and temperature distributions are
taken to be as follows, where Tris the water surface elevation:
u = u
+ VcosO
AT - AT
u
=
Q<jyj<s
c
u fc
) + Vcose
O<jyj<s
AT = AT t(C )
u =u f(c
) + Vcos6
c
y
s<IyI<s+b
AT = ATc y )
u = uc f(y )
z) + VcosO
s< y j<s+b
AT = AT t(c )t( Z)
where
y
f bb .
and
-z-r
z
=
h
-18-
-(r+h)<z<-r
(2-28)
Cross Flow = V = V(x)
kIlt H
E)
ATO
o
I-
2
0V
~1
e
y
N
Top
View
**,*N
b+s
x
y
0
z
ATO
u
Jet Centerline
.x
IV
0
f
Jet Boundary
'I
Figure 2-3:
Coordinate Definitions
z
h
S
r
0
AT
c
x
_
- -
h
Side
View
I_~'
___
Region
Veloci ty
Distribution
vC
Temperature
Distribution
v
4go
I.'
0
b
boisLJci
x
K
--- _
-
Top
View
Figure 2-4:
Discharge Structure
jRegion 1
Rego
Cross Section
The lengths r and s pertain to the initial core region and
h and b to the turbulent region of the jet (see Figure 2-4).
The particular forms of the similarity functions are assumed to
be as follows:
(2-29)
i?
-1
t(Q)
The lateral velocity is geometrically related to the
longitudinal velocity by:
-
u
(2-30)
tan $
where $ is the lateral jet stream line angle from the centerline
in excess of the non-buoyant value.
v
db
+ (f
- E)u C
1/2
Then
s<|yi<s+b
(2-31)
v
0
elsewhere
where the following conditions are satisfied:
0 at y = 0
1)
tan$
2)
tan $ = (
dx
) at y = b+s, where e is the lateral
spreading rate of a non-buoyant jet under the same conditions.
Since the gravitational spread is induced by
the lateral temperature gradient, the y dependence of
is used to distribute tan $ between y = 0 and
-21-
y
=
b+s.
The boundary conditions are then given to be
v = u'v' = v'T' = 0
y = 0
(2-32)
-r
(2-33)
jyl=s
(2-34)
uw' = 0
w = wr
r
<yl<s
z
W - Wh
W
s+b< y I
W0
0
=+
vs
v
s< Iyt<s+b
y)
u'V't
v
v-
=
-r<z<l
-(r+h)<z<-r
+ v Sb (Z)
V~ 0
z<-(r+h)
u + vT
ax
W
Dy
z = fl
(2-35)
z =
(2-36)
u'w' - 0
w'T'
k(T
-
T )
11
The outer boundaries of the jet occur at the entrainment surface
where no heat is transferred.
The boundary conditions are:
u'w' = w'T' = 0
w =
e
dh
- Vcos --dx
W = w f(
e
y
-
0<Iyl<s
z = -(r+h)
dh
Vcosq d
dx
s<IyI<s+b
-22-
(2-37)
u'v' = v'T' = 0
v =+ v
+ Vcos
-+e
-r<z<Tl
-d
dx
y
v - + v f (C ) + Vcose --where w
e
z
e
-
and v
e
=
s+b
(2-38)
-(r+h)<z<-r
dx
are the entrainment velocities.
The entrainment
velocities are assumed to be given by
V
uC
we
gAT Ch
mz
a
h
exp[-C
U z2
C
c
(2-39)
1C
uc
where the exponent is in the form of a Richardson number.
The entrainment coefficients, a
y
and (x , are determined such that
z
the solution for the non-buoyant case (T0
=
T ) agrees with the
experimental observations that the growth of a non-buoyant
turbulent region is symmetrical:
db
dh
dx
dy
(2-40)
ds _dr
dx
dx
For non-buoyant jets discharging into a quiescent receiving
water the spread rate, e
,
is constant.
In these cases
= 0.22 for the similarity functions, f and k, used here.
6
boundary conditions at x
=
The
0 are related to the discharge channel
geometry, the flow rate Q , and the initial discharge temperature
T.
0
-23-
r
=h
s
-b
h
-b
-0
U
M U
-
0
0
h
2h b
+ Vcos
00
AT
- AT
C
0
x-0
(2-41)
0
0
x
=0
-y
Using their numerical model, Stolzenbach et al found the
following trends in the stable region of the surface jet, for
F
>
3:
0
AT
-A
AT
D -
IF '
o
-1.4
5
(2-42)
AT
0-)
(AT ac
a
F
(2-43)
and
h
max
0.42 F '
(2-44)
XiT
00
where
AT
o
(AT)
8-
T
0
- T
a
average fractional stable excess surface temperature
rise in the jet
(AT s
= stable surface centerline temperature rise
-24-
F
densimetric Froude number - u //g'
0
-
0
A
0
aspect ratio - h /b
m
o1/4
IF
u //g'(hb)
0
u
0
0 0
to F A
0
discharge velocity
m
-
Q /2h b
0
00
- maximum vertical penetration of the jet.
h
max
The circular discharge (Single-port) structure can be
schematized so as to be used in their predictive model.
The
geometric form of the discharge is described by an aspect ratio
h
A
(2-45)
0
where
a)
h
h
is the actual maximum discharge channel depth;
b)
0
b
=D
0
is such that the correct discharge channel area is
preserved:
b
o
channel area
2h
(2-46)
0
-h
Hence
2h 2
A0
channel area
The aspect ratio of a circle is A
-25-
2.55.
See Figure 2-5.
,
,
,
ATApQ
0
,
,
0
0
,~
/
/
h
/
max
/
/
I~
/
/
my
/ ,
Figure 2-5:
f
f
/
/
/
/
/
/
Schematic of the Single-port Heated Discharge
/
/
/
/
III
EXPERIMENTAL EQUIPMENT AND PROCEDURES
3.1
Experimental Program
The experimental program considers a discharge
water at temperature T
diameter D
Q of heated
and density p0 from a circular pipe of
at the edge of a receiving body of water of large
extent, whose temperature Ta, density pa and depth H are uniform.
A uniform current v may be present in the receiving water and is
parallel to the shoreline.
See Figure 3-1.
For the results of the experiments to be relevant to field
conditions, the correct scaling laws were observed.
Dimensional
analysis and a study of the equations governing turbulent jet
behavior provide the dimensionless parameters which must be
modeled.
In this study the scaling length is the diameter of the
outfall, D .
Stolzenbach has shown that the basic scaling
length should be proportional to the square root of the discharge
flow area 2h b .
In his study this length is taken as the
square root of one half of the discharge flow area,
h bT.
0 0
From
Equations (2-45) to (2-47)
VU Ab
0 0
0.63 D
(3-1)
0
Since entrainment increases with increasing jet momentum
and decreases with increasing jet buoyancy, the densimetric
Froude number
F
is used as a parameter for jet induced mixing.
The densimetric Froude number is defined by
-27-
z
h
H
D0
7
Side View
77
Ambient Crossflow V
-- L]c
DT
0
Plain
View
Figure 3-1:
Schematic of Heated Discharge
-28-
I
u
=
IF
S
(3-2)
0
/g'D0
where g' = (p0 - Pa /Pa)g is the reduced acceleration of gravity
at the discharge port.
A more general Froude number is the Aspect Densimetric
Froude number which has been defined as
F'
o
- I 0 A1/4 =
u
/g
(3-3)
AT0b0
It incorporates the geometric as well as the dynamic characteristics of the discharge into one parameter and is useful when
applying the results of this study to other discharge configurations.
The dimensionless water depth parameter is H/D0, the
relative discharge submergence is z/H and the crossflow parameter
is v/u
.
The remaining dimensionless parameter characterizing
the discharge is the Reynolds number, IRe, defined as:
u D
R
e
(3-4)
V
in which V is the kinematic viscosity of water.
In many free
shear flows the gross characteristics of the flow fields are
independent of Reynolds number provided that the Reynolds
number is great enough for the flow to be turbulent throughout.
-29-
3.2
Experimental Limitations
The steady-state temperature concentrations induced by a
single-port thermal discharge in a shallow body of water of large
extent is desired.
This relatively unconfined prototype situation,
out of laboratory necessity, is confined in a basin model of
finite extent.
As a consequence, correct steady state results
can never be achieved for long periods of time.
The size of the
model within the basin determines the duration that the model is
allowed to run before significant boundary distortion comes
into play.
The scale size should be chosen small enough so that
the near field mixing occurs in a small portion of the model and
boundaries have small effect on the induced flow pattern and
yet the scale size must be large enough to provide resolution
in measurement and avoid scale effects.
A comparative study of the performance of different discharge configurations on a relative basis is easily achieved.
But the results of the laboratory experiments as applied to
prototype design problems are subject to a variety of interpretations.
-30-
3.3
Experimental Set-Up
Figure 3-2 shows the model set-up.
The basin is 60' x 40' x
1 1/2' and is located on the first floor of the R. M. Parsons
Laboratory.
Being situated in an enclosed area, the model is free
from undesirable disturbances due to weather.
The shoreline is
in effect a vertical breakwater constructed of 8" cinderblocks
and the floor is covered with a 30 gauge vinyl liner.
A
recirculating crossflow is achieved using five (5) hp pumps drawing
from five equal length manifolds on the suction side and
supplying water to a mixing manifold which feeds five equal
length manifolds on the pressure side.
The purpose of the mixing
manifold is to provide water of uniform temperature across the
basin.
A uniform flow distribution is maintained by using
vertical slot weirs and a 4" thick section of rubberized horsehair
matting on both upstream and downstream sections of the basin.
Discharge flow is warmed by passage through a steam heat
exchanger and is mixed in a constant heat tank above the basin.
The discharge structure is a section of PVC 80 pipe.
The depth
of the discharge can be adjusted from near surface to near bottom.
Dye may be injected into the discharge to visualize the flow
development and a small pump at the end of the basin removes
water at the same rate as the discharge flow.
Temperatures are measured using an array of 100 Yellow
Springs Instrument thermistors (Series 700, time constant = 9
-31-
Mixing
nifold
From Crossflow Pumps
Crossf low Manifolds
Probe SupportFrames
ubberized
Horsehair
Vertical
Slot
Crossflow
Weir
Li
Heated
Water
__
Discharge
Box
Breakwater
-
/0///
Model Wall
To Crossflow Pumps
"60'
Figure 3-2:
Experimental Setup
//0/0/
To Intake
Pump
seconds).
98 probes are mounted on two wooden probe platforms
using aluminum Dexion and two additional probes monitor hot
water In the heaid tank and in the discharge box.
Probe elevation
may be adjusted during run operation by turning light handoperated screw jacks located in the corners of the platforms.
A computer data acquisition system consisting of a digital
thermometer and an electronic scanner manufactured by Digitec
and a Hewlett Packard 2114B computer are used to record temperatures
on a digitized tape.
The tape is then converted to cards and
data is run through a Fortran program which reduces it to
dimensionless temperature rises.
The results are printed in a
format corresponding to the probe arrangement in the basin.
3.4
Procedure and Data Acquisition
A typical run takes about 60 minutes and starts when the
basin is quiet and well-mixed.
Initial scans on the surface
and the bottom are taken to determine if any initial stratification exists and to reference subsequent temperature differences.
Discharge and intake waters are turned on, a small quantity of
dye is injected into the discharge and the plume is allowed to
develop.
After about 10 minutes scans are begun starting with
the near surface and continuing to the near bottom, followed by
a final scan on the.surface.
3 1/2 minutes:
Each scan requires approximately
2 minutes for scanning and 1 1/2 minutes for
recording on digitized tape, during which time the platform is
-33-
cranked into position for the next scan.
From 7 to 9 scans
(including the initial two scans) were performed for each of
the runs, depending on the water depth.
Each run thus consists of
700 to 900 temperatures which are read into the computer.
is in the form of a dimensionless temperature rise for each
probe at each scan.
-34-
Output
IV
EXPERIMENTAL RESULTS
4.1
Introductio
The parametric study consisted of 49 laboratory experiments.
The relevant physical variables and non-dimensional parameters
are tabulated in Table 4.1.
The densimetric Froude number
ranged between 4.9 and 15.7, the relative water depth H/D
IF
0
between 1.9 and 6.3, the relative crossflow v/u
ranged
ranged between
0.020 and 0.074, and the relative discharge submergence z/H
ranged between near surface (z/H % 0) and near bottom (z/11 % 1).
The jet Reynolds number IRa varied between 7.900 and 12.000
indicative of turbulent flow.
The test results were analyzed with respect to induced
surface temperature rise.
rise AT s/AT
AT
AT
s
The non-dimensional temperature
at the surface is defined as
T
ace-
ufae
-
a(
T
a
T-
o
T
o
The particular case of the non-dimensional surface centerAT
line temperature at the surf ace
sc is defined as
AT
T
ATsc
AT
0
T
AT
face centerline
T
0
-T
a
-35-
0
Ta
4-2
TABLE 4-1
EXPERIMENTAL DATA OF PARAMETRIC STUDY
ON'
I'
U
v
Run H
No. (ft) (fps)
U0
(fps)
Experimental
Results
Non-Dimensional Parameters
Physical Parameters
D
(ft) (f t) AT
H
h
00
( * F)
F
IFT
z/H
v/u
0.0
a
/
AT
H/Do H/
6.3
10
0.46
--
6.3
10
0.37
12017
--
6.3
10
0.26
0.0
12017
--
6.3
10
0.18
0.0
12017 1.00
12017 0.75
1
0.67
0.0
1.13
0.07
.106
16.7
17.9
14.2
0
2
0.67
0.0
1.13
0.07
.106
16.8
17.5
13.9
.33 0.0
12017
3
0.67
0.0
1.13
0.07
.106
18.4
16.7
13.2
.67 0.0
4
0.67
0.0
1.13
0.07
.106
17.0
17.8
14.1 1.0
5
0.48
0.0
1.13
0.07
.106
17.6
17.3
13.7
0
6 0.48
0.0
1.13
0.07
.106
15.6
19.8
15.7
.33 0.0
12017
7
0.48
0.0
1.13
0.07
.106
16.5
17.5
13.8
.67 0.0
8
0.48
0.0
1.13
0.07
.106
16.9
17.0
13.5 1.0
9 0.40
0.0
1.13
0.07
.106
16.6
19.1
15.1
0
10
0.40
0.0
1.13
0.07
.106
11
0.40
0.0
1.13
0.07
.106
12
0.40
0.0
1.13
0.07
13
0.20
0.0
1.13
14
0.20
0.0
15
0.20
16
0.79
5.0
7.2
0.50
--
5.0
7.2
0.37
12017
--
5.0
7.2
0.26
0,0
12017
--
5.0
7.2
0.19
0.0
12017 1.34
3.8
6
0.37
--
--
.33:0.0
12017
--
3.8
6
--
17.9
18.4
14.5
.67 0.0
12017
-
3.8
6
0.33
.106
16.7
19.0
15.0 1.0
0.0
12017
--
3.8
6
0.20
0.07
.106
16.4
18.2
14.4
0.0
12017 2.55
1.9
3
0.41
1.13
0.07
.106
17.3
17.2
13.6 0.5
0.0
12017
--
1.9
3
0.44
0.0
1.13
0.07
.106
16.4
18.3
14.5 1.0
0.0
12017
--
1.9
3
0.35
0.0
0.82
0.08
.125
16.1
11.5
0.0
10191 0.42
6.3
10
0.37
-
9.1
0
0
TABLE 4-1 (CONTINUED)
EXPERIMENTAL DATA OF PARAMETRIC STUDY
Physical Parameters
V. ..
Run H
v
u
o o Do
No. (ft) (fps) (fps) Po
(ft) (ft)
AT (OF)
0
(ft)AT0
I
LO
kxperimental
Results
Non-Dimensional Parameters
h
F t F
0
0
(f1
z/H
/
v/u
'e
e
H
11/%
H/E
AT
AT
o o AT9
17
0.79
0.0
0.82
0.08
.125
16.1
11.7
9.3
.33
0.0
10191
6.31
10
0.50
18
0.79
0.0
0.82
0.08
.125
16.3
~11.1
8.8
.67
0.0
10191
6.3
10
0.20
19
0.79
0.0
0.82
0.08
.125
15.7
11.4
9.0
0.0
10191
6.3
10
0.16
20
:0.47
0.0
0.82
0.08
.125
17.4
11.0
8.7
0
0.0
10191 0.78
3.81
6
0.46
21
0.47
0.0
0.82
0.08
.125
17.7
10.9
8.7
.33
0.0
10191
3.81
6
0.43
22
0.47
0.0
0.82
0.08
.125
16.3
11.5
9.1i .67 0.0
10191
3.8
6
0.25
23
0.47
0.0
0.82
0.08
.125
17.1
11.0
8.7
0.0
10191
3.8
6
0.25
24
0.24
0.0
0.82
0.08
.125
16.6
11.0
8.7
0.0
10191 1.54
1.9
3
0.44
25 0.24
0.0
0.82
0.08
.125
16.6
11.0
8.7
0.5
0.0
10191
1.9
3
0.41
26
0.24'
0.0
0.82
0.08
.125
16.4
11.1
8.8
1.0
0.0
10191
1.91
3
0.31
27
0.82,
0.0
0.49
0.10
.161
16.1
6.2
4.9
0 10.0
7912 0.33
4.51
8
0.53
28
0.82
0.0
0.49
0.10
.161
16.5
5.9
4.6
.33 0.0
7912
4.51
8
0.32
29
0.82
0.0
0.49
0.10
.161
16.1
6.3
5.0
.67 0.0
7912
4.5
8
0.32
30 0.82
0.0
0.49
0.10
.161
16.6
6.2
4.9
0.0
79121
4.5!,
8
0.21
31 0.61
0.0
0.49
0.10
.161
15.7
6.4
5.1
0
0.0
79121 0.45
3.8
6
0.59
0.61
0.0
0.49
, 0.10,
.161.
15.2
6.4
5.1
.33
0.0
7912
3.8
6
32
1.0
1.0
0
1.0
.
0.41
TABLE 4-1 (CONTINUED)
EXPERIMENTAL DATA OF PARAMETRIC STUDY
33
0.61
0.0
.49
0.10
.161
14.9
Non-Dimensional Parameters
/T
h
e
x /D
H/W
IF
IF z/H v/u
o
o
o
H
0
6
3.8
7912
5.2 .67 0.0
6.5
34
0.61
0.0
.49
0.10
.161
15.7
6.4
5.1 1.0
0.0
7912
36
0.31
0.0
.49
0.10
.161
16.8
6.3
5.1
0.0
7912
37
0.31
0.0
.49
0.10
.161
17.8
6.0
4.8
.5 0.0
7912
-
38
0.31
0.0
.49
0.10
.161
15.2
6.7
5.3 1.0
7912
-
50
0.40
0.060 1.13
0.07
.106
17.8
16.3
12.9
0
.049 12017
51
0.40
0.060 1.13
0.07
.106
16.9
17.1
13.6 1.0
.049 12017
54
0.47
0.047 0.82
0.08
.125
0
.058 10191
55
0.47
0.047 0.82
0.08
.125
16.7
11.2
8.9 1.0
.058 10191
56
0.61
0.036 0.49
0.10
.161
17.0
6.0
4.8
0
.074
7912
57
0.61
0.036 0.49
0.10
.161
16.8
6.0
4.8 1.0
.074
7912
60
0.40
0.060 1.13
0.07
.106
17.4
16.5
13.0
0
.020 12017
61
0.40
0.060 1.13
0.07
.106
16.3
17.4
13.7 1.0
.020 12017
64
0.47
0.047 0.82
0.08
.125
16.7
11.2
8.9
0
.023 10191
65
0.47
0.047 0.82
0.08
.125
16.4
11.3
9.0 1.0
.023 10191
66
0.61
0.036 0.49
0.10
.161
16.4
6.1
4.8
0
.030
7912
67
0.61
0.036 0.49
0.10
.161
16.2
6.1
4.8 1.0
.030
7912
Physical Parameters
Run
H
No. (ft)
u
D
AT
(fps) (fps) (ft)
(ft)
0
(*F)
V H
0
00
-
Experimental
Results
max
0
AT0
.41
3.8
6
.32
0.88 1.9
3
.57
1.9
3
.57
1.9
3
.42
1.25 3.8
6
.22
3.8
6
.14
0.78 3.8
6
.25
3.8
6
.19
0.45 3.8
6
.48
35
00
I
-
-
-
0
0.0
-
3.8
6
1.25 3.8
6
.34
3.8
6
.22
0.78 3.8
6
.28
3.8
6
.20
0.45 3.8
6
.48
6
.32
--
3.8
-
4.2
Single-port Discharge Without Crossflow
4.2.1
Near-Surface Discharge
Preliminary Obserat tons
In the absence of ambient currents the most critical parameters
governing the near-surface discharge behavior are the Froude number
F
and the relative water depth H/D
1 and 2,
.
At Froude numbers between
the jet mixing is observed to be restricted to the lateral
surface and the heated discharge is essentially "floated" on to the
receiving water.
At higher Froude numbers,
increased mixing
results in a greater volume of entrained water causing the jet
penetrate deeper and become attached to the bottom.
to
The jet
remains attached until buoyant forces overcome the effects of the
entrainment.
In relatively shallow depths, the results indicate
substantial deviation of temperature distributions from those
corresponding to the ideal conditions of unrestricted water depth
characterizing Stolzenbach's
(1971)
predictive model for surface
discharges.
Centerline and Areal Dilutions
Figures 4-1 to 4-4 are plots of centerline temperature rise
versus longitudinal distance.
Figures 4-5 to 4-7 are plots of
excess temperature contours versus enclosed surface area.
These figures illustrate that in shallow water the temperature
dilution is dependent upon the interrelationship between the relative water depth and the Froude number.
has important physical meaning.
The shape of the curves
Note that with increasing
-39-
1.0
I
I
F
I
0
I
I
I
I
I
~ 14.0
..v/uu
o Run 1
0
0
H/D
O
6.3
14.2
13.7
15.1
14.4
6 Run 5
4.5
o Run 9
3.8
9 Run 13 1.9
h max /H
0.75
1.00
1.34
2.55
Stol2zenbach
S(3
h
max
&13a
.10
0
AT
Sc
AT
-
o
h
/H - 1.34
max
ao
a0
/H - 2.55
max/H
o
h
max /H
0
.01
101
.
Figure 4-1:
I
I
.
. .
I
I
I
I
-
1.00
-
0.75
I
.
I
.
.
103
x
L 2
Do
Surface Centerline Temperature Rise vs.
Longitudinal Distance with Constant:F 0~ 14.0
-40-
1.0
1
F
I
a
I
9.0
0
z/H
v/u
-
I
H/D
o Run 16
6 Run 20
0
0
Run 24
0
a
0
IF
I
I
h
0
6.3
3.8
1.9
9.1
8.7
8. 7
Stolzen bach
I
1
1
/H
max
0.42
0.78
1.54
0
0
h
0
0
0
0
AT
0 h
max
max
/H - 1.54
/H - 0.78
00 00
Sc
AT,
oh max /H
0
.01
I
I
.
I
b
I
.
0.42
=
I
I
I
9t
i2
10ol1
x
0
Figure 4-2:
Surface Centerline Temperature Rise vs.
Longitudinal Distance with ConstantIF 0
-41-
9.0
a
i
IF
a
I
1
1
1
I
5
0
Z/H
v/u
H/D
m0
-
0
P0
0
00
O Run 27
5.0
4.9
6 Run 31
3.8
5.1
36
1.9
5.1
0)Run
I
I
h max /H 0.33
0.45
0.88
Stolzenba ch
n0
0
'~,0omax
03
h
/H - 0.88
h
/H - 0.45
h
/H = 0.33
.10AT
sc
AT
0
.01
i
I
i
t
I
101
I
I
I
-
-
- -
102
x
D
0
Figure 4-3:
Surface Centerline Temperature Rise vs.
Longitudinal Distance with Constant IF 0
-42-
5.0
1.0
hmax/H
0.80
z/H = 0
v/u 0 = 0Run
o'Run 1
20
6Run 36
13-
H/D
IF
6.3
3.8
1.9
19.2
8.7
5.1
x/H
h
0.75
0.80
0.85
Stolzenbach
IF =5.1, H/D =1.9
.10
Mn
10
AT
00-
8.7, H/D 0-3.8
BC
AT
0
0
IF oo-14.2, H/D -6.3
.01
102
101
xD
0
Figure 4-4:
Surface Centerline Temperature Rise vs.
Longitudinal Distance with Constant
hmax /H % 0.80
-43-
103
1.0
V
*
7V
-010
z/H
0
0 Run 1
v/U 0
0
6 Run 5
0 Run 9
V Run 13
.---
01
i,
10
6.3
0.75
4.5
1.00
3.8
1.34
1.9
2.50
IWStolzenbach
HID 2
10
10
10
0
Figure 4-5:
Excess Temperature Contours vs. Enclosed Surface
Area with Constant IF
14.0
0
.10
.10
AT
sc
IF
0
/H
/
00
9.0
0Run
0
0-
3
0
0
hmx/H
H/D
oRun 16
0.42
6.3
20
ORun 24
0.78
1.54
3.8
1.9
0
Stolzenbach
.01
10
Figure 4-6:
102
2
A/
A/D
10 3104
Excess Temperature Contours vs. Enclosed Surface
Area with Constant IF
9.0
0
-44-
1'.0
I
I
I
h
I
P
a
I~
l
ii
I
.10
AT
AT
S
0
5.0
S0F
z/H
H/D 0
0
v/u WO
h
/H
O Run 27
0 Run 31
5.0
3.8
0.33
0.45
8 Run 36
1.9
0.88
-
Stolzenbach
.01
.1 #
. &
,1
,~.I
,A
1
I
1
1
'[C
A/D 2
Figure 4-7:
Excess Temperature Contours vs. Enclosed Surface
Area with Constant F = 5.0
0
-45-
distance from the discharge the curves become flat.
Hence, a
large increase in distance or surface area results in a small incremental decrease in the temperature rise, AT /AT .
5
0
The results show that where horizontal inertial forces
dominate, temperature dilutions increase with increasing Froude
number or increasing water depth.
The centerline temperature
rises show increasing agreement and the areal temperature rises
show fair agreement with Stolzenbach's model as H/D
Obviously,
increases.
the theoretical results give unrealiztically low
temperature concentrations at low water depths with the discrepancy increasing with decreasing relative water depth,
(see Figures 4-1 to 4-3).
What "deep water" is depends on the relative magnitude of
the Froude number.
This can be reflected in the relative jet
h
penetration parameter,
x which is defined in Chapter II
h
max
= 0.42
F
0
'
hb
(2-41)
00
Note the magnitude of hmax/H in Figures 4-1 to 4-4, for those
discharge configurations that show good agreement with Stolzenbach's
prediction,
i.e.,
"deep water" situations.
that for a given Froude numb-er,
The results suggest
there is a critical depth of water,
beyond which the bottom does not significantly restrict jet
entrainment.
For the circular outfall, this critical configuration
can be parameterized as
-46-
h
(
)
H
crit
= f (F
The importance of h
0
, H/D)
(4-3)
0
/11 with respect to temperature dilutions will
be investigatcd further in the next section.
The fact that there is good agreement between the experimental
results and Stolzenbach's prediction in "deep water" suggests that
the hydraulic model was capable of simulating a semi-steady state
condition before basin boundary effects dominated the flow pattern.
Such a state is of short duration however.
Figure 4-8 is a plot of the relative maximum jet penetration
depth, h
/H.
Both experimental results and theoretical
prediction are presented.
Figure 4-9 shows a typical vertical
section of a surface jet.
The isotherm AT/ATO = 0.0 is used to
define the boundary of the jet's penetration in the experimental
results.
These results show good agreement with Stolzenbach's et al
(1972) prediction of the jet's maximum penetration
h
max
Q,42 IF '
H
0
Ab
(
(44
0 0
H
and the maximum penetration of a round near-surface jet is
accurately predicted by Equation (4-4) when
]F (D/H) < 3.1
(4-5)
-47-
A a 2.55
Z/H - 0
v/u - 0
0z
//
16
0I
00
14
<1 . >
<1.0>
<. 61
0
0
0~
12
0~
10
<1.0>
>
0
F
0
0<.5>
8
'z-I
o
6
<1. 0>0
<.4>
<.
0
0
4
2
D
F
0 ) < 3.1
--
o Experimental Results
Stolzenbach
(Criteria for Full Penetration)
0
1
2
3
4
5
6
H/D
Figure 4-8:
Maximum Jet Penetration Depth of Surface Discharge
-48-
Depth (Ft)
0.18 0.15
0.12
0.09
Sz
~~....6
...
.4 8 3
AT
= 0.0
0
5
Figure 4-9;
10
x(Ft)
Schematic of Isotherms AT/AT
15
20
in the Vertical Plant, y
25
=
0.
Run No. 5
Stable Region Dilutions
Figure 4-10 characterizes the performance of a given discharge configuration (F
AT
temperature rise (
s.
,
H/D ) in terms of the stable centerline
The stable centerline temperature is
0
in principle the asymptotic limit of the ATsc /AT
see Figures 4-1 to 4-3.
H/D
vs x/D
curve;
The asymptotic values of (ATsc AT)
as
oo are obtained from Stolzenbach's model which is applicable
-
in deep water.
This is given by the inverse of Equation (2-40)
AT
(
l/IF
Sc
(4-6)
0
These values are indicated on the right-hand side of the plots.
lines (AT
/AT )
The
- constant can be obtained by interpolating
between the experimental values and then-connecting the asymptotic
points.
Three separate regions can be distinguished.
Region I:
The flow pattern resembles that of the unrestricted
water depth condition.
Consider a fixed value of 1F0 representing
a given discharge condition.
For increasing values of H/D0 , the
stable centerline temperature rise (AT
a maximum value of (H/D
) crit.
Sc
/AT
)
0s
decreases down to
This indicates the dividing line
between Regions I and II, and represents
the point at which the
assumption of an infinite extent of the ambient water becomes
valid.
The equation of the line in terms of hmax is:
Hrt
3.3
mn(
ax
-50-
(4-7)
h
max
H
20
19
18-
45
D
3.3H/D
H4i-
h
max-1.
H
17
16
tp
15
.13
06
0
14
13
.06
12
IF
AT
sc
07
11
0
0
0
9.
8
-.08
S.09
.4.09
10
7.11
7
6
5
4
3.
2
0
1
21
2
.12
413
14
16
20
..
3
4
H/D
Figure 4-10:
5
6
7
8
9
0
Stable Region Temperature Rise Near
Surface Discharge
-51-
10
and
If
3.3
L>
D
-
If
<
n(--!)
h
.45D
D
= f (F
n h.
Ds
)
(4-9)
o
s-
(4-9)
-,HD
0
0
for Froude numbers 5 to 15. D is surface temperature dilution,
AT
s
( SC
D
s
AT
0
Region II:
The effect of decreasing relative water depth
is to decrease temperature dilution and increase the areal distribution of the induced temperature rise.
The ambient water does
not remain stagnant since measureable currents are generated to
replace the entrained water.
From dye studies conducted in the
model, large symmetrical opposing eddies are observed in the area
120 from the discharge;
of x/D 0
see Figures 4-11 and 4-12.
The jet is observed to be two dimensional in character as greater
lateral entrainment combined with buoyant surface spread leads to
re-entrainment of the heat. This phenomena results in a limited
recirculation thus decreasing the validity of the equation of heat
h
conservation (2-15).
Note the position of the line
max = 1.
It
H
is significant since it shows that for a fixed value of IF0 the
bottom boundary affects jet behavior at depths of water greater
than the depth of the jet's penetration.
Region III:
(ATSC/AT
)
on IF
In this region there is little
when H/D
is small.
dependence of
The water along the
longitudinal axis of the discharge approaches fully mixed condition.
-52-
25sT
=0 .0
AT
.08
20-
15-
.10
I~j
.11
10-
13
Recirculatiorn
5-
5
Figure 4-11:
ld
b
Surface Horizontal Temperature Distribution.
Run No. 16,
z/H n 0
25AT /AT
5
0.15
0
20-
.16
15-
0.17
10
8
5
.30
Recirculation
15
10
Figure 4-12:
5
0
5
Surface Horizontal Temperature Distribution-.
10
Run No. 31, z/H
15
0
in this region
D
s
- f(H/D )
4.2.2
(4-10)
0
Discharaes with Variable Submergence
Preliminary Observations
With increasing submergence, the observed effect of buoyancy
is to deflect the jet trajectory toward the free surface and the
greater the Froude number, the longer the trajectory.
relatively low water depths, H/D
Due to the
< 6.3, the jet intersects the
water surface at an angle ranging from 0* for near surface discharge to less than 90* as the discharge submergence approaches
near bottom.
Thus,
the jet
generally has a substantial horizontal
velocity component at the surface which, for constant submergence,
increases with increasing
F
0
Surface Centerline Dilutions
Figures 4-13 to 4-22 are plots of centerline temperature rise
versus longitudinal distance.
They show the effect of relative
submergence z/H on temperature dilution with constant
Figures 4-13 to 4-16 can be grouped with constant
H/D
ranging from 6.3 to 1.9.
IF
and H/D .
'F 11, 14.0 and
0
Similar groupings are possible for
Figures 4-17 to 4-19 and for Figures 4-20 to 4-22 with IF0'
and 5.0, respectively.
The following phenomena are noted:
-55-
9.0
1.0
V
F
0
v/u 0-
14.0
0
H/D
0
-U
0A
Run 1
6.3
V Run 4
z/H
3F
0.0
0.33
0.66
1.00
14.2
13.9
13.3
14.1
0
Stolzenbach
/0
0
.10
/
0
sc
AT
z /H
3
t3 C31
0
0(
0n
r
-
AT
z/H
z/H
0
.66
.33
0.0
0
V V%
-01
I
I
I
I I
101
.,.~,
x
I
I
AI I
z/H = 1.0
I
102
D0
Figure 4-13:
Surface Centerline Temperature Rise vs.
Longitudinal Distance with Constant
F
0
~14.0, H/D - 6.3
0
-56-
"
-
1.0
,
I
IF 0 ~ 14.0
v/u
-0
o Run 5
* Run 6
H/D 0 - 4.5
o Run 7
V Run 8
--
.10
-
AT
Sc
/
/
z/H
F
0.00
0.33
0.67
1.00
13.7
15.7
13.8
13.5
0
'
13
a% (WO
0
.01
101
10 2
D
0
Figure 4-14:
Surface Centerline Temperature Rise vs.
Longitudinal Distance with Constant
F
~ 14.0, H/D = 4.5
-57-
~
A...
S
I
F
00
5
I
5
I
Ij
I
~5.0
H/D 0
3.8
v/
-
0
10
x
I
8
z/H
F
0 Run 9
0.00
15.1
0 Run 11
0.33
5
1-
F
--
O Runl11
0.67
14.5
V Run 12
1.00
14.9
.10
AT
AT
Sc
0
.01
102
D0
Figure 4415:
Surface Centerline Temperature Rise vs.
Longitudinal Distance with Constant
IF0
15.0, H/D0 - 3.8
-58-
103
1
I
V0
V/u
I
4
14.0
H/D 0
6
*1
4
I
0
1.0
0 Run 13
6 Run 14
Run 15
W 0
0
I
1
I
I
z/H
IFT
0.0
0.5
1.0
14.4
13.6
14.5
I
I
~I
,I
V
1
1--tjJ
9
0
.10
AT
sc
AT
0
a
. .
.01
10 2
101
a
10
0
Figure 4-16:
Surface Centerline Temperature Rise vs.
Longitudinal Distance with Constant IF
-59-
14.0
1.0
.I
IF
I
I*
i
~9.O
z/H
H/D 0
6.3
V/u
0
0
I
o Run 16
0.00
Run 17
0.33
0.67
DRun 18
V Run 19
0
1.00
I
I
IF
9.1
9.3 NG
8.8
9.0
0\0
S00
.10
003 VVV 0 0
D30
-S-C
A~T
v9
O C[
0
.01
.
j
I.
.
.
.
.
o
j
z/H - 0.00
z/h - 0.66,
z/h = 1.00
I
I-
ic
x
0
Figure 4-17:
Surface Centerline Temperature Rise vs.
Longitudinal Distance with Constant
IF0
9.0, H/D = 6.3
-
~ .0 hID= 6.
-60-
I
I
I
I
I
90
H/D
0
9
V/U
O Run 20
21
eRun 22
V Run 23
- 3.8
aRun
0
aC
Z/H
IF
0.00
0.33
8.7
8.7
0.67
9.1
1.06
8.7
M
D
V
.1
o
087
AT
):1-
SI
101
I
10
I
I
2
0
Figure 4-18:
Surface Centerline Temperature Rise vs.
Longitudinal Distance with Constant
9.0, H/D0 = 3.8
F0
-61-
I
1.O Mi
..
--
--- .
T
,
9.0
0
H/D
0
8v/u0
I
I
IC,
I
F
z/H
- 1.9
o Run 24
6 Run 25
o Run 26
-0
I
0.0
0.5
1.0
1
-
1
0
8.7
8.7
8.8
0
200
00 0
6 0
6
00
Q
.10
0 00
6o
6 0
z/H
0.0
=
z/H - 0.5,
z/H = 1.0
AT
Sc
ZT
0
.01
i
Ie
a
r
II
n'a,,
C
I
10.
0
0
I
I
I
.I
10 Z
x
D
0
Figure 4-19:
Surface Centerline Temperature Rise vs.
Longitudinal Distance with Constant
9.0, H/D - 1.9
IF 0
0
0
-62-
I #I
103
I
I
.
1.0
F
i
I
I
I
5.0
0
H/D
5.0
0
v/u 0 -0
0
9 Run 30
4.9
4.6
5.0
4.9
o oo z/H-
0.00
o Run 27
* Run 28
* Run 29
U
U
z/H
r
0.00
0.33
0.67
1.00
H
0
0
0 0 000
e
7
.10i
AT
0
D
Sc
I/H
-
0.66
4VV V VV z/H
-
0.33
az/H
-
1.00
AT
0
.01
A
.
.
I
a
6
a
1
a
a
I
I
101
x
0
Figure 4-20:
Surface Centerline Temperature Rise vs.
Longitudinal Distance with Constant
IF
= 5.0, H/D
- 5.0
-63-
aa
aa
~a
0
1.0
1
F
0
-
dq
1. 1
1
1
1
1
IF
~ 5.1
0
H/D
-
3.8
o Run 31
0 Run 32
6 Run 33
9 Run 34
v/u 0 -0
C
0
1
0
z/H
5.1
0.00
5.1
U.J3
0.66
1.00
5.1
5.1
0
0000000 0 00
6
z/H - 0.00
z/H - 0.33,
9
.10
0.66
z/H - 1.00
AT
SC
AT
0
.01
3
101
.3.3.1
MOMONNObSOMWAM
i
i
x
0
Figure 4-21:
Surface Centerline Temperature Rise vs.
Longitudinal Distance with Constant
IF
0
~5.1, H/D 0
3.8
-64-
!
2
.
.
d=W
1.0
I
U
5.0
0
v/u 0
5.0-6.3
-
o Run 36
6 Run 37
) Run 38
-0
.
IF
z/H
5.1
4.8
5.3
0.0
-
.
1.0
0
00o
00
z/H - 0.0
z/H - 0.5
z/H - 1.0
sC
AT
0
A b
.01
101
i
' a
I
I
I
I
I
x
D
0
Figure 4-22:
Surface Centerline Temperature Rise vs.
Longitudinal Distance with Constant
IF 0
5.0, H/D = 1.9
0
0
-65-
I
-
0.5
r(
4
dDo
13
AT
0
H/D
.
-
hull
I
1)
For increasing values of
W 0, the temperature dilutions
increase with constant discharge submergence z/H.
2)
For increasing values of relative water depth H/D ,
temperature dilutions increase with constant Froude number,
IF.
0
3)
For a discharge configuration ( IF
and H/D0 ),
increasing
values of z/H significantly increase the temperature dilution
in the immediate vicinity of the discharge.
There is observed
a positive tendency for surface dilutions to increase in the
stable region.
This becomes less apparent as the relative
water depths decrease.
4)
Maximum observed surface temperatures decrease with
increasing relative discharge submergence.
Figures 4-23 to 4-28 are plots of centerline temperature
rise versus longitudinal distance for near-bottom discharges,
z/H N 1.0.
Figures 4-23 to 4-25 illustrate the effect of relative
water depth H/D0 on temperature dilution, while Figures 4-26 to
4-28 show the effect of Froude number IF0 on temperature dilution.
Temperature dilution increases with increasing Froude number and
increasing water depth.
There is less dependence on IF0 with
decreasing H/D.
4.2.3
Summary
In general, with decreasing relative water depth, two major
phenomena interfere with jet entrainment and turbulent development:
-66-
1
1.
A
.V
I1
.
-
v/u 0
.10
I
1.0
z/HH/D
-
a
0
/3
-M
M
6.3
6.3
5.0
A
0
AT
14.1
9.0
4.9
o Run 4
6 Run 19
0 Run 30
I
H/D
0
5.0-6.3
I
caa
00
0d
IF
00
0
- 4.9
W0 -9.0
o0
0
I.
&........
o oo .F 0
14.1
I
101
x
10 2
0
Figure 4-23:
Surface Centerline Temperature Rise vs.
Longitudinal Distance with z/H - 1.0,
H/D
0
-
5.Q-6.3
-67-
1I
1
-UI
1. 0
-
I
z/H
-
1.0
0
-
-
IF
0
H/D - 3.8
v/u
- -
o Run 12
6 Run 23
0
o Run
14.9
8.7
5.1
34
-~\
A
.10
AT
AT
Il
0
0
A
e' ^
6
E oo 63e
n
o oo
AA
A
S~c
2'
7o -55
$0
.1, IF -14 .9
8.7
0
0
.015
.01
.
10
a
I
.
x
k a
.
. I
i
I
a
I
1
I
6
I
102
D0
Figure 4-24:
Surface Centerline Tepperature Rise vs.
Longitudinal Distance with z/H = 1.0,
H/D - 3.8
-68-
.
.
.
1.01
Z/H - 1.0
0
H/D - 1.9
0
v/u 0 M 00
0 Run 15
tun 26
tun 38
14.5
8.8
5.3
*00
0 000)0MOr
6
S6
.10
AT
8
= 5.3, F0 = 14.5
IF
=
8.8
0c
.01 a
.I
.
10
aSI
, .
I
10
x
0
Figure 4-25:
Surface Centerline Temperature Rise vs.
Longitudinal Distance with z/H = 1.0,
'H/D
-
1.9
-69-
1.0
P
0
= 14.0
H/D0
0
o Run 4
* Run 8
O Run 12
V Run 15
z/H - 1.0
v/u - 0
0
14.1
13.5
14.9
14.5
6.3
4.5
3.8
1.9
9o
0
.10 -
-
AT
ii
0r0
6A
0 3p 0 0
A
H/D
- 1.9
H/D
- 3.8
6 6 H/D
-
0
- 4.5
.00
LT0
0 0
0
0
o o o H/D0 -
.01
I
I
I
x
I
I
I
II
I
p
6.3
f
102
0
Figure 4-26:
Surface Centerline Temperature Rise vs.
Longitudinal Distance with z/H - 1.0,
P
= 14.0
-70-
p
*
I
1.0
F
-
5.0
0
H/D
z/H - 1.0
ORun 30
4.9
5.0
0
aRun 34
D Run 38
5.1
5.3
3.8
1.9
0 0M
-
1.9
H/D 0 -
3.8
v/u
0
F
-
0
a
e9
0
H/D
4
0
.10
a
0
00
ac
000 0 00
H/D
- 5.0
0
.01 i
.
.
. , , A I, i
.
10
102
x
0
Figure 4-27:
Surface Centerline Temperature Rise vs.
Longitudinal Distance with z/H - 1.0,
P
0
5.0
-71-
1.0
I
V0
9.0
0
-
O Run 19
-Run 23
0Run 26
0
H/D
9.0
8.7
6.3
I
I
I
I
a
I I
IT
3.8
1.9
8.8
n
0
0
IF
0
-/H1.0
v/u
I
0
66 CD
.10 "M
AT
8c
00
00
0
t
31
a
n
000
H/D
-
1.9
-
3.8
0
c6c6
H/D
0-0
- 6.3
H/D
. 10
0 0
.01 1
10
.
-
L
.
. -I.
I
.1
I
I
I
102
x
D
0
Figure 4-28:
Surface Centerline Temperature Rise vs.
Longitudinal Distance with z/H - 1.0,
F0 = 9..0
-72-
1)
Observations using dye injection suggest that the effect
of bottom friction on the velocity distribution and entrainment rate becomes more pronounced in shallow water.
2)
Because of the increasing restriction on the extent of
the ambient water,
will
the entrainment of the latter by the jet
generate appreciable currents to replace the entrained
water and eventually part of the heated surface layer will
be re-entrained by the jet.
This re-entrainment increases
the temperature concentration at the surface.
4.3
Single-port Discharge with Crossflow
4.3.1
Near-Surface Discharge
The non-dimensional relative jet
penetration parameter
h
ax is important in characterizing the phenomena observed with
ambient crossflows.
All results of laboratory experiments presented
were conducted at constant relative water depth, H/D
increasing Froude number and H/D
- 3.8.
With
constant, the water depth
becomes "relatively" shallow due to increasing bottom interaction
with the flow of ambient entrainment into the jet.
Figures 4-29 to 4-32 are plots of centerline temperature rise
versus longitudinal distance.
Figures 4-33 and 4-34 are plots of
excess temperature contours versus enclosed surface area.
They
show the effect of Froude number and crossflow strength on
temperature dilution.
This is reflected in the relative jet
h
penetration parameter
max, since
H
-73-
1.0
h
max
o
H
O Run 60 1 2.9 .1.25 .020
a Run 64
8.9 0.78 .023
ORun 66
4.8 0.45 .030
-S tolzenbach
z/H - 0
H/D
- 3.8
ao &
o94.8I
1
3 -13.
6 3F 09.0
.10
AT
0
0
0
0
Sc
0T
&
.01
101
Figure 4-29:
a
a
..
x
D
...
I
.
102
Surface Centerline Temperature Rise vs.
Longitudinal Distance with near Constant
v/u 0.^ 0.060, H/D = 3.8
-74-
1.0
z/H - 0
H/D
-
* hmax
7
0
12.9
8.9
4.8
o Run 50
0 Run 54
3.8
13 Run 56
--
v/u
H
1.25
0.78
0.45
.049
.058
.074
-
Stolzenbach
1Fu-4.8
IF 0- 9.0 0
.10
AT
0
sc
0
- 13.0
0
0
-
AT
.01
I
C
I
101
x
I
I
-
0
Figure 4-30:' Surface Centerline Temperature Rise vs.
Longitudinal Distance with Near
Constant v/u "' .025, H/D - 3.8
0
1
-75-
0
I
C
eq
mum
1.0
o
o
max
v/u0
64
66
9
20
13.7
8.9
4.8
12.5
9.0
1.25
0.78
0.45
1.25
0.78
.020
.023
.030
0
0
31
5.0
0.45
0
0 Run 60
Z/H - 0
HID o
0
a Run
o Run
*Run
0
£Run
*Run
3.8
F
oa-N
OUM
Ae 0.0
0
00
cA&4$
.10
A
*
*c-
AT
8C
0
La-
.01
L01
x
LU
0
Figure 4-31:
Surface Centerline Temperature Rise vs.
Longitudinal Distance with Variable
v/u 0 , H/D - 3.8
-76-
Sam"
1.0
M a
I
I
*
1
z/h -0
H/D
-
o
A
o
*
*
*
3.8
I
&
em
0
6%
AU
9
20
31
&M
.074"
0
0
0
RON
E
o
0
'S
.10
ola
L .0
0
0
0
8C
AT
.
.01
..
A
.
..
I
I
f
I
I
102
101
D
Figure 4-32:
I
0
Surface Centerline Temperature Rise vs.
Longitudinal Distance with v/u - 0 to
.074, H/D - 3.8
-77-
0
.049_
.058
1.25
0.78
0.45
1.25
0.78
0.45
~*I
AU
AT
12.9
8.9
4.8
12t5
9.0
5.0
50
54
56
M
A^
.- ~
Run
Run
Run
Run
Run
Run
1max v/u
a
a
II
1.0
H/D 0 3.8
z/H
0
0 Run 60
6 Run 64
o Run 66
Do c13
max
H
1.25
0.78
0.45
Fo
13.7
8.9
4.8
v/uo.02Q
.023
.01
~Oj
0o
a00
.10
.
0
T0
.01
1 2
10 1
Figure 4-33:
1.0
11
Excess Temperature Contours vs. Enclosed
Surface Area with v/u0
.025
-'
T
T ~1
1
~IJ-
H/D0
0.
- 0
z/H
0
0
A/D0 2
IF
0
3.8
&
o Run 50
a Run 54
o Run 56
0
0
0
13.5
8.8
4.8
II
h
v/u
max
H
1.25
0.78
0.45
.049
.058
.074
61
0
.10
S
0
0.
AT
sc
AT
0
.01
I
d.
I
10
I
1
0
A
I
I
I
I
I
.1111
i
I
I
0,
I
1
10z
Figure 4--34:
A/D 2
Excess Temperature Contours vs. Enclosed
Surface Area with v/u \. .060
0
-78-
I
a
I
A
I in
0.42 A
1 4
or
hb
(4-10)
- a constant for these tests
H0]
and
0.42 A /4
h
H
0x--
b
(4-11)
0
Thus, effectively
h
S- f (F)
(4-12)
Figures 4-29 and 4-30 show that there is poor agreement of the
crossflow configuration with Stolzenbach's prediction.
In part,
this is due to the relative shallow water depth at which the
crossflow experiments were run.
The observed phenomena can be divided into two parts according
to the magnitude of the jet penetration parameter h
/H.
h
max
1 is an indication that the jet has become attached to the
H
h
bottom.
1)
For -
< 1, the following observations are noted:
As compared with the non-crossflow case, increased
entrainment on the outer face of the jet due to a small
crossflow increases dilution.
2)
See Figures 4-31 and 4-32.
A further increase in crossflow v/u
induces a small but
positive increase in temperature dilution.
3)
Temperature dilution increases with increasing Froude
number.
4)
The jet deflection increases with increasing Froude
number.
See Figures 4-35 to 4-37.
-79-
25-
T
20--
.17
15-
00
0
105
5-
15
10
Figure 4-35:
5
0
5
Surface Horizontal Temperature Distribution.
10
Run No. 66, IF
15
= 4.8
25-
AT
0. 05
200
20-
.06
15-
.07
10.08
5-
15
.10
Figure 4-36:
5
0
5
Surface Horizontal Temperature Distribution.
10
Run No. 64, IF
15
=8.9
25-
AT /AT 0
S
0.10
0
15
10-
.11
.1
.1
5-
15
10
Figure 4-37:
5
0
5
Surface Horizontal Temperature Distribution.
10
Run No. 60, IF
15
=
13.0
5)
Semi-steady state conditions in the hydraulic model can
be achieved.
With increasing
IF0 , (v/u - constant, H/D
0
0
-
constant), the
jet's vertical penetration increases, effectively causing increased
blockage of the crossflow.
See Figure 4-38.
The result is a
decrease in the volume of ambient crossflow that penetrates beneath
the plume.
A large re-entrainment eddy on the lee side of the jet
develops and intensifies.
See Figure 4-39.
The results suggest
that increasing the Froude number has a positive effect on
h
temperature dilution until
max
1.
hH
For
max > 1, the jet'becomes attached to the bottom.
Increasing
IF
increases the area of jet attachment and all of the
crossflow is prevented from passing to the lee side of the plume.
The temperature concentrations in the re-entrainment eddy increases
until a steady state is achieved.
Increasing
IF
further in-
creases the re-entrainment causing the temperature concentrations
to increase.
4.3.2
Near-Bottom Discharge
The results presented were conducted at constant relative
water depth, H/D
- 6.
Figures 4-40 and 4-41 are plots of excess
temperature contours versus enclosed surface area.
They illustrate
the effect of Froude number and crossflow on temperature dilution.
The results suggest that:
-83-
y
v'7
y
h
max<
H
H
V
x-const
;7
47 7
or
T7
or ,o- '
V
max >
H
H
V
xnconst.
Figure 4-38: Typical Vertical Cross-section of Isotherm,
x - constant, constant H/D and v/u , z/H = 0
00
-84-
20
-
15
z=O
CO
Ln
AT
10-
=08
.09
.10
5-
Recirc ulation Eddy
I
5
I.
10
Figure 4-39:
0
5
Typical Plane View of Discharge in a Crossflow, h
z/H = 0, Run No. 50
10
/H > 1,
r
I.
1.0U
a
H/D
-
.
I
91
O Run 51
6 Run 55
* Run 12
0
I
IF0
v/u0
13.0
8.8
14.9
.049
.058
0
3.8
1
z/H -
.
1I
1
1 11'
I
I
I
C
.10
0
n
06
A T -0
.01
k.
I.
i
I
i
ll
I
I
I
A/D
0
II
IaI
I
A
I
I
10 2
101
Figure 4-40.
Excess Temperature Contours vs. Enclosed Surface
Area with
1.0
/u0
I
H/D
-
0.06
I4 I
I I II
I
3.8
I
0
z/H - 1.0
0
2
Run 61
* Run 65
8.8
4.8
67
0 Run
0
v/u
13.0
O
I
.020
.023
.030
Do
6
O
0
.10
C3
a
ZT.mc
0
I -
.01
I
101
Figure 4-41:
I
I f
I Ai
I
102
r
A/D
I
I
2
I
Iia
I
1
103
Excess Temperature Contours vs. Enclosed
Surface Area with v/u o .025
.0
-86-
ag
I f
1)
Increasing the crossflow velocity increases temperature
dilution.
2) Near-bottom discharges show small but positive increase
in temperature dilution as compared to near-surface discharge.
Compare Figures 4-33 and 4-34 with Figures 4-40
and 4-41.
3)
There is less dependence of dilution on the value of
as compared with the near-surface discharge.
as
IF 0 is increased,
the jet
F
However,
meanders along the bottom,
increasing blockage of the crossflow and re-entrainment
on the lee side.
-87-
SUMMARY AND CONCLUSIONS
V
An experimental investigation of the temperature field
induced by the heated effluent from a submerged single-port discharge is conducted.
Primary emphasis is directed to the study
of the interaction of a shallow water jet with the bottom and the
free surface.
The experimental program considers a discharge
of heated water at temperature T
pipe of diameter D
00
and density
Q
P0 from a circular
at the edge of a receiving body of water of
large extent, with temperature Ta, density pa and depth H are
uniform.
A uniform current v may be present in the receiving
water and is parallel to the shoreline.
number
H/D
F
The densimetric Froude
ranges between 4.9 and 15.7, the relative water depth
ranges between 1.9 and 6.3,
the relative crossflow V/u
0
ranges between 0.020 and 0.074, and the relative discharge submergence Z/H ranges between near surface (Z/H % 0) and near bottom
(Z/H
"- 1).
Graphic dimensionless relationships among the
pertinent parameters is presented to illustrate the jet's
behavior
and for use in the preliminary design of shallow water thermal
out falls.
In general, with decreasing relative water depth, two major
phenomena interfere with jet entrainment and turbulent development.
1)
The effect of bottom friction on the velocity distribution and entrainment rate becomes more pronounced in
shallow water.
2)
Because of the increasing restriction on the extent of
the ambient water, the entrainment of the latter by
the jet
will generate appreciable currents to replace
the entrained water and eventually part of the heated
surface layer will be re-entrained by the jet.
The
re-entrainment increases the temperature concentrations
at the surface.
In the absence of ambient currents the most critical
parameters governing the near surface discharge behavior are the
Froude number W
and the relative water depth H/D
.
In
relatively shallow depths, the results indicate substantial
deviation of temperature concentrations from those corresponding
to the ideal conditions of unrestricted water depth characterizing
Stolzenbach's (1971) predictive model for surface discharges.
The jet penetration parameter h
max
/H defines the discharge conFor the range of
figuration applicable to Stolzenbach's model.
parameters here in studied, it is found that if
H
>
h
max
'5> 3.3 kn( .45
o
0
the flow field is a function of the densimetric Froude number IF
and Stolzenbach's model is applicable with respect to the assumption that the bottom does not interfere -with the jet's performance.
However, if
H
~
max
< 3.3 kn()
E-890
0
-89-
then the flow field is a function of the densimetric Froude
number
IF
and the relative water depth H/D
.
The theoretical
results give unrealistically low temperature concentrations at
low water depths with the discrepancy increasing with decreasing
relative water depth.
The experimental results show good
agreement with Stolzenbach's et al prediction for the
jet
maxi-
mum penetration depth in deep water.
Varying the jet's relative submergence from near surface to
near bottom significantly increases the near field temperature
dilution and decreases maximum temperature concentrations.
Dilutions in the stable region increase with submergence, but
this becomes less apparent as relative water depths decrease.
The non-dimensional relative jet penetration parameter h
/H
is important in characterizing the phenomena observed with ambient
crosaflows.
The jet's interaction with the crossflow can be
divided into two parts according to whether h
max
/H is less than or
greater than one, i.e., whether the jet is, or is not, attached
to the bottom.
The results suggest that maximum temperature dilu-
tion is achieved with a crossflow when the discharge configuration
satisfies the criteria
h
max
H
The deflection of the jet plume increases with increasing
Froude number.
Temperature dilutions also increases with an in-
crease in the crossflow velocity y/u 0 , given that h
constant.
/H remains
Stolzenbach's prediction with crossflows correlate
-90-
poorly with the experimental results, which is likely due to the
shallow depths at which the tests were performed.
-91-
NO]MENCLATURE
A
discharge channel aspect ratio, h /b
b
local width of jet, 2-D
b
horizontal surface distance from core boundary to jet
boundary, 3-D
b
one half the width of rectangular channel
c
coefficient in the exponent of Ellison and Turner's vertical
entrainment velocity function
cn
concentration of heat in the plume in terms of density of water
D
dilution
D0
outfall nozzle inside diameter
F0
densimetric Froude number of the discharge
IF 'a
-
ratio of flow in the jet to the initial flow
characteristic Froude number
-
F A
f
a functional
f
similarity function for velocity
g
acceleration of gravity
g'
Ap /p g
H
maximum allowable penetration of the jet
h
vertical centerline distance from core boundary to jet
-
(1-C3/2
2
boundary
hmax maximum value of h obtained in a heated discharge
h0
depth of discharge channel
K
experimentally determined dimensionless coefficient describing
the gross effects of the turbulent mixing process
k
coefficient of heat loss
P
pressure
-92-
-
.......
. .....
-
-
,
I--
......
.....
Q
discharge flow
Q1
rate of entrainment of the ambient water per unit length of
the jet
r
radial cylindrical coordinate
r
vertical distance from the jet centerline to the boundary of
of the core region
s
longitudinal cylindrical coordinate
s
horizontal distance from the jet centerline to the boundary
of the core region
T
mean local temperature
t
similarity function for temperature
T'
temperature fluctuations
Ta
ambient temperature of water
Tc
jet centerline temperature
T
temperature of water at jet
Ts
surface temperature
Tsc
jet
AT
the local temperature rise,
T-T a
AT
C
-
(l-C)3/2
exit
centerline temperature at the surface
temperature rise at the centerline,
T C -T a
AT
temperature difference between the discharge and the ambient
water, T -T
0
a
AT
surface temperature rise,
T.-Ta
ATsc surface centerline temperature rise
(AT) saverage fractional stable excess surface temperature rise in
the jet
(AT s
u,v
stable surface centerline temperature
rise, Tsc
mean velocities in s,r
direction
u'v' velocity fluctuations in s,r direction
-93-
a
ujvw
velocity components in the coordinate system relative to
the centerline of a deflected jet
uWvw
velocity components in the fixed coordinate system
u'v'w'
turbulent fluctuating velocity components
uc
centerline jet velocity
u0
discharge velocity -
V,v
ambient crossflow velocity
v
lateral velocity of the entrained flow at the jet
boundary
vs
an internal velocity
vb
an internal velocity
W,avertical
Q0 /2h b
velocity in the jet at z -- r and 0 < y < 8
wh
internal velocity
wr
internal velocity
xyz
coordinate direction relative to the centerline of a
deflected jet
xFyz
fixed coordinate direction
experimentally determined entrainment coefficient
lateral entrainment coefficient in non-buoyant jet
(Iz
vertical entrainment coefficient in a non-buoyant jet
8
coefficient of thermal expansion for water
spread, db/dx of the turbulent region of a non-buoyant
jet
E
spread, db/dx, of the turbulent region in an undeflected
non-buoyant jet
either of
or
r
-94-
Y
Cz
dimensionless width of the turbulent region of a jet,
Iy1-s/b
dimensionless depth of the turbulent region of a jet,
z-v/h
lateral jet stream line from the centerline in excess of
the non-buoyant value
G
angle between x axis and s axis
0
angle between the jet centerline (x axis) and the - axis
00
angle between the discharge channel centerline and the y
axis
water surface elevation
p
mean local density of water
Pa
ambient density of water
PC
density of the jet centerline
pO
density of water at jet
Ap
difference between the ambient water density and the
water density, p.-P
APeCdensity
exit
deficit at the centerline, p C-P
Ap0
difference between the ambient water density and the
density of the heated flow at the discharge
exit, paPO
A
experimentally determined dimensionless coefficients
describing the gross effects of the turbulent mixing
process
V
kinematic viscosity
-95-
LIST OF FIGURES
Page
Figure 2-1:
Region of Physical Processes that
Govern a Single-port Thermal Discharge
9
Figure 2-2:
Definition Diagram for Round Buoyant Jet
11
Figure 2-3:
Coordinate
19
Figure 2-4:
Discharge Structure
20
Figure 2-5:
Schematic of the Single-port Heated
Discharge
26
Figure 3-1:
Schematic of Heated Discharge
28
Figure 3-2:
Experimental Setup
32
Figure 4-1:
Surface Centerline Temperature Rise
vs. Longitudinal Distance with
ConstantIF
14.0
40
Definitions
0
Figure 4-2:
Surface Centerline Temperature Rise
vs. Longitudinal Distance with
Constant F
9.0
0
Figure 4-3:
Surface Centerline Temperature Rise
vs. Longitudinal Distance with
ConstantWF
5.0
41
42
0
Figure 4-4:
Figure 4-5:
Surface Centerline Temperature Rise
vs. Longitudinal Distance with
Constant hm
H ' 0.80
43
Excess Temperature Contours vs.
Enclosed Surface Area with
14.0
ConstantIF
44
0
Figure 4-6:
Excess Temperature Contours vs.
Enclosed Surface Area with
ConstantJF
9.0
0
Figure 4-7:
Excess Temperature Contours vs.
Enclosed Surface Area with
Constant F
5.0
0
44
45
Page
Figure 4-8:
Figure 4-9:
Figure 4-10:
Figure 4-11:
Figure 4-12:
Figure 4-13:
Maximum Jet Penetration Depth of
Surface Discharge
48
Schematic of Isotherms AT/AT in the
Vertical Plant, y-0. Run No. 5
49
Stable Region Temperature Rise Near
Surface Discharge
51
Surface Horizontal Temperature
Distribution. Run No. 16, z/H = 0
53
Surface Horizontal Temperature
Distribution. Run No. 31, z/H = 0
54
Surface Centerline Temperature Rise
vs. Longitudinal Distance with
Constant IF
14.0, H/D - 6.3
0
Figure 4-14:
Surface Centerline Temperature Rise
vs. Longitudinal Distance with
Constant P0= 14.0, H/D0 - 4.5
Figure 4-15:
Figure 4-16:
Surface Centerline Temperature Rise
vs. Longitudinal Distance with
ConstantIF
15.0, H/D
1.8
0
0
Surface Centerline Temperature Rise
vs. Longitudinal Distance with
ConstantlF
14.0
0
Figure 4-17:
56
0
57
58
59
Surface Centerline Temperature Rise
vs. Longitudinal Distance with
Constant
Figure 4-18:
Figure 4-20:
- 6.3
60
Surface Centerline Temperature Rise
vs. Longitudinal Distance with
Constant
Figure 4-19:
0 = 9.0, H/D
0
9.0, H/D 0
3.8
61
Surface Centerline Temperature Rise
vs. Longitudinal Distance with
Constant F = 9.0, H/D0
1.9
62
Surface Centerline Temperature
Rise vs. Longitudinal Distance
with Constant F0 = 5.0, H/D 0
5.0
63
-97-
Page
Figure 4-21:
Figure 4-22:
Figure 4-23:
Figure 4-24:
Surface Centerline Temperature Rise
vs. Longitudinal Distance with
Constant W = 5.1, H/D - 3.8
64
Surface Centerline Temperature Rise
vs. Longitudinal Distance with
Constant F0 = 5.0, H/D 0= 1.9
65
Surface Centerline Temperature Rise
vs. Longitudinal Distance with
z/H - 1.0, H/D0 - 5.0-6.3
67
Surface Centerline Temperature Rise
vs. Longitudinal Distance with z/H 1.0, H/D - 3.8
68
Surface Centerline Temperature Rise
vs. Longitudinal Distance with
z/H - 1.0, H/D - 1.9
69
0
Figure 4-25:
Figure 4-26:
Surface Centerline Temperature Rise
vs. Longitudinal Distance with z/H -
1.0, F
Figure 4-27:
Figure 4-28:
= 14.0
Surface Centerline Temperature Rise
- vs. Longitudinal Distance with
z/H - 1.0, IF = 5.0
Figure 4-30:
Figure 4-31:
71
Surface Centerline Temperature Rise
vs. Longitudinal Distance with
z/H = 1.0, F
Figure 4-29:
70
= 9.0
72
Surface Centerline Temperature Rise
vs. Longitudinal Distance with near
Constant v/u0 I' 0.060, H/D - 3.8
74
Surface Centerline Temperature Rise
vs. Longitudinal Distance with near
Constant v/u 0I
.025, H/D 0
3.8
75
Surface Centerline Temperature Rise
vs. Longitudinal Distance with
Variable v/u0 , H/D - 3.8
76
-98-
Page
Figure 4-32:
Figure 4-33:
Surface Centerline Temperature Rise vs.
Longitudinal Distance with v/u 0to .074, H/D - 3.8
77
Excess Temperature Contours vs. Enclosed
Surface Area with v/u '\' .025
78
0
Figure 4-34:
Figure 4-35:
Figure 4-36:
Figure 4-37:
Figure 4-38:
Excess Temperature Contours vs. Enclosed
Surface Area with v/u 0
.060
78
Surface Horizontal Temperature Distribution. Run No. 66,3F - 4.8
80
Surface Horizontal Temperature Distribution, Run No. 64, IF - 8.9
81
Surface Horizontal Temperature Distribution. Run No. 60,IF - 13.0
82
Typical Vertical Cross-section of
Isotherm, x - constant, constant H/D
and
Figure 4-39:
Figure 4-40:
/u , Z/H-0
0
84
Typical Plane View of Discharge in a
Crossflow, h
/H > 1, z/H ~ 0, Run No.
50
max
85
Excess Temperature Contours vs. Enclosed
Surface Area with v/u "v 0.06
86
Excess Temperature Contours vs. Enclosed
Surface Area with v/u 0'o .025
86
0
Figure 4-41:
-99-
REFERENCES
1.
Abraham, G., "Jet Diffusion in Stagnant Ambient Fluid",
Delft Hydraulics Laboratory Publication No. 29 (1963)
2.
Abramovich, G.N., The Theory of Turbulent Jets, The M.I.T.
Press, M.I.T., Cambridge, Massachusetts (1963).
3.
Fan, L.-N, "Turbulent Buoyant Jets into Stratified or Flowing
Ambient Fluids", W.M. Keck Laboratory of Hydraulics and
Water Resources, California Institute of Technology, Report
No. KH-R-15, June (1967).
4.
Partheniades, E., Beechley, B.C., and Jen, Y., "A Parametric
Study for Surface Temperature Concentration Due to Submerged
Heated Water Jets in Shallow Water", Coastal and Oceanographic
Engineering Laboratory, College of Engineering, University of
Florida, Technical Report No. 17, May, 1973.
5.
Stolzenbach, K.D. and Harleman, D.R.F., "An Analytical and
Experimental Investigation of Surface Discharges of Heated
Water", Ralph M. Parsons Laboratory for Water Resources and
Hydrodynamics, Department of Civil Engineering, M.I.T.,
Technical Report No. 135, February, 1971.
6.
Stolzenbach, K.D., Adams, E.E., and Harleman, D.R.F., "A
User's Manual for Three-Dimensional Heated Surface Discharge
Computations", Ralph M. Parsons Laboratory for Water Resources
and Hydrodynamics, Department of Civil Engineering, M.I.T.,
Technical Report No. 156, September, 1972.
-100-