I'm having some trouble grasping the concept of the concentration factor on csp systems and how that equates into heat flux. The gist of what I'm trying to do is to model a csp system using an organic rankine cycle.
For my initial calculations I was considering a raw system efficiency of ~20%, the idea is to get ~30kW at the turbine, which means a solar input of ~150kW at the exchanger. What I don't fully understand is how I equate that into mirror area using a concentration factor.
From what I've gathered, the concentration factor C is simply the ratio between the mirror area and the exchanger area and, for fresnel reflectors, that can go from 20~100. However, I'm not sure if that's correct and how exactly does it work. For example, can I just assume a C = 50 and that'll hold true as long as my area ratios are 50?
Then to find my heat input, I've used: Q = DNI * C * Area_mirror, but with DNI = 1kW/m² and C = 50 it can't mean that I only need 3m² of mirror to get all this power, can it?
And how would that heat flux translate to my exchanger? Does it need to have .06 m² to maintain the concentration ratio? And would the heat flux then by 150kW/.06m² = 2.5MW/m²? That's unbelievably high and I doubt the analysis is correct.
Is anyone able to shed some light into this or point me to somewhere I can get that info reliably? Thanks!
The concentration factor is the ratio of the radiant power density at the the collector divided by the radiant power density of the sun without any concentration - about 1 kW/m2. You don't increase the energy by concentrating - only the energy density. So to get 150 kW at the collector you need to gather 150 kW in free space and then concentrate it. So your concentrator area should be 150 m2, and with a concentration factor of 50 your collector would be 3 m2 in area. Your heat flux - energy density - at the collector will be 50 kW/m2.
Thank you for the answer, Tony! That definitely cleared some things up for me. I do have a few follow-up questions:
If fresnel reflectors are limited to concentration ratios of 100 does that mean I can't get a flux of 150kW/m² on my collector (the heat exchanger)? And how do I go about deciding the ratio, or better worded, how do I find out what's my ratio based on a set of mirrors? Is it arbitrary? Is a concentration of 100 for fresnel reflectors realistic?
Thank you once again!
Yo have done an important mistake. You have not taken into acount the optical and the tehrmal losses of the solar collector.
You need 150 kW of useful heat
If you assume 60% thermla efficieny then you need 150/0.6 kW from sun
SO, the absirber area is 3m^2/0.6
I advice you to read more about solar collectors and for their performance
@Evangelos, I'm already including an overall system efficiency of 20% before I finish modelling everything and that is taking into account losses from the turbine and thermal/optical losses from the collector. You mean to say I have to consider an extra 60% efficiency reducing my overall efficiency to 12%?
20% is the thermodynamic efficieny of the ORC
The solar efficiency is different
Let me try and summarise the advice you have been offered. If you want 150kW of useful heat absorbed by the ORG, first allow for inefficiencies in the absorber. Say it's 90% efficient. That means you need 150/0.9 = 166.7 kW after concentration. How efficient is your concentrator - say again 90%, so that means you need to collect 166.7/0.9 = 185.2 kW. So allowing for typical air mass density, you will need a collector area at least 186 m2, not 150 m2. Put in the efficiency figures for your particular system and re-work the calculation. Best wishes with your research!
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