Mech-HT 120 Lect-06 Transient

Chapter 6

Transient Thermal Analysis

6-1ANSYS, Inc. Proprietary© 2009 ANSYS, Inc. All rights reserved.

August 2009Inventory #002667

ANSYS Mechanical Heat Transfer


Training ManualChapter Contents

A. Transient TheoryB. Time SteppingC. Transient LoadingD. Transient Post ProcessingE. Workshop




Training Manual

• Like steady-state analyses, transient analyses may be linear or nonlinear. If nonlinear, the same preprocessing co nsiderations apply as with steady-state nonlinear analysis (described in Chapter 5).

• The most significant difference between steady-stat e and transient analyses lies in the Loading and Solution procedures.

• We will focus on these procedures after a brief pre sentation of the numerical methods employed during transient thermal analysis.

A. Transient Theory




Training Manual

• Recall the governing equation for thermal analysis of a linear system written in matrix form. The inclusion of the heat storage term differentiates transient systems from steady-state systems:

[ ]{ } [ ]{ } { }QTKTC =+&

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

. . . Transient Theory



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

• . . . or, in the case of a nonlinear transient anal ysis, time AND temperature:

[ ]{ } [ ]{ } ( ){ }tQTKTC =+&

( )[ ]{ } ( )[ ]{ } ( ){ }tTQTTKTTC ,=+&


Training Manual

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




Time-Varying Loads Time-Varying Response

• Thermal energy storage effects are now included. T ime has physical meaning.


Training Manual

• Material Property Considerations for Transient Anal yses:

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

– These material properties are used to calculate the heat storage characteristics of each element which are then comb ined in the Specific Heat Matrix [C]





Training Manual

• The temperature of a linear thermal system changes continuously from instant to instant:

• When performing a thermal transient analysis, a tim e integration procedure is used to obtain solutions to the system equations at discrete points in time. The change in time betwee n solutions is

T

t

B. Time Stepping



discrete points in time. The change in time betwee n solutions is called the integration time step (ITS).

• Generally, the smaller the ITS, the more accurate the soluti on becomes.

T

t∆ ∆ ∆ ∆ t

tn tn+1 tn+2


Training Manual

• Selection of a reasonable time step size is importa nt because of its impact on solution accuracy and stability:

– If the time step size is too small, then solution oscillations may occur which could result in temperatures which are not physically meaningful (e.g. thermal undershoot)

– If the time step is too large, then temperature gradients will not be adequately captured

• One approach is to specify a relatively conservativ e initial time

. . . Time Stepping



• One approach is to specify a relatively conservativ e initial time step and allow Automatic Time Stepping to increase the time step as needed

• The guidelines on the following slides are presente d as a way toapproximate a reasonable initial time step size for use with Automatic Time Stepping


Training Manual. . . Time Stepping

• A reasonable time step size for thermal transient a nalyses can be approximated using the “Fourier modulus”:

• Where:– ∆t is ITS time step– x is the average element length– K is the average thermal conductivity– ρ is average density– C is average specific heat

2)(**

**4

xC

tKFo

∆∆=

ρ

2 ρ∆



– C is average specific heat

• A suggested minimum integration time step (ITS):

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

K

cxt

*4

**2 ρ∆=∆


Training Manual

• To help evaluate the accuracy of the time integrati on algorithm, ANSYS computes and reports some helpful quantities after every solution:

• The Response Eigenvalue represents the dominant sys tem eigenvalue for the most recent time step solution ( reported in Solution information)

– If the Eigenvalue is small, a larger time step is u sed and vice versa

• The Oscillation Limit is a dimensionless quantity t hat is simply the

. . . Time Stepping



• The Oscillation Limit is a dimensionless quantity t hat is simply the product of the Response Eigenvalue and the current time step size (reported in Solution information)

– It is typically desirable to maintain the oscillati on limit below 0.5 to insure that the transient response of the system is being adequately characterized

• See next page


Training Manual

By default, the Automatic Time Stepping (ATS) feature bases time step prediction on the Oscillation Limit. ATS seeks to maintain the Oscillation Limit below 0.5 within a tolerance, and will adjust the ITS to satisfy this criterion.

. . . Time Stepping

Time step metrics can be viewed in the Solution Inf ormation.



Notice how ATS gradually reduces the ITS based on the Oscillation Limit. This sample was taken from the ANSYS Output Window during a nonlinear transient analysis.


Training ManualC. Transient Loading

• While loads can be applied as constants in transien t analyses, often they vary with time

• In Mechanical, thermal loads can be defined as cons tants, tables or functions

• Recall that in chapter 3 we outlined non-constant l oading. Here we will illustrate using specific examples



Table Loads Function Loads


Training Manual. . . Transient Loading

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

– Notice in the table a small time increment is used to ramp the load on and off quickly, simulating a step function

– Each new time point must increase in value




Training Manual. . . Transient Loading

• Example 2: the same heating coil undergoes sinusoidal loading according to the function (0.1+(0.1*sin(180*time)))

– Notice the table is populated by evaluating the function at 200 equally spaced time points




Training ManualD. Transient Post Processing• Post processing transient results is done by reques ting results from

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

This Result”OR

– Enter the desired time in the details for a result and RMB “Retrieve This Result”




Training Manual. . . Transient Post Processing

• Often the desired quantity is the result variation over time at a point rather than a contour of the overall model

• A graph is useful in displaying results vs. time

• Here a temperature probe is scoped to



• Here a temperature probe is scoped to a local coordinate system and the temperature variation is plotted in the graph area

Workshop 6

Soldering Iron



ANSYS Mechanical Heat Transfer

Mech-HT 120 Lect-06 Transient

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