FLUENT 6.3 User’s Guide
`
`September 2006
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`Copyright c(cid:13) 2006 by Fluent Inc.
`All Rights Reserved. No part of this document may be reproduced or otherwise used in
`any form without express written permission from Fluent Inc.
`
`Airpak, FIDAP, FLUENT, FLUENT for CATIA V5, FloWizard, GAMBIT, Icemax, Icepak,
`Icepro, Icewave, Icechip, MixSim, and POLYFLOW are registered trademarks of Fluent
`Inc. All other products or name brands are trademarks of their respective holders.
`
`CHEMKIN is a registered trademark of Reaction Design Inc.
`
`Portions of this program include material copyrighted by PathScale Corporation
`2003-2004.
`
`Fluent Inc.
`Centerra Resource Park
`10 Cavendish Court
`Lebanon, NH 03766
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`Modeling Discrete Phase
`
`randomly selected in the plane orthogonal to the direction vector of the parent parcel,
`and the momentum of the parent parcel is adjusted so that momentum is conserved. The
`velocity magnitude of the new parcel is the same as the parent parcel.
`
`You must also specify the model constants which determine how the gas phase interacts
`with the liquid droplets. For example, the breakup time constant B1 is the constant
`multiplying the time scale which determines how quickly the parcel will loose mass.
`Therefore, a larger number means that it takes longer for the particle to loose a given
`amount. A larger number for B1 in the context of interaction with the gas phase would
`mean that the interaction with the subgrid is less intense. B0 is the constant for the drop
`size and is generally taken to be 0.61.
`
`22.8 Atomizer Model Theory
`
`All of the atomization models use physical atomizer parameters, such as orifice diameter
`and mass flow rate, to calculate initial droplet size, velocity, and position.
`
`For realistic atomizer simulations, the droplets must be randomly distributed, both spa-
`tially through a dispersion angle and in their time of release. For other types of injections
`in FLUENT (nonatomizer), all of the droplets are released along fixed trajectories at the
`beginning of the time step. The atomizer models use stochastic trajectory selection and
`staggering to attain a random distribution. Further information on staggering can be
`found in section Section 22.2.2: Stochastic Staggering of Particles.
`
`Stochastic trajectory selection is the random dispersion of initial droplet directions. All
`of the atomizer models provide an initial dispersion angle, and the stochastic trajectory
`selection picks an initial direction within this angle. This approach improves the accuracy
`of the results for spray-dominated flows. The droplets will be more evenly spread among
`the computational cells near the atomizer, which improves the coupling to the gas phase
`by spreading drag more smoothly over the cells near the injection. Source terms in
`the energy and species conservation equations are also more evenly distributed among
`neighboring cells, improving solution convergence.
`
`Five atomizer models are available in FLUENT to predict the spray characteristics from
`knowledge of global parameters such as nozzle type and liquid flow rate:
`
`• plain-orifice atomizer
`• pressure-swirl atomizer
`• flat-fan atomizer
`• air-blast/air-assisted atomizer
`• effervescent/flashing atomizer
`
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`22.8 Atomizer Model Theory
`
`You can choose them as injection types and define the associated parameters in the Set
`Injection Properties panel, as described in Section 22.12.1: Injection Types. Details about
`the atomizer models are provided below.
`
`22.8.1 The Plain-Orifice Atomizer Model
`
`The plain-orifice is the most common type of atomizer and the most simply made. How-
`ever there is nothing simple about the physics of the internal nozzle flow and the exter-
`nal atomization. In the plain-orifice atomizer model in FLUENT, the liquid is accelerated
`through a nozzle, forms a liquid jet and then breaks up to form droplets. This apparently
`simple process is dauntingly complex. The plain orifice may operate in three different
`regimes: single-phase, cavitating and flipped [348]. The transition between regimes is
`abrupt, producing dramatically different sprays. The internal regime determines the
`velocity at the orifice exit, as well as the initial droplet size and the angle of droplet
`dispersion. Diagrams of each case are shown in Figures 22.8.1, 22.8.2, and 22.8.3.
`
`r
`
`p
`1
`
`d
`
`liquid jet
`
`p2
`
`orifice walls
`
`downstream
`gas
`
`L
`
`Figure 22.8.1: Single-Phase Nozzle Flow (Liquid Completely Fills the Ori-
`fice)
`
`c(cid:13) Fluent Inc. September 29, 2006
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`Modeling Discrete Phase
`
`vapor
`
`liquid jet
`
`vapor
`orifice walls
`
`downstream
`gas
`
`Figure 22.8.2: Cavitating Nozzle Flow (Vapor Pockets Form Just after the
`Inlet Corners)
`
`liquid jet
`
`orifice walls
`
`downstream
`gas
`
`Figure 22.8.3: Flipped Nozzle Flow (Downstream Gas Surrounds the Liquid
`Jet Inside the Nozzle)
`
`22-48
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`22.8 Atomizer Model Theory
`
`Internal Nozzle State
`
`To accurately predict the spray characteristics, the plain-orifice model in FLUENT must
`identify the correct state of the internal nozzle flow because the nozzle state has a tremen-
`dous effect on the external spray. Unfortunately, there is no established theory for deter-
`mining the nozzle state. One must rely on empirical models obtained from experimental
`data. FLUENT uses several dimensionless parameters to determine the internal flow
`regime for the plain-orifice atomizer model. These parameters and the decision-making
`process are summarized below.
`
`A list of the parameters that control internal nozzle flow is given in Table 22.8.1. These
`parameters may be combined to form nondimensional characteristic lengths such as r/d
`and L/d, as well as nondimensional groups like the Reynolds number based on hydraulic
`“head” (Reh) and the cavitation parameter (K).
`
`Table 22.8.1: List of Governing Parameters for Internal Nozzle Flow
`
`nozzle diameter
`nozzle length
`radius of curvature of the inlet corner
`upstream pressure
`downstream pressure
`viscosity
`liquid density
`vapor pressure
`
`d
`L
`r
`p1
`p2
`µ
`ρl
`pv
`
`Reh =
`
`dρl
`µ
`
`K =
`
`(cid:115)2(p1 − p2)
`ρl
`p1 − pv
`p1 − p2
`
`(22.8-1)
`
`(22.8-2)
`
`The liquid flow often contracts in the nozzle, as can be seen in Figures 22.8.2 and 22.8.3.
`Nurick [266] found it helpful to use a coefficient of contraction (Cc) to represent the
`reduction in the cross-sectional area of the liquid jet. The coefficient of contraction is
`defined as the area of the stream of contracting liquid over the total cross-sectional area
`of the nozzle. FLUENT uses Nurick’s fit for the coefficient of contraction:
`
`1(cid:113) 1
`− 11.4r
`
`C2
`ct
`
`d
`
`Cc =
`
`c(cid:13) Fluent Inc. September 29, 2006
`
`(22.8-3)
`
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`Modeling Discrete Phase
`
`Here, Cct is a theoretical constant equal to 0.611, which comes from potential flow analysis
`of flipped nozzles.
`
`Coefficient of Discharge
`
`Another important parameter for describing the performance of nozzles is the coefficient
`of discharge (Cd). The coefficient of discharge is the ratio of the mass flow rate through
`the nozzle to the theoretical maximum mass flow rate:
`
`Cd =
`
`˙meff
`
`A(cid:113)2ρl(p1 − p2)
`
`where ˙meff is the effective mass flow rate of the nozzle, defined by
`
`˙meff =
`
`2π ˙m
`∆φ
`
`(22.8-4)
`
`(22.8-5)
`
`˙m is the mass flow rate specified in the user interface, and ∆φ is the difference
`Here,
`between the azimuthal stop angle and the azimuthal start angle
`
`∆φ = φstop − φstart
`
`(22.8-6)
`
`as input by the user (see Section 22.12.1: Point Properties for Plain-Orifice Atomizer
`Injections). Note that the mass flow rate input by the user should be for the appropriate
`start and stop angles, in other words the correct mass flow rate for the sector being
`modeled. Note also that for ∆φ of 2π, the effective mass flow rate is identical to the
`mass flow rate in the interface.
`
`The cavitation number (K in Equation 22.8-2) is an essential parameter for predicting
`the inception of cavitation. The inception of cavitation is known to occur at a value
`
`rounding and viscosity, an empirical relationship is used:
`
`of Kincep ≈ 1.9 for short, sharp-edged nozzles. However, to include the effects of inlet
`Kincep = 1.9(cid:18)1 − r
`(cid:19)2 − 1000
`
`d
`
`Reh
`
`(22.8-7)
`
`Similarly, a critical value of K where flip occurs is given by
`
`Kcrit = 1 +
`
`(cid:16)1 + L
`
`
`4d(cid:17)(cid:16)1 + 2000Reh(cid:17) e70r/d
`
`1
`
`(22.8-8)
`
`If r/d is greater than 0.05, then flip is deemed impossible and Kcrit is set to 1.0.
`
`22-50
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`22.8 Atomizer Model Theory
`
`The cavitation number, K, is compared to the values of Kincep and Kcrit to identify the
`nozzle state. The decision tree is shown in Figure 22.8.4. Depending on the state of the
`nozzle, a unique closure is chosen for the above equations.
`
`For a single-phase nozzle (K > Kincep, K ≥ Kcrit)
`
`[207], the coefficient of discharge is
`
`given by
`
`Cd =
`
`1
`+ 20 (1+2.25L/d)
`Reh
`
`1
`Cdu
`
`(22.8-9)
`
`where Cdu is the ultimate discharge coefficient, and is defined as
`
`Cdu = 0.827 − 0.0085
`For a cavitating nozzle (Kcrit ≤ K ≤ Kincep) [266] the coefficient of discharge is deter-
`
`(22.8-10)
`
`L d
`
`mined from
`
`√
`
`Cd = Cc
`
`K
`
`(22.8-11)
`
`For a flipped nozzle (K < Kcrit) [266],
`
`Cd = Cct = 0.611
`
`(22.8-12)
`
`K £
`
` K
`
`incep
`
`K > K
`
`incep
`
`K < K
`
`crit
`
`K ‡
`
` K
`
`crit
`
`K < K
`crit
`
`K ‡
`
` K
`crit
`
`flipped
`
`cavitating flipped
`
`single phase
`
`Figure 22.8.4: Decision Tree for the State of the Cavitating Nozzle
`
`All of the nozzle flow equations are solved iteratively, along with the appropriate relation-
`ship for coefficient of discharge as given by the nozzle state. The nozzle state may change
`as the upstream or downstream pressures change. Once the nozzle state is determined,
`the exit velocity is calculated, and appropriate correlations for spray angle and initial
`droplet size distribution are determined.
`
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`Modeling Discrete Phase
`
`Exit Velocity
`
`For a single-phase nozzle, the estimate of exit velocity (u) comes from the conservation
`of mass and the assumption of a uniform exit velocity:
`
`u =
`
`˙meff
`ρlA
`
`(22.8-13)
`
`For the cavitating nozzle, Schmidt and Corradini [323] have shown that the uniform exit
`velocity is not accurate. Instead, they derived an expression for a higher velocity over a
`reduced area:
`
`u =
`
`2Ccp1 − p2 + (1 − 2Cc)pv
`Cc(cid:113)2ρl(p1 − pv)
`
`(22.8-14)
`
`This analytical relation is used for cavitating nozzles in FLUENT. For the case of flipped
`nozzles, the exit velocity is found from the conservation of mass and the value of the
`reduced flow area:
`
`u =
`
`˙meff
`ρlCctA
`
`(22.8-15)
`
`Spray Angle
`
`The correlation for the spray angle (θ) comes from the work of Ranz [295]:
`
`−1(cid:104) 4π
`CA(cid:113) ρg
`
`ρl
`
`tan
`
`√
`
`6 (cid:105)
`
`3
`
`single phase, cavitating
`
`(22.8-16)
`
`0.01
`
`flipped
`
`
`
`=
`
`θ 2
`
`The spray angle for both single-phase and cavitating nozzles depends on the ratio of the
`gas and liquid densities and also the parameter CA. For flipped nozzles, the spray angle
`has a constant value.
`
`The parameter CA, which you must specify, is thought to be a constant for a given nozzle
`geometry. The larger the value, the narrower the spray. Reitz [300] suggests the following
`correlation for CA:
`
`CA = 3 +
`
`L
`3.6d
`
`(22.8-17)
`
`22-52
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`22.8 Atomizer Model Theory
`
`The spray angle is sensitive to the internal flow regime of the nozzle. Hence, you may
`wish to choose smaller values of CA for cavitating nozzles than for single-phase nozzles.
`Typical values range from 4.0 to 6.0. The spray angle for flipped nozzles is a small,
`arbitrary value that represents the lack of any turbulence or initial disturbance from the
`nozzle.
`
`Droplet Diameter Distribution
`
`One of the basic characteristics of an injection is the distribution of drop size. For
`an atomizer, the droplet diameter distribution is closely related to the nozzle state.
`FLUENT’s spray models use a two-parameter Rosin-Rammler distribution, characterized
`by the most probable droplet size and a spread parameter. The most probable droplet
`size, d0 is obtained in FLUENT from the Sauter mean diameter, d32 [200]. For more
`information about the Rosin-Rammler size distribution, see Section 22.12.1: Using the
`Rosin-Rammler Diameter Distribution Method.
`
`For single-phase nozzle flows, the correlation of Wu et al. [407] is used to calculate d32
`and relate the initial drop size to the estimated turbulence quantities of the liquid jet:
`
`d32 = 133.0λWe
`
`−0.74,
`
`(22.8-18)
`
`where λ = d/8, λ is the radial integral length scale at the jet exit based upon fully-
`developed turbulent pipe flow, and We is the Weber number, defined as
`
`We ≡ ρlu2λ
`σ
`
`.
`
`(22.8-19)
`
`Here, σ is the droplet surface tension. For a more detailed discussion of droplet surface
`tension and the Weber number, see Section 22.7.2: Droplet Breakup Models. For more
`information about mean particle diameters, see Section 22.16.8: Summary Reporting of
`Current Particles.
`
`For cavitating nozzles, FLUENT uses a slight modification of Equation 22.8-18. The
`initial jet diameter used in Wu’s correlation, d, is calculated from the effective area of
`the cavitating orifice exit, and thus represents the effective diameter of the exiting liquid
`jet, deff. For an explanation of effective area of cavitating nozzles, please see Schmidt
`and Corradini [323].
`
`The length scale for a cavitating nozzle is λ = deff/8, where
`
`deff =(cid:115) 4 ˙meff
`
`πρlu
`
`.
`
`(22.8-20)
`
`22-53
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`Modeling Discrete Phase
`
`For the case of the flipped nozzle, the initial droplet diameter is set to the diameter of
`the liquid jet:
`
`d0 = d(cid:113)Cct
`
`(22.8-21)
`
`where d0 is defined as the most probable diameter.
`
`The second parameter required to specify the droplet size distribution is the spread
`parameter, s. The values for the spread parameter are chosen from past modeling expe-
`rience and from a review of experimental observations. Table 22.8.2 lists the values of s
`for the three nozzle states. The larger the value of the spread parameter, the narrower
`the droplet size distribution.
`
`Table 22.8.2: Values of Spread Parameter for Different Nozzle States
`
`State
`single phase
`cavitating
`flipped
`
`Spread Parameter
`3.5
`1.5
`∞
`
`Since the correlations of Wu et al. provide the Sauter mean diameter, d32, these are
`converted to the most probable diameter, d0. Lefebvre [200] gives the most general
`relationship between the Sauter mean diameter and most probable diameter for a Rosin-
`Rammler distribution. The simplified version for s=3.5 is as follows:
`
`d0 = 1.2726d32(cid:18)1 − 1
`
`s
`
`(cid:19)1/s
`
`(22.8-22)
`
`At this point, the droplet size, velocity, and spray angle have been determined and the
`initialization of the injections is complete.
`
`22-54
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