StaticWaterWaterExchanger#
Copyright © EDF 2002 - 2026#
ThermoSysPro Version 4.2#
This component model is documented in Sect. 9.6.2 of the ThermoSysPro book.
Static water water exchanger#
This static plate heat exchanger is the steady-state version of the dynamic water water exchanger.
In addition to the dynamic model assumptions, the specific heats and mass flow rates of both fluids are supposed constant.
Modelica component model#
The equations mentioned below are implemented in the component StaticWaterWaterExchanger, located in the WaterSteam.HeatExchangers sub-library.
Nomenclature#
Symbol |
Description |
Unit |
Definition |
Modelica name |
|---|---|---|---|---|
\(A\) |
Heat exchange surface |
\(\mathrm{m}^{2}\) |
\(\left(N_{\mathrm{p}}-2\right) \cdot S_{\mathrm{p}}\) |
S |
\(m_{\mathrm{h}}\) |
Hot fluid mass flow rate |
\(\mathrm{kg} / \mathrm{s}\) |
Qc |
|
\(m_{\mathrm{c}}\) |
Cold fluid mass flow rate |
\(\mathrm{kg} / \mathrm{s}\) |
Qf |
|
\(N_{\mathrm{c}}\) |
Number of channels of each fluid |
\(-\) |
\(\left(N_{\mathrm{p}}-1\right) / 2\) |
N |
\(N_{\mathrm{p}}\) |
Number of plates |
\(-\) |
nbp |
|
\(P_{\mathrm{c}, \mathrm{i}}\) |
Cold fluid pressure at the inlet |
\(\mathrm{Pa}\) |
Ef.P |
|
\(P_{\mathrm{c}, \mathrm{o}}\) |
Cold fluid pressure at the outlet |
\(\mathrm{Pa}\) |
Sf.P |
|
\(P_{\mathrm{h}, \mathrm{i}}\) |
Hot fluid pressure at the inlet |
\(\mathrm{Pa}\) |
Ec.P |
|
\(P_{\mathrm{h}, \mathrm{o}}\) |
Hot fluid pressure at the outlet |
\(\mathrm{Pa}\) |
Sc.P |
|
\(T_{\mathrm{c}, \mathrm{i}}\) |
Cold fluid temperature at the inlet |
\(\mathrm{K}\) |
Tef |
|
\(T_{\mathrm{c}, \mathrm{o}}\) |
Cold fluid temperature at the outlet |
\(\mathrm{K}\) |
Tsf |
|
\(T_{\mathrm{h}, \mathrm{i}}\) |
Hot fluid temperature at the inlet |
\(\mathrm{K}\) |
Tec |
|
\(T_{\mathrm{h}, \mathrm{o}}\) |
Hot fluid temperature at the outlet |
\(\mathrm{K}\) |
Tsc |
|
\(U\) |
Global heat transfer coefficient (internal overall heat exchange coefficient) |
\(\mathrm{W} / \mathrm{m}^{2} / \mathrm{K}\) |
K |
|
\(W\) |
Thermal power exchanged between the two fluids |
\(\mathrm{W}\) |
W |
|
\(\Delta T_{1}\) |
Temperature difference 1 |
\(\mathrm{K}\) |
For counter flow \(T_{\mathrm{h}, \mathrm{i}}-T_{\mathrm{c}, \mathrm{o}}\) For parallel flow \(T_{\mathrm{h}, \mathrm{i}}-T_{\mathrm{c}, \mathrm{i}}\) |
DT1 |
\(\Delta T_{2}\) |
Temperature difference 2 |
\(\mathrm{K}\) |
For counter flow \(T_{\mathrm{h}, \mathrm{o}}-T_{\mathrm{c}, \mathrm{i}}\) For parallel flow \(T_{\mathrm{h}, \mathrm{o}}-T_{\mathrm{c}, \mathrm{o}}\) |
DT2 |
\(\Lambda_{\mathrm{c}}\) |
Friction pressure loss coefficient of the entire length of the exchanger for the cold fluid |
\(\mathrm{m}^{-4}\) |
p_Kf |
|
\(\Lambda_{\mathrm{h}}\) |
Friction pressure loss coefficient of the entire length of the exchanger for the hot fluid |
\(\mathrm{m}^{-4}\) |
p_Kc |
|
\(\rho_{\mathrm{c}}\) |
Cold fluid density |
\(\mathrm{kg} / \mathrm{m}^{3}\) |
rhof |
|
\(\rho_{\mathrm{h}}\) |
Hot fluid density |
\(\mathrm{kg} / \mathrm{m}^{3}\) |
rhoc |
Governing equations#
Energy balance equation (hot fluid)#
Validity domain:
\(\forall \dot{m}_{\mathrm{h}}\)
Mathematical formulation:
Energy balance equation (cold fluid)#
Validity domain:
\(\forall \dot{m}_{\mathrm{c}}\)
Mathematical formulation:
Heat exchanged between the fluid and the wall#
Validity domain:
\(\dot{m}_{\mathrm{h}} \neq 0, \dot{m}_{\mathrm{c}} \neq 0, \Delta T_{1} \neq 0\) and \(\Delta T_{2} \neq 0\)
Mathematical formulation:
Comments:
Momentum balance equation (hot fluid)#
Validity domain:
\(\forall \dot{m}_{\mathrm{h}}\)
Mathematical formulation:
Comments:
Momentum balance equation (cold fluid)#
Validity domain:
\(\forall \dot{m}_{\mathrm{c}}\)
Mathematical formulation:
Comments:
References#
El Hefni, Baligh and Bouskela, Daniel (2019). Modeling and Simulation of Thermal Power Plants with ThermoSysPro, sect. 9.6.2. Springer Nature Switzerland AG.