This session discusses the thermodynamics of heat exchangers, and explains how to build them in Thermoptim.
The calculations are based on the NTU method, which gives access to the product UA of the overall heat exchange coefficient by the exchanger surface.
In Thermoptim phenomenological version, it is not possible to calculate U, due to the absence of a detailed geometrical description of the exchanger.
This approach, however, already allows for sizing heat exchangers that are involved in many energy systems.
Professional and industrial versions of Thermoptim include a powerful optimization method, derived from the pinch method, which enables the design of complex networks of heat exchangers.
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(Session realized on 06/16/11 by Renaud Gicquel)index h : hot fluid
index c : cold fluid
index i : fluid inlet
index o : outlet
Tci : cold fluid inlet temperature
m dot : flow rate
$\phi =UA\Delta {T}_{\text{ml}}$
$\Delta {T}_{\text{ml}}=\frac{\Delta {T}_{0}-\Delta {T}_{L}}{ln\frac{\Delta {T}_{0}}{\Delta {T}_{L}}}$
h = λ Nu/d_{h} = f(Re,Pr)
$\mathrm{Re}=\frac{\rho V{d}_{h}}{\mu}$
$\mathrm{Pr}=\frac{\mu {c}_{p}}{\lambda}$
Number of Transfer Units method
$\mathrm{NTU}=\frac{UA}{{\left(\stackrel{\xb7}{m}{C}_{p}\right)}_{\text{min}}}$
$R=\frac{{\left(\stackrel{\xb7}{m}{C}_{p}\right)}_{\text{min}}}{{\left(\stackrel{\xb7}{m}{C}_{p}\right)}_{\text{max}}}$
$\epsilon =\frac{\phi}{{\phi}_{\text{max}}}$
$\epsilon =\frac{\Delta {T}_{\text{max}}}{\Delta {T}_{i}}$
${\left(\stackrel{\xb7}{m}{C}_{p}\right)}_{h}{\left(\stackrel{\xb7}{m}{C}_{p}\right)}_{c}$
$\epsilon =\frac{{T}_{\mathrm{hi}}-{T}_{\mathrm{ho}}}{{T}_{\mathrm{hi}}-{T}_{\mathrm{ci}}}$
$\mathrm{NUT}=\frac{1}{1-R}ln\frac{1-\epsilon R}{1-\epsilon}$
$\epsilon =\frac{1-exp\left(-\mathrm{NUT}\left(1-R\right)\right)}{1-Rexp\left(-\mathrm{NUT}\left(1-R\right)\right)}$
This session discusses the thermodynamics of heat exchangers, and explains how to build them in Thermoptim.
It showed the following:
Setting heat exchangers
For temperatures, we can set explicit constraints (e.g. set inlet fluid temperature), or implicit constraints (we set the exchanger effectiveness value, or the pinch minimum value).
For the problem to have a solution, we must set a total of five constraints, among which one set flow. If one of them is implicit (set pinch or effectiveness), four explicit must be (3 temperatures and a set flow, or 2 temperatures and 2 set flows). Otherwise five must be set.
Examples of construction of heat exchangers
In addition to the one built in this session, three exercises show you how to construct heat exchangers (the links below give you direct access to them):