Condenser optimization question

[Martin Harris]

TL;DR Summary

Trying to optimize the condenser such as reducing the analytic error by tweaking wall temperature and condensing temperature.

Hi,

I have an attempt at a plate heat exchanger (condenser) that uses water to condenser refrigerant, as a part of a heat pump.

I have a total heat load of 12.01 kW.

My current heat load is 10 kW.
I have an analytical error on the wall temperature of about 23%, if I use Excel's Solver to minimize the error by changing the Wall temperature by multiple iterations, then the new wall temperature will decrease from 38.6 deg C to 37.81 deg C and the heat load would also decrease from 10 kW to 9.96 kW and thus have a higher thermal gradient.

If I try to minimize the analytic error of around 30% on the condensing temperature whilst the wall temperature is minimum (37.81 deg C) , this will increase the condensing temperature (from 44.3 deg C to 47.5 deg C), and the wall temperature will no longer be minimum(from 37.81 deg C to 38.74 deg C), then my heat load will increase to 12.0 kW, reaching almost the maximum heat load. It seems like my heat flux q (W/m²) depends on both wall temp and condensing temp. This is sort of the opposite of having a minimum wall temp, as it increases with the increase of condensing temp.

Any idea how to optimize this? What am I doing wrong? How should I proceed when it comes down to wall temperature and condensing temperature? Does it make more sense to have just a minimum wall temperature of 37.81 deg C and leave the condensing temperature default at 44.3 deg C), or does it make more sense to increase both?

I'm trying to minimize the analytical error, I can do it either for the wall temperature, which will yield a minimum wall temp 37.81 deg C, or I can do it to minimize the analytic error for the condensing temperature and have a condensing temp of 47.5 deg C, and hence my wall temperature will also increase to 38.74 deg C. How is it correct though? Which one of the 2 methods would make more sense? Optimizing for minimum wall temperature? Or optimizing for condensing temperature?

 

[anorlunda]

ping @Chestermiller and @russ_watters

 

[Chestermiller]

What does the term "analytical error" mean? Can you please provide the dimensions of your condenser design, the mass flow rates, and the inlet temperatures? It is not clear to me what your design issue is.

 

[Martin Harris]

What does the term "analytical error" mean? Can you please provide the dimensions of your condenser design, the mass flow rates, and the inlet temperatures? It is not clear to me what your design issue is.

Hi
Thanks for the reply.

Sure.

We are dealing with a condenser with plates that uses water to condense Chlorodifluoromethane.

The total calculated heat load is 12.01 kW

Condenser dimensions width: w=0.07m, length L=0.2m , height of the flowing channel: H0=2.2mm, equivalent hydraulic diameter hd=4.4mm.

Number of plates: 28, number of channels:27, number of water channels:14, number of channels for refrigerant: 13, plate thickness: 0.8mm, surface of a plate:0.014m², plates surface: 0.364 m²

Mass flowrate for water: 0.7kg/s, mass flowrate for refrigerant: 0.06 kg/s

Inlet temperature for water:30.89 deg C, outlet water temp:35 deg C

Initial calculated wall temp:38.6 deg c, initial calculated condensing temp: 44.28 deg C

Analytical error for the wall temperature of the condenser = ((|qrf-qw|)/qw)*100 Where qrf and qw are the thermal heat fluxes for refrigerant and water respectively.

Then I imposed Excel's Solver to minimize this error by changing the wall temperature which was initially 38.6 deg C, such that the wall temperature decreased to 37.81 deg C, and the heat load decreased from 10.1 kW to 9.96 kW.

Now I also tried to calculate the analytical error for the condensing temperature as this:

Analytical error for condensing temp: ((|calculated heat load-total heat load|)/heat load)*100

Then I imposed Excel's Solver to minimize this error by changing the condensing temperature to 47.49 deg C , and it increased it and also the wall temperature to 38.74 deg C, thus the heat load which initially was 10.1 kW (and 9.6 kW after decreasing wall temp), has now become 11.99 kW.

 

[Chestermiller]

I thought we had analyzed this problem previously in this thread: https://www.physicsforums.com/threads/condenser-calculations-uncertainty.1000682/

What has changed now?

 

[Martin Harris]

Right, I went to a further stage, and am trying to optimize the condenser wall temperature or the condensing temperature. I don't know if what I'm doing is right though (Post #4 from this thread)

 

[Chestermiller]

Right, I went to a further stage, and am trying to optimize the condenser wall temperature or the condensing temperature. I don't know if what I'm doing is right though (Post #4 from this thread)

What does optimizing the wall temperature mean?

 

[Martin Harris]

Such as reducing the analytical error by optimizing the wall temperature, in this case the wall temperature decreased from 38.6 deg C to 37.81 deg C...I guess that would yield a higher thermal gradient.

 

[Chestermiller]

Sorry, I’m lost.

 

[Martin Harris]

Right, no worries.

I have a total heat load of 12.01 kW, right?
My calculated heat load is 10 kW.

When I try to minimize the analytical error with respect to the wall temperature which decreases my heat load becomes 9.96 kW.

When I try to minimize the analytical error with respect to the condensing temperature which increases, and also my wall temp increases, my heat load becomes 11.99 kW.

Does any of those 2 attempts make any sense?

 

[Chestermiller]

How accurate are those 1 significant digit flow rates?

 

[Martin Harris]

Pretty accurate I'd say.

 

[Chestermiller]

Pretty accurate I'd say.

So, really 0.060 and 0.70?

 

[Martin Harris]

Yeah, this is what I've been given 0.06kg/s for the refrigerant and 0.7 kg/s for water.

 

[Chestermiller]

This is refrigerant 134a, correct?

 

[Martin Harris]

The refrigerant is R22.

 

[Chestermiller]

For R22, 12 kW would be sufficient to cool the stream down to about 10 C. This is inconsistent with the inlet temperature of the water. So it seems that something in the data must be off.

The water flow rate

The water inlet temperture

The water exit temperature

The F22 temperature or saturation at inlet

The F22 temperature or saturation at outlet

The F22 flow rate

 

[Martin Harris]

Hi
Thanks for the reply.
How is 30.89 deg C for the water inlet temperature in the condenser incompatible?

 

[Chestermiller]

That temperature for the inlet water implies a heat load of 12 kW. If the F22 entered the condenser as a saturated vapor at 44 C, such a heat load would require it to give up 200 kJ/kG, which would require it to exit the condenser as a sub-cooled liquid at about 10 C. It can't exit below the inlet temperature of the water.