6.9. Heat exchanger

Fall type

Type label	Symbol	Description	Active
Heat supply QHeat in		Supply heat to or extract heat from the fluid by directly specifying a heat input	Yes
Heat supply Tdown		Supply heat or extract heat to the fluid by specifying a temperature at downstream Heat node	Yes
Heat supply QHeat with limits on T		Supply heat to or extract heat from the fluid by directly specifying a heat input, with user specified limits for the minimum and maximum temperatures	Yes
Heat exchanger		Exchange heat with surroundings due to temperature difference between fluid and ambient temperature.	Yes
Heat demand		Heat demand for district heating systems with different time scales for heating and warm (tap) water.	Yes
Gas boiler		Supply heat to the fluid by gas combustion	Yes
Solar collector		Heat supply via a solar collector	Yes
Solar collector based on ISO 9806:2017		Heat supply via a solar collector based on ISO 9806:2017	Yes

6.9.1. Heat supply QHeat in

The heat supply is used to supply a constant heat flux to the system. The user sets the amount of heat supplied (+) or extracted (-). Wanda calculates how much the fluid heats or cools down as a result. Next to this, the hydraulic losses are also included via a loss coefficient. This hydraulic loss can be converted to heat by the fraction-generated heat to fluid.

6.9.1.1. Mathematical model

The head loss (definition based on liquid domain) is given by:

(6.9.1)\[\Delta H = CQ^{2}\]

with:

variable	Description	Units
\(\Delta H\)	Head loss	m
C	the loss coefficient	s2/m5
Q	the flow rate	m3/s

This can be rewritten in terms of a pressure drop and mass flow as follows:

(6.9.2)\[\Delta p = \rho g\left( C\frac{{\dot{m}}^{2}}{\rho^{2}} - \Delta z \right)\]

with:

variable	Description	Units
\(\Delta p\)	pressure drop	N/m2
\(\rho\)	density of the fluid at the upstream side	kg/m3
\(g\)	gravitational acceleration	m/s2
\(\dot{m}\)	mass flow rate	kg/s
\(\Delta z\)	height difference between connection points	m

The temperature change is computed from:

(6.9.3)\[\dot{m}\left( c_{p1}T_{1} - c_{p2}T_{2} \right) + Q_{\text{input}} + fr \cdot Q_{\text{gen}} = 0\]

with:

variable	Description	Units
\(c_{p1}/c_{p2}\)	specific head of the fluid	J/kg/K
\(T_{1}/T_{2}\)	upstream/ downstream temperature	K
\(Q_{input}\)	heat supplied to the system	W
\(Q_{gen}\)	generated heat	W
\(fr\)	Fraction of generated heat transferred to the fluid	-

The generate heat flux is given by:

(6.9.4)\[Q_{gen} = C g \frac{\dot{m}^3}{\rho^2}\]

The heat input is always supplied and therefore zero flow is not possible, since this would result in an infinite temperature. The heat supplied is calculated as:

(6.9.5)\[Q_{s} = Q_{\text{input}} + fr Q_{\text{gen}}\]

6.9.1.2. Hydraulic specifications

Description	Input	SI-units	remarks
C-value dH=CQ^2	real	[s2/m5]	Q is fluid flow rate
Fraction gen. heat to fluid	real	[-]	Default = 0
Initial heat supply	real	[W]	Can be controlled by action table

6.9.1.3. Component specific output

• Heat supplied [W]

• Generated Heat flux [W]

6.9.1.4. Component messages

Message	Type	Explanation
Zero flow not allowed	Error	Heat input with zero flow not possible, because that would require the temperature to become infinite.

6.9.1.5. Actions

The action table (control connection) of this component controls the heat supply as function of time.

6.9.2. Heat supply Tdown

The heat supply Tdown is used to specify a fixed downstream temperature (constant or time-variable through action table). The amount of heat supplied (+) to or heat extracted (-) from the fluid is calculated by Wanda. The location of the downstream side is based on the actual flow direction (thus not based on the scheme definition).

6.9.2.1. Mathematical model

The head loss (definition based on liquid domain) is given by:

(6.9.6)\[\Delta H = C Q^2\]

with:

variable	Description	Units
\(\Delta H\)	Head loss	m
\(C\)	Loss coefficient	s2/m5
\(Q\)	Flow rate	m3/s

This can be rewritten in terms of a pressure drop and mass flow as follows:

(6.9.7)\[\Delta p = \rho g\left( C\frac{{\dot{m}}^{2}}{\rho^{2}} - \Delta z \right)\]

with:

variable	Description	Units
\(\Delta p\)	pressure drop	N/m2
\(\rho\)	density of the fluid at the upstream side	kg/m3
\(g\)	gravitational acceleration	m/s2
\(\dot{m}\)	mass flow rate	kg/s
\(\Delta z\)	height difference between connection points	m

The downstream temperature is set based on the user specified input. A change in flow direction will set the specified temperature at the opposite connection point.

The heat supplied is calculated from:

(6.9.8)\[Q_s = \dot{m} \left( c_{p1} T_1 - c_{p2} T_2 \right)\]

variable	Description	Units
\(Q_s\)	Heat supplied	W
\(c_{p1}/c_{p2}\)	Upstream/downstream specific heat of the fluid	J/kg/K
\(T_1/T_2\)	Upstream/downstream temperature of the fluid	K

The generate heat flux is given by:

(6.9.9)\[Q_{gen} = C g \frac{\dot{m}^3}{\rho^2}\]

6.9.2.2. Hydraulic specifications

Description	Input	SI-units	remarks
C-value (dH=CQ^2)	real	[s2/m5]	Q is fluid flow rate
Fraction gen. heat to fluid	real	[-]	Default = 0
Initial downstr temp	real	[°C]	Can be controlled by action table

6.9.2.3. Component specific output

• Heat supplied [W]

• Generated Heat flux [W]

6.9.2.4. Component messages

None

6.9.2.5. Actions

The action table (control connection) of this component controls the downstream temperature as function of time.

6.9.3. Heat supply QHeat with limits on T

The heat supply is used to supply a constant heat flux to the system. The user sets the amount of heat supplied (+) or extracted (-). Wanda calculates how much the fluid heats or cools down as a result, the downstream temperature is limited by user specified boundaries. The hydraulic losses are included via a loss coefficient. This hydraulic loss can be converted to heat by the fraction-generated heat to fluid.

6.9.3.1. Mathematical model

The head loss (definition based on liquid domain) is given by:

(6.9.10)\[\Delta H = C Q^2\]

with:

variable	Description	Units
\(Q\)	Flow rate	m3/s
\(C\)	Loss coefficient	s2/m5
\(\Delta H\)	Head loss	m

This can be rewritten in terms of a pressure drop and mass flow as follows:

(6.9.11)\[\Delta p = \rho g\left( C\frac{{\dot{m}}^{2}}{\rho^{2}} - \Delta z \right)\]

with:

variable	Description	Units
\(\Delta p\)	pressure drop	N/m2
\(\rho\)	density of the fluid at the upstream side	kg/m3
\(g\)	gravitational acceleration	m/s2
\(\dot{m}\)	mass flow rate	kg/s
\(\Delta z\)	height difference between connection points	m

The temperature change is computed from:

(6.9.12)\[\dot{m}\left( c_{p1}T_{1} - c_{p2}T_{2} \right) + Q_{\text{input}} + fr \cdot Q_{\text{gen}} = 0\]

with:

variable	Description	Units
\(c_{p1}/c_{p2}\)	specific head of the fluid	J/kg/K
\(T_{1}/T_{2}\)	upstream/ downstream temperature	K
\(Q_{input}\)	heat supplied to the system	W
\(Q_{gen}\)	generated heat	W
\(fr\)	Fraction of generated heat transferred to the fluid	-

If the downstream temperature comes below or above the user specified extremes the temperature is set to this value, the user is informed by a message. The actual used heat flux is given as result. The generate heat flux is given by:

(6.9.13)\[Q_{gen} = C g \frac{\dot{m}^3}{\rho^2}\]

The heat supplied is calculated as:

(6.9.14)\[Q_{s} = Q_{\text{input}} + fr Q_{\text{gen}}\]

6.9.3.2. Hydraulic specifications

Description	Input	SI-units	remarks
C-value (dH=CQ^2)	real	[s2/m5]	Q is fluid flow rate
Fraction gen. heat to fluid	real	[-]	Default = 0
Minimum supply temperature	Real	[oC]
Maximum supply temperature	Real	[oC]
Initial heat supply	real	[W]	Can be controlled by action table

6.9.3.3. Component specific output

• Heat supplied [W]

• Generated Heat flux [W]

6.9.3.4. Component messages

Message	Type	Explanation
Temperature set to upper bound	Info	This message is given once when the heat temperature is set to the upper bound
Temperature set to lower bound	info	This message is given once when the heat temperature is set to the lower bound
Temperature within bounds	info	This message is given when the temperature is again within bounds

6.9.3.5. Actions

The action table (control connection) of this component controls the heat supply as function of time.

6.9.4. Heat exchanger

The heat exchanger component calculates in the transient state the heat transfer depending on the temperature difference between the ambient temperature and the fluid temperature using an integrated heat transfer coefficient.

Four different initial states are possible:

• Heat exchanger

• DownT and C- coef

• DownT and Q supplied

• DeltaT and Q supplied.

These are detailed in the Mathematical model.

6.9.4.1. Mathematical model

The head loss is defined as:

(6.9.15)\[\Delta H = C Q^2\]

with:

variable	Description	Units
\(Q\)	Flow rate	m3/s
\(C\)	Loss coefficient	s2/m5
\(\Delta H\)	Head loss	m

This can be rewritten in terms of a pressure drop and mass flow as follows:

(6.9.16)\[\Delta p = \rho g\left( C\frac{{\dot{m}}^{2}}{\rho^{2}} - \Delta z \right)\]

with:

variable	Description	Units
\(\Delta p\)	pressure drop	N/m2
\(\rho\)	density of the fluid at the upstream side	kg/m3
\(g\)	gravitational acceleration	m/s2
\(\dot{m}\)	mass flow rate	kg/s
\(\Delta z\)	height difference between connection points	m

The heat flow to (+) or from (-) the fluid is defined as:

(6.9.17)\[Q_{input} = h(T_\infty - T_f)\]

with:

variable	Description	Units
\(Q_{input}\)	Heat supplied to the system	W
\(h\)	Heat transfer coefficient	W/K
\(T_\infty\)	External temperature (i.e., not influenced by the heat transfer)	K
\(T_f\)	Fluid temperature	K

The energy equation is defined as:

(6.9.18)\[\dot{m}\left( c_{p1}T_{1} - c_{p2}T_{2} \right) + h\left( T_{\infty} - T_{f} \right) + fr Q_{\text{gen}} = 0\]

The generate heat flux is given by:

(6.9.19)\[Q_{gen} = C g \frac{\dot{m}^3}{\rho^2}\]

The heat supplied is defined as:

(6.9.20)\[Q_{s} = Q_{\text{input}} + fr Q_{\text{gen}}\]

Several options are available for the steady state computation (initial state). This setting defines how the steady state is calculated. Based on this initial state a constant heat transfer coefficient and/or a loss coefficient are calculated which is used throughout the transient computation.

• Heat Exchanger

  The initial state is calculated based on a heat transfer coefficient input by the user.
• DownT and C-coeff

  Initial state is based on downstream temperature and a C-value. The downstream side is based on the initial flow direction and may differ from the scheme definition. The heat transfer coefficient is calculated as a result.
• DownT and Qhsup

  Initial state is based on downstream temperature and a fixed heat supply. The downstream side is based on the initial flow direction and may differ from the scheme definition. The C-value and heat transfer coefficients are calculated as result of this initial steady state.
• DT and Qhsup

  Initial state is based on a temperature difference (T1-T2) over the component and a fixed heat supply. The C-value and heat transfer coefficient are calculated as result of this initial steady state.

6.9.4.2. Hydraulic specifications

Description	Input	SI-units	remarks
Initial state	Heat exchange DownT and C-coef DownT and Qhsup DT and Qhsup		Only used for initial (steady state) calculation
C-value (dH=CQ^2)	real	[s2/m5]	Only if Initial state is: “Heat exchange” or “DownT and C-coef”
Fraction gen. heat to fluid	real	[-]	Default = 0
Heat transfer coefficient	real	[W/K]	Only if Initial state is “Heat exchange”
Initial heat supply	real	[kW]	Only if Initial state is “DownT and Qhsup” or “DT and Qhsup”
Initial downstr temp	real	[°C]	Only if Initial state is “DownT and C-coef” or “DownT and Qhsup”
Initial delta T	real	[°C]	Only if Initial state is “DT and Qhsup”
Initial ambient temperature	real	[°C]	Can be controlled by action table

6.9.4.3. Component specific output

• Heat supplied [W]

• Generated Heat flux [W]

• Ambient temperature [°C]

6.9.4.4. Component messages

Message	Type	Explanation
Unable to determine resistance and heat transfer coefficient: zero flow	Error	To calculate the C-value the flow needs to be non-zero
No heat transfer: outside temperature equals inside temperature	Error	The heat transfer coefficient cannot be determined when the ambient temperature equals the fluid temperature.
Unable to determine resistance: zero head difference	Error	To calculate the C-value the head difference needs to be non-zero
Negative hydraulic loss coefficient	Warning	Negative hydraulic loss adds energy to the system, which is probably not intended by the user.
Heat supply and delta T should have opposite signs	Error	If this is not the case the heat flow would be in a physical impossible direction

6.9.4.5. Actions

The action table (control connection) of this component controls the ambient temperature as function of time.

6.9.5. Heat demand

This component can be used to model the heat demand of a number of users in a district heating system. The heat demand consists of 2 parts: space heating and tap water heating.

6.9.5.1. Mathematical model

The head loss is defined as:

(6.9.21)\[\Delta H = C Q^2\]

with:

variable	Description	Units
\(Q\)	Flow rate	m3/s
\(C\)	Loss coefficient	s2/m5
\(\Delta H\)	Head loss	m

This can be rewritten in terms of a pressure drop and mass flow as follows:

(6.9.22)\[\Delta p = \rho g\left( C\frac{{\dot{m}}^{2}}{\rho^{2}} - \Delta z \right)\]

with:

variable	Description	Units
\(\Delta p\)	pressure drop	N/m2
\(\rho\)	density of the fluid at the upstream side	kg/m3
g	gravitational acceleration	m/s2
\(\dot{m}\)	mass flow rate	kg/s
\(\Delta z\)	height difference between connection points	m

The temperature change is defined as:

(6.9.23)\[\dot{m}\left( c_{p1}T_{1} - c_{p2}T_{2} \right) - Q_{\text{demand}} + fr \cdot Q_{\text{gen}} = 0\]

with:

variable	Description	Units
\(c_{p1}/c_{p2}\)	specific head of the fluid	J/kg/K
\(T_{1}/T_{2}\)	upstream/ downstream temperature	K
\(Q_{input}\)	heat supplied to the system	W
\(Q_{gen}\)	generated heat	W
\(fr\)	Fraction of generated heat transferred to the fluid	-

The heat demand is calculated from:

(6.9.24)\[Q_{demand} = Q_{heat} + \rho_f c_{pf} \left( T_{hot} - T_{cold} \right) Q_{hot}\]

with:

variable	Description	Units
\(Q_{demand}\)	Demand from the system	W
\(Q_{heat}\)	Heat demand specified by the user	W
\(Q_{hot}\)	Hot water flow rate demand	W
\(T_{hot}\)	Hot water temperature	K
\(T_{cold}\)	Cold water temperature	K
\(\rho_f\)	Average density of the tap water based on the temperature by the user	kg/m3
\(c_{pf}\)	Average specific heat based on the temperature specified by the user	J/kg/K

The generate heat flux is given by:

(6.9.25)\[Q_{gen} = C g \frac{\dot{m}^3}{\rho^2}\]

The total heat demanded is calculated as:

(6.9.26)\[Q_{d} = Q_{\text{demand}} - \text{fr} \cdot Q_{\text{gen}}\]

Please note that this component always extracts the heat independent on the hot and cold water temperature. This also result in that zero flow is not possible.as this would result in an infinite temperature.

6.9.5.2. Hydraulic specifications

Description	Input	SI-units	Remarks
C-value (dH=CQ^2)	real	[-]
Fraction gen. heat to fluid	real	[-]	Default = 0
Heat demand	Constant Time varying
Constant heat demand	real	[W]	If Heat demand = Constant
Heat demand time table	table		If Heat demand = Time varying
Cold water temperature	real	[°C]	Input temperature of the secondary fluid (to be heated)
Hot water temperature	real	[°C]	Output temperature of the secondary fluid (after heating)
Hot water demand	real	[m³/s]	Controlled by action table

6.9.5.3. Component specific output

• Total heat demanded [W]

• Generated heat flux [W]

6.9.5.4. Component messages

Message	Type	Explanation
Zero flow not allowed	Error	Heat input with zero flow not possible, because that would require the temperature to become infinite.

6.9.5.5. Actions

The action table (control connection) of this component controls the hot water demand in [m³/s] as function of time.

6.9.6. Gas boiler

The heat supply is used to supply a constant heat flux to the system. The user sets the amount of heat supplied (+). Wanda calculates how much the fluid heats or cools down as a result. Next to this, the hydraulic losses are also included via a loss coefficient. This hydraulic loss can be converted to heat by the fraction-generated heat to fluid.

6.9.6.1. Mathematical model

The head loss is defined as:

(6.9.27)\[\Delta H = C Q^2\]

with:

variable	Description	Units
\(Q\)	Flow rate	m3/s
\(C\)	Loss coefficient	s2/m5
\(\Delta H\)	Head loss	m

This can be rewritten in terms of a pressure drop and mass flow as follows:

(6.9.28)\[\Delta p = \rho g\left( C\frac{{\dot{m}}^{2}}{\rho^{2}} - \Delta z \right)\]

with:

variable	Description	Units
\(\Delta p\)	pressure drop	N/m2
\(\rho\)	density of the fluid at the upstream side	kg/m3
\(g\)	gravitational acceleration	m/s2
\(\dot{m}\)	mass flow rate	kg/s
\(\Delta z\)	height difference between connection points	m

The temperature change is defined as:

(6.9.29)\[\dot{m} \left( c_{p1} T_1 - c_{p2} T_2 \right) + Q_{input} + fr Q_{gen} = 0\]

with:

variable	Description	Units
\(c_{p1}/c_{p2}\)	specific head of the fluid	J/kg/K
\(T_{1}/T_{2}\)	upstream/ downstream temperature	K
\(Q_{input}\)	heat supplied to the system	W
\(Q_{gen}\)	generated heat	W
\(fr\)	Fraction of generated heat transferred to the fluid	-

The generated heat flux is defined as:

(6.9.30)\[Q_{gen} = C g \frac{\dot{m}^3}{\rho^2}\]

The heat input is always defined and therefore zero flow is not possible, since this would result in an infinite temperature. The heat supply is defined as:

(6.9.31)\[Q_{s} = Q_{\text{input}} + fr \cdot Q_{\text{gen}}\]

The gross primary energy input by the fuel combustion is given by:

(6.9.32)\[Q_{\text{primary}} = \frac{Q_{\text{input}}}{\eta}\]

variable	Description	Units
\(\eta\)	Boiler efficiency	-

The fuel required to generate the necessary primary energy (\(Q_{\text{primary}}\)) is calculated as:

(6.9.33)\[V_{\text{fuel}} = \frac{Q_{\text{primary}}}{c_{\text{fuel}}\rho_{\text{fuel}}}\text{dt}\]

with:

variable	Description	Units
\(V_{\text{fuel}}\)	Required fuel volume	m3
\(c_{\text{fuel}}\)	Specific heat of the fuel	J/kg
\(\rho_{\text{fuel}}\)	Fuel density	kg/m3

6.9.6.2. Hydraulic specifications

Description	Input	SI-units	remarks
C-value (dH=CQ^2)	Real	[s2/m5]
Fraction gen. heat to fluid	Real	[-]	Default = 0
Initial heat supply	Real	[W]	Can be activated by action table or control
Combustion heat fuel	Real	[J/kg]
Efficiency boiler	Real	[-]
Density fuel	Real	[kg/m3]

6.9.6.3. Component specific output

• Temperature change [°C]

• Heat supplied [W]

• Generated Heat flux [W]

• Primary energy [W]

• Discharge of fuel used [m³/s]

6.9.6.4. Component messages

Message	Type	Explanation
Zero flow not allowed	Error	Heat input with zero flow not possible, because that would require the temperature to become infinitive.

6.9.6.5. H-actions

The action table (control connection) of this component controls the heat supply as function of time.

6.9.7. Solar collector

Heat supply by solar radiation

6.9.7.1. Mathematical model

The solar collector collects energy from the sun that heats the fluid flowing through the solar collector. The hydraulic head loss in the solar collector is defined as:

(6.9.34)\[\Delta H = C Q^2\]

with:

variable	Description	Units
\(Q\)	Flow rate	m3/s
\(C\)	Loss coefficient	s2/m5
\(\Delta H\)	Head loss	m

This can be rewritten in terms of a pressure drop and mass flow as follows:

(6.9.35)\[\Delta p = \rho g\left( C\frac{{\dot{m}}^{2}}{\rho^{2}} - \Delta z \right)\]

with:

variable	Description	Units
\(\Delta p\)	pressure drop	N/m2
\(\rho\)	density of the fluid at the upstream side	kg/m3
\(g\)	gravitational acceleration	m/s2
\(\dot{m}\)	mass flow rate	kg/s
\(\Delta z\)	height difference between connection points	m

The temperature change is defined as:

(6.9.36)\[\dot{m} \left( c_{p1} T_1 - c_{p2} T_2 \right) + A\phi_{\text{sun}} - A\phi_{\text{hloss}} + fr Q_{gen} = 0\]

with:

variable	Description	Units
\(c_{p1}/c_{p2}\)	specific head of the fluid	J/kg/K
\(T_{1}/T_{2}\)	upstream/ downstream temperature	K
\(Q_{input}\)	heat supplied to the system	W
\(Q_{gen}\)	generated heat	W
\(fr\)	Fraction of generated heat transferred to the fluid	-
\(A\)	Surface area of the solar collector	m2
\(\phi_{\text{sun}}\)	Heat flux from the sun	W/m2
\(\phi_{\text{loss}}\)	Heat flux to the surrounding	W/m2

The generated heat flux is given by:

(6.9.37)\[Q_{gen}=C g \frac{\dot{m}^{3}}{\rho^{2}}\]

The heat supply is calculated as:

(6.9.38)\[Q_{s} = A\phi_{\text{sun}} - A\phi_{\text{loss}} + fr Q_{\text{gen}}\]

The heat loss flux is defined as:

(6.9.39)\[\phi_{loss} = \alpha_1 \left( \frac{T_1 + T_2}{2} - T_{\text{ambient}} \right) + \alpha_2 \left( \frac{T_1 + T_2}{2} - T_{\text{ambient}} \right)^2 + e \sigma \left(\frac{T_1 + T_2}{2} \right)^4\]

with:

variable	Description	Units
\(T_{1}/T_{2}\)	upstream/ downstream temperature	K
\(T_{\text{ambient}}\)	ambient temperature	K
\(\alpha_1\)	Head loss coefficient 1	W/m2/K
\(\alpha_2\)	Head loss coefficient 2	W/m2/K
\(\sigma\)	Stefan-Boltzmaan constant (i.e., typical value \(5.670..\times 10^{-8}\))	W/m2/K4
\(e\)	Emission coefficient	-

6.9.7.2. Hydraulic specifications

description	Input	unit	range	default	remarks
C-value (dH=CQ^2)	Real	[s2/m5]	0.001-200
fraction generated heat to fluid	Real	[-]	0-1	0
Heat loss coefficient 1	Real	[W/m2/K]
Heat loss coefficient 2	Real	[W/m2/K2]
Area of the collector	Real	[m2]
Initial solar heat flux	Real	[W/m2]
Emission coefficient	Real	[-]	0-1	1
Ambient temperature	Constant, time varying	[-]
Constant Tamb	Real	[oC]	0-500		Only if Ambient temperature = constant
Tamb time table	Real (Table)	[oC]			Only if Ambient temperature = time varying see remark

Remark

The Tamb time table is a pattern table. When it reaches the last entry it restarts at the beginning. This enables to include a day variation for the temperature.

6.9.7.3. Component specific output

Qsuplied [W]

Qgenerated [W]

6.9.7.4. H-actions

The action table (control connection) of this component controls the solar heat flux as function of time

6.9.7.5. Component messages

Message	Type	Explanation

6.9.8. Solar collector based on ISO 9806:2017

The terminology and mathematical conventions for this component are based on the ISO 9806:2017 standard an can deviate from other WANDA components. Heat supply by solar radiation based upon the ISO 9806:2017 Solar energy — Solar thermal collectors — Test methods.

6.9.8.1. Mathematical model

The solar collector collects energy from the sun that heats the fluid flowing through the solar collector. The hydraulic head loss of the fluid floiwing through the solar collector is defined as:

(6.9.40)\[\Delta P = a Q^2 + b Q\]

with:

variable	Description	Units
\(Q\)	Flow rate	m3/s
\(a\)	Quadratic loss coefficient	Pa s2 / m6
\(b\)	Linear loss coefficient	Pa s/ m3
\(\Delta P\)	Pressure loss over collector	Pa

This can be rewritten in terms of a pressure drop and mass flow as follows:

(6.9.41)\[\Delta p = a \left( \frac{\dot{m}}{\rho}\right)^2 + b \frac{\dot{m}}{\rho}\]

The temperature change is defined as:

(6.9.42)\[\dot{m} \left( c_{p1} T_1 - c_{p2} T_2 \right) + Q_{heat} = 0\]

with:

variable	Description	Units
\(c_{p1}/c_{p2}\)	specific head of the fluid	J/kg/K
\(T_{1}/T_{2}\)	upstream/ downstream temperature	K
\(Q_{heat}\)	Total heat supplied to the system	W

The heat supply is calculated as:

(6.9.43)\[Q_{heat} = A_G \left[\eta_{0,b} K_b G_b + \eta_{0,b}K_d G_d - a_1\left(T_m - T_a \right) - a_2\left(T_m - T_a \right)^2 - a_3 u \left(T_m - T_a \right) + a_4\left(E_L - \sigma T_{a}^4 \right) - a_5 \left(\frac{dT_m}{dt} \right) -a_6 u G - a_7 u \left(E_L - \sigma T_{a}^4 \right) - a_8\left(T_m - T_a \right)^4 \right]\]

with:

variable	Description	Units
\(A_G\)	Gross area of the solar collector	m2
\(K_b\)	Incident angle modifier of beam solar irradiance	rad
\(\eta_{0,b}\)	Peak collector efficiency based on beam irradiance \(G_b\)
\(G_b\)	Beam solar irradiance	W/m2
\(K_d\)	Incident angle modifier of diffuse solar irradiance	rad
\(G_d\)	Diffuse solar irradiance	W/m2
\(a_1\)	Linear heat loss coefficient	W/m2/K
\(T_{m}\)	Mean fluid temperature	K
\(T_{\text{a}}\)	Ambient temperature	K
\(a_2\)	Temperature depended heat loss coefficient	W/m2/K2
\(a_3\)	Wind speed dependent heat loss coefficient	J/m3/K
\(u\)	Wind speed	m/s
\(a_4\)	Sky temperature dependent heat loss coefficient
\(a_5\)	Effective thermal capacity	J/m2/K
\(a_6\)	Wind speed dependent zero loss efficiency	s / m
\(G\)	Hemispherical solar irradiance	W/m2
\(a_7\)	Wind speed dependence of IR radiation exchange	s / m
\(E_L\)	Long wave irradiance (\(\lambda > 3\mu m\))	W/m2
\(\sigma\)	Stefan-Boltzmaan constant (i.e., typical value \(5.670..\times 10^{-8}\))	W/m2/K4
\(a_8\)	Coefficient for radiation losses	W/m2/K4

K_b is a function of the incidence angle of the beam of the solar irradiance, which can be split in a longitudinal and transversal part. The total angle modifier is the sum of both parts.

6.9.8.2. Hydraulic specifications

description	Input	unit	range	default	remarks
Linear loss coefficient	Real	[Pas m3]
Quadratic loss coefficient	Real	[Pas2 m6]
Area of solar collector	Real	[m2]
Linear Heat loss coefficient	Real	[W/m2/K]
Quadratic heat loss coefficient	Real	[W/m2/K2]
Wind dep. heat loss coefficient	Real	[J/m2/K]
Sky temp dep heat loss coefficient	Real	[-]
Effective thermal capacity	Real	[J/m2/K]
Wind dep. zero loss efficiency	Real	[s/m]
Wind speed IR radiation exchange	Real	[s/m]
Coefficient for radiation losses	Real	[W/m2/K4]
Peak collector efficiency	Real	[-]
Long wave irradiance	Real	[W/m2]
Angle of panel	Real	[/degree]
Modifier for diffuse radiation	Real	[-]
Environment time table	Real (Table)				Time table with the different time Depended environmental properties
Angle modifier table	Real (Table)

6.9.8.3. Component specific output

Qsuplied [W]

Qgenerated [W]

6.9.8.4. H-actions

6.9.8.5. Component messages

Message	Type	Explanation