How to get recirculation factor (by mass) used for underhood front-end simulation?

Recirculation factor (RF) is a useful parameter for front-end underhood
application. Air enters the top and bottom grille. Some of this flows through
the cooling package (it enters the condenser-inlet and then the radiator). All
of this air that has entered the cooling package through the condenser-inlet
exits on the other side from the radiator-outlet.

Not all the air that enters the condenser-inlet comes from the grille. Some
comes from the tire region, some through recirculation, and some from radiator back flow.

Some of the air that has exited the cooling package through radiator-outlet
exits the unerhood and some returns back (recirculates) to the
condenser-inlet. Client would like to know the fraction (by mass) of the air
recirculated. How to calculate RF?
1. Obtain flow solution as usual.

2. Activate User Defined Scalar
a) increase "Number of User-Defined Scalar" to 1
b) select "mass flow rate" for "Flux Function"
c) click on OK
d) clicjk on OK for the new message window
"mass flow rate" will use UDS = density * velocity.

3. Set UDS Deffusivity
a) select 'fluid' under 'Material Type'
b) select the material name under 'Fluid Materials'
c) click on 'Edit...' for 'UDS Diffusivity'
Another panel will open.
d) select UDS-0 under 'User Defined Scalar Di'
e) select Constant under Coefficient
f) enter a value 0.0. This implies that UDS transports only by convection process and not by diffusion. In many cases, this assumption is true where diffusion is very less. But for more accurate results, UDS diffusion also needs to be accounted for and the UDS diffusivity is given by turbulent_diffusivity*Schmidt_number. This could be provided to Fluent through an UDF.

4. Assign value of 1.00 for "User defined scale-0 (UDS-0)
Define->Boundary Conditions
a) select radiator cell zone under Zone
b) click on Set

c) select "Fixed Values"
d) enter 1.00 for "User defined scalar-0"
e) click on OK

Fluent will add proper source/sink terms so that the fixed value is 1.0.

5. Assign zero UDS VALUE at all inlets
Define->Boundary Conditions
a) select the inlet zone under Zone
b) click on Set

c) select "Specified Value" for Scale-0 under UDS Boundary Condition"
d) enter0.00 for Scalar-0 under "UDS Boundary Value
e) click on OK
Repeat step 4 for other inlets.

NOTE: By default all walls and outlets will have UDS flux of zero.

NOTE2: We need to provide zero VALUE entering the domain and zero FLUX at all the walls. If we provide zero flux at all the boundaries, then it may not converge and/or give wrong result.

6. Patch UDS of 0.00 in all the cells.

7. Use Underrelaxation Factor (URF) of 1.0 for UDS
Solve -> Controls -> Solution
a) enter 1.0 for "User defined Scalar-0" under "Under-Relaxation Factors"

b) select ONLY "User defined scalar-0" under Equations

8. You need to converge the UDS equation down to 3e-5. Run only the UDS equation. You first start with underrelaxation factor (URF) of 0.8, iteration about 10 times, and then increase URF to 1.0 and then iterate to reach residual value of about 3e-5. Then you can change to second-order UDS and continue iteration.


9. Report -> Surface Integrals
a) select condenser-in under Surfaces.

Note that condenser-in should be selected. Radiator-in should not be selected because it is attached to radiator cell that has fixed value of UDS of 1.0. If radiator-in is selected, it will average the values of upstream and downstream cells. The downstream cell has a fixed value of 1.0 which should not be included in the report-integrals.

b) select "Flow Rate" under "Report Type"
c) select "User Defined Scalars" under "Field Variables"
d) select "Scalar-0" under "User Defined Scalars"
e) click on Compute

The UDS will vary from 0.00 to its fixed value of 1.00. Integrating UDS using
"Flow Rate" will lead to mass flow rate of UDS, which is the same as mass flow rate of air recirculated. See
<a target=_blank href=""></a> for definition for "Flow Rate" integration.

It will print out the mass flow rates of UDS in the cortex window. It will be the amount recirculated. You can get the total mass-flow rate using Report-Fluxes through this same surface to get the ratio.

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