Two Stage Recuperator Effectiveness

[BretCahill]

If the mass flow rates / heat capacities are the same on both sides, what would be the overall effectiveness of two regenerators in series with different effectivenesses?


Bret Cahill

 

[25362]

The effectiveness of each recuperator (regenerator?) is a function of the number of transfer units NTU[sub]max[/sub] = AU/C[sub]min[/sub].

Where C[sub]min[/sub] = (mc)[sub]min[/sub]

I leave it to yourself to see what happens with NTU with the two units in series, when the mass flow rates and the heat capacities values are equal for both sides ie, the ratio (mc)[sub]cold[/sub]/(mc)[sub]hot[/sub] = 1.

The effectiveness, [ε], values from Holman (fig. 10-13) for countercurrent flow are:

NTU [ε], %
0.5 30
1 50
2 67
3 75
4 80

For parallel flow and NTU values greater than 2.5, [ε] is constant at 50%. It is approximately the same for cross-flow units with [ε] at around 60-63%.

 

[BretCahill]

So the overall effectiveness of regenerators in series can be determined by adding the HTUs, for example, a regenerator with ? = 50% in series with a regenerator of ? = 75% has an overall ? of 80%.

Or overall ? = (?/(1-?) + ?/(1-?). . .) / (?/(1-?) + ?/(1-?). . . + 1)

(Subscripts omitted)

Effectiveness is deceptive. It doesn't really flag the diminishing returns. Going from 90% to 97.5% ? doesn't seem like such a big deal until you realize it requires more than 4 times the material. The HTU number is a better indicator of how big and heavy and expensive the thing is going to be.


Bret Cahill

 

[25362]

Series recuperators (are pre-heaters) are available in the market. Some are pure convection types others are pure radiation types. Some are combinations.

A Google review may show you some interesting sites on this issue.