Lappeenranta WA 1 CFD
Transcript of Lappeenranta WA 1 CFD
-
7/30/2019 Lappeenranta WA 1 CFD
1/69
11
Basic Concepts about CFD ModelsBasic Concepts about CFD Models
Walter AmbrosiniWalter Ambrosini
Associate Professor inAssociate Professor inNuclearNuclearPlantsPlants
at theat theUniversityUniversityofofPisaPisa
Lappeenranta University of TechnologyLappeenranta University of Technology
Summer School in Heat and Mass TransferSummer School in Heat and Mass TransferAugust 18August 1820, 201020, 2010
-
7/30/2019 Lappeenranta WA 1 CFD
2/69
22
SummarySummary
General remarks on turbulent flowGeneral remarks on turbulent flow
Instability of laminar flowInstability of laminar flow
Statistical treatment of turbulent flowStatistical treatment of turbulent flow
Momentum transfer in turbulent flowMomentum transfer in turbulent flow
Heat transfer in turbulent flowHeat transfer in turbulent flow
Basic concepts about computational modelling of turbulent flowsBasic concepts about computational modelling of turbulent flows
Length scales in turbulenceLength scales in turbulence
Direct Numerical Simulation (DNS)Direct Numerical Simulation (DNS)
Large Eddy Simulation (LES)Large Eddy Simulation (LES)
Reynolds AveragedReynolds Averaged NavierNavier--Stokes equations (RANS)Stokes equations (RANS)
TwoTwo--phase flow applicationsphase flow applications
Prediction of heat transfer deteriorationPrediction of heat transfer deterioration
-
7/30/2019 Lappeenranta WA 1 CFD
3/69
33
General remarks on turbulent flowGeneral remarks on turbulent flowInstability of Laminar FlowInstability of Laminar Flow -- 11
The transition from laminar flow to turbulence isThe transition from laminar flow to turbulence is an example ofan example offlow instabilityflow instability::
beyond a certain threshold,beyond a certain threshold, inertia overcomes viscousinertia overcomes viscous
forcesforces and the motion cannot be anymore orderedand the motion cannot be anymore ordered
this was shown bythis was shown by Osborne ReynoldsOsborne Reynolds in a classicalin a classical
experimentexperiment
-
7/30/2019 Lappeenranta WA 1 CFD
4/69
44
This transition occurs in many different systems:This transition occurs in many different systems: pipe flowpipe flow
boundary layersboundary layers
General remarks on turbulent flowGeneral remarks on turbulent flowInstability of Laminar FlowInstability of Laminar Flow -- 22
-
7/30/2019 Lappeenranta WA 1 CFD
5/69
55
free jetsfree jets
wakeswakes
General remarks on turbulent flowGeneral remarks on turbulent flowInstability of Laminar FlowInstability of Laminar Flow -- 33
-
7/30/2019 Lappeenranta WA 1 CFD
6/69
66
In order to study stability of a nonlinear system by analyticalIn order to study stability of a nonlinear system by analyticalmeans the methodology ofmeans the methodology of linear stability analysislinear stability analysis is oftenis often
adoptedadopted
This has the objective to determineThis has the objective to determine the stability conditionsthe stability conditions
consequent to infinitesimal perturbationsconsequent to infinitesimal perturbations: e.g., for a 2D: e.g., for a 2D
boundary layer it isboundary layer it is
General remarks on turbulent flowGeneral remarks on turbulent flowInstability of Laminar FlowInstability of Laminar Flow -- 44
EXAMPLES OF TRANSIENTEXAMPLES OF TRANSIENT
ANALYSESANALYSES
CavityCavityRB ConvectionRB Convection
Buoyant JetBuoyant Jet
-
7/30/2019 Lappeenranta WA 1 CFD
7/69
77
Turbulence introduces a large degree ofTurbulence introduces a large degree of sensitivity to initialsensitivity to initialconditions (SIC)conditions (SIC) that is typical ofthat is typical of deterministic chaosdeterministic chaos
By this, it is meant thatBy this, it is meant that turbulent motion is notturbulent motion is not randomrandom,,
though it appears fluctuating in a similar manner,though it appears fluctuating in a similar manner, since thesince the
equations governing the system are well definedequations governing the system are well defined
This characteristic is shared with many differentThis characteristic is shared with many different chaoticchaotic
systemssystems, even governed by simple equations, even governed by simple equations
General remarks on turbulent flowGeneral remarks on turbulent flowInstability of Laminar FlowInstability of Laminar Flow -- 55
dRe
d= Gr
1
2-
L
Df'(Re) Re |Re|
d1
d= Re 1 -
2 Fo 1 +4
sin
d1
d = - Re 1 - 2 Fo 1 +4
cos Heating
Cooling
-
7/30/2019 Lappeenranta WA 1 CFD
8/69
88
Owing to the fluctuating nature of the turbulent flow field, itOwing to the fluctuating nature of the turbulent flow field, it isiscustomary (after Reynolds)customary (after Reynolds) to introduce an appropriate timeto introduce an appropriate time
averagingaveraging of any specific value (of any specific value (intensiveintensive) of major) of major
extensiveextensive variablesvariables
The attempt is quite evidently to writeThe attempt is quite evidently to write equations in terms ofequations in terms of
time averaged variablestime averaged variables, structurally similar to those of, structurally similar to those of
laminar flowlaminar flow
This attempt is successful, butThis attempt is successful, but fluctuations cannot be forgottenfluctuations cannot be forgotten
General remarks on turbulent flowGeneral remarks on turbulent flowStatistical Treatment of Turbulent FlowStatistical Treatment of Turbulent Flow -- 11
-
7/30/2019 Lappeenranta WA 1 CFD
9/69
99
In particular,In particular,
the following quantities have overwhelmingthe following quantities have overwhelming
importanceimportance
Turbulence intensity is strictly related to the turbulence kinetTurbulence intensity is strictly related to the turbulence kineticic
energyenergy
This is one of the most important quantities adopted in presentThis is one of the most important quantities adopted in present
CFD codesCFD codes, mostly making use of, mostly making use of twotwo--equation modelsequation models, to be, to be
described later ondescribed later on
General remarks on turbulent flowGeneral remarks on turbulent flowStatistical Treatment of Turbulent FlowStatistical Treatment of Turbulent Flow -- 22
-
7/30/2019 Lappeenranta WA 1 CFD
10/69
1010
The general balance equations in local and instantaneousThe general balance equations in local and instantaneousformulation are then averagedformulation are then averaged making use of the abovemaking use of the above
described averaging operatordescribed averaging operator
After simplifications (described in lecture notes), an averagedAfter simplifications (described in lecture notes), an averaged
form is finally reached showing that the attempt to get equationform is finally reached showing that the attempt to get equationss
similar to those of laminar flow leaves an additional termsimilar to those of laminar flow leaves an additional term
This term, having a clearThis term, having a clear advectiveadvective nature, points out thatnature, points out that
fluctuations do play a role in transfers: this role represents afluctuations do play a role in transfers: this role represents a
sort of additionalsort of additional mixingmixing due to turbulencedue to turbulence
General remarks on turbulent flowGeneral remarks on turbulent flowStatistical Treatment of Turbulent FlowStatistical Treatment of Turbulent Flow -- 33
-
7/30/2019 Lappeenranta WA 1 CFD
11/69
1111
In analogy with the molecular motion, the basic idea is thereforIn analogy with the molecular motion, the basic idea is thereforeeto interpret such term as anto interpret such term as an additional diffusion due toadditional diffusion due to
turbulenceturbulence
The momentum and energy balance equations contain this termThe momentum and energy balance equations contain this term
that calls for a proper modellingthat calls for a proper modelling
General remarks on turbulent flowGeneral remarks on turbulent flowStatistical Treatment of Turbulent FlowStatistical Treatment of Turbulent Flow -- 44
-
7/30/2019 Lappeenranta WA 1 CFD
12/69
1212
TheThe Reynolds stress tensorReynolds stress tensor appears in momentum equationsappears in momentum equations
The Reynolds stresses account for the additional momentumThe Reynolds stresses account for the additional momentum
flux due to eddiesflux due to eddies
General remarks on turbulent flowGeneral remarks on turbulent flowMomentum Transfer in Turbulent FlowMomentum Transfer in Turbulent Flow -- 11
-
7/30/2019 Lappeenranta WA 1 CFD
13/69
1313
It is then customary to adopt theIt is then customary to adopt the BoussinesqBoussinesq approximationapproximationbased on a definition ofbased on a definition of turbulent momentum diffusivityturbulent momentum diffusivity (eddy(eddy
viscosity)viscosity), trying to define a simple constitutive relationship for, trying to define a simple constitutive relationship for
the Reynolds stressthe Reynolds stress
The quantityThe quantity TT is no more a property of the fluid, but alsois no more a property of the fluid, but also
depends on flow.depends on flow.
Of course,Of course, thethe BoussinesqBoussinesq approximation shifts the toughnessapproximation shifts the toughness
of the modelling problem to the definition of the eddy viscosityof the modelling problem to the definition of the eddy viscosity
General remarks on turbulent flowGeneral remarks on turbulent flowMomentum Transfer in Turbulent FlowMomentum Transfer in Turbulent Flow -- 22
-
7/30/2019 Lappeenranta WA 1 CFD
14/69
1414
By the way, many different kinds of turbulence can beBy the way, many different kinds of turbulence can be
envisaged, ranging from ideally homogeneous and isotropic toenvisaged, ranging from ideally homogeneous and isotropic to
more realistically heterogeneous and anisotropicmore realistically heterogeneous and anisotropic
Wall turbulenceWall turbulence is a classical example of the latter cases:is a classical example of the latter cases:
Eddy viscosity models have therefore the very tough job toEddy viscosity models have therefore the very tough job to
reintroduce the complexity lost in the simplereintroduce the complexity lost in the simple BoussinesqBoussinesq
approximationapproximation
General remarks on turbulent flowGeneral remarks on turbulent flowMomentum Transfer in Turbulent FlowMomentum Transfer in Turbulent Flow -- 33
-
7/30/2019 Lappeenranta WA 1 CFD
15/69
1515
It is rather instructive and useful to considerIt is rather instructive and useful to consider the distribution ofthe distribution ofvelocity close to a plane wallvelocity close to a plane wall; different quantities of widespread; different quantities of widespread
use in CFD are introduced at this stageuse in CFD are introduced at this stage
AA universal logarithmic velocity profileuniversal logarithmic velocity profile is found both on theis found both on the
basis of simple theoretical considerations and experimentsbasis of simple theoretical considerations and experiments
General remarks on turbulent flowGeneral remarks on turbulent flowMomentum Transfer in Turbulent FlowMomentum Transfer in Turbulent Flow -- 44
-
7/30/2019 Lappeenranta WA 1 CFD
16/69
1616
The effect of turbulence in the transport of momentum can beThe effect of turbulence in the transport of momentum can beclearly seen in comparing the distributions of velocity in theclearly seen in comparing the distributions of velocity in the
classical case of a circular pipe for laminar and turbulent flowclassical case of a circular pipe for laminar and turbulent flowss
The flatter profile observed in the case of turbulent flow is thThe flatter profile observed in the case of turbulent flow is thee
direct consequence of thedirect consequence of the increasing efficiency in momentumincreasing efficiency in momentum
transfer far from the walltransfer far from the wall due to the mixing promoted bydue to the mixing promoted by
turbulenceturbulence
General remarks on turbulent flowGeneral remarks on turbulent flowMomentum Transfer in Turbulent FlowMomentum Transfer in Turbulent Flow -- 55
-
7/30/2019 Lappeenranta WA 1 CFD
17/69
1717
TheThe averaged total energy equationaveraged total energy equation and theand the steady thermalsteady thermalenergy equation in terms of temperatureenergy equation in terms of temperature can be written ascan be written as
Also in these cases additional terms to be modelled appear, e.g.Also in these cases additional terms to be modelled appear, e.g.::
The rationale for evaluating the turbulent contribution is similThe rationale for evaluating the turbulent contribution is similarar
as in the case of momentumas in the case of momentum
wherewhere TT is theis the turbulent thermal diffusivityturbulent thermal diffusivity
General remarks on turbulent flowGeneral remarks on turbulent flowHeat Transfer in Turbulent FlowHeat Transfer in Turbulent Flow -- 11
-
7/30/2019 Lappeenranta WA 1 CFD
18/69
1818
The picture of the turbulent transfer phenomenon is thereforeThe picture of the turbulent transfer phenomenon is thereforethe same as for momentum:the same as for momentum:
The relation between the two turbulent diffusivities of heat andThe relation between the two turbulent diffusivities of heat and
momentum poses an additional problemmomentum poses an additional problem
General remarks on turbulent flowGeneral remarks on turbulent flowHeat Transfer in Turbulent FlowHeat Transfer in Turbulent Flow -- 22
-
7/30/2019 Lappeenranta WA 1 CFD
19/69
1919
A simple but effective way to establish this relationship is toA simple but effective way to establish this relationship is todefine a constantdefine a constant turbulentturbulent PrandtlPrandtl numbernumber,, in analogy within analogy with
the molecular one assuming that, as a consequence of thethe molecular one assuming that, as a consequence of the
Reynolds analogy, this could be in the range of unityReynolds analogy, this could be in the range of unity
The assumptionThe assumption in this casein this case is that the same coherentis that the same coherent
structures carrying momentum are also responsible of heatstructures carrying momentum are also responsible of heat
transfertransfer
However,However, this assumption holds acceptably for fluids havingthis assumption holds acceptably for fluids having
nearly unity molecularnearly unity molecular PrandtlPrandtl numbernumber; in the other cases,; in the other cases,
different approaches should be useddifferent approaches should be used
General remarks on turbulent flowGeneral remarks on turbulent flowHeat Transfer in Turbulent FlowHeat Transfer in Turbulent Flow -- 33
-
7/30/2019 Lappeenranta WA 1 CFD
20/69
2020
In turbulent flow anIn turbulent flow an energy cascadeenergy cascade occurs representing theoccurs representing thetransfer of turbulence kinetic energy from larger to smallertransfer of turbulence kinetic energy from larger to smaller
eddieseddies
Basic concepts about computationalBasic concepts about computational
modelling of turbulent flowsmodelling of turbulent flowsLength Scales in TurbulenceLength Scales in Turbulence -- 11
As such, turbulence can beAs such, turbulence can be
considered asconsidered as a phenomenona phenomenon
characterised by a wide range ofcharacterised by a wide range of
lengthslengths at which interestingat which interesting
phenomena do occur:phenomena do occur:
fromfrom the integral lengththe integral length
scalescale,, llllllll, at which energy is, at which energy isextracted from the mean flowextracted from the mean flow
toto thethe KolmogorovKolmogorov lengthlength
scalescale,, , at which turbulence, at which turbulence
kinetic energy is finallykinetic energy is finally
dissipated into heatdissipated into heat
-
7/30/2019 Lappeenranta WA 1 CFD
21/69
2121
It must be noted that theIt must be noted that the KolmogorovKolmogorov length scale,length scale, ,,
is smallis smallbut still large with respect to the molecularbut still large with respect to the molecular mean free pathmean free path::
so, turbulence can still be studiedso, turbulence can still be studied
basing on the continuum assumptionbasing on the continuum assumption
The integral length scale,The integral length scale, llllllll,, characterising large eddies can becharacterising large eddies can bedefined as the average length over which a fluctuatingdefined as the average length over which a fluctuating
component keeps correlated, i.e. the quantitycomponent keeps correlated, i.e. the quantity is notis not
negligiblenegligible
On both dimensional and experimental basis, it can be shownOn both dimensional and experimental basis, it can be shownthatthat
andand
withwith ; therefore,; therefore,
Basic concepts about computationalBasic concepts about computational
modelling of turbulent flowsmodelling of turbulent flowsLength Scales in TurbulenceLength Scales in Turbulence -- 22
-
7/30/2019 Lappeenranta WA 1 CFD
22/69
2222
Basing on these considerations,Basing on these considerations, it can be concluded that:it can be concluded that:
an adequate representation of turbulence shouldan adequate representation of turbulence should take intotake into
account the phenomena of production and dissipation ofaccount the phenomena of production and dissipation of
turbulence kinetic energy at the different scalesturbulence kinetic energy at the different scales
in this respect,in this respect, two different strategiestwo different strategies can be envisaged:can be envisaged: simulating the transient evolution of vortices of differentsimulating the transient evolution of vortices of different
sizessizes, putting a convenient lower bound for the smallest, putting a convenient lower bound for the smallest
scalescale (DNS, LES, DES)(DNS, LES, DES)
simulating turbulence on the basis of the above describedsimulating turbulence on the basis of the above describedstatistical approachstatistical approach, introducing appropriate production, introducing appropriate production
and dissipation terms to approximately represent theand dissipation terms to approximately represent the
effects of the energy cascadeeffects of the energy cascade (RANS)(RANS)
Basic concepts about computationalBasic concepts about computational
modelling of turbulent flowsmodelling of turbulent flowsLength Scales in TurbulenceLength Scales in Turbulence -- 33
-
7/30/2019 Lappeenranta WA 1 CFD
23/69
2323
Basic concepts about computationalBasic concepts about computational
modelling of turbulent flowsmodelling of turbulent flowsDirect Numerical Simulation (DNS)Direct Numerical Simulation (DNS) -- 11
This methodology follows the former of the two mentionedThis methodology follows the former of the two mentioned
routes,routes, trying to simulate with the highest possible space andtrying to simulate with the highest possible space andtime detail the evolution of vortices of all relevant sizestime detail the evolution of vortices of all relevant sizes
The assumption behind this technique is that theThe assumption behind this technique is that the NavierNavier--StokesStokes
equations are rich enough to describe the turbulent flowequations are rich enough to describe the turbulent flow
behaviour with no need of additional constitutive laws; forbehaviour with no need of additional constitutive laws; forincompressible flow it is:incompressible flow it is:
The web is full of fascinating pictures and movies about DNSThe web is full of fascinating pictures and movies about DNS
resultsresults
-
7/30/2019 Lappeenranta WA 1 CFD
24/69
2424
Basic concepts about computationalBasic concepts about computational
modelling of turbulent flowsmodelling of turbulent flowsDirect Numerical Simulation (DNS)Direct Numerical Simulation (DNS) -- 22
The application of this technique isThe application of this technique is very demanding in terms ofvery demanding in terms of
computational resourcescomputational resources: representing flows of technical: representing flows of technicalinterest is very challenging and requires massive parallelinterest is very challenging and requires massive parallel
computingcomputing
However the technique is very promising and it isHowever the technique is very promising and it is sometimessometimesused to provide data having a similar reliability to experimentsused to provide data having a similar reliability to experiments
with greater detail in local valueswith greater detail in local values
In fact, if used with enough detail, DNS can provide data whichIn fact, if used with enough detail, DNS can provide data which
can be hardly obtained in similar detail with experimentscan be hardly obtained in similar detail with experiments
In addition to be an interesting field of research,In addition to be an interesting field of research, DNS isDNS is
therefore used also to provide data on which empiricaltherefore used also to provide data on which empirical
turbulence model can be validatedturbulence model can be validatedCFDCFD--FigureFigure--1.ppt1.ppt
-
7/30/2019 Lappeenranta WA 1 CFD
25/69
2525
Basic concepts about computationalBasic concepts about computational
modelling of turbulent flowsmodelling of turbulent flowsLarge Eddy Simulation (LES)Large Eddy Simulation (LES) -- 11
At a more reduced level of detail,At a more reduced level of detail, LES is aimed at simulatingLES is aimed at simulating
only larger eddies, while the smaller scales are treated byonly larger eddies, while the smaller scales are treated bysubgridsubgrid--scale (SGS) modelsscale (SGS) models
In other words, there areIn other words, there are two different length scalestwo different length scales::
the large scales that are directly solved as in DNS;the large scales that are directly solved as in DNS; the smaller scales that are treated by SGS modelsthe smaller scales that are treated by SGS models
As such, LES is computationally more efficient than DNS andAs such, LES is computationally more efficient than DNS and
may be also relatively accuratemay be also relatively accurate
A key point in LES is introducing a spatial filtering for theA key point in LES is introducing a spatial filtering for the
smaller scalessmaller scales
-
7/30/2019 Lappeenranta WA 1 CFD
26/69
2626
Basic concepts about computationalBasic concepts about computational
modelling of turbulent flowsmodelling of turbulent flowsLarge Eddy Simulation (LES)Large Eddy Simulation (LES) -- 22
The filters can be of different types:The filters can be of different types:
-
7/30/2019 Lappeenranta WA 1 CFD
27/69
2727
Basic concepts about computationalBasic concepts about computational
modelling of turbulent flowsmodelling of turbulent flowsLarge Eddy Simulation (LES)Large Eddy Simulation (LES) -- 33
-
7/30/2019 Lappeenranta WA 1 CFD
28/69
2828
Basic concepts about computationalBasic concepts about computational
modelling of turbulent flowsmodelling of turbulent flowsLarge Eddy Simulation (LES)Large Eddy Simulation (LES) -- 44
Once the resolvable scales are defined, the averaged NOnce the resolvable scales are defined, the averaged N--S equationsS equationsare written in averaged formare written in averaged form
-
7/30/2019 Lappeenranta WA 1 CFD
29/69
2929
Basic concepts about computationalBasic concepts about computational
modelling of turbulent flowsmodelling of turbulent flowsLarge Eddy Simulation (LES)Large Eddy Simulation (LES) -- 55
The advection term can be manipulated asThe advection term can be manipulated as
or alsoor also
Anyway, introducing theAnyway, introducing the subgridsubgrid--scale stresses (or adopting slightlyscale stresses (or adopting slightly
different definitions)different definitions)
it can be finally obtainedit can be finally obtained
-
7/30/2019 Lappeenranta WA 1 CFD
30/69
3030
Basic concepts about computationalBasic concepts about computational
modelling of turbulent flowsmodelling of turbulent flowsLarge Eddy Simulation (LES)Large Eddy Simulation (LES) -- 66
So,So, the fundamental problem is defining thethe fundamental problem is defining the subgridsubgrid scale stressesscale stresses
In 1963,In 1963, SmagorinskySmagorinsky defined a model based on the followingdefined a model based on the following
equationsequations
where Cwhere CSS is theis the SmagorinskySmagorinsky coefficient representing a parameter tocoefficient representing a parameter tobe adjusted for the particular problem to be dealt with; valuesbe adjusted for the particular problem to be dealt with; values in thein the
range 0.10 to 0.24 have been adopted for typical problemsrange 0.10 to 0.24 have been adopted for typical problems
LESLES is presently promising as a design tool, but still heavy from this presently promising as a design tool, but still heavy from thee
computational point of viewcomputational point of view
-
7/30/2019 Lappeenranta WA 1 CFD
31/69
3131
Basic concepts about computationalBasic concepts about computational
modelling of turbulent flowsmodelling of turbulent flowsReynolds AveragedReynolds Averaged NavierNavier--Stokes (RANS) modelsStokes (RANS) models -- 11
As already mentioned, the Reynolds averaging process leads toAs already mentioned, the Reynolds averaging process leads to
momentum equations in which turbulence is represented bymomentum equations in which turbulence is represented by thetheReynolds stressReynolds stress
TheThe BoussinesqBoussinesq approximation suggests thatapproximation suggests that
Moreover if the Reynolds analogy is adopted by specifying a consMoreover if the Reynolds analogy is adopted by specifying a constanttant
turbulentturbulent PrandtlPrandtl number, also the eddy thermal diffusivity is related tonumber, also the eddy thermal diffusivity is related to
the eddy viscositythe eddy viscosity
So,So, the main problem is reduced to specifying the eddy viscositythe main problem is reduced to specifying the eddy viscosity
2 22
3 3
jiij T ij ij T ij
j i
wwS k k
x x
= = +
-
7/30/2019 Lappeenranta WA 1 CFD
32/69
3232
Basic concepts about computationalBasic concepts about computational
modelling of turbulent flowsmodelling of turbulent flowsReynolds AveragedReynolds Averaged NavierNavier--Stokes (RANS) modelsStokes (RANS) models -- 22
Models of different complexity can be adoptedModels of different complexity can be adopted in this aim, classifiedin this aim, classified
on the basis of the number of the additional partial differentiaon the basis of the number of the additional partial differentiallequations to be solved:equations to be solved:
1.1. Algebraic or zeroAlgebraic or zero--equation modelsequation models
2.2. OneOne--equation modelsequation models
3.3. TwoTwo--equation modelsequation models
An important distinction between turbulence models is anyway theAn important distinction between turbulence models is anyway the
one betweenone between complete and incomplete modelscomplete and incomplete models::
completenesscompleteness of the model is related to its capability toof the model is related to its capability to
automatically define a characteristic length of turbulenceautomatically define a characteristic length of turbulence in a complete model, therefore, only the initial and boundaryin a complete model, therefore, only the initial and boundary
conditions are specifiedconditions are specified, with no need to define case by case, with no need to define case by case
parameters depending on the particular considered flowparameters depending on the particular considered flow
-
7/30/2019 Lappeenranta WA 1 CFD
33/69
3333
Basic concepts about computationalBasic concepts about computational
modelling of turbulent flowsmodelling of turbulent flowsReynolds AveragedReynolds Averaged NavierNavier--Stokes (RANS) modelsStokes (RANS) models -- 33
ALGEBRAIC MODELSALGEBRAIC MODELS
Possibly the best known algebraic model is the one obtained by tPossibly the best known algebraic model is the one obtained by thehemixing length theory ofmixing length theory of PrandtlPrandtl (1925)(1925)
wherewhere llllllllmixmix is the mixing length; the model is similar to the one foris the mixing length; the model is similar to the one for
molecular viscositymolecular viscosity in which kinematic viscosity is a interpreted asin which kinematic viscosity is a interpreted as
the product of a mean molecular velocity by a length (the mean fthe product of a mean molecular velocity by a length (the mean freeree
path)path)
In the presence of a wall, it is assumedIn the presence of a wall, it is assumed where the constantwhere the constantmust be adjusted on an empirical basismust be adjusted on an empirical basis
The mixing length theory has received different reformulations,The mixing length theory has received different reformulations, butbut
its character of incompleteness makes models based on transportits character of incompleteness makes models based on transport
equations to be preferableequations to be preferable
-
7/30/2019 Lappeenranta WA 1 CFD
34/69
3434
Basic concepts about computationalBasic concepts about computational
modelling of turbulent flowsmodelling of turbulent flowsReynolds AveragedReynolds Averaged NavierNavier--Stokes (RANS) modelsStokes (RANS) models -- 44
PARTIAL DIFFERENTIAL EQUATION MODELSPARTIAL DIFFERENTIAL EQUATION MODELS
Referring from here on to the specific Reynolds stress tensorReferring from here on to the specific Reynolds stress tensor
it is possible to derive ait is possible to derive a Reynolds stress transport modelReynolds stress transport model byby
applying the time averaging operator as followsapplying the time averaging operator as follows
wherewhere
it is foundit is found
-
7/30/2019 Lappeenranta WA 1 CFD
35/69
3535
Basic concepts about computationalBasic concepts about computational
modelling of turbulent flowsmodelling of turbulent flowsReynolds AveragedReynolds Averaged NavierNavier--Stokes (RANS) modelsStokes (RANS) models -- 55
This equation showsThis equation shows the typical difficulties encountered whenthe typical difficulties encountered when
trying totrying to closeclose the turbulence equationsthe turbulence equations. In fact:. In fact: the application of the timethe application of the time--averaging operator to theaveraging operator to the NavierNavier--
Stokes equations makes the Reynolds stress tensor toStokes equations makes the Reynolds stress tensor to
appear as a SECOND ORDER tensor ofappear as a SECOND ORDER tensor of correlationcorrelation betweenbetween
two fluctuating velocity componentstwo fluctuating velocity components
the derivation of transport equations for the Reynolds stressthe derivation of transport equations for the Reynolds stresstensor makestensor makes HIGHER ORDER correlation terms to appearHIGHER ORDER correlation terms to appear
The transport equation for turbulent kinetic energy can be obtaiThe transport equation for turbulent kinetic energy can be obtainedned
by taking the trace of the system of Reynolds stress transportby taking the trace of the system of Reynolds stress transportequations; in factequations; in fact
-
7/30/2019 Lappeenranta WA 1 CFD
36/69
3636
Basic concepts about computationalBasic concepts about computational
modelling of turbulent flowsmodelling of turbulent flowsReynolds AveragedReynolds Averaged NavierNavier--Stokes (RANS) modelsStokes (RANS) models -- 66
The k equation has the formThe k equation has the form
The Reynolds stress appearing in this equation has the formThe Reynolds stress appearing in this equation has the form
and the dissipation term has the formand the dissipation term has the form
and is evaluated by the relationshipand is evaluated by the relationship
-
7/30/2019 Lappeenranta WA 1 CFD
37/69
3737
Basic concepts about computationalBasic concepts about computational
modelling of turbulent flowsmodelling of turbulent flowsReynolds AveragedReynolds Averaged NavierNavier--Stokes (RANS) modelsStokes (RANS) models -- 77
AA one equation model wasone equation model was proposed byproposed by PrandtlPrandtl in the formin the form
withwith the additional closure equationthe additional closure equation
In general, oneIn general, one--equation models are incomplete, since theequation models are incomplete, since the
turbulence length scale,turbulence length scale, llllllll , must be defined on a case by case basis;, must be defined on a case by case basis;complete versions are anyway available which specifycomplete versions are anyway available which specify
independently this length (e.g., Baldwinindependently this length (e.g., Baldwin-- Barth, 1990).Barth, 1990).
In order to obtain complete models,In order to obtain complete models, an additional quantity must bean additional quantity must be
defineddefined also subjected to a transport equationalso subjected to a transport equation
-
7/30/2019 Lappeenranta WA 1 CFD
38/69
3838
Basic concepts about computationalBasic concepts about computational
modelling of turbulent flowsmodelling of turbulent flowsReynolds AveragedReynolds Averaged NavierNavier--Stokes (RANS) modelsStokes (RANS) models -- 88
TwoTwo--equation modelsequation models are mostly based on the definition of thisare mostly based on the definition of this
further quantity in the form offurther quantity in the form of oror basing on the followingbasing on the followingrelationships thatrelationships that closeclose the problem (other versions are available)the problem (other versions are available)
forfor kk-- models it ismodels it is
in particular for the Wilcox (1998) model it isin particular for the Wilcox (1998) model it is
with appropriate values of the constants and, in particular:with appropriate values of the constants and, in particular:
-
7/30/2019 Lappeenranta WA 1 CFD
39/69
3939
Basic concepts about computationalBasic concepts about computational
modelling of turbulent flowsmodelling of turbulent flowsReynolds AveragedReynolds Averaged NavierNavier--Stokes (RANS) modelsStokes (RANS) models -- 99
forfor kk-- models it ismodels it is
the dissipation equation can be derived exactly and has thethe dissipation equation can be derived exactly and has the
classical formclassical form
TheThe standardstandard kk-- modelmodel adopts the definitionsadopts the definitions
-
7/30/2019 Lappeenranta WA 1 CFD
40/69
4040
Basic concepts about computationalBasic concepts about computational
modelling of turbulent flowsmodelling of turbulent flowsReynolds AveragedReynolds Averaged NavierNavier--Stokes (RANS) modelsStokes (RANS) models -- 1010
As presented, the above turbulence models are mostly suited forAs presented, the above turbulence models are mostly suited for
dealing with turbulence conditions far from wallsdealing with turbulence conditions far from walls
When wall phenomena must be dealt withWhen wall phenomena must be dealt with two possible approachestwo possible approaches
are available:are available:
use ofuse of wall functionswall functions:: the logarithmic trend observed forthe logarithmic trend observed for
velocity close to a flat surface is assumed to holdvelocity close to a flat surface is assumed to holdapproximately near the specific considered wall, togetherapproximately near the specific considered wall, together
with a corresponding temperature trend;with a corresponding temperature trend; in this case, thein this case, the
value of y+ in the first node close to the wall must bevalue of y+ in the first node close to the wall must be
conveniently large (e.g., y+ > 30conveniently large (e.g., y+ > 30););
use of low Reynolds number models:use of low Reynolds number models: these models arethese models areconceived to simulate the actual trend of turbulence close toconceived to simulate the actual trend of turbulence close to
the wall, by the adoption ofthe wall, by the adoption of damping functionsdamping functions;; the value ofthe value of
y+ in the first node must be very small (typically y+
-
7/30/2019 Lappeenranta WA 1 CFD
41/69
4141
Basic concepts about computationalBasic concepts about computational
modelling of turbulent flowsmodelling of turbulent flowsReynolds AveragedReynolds Averaged NavierNavier--Stokes (RANS) modelsStokes (RANS) models -- 1111
On one hand,On one hand, the use of wall functions is computationallythe use of wall functions is computationally
convenientconvenient, since refining the mesh close to the wall is expensive in, since refining the mesh close to the wall is expensive interms of resources (see the figure fromterms of resources (see the figure from SharabiSharabi, 2008), 2008)
On the other hand,On the other hand, wall functions are not able to properly detectwall functions are not able to properly detect
some boundary layer phenomenasome boundary layer phenomena for which they were notfor which they were not
conceived (e.g., buoyancy effects in heat transfer, etc.)conceived (e.g., buoyancy effects in heat transfer, etc.)
Nevertheless, even lowNevertheless, even low--Reynolds number models are not alwaysReynolds number models are not always
completely accuratecompletely accurate
(a) Wall functions mesh (b) Low-Reynolds number mesh
-
7/30/2019 Lappeenranta WA 1 CFD
42/69
4242
Basic concepts about computationalBasic concepts about computational
modelling of turbulent flowsmodelling of turbulent flowsDamping functions in lowDamping functions in low--Re modelsRe models
InIn lowlow--Reynolds number modelsReynolds number models the definition of eddy viscosity isthe definition of eddy viscosity is
changed from the classical formulationchanged from the classical formulation
to various forms includingto various forms including damping functions,damping functions, ff
that provide forthat provide for the decrease of the eddy viscosity whilethe decrease of the eddy viscosity while
approaching the wallapproaching the wall
This allowsThis allows integration of the turbulence models through theintegration of the turbulence models through the
boundary layer up to the wall itselfboundary layer up to the wall itself
Different assumptions lead to various formulations of the lowDifferent assumptions lead to various formulations of the low--ReRe
models and, generally, to different resultsmodels and, generally, to different results
2T C f k = 0 0f for y
-
7/30/2019 Lappeenranta WA 1 CFD
43/69
4343
Basic concepts about computationalBasic concepts about computational
modelling of turbulent flowsmodelling of turbulent flowsLowLow--Re models vs. wall functionsRe models vs. wall functions
Providing an answer toProviding an answer to the questionthe question if the use of wall functionsif the use of wall functions
should be preferred or notshould be preferred or not to models having a lowto models having a low--Re capabilityRe capability isisnot trivial, since:not trivial, since:
it heavily depends on the applicationit heavily depends on the application
it is strictly linked to the purpose of the analysisit is strictly linked to the purpose of the analysis
In this lecture I will proposeIn this lecture I will propose a case in whicha case in which WFsWFs are not applicableare not applicable,,since they completely overlook phenomena related to buoyancysince they completely overlook phenomena related to buoyancy
In a lecture to come on condensation,In a lecture to come on condensation, I will show that the use ofI will show that the use of
some minimum lowsome minimum low--Re number capabilities is useful to get relativelyRe number capabilities is useful to get relatively
good agreement with experimental data though approximategood agreement with experimental data though approximatemethod are also acceptablemethod are also acceptable; however, pending questions are:; however, pending questions are:
could we afford describing a whole nuclear reactorcould we afford describing a whole nuclear reactor
containment with such a strong refinement at the walls?containment with such a strong refinement at the walls?
couldncouldnt we instead accept a more approximate view of localt we instead accept a more approximate view of local
phenomena to get a reasonable overall picture?phenomena to get a reasonable overall picture?
-
7/30/2019 Lappeenranta WA 1 CFD
44/69
4444
Basic concepts about computationalBasic concepts about computational
modelling of turbulent flowsmodelling of turbulent flowsAnisotropic RANSAnisotropic RANS -- 11
This choice is anyway heavyfor the number of equationsto be solved
A further possibility is to usean anisotropic RANS modelsin which the simpleBoussinesq approximation isabandoned
The assumption of an isotropic value ofThe assumption of an isotropic value of TT is not suitable foris not suitable forsimulating details of flow in noncircular passagessimulating details of flow in noncircular passages
This is particularly true forThis is particularly true for secondary flowssecondary flows in the directionin the direction
orthogonal to the main flow that would require the fullorthogonal to the main flow that would require the full
Reynolds stress transport models to be predictedReynolds stress transport models to be predicted
RSM application fromRSM application from SharabiSharabi (2008)(2008)
-
7/30/2019 Lappeenranta WA 1 CFD
45/69
4545
Basic concepts about computationalBasic concepts about computational
modelling of turbulent flowsmodelling of turbulent flowsAnisotropic RANSAnisotropic RANS -- 22
In particular, it is possible to useIn particular, it is possible to use algebraic expressionsalgebraic expressions of the kindof the kind
(see e.g.,(see e.g., BagliettoBaglietto et al., 2006) which is limited to second orderet al., 2006) which is limited to second order
terms in the strain and the rotational ratesterms in the strain and the rotational rates SSijij andand ijij with respectwith respect
to the original third order formulationto the original third order formulation
((BagliettoBaglietto et al., 2006)et al., 2006)
-
7/30/2019 Lappeenranta WA 1 CFD
46/69
4646
TwoTwo--phase flow applicationsphase flow applicationsFew general considerationsFew general considerations
TwoTwo--phase flow introducesphase flow introduces additional complexityadditional complexity to theto the
already complex problem of simulating turbulent flowalready complex problem of simulating turbulent flow
The presence of two phases and ofThe presence of two phases and of the related interfacesthe related interfacesrequires particular care in modellingrequires particular care in modelling
Ambitious goals of modelling twoAmbitious goals of modelling two--phase flow with CFDphase flow with CFDwould be, for instance, to represent important phenomenawould be, for instance, to represent important phenomenalike CHF from first principleslike CHF from first principles
-
7/30/2019 Lappeenranta WA 1 CFD
47/69
4747
TwoTwo--phase flow applicationsphase flow applicationsFew general considerations (contFew general considerations (contd)d)
The work in the application of CFD techniques to twoThe work in the application of CFD techniques to two--phase flowsphase flows
was developed for more than a decade, though nowadays it is stilwas developed for more than a decade, though nowadays it is stil llnoted that thenoted that the obtained models are not yet so mature as the onesobtained models are not yet so mature as the ones
for singlefor single--phase flowsphase flows (foreword to(foreword to NuclNucl. Eng. Des., 240 (2010)). Eng. Des., 240 (2010))
The field is therefore one of active research, requiringThe field is therefore one of active research, requiring hugehuge
computational resources;computational resources; the brand name of Computational Multithe brand name of Computational Multi--Fluid Dynamics (CMFD) was proposed for this field of research byFluid Dynamics (CMFD) was proposed for this field of research by
Prof.Prof.YadigarogluYadigaroglu (Int. J.(Int. J. MultiphMultiph. Flow, 23, 2003). Flow, 23, 2003)
In principle, DNS, LES and RANS techniques can be all usedIn principle, DNS, LES and RANS techniques can be all used for twofor two--
phase flowphase flow, though the scenario of their application is strongly, though the scenario of their application is stronglychanged with respect to singlechanged with respect to single--phasephase
In particular, in addition to the integral length scale and theIn particular, in addition to the integral length scale and the
smallest turbulent scale,smallest turbulent scale, the scales of twothe scales of two--phase flow structuresphase flow structures
(e.g., bubbles)(e.g., bubbles) are called into playare called into play
-
7/30/2019 Lappeenranta WA 1 CFD
48/69
4848
TwoTwo--phase flow applicationsphase flow applicationsFew general considerations (contFew general considerations (contd)d)
In the case of theIn the case of the RANS approachRANS approach,, mass energy and momentum balancemass energy and momentum balanceequationsequations are written inare written in 3D geometry3D geometry for each phase k (see e.g.,for each phase k (see e.g., BestionBestion
et al. 2005;et al. 2005; MimouniMimouni et al., 2008,et al., 2008, GalassiGalassi et al., 2009 for NEPTUNE)et al., 2009 for NEPTUNE)
These equations are accompanied by an extension to twoThese equations are accompanied by an extension to two--phase flow ofphase flow ofaakk-- modelmodel
where additional terms ofwhere additional terms of turbulence productionturbulence production appear due to theappear due to theinteraction between the phases.interaction between the phases.
AnAn interfacial area concentration transport equationinterfacial area concentration transport equation is also usedis also used
( ) kkkkkk w
t=+
( ) ( )Tk k k k k k k k k k k k k k
ww w p M g
t
+ = + + + +
( )2 2 2
, , ,2 2 2
Tk k kk k k k k k k k k k k k k i k i i w k k k k
w w wph h w g w h q a q q q
t t
+ + + = + + + + + +
[ ],1
Production terms
Tik k k k
k k i k k k K
i k j K j
k k kw P
t x x x
+ = + +
[ ], 1 11
C Production terms C
Tik k k k k
k k i k k k
i k j j k
w Pt x x x k
+ = + +
-
7/30/2019 Lappeenranta WA 1 CFD
49/69
4949
TwoTwo--phase flow applicationsphase flow applicationsFew general considerations (contFew general considerations (contd)d)
Needless to say,Needless to say, this model relies on thethis model relies on the BoussinesqBoussinesq
assumptionassumption; turbulent viscosity is moreover given simply by; turbulent viscosity is moreover given simply by
Its is quite clear thatIts is quite clear that the success of such a model is strictlythe success of such a model is strictlylinked to its ingredients in terms of constitutive relationshipslinked to its ingredients in terms of constitutive relationships
that must be suitable for the particular considered flow regimethat must be suitable for the particular considered flow regime In particular, for a bubbly flow the momentum transfer term,In particular, for a bubbly flow the momentum transfer term,
MMkk, should account for, should account for mass transfermass transfer, the, the dragdrag andand liftlift forces,forces,thethe addedadded mass termmass term and theand the turbulent dispersion of bubblesturbulent dispersion of bubbles
A major lack of RANS approaches is anyway in the fact thatA major lack of RANS approaches is anyway in the fact thatsome twosome two--phase flow fields are naturally unstable:phase flow fields are naturally unstable: timetimeaveraging is therefore suitable only to have a globalaveraging is therefore suitable only to have a globalaveragedaveragedpicturepicture of what happens, loosing instantaneous details (seeof what happens, loosing instantaneous details (seee.g., the discussion ine.g., the discussion inYadigarogluYadigaroglu et al., 2008)et al., 2008)
k
kk
T
k
kC
2
=
-
7/30/2019 Lappeenranta WA 1 CFD
50/69
5050
By the way, unsteady calculations with RANS may showBy the way, unsteady calculations with RANS may show
oscillations that may somehow match with experimentaloscillations that may somehow match with experimentalobservations (observations (ZborayZboray and Deand De CahardCahard, 2005), 2005)
LES modelsLES models, of course, reintroduce the possibility to address, of course, reintroduce the possibility to address
varying flow fields like the fluctuations of bubble plumes; suchvarying flow fields like the fluctuations of bubble plumes; such
applications are interestingly discussed, among the others, byapplications are interestingly discussed, among the others, by
YadigarogluYadigaroglu et al., (2008) and in works there referred to, andet al., (2008) and in works there referred to, and
byby NicenoNiceno et al., (2008)et al., (2008)
In such discussions, it can be noted that, in similarity with thIn such discussions, it can be noted that, in similarity with theecase of RANS,case of RANS, LES models require accurate closure models forLES models require accurate closure models for
the different terms appearing in the equations in addition tothe different terms appearing in the equations in addition to
adequate SGS modelsadequate SGS models
TwoTwo--phase flow applicationsphase flow applicationsFew general considerations (contFew general considerations (contd)d)
-
7/30/2019 Lappeenranta WA 1 CFD
51/69
5151
LaheyLahey (2009) recently discussed the capabilities of(2009) recently discussed the capabilities of DNSDNS
modelsmodels in representing twoin representing two--phase flowsphase flows As in case of singleAs in case of single--phase flow, the attractiveness of thisphase flow, the attractiveness of this
technique lies in the fact that there is no need totechnique lies in the fact that there is no need tointroduce empirical models to obtain accurateintroduce empirical models to obtain accuratepredictions; the obvious drawback is the heavypredictions; the obvious drawback is the heavy
computational loadcomputational load
In the case of twoIn the case of two--phase flows,phase flows, interface trackinginterface trackingalgorithmsalgorithms must be introduced; in the mentioned paper,must be introduced; in the mentioned paper,an algorithm based on the signed distance form thean algorithm based on the signed distance form theinterface is used in the PHASTA codeinterface is used in the PHASTA code
Dam break problems, bubble interactions and plungingDam break problems, bubble interactions and plungingjets are within the predictive capabilities, wheneverjets are within the predictive capabilities, wheneverappropriate computational resources are made availableappropriate computational resources are made available
CFDCFD--FigureFigure--2.ppt2.ppt
TwoTwo--phase flow applicationsphase flow applicationsFew general considerations (contFew general considerations (contd)d)
-
7/30/2019 Lappeenranta WA 1 CFD
52/69
5252
Prediction of heat transfer deteriorationPrediction of heat transfer deteriorationAddressed experimental dataAddressed experimental data
As in Sharabi et al. [2007], the considered experimental
data are those by Pismenny et al. [2006]:
National Technological University of Ukraine
turbulent heat transfer in vertical tubes for supercriticalwater
operating pressure of23.5 MPa inlet temperature and heating conditions involved in these
analyses resulted in both dense and gas-like fluid to bepresent in the test section
thin wall stainless steel tubes with inner diameters of 6.28and 9.50 mm were adopted, with a 600 mm long heated
section preceded by a 64 diameters long unheated region cromel-alumel thermocouples were adopted to measure
the inlet and outlet fluid temperature, as well as the outertemperature of the tubes.
-
7/30/2019 Lappeenranta WA 1 CFD
53/69
5353
Prediction of heat transfer deteriorationPrediction of heat transfer deteriorationPrevious resultsPrevious results
Previous results obtained by Sharabi et al. [2007] with anin-house code
(AKN = Abe et al. [1994]; CH = Chien [1982]; JL = Jones and Launder [1972];LB = Lam and Bremhorst, [1981]; LS = Launder and Sharma [1974]; YS =Yang and Shih [1993], WI=Wilcox [1994], SP=Speziale et al. [1990])
a) 6.28 mm ID, q=390 kW/m
2, G= 590 kg/(m
2s),
Tinlet =300 C, upward flowb) 6.28 mm ID, q=390 kW/m
2, G= 590 kg/(m
2s),
Tinlet =300 C, downward flow
-
7/30/2019 Lappeenranta WA 1 CFD
54/69
5454
It can be noted that:
k- models predict in a qualitatively reasonable way the onsetof heat transfer deterioration occurring in upward flow
however, despite of quantitative differences between theresults of the different k- models, they all tend to predict a
larger wall temperature increase than observed on the other hand, the Wilcox [1994] k- model (WI) and the
Speziale et al. [1990] k- model (SP) were seen to predict nodeterioration or a very delayed one
in the case of upward flow, all the models provided similar
results, characterised by the absence of any deteriorationphenomenon, in qualitative agreement with experimentalobservations
Prediction of heat transfer deteriorationPrediction of heat transfer deteriorationPrevious results (contPrevious results (contd)d)
-
7/30/2019 Lappeenranta WA 1 CFD
55/69
5555
Velocity distribution predicted by the YS model
(upward flow, G=509 kg/(m2s), q=390 kW/m2,
tin=300 C)
Velocity distribution predicted by the
WImodel (upward flow, with G=509
kg/(m2s), q=390 kW/m2, tin=300 C)
(Longer pipe)
Buoyancy forces accelerate
the flow at the wall and leadto an m-shaped velocityprofile
Reasons for Heat
TransferDeterioration
Prediction of heat transfer deteriorationPrediction of heat transfer deteriorationPrevious results (contPrevious results (contd)d)
-
7/30/2019 Lappeenranta WA 1 CFD
56/69
5656
Turbulent kinetic energy distribution predicted
by the YS model (upward flow, G=509 kg/(m2s),
q=390 kW/m2, tin=300 C)
Turbulent kinetic energy distribution
predicted by the WImodel (upward
flow, G=509 kg/(m2s), q=390 kW/m2,
tin=300 C)
(Longer pipe)
In the transition to the m-shapedprofile velocity gradients are
suppressed and turbulenceproduction decreases
Prediction of heat transfer deteriorationPrediction of heat transfer deteriorationPrevious results (contPrevious results (contd)d)
-
7/30/2019 Lappeenranta WA 1 CFD
57/69
5757
With the STAR-CCM+ code, the following modelling choices weremade:
The adopted 2D axi-symmetric mesh included 20 radial nodes in a 0.54 mm thick prismatic layer region close to the
wall
26 uniform nodes in the remaining core region, having a radius of 2.6mm
The stretching factor adopted in the prismatic layer was 1.2
Trimmed meshes were selected for the core region
Though slightly coarser than in the in-house code calculations, the gridwas found to be suitable to provide enough accurate results with areasonable computational effort
Later, the results obtained by this grid have been compared to thoseobtained by a finer one (68 radial and 500 axial nodes) showing littledifferences
Default code options were adopted in relation to advection schemes
(2nd order) The steady-state iteration algorithm of the code was adopted, starting
with coupled flow and energy iterations and then shifting to thesegregated equation approach
In all the code runs, it was checked that the requirement y+ < 1 wasrespected with due margin
Prediction of heat transfer deteriorationPrediction of heat transfer deteriorationSTARSTAR--CCM+ ResultsCCM+ Results
-
7/30/2019 Lappeenranta WA 1 CFD
58/69
5858
Concerning water properties at 23.5 MPa, the code allows assigningthe dependence of density and specific heat on temperature in
polynomial form Thermal conductivity and dynamic viscosity can be instead assigned
adopting user defined field functions.
Suitable local cubic spline polynomials were then used for theseproperties, whose coefficients were generated on the basis of tablesobtained by the NIST package
0
200
400
600
800
1000
1200
0 200 400 600 800 1000 1200 1400 1600 1800 2000
Temperature [K]
Density[kg/m
3]
Data
Splines
Interval Boundaries
0
20000
40000
60000
80000
100000
120000
140000
160000
180000
200000
0 200 400 600 800 1000 1200 1400 1600 1800 2000
Temperature [K]
C
p[J/(kgK)]
Data
Splines
Interval Boundaries
0.0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0 200 400 600 800 1000 1200 1400 1600 1800 2000
Temperature [K]
ThermalC
onductivity[W/(mK)]
Data
Splines
Interval Boundaries
0.0E+00
2.0E-04
4.0E-04
6.0E-04
8.0E-04
1.0E-03
1.2E-03
1.4E-03
1.6E-03
1.8E-03
2.0E-03
0 200 400 600 800 1000 1200 1400 1600 1800 2000
Temperature [K]
DynamicViscosity[kg/(ms)]
Data
Splines
Interval Boundaries
0
20000
40000
60000
80000
100000
120000
140000
160000
180000
200000
640 645 650 655 660 665 670 675 680
Temperature [K]
C
p[J/(kgK)]
Data
Splines
Interval Boundaries
0.00
0.05
0.10
0.15
0.20
0.25
0.30
0.35
0.40
0.45
0.50
640 650 660 670 680 690 700
Temperature [K]
ThermalC
onductivity[W/(mK)]
Data
Splines
Interval Boundaries
Prediction of heat transfer deteriorationPrediction of heat transfer deteriorationSTARSTAR--CCM+ Results (contCCM+ Results (contd)d)
-
7/30/2019 Lappeenranta WA 1 CFD
59/69
5959
The analysis reported herein was limited to four k- models:
the Two-Layer All y+ Wall Treatment (referred to in the following asall y+), suggested for simulating with a reasonable accuracydifferent kinds of flows;
the standard Low-Reynolds Number K-Epsilon Model (referred to in
the following as low-Re) suggested by code guidelines for naturalconvection problems and referred to a model published by Lien etal. [1996];
the AKN model, already used with the in-house code [Abe et al.,1994];
the V2F model that, besides the k and equations, solves twoadditional transport and algebraic equations; this model issuggested to capture more accurately near wall phenomena[Durbin, 1991; Durbin, 1996; Lien et al., 1998].
Prediction of heat transfer deteriorationPrediction of heat transfer deteriorationSTARSTAR--CCM+ Results (contCCM+ Results (contd)d)
-
7/30/2019 Lappeenranta WA 1 CFD
60/69
6060
300
400
500
600
700
800
900
0 20 40 60 80 100
x / D
WallTemperature[C]
Low-ReAKN
V2F
All y+
Low-Re (finer mesh)
Experiment
a) 6.28 mm ID, q=390 kW/m
2, G= 590 kg/(m
2s),
Tinlet =300 C, upward flow
Prediction of heat transfer deteriorationPrediction of heat transfer deteriorationSTARSTAR--CCM+ Results (contCCM+ Results (contd)d)
-
7/30/2019 Lappeenranta WA 1 CFD
61/69
6161
300
400
500
600
700
800
900
0 20 40 60 80 100
x / D
WallTem
perature[C]
Low-Re
AKN
V2F
All y+
Experiment
a) 6.28 mm ID, q=390 kW/m
2, G= 590 kg/(m
2s),
Tinlet =300 C, downward flow
Prediction of heat transfer deteriorationPrediction of heat transfer deteriorationSTARSTAR--CCM+ Results (contCCM+ Results (contd)d)
-
7/30/2019 Lappeenranta WA 1 CFD
62/69
6262
It can be noted that:
the Two-Layer All y+ Wall Treatment was unable to detectthe start of deterioration phenomena in upward flow
all the other k- models showed a behaviour similar to theone already observed in the previous study:
they are able to detect the onset of deterioration they tend to overestimate the effect of deterioration on wall
temperature prediction
all the models have no difficulty to predict the behaviourobserved in downward flow, in which no deterioration was
detected
The reasons of this behaviour were found to be the same asobserved in the previous study (see below)
Prediction of heat transfer deteriorationPrediction of heat transfer deteriorationSTARSTAR--CCM+ Results (contCCM+ Results (contd)d)
-
7/30/2019 Lappeenranta WA 1 CFD
63/69
6363
0
0.2
0.4
0.6
0.8
1
1.2
0.0000 0.0005 0.0010 0.0015 0.0020 0.0025 0.0030 0.0035
Radius [m]
X-VelocityComponent[m/s] Pipe Inlet
0
16
32
48
64
80
88
Low-Re Model, Upward Flow
x/D
0
0.2
0.4
0.6
0.8
1
1.2
0.0000 0.0005 0.0010 0.0015 0.0020 0.0025 0.0030 0.0035
Radius [m]
X-VelocityComponent[m/s] Pipe Inlet
0
16
32
48
64
80
88
AKN Model, Upwar d Flow
x/D
0
0.2
0.4
0.6
0.8
1
1.2
0.0000 0.0005 0.0010 0.0015 0.0020 0.0025 0.0030 0.0035
Radius [m]
X-VelocityCompo
nent[m/s] Pipe Inlet
0
16
3248
64
80
88
V2F Model, Upward Flow
x/D
0
0.2
0.4
0.6
0.8
1
1.2
0.0000 0.0005 0.0010 0.0015 0.0020 0.0025 0.0030 0.0035
Radius [m]
X-VelocityCompo
nent[m/s] Pipe Inlet
0
16
3248
64
80
88
All y+ Model, Upward Flow
x/D
Figure 1: Radial distribution of the axial velocity component in the upward flow case
Prediction of heat transfer deteriorationPrediction of heat transfer deteriorationSTARSTAR--CCM+ Results (contCCM+ Results (contd)d)
-
7/30/2019 Lappeenranta WA 1 CFD
64/69
6464
0.000
0.001
0.002
0.003
0.004
0.005
0.006
0.007
0.008
0.0000 0.0005 0.0010 0.0015 0.0020 0.0025 0.0030 0.0035
Radius [m]
TurbulentKineticEnergy[J/kg]
Pipe Inlet
0
16
32
48
64
80
88
Low-Re Model, Upward Flow
x/D
0.000
0.001
0.002
0.003
0.004
0.005
0.006
0.007
0.008
0.0000 0.0005 0.0010 0.0015 0.0020 0.0025 0.0030 0.0035
Radius [m]
TurbulentKineticEnergy[J/kg]
Pipe Inlet
0
16
32
48
64
80
88
AKN Model, Upward Flow
x/D
0.000
0.001
0.002
0.003
0.004
0.005
0.006
0.007
0.008
0.0000 0.0005 0.0010 0.0015 0.0020 0.0025 0.0030 0.0035
Radius [m]
TurbulentKineticEn
ergy[J/kg] Pipe Inlet
0
16
3248
64
80
88
V2F Model, Upward Flow
x/D
0.000
0.001
0.002
0.003
0.004
0.005
0.006
0.007
0.008
0.0000 0.0005 0.0010 0.0015 0.0020 0.0025 0.0030 0.0035
Radius [m]
TurbulentKineticEn
ergy[J/kg] Pipe Inlet
0
16
3248
64
80
88
All y+ Model, Upward Flow
x/D
Figure 1: Radial distribution of turbulent kinetic energy in the upward flow case
Prediction of heat transfer deteriorationPrediction of heat transfer deteriorationSTARSTAR--CCM+ Results (contCCM+ Results (contd)d)
P di ti f h t t f d t i ti
-
7/30/2019 Lappeenranta WA 1 CFD
65/69
6565
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
0.0000 0.0005 0.0010 0.0015 0.0020 0.0025 0.0030 0.0035
Radius [m]
X-VelocityComponent[m/s] Pipe Inlet
0
16
32
48
64
80
88
Low-Re Model, Downward Flow
x/D
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
0.0000 0.0005 0.0010 0.0015 0.0020 0.0025 0.0030 0.0035
Radius [m]
X-VelocityComponent[m/s] Pipe Inlet
0
16
32
48
64
80
88
AKN Model, Downward Flow
x/D
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
0.0000 0.0005 0.0010 0.0015 0.0020 0.0025 0.0030 0.0035
Radius [m]
X-VelocityCompo
nent[m/s] Pipe Inlet
0
16
3248
64
80
88
V2F Model, Downward Flow
x/D
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
0.0000 0.0005 0.0010 0.0015 0.0020 0.0025 0.0030 0.0035
Radius [m]
X-VelocityCompo
nent[m/s] Pipe Inlet
0
16
3248
64
80
88
All y+ Model, Downw ard Flow
x/D
Figure 1: Radial distribution of the axial velocity component in the downward flow case
Prediction of heat transfer deteriorationPrediction of heat transfer deteriorationSTARSTAR--CCM+ Results (contCCM+ Results (contd)d)
P di ti f h t t f d t i ti
-
7/30/2019 Lappeenranta WA 1 CFD
66/69
6666
0.000
0.001
0.002
0.003
0.004
0.005
0.006
0.007
0.008
0.0000 0.0005 0.0010 0.0015 0.0020 0.0025 0.0030 0.0035
Radius [m]
TurbulentKineticEnergy[J/kg]
Pipe Inlet0
16
32
48
64
80
88
Low-Re Model, Downward Flow
x/D
0.000
0.001
0.002
0.003
0.004
0.005
0.006
0.007
0.008
0.0000 0.0005 0.0010 0.0015 0.0020 0.0025 0.0030 0.0035
Radius [m]
TurbulentKineticEnergy[J/kg]
Pipe Inlet0
16
32
48
64
80
88
AKN Model, Downward Flow
x/D
0.000
0.001
0.002
0.003
0.004
0.005
0.006
0.007
0.008
0.0000 0.0005 0.0010 0.0015 0.0020 0.0025 0.0030 0.0035
Radius [m]
TurbulentKineticE
nergy[J/kg] Pipe Inlet
0
16
32
48
64
80
88
V2F Model, Downward Flow
x/D
0.000
0.001
0.002
0.003
0.004
0.005
0.006
0.007
0.008
0.0000 0.0005 0.0010 0.0015 0.0020 0.0025 0.0030 0.0035
Radius [m]
TurbulentKineticE
nergy[J/kg] Pipe Inlet
0
16
32
48
64
80
88
All y+ Model, Downward Flow
x/D
Figure 1: Radial distribution of turbulent kinetic energy in the downward flow case
Prediction of heat transfer deteriorationPrediction of heat transfer deteriorationSTARSTAR--CCM+ Results (contCCM+ Results (contd)d)
In summary
-
7/30/2019 Lappeenranta WA 1 CFD
67/69
6767
CFD and CMFD are very powerful tools, whose
capabilities are conditioned to our understanding ofphenomena and to computer power
The smaller is the degree of empiricism we wish tointroduce in the models, the greatest is the computerpower needed
It is a very fascinating world in which smart ideas areneeded to discover newer and newer possibilities
In summaryIn summary
-
7/30/2019 Lappeenranta WA 1 CFD
68/69
6868
ThankThankThankThankThankThankThankThank youyouyouyouyouyouyouyou forforforforforforforfor youryouryouryouryouryouryouryour attentionattentionattentionattentionattentionattentionattentionattention,,,,,,,,
Walter AmbrosiniWalter AmbrosiniWalter AmbrosiniWalter AmbrosiniWalter AmbrosiniWalter AmbrosiniWalter AmbrosiniWalter Ambrosini
-
7/30/2019 Lappeenranta WA 1 CFD
69/69