DynamicWaterWaterExchanger#
Copyright © EDF 2002 - 2026#
ThermoSysPro Version 4.2#
This component model is documented in Sect. 9.6.1 of the ThermoSysPro book.
Dynamic water water exchanger#
The plate heat exchanger is composed of thousand sheets separated from each other by a small space where fluids flow. The plates exhibit a wavy surface to create a turbulent flow that generates better heat transfers. This type of exchanger is widely used in the food industry as it can easily be taken apart for cleanup.
This model represents a single-phase counter-flow thermal exchange between the hot fluid and the cold fluid. The two fluids are separated by a wall through which heat transfer takes place by conduction. Convection transfers the heat between each fluid and the wall.
Following assumptions are made:
the flow in each mesh cell is single-phase.
the energy accumulation in the wall is neglected.
the phenomenon of longitudinal heat conduction in the wall and in the fluid is neglected.
the pressure and specific enthalpy are assumed constant in each mesh cell.
For a steady-state plate heat exchanger, see static water water exchanger.
Modelica component model#
The equations mentioned below are implemented in the component DynamicWaterWaterExchanger, located in the WaterSteam.HeatExchangers sub-library.
Nomenclature#
Symbol |
Description |
Unit |
Definition |
Modelica name |
|---|---|---|---|---|
\(c_{p, c, i}\) |
Cold fluid specific heat in thermal cell \(i\) |
\(\mathrm{J} / \mathrm{kg} / \mathrm{K}\) |
prof[i].cp |
|
\(c_{p, \mathrm{h}, i}\) |
Hot fluid specific heat in thermal cell \(i\) |
\(\mathrm{J} / \mathrm{kg} / \mathrm{K}\) |
proc[i].cp |
|
\(D_{\mathrm{h}}\) |
Hydraulic diameter |
\(\mathrm{m}\) |
- |
|
\(e_{\mathrm{m}}\) |
Wall thickness |
\(\mathrm{m}\) |
emetal |
|
\(h_{\mathrm{c}, i}\) |
Cold fluid specific enthalpy in thermal cell \(i\) |
\(\mathrm{J} / \mathrm{kg}\) |
Hmf[i] |
|
\(h_{\mathrm{c}, i: i+1}\) |
Cold fluid specific enthalpy in hydraulic cell \(i: i+1\) |
\(\mathrm{J} / \mathrm{kg}\) |
Hcf[i] |
|
\(h_{\mathrm{h}, i}\) |
Hot fluid specific enthalpy in thermal cell \(i\) |
\(\mathrm{J} / \mathrm{kg}\) |
Hmc[i] |
|
\(h_{\mathrm{h}, i: i+1}\) |
Hot fluid specific enthalpy in hydraulic cell \(i: i+1\) |
\(\mathrm{J} / \mathrm{kg}\) |
Hcc[i] |
|
\(K_{\mathrm{c}, i}\) |
Convective heat exchange coefficient for the cold fluid in thermal cell \(i\) |
\(\mathrm{W} / \mathrm{m}^{2} / \mathrm{K}\) |
hf[i] |
|
\(K_{\mathrm{h}, i}\) |
Convective heat exchange coefficient for the hot fluid in thermal cell \(i\) |
\(\mathrm{W} / \mathrm{m}^{2} / \mathrm{K}\) |
hc[i] |
|
\(m_{\mathrm{c}, i: i+1}\) |
Cold fluid mass flow rate in hydraulic cell \(i:\) \(i+1\) |
\(\mathrm{kg} / \mathrm{s}\) |
Qcf[i] |
|
\(m_{\mathrm{h}, i: i+1}\) |
Hot fluid mass flow rate in hydraulic cell \(i:\) \(i+1\) |
\(\mathrm{kg} / \mathrm{s}\) |
Qcc[i] |
|
\(N\) |
Number of hydraulic cells |
\(-\) |
N + 1 |
|
\(N_{\mathrm{c}}\) |
Number of channels of each fluid |
\(-\) |
\(\left(N_{\mathrm{p}}-1\right) / 2\) |
- |
\(N_{\mathrm{p}}\) |
Number of plates |
\(-\) |
nbp |
|
\(P_{\mathrm{c}, i}\) |
Cold fluid pressure at the outlet of thermal cell \(i\) |
\(\mathrm{Pa}\) |
Pcf[i + 1] |
|
\(P_{\mathrm{h}, i}\) |
Hot fluid pressure at the outlet of thermal cell \(i\) |
\(\mathrm{Pa}\) |
Pcc[i + 1] |
|
\(P r_{\mathrm{c}, i}\) |
Prandtl number of the cold fluid in thermal cell \(i\) |
\(-\) |
\(\frac{\mu_{\mathrm{c}, i} \cdot c_{p, \mathrm{c}, i}}{\lambda_{\mathrm{c}, i}}\) |
- |
\(P r_{h, i}\) |
Prandtl number of the hot fluid in thermal cell \(i\) |
\(-\) |
\(\frac{\mu_{\mathrm{h}, i} \cdot c_{p, \mathrm{h}, i}}{\lambda_{\mathrm{h}, i}}\) |
- |
\(R e_{c, i:i+1}\) |
Reynolds number of the cold fluid in hydraulic cell \(i: i+1\) |
\(-\) |
\(\frac{4 \cdot m_{\mathrm{c}, i: i+1}}{\pi \cdot D_{\mathrm{h}} \cdot \mu_{\mathrm{c}, i} \cdot N_{\mathrm{c}}}\) |
- |
\(R e_{\mathrm{h}, i: i+1}\) |
Reynolds number of the hot fluid in hydraulic cell \(i: i+1\) |
\(-\) |
\(\frac{4 \cdot \dot{m}_{\mathrm{h}, i: i+1}}{\pi \cdot D_{\mathrm{h}} \cdot \mu_{\mathrm{h}, i} \cdot N_{\mathrm{c}}}\) |
- |
\(S_{\mathrm{p}}\) |
Plate area |
\(\mathrm{m}^{2}\) |
Sp |
|
\(T_{\mathrm{c}, i}\) |
Temperature of the cold fluid in thermal cell \(i\) |
\(\mathrm{K}\) |
Tmf[i] |
|
\(T_{\mathrm{h}, i}\) |
Temperature of the hot fluid in thermal cell \(i\) |
\(\mathrm{K}\) |
Tmc[i] |
|
\(T_{\mathrm{w}, \mathrm{c}, i}\) |
Wall temperature of for cold fluid in thermal cell \(i\) |
\(\mathrm{K}\) |
Tmf[i] |
|
\(T_{\mathrm{w}, \mathrm{h}, i}\) |
Wall temperature for the hot fluid in thermal cell \(i\) |
\(\mathrm{K}\) |
Tmc[i] |
|
\(U_{i}\) |
Global heat transfer coefficient for thermal cell \(i\) |
\(\mathrm{W} / \mathrm{m}^{2} / \mathrm{K}\) |
K[i] |
|
\(V_{\mathrm{c}}\) |
Cold fluid volume |
\(\mathrm{m}^{3}\) |
Vf |
|
\(V_{\mathrm{h}}\) |
Hot fluid volume |
\(\mathrm{m}^{3}\) |
Vc |
|
\(\Delta A_{i}\) |
Heat exchange surface for thermal cell \(i\) |
\(\mathrm{m}^{2}\) |
\(\frac{s_{\mathrm{p}} \cdot\left(N_{\mathrm{p}}-2\right)}{N-1}\) |
dS |
\(\Delta W_{i}\) |
Thermal power released by the hot fluid to the cold fluid for thermal cell \(i\) |
\(\mathrm{W}\) |
dW[i] |
|
\(\lambda_{\mathrm{c}, i}\) |
Cold fluid thermal conductivity in thermal cell \(i\) |
\(\mathrm{W} / \mathrm{m} / \mathrm{K}\) |
lambdaf[i] |
|
\(\lambda_{\mathrm{h}, i}\) |
Hot fluid thermal conductivity in thermal cell \(i\) |
\(\mathrm{W} / \mathrm{m} / \mathrm{K}\) |
lambdac[i] |
|
\(\lambda_{\mathrm{m}}\) |
Metal thermal conductivity |
\(\mathrm{W} / \mathrm{m} / \mathrm{K}\) |
lambdam |
|
\(\Lambda_{\mathrm{c}}\) |
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 |
|
\(\mu_{\mathrm{c}, i}\) |
Cold fluid dynamic viscosity in thermal cell \(i\) |
\(\mathrm{Pa} \mathrm{s}\) |
muf[i] |
|
\(\mu_{\mathrm{c}, i: i+1}\) |
Cold fluid dynamic viscosity in hydraulic cell \(i: i+1\) |
\(\mathrm{Pa} \mathrm{s}\) |
muf[i] |
|
\(\mu_{\mathrm{h}, i}\) |
Hot fluid dynamic viscosity in thermal cell \(i\) |
\(\mathrm{Pa} \mathrm{s}\) |
muc[i] |
|
\(\mu_{\mathrm{h}, i: i+1}\) |
Hot fluid dynamic viscosity in hydraulic cell \(i: i+1\) |
\(\mathrm{Pa} \mathrm{s}\) |
muc[i] |
|
\(\rho_{\mathrm{c}, i}\) |
Cold fluid density in thermal cell \(i\) |
\(\mathrm{kg} / \mathrm{m}^{3}\) |
rhof[i] |
|
\(\rho_{\mathrm{h}, i}\) |
Hot fluid density in thermal cell \(i\) |
\(\mathrm{kg} / \mathrm{m}^{3}\) |
rhoc[i] |
Governing equations#
The following set of equations must be completed by the state equations for the following water and steam properties \(c_{p, c}, c_{p, h}, \rho_{c}, \rho_{h}, \mu_{c}, \mu_{h}, \lambda_{c}\) and \(\lambda_{h}\).
Steady-state mass balance equation (hot fluid)#
Validity domain:
\(\forall \dot{m}_{\mathrm{h}, i:i+1}\)
Mathematical formulation:
Comments:
Steady-state mass balance equation (cold fluid)#
Validity domain:
\(\forall \dot{m}_{\mathrm{c}, i:i+1}\)
Mathematical formulation:
Comments:
Dynamic energy balance equation (hot fluid)#
Validity domain:
\(\forall \dot{m}_{\mathrm{h}, i:i+1}\)
Mathematical formulation:
Comments:
The fluid is assumed to be incompressible.
Dynamic energy balance equation (cold fluid)#
Validity domain:
\(\forall \dot{m}_{c, i:i+1}\)
Mathematical formulation:
Comments:
The fluid is assumed to be incompressible.
Heat exchanged between the hot and cold fluids#
Validity domain:
\(\forall T_{\mathrm{h}, i}\) and \(\forall T_{\mathrm{c}, i}\)
Mathematical formulation:
Comments:
The global heat transfer coefficient \(U_{i}\) between the two fluids is given by \(\frac{1}{U_{i}}=\frac{1}{K_{\mathrm{h}, i}}+\frac{1}{\lambda_{\mathrm{m}}}+\frac{1}{K_{\mathrm{c}, i}}\).
Momentum balance equation (hot fluid)#
Validity domain:
\(\forall \dot{m}_{\mathrm{h}, i:i+1}\)
Mathematical formulation:
Comments:
Only pressure losses due to friction are taken into account. The friction coefficient \(\Lambda_{\mathrm{h}}\) can be directly provided by the user or computed using a correlation.
Momentum balance equation (cold fluid)#
Validity domain:
\(\forall \dot{m}_{\mathrm{c}, i:i+1}\)
Mathematical formulation:
Comments:
Only pressure losses due to friction are taken into account. The friction coefficient \(\Lambda_{\mathrm{c}}\) can be directly provided by the user or computed using a correlation.
References#
El Hefni, Baligh and Bouskela, Daniel (2019). Modeling and Simulation of Thermal Power Plants with ThermoSysPro, sect. 9.6.1. Springer Nature Switzerland AG.