Calculations of Residence Time in CFD

Michael Mansour

CFD Meeting - LSS11.04.2018

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What is Residence Time?

ሶ𝑚

Average time (𝜏) =Fluid mass (𝑚)

Mass flow rate ሶ(𝑚)=

Fluid volume (𝑉)

Volume flow rate ሶ(𝑉)

• 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?

• Different RT Different process time

• lower mixing

• Lower heat transfer

• Less homogeneous temperature distribution

• Lower reaction rates

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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).

𝐸 𝑡 =𝐶(𝑡)

0∞𝐶 𝑡 . 𝑑𝑡

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What is Residence Time Distribution (RTD)?

Exit age distribution function

Cumulative function

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Comparisons of (RTD)

• 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

• The passive scalar model can be used to trackthe 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

𝜕

𝜕𝑡න𝑉

𝜌𝜑 𝑑𝑉 +න𝐴

𝜌𝜑 𝑉. 𝑑𝐴 =𝑑∅

𝑑𝑡

∅: Transported quantiny (extensive property)𝜑: intensive property of ∅∅ = 𝜑 m m: mass

𝜑 → 𝑡 residence time∅ = 𝑡 m

𝜕

𝜕𝑡න𝑉

𝜌𝑡 𝑑𝑉 +න𝐴

𝜌𝑡 𝑉. 𝑑𝐴 =𝑑(𝑡𝑚)

𝑑𝑡= 𝑚

𝑑𝑡

𝑑𝑡+ 𝑡

𝑑𝑚

𝑑𝑡

𝜕

𝜕𝑡න𝑉

𝜌𝑡 𝑑𝑉 +න𝐴

𝜌𝑡 𝑉. 𝑑𝐴 = 𝑚

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How to calculate the RT in Star-CCM+?

𝜕

𝜕𝑡න𝑉

𝜌 𝜑 𝑑𝑉 +න𝐴

𝜌 𝜑 𝑉. 𝑑𝐴 = න𝑉

𝑆𝜑 𝑑𝑉

Passive scalar model in Star-CCM+

𝜕

𝜕𝑡න𝑉

𝜌 𝑡 𝑑𝑉 + න𝐴

𝜌 𝑡 𝑉. 𝑑𝐴 = 𝑚

න𝑉

𝑆𝜑 𝑑𝑉 = 𝑚

𝑺𝝋 = 𝝆

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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 (ϴ)

Straight pipe

Helical pipe

𝜽 =𝒕 − 𝒕𝒎𝒊𝒏

𝝉

𝐑𝐞 = 𝟒𝟎 𝐑𝐞 = 𝟐𝟎𝟎𝟎

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 (ϴ)

Straight pipe

Helical pipe

Straightpipe

Helicalpipe

Thank you!

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