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11
Basic Concepts about CFD ModelsBasic Concepts about CFD Models
Walter AmbrosiniWalter Ambrosini
Associate Professor in Associate Professor in NuclearNuclear PlantsPlants
at the at the UniversityUniversity ofof PisaPisa
Lappeenranta University of TechnologyLappeenranta University of Technology
Summer School in Heat and Mass TransferSummer School in Heat and Mass TransferAugust 18 August 18 –– 20, 201020, 2010
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 Averaged Reynolds Averaged NavierNavier--Stokes equations (RANS)Stokes equations (RANS)
�� TwoTwo--phase flow applicationsphase flow applications
�� Prediction of heat transfer deterioration Prediction of heat transfer deterioration
33
General remarks on turbulent flowGeneral remarks on turbulent flowInstability of Laminar Flow Instability of Laminar Flow -- 11
•• The transition from laminar flow to turbulence is The transition from laminar flow to turbulence is an example of an example of
flow instabilityflow instability::
→→ beyond a certain threshold, beyond a certain threshold, inertia overcomes viscous inertia overcomes viscous
forcesforces and the motion cannot be anymore orderedand the motion cannot be anymore ordered
→→ this was shown by this was shown by Osborne ReynoldsOsborne Reynolds in a classical in a classical
experimentexperiment
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 Flow Instability of Laminar Flow -- 22
55
→→ free jetsfree jets
→→ wakeswakes
General remarks on turbulent flowGeneral remarks on turbulent flowInstability of Laminar Flow Instability of Laminar Flow -- 33
66
•• In order to study stability of a nonlinear system by analytical In order to study stability of a nonlinear system by analytical
means the methodology of means the methodology of linear stability analysislinear stability analysis is often is often
adoptedadopted
•• This has the objective to determine This has the objective to determine the stability conditions the 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 Flow Instability of Laminar Flow -- 44
EXAMPLES OF TRANSIENT EXAMPLES OF TRANSIENT
ANALYSESANALYSES
CavityCavity
RB ConvectionRB Convection
Buoyant JetBuoyant Jet
77
•• Turbulence introduces a large degree of Turbulence introduces a large degree of ““sensitivity to initial sensitivity to initial
conditions (SIC)conditions (SIC)”” that is typical of that is typical of ““deterministic chaosdeterministic chaos””
•• By this, it is meant that By this, it is meant that turbulent motion is not turbulent motion is not ““randomrandom””, ,
though it appears fluctuating in a similar manner, though it appears fluctuating in a similar manner, since the since the
equations governing the system are well definedequations governing the system are well defined
•• This characteristic is shared with many different This 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 Flow Instability of Laminar Flow -- 55
dRe
dτ = Gr
Ψ12
- L
D f'(Re) Re |Re|
dΨ1
dτ = π Re Ω1 - π
2 Fo Ψ1 + 4
π sin γ (
d
dΩ1
dτ = - π Re Ψ1 - π
2 Fo Ω1 + 4
π cos γ
Heating
Cooling
γ
88
•• Owing to the fluctuating nature of the turbulent flow field, it Owing to the fluctuating nature of the turbulent flow field, it is is
customary (after Reynolds) customary (after Reynolds) to introduce an appropriate time to 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 write The attempt is quite evidently to write equations in terms of equations 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, but This attempt is successful, but fluctuations cannot be forgottenfluctuations cannot be forgotten
General remarks on turbulent flowGeneral remarks on turbulent flowStatistical Treatment of Turbulent Flow Statistical Treatment of Turbulent Flow -- 11
99
•• In particular, In particular, the following quantities have overwhelming the following quantities have overwhelming
importanceimportance
•• Turbulence intensity is strictly related to the turbulence kinetTurbulence intensity is strictly related to the turbulence kinetic ic
energyenergy
•• This is one of the most important quantities adopted in present This 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 Flow Statistical Treatment of Turbulent Flow -- 22
1010
•• The general balance equations in local and instantaneous The general balance equations in local and instantaneous
formulation are then averagedformulation are then averaged making use of the above making use of the above
described averaging operatordescribed averaging operator
•• After simplifications (described in lecture notes), an averaged After 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 equations s
similar to those of laminar flow leaves an additional termsimilar to those of laminar flow leaves an additional term
•• This term, having a clear This term, having a clear ““advectiveadvective”” nature, points out that nature, 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 additional sort of additional ““mixingmixing”” due to turbulencedue to turbulence
General remarks on turbulent flowGeneral remarks on turbulent flowStatistical Treatment of Turbulent Flow Statistical Treatment of Turbulent Flow -- 33
1111
•• In analogy with the molecular motion, the basic idea is thereforIn analogy with the molecular motion, the basic idea is therefore e
to interpret such term as an to interpret such term as an additional diffusion due to additional diffusion due to
turbulenceturbulence
•• The momentum and energy balance equations contain this term The 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 Flow Statistical Treatment of Turbulent Flow -- 44
1212
•• The The ““Reynolds stress tensorReynolds stress tensor”” appears in momentum equationsappears in momentum equations
•• The Reynolds stresses account for the additional momentum The 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 Flow Momentum Transfer in Turbulent Flow -- 11
1313
•• It is then customary to adopt the It is then customary to adopt the ““BoussinesqBoussinesq approximationapproximation””
based on a definition of based 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 ννννννννTT is no more a property of the fluid, but also is no more a property of the fluid, but also
depends on flow. depends on flow.
•• Of course, Of course, the the BoussinesqBoussinesq approximation shifts the toughness approximation 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 Flow Momentum Transfer in Turbulent Flow -- 22
1414
•• By the way, many different kinds of turbulence can be By the way, many different kinds of turbulence can be
envisaged, ranging from ideally homogeneous and isotropic to envisaged, 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 to Eddy viscosity models have therefore the very tough job to
reintroduce the complexity lost in the simple reintroduce the complexity lost in the simple BoussinesqBoussinesq
approximationapproximation
General remarks on turbulent flowGeneral remarks on turbulent flowMomentum Transfer in Turbulent Flow Momentum Transfer in Turbulent Flow -- 33
1515
•• It is rather instructive and useful to consider It is rather instructive and useful to consider the distribution of the distribution of
velocity 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
•• A A universal logarithmic velocity profileuniversal logarithmic velocity profile is found both on the is 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 Flow Momentum Transfer in Turbulent Flow -- 44
1616
•• The effect of turbulence in the transport of momentum can be The effect of turbulence in the transport of momentum can be
clearly seen in comparing the distributions of velocity in the clearly 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 the e
direct consequence of the direct consequence of the increasing efficiency in momentum increasing efficiency in momentum
transfer far from the walltransfer far from the wall due to the mixing promoted by due to the mixing promoted by
turbulenceturbulence
General remarks on turbulent flowGeneral remarks on turbulent flowMomentum Transfer in Turbulent Flow Momentum Transfer in Turbulent Flow -- 55
1717
•• The The averaged total energy equationaveraged total energy equation and the and the steady thermal steady thermal
energy 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 similar ar
as in the case of momentumas in the case of momentum
where where ααααααααTT is the is the ““turbulent thermal diffusivityturbulent thermal diffusivity””
General remarks on turbulent flowGeneral remarks on turbulent flowHeat Transfer in Turbulent Flow Heat Transfer in Turbulent Flow -- 11
1818
•• The picture of the turbulent transfer phenomenon is therefore The picture of the turbulent transfer phenomenon is therefore
the 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 Flow Heat Transfer in Turbulent Flow -- 22
1919
•• A simple but effective way to establish this relationship is to A simple but effective way to establish this relationship is to
define a constant define a constant ““turbulent turbulent PrandtlPrandtl numbernumber””,, in analogy with in analogy with
the molecular one assuming that, as a consequence of the the 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 case in this case is that the same coherent is that the same coherent
structures carrying momentum are also responsible of heat structures carrying momentum are also responsible of heat
transfertransfer
•• However, However, this assumption holds acceptably for fluids having this assumption holds acceptably for fluids having
nearly unity molecular nearly 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 Flow Heat Transfer in Turbulent Flow -- 33
2020
•• In turbulent flow an In turbulent flow an ““energy cascadeenergy cascade”” occurs representing the occurs representing the
transfer of turbulence kinetic energy from larger to smaller transfer of turbulence kinetic energy from larger to smaller
eddieseddies
Basic concepts about computational Basic concepts about computational
modelling of turbulent flowsmodelling of turbulent flowsLength Scales in Turbulence Length Scales in Turbulence -- 11
•• As such, turbulence can be As such, turbulence can be
considered as considered as a phenomenon a phenomenon
characterised by a wide range of characterised by a wide range of
lengthslengths at which interesting at which interesting
phenomena do occur:phenomena do occur:
→→ from from the integral length the integral length scalescale, , llllllll, at which energy is , at which energy is
extracted from the mean flowextracted from the mean flow
→→ to to the the KolmogorovKolmogorov length length
scalescale, , ηηηηηηηη, at which turbulence , at which turbulence kinetic energy is finally kinetic energy is finally
dissipated into heatdissipated into heat
2121
•• It must be noted that the It must be noted that the KolmogorovKolmogorov length scale, length scale, ηηηηηηηη,, is small is small
but still large with respect to the molecular but still large with respect to the molecular ““mean free pathmean free path””::
so, turbulence can still be studied so, 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 be characterising large eddies can be
defined as the average length over which a fluctuating defined as the average length over which a fluctuating
component keeps correlated, i.e. the quantity component keeps correlated, i.e. the quantity is not is not
negligible negligible
•• On both dimensional and experimental basis, it can be shown On both dimensional and experimental basis, it can be shown
thatthat
andand
with with ; therefore, ; therefore,
Basic concepts about computational Basic concepts about computational
modelling of turbulent flowsmodelling of turbulent flowsLength Scales in Turbulence Length Scales in Turbulence -- 22
2222
Basing on these considerations, Basing on these considerations, it can be concluded that:it can be concluded that:
•• an adequate representation of turbulence should an adequate representation of turbulence should take into take into
account the phenomena of production and dissipation of account 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 different simulating the transient evolution of vortices of different
sizessizes, putting a convenient lower bound for the smallest , putting a convenient lower bound for the smallest
scale scale (DNS, LES, DES)(DNS, LES, DES)
→→ simulating turbulence on the basis of the above described simulating turbulence on the basis of the above described
statistical approachstatistical approach, introducing appropriate production , introducing appropriate production
and dissipation terms to approximately represent the and dissipation terms to approximately represent the
effects of the energy cascade effects of the energy cascade (RANS)(RANS)
Basic concepts about computational Basic concepts about computational
modelling of turbulent flowsmodelling of turbulent flowsLength Scales in Turbulence Length Scales in Turbulence -- 33
2323
Basic concepts about computational Basic 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 mentioned This methodology follows the former of the two mentioned
routes, routes, trying to simulate with the highest possible space and trying to simulate with the highest possible space and
time 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 the The assumption behind this technique is that the NavierNavier--Stokes Stokes
equations are rich enough to describe the turbulent flow equations are rich enough to describe the turbulent flow
behaviour with no need of additional constitutive laws; for behaviour with no need of additional constitutive laws; for
incompressible flow it is:incompressible flow it is:
•• The web is full of fascinating pictures and movies about DNS The web is full of fascinating pictures and movies about DNS
resultsresults
2424
Basic concepts about computational Basic concepts about computational
modelling of turbulent flowsmodelling of turbulent flowsDirect Numerical Simulation (DNS) Direct Numerical Simulation (DNS) -- 22
•• The application of this technique is The application of this technique is very demanding in terms of very demanding in terms of
computational resourcescomputational resources: representing flows of technical : representing flows of technical
interest is very challenging and requires massive parallel interest is very challenging and requires massive parallel
computingcomputing
•• However the technique is very promising and it is However the technique is very promising and it is sometimes sometimes
used 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 which In 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 is DNS is
therefore used also to provide data on which empirical therefore used also to provide data on which empirical
turbulence model can be validatedturbulence model can be validated
CFDCFD--FigureFigure--1.ppt1.ppt
2525
Basic concepts about computational Basic 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 simulating LES is aimed at simulating
only larger eddies, while the smaller scales are treated by only larger eddies, while the smaller scales are treated by
subgridsubgrid--scale (SGS) modelsscale (SGS) models
•• In other words, there are In 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 and As 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 the A key point in LES is introducing a spatial filtering for the
smaller scalessmaller scales
2626
Basic concepts about computational Basic 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:
2727
Basic concepts about computational Basic concepts about computational
modelling of turbulent flowsmodelling of turbulent flowsLarge Eddy Simulation (LES) Large Eddy Simulation (LES) -- 33
2828
Basic concepts about computational Basic 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 equations S equations
are written in averaged formare written in averaged form
2929
Basic concepts about computational Basic 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 the Anyway, introducing the subgridsubgrid--scale stresses (or adopting slightly scale stresses (or adopting slightly
different definitions)different definitions)
it can be finally obtainedit can be finally obtained
3030
Basic concepts about computational Basic 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 the the fundamental problem is defining the subgridsubgrid scale stressesscale stresses
•• In 1963, In 1963, SmagorinskySmagorinsky defined a model based on the following defined a model based on the following
equationsequations
where Cwhere CSS is the is the SmagorinskySmagorinsky coefficient representing a parameter to coefficient representing a parameter to
be adjusted for the particular problem to be dealt with; values be adjusted for the particular problem to be dealt with; values in the in the
range 0.10 to 0.24 have been adopted for typical problemsrange 0.10 to 0.24 have been adopted for typical problems
•• LES LES is presently promising as a design tool, but still heavy from this presently promising as a design tool, but still heavy from the e
computational point of viewcomputational point of view
3131
Basic concepts about computational Basic concepts about computational
modelling of turbulent flowsmodelling of turbulent flowsReynolds Averaged Reynolds Averaged NavierNavier--Stokes (RANS) models Stokes (RANS) models -- 11
•• As already mentioned, the Reynolds averaging process leads to As already mentioned, the Reynolds averaging process leads to
momentum equations in which turbulence is represented by momentum equations in which turbulence is represented by the the
Reynolds stressReynolds stress
•• The The 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 constant tant
turbulent turbulent PrandtlPrandtl number, also the eddy thermal diffusivity is related to number, 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 xτ ρν ρ δ ρν ρ δ
∂∂= − = + − ∂ ∂
3232
Basic concepts about computational Basic concepts about computational
modelling of turbulent flowsmodelling of turbulent flowsReynolds Averaged Reynolds Averaged NavierNavier--Stokes (RANS) models Stokes (RANS) models -- 22
•• Models of different complexity can be adoptedModels of different complexity can be adopted in this aim, classified in this aim, classified
on the basis of the number of the additional partial differentiaon the basis of the number of the additional partial differential l
equations 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 between one between complete and incomplete modelscomplete and incomplete models::
�� completenesscompleteness of the model is related to its capability to of 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 boundary in 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
3333
Basic concepts about computational Basic concepts about computational
modelling of turbulent flowsmodelling of turbulent flowsReynolds Averaged Reynolds Averaged NavierNavier--Stokes (RANS) models Stokes (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 the he
mixing length theory of mixing length theory of PrandtlPrandtl (1925)(1925)
where where llllllllmixmix is the mixing length; the model is similar to the one for is the mixing length; the model is similar to the one for
molecular viscositymolecular viscosity in which kinematic viscosity is a interpreted as in 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 free ree
path)path)
•• In the presence of a wall, it is assumed In the presence of a wall, it is assumed where the constant where the constant
must 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, but but
its character of incompleteness makes models based on transport its character of incompleteness makes models based on transport
equations to be preferableequations to be preferable
3434
Basic concepts about computational Basic concepts about computational
modelling of turbulent flowsmodelling of turbulent flowsReynolds Averaged Reynolds Averaged NavierNavier--Stokes (RANS) models Stokes (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 a it is possible to derive a ““Reynolds stress transport modelReynolds stress transport model”” by by
applying the time averaging operator as followsapplying the time averaging operator as follows
wherewhere
it is foundit is found
3535
Basic concepts about computational Basic concepts about computational
modelling of turbulent flowsmodelling of turbulent flowsReynolds Averaged Reynolds Averaged NavierNavier--Stokes (RANS) models Stokes (RANS) models -- 55
•• This equation shows This equation shows the typical difficulties encountered when the typical difficulties encountered when
trying to trying to ““closeclose”” the turbulence equationsthe turbulence equations. In fact:. In fact:
�� the application of the timethe application of the time--averaging operator to the averaging operator to the NavierNavier--
Stokes equations makes the Reynolds stress tensor to Stokes equations makes the Reynolds stress tensor to
appear as a SECOND ORDER tensor of appear as a SECOND ORDER tensor of ““correlationcorrelation”” between between
two fluctuating velocity componentstwo fluctuating velocity components
�� the derivation of transport equations for the Reynolds stress the derivation of transport equations for the Reynolds stress
tensor makes tensor 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 obtained ned
by taking the trace of the system of Reynolds stress transport by taking the trace of the system of Reynolds stress transport
equations; in factequations; in fact
3636
Basic concepts about computational Basic concepts about computational
modelling of turbulent flowsmodelling of turbulent flowsReynolds Averaged Reynolds Averaged NavierNavier--Stokes (RANS) models Stokes (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
3737
Basic concepts about computational Basic concepts about computational
modelling of turbulent flowsmodelling of turbulent flowsReynolds Averaged Reynolds Averaged NavierNavier--Stokes (RANS) models Stokes (RANS) models -- 77
•• A A one equation model wasone equation model was proposed by proposed by PrandtlPrandtl in the formin the form
with with the additional closure equationthe additional closure equation
•• In general, oneIn general, one--equation models are incomplete, since the equation 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 specify complete 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 be an additional quantity must be
defineddefined also subjected to a transport equationalso subjected to a transport equation
3838
Basic concepts about computational Basic concepts about computational
modelling of turbulent flowsmodelling of turbulent flowsReynolds Averaged Reynolds Averaged NavierNavier--Stokes (RANS) models Stokes (RANS) models -- 88
•• TwoTwo--equation modelsequation models are mostly based on the definition of this are mostly based on the definition of this
further quantity in the form of further quantity in the form of εεεεεεεε or or ω ω ω ω ω ω ω ω basing on the following basing on the following
relationships that relationships that ““closeclose”” the problem (other versions are available)the problem (other versions are available)
�� for for kk--ωωωωωωωω 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:
3939
Basic concepts about computational Basic concepts about computational
modelling of turbulent flowsmodelling of turbulent flowsReynolds Averaged Reynolds Averaged NavierNavier--Stokes (RANS) models Stokes (RANS) models -- 99
•• for for kk--εεεεεεεε models it ismodels it is
the dissipation equation can be derived exactly and has the the dissipation equation can be derived exactly and has the
classical formclassical form
The The standard standard kk--εεεεεεεε modelmodel adopts the definitionsadopts the definitions
4040
Basic concepts about computational Basic concepts about computational
modelling of turbulent flowsmodelling of turbulent flowsReynolds Averaged Reynolds Averaged NavierNavier--Stokes (RANS) models Stokes (RANS) models -- 1010
•• As presented, the above turbulence models are mostly suited for As 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 approaches two possible approaches
are available:are available:
�� use of use of ““wall functionswall functions””:: the logarithmic trend observed for the logarithmic trend observed for
velocity close to a flat surface is assumed to hold velocity close to a flat surface is assumed to hold
approximately near the specific considered wall, together approximately near the specific considered wall, together
with a corresponding temperature trend; with a corresponding temperature trend; in this case, the in this case, the
value of y+ in the first node close to the wall must be value 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 are these models are
conceived to simulate the actual trend of turbulence close to conceived to simulate the actual trend of turbulence close to
the wall, by the adoption of the wall, by the adoption of damping functionsdamping functions; ; the value of the value of
y+ in the first node must be very small (typically y+
4141
Basic concepts about computational Basic concepts about computational
modelling of turbulent flowsmodelling of turbulent flowsReynolds Averaged Reynolds Averaged NavierNavier--Stokes (RANS) models Stokes (RANS) models -- 1111
•• On one hand, On one hand, the use of wall functions is computationally the 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 in
terms of resources (see the figure from terms of resources (see the figure from SharabiSharabi, 2008), 2008)
•• On the other hand, On the other hand, wall functions are not able to properly detect wall functions are not able to properly detect
some boundary layer phenomenasome boundary layer phenomena for which they were not for 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 always Reynolds number models are not always
completely accuratecompletely accurate……
(a) Wall functions mesh (b) Low-Reynolds number mesh
4242
Basic concepts about computational Basic concepts about computational
modelling of turbulent flowsmodelling of turbulent flowsDamping functions in lowDamping functions in low--Re modelsRe models
•• In In lowlow--Reynolds number modelsReynolds number models the definition of eddy viscosity is the definition of eddy viscosity is
changed from the classical formulationchanged from the classical formulation
to various forms including to various forms including damping functions, damping functions, ffµµµµµµµµ
that provide for that provide for the decrease of the eddy viscosity while the decrease of the eddy viscosity while
approaching the wallapproaching the wall
•• This allows This allows integration of the turbulence models through the integration 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--Re Re
models and, generally, to different resultsmodels and, generally, to different results……
2
T C f kµ µν ε= 0 0f for yµ → →
4343
Basic concepts about computational Basic concepts about computational
modelling of turbulent flowsmodelling of turbulent flowsLowLow--Re models vs. wall functionsRe models vs. wall functions
•• Providing an answer to Providing an answer to the questionthe question if the use of wall functions if 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 is is
not 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 propose In this lecture I will propose a case in which a 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 of I will show that the use of
some minimum lowsome minimum low--Re number capabilities is useful to get relatively Re number capabilities is useful to get relatively
good agreement with experimental data though approximate good agreement with experimental data though approximate
method are also acceptablemethod are also acceptable; however, pending questions are: ; however, pending questions are:
�� could we afford describing a whole nuclear reactor could 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?
�� couldncouldn’’t we instead accept a more approximate view of local t we instead accept a more approximate view of local
phenomena to get a reasonable overall picture?phenomena to get a reasonable overall picture?
4444
Basic concepts about computational Basic concepts about computational
modelling of turbulent flowsmodelling of turbulent flowsAnisotropic RANS Anisotropic RANS -- 11
This choice is anyway heavy for the number of equations to be solved
A further possibility is to use an anisotropic RANS modelsin which the simple Boussinesq approximation is abandoned
�� The assumption of an isotropic value ofThe assumption of an isotropic value of ννννννννTT is not suitable for is not suitable for simulating details of flow in noncircular passagessimulating details of flow in noncircular passages
�� This is particularly true for This is particularly true for secondary flowssecondary flows in the direction in the direction
orthogonal to the main flow that would require the full orthogonal to the main flow that would require the full
Reynolds stress transport models to be predictedReynolds stress transport models to be predicted
RSM application from RSM application from SharabiSharabi (2008)(2008)
4545
Basic concepts about computational Basic concepts about computational
modelling of turbulent flowsmodelling of turbulent flowsAnisotropic RANS Anisotropic RANS -- 22
In particular, it is possible to use In 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 order et al., 2006) which is limited to second order
terms in the strain and the rotational rates terms in the strain and the rotational rates SSijij and and ΩΩΩΩΩΩΩΩijij with respect with respect
to the original third order formulationto the original third order formulation
((BagliettoBaglietto et al., 2006)et al., 2006)
4646
TwoTwo--phase flow applicationsphase flow applicationsFew general considerationsFew general considerations
�� TwoTwo--phase flow introduces phase flow introduces additional complexityadditional complexity to the to the already complex problem of simulating turbulent flowalready complex problem of simulating turbulent flow
�� The presence of two phases and of The 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 CFD phase flow with CFD would be, for instance, to represent important phenomena would be, for instance, to represent important phenomena like CHF from first principleslike CHF from first principles
4747
TwoTwo--phase flow applicationsphase flow applicationsFew general considerations (contFew general considerations (cont’’d)d)
�� The work in the application of CFD techniques to twoThe work in the application of CFD techniques to two--phase flows phase flows
was developed for more than a decade, though nowadays it is stilwas developed for more than a decade, though nowadays it is still l
noted that the noted that the obtained models are not yet so mature as the ones obtained models are not yet so mature as the ones
for singlefor single--phase flows phase flows (foreword to (foreword to NuclNucl. Eng. Des., 240 (2010)). Eng. Des., 240 (2010))
�� The field is therefore one of active research, requiring The field is therefore one of active research, requiring huge huge
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 strongly
changed with respect to singlechanged with respect to single--phasephase
�� In particular, in addition to the integral length scale and the In 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
4848
TwoTwo--phase flow applicationsphase flow applicationsFew general considerations (contFew general considerations (cont’’d)d)
�� In the case of the In the case of the RANS approachRANS approach, , mass energy and momentum balance mass energy and momentum balance equationsequations are written in are written in 3D geometry3D geometry for each phase k (see e.g., for each phase k (see e.g., BestionBestionet 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 of phase flow of a a kk--εεεεεεεε modelmodel
where additional terms of where additional terms of turbulence productionturbulence production appear due to the appear due to the interaction between the phases. interaction between the phases.
An An interfacial area concentration transport equationinterfacial area concentration transport equation is also usedis also used
( ) kkkkkk wt
Γ=⋅∇+∂
∂ �ρα
ρα( ) ( )Tk k k k k k k k k k k k k k
ww w p M g
t
α ρα ρ α α ρ α τ τ
∂ + ∇ ⋅ = − ∇ + + + ∇ ⋅ + ∂
�
� ��
� � � � �
( )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 tα ρ α ρ α α ρ Γ α ∂ ∂
′′ ′′′+ + ∇ ⋅ + = + ⋅ + + + + − ∇ ⋅ + ∂ ∂
� � �
[ ],1
Production termsT
ik k k kk k i k k k K
i k j K j
k k kw P
t x x x
µρ α ρ ε
α σ
∂ ∂ ∂∂+ = + − +
∂ ∂ ∂ ∂
[ ], 1 11
C Production terms CT
ik k k k kk k i k k k
i k j j k
w Pt x x x k
ε ε ε
ε
ε ε µ ε ερ α ρ ε
α σ
∂ ∂ ∂∂+ = + − +
∂ ∂ ∂ ∂
4949
TwoTwo--phase flow applicationsphase flow applicationsFew general considerations (contFew general considerations (cont’’d)d)
�� Needless to say, Needless to say, this model relies on the this model relies on the BoussinesqBoussinesqassumptionassumption; turbulent viscosity is moreover given simply by; turbulent viscosity is moreover given simply by
�� Its is quite clear that Its is quite clear that the success of such a model is strictly the success of such a model is strictly linked to its ingredients in terms of constitutive relationshipslinked to its ingredients in terms of constitutive relationshipsthat 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, MMk k , should account for , should account for mass transfermass transfer, the , the dragdrag and and liftlift forces, forces, the the addedadded mass termmass term and the and the turbulent dispersion of bubblesturbulent dispersion of bubbles
�� A major lack of RANS approaches is anyway in the fact that A major lack of RANS approaches is anyway in the fact that some twosome two--phase flow fields are naturally unstable: phase flow fields are naturally unstable: time time averaging is therefore suitable only to have a global averaging is therefore suitable only to have a global ““averagedaveraged””picturepicture of what happens, loosing instantaneous details (see of what happens, loosing instantaneous details (see e.g., the discussion in e.g., the discussion in YadigarogluYadigaroglu et al., 2008)et al., 2008)
k
kk
T
k
kC
ερµ µ
2
=
5050
�� By the way, unsteady calculations with RANS may show By the way, unsteady calculations with RANS may show
oscillations that may somehow match with experimental oscillations that may somehow match with experimental
observations (observations (ZborayZboray and De and 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, by applications are interestingly discussed, among the others, by
YadigarogluYadigaroglu et al., (2008) and in works there referred to, and et al., (2008) and in works there referred to, and
by by 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 the e
case of RANS, case of RANS, LES models require accurate closure models for LES models require accurate closure models for
the different terms appearing in the equations in addition to the 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 (cont’’d)d)
5151
�� LaheyLahey (2009) recently discussed the capabilities of (2009) recently discussed the capabilities of DNS DNS modelsmodels in representing twoin representing two--phase flowsphase flows
�� As in case of singleAs in case of single--phase flow, the attractiveness of this phase flow, the attractiveness of this technique lies in the fact that there is no need to technique lies in the fact that there is no need to introduce empirical models to obtain accurate introduce empirical models to obtain accurate predictions; the obvious drawback is the heavy predictions; the obvious drawback is the heavy computational loadcomputational load
�� In the case of twoIn the case of two--phase flows, phase flows, interface tracking interface tracking algorithmsalgorithms must be introduced; in the mentioned paper, must be introduced; in the mentioned paper, an algorithm based on the signed distance form the an algorithm based on the signed distance form the interface is used in the PHASTA codeinterface is used in the PHASTA code
�� Dam break problems, bubble interactions and plunging Dam break problems, bubble interactions and plunging jets are within the predictive capabilities, whenever jets are within the predictive capabilities, whenever appropriate 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 (cont’’d)d)
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 Pis’menny et al. [2006]:
– National Technological University of Ukraine
– turbulent heat transfer in vertical tubes for supercritical water
– operating pressure of 23.5 MPa
– inlet temperature and heating conditions involved in these analyses resulted in both dense and gas-like fluid to be present in the test section
– thin wall stainless steel tubes with inner diameters of 6.28 and 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 outer temperature of the tubes.
5353
Prediction of heat transfer deteriorationPrediction of heat transfer deteriorationPrevious resultsPrevious results
� Previous results obtained by Sharabi et al. [2007] with an in-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 flow b) 6.28 mm ID, q”=390 kW/m
2, G= 590 kg/(m
2s),
Tinlet =300 °C, downward flow
5454
� It can be noted that:
– k-εεεε models predict in a qualitatively reasonable way the onset of heat transfer deterioration occurring in upward flow
– however, despite of quantitative differences between the results of the different k-εεεε models, they all tend to predict a larger wall temperature increase than observed
– on the other hand, the Wilcox [1994] k-ωωωω model (WI) and the Speziale et al. [1990] k-ττττ model (SP) were seen to predict no deterioration or a very delayed one
– in the case of upward flow, all the models provided similar results, characterised by the absence of any deterioration phenomenon, in qualitative agreement with experimental observations
Prediction of heat transfer deteriorationPrediction of heat transfer deteriorationPrevious results (contPrevious results (cont’’d)d)
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
WI model (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 lead to an “m-shaped velocity
profile”
Reasons for HeatTransfer
Deterioration
Prediction of heat transfer deteriorationPrediction of heat transfer deteriorationPrevious results (contPrevious results (cont’’d)d)
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 WI model (upward
flow, G=509 kg/(m2s), q=390 kW/m2,
tin=300 °C)
(Longer pipe)
In the transition to the “m-shaped profile” velocity gradients are suppressed and turbulence production decreases
Prediction of heat transfer deteriorationPrediction of heat transfer deteriorationPrevious results (contPrevious results (cont’’d)d)
5757
� With the STAR-CCM+ code, the following modelling choices were made:– 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 2.6 mm
� 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 grid was found to be suitable to provide enough accurate results with a reasonable computational effort
– Later, the results obtained by this grid have been compared to those obtained by a finer one (68 radial and 500 axial nodes) showing little differences
– 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 was respected with due margin
Prediction of heat transfer deteriorationPrediction of heat transfer deteriorationSTARSTAR--CCM+ ResultsCCM+ Results
5858
� Concerning water properties at 23.5 MPa, the code allows assigning the 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 these properties, whose coefficients were generated on the basis of tables obtained by the NIST package
0
200
400
600
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0 200 400 600 800 1000 1200 1400 1600 1800 2000
Temperature [K]
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Data
Splines
Interval Boundaries
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erm
al
Co
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ucti
vit
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0.0E+00
2.0E-04
4.0E-04
6.0E-04
8.0E-04
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1.6E-03
1.8E-03
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Prediction of heat transfer deteriorationPrediction of heat transfer deteriorationSTARSTAR--CCM+ Results (contCCM+ Results (cont’’d)d)
5959
The analysis reported herein was limited to four k-εεεε models:
� the Two-Layer All y+ Wall Treatment (referred to in the following as “all y+”), suggested for simulating with a reasonable accuracy different kinds of flows;
� the standard Low-Reynolds Number K-Epsilon Model (referred to in the following as “low-Re”) suggested by code guidelines for natural convection 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 εεεε equations, solves two additional transport and algebraic equations; this model is suggested 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 (cont’’d)d)
6060
300
400
500
600
700
800
900
0 20 40 60 80 100
x / D
Wall
Tem
per
atu
re [
°C]
Low-Re
AKN
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 (cont’’d)d)
6161
300
400
500
600
700
800
900
0 20 40 60 80 100
x / D
Wa
ll T
emp
eratu
re [
°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 (cont’’d)d)
6262
It can be noted that:
� the Two-Layer All y+ Wall Treatment was unable to detect the start of deterioration phenomena in upward flow
� all the other k-εεεε models showed a behaviour similar to the one 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 as observed in the previous study (see below)
Prediction of heat transfer deteriorationPrediction of heat transfer deteriorationSTARSTAR--CCM+ Results (contCCM+ Results (cont’’d)d)
6363
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t [m
/s] Pipe Inlet
0
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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 (cont’’d)d)
6464
0.000
0.001
0.002
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Low-Re Model, Upward Flow
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V2F Model, Upward Flow
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g]
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0
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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 (cont’’d)d)
6565
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All y+ Model, Downward 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 (cont’’d)d)
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]
Tu
rb
ule
nt
Kin
etic
En
erg
y [
J/k
g]
Pipe Inlet
0
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]
Tu
rb
ule
nt
Kin
etic
En
erg
y [
J/k
g]
Pipe Inlet
0
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]
Tu
rb
ule
nt
Kin
etic
En
erg
y [
J/k
g]
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]
Tu
rb
ule
nt
Kin
etic
En
erg
y [
J/k
g]
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 (cont’’d)d)
6767
CFD and CMFD are very powerful tools, whose capabilities are conditioned to our understanding of phenomena and to computer power
The smaller is the degree of empiricism we wish to introduce in the models, the greatest is the computer power needed
It is a very fascinating world in which smart ideas are needed to discover newer and newer possibilities
In summaryIn summary……
6868
ThankThankThankThankThankThankThankThank youyouyouyouyouyouyouyou forforforforforforforfor youryouryouryouryouryouryouryour attentionattentionattentionattentionattentionattentionattentionattention,,,,,,,,
Walter AmbrosiniWalter AmbrosiniWalter AmbrosiniWalter AmbrosiniWalter AmbrosiniWalter AmbrosiniWalter AmbrosiniWalter Ambrosini
6969
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•• D.C. Wilcox D.C. Wilcox ““Turbulence Turbulence ModelingModeling for CFDfor CFD””, 2nd Edition, DCW Industries, 1998., 2nd Edition, DCW Industries, 1998.
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Engineering and Design 236 (2006) 1503Engineering and Design 236 (2006) 1503––15101510
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Installations, Volume 2009, Article ID 950536, 12 pages, doi:10.Installations, Volume 2009, Article ID 950536, 12 pages, doi:10.1155/2009/9505361155/2009/950536
•• D. D. BestionBestion and A. and A. GuelfiGuelfi, Status and Perspective of Two, Status and Perspective of Two--Phase Flow Phase Flow ModellingModelling in the Neptune in the Neptune MultiscaleMultiscale ThiermalThiermal--
Hydraulic Platform for Nuclear Reactor Simulation, NUCLEAR ENGINHydraulic Platform for Nuclear Reactor Simulation, NUCLEAR ENGINEERING AND TECHNOLOGY, VOL.37 NO.6 EERING AND TECHNOLOGY, VOL.37 NO.6
DECEMBER 2005DECEMBER 2005
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flows with the NEPTUNE CFD code, Nuclear Engineering and Design flows with the NEPTUNE CFD code, Nuclear Engineering and Design 238 (2008) 680238 (2008) 680––692692
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4th International Symposium on Supercritical Water4th International Symposium on Supercritical Water--Cooled Reactors, March 8Cooled Reactors, March 8--11, 2009, Heidelberg, Germany, Paper No. 8311, 2009, Heidelberg, Germany, Paper No. 83
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