Super simple temperature test. 38.6% error. Do you know why?

General discussion about Elmer
ScientistRenzo
Posts: 57
Joined: 14 Mar 2021, 21:01
Antispam: Yes

Super simple temperature test. 38.6% error. Do you know why?

Post by ScientistRenzo »

I simed the expected temperature rise of a cube of water.
A 1 kg cube of water applied 1 Grey is expected to rise in temperature everywhere by ≈ 0.25 mK

Cube of Water - Volume: 0.1001 m * 0.1001 m * 0.1001 m = 0.001001 m³
Reason: I want mass = 1 kg.
ρ ≈ 997 kg/m³ = m/V
∴ m = 997 * 0.001001 = 1 kg

Applying 1 Grey = 1 J / kg should raise temp. everywhere by 0.25 mK
Q = mcΔT = (1)(4148)(ΔT) = 1 J
∴ ΔT ≈ .241 mK ≈ .25 mK

Heat Source in W/kg = (J/s)/kg = J/(s*kg)
I want 1 J applied to this 1 kg cube of water
I choose 10 seconds.
∴ (0.1 J/(s*kg)) * (10 s) * (1 kg) = 1 J.

Expected ΔT = 0.241 mK.
Sim Results ΔT = 0.17382 mK.
% Error = 38.6%

I wonder why?

My cube has Idealized Emissivity = 0.95.
I.C. 273 K and B.C. 273 K.

So my expected result must be for a cube that does not experience heat flow to it's surroundings/radiate!

Is that right? Everything look alright? Any input?
Image https://imgur.com/a/nhjmYrT

Edit 1: Without Idealized Radiation, Radiation disabled, ΔT = 0.17441 mK. Barely change.
kevinarden
Posts: 2237
Joined: 25 Jan 2019, 01:28
Antispam: Yes

Re: Super simple temperature test. 38.6% error. Do you know why?

Post by kevinarden »

With an initial condition of 273 and an external temp of 273 I get the 0.17mK
With an initial condition of 0 and and external temp of 0 I get the 0.24mK
ScientistRenzo
Posts: 57
Joined: 14 Mar 2021, 21:01
Antispam: Yes

Re: Super simple temperature test. 38.6% error. Do you know why?

Post by ScientistRenzo »

Good!

I wonder why the results are different at 273 K because the difference of internal and ext. temperature are the same.
kevinarden
Posts: 2237
Joined: 25 Jan 2019, 01:28
Antispam: Yes

Re: Super simple temperature test. 38.6% error. Do you know why?

Post by kevinarden »

At 273 with 10, 0.1 second steps I get the .17
At 273 with 1, 1 second step I get 0.23
ScientistRenzo
Posts: 57
Joined: 14 Mar 2021, 21:01
Antispam: Yes

Re: Super simple temperature test. 38.6% error. Do you know why?

Post by ScientistRenzo »

I believe you are applying the same amount of Joules when you apply 1 Joule in 1 second, regardless of whether the simulation evaluates data every second, or .1 second ten times for a total of 1 second simulation.

I wonder why these differences are there

Thanks for experimenting and sharing your results :D!
raback
Site Admin
Posts: 4812
Joined: 22 Aug 2009, 11:57
Antispam: Yes
Location: Espoo, Finland
Contact:

Re: Super simple temperature test. 38.6% error. Do you know why?

Post by raback »

Hi

For nonlinear systems the result will depend on the time discretization. Without radiation the system should be linear and hence there should not be effect on time stepping.

-Peter
ScientistRenzo
Posts: 57
Joined: 14 Mar 2021, 21:01
Antispam: Yes

Re: Super simple temperature test. 38.6% error. Do you know why?

Post by ScientistRenzo »

Oh okay. Thanks Peter.

So then, I'd like to understand how to make allowances for the effects of time discretization in nonlinear systems.

In this experiment,
time discretization with small intervals produced .17 mK
time discretization with large intervals produced .23 mK

The expected result was .24 mK; Did a finer sampling rate produce more error?

I think a higher sampling rate produces more accurate results, and less extrapolation.

Any input?
raback
Site Admin
Posts: 4812
Joined: 22 Aug 2009, 11:57
Antispam: Yes
Location: Espoo, Finland
Contact:

Re: Super simple temperature test. 38.6% error. Do you know why?

Post by raback »

The expected results without any cooling? I thought you had some black body radiation that kicks in when the object starts heating. -Peter
kevinarden
Posts: 2237
Joined: 25 Jan 2019, 01:28
Antispam: Yes

Re: Super simple temperature test. 38.6% error. Do you know why?

Post by kevinarden »

My boundary condition is this
Boundary Condition 1
Target Boundaries(6) = 1 2 3 4 5 6
Heat Flux BC = Logical True
External Temperature = 273
Heat Transfer Coefficient = 1.0
End

but if I use idealized radiation with the same external temperature, the results are the same.
ScientistRenzo
Posts: 57
Joined: 14 Mar 2021, 21:01
Antispam: Yes

Re: Super simple temperature test. 38.6% error. Do you know why?

Post by ScientistRenzo »

I set boundaries to have Idealized Radiation: Emissivity 0.95, Because without this emissivity, the model is less realistic, right??

The object has a constant heat applied for 10 seconds, (or for 1 second, depending on the time steps/intervals/discretization used).

Because I'm new in this stuff, I'm surprised by the larger error between the theoretical results and simulated results when I use higher sampling.

Thanks :D!
Post Reply