Thermal undershoot

How To Address Thermal Undershoot Problem

ANSYS HowTo Documents


Thermal Undershoot

• Consider the slab shown at the right.

• One face has a uniform heat flux applied, the other has an uniform convection to ambient air @ 70 ºF.

• A thermal transient analysis is performed. Boundary conditions are step changed at time=0 sec

Uniform Heat Flux of 100 BTU/sec*in2

Uniform convection to ambient

h = 2 BTU/ft2*hr*ºF



Thermal Undershoot

• The results of the transient analysis are shown at the right.

• In spite of an initial temperature of 70 ºF, and an ambient temperature of 70 ºF, the minimum temperature during the transient falls below 70 ºF.

Tranient temperture falls below ambient 70ºF



Thermal Undershoot• From the Thermal Analysis Guide, Section 3.4.3.2:

In regions of severe thermal gradients during a transient (e.g., surfaces of quenched bodies), there is a relationship between the largest element size in the direction of the heat flow and the smallest time step size that will yield good results. Using more elements for the same time step size will normally give better results, but using more substeps for the same mesh will often give worse results. When using automatic time stepping and elements with midside nodes (quadratic elements), ANSYS recommends that you control the maximum time step size by the description of the loading input and define the minimum time step size (or maximum element size) based on the following relationship:

ITS = Δ2 / 4 αThe Δ value is the conducting length of an element (along the direction of heat flow) in the expected highest temperature gradient. The α value is the thermal diffusivity, given by k/ρC. The k value is the thermal conductivity, ρ is the mass density, and C is the specific heat.

If the above relationship (ITS = Δ2 / 4 α) is violated when using elements with midside nodes, ANSYS typically computes unwanted oscillations and temperatures outside of the physically possible range. When using elements without midside nodes, the unwanted oscillations are unlikely to occur, and the above recommendation for the minimum time step can be considered somewhat conservative.



Thermal Undershoot

• Lets check this criteria out against our model.– Δ = 1/3 = 0.333 inch– K = 8.0917x10-4 BTU/s*in*ºF– ρ = 0.2838 lb/in3

– Cp = 0.10358 BTU/lb*ºF

– α = 0.02753 in2/sec– ITS = Δ2 / 4*α– ITS = (0.333)2/(4*0.02753) = 1.009 sec

• From the Analysis Settings we can see that the minimum time step size is set to 0.01. This value is too small for the current mesh sizing. We can either increase the mesh density or increase the minimum time step size.

• ITS = 0.01 ---> Δreq = 0.033 in (30 elements thru thickness)

• ITS = 0.1 ---> Δreq = 0.105 in (10 elements thru thickness)

• Lets try the latter, Δreq = 0.105

1 inch



Thermal Undershoot

• We insert a Edge Sizing object into the Mesh branch

• In the Details windows, specify Number of Divisions under Type

• Set the Number of Divisions to 10

• The resulting mesh



Thermal Undershoot

• The revised transient analysis show no thermal undershoot

Engineering

Thermal undershoot