What free stream/bulk temperature to take in this case?

Thomasbr · August 10, 2016, 10:17

Hello,

I am trying to estimate the heat transfer coefficient for the circled zone of the cylinder (that is, the bottom wall of the cylinder, see attachment). The temperature curve starting from green point and continuing vertically has been obtained through CFX Post (for a certain instant).

The wall heat flux is provided by CFX and the wall temperature is known. The heat transfer coefficient depends on the so called Bulk Temperature
$T_\text{Bulk}$ :

$\alpha=q_\text{Wall}/(T_\text{Wall}-T_\text{Bulk})$

But what temperature can I take? In the attachment we clearly see, that away from the wall, the temperature tends to be constant, T "free stream. But before that the temperature increases and then decreases...

In my case, the flow is highly turbulent and defining a bulk temperature is not simple at all.

flotus1 · August 10, 2016, 10:59

In my experience, the question about the "correct" reference quantity is has little relevance.
The more important question usually is: what do you want need the coefficient for?

Compare your results to other peoples research: use the same reference quantities they used.
Produce your own data independently: use whatever reference quantity you think is relevant. In your case the most straightforward choice seems to be the temperature at the inlet of the computational domain. Of course in this case, along with your results, you have to document the reference values you used.

Thomasbr · August 10, 2016, 15:18

Hello Alex,

thank you very much for this instructive answer. As far as I know (I will clear that with my instructor), I will not compare my HTC's with other HTC's. What I am sure of, is that I will need to compare the HTC's of

the bottom of the cylinder
the side of the cylinder
the ceiling of the cylinder

together in order to check which area of the cylinder has the greatest influence on the heat transfer. I need then the relative values of these HTC's more than their "absolute" values. For this matter, I think that for each area, the chosen reference temperature should be consistent with the others.
The temperature curves for the side of the cylinder look better (ie easier to handel, see attachment). As the temperatures away from the wall tend to have a constant value, I did the average of this temperature over the domain which one can see in the attachment (the domain is a cross section of the cylinder, bounded through 0,6R < r < R because for smaller r, it is the jet which is very cold (due to high speed)).

As the flow is strongly compressible, I cannot use a simple averaging of the temperature but a mass weighted averaging method. Although the flow in the cylinder is not a one dimensional flow, I used a temperature averaging based on the mean temperature (weight = mass flow rate):

$T_\text{mean}=\frac{\iint_A\rho u T\ \text{d}A}{\dot{m}}$ where A is the cross section and u the velocity of the flow.

I also tried with the mass temperature (weight = mass (well it should be a volume integral))

$T_\text{mass}=\frac{\iint_A\rho T\ \text{d}A}{\iint_A \rho\ \text{d}A}$

In my case, $T_\text{mean}\approx T_\text{mass}$ , so that I can use any of the two above reference temperatures.

Or I also could use the inlet temperature (which varies upon time) as a reference temperature for every HTC? I would be able to compare them aswell. But this definition of the reference temperature bothers me a little, because it is very far away from the walls...

flotus1 · August 11, 2016, 04:59

I think you are making thinks more complicated than they actually are.

Let me put it this way: if you use a reference temperature based on the RESULT of your simulation (e.g. the averaging you are trying, or even worse a local temperature near the wall) the following can happen: for two slightly different simulation setups the actual heat transfer is different, but the heat transfer coefficient could be the same. This can even mean that in a setup where the heat transfer coefficients are lower, the amount of heat transferred can be higher. This is definitely not desirable.
On the other hand, think about the implications if you choose a "wrong", but constant reference temperature (please note the quotation marks, there is no wrong value): the magnitude of the heat transfer coefficient will be different, that much is true. But the qualitative shape of the htc will be the same. Every engineer around the world will be able to deduce the actual amount of heat transferred using your htc and reference temperature. And if the htc for one setup is lower than for a different one, you can be sure that the amount of heat transferred is also lower in the latter case.
The only important thing, and I can not emphasize this enough, is that you give the reference values along with your results.

August 10, 2016, 10:59		#2
flotus1 Super Moderator Alex Join Date: Jun 2012 Location: Germany Posts: 3,427 Rep Power: 49	In my experience, the question about the "correct" reference quantity is has little relevance. The more important question usually is: what do you want need the coefficient for? Compare your results to other peoples research: use the same reference quantities they used. Produce your own data independently: use whatever reference quantity you think is relevant. In your case the most straightforward choice seems to be the temperature at the inlet of the computational domain. Of course in this case, along with your results, you have to document the reference values you used. Last edited by flotus1; August 10, 2016 at 15:36.

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August 11, 2016, 04:59		#4
flotus1 Super Moderator Alex Join Date: Jun 2012 Location: Germany Posts: 3,427 Rep Power: 49	I think you are making thinks more complicated than they actually are. Let me put it this way: if you use a reference temperature based on the RESULT of your simulation (e.g. the averaging you are trying, or even worse a local temperature near the wall) the following can happen: for two slightly different simulation setups the actual heat transfer is different, but the heat transfer coefficient could be the same. This can even mean that in a setup where the heat transfer coefficients are lower, the amount of heat transferred can be higher. This is definitely not desirable. On the other hand, think about the implications if you choose a "wrong", but constant reference temperature (please note the quotation marks, there is no wrong value): the magnitude of the heat transfer coefficient will be different, that much is true. But the qualitative shape of the htc will be the same. Every engineer around the world will be able to deduce the actual amount of heat transferred using your htc and reference temperature. And if the htc for one setup is lower than for a different one, you can be sure that the amount of heat transferred is also lower in the latter case. The only important thing, and I can not emphasize this enough, is that you give the reference values along with your results.