Calculations of Residence Time in CFD CFD Meeting - LSS 11.04.2018 - - PowerPoint PPT Presentation

Calculations of Residence Time in CFD

Michael Mansour CFD Meeting - LSS 11.04.2018

11/04/2018

Calculations of Residence Time in CFD

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What is Residence Time?

ሶ 𝑛

Average time (𝜐) = Fluid mass (𝑛) Mass flow rate

ሶ (𝑛) =

Fluid volume (𝑊) Volume flow rate

ሶ (𝑊)

• 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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Calculations of Residence Time in CFD

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How to measure the Residence Time?

C : concentration

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Calculations of Residence Time in CFD

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Why is Residence Time important?

• Different RT

Different process time

• lower mixing
• Lower heat transfer
• Less homogeneous temperature distribution
• Lower reaction rates

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Calculations of Residence Time in CFD

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What is Residence Time Distribution (RTD)?

• a probability distribution function that describes

the time a fluid element could spend in the system

• The RTD is usually represented by a function

called the exit age distribution function, E(t).

𝐹 𝑢 = 𝐷(𝑢) ׬

∞ 𝐷 𝑢 . 𝑒𝑢

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Calculations of Residence Time in CFD

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What is Residence Time Distribution (RTD)?

Exit age distribution function Cumulative function

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Calculations of Residence Time in CFD

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Comparisons of (RTD)

• RTD 2 is narrower than RTD 1, showing better

process 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

• The passive scalar model can be used to track

the accumulation of a field in the flow simulation

• If the transported scalar function represents the

time, then the source term should be set as the density

• 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

𝜖 𝜖𝑢 න

𝑊

𝜍𝜒 𝑒𝑊 + න

𝐵

𝜍𝜒 𝑊. 𝑒𝐵 = 𝑒∅ 𝑒𝑢

∅: Transported quantiny (extensive property) 𝜒: intensive property of ∅ ∅ = 𝜒 m m: mass 𝜒 → 𝑢 residence time ∅ = 𝑢 m

𝜖 𝜖𝑢 න

𝑊

𝜍𝑢 𝑒𝑊 + න

𝐵

𝜍𝑢 𝑊. 𝑒𝐵 = 𝑒(𝑢𝑛) 𝑒𝑢 = 𝑛 𝑒𝑢 𝑒𝑢 + 𝑢 𝑒𝑛 𝑒𝑢 𝜖 𝜖𝑢 න

𝑊

𝜍𝑢 𝑒𝑊 + න

𝐵

𝜍𝑢 𝑊. 𝑒𝐵 = 𝑛

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How to calculate the RT in Star-CCM+?

𝜖 𝜖𝑢 න

𝑊

𝜍 𝜒 𝑒𝑊 + න

𝐵

𝜍 𝜒 𝑊. 𝑒𝐵 = න

𝑊

𝑇𝜒 𝑒𝑊 Passive scalar model in Star-CCM+ 𝜖 𝜖𝑢 න

𝑊

𝜍 𝑢 𝑒𝑊 + න

𝐵

𝜍 𝑢 𝑊. 𝑒𝐵 = 𝑛 න

𝑊

𝑇𝜒 𝑒𝑊 = 𝑛 𝑻𝝌 = 𝝇

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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

Outlet surface

Sectional plane

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Example: RT for a helical pipe

Outlet surface

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Comparison of RTD

10 20 30 40 50 60 70 80 90 100 0.25 0.5 0.75 1 1.25 1.5 1.75 2 Cumulative function F Dimensionless residence time (ϴ) Straight pipe Helical pipe

𝜾 = 𝒖 − 𝒖𝒏𝒋𝒐 𝝊

𝐒𝐟 = 𝟓𝟏 𝐒𝐟 = 𝟑𝟏𝟏𝟏

10 20 30 40 50 60 70 80 90 100 1 2 3 4 5 6 7 8 Cumulative function F Dimensionless residence time (ϴ) Straight pipe Helical pipe

Straight pipe Helical pipe

Thank you!

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