From: Johan.Winberg@vok.lth.se (Johan Winberg)
Newsgroups: sci.energy
Subject: Thermal stratification: estimating model parameters
Keywords: district heating, subscriber stations, thermal stratification, domestic hot water, storage tanks
Date: 5 Jan 93 10:35:21 GMT
Organization: Lund Institute of Technology, Dept of Heat and Power Eng.

Hello,
is there anybody interested in or working with mathematical models of 
thermal stratification in domestic hot water storage tanks? I would like 
to get in contact with you! I am working in a research project on hot
water storage tanks (mostly for district heating) where it is essential
to produce as low return temperature as possible. I am trying to use
a one-dimensional model for the temperature distribution in the storage
tank known in the literature. Later, I would like to connect this model
to other components such as pipes, heat exchangers and controllers, in
order to do some system analysis.

I would like to get response on the following problem:

I am trying an analytical model of Cole & Bellinger which I like 
because of its ability to accurately compute the transport case 
(i.e. the stratified water is moving downwards or upwards, as by 
charging or emptying the tank). However, there are some empirical
parameters in this model which should be determined. When I try 
this, I find that the electro-magnetic flow meter I use in the 
experiments seems to have an error of -5 to -6 %. As everyone who
have tried laboratory activities know, it is probably not at all
impossible with such an error on flowrate measurements. 

Even more, it seems to me as if the correlation of Cole & Bellinger 
does not fit my data. The most interesting parameter is c, a mixing 
parameter which is introduced to take care of the mixing at the 
inlet of the storage tank. The correlation is on the form 
c=a1*Fo^a2*exp(a3*Ri):

Original correlation(0):  c=2.44e-5*Fo^-1.5 *exp(-0.0134*Ri)
My correlation (1):       c=1.66e-5*Fo^-1.5 *exp(-0.0419*Ri) (a2=-1.5, fixed)
My correlation (2):       c=2.29e-5*Fo^-1.44*exp(-0.0149*Ri) (a2 estimated)

RMS errors for the three correlations are:
   corr   lossf [-]
    0       31.5
    1        6.1
    2        5.8
, which means that my second correlation is the best one.

Cole & Bellinger also propose that the parameter H (normalised film heat
transfer coefficient) should be 7.7, but I have found that it should be 12.

I have used the Matlab Optimization Toolbox to find the parameters c, H 
and the flow meter error in a series of charging experiments (fminu). 
Then I use the leastsq routine to find the coefficients in the proposed
correlation.

I am wondering if anyone has similar experiences as I have?
How good is the correlation of Cole & Bellinger?
Do you know anything of their underlying experiments?
Is there more people on the net interested in this kind of problems?

Literature:
	Cole, R.L.; Bellinger,F.O.: Natural thermal stratification in tanks. 
	ANL-82-5, Argonne National Laboratories, (1982), Argonne.

Sincerely,
_________________________________________________________________
Johan Winberg              		Dept. of Heat & Power Engineering
johan.winberg@vok.lth.se       	Lund Institute of Technology
vox: +46-(0)46 104302          	P.O. Box 118
fax: +46-(0)46 104717          	S-221 00 LUND, Sweden
Newsgroups: sci.energy