Monroe L. Weber- Shirk School of Civil and Environmental Engineering Turbulent Jets and Plumes
Monroe L. Weber-Shirk S chool of Civil and Environmental Engineering Turbulent Jets and Plumes.
Jan 12, 2016
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Monroe L. Weber-Shirk
School of Civil and Environmental Engineering
Turbulent Jets and PlumesTurbulent Jets and Plumes
Turbulent Jets and PlumesTurbulent Jets and Plumes
Discharge of society’s wastes into the environment smokestacks wastewater discharges automobile exhaust
Natural events volcanoes forest fires dragons
Discharge of society’s wastes into the environment smokestacks wastewater discharges automobile exhaust
Natural events volcanoes forest fires dragons
DragonsDragons
http://www.riverdale.k12.or.us/helens/slides/
slide.htm
Some definitionsSome definitions
momentummomentum
densitydensity
momentummomentum
buoyancybuoyancy
Jet driven by _________ of the source Ex. garden hose submerged in swimming pool
Plume driven by ________ differences Ex. smoke from open fire
Buoyant Jet combination of momentum of source and density Ex. Wastewater discharge into ocean initial flow controlled by _________ far from source controlled by _________
Jet driven by _________ of the source Ex. garden hose submerged in swimming pool
Plume driven by ________ differences Ex. smoke from open fire
Buoyant Jet combination of momentum of source and density Ex. Wastewater discharge into ocean initial flow controlled by _________ far from source controlled by _________
Turbulent Jet and Plume Characteristics
Turbulent Jet and Plume Characteristics
Jet efficient mixing with the ambient fluid kinetic energy is lost to turbulence momentum is conserved
Plume efficient mixing with the ambient fluid potential energy is converted to kinetic energy kinetic energy is lost to turbulence momentum is conserved (but must take body force into
account)
Jet efficient mixing with the ambient fluid kinetic energy is lost to turbulence momentum is conserved
Plume efficient mixing with the ambient fluid potential energy is converted to kinetic energy kinetic energy is lost to turbulence momentum is conserved (but must take body force into
account)
Jet ParametersJet Parameters
initial jet velocity initial turbulence of discharge jet mass flux jet momentum flux jet tracer material
heat salinity contaminant
initial jet velocity initial turbulence of discharge jet mass flux jet momentum flux jet tracer material
heat salinity contaminant
Environmental ParametersEnvironmental Parameters
ambient turbulence levels currents
cross flows co flows counter flows
density stratification thermal salinity
ambient turbulence levels currents
cross flows co flows counter flows
density stratification thermal salinity
Geometrical FactorsGeometrical Factors
jet discharge port shape orientation proximity to adjacent jets proximity to solid boundaries attitude of the jet distance to free surface
jet discharge port shape orientation proximity to adjacent jets proximity to solid boundaries attitude of the jet distance to free surface
What we’d like to knowWhat we’d like to know
Contaminant concentration as function of distance from source
Velocity of jet or plume as function of distance
Width of jet or plume as function of distance
Contaminant concentration as function of distance from source
Velocity of jet or plume as function of distance
Width of jet or plume as function of distance
3 unknowns, so we need 3 equations!3 unknowns, so we need 3 equations!
Tools to get thereTools to get there
From basic principles conservation of momentum conservation of mass (of tracer) conservation of energy rate of spread of jet (spreading law)?
From dimensional analysis need to identify the important parameters still need spreading law
From basic principles conservation of momentum conservation of mass (of tracer) conservation of energy rate of spread of jet (spreading law)?
From dimensional analysis need to identify the important parameters still need spreading law
Cases to analyzeCases to analyze
Jet round jet plane jet
Plume round plume plane plume
Jet round jet plane jet
Plume round plume plane plume
Axisymmetric JetAxisymmetric Jet
Geometry round axisymmetric 3-d problem
Ambient water much less shear
than in jet no flow (for this
simple case)
Geometry round axisymmetric 3-d problem
Ambient water much less shear
than in jet no flow (for this
simple case)
ddJet: , Vo, CoJet: , Vo, Co
edge of jet turbulenceedge of jet turbulence
velocity profile(statistical mean)velocity profile(statistical mean)
Ambient: , V=0, C=0Ambient: , V=0, C=0
bb
Simple Jet SpreadingSimple Jet Spreading
dd
Vu ' Vu '
V
u
ds
db 'V
u
ds
db '
sb sb
velocity fluctuations at any location are proportional to the velocity of the jet at that location
velocity fluctuations at any location are proportional to the velocity of the jet at that location
ss
dsuVdb ' dsuVdb '
Momentum: Axisymmetric JetMomentum: Axisymmetric Jet
2
4bA
2
4bA
jet spreading equationjet spreading equation
02
02 AVAV 0
20
2 AVAV
220
22
44dVbV
22
022
44dVbV
dVVb o dVVb o b
dVV o
b
dVV o
s
dVV o s
dVV o
external forces balance external forces balance b
dd
ss
controlvolumecontrolvolume
substitute for areasubstitute for area
sspp FFFWMM 00 sspp FFFWMM 00
020
20 AVAV 02
02
0 AVAV
sb sb
M term
here?
Concentration of Conservative Tracer: Axisymmetric Jet
Concentration of Conservative Tracer: Axisymmetric Jet
MM 0 MM 0
QCCQ 00 QCCQ 00
QCM QCM
VbAVQ 2
4
VbAVQ 2
4
02
00
4VdVAQo
0
200
4VdVAQo
VCbCVd 200
2
44
VCbCVd 2
002
44
at steady state mass flux [M/T] is constantat steady state mass flux [M/T] is constant
b
dd
ss
Concentration of Conservative Tracer: Axisymmetric Jet
Concentration of Conservative Tracer: Axisymmetric Jet
b
dd
ss
Vb
CVdC
2
002
Vb
CVdC
2
002
s
dVs
CVdC
02
002
s
dVs
CVdC
02
002
s
dVV o s
dVV o
s
dCC 0s
dCC 0
(jet spreading)(jet spreading)
(velocity in jet)(velocity in jet)
VCbCVd 200
2 VCbCVd 200
2
sb sb
Round Jet: Empirical ConstantsRound Jet: Empirical Constants
s
dVV o s
dVV o
s
dCC 0s
dCC 0
sb 107.0 sb 107.0
s
dVV oc 2.6
s
dVV oc 2.6
s
dCC oc 0.5
s
dCC oc 0.5
sb sb
b is defined such that the velocity is ____________ of the centerline velocity
ddJet: , Vo, CoJet: , Vo, CoCenterline velocity and concentration
37% (1/e)37% (1/e)
Plane: (2-D) JetsPlane: (2-D) Jets
Spreading of the jet will be by the same mechanism
Momentum conservation will give a different relationship for centerline velocity
Spreading of the jet will be by the same mechanism
Momentum conservation will give a different relationship for centerline velocity
020
20 bVbV 02
02
0 bVbV
b
bVV o
0 b
bVV o
0 s
bVV o
0 s
bVV o
0 show this for HWshow this for HW
00 MM 00 MM
020
20 AVAV 02
02
0 AVAV
s
bCC o
0s
bCC o
0
sb sb
Per unit lengthPer unit length
Plane Jets: Empirical Coefficients
Plane Jets: Empirical Coefficients
s
bVV o
0 s
bVV o
0
s
bCC o
0s
bCC o
0
sb 116.0 sb 116.0
s
bVV oc
041.2 s
bVV oc
041.2
s
bCC oc
038.2s
bCC oc
038.2
sb sb
Jet Design ProblemJet Design Problem
Given a discharge with an environmental requirement of achieving a high dilution measured at the surface of a body of water. What are the three things you can do to maximize the dilution of the discharge before the jet reaches the water surface?
Given a discharge with an environmental requirement of achieving a high dilution measured at the surface of a body of water. What are the three things you can do to maximize the dilution of the discharge before the jet reaches the water surface?
s
dCC oc 0.5
s
dCC oc 0.5
s
bCC oc
038.2s
bCC oc
038.2
round jetround jet
plane jetplane jetIncrease depth of submergenceIncrease depth of submergence
Decrease port size (multiple ports!)Decrease port size (multiple ports!)
Discharge at an angleDischarge at an angle
PlumesPlumes
less well defined boundary between plume and ambient (billows)
full description of velocities and concentrations is very complex
time averaged shape of plume similar to jet (same spreading law)
momentum still conserved but with inclusion of a ____ force (due to buoyancy)
less well defined boundary between plume and ambient (billows)
full description of velocities and concentrations is very complex
time averaged shape of plume similar to jet (same spreading law)
momentum still conserved but with inclusion of a ____ force (due to buoyancy)bodybody
Plume ExercisePlume Exercise
What parameters are important in determining the time averaged centerline velocity in the plume?
Develop an expression for centerline velocity that is dimensionally correct.
Does your expression make sense?
What parameters are important in determining the time averaged centerline velocity in the plume?
Develop an expression for centerline velocity that is dimensionally correct.
Does your expression make sense?
Round Plume:Equation Development
Round Plume:Equation Development
),( sBfV ),( sBfV
3
4
][T
LB
3
4
][T
LB
3/1
s
BV
3/1
s
BV
QCCQ 00 QCCQ 00VCbCQ 2
00
4
VCbCQ 2
00
4
Vb
CQC
2
004
Vb
CQC
2
004
sb sb
DimensionalanalysisDimensionalanalysis
tracer mass conservationtracer mass conservation
3/1
s
BV
3/1
s
BV
0gQB 0gQB
3/1
2
004
s
Bs
CQC
3/1
2
004
s
Bs
CQC
3/13/5
00
Bs
CQC
3/13/5
00
Bs
CQC
Buoyancy fluxBuoyancy flux
Plume coefficientsPlume coefficients
round plumeround plume plane plumeplane plume
sb 1.0 sb 1.0
3/13/5
001.9Bs
CQCc
3/13/5
001.9Bs
CQCc
3/1
7.4
s
BVc
3/1
7.4
s
BVc
sb 12.0 sb 12.0
3/166.1 BVc 3/166.1 BVc
3/1
0038.2sB
CqCc
3/1
0038.2sB
CqCc
q0 discharge per unit lengthq0 discharge per unit length
gQBa gQBa gqB
a gqBa
Independent of s!
Buoyant JetsBuoyant Jets
A jet whose density differs from the receiving water
Jet-like characteristics close to the source Plume-like characteristics far from the
source the plume-like characteristics always win!
Examples
A jet whose density differs from the receiving water
Jet-like characteristics close to the source Plume-like characteristics far from the
source the plume-like characteristics always win!
Examples
CORMIXCORMIX
Simulation of turbulent buoyant jet mixing behavior in the… near-field (the initial jet characteristics of momentum flux, buoyancy
flux, and outfall geometry influence the jet trajectory and mixing) far-field (density current region followed by a passive diffusion
region) The hydrodynamic simulation system contains a collection of
regional flow models based on… Integral (conservation of mass, heat, and momentum) length scale (based on dimensional analysis) passive diffusion (turbulence in the ambient environment becomes the
dominating mixing mechanism)
CORMIX
Jets and Plumes:Summary
Jets and Plumes:Summary
Simple analytical equations describe time averaged values for velocity and concentrations in jets and plumes
Interactions with the environment (boundaries, cross flows, density differences) complicate the description of jets and plumes
Computer based expert system developed at Cornell (CORMIX) can be used to predict interaction of jets and plumes with the environment
Predictions based on combination of theory and empirical studies using dimensional analysis
Simple analytical equations describe time averaged values for velocity and concentrations in jets and plumes
Interactions with the environment (boundaries, cross flows, density differences) complicate the description of jets and plumes
Computer based expert system developed at Cornell (CORMIX) can be used to predict interaction of jets and plumes with the environment
Predictions based on combination of theory and empirical studies using dimensional analysis
Dragon Day Plume
Mount Saint HelensMount Saint Helens
http://www.riverdale.k12.or.us/helens/slides/slide.htm
Integrated Forest Fire Management Project
(IFFM)Indonesia
Integrated Forest Fire Management Project
(IFFM)Indonesia
Slurry PlumesSlurry Plumes
slurry plumes for three increasing sizes of near-uniform sand diffusing in an ambient. The smallest size is around
0.2mm
slurry plumes for three increasing sizes of near-uniform sand diffusing in an ambient. The smallest size is around
0.2mm
http://maligne.civil.ualberta.ca/water/research/restopics/arbind/slplume.html
Momentum of DischargeMomentum of Discharge
small portsmall port momentummomentum jet mixingjet mixing
large portlarge port momentummomentum jet mixingjet mixing
Multiport Diffuser ValvesMultiport Diffuser Valves
http://www.redvalve.com/brochure/diffuser.html
Boston HarborBoston Harbor
http://crusty.er.usgs.gov/
Massachusetts Bay Massachusetts Bay
http://crusty.er.usgs.gov/
Tidal Flushing of Boston Harbor
Tidal Flushing of Boston Harbor
http://crusty.er.usgs.gov/
Boston Harbor tidal cycles
Simulation of tidal exchange in Boston Harbor , based on a high-resolution (100 m grid spacing) depth-averaged computer model. Water in Boston Harbor is dyed red, and tracked over three tidal cycles. Colors between red and blue represent mixing of Boston Harbor water with Massachusetts Bay water (dyed blue). Due to the jet-like behavior of the ebb tidal currents, water is expelled from the harbor in pulses, leading to effective flushing of the harbor over several days.
Spring Freshet in Massachusetts Bay: April-May 1992
Spring Freshet in Massachusetts Bay: April-May 1992
Spring Freshet
Near-surface salinity (2 m depth) is tracked during May 1992, revealing a plume of fresh water from the Merrimack River that moves into Massachusetts Bay. The yellow arrow that flops around indicates the wind direction and speed. Note that a snapshot of the salinity on May 22 (as one might sample from a monthly CTD cruise) would give the distinct visual impression of a large plume from Boston Harbor, when in fact most of this water came from the Merrimack River!
http://crusty.er.usgs.gov/
Boston Harbor Sewage Outfalls Effluent Concentration
Boston Harbor Sewage Outfalls Effluent Concentration
Effect of new Boston Outfall
Simulation of effluent dilution from the existing and future Boston Sewage effluent outfalls based on a three-dimensional circulation model of Massachusetts Bay during Jan-Mar 1990 and Jun-Aug 1990. Isosurfaces (three-dimensional contours) of effluent concentration are shown representing 1 part effluent to 200 parts seawater. This is a level below which nutrient inputs due to the outfall should be hard to distinguish above background fluctuations. During both the winter and summer months the effluent from the future outfall (represented by the blue isosurface) covers a smaller region than the effluent from the existing outfall (represented by the purple isosurface).
These simulations were used as evidence to assess the impact of the future outfall on endangered right whales.
http://crusty.er.usgs.gov/
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