Mech-HT 13.0 L07 Transient

8/12/2019 Mech-HT 13.0 L07 Transient

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Customer Training Material

ec ure

Transient ThermalAnalysis

Heat Transfer

L7-1 ANSYS, Inc. Proprietary 2010 ANSYS, Inc. All rights reserved.

Release 13.0December 2010


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ANSYS Mechanical Heat Transfer

Customer Training Material Chapter Contents

A. Transient TheoryB. Time SteppingC. Transient Loadin

D. Transient Post ProcessingE. Workshop 7, Soldering Iron




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Customer Training Material A. Transient Theory

Like steady-state analyses, transient analyses may be linear ornonlinear. If nonlinear, the same preprocessing considerations applyas with steady-state nonlinear analysis (described in Chapter 5).

The most significant difference between steady-state and transientanalyses lies in the Loading and Solution procedures.

numerical methods employed during transient thermal analysis.




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Customer Training Material . . . Transient Theory

Recall the governing equation for thermal analysis of a linear systemwritten in matrix form. The inclusion of the heat storage termdifferentiates transient systems from steady-state systems:

[ ] [ ]{ } { }QT K T C =+&

In a transient analysis, loads may vary with time . . .

Heat Storage Term = (Specific Heat Matrix) x(Time Derivative of Temperature)

[ ] [ ]{ } ( ){ }tQT K T C =+&

. . . , ,temperature:( )[ ] ( )[ ]{ } ( ){ }tT QT T K T T C ,=+&




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When the response of a system over time is required due to loadsand/or boundary conditions change over time, a Transient Analysisis performed.

Time-Varying Loads Time-Varying Response

Thermal energy storage effects are now included. Time hasphysical meaning.




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Material Property Considerations for Transient Analyses:

In addition to thermal conductivity (k), density ( ) and specific heat (c )material properties must be specified for entities which can conductand store thermal energy.

These material properties are used to calculate the heat storagecharacteristics of each element which are then combined in the SpecificHeat Matrix [C].




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Customer Training Material B. Time Stepping

The temperature of a linear thermal system changes continuouslyfrom instant to instant: T

When erformin a thermal transient anal sis a time inte ration

t

procedure is used to obtain solutions to the system equations atdiscrete points in time. The change in time between solutions iscalled the integration time step (ITS).

T

Generall the smaller the ITS the more accurate the solution

t

t n t n+1 t n+2



becomes.


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Customer Training Material . . . Time Stepping

Selection of a reasonable time step size is important because ofits impact on solution accuracy and stability:

If the time ste size is too small then solution oscillations maoccur which could result in temperatures which are not physicallymeaningful (e.g. thermal undershoot).

If the time ste is too lar e then tem erature radients will not beadequately captured.

One approach is to specify a relatively conservative initial timeste and allow Automatic Time Ste in to increase the time steas needed.

The guidelines on the following slides are presented as a way toapproximate a reasonable initial time step size for use withAutomatic Time Stepping.




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A reasonable time step size for thermal transient analyses canbe approximated using the Fourier modulus:

Where: 2**4 t K

Fo

=

t is ITS time step x is the average element length K is the average thermal conductivity is average density C is average specific heat

A su ested minimum inte ration time ste ITS : c xt **2

=

When t is 100 times the ITS suggestion, a warning appears:

*4




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To help evaluate the accuracy of the time integration algorithm,ANSYS computes and reports some helpful quantities after everysolution:

The Response Eigenvalue represents the dominant systemeigenvalue for the most recent time step solution (reported inSolution information).

If the Eigenvalue is small, a larger time step is used and vice versa.

The Oscillation Limit is a dimensionless quantity that is simply theproduct of the Response Eigenvalue and the current time step size(reported in Solution information).

It is typically desirable to maintain the oscillation limit below 0.5 to insurethat the transient response of the system is being adequately

. See next page . . .




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By default, the Automatic Time Stepping (ATS) feature

Time step metrics can be viewed in the Solution Information.

ases me s ep pre c on on e sc a on m .

seeks to maintain the Oscillation Limit below 0.5 within atolerance, and will adjust the ITS to satisfy this criterion.

Notice how ATS

ITS based on theOscillation Limit. Thissample was taken from

Window during anonlinear transientanalysis.




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Customer Training Material C. Transient Loading

While loads can be applied as constants in transient analyses, oftenthey vary with time.

In Mechanical, thermal loads can be defined as constants, tables orfunctions.

Recall that in chapter 3 we outlined non-constant loading. Here wewill illustrate using specific examples.

Table Loads Function Loads




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Customer Training Material . . . Transient Loading

Example 1: the heating coil experiences jouleheating as power is cycled on and off at 1second intervals:

Notice in the table a small time increment isused to ramp the load on and off quickly,simulating a step function.

.




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Customer Training Material . . . Transient Loading

Example 2: the same heating coilundergoes sinusoidal loading accordingto the function (0.1+(0.1*sin(180*time))):

Notice the table is populated by evaluatingthe function at 200 equally spaced timepoints.




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Customer Training Material D. Transient Post Processing Post processing transient results is done by requesting results from

particular time points: RMB on the graph or table at the desired time point and choose Retrieve

.

OR Enter the desired time in the details for a result and RMB Retrieve This

Result.




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Customer Training Material . . . Transient Post Processing

Often the desired quantity is the resultvariation over time at a point ratherthan a contour of the overall model.

A graph is useful in displaying resultsvs. time.

Here a temperature probe is scoped toa local coordinate s stem and thetemperature variation is plotted in thegraph area.




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Customer Training Material

or s op

Soldering Iron

Heat Transfer



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Mech-HT 13.0 L07 Transient

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