Heat Exchanger (Concentric tube) (TL)#

The Heat Exchanger (Concentric tube) (TL)block simulates the heat exchange process between two media separated by a wall.

The heat flow between media is calculated using the NTU method, the Parallel Flow or Counterflow mode is determined automatically depending on the signs of mass flow rate in the heat exchanger.

1. Calculation of pressure losses (1), (2) :

(1)#\[\begin{split} \Delta p_{loss}^{A} = \begin{equation} \left\{ \begin{array}{ll} \dot m_{A}\cdot\mu_{A}\cdot K_{потерь} \cdot Re_{L}\frac{1}{4\cdot d_{г}\cdot\rho_{A}\cdot S_{мин}}, Re_{A} \le Re_{L}\\ K_{потерь}\cdot\frac{\dot m_{A}\cdot\left| \dot m_{A} \right|}{4\cdot\rho_{A}\cdot S_{мин}^{2}}, Re_{B} \geq Re_{T}\end{array}\right. \end{equation} \end{split}\]

(2)#\[\begin{split} \Delta p_{loss}^{B} = \begin{equation} \left\{ \begin{array}{ll} \dot m_{B}\cdot\mu_{B} \cdot K_{потерь}\cdot Re_{L}\cdot\frac{1}{4\cdot d_{г}\cdot\rho_{A} \cdot S_{мин}}, Re_{B} \le Re_{L}\\ K_{потерь}\cdot\frac{\dot m_{B}\cdot\left| \dot m_{B} \right|}{4\cdot\rho_{B}\cdot S_{мин}^{2}}, Re_{B} \geq Re_{T}\end{array}\right. \end{equation} \end{split}\]

where:

\(\dot m_{A}\) и \(\dot m_{B}\) - mass flow rate through the input and output ports;

\(\mu_{A}\) и \(\mu_{B}\) - dynamic viscosity of liquid for input and output ports;

\(Re_{A}\) и \(Re_{B}\) - Reynolds number for input and output ports;

\(K_{losses}\) - pressure loss factor;

\(Re_{L}\) - upper limit of Reynolds number for laminar flow;

\(Re_{T}\) - lower limit of Reynolds number for turbulent flow;

\(S_{min}\) - minimum passage area;

\(d_{h}\) - hydraulic diameter for calculation of pressure losses.

\(d_{h} = d_{ext} - d_{int}\)

where:

\(d_{ext}\) - external diameter of annular gap;

\(d_{int}\) - internal diameter of annular gap.

2. Mass flow rate calculation

Law of conservation of mass (3) :

(3)#\[ \dot m_{A}+\dot m_{B}\:=\:0 \]

3. Momentum balance (4) :

(4)#\[ p_{A} - p_{B} = \Delta p_{loss}^{A} + \Delta p_{loss}^{B} \]

where:

\(p_A\) и \(p_B\) — input and output port pressure;

\(Δp_{loss}^{A}\) и \(Δp_{loss}^{B}\) – pressure losses between the input port and the center of the pipe and between the center of the pipe and the output port, respectively.

4.Energy balance

Law of conservation of energy (5) :

(5)#\[ \phi_{A}+ \phi_{B} + Q\:=\:\frac{dE}{dt} \]

where:

\(\phi_А\) - energy flow at the input;

\(\phi_В\) - energy flow at the output;

\(Q\) - heat flux through the wall:

\(E\) - total internal energy (6) :

(6)#\[E = \bar \rho \cdot u\cdot V\]

where:

\(\bar ρ\) - average density of liquid;

\(u\) - specific internal energy of liquid;

\(V\) - liquid volume in the heat exchanger.

5. Heat flux calculation

Heat flux is determined using the NTU method (7) :

(7)#\[ -Q_{1}+ Q_{2}\:=\:\epsilon \cdot Q_{макс} \]

where:

\(Q_{1}\) и \(Q_{2}\) - heat flow for medium 1 and medium 2;

\(Q_{max}\) - maximum possible heat flux between medium 1 and medium 2 at specified working conditions;

\(\epsilon\) - efficiency factor ( 0 < ε < 1).

\(Q_{max} = С_{min}(T_{1inp} - T_{2inp})\)

where:

\(С_{min} = min(\dot m_{1}c_{p1}, \dot m_{2}c_{p2})\)

\(\dot m_{1}\) и \(\dot m_{2}\) - mass flow rate for medium 1 and medium 2;

\(c_{p1}\) и \(c_{p2}\) - specific heat capacity for medium 1 and medium 2;

\(T_{1inp}\) и \(T_{2inp}\) - temperature at heat exchanger input for medium 1 and medium 2.

Determination of efficiency factor for concentric pipes

Counterflow (8):

(8)#\[\begin{split} \epsilon = \begin{equation} \left\{ \begin{array}{ll} \frac{1-e^{-NTU\cdot(1-C_{отн})}}{1-С_{отн}\cdot e^{-NTU\cdot (1-C_{отн})}}, для С_{отн} < 1\\ \frac{NTU}{1+NTU}, для С_{отн} = 1\end{array}\right. \end{equation} \end{split}\]

Forward flow (9):

(9)#\[\epsilon = \frac{1-e^{-NTU\cdot(1+C_{отн})}}{1+С_{отн}}\]

where:

\(С_{rel} = \frac{C_{min}}{C_{max}}\);

\(NTU\) = \(\frac{1}{C_{min}R_{ent}}\) - number of transfer units;

\(R_{wall}\) - thermal resistance of the wall (10) :

(10)#\[R_{полн} = \frac{1}{\alpha_{1}\cdot F_{1}} + R_{стенки} + \frac{1}{\alpha_{2}\cdot F_{2}}\]

where:

\(\alpha_{1}\) и \(\alpha_{2}\) - heat transfer factor for medium 1 and medium 2;

\(F_{1}\) и \(F_{2}\) - heat exchange surface area for medium 1 and medium 2;

\(R_{wall}\) - thermal resistance of the wall.

1. Properties#

Property	Default Value	Description	Units of measurement
Minimum cross-sectional area (medium 1)	0.01	-	m\(^2\)
Hydraulic diameter for pressure loss calculation (medium 1)	0.1	-	m
Laminar flow upper Reynolds number limit (medium 1)	2000.0	-	-
Turbulent flow lower Reynolds number limit (medium 1)	4000.0	-	-
Pressure loss coefficient (medium 1)	0.1	-	-
Liquid - wall heat transfer coefficient (medium 1)	100.0	-	W/m²·°C
Heat transfer surface area (medium 1)	0.01	-	m\(^2\)
Thermal liquid volume (medium 1)	0.5	-	m\(^2\)
Initial medium temperature in heat exchanger (medium 1)	20.0	-	°C
Minimum cross-sectional area (medium 2)	0.01	-	m\(^2\)
Hydraulic diameter for pressure loss calculation (medium 2)	0.1	-	m
Laminar flow upper Reynolds number limit (medium 2)	2000.0	-	-
Turbulent flow lower Reynolds number limit (medium 2)	4000.0	-	-
Pressure loss coefficient (medium 2)	0.1	-	-
Liquid - wall heat transfer coefficient (medium 2)	100.0	-	W/m²·°C
Heat transfer surface area (medium 2)	0.01	-	m\(^2\)
Thermal liquid volume (medium 2)	0.5	-	m\(^2\)
Initial medium temperature in heat exchanger (medium 2)	20.0	-	°C
Wall thermal resistance	1.6E-4	-	°C/W

2. Inputs and outputs#

Parameters	Input/Output	Description	Units of measurement	Port type
Medium 1 inlet	Input	-	-	Thermohydraulics
Medium 2 inlet	Input	-	-	Thermohydraulics
Medium 1 outlet	Output	-	-	Thermohydraulics
Medium 2 outle	Output	-	-	Thermohydraulics

In order to see the connection capabilities of the block, you need to go to page Description of block ports