Defining Transient Time Scales and Stopping Criteria

The flow of exhaust gas and the heating of the solid manifold are both simulated with the implicit unsteady time solver using different time step sizes. Simcenter STAR-CCM+ handles multiple time step sizes using time scales—one time scale for each continuum.

When you use time scales in running a simulation, you can specify stopping criteria that apply whenever that time scale is active.

Each stopping criterion has a property called Logical Rule which defines how the criterion interacts with other active stopping criteria. The Logical Rule can be set to AND or OR with meaning as follows:

AND — requires that this criterion and all others having Logical Rule set to AND must be satisfied before they stop the solver.
OR — indicates that this criterion alone, when satisfied, is sufficient to stop the solver

In the following setup, several criteria are defined having Logical Rule set to AND, which means that they must be satisfied together before the solver stops.

For the fluid continuum, you define a time scale with a time step corresponding to two degrees of crank angle.

To specify the fluid time scale:

Right-click the Automation > Time Scales node and select New Time Scale.

Rename the node Implicit Unsteady Time Scale to Fluid Time Scale and set the properties as follows:


Property	Setting
Physics Continua	Physics Fluid
Time-Step	${FluidTimeStep(s)}

To control the fluid-only solution, you specify stopping criteria for the fluid time scale. One criterion sets a minimum run time and another checks for the solution coming to a stable condition based on the heat flux across the solid-fluid interface.

To ensure that the fluid solution runs for at least one cycle each time, you specify a fixed physical time stopping criterion whose duration is one cycle:

Right-click the Time Scales > Fluid Time Scale > Stopping Criteria node and select New Criterion > Fixed Physical Time.
Rename the Fixed Physical Time node to Minimum Fixed Fluid Run Time.

Select the Minimum Fixed Fluid Run Time node and set the properties as follows:


Property	Setting
Fixed Physical Time	${FluidCycleLength(s)}
Logical Rule	And

After ensuring a minimum run time for the fluid, you then want to run for as long as it takes to observe a near-constant average value of boundary heat flux on the fluid side of the interface.

First, create a report for the surface average boundary heat flux:

Right-click the Reports > New > Metrics > Surface Average.
Rename the Surface Average 1 node to SA_TA_BoundaryHeatFlux.

Select the SA_TA_BoundaryHeatFlux node and set the properties as follows:

Property

Setting

Field Function

Time Averaged Boundary Heat Flux

Note	This field function appears when the Time Averaging Option of the solid interface boundary is set to Time Averaging Option.

Parts

Regions > Exhaust Gas > Faces[Exhaust Gas/Manifold Solid]]

Note	Here you select the fluid interface boundary since the time averaged boundary heat flux is mapped to the fluid side.

To create a monitor and stopping criterion from this report:

Right-click the SA_TA_BoundaryHeatFlux node and select Create Monitor from Report.
To define a new monitor criterion, right-click the Automation > Time Scales > Fluid Time Scale > Stopping Criteria node and select New Monitor Criterion.
In the Select Monitor dialog, select the SA_TA_BoundaryHeatFlux Monitor and click OK.

Select the SA_TA_BoundaryHeatFlux Monitor Criterion node and set the properties as follows:


Property	Setting
Criterion Option	Asymptotic
Logical Rule	And
Stop Inner Iterations	Deactivated

To set up the asymptotic limit, select the SA_TA_BoundaryHeatFlux Monitor Criterion > Asymptotic Limit node and set the properties as follows:


Property	Setting
Refresh Sampling	✓
[Max-Min]	5.0 W/m^2
Normalized	Deactivated

To prevent an endless run, specify a Fixed Physical Time criterion with a 5 cycle time period:

Right-click the Time Scales > Fluid Time Scale > Stopping Criteria node and select New Criterion > Fixed Physical Time.
Rename the Fixed Physical Time node to Maximum Fixed Fluid Run Time.

Select the Maximum Fixed Fluid Run Time node and set the properties as follows:

Property

Setting

Fixed Physical Time

5.0*${FluidCycleLength(s)}

Logical Rule

Note	Or is used here in order to override all other criteria in the event that the others fail to stop the solver.

To control the number of inner iterations within a time step, add a Maximum Inner Iterations criterion:

Right-click the Time Scales > Fluid Time Scale > Stopping Criteria node and select New Criterion > Maximum Inner Iterations.

Select the Maximum Inner Iterations node and set the properties as follows:


Property	Setting
Maximum Inner Iterations	5
Logical Rule	Or

To control the solution for the solid-only run, you specify stopping criteria for the solid time scale. Two criteria set the minimum and maximum run time respectively. Another criterion monitors the change in temperature of the solid and ends the solid run when the temperature change reaches 5%.

To specify the time scale for the manifold solid:

Right-click the Automation > Time Scales node and select New Time Scale.

Rename the sub-node Implicit Unsteady Time Scale to Solid Time Scale and set the properties as follows:


Property	Setting
Physics Continua	Physics Solid
Time-Step	${SolidTimeStep(s)}

You specify the following stopping criteria for the Solid Time Scale to control the solid-only run:

To set an upper limit on the solid run:

Right-click Time Scales > Solid Time Scale > Stopping Criteria node and select New Criterion > Fixed Physical Time.
Rename the Fixed Physical Time node to Maximum Fixed Solid Run Time

Select the Maximum Fixed Solid Run Time node and set the properties as follows:


Property	Setting
Fixed Physical Time	100.0 s
Logical Rule	Or

Using solution-based monitor criteria prevents the solver from running longer than necessary. Here, you specify one that monitors the volume-average solid temperature. When the monitor detects that the relative change exceeds 5%, the solid run stops and another fluid run begins.

To set up the monitor criterion for the volume averaged solid temperature:

Define the report as follows:

Right-click the Reports node and select New > Metrics > Volume Average.
Rename the Volume Average 1 node to VA_T_Solid.

Select the VA_T_Solid node and set the properties as follows:


Property	Setting
Units Function	C
Field Function	Temperature
Parts	Region > Manifold Solid

Right-click the VA_T_Solid node and select Create Monitor from Report.

To define the monitor criterion:

Right-click the Automation > Time Scales > Solid Time Scale > Stopping Criteria node and select New Monitor Criterion.
In the Select Monitor dialog, select the in the previous step created VA_T_Solid Monitor and click OK.

Select the VA_T_Solid Monitor Criterion node and set the properties as follows:


Property	Setting
Criterion Option	Relative Change
Logical Rule	Or
Stop Inner Iterations	Deactivated

Select the VA_T_Solid Monitor Criterion > Relative Change node and set the properties as follows:


Property	Setting
Refresh Sampling	✓
Relative Change	1.05

To add a stopping criterion for the maximum number of inner iterations in each time step:

Right-click the Time Scales > Solid Time Scale > Stopping Criteria and select New Criterion > Maximum Inner Iterations.

Select the Maximum Inner Iterations node and set the properties as follows:


Property	Setting
Maximum Inner Iterations	5
Logical Rule	Or

Besides the time scale specific stopping criteria, you also specify the maximum physical run time as a global stopping criterion.

In the simulation tree, select the Stopping Criteria > Maximum Physical Time node and set the Maximum Physical Time to 350.0 s.
Delete all the other global stopping criteria other than the Maximum Physical Time defined above.
Save the simulation.