Calculations of Residence Time in CFD
Michael Mansour
CFD Meeting - LSS11.04.2018
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What is Residence Time?
αΆπ
Average time (π) =Fluid mass (π)
Mass flow rate αΆ(π)=
Fluid volume (π)
Volume flow rate αΆ(π)
β’ the time that a particle spends in a particular system
Not all particles (fluid elements) spend the same time in the system
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How to measure the Residence Time?
C : concentration
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Why is Residence Time important?
β’ Different RT Different process time
β’ lower mixing
β’ Lower heat transfer
β’ Less homogeneous temperature distribution
β’ Lower reaction rates
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What is Residence Time Distribution (RTD)?
β’ a probability distribution function that describes the time a fluid element could spend in the system
β’ The RTD is usually represented by a function called the exit age distribution function, E(t).
πΈ π‘ =πΆ(π‘)
0βπΆ π‘ . ππ‘
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What is Residence Time Distribution (RTD)?
Exit age distribution function
Cumulative function
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Comparisons of (RTD)
β’ RTD 2 is narrower than RTD 1, showing betterprocess performance of system 1 (better mixing)
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How to calculate the RT in Star-CCM+?
1. For Lagrangian multiphase simulations
Go to Physics 1 > Lagrangian Multiphase > Phase 1 > Models > Activate Residence Time Model
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How to calculate the RT in Star-CCM+?
2. For single-phase simulations
Using a Passive Scalar
β’ The passive scalar model can be used to trackthe accumulation of a field in the flow simulation
β’ If the transported scalar function represents the time, then the source term should be set as the density
β’ This attaches a virtual clock to each volume element of the fluid.
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How to calculate the RT in Star-CCM+?General transport equation
π
ππ‘ΰΆ±π
ππ ππ +ΰΆ±π΄
ππ π. ππ΄ =πβ
ππ‘
β : Transported quantiny (extensive property)π: intensive property of β β = π m m: mass
π β π‘ residence timeβ = π‘ m
π
ππ‘ΰΆ±π
ππ‘ ππ +ΰΆ±π΄
ππ‘ π. ππ΄ =π(π‘π)
ππ‘= π
ππ‘
ππ‘+ π‘
ππ
ππ‘
π
ππ‘ΰΆ±π
ππ‘ ππ +ΰΆ±π΄
ππ‘ π. ππ΄ = π
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How to calculate the RT in Star-CCM+?
π
ππ‘ΰΆ±π
π π ππ +ΰΆ±π΄
π π π. ππ΄ = ΰΆ±π
ππ ππ
Passive scalar model in Star-CCM+
π
ππ‘ΰΆ±π
π π‘ ππ + ΰΆ±π΄
π π‘ π. ππ΄ = π
ΰΆ±π
ππ ππ = π
πΊπ = π
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How to calculate the RT in Star-CCM+?
1. Activate the Passive Scalar model.
2. Create a passive scalar and rename it ResidenceTime.
3. Create a field function and rename
it ResidenceTimeSource with a definition of
${Density}
Or ($ResidenceTime < 10000)? ${Density} : 0
The value of 10000 represents a maximum time, which is necessary if the flow field has a vortex or recirculation. Otherwise, time would grow to infinity.
4. Select the Regions > Fluid > Physics
Conditions > Passive Scalar Source Option node and
select Mass flux for Source Definition.
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How to calculate the RT in Star-CCM+?
5. Open the Regions > [Region] > Physics Values node and select the
Passive Scalar Source node.
6. In the Method property, select Composite.
7. Open the Composite node and select
the ResidenceTime node.
8. In the Method property of the ResidenceTime node,
select Field Function.
9. Select the Field Function node and set its Scalar
Function property to ResidenceTimeSource, which is the
field function that you defined.
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Example: RT for a straight pipe
Outletsurface
Sectional plane
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Example: RT for a helical pipe
Outlet surface
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Comparison of RTD
0
10
20
30
40
50
60
70
80
90
100
0 0.25 0.5 0.75 1 1.25 1.5 1.75 2
Cu
mu
lati
ve f
un
ctio
n F
Dimensionless residence time (Ο΄)
Straight pipe
Helical pipe
π½ =π β ππππ
π
ππ = ππ ππ = ππππ
0
10
20
30
40
50
60
70
80
90
100
0 1 2 3 4 5 6 7 8
Cu
mu
lati
ve f
un
ctio
n F
Dimensionless residence time (Ο΄)
Straight pipe
Helical pipe
Straightpipe
Helicalpipe
Thank you!
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