.Annex60.Fluid.HeatExchangers.Radiators.RadiatorEN442_2

Information

This is a model of a radiator that can be used as a dynamic or steady-state model. The required parameters are data that are typically available from manufacturers that follow the European Norm EN 442-2.

However, to allow for varying mass flow rates, the transferred heat is computed using a discretization along the water flow path, and heat is exchanged between each compartment and a uniform room air and radiation temperature. This discretization is different from the computation in EN 442-2, which may yield water outlet temperatures that are below the room temperature at low mass flow rates. Furthermore, rather than using only one room temperature, this model uses a room air and room radiation temperature.

The transferred heat is modeled as follows: Let N denote the number of elements used to discretize the radiator model. For each element i ∈ {1, … , N}, the convective and radiative heat transfer Qⁱ_c and Qⁱ_r from the radiator to the room is

Qⁱ_c = sign(Tⁱ-T_a) (1-f_r) UA ⁄ N |Tⁱ-T_a|ⁿ

Qⁱ_r = sign(Tⁱ-T_r) f_r UA ⁄ N |Tⁱ-T_r|ⁿ

where Tⁱ is the water temperature of the element, T_a is the temperature of the room air, T_r is the radiative temperature, 0 < f_r < 1 is the fraction of radiant to total heat transfer, UA is the UA-value of the radiator, and n is an exponent for the heat transfer. The model computes the UA-value by numerically solving the above equations for given nominal heating power, nominal temperatures, fraction radiant to total heat transfer and exponent for heat transfer.

The parameter energyDynamics (in the Assumptions tab), determines whether the model computes the dynamic or the steady-state response. For the transient response, heat storage is computed using a finite volume approach for the water and the metal mass, which are both assumed to be at the same temperature.

The default parameters for the heat capacities are valid for a flat plate radiator without fins, with one plate of water carying fluid, and a height of 0.42 meters.

Revisions

• November 17, 2016, by Filip Jorissen:
  Added pressure drop equations and parameters.
  This is for #586.
• November 3, 2016, by Michael Wetter:
  Set preHea(final alpha=0) as this allows to simplify the system of equations.
  This is for #570.
• March 17, 2016, by Michael Wetter:
  Reformulated model to reduce the dimension of the nonlinear system of equations. This is for #435.
• November 19, 2015, by Michael Wetter:
  Removed assignment of parameter showDesignFlowDirection in extends statement. This is for #349.
• April 11, 2015, by Filip Jorissen:
  Propagated vol.massDynamics to top level parameter massDynamics instead of energyDynamics.
• November 25, 2014, by Carles Ribas Tugores:
  Interchange position of fraRad parameter and the complementary (1-fraRad) in the equation used to calculate the nominal heating power of each element, QEle_flow_nominal[i].
• October 29, 2014, by Michael Wetter:
  Made assignment of mFactor final, and changed computation of density to use default medium states as are also used to compute the specific heat capacity.
• October 21, 2014, by Filip Jorissen:
  Added parameter mFactor and removed thermal capacity which can lead to an index reduction.
• May 29, 2014, by Michael Wetter:
  Removed undesirable annotation Evaluate=true.
• October 8, 2013 by Michael Wetter:
  Removed conditional statement in the declaration of the parameter mDry, as this is incorrect syntax.
• September 26, 2013 by Michael Wetter:
  Reformulated implementation to avoid mixing textual and graphical declarations in the equation section.
• April 4, 2011 by Michael Wetter:
  Changed the implementation to use Annex60.Utilities.Math.Functions.regNonZeroPower. This allows formulating the model without any non-differentiable function inside the equation section.
• April 2, 2011 by Michael Wetter:
  Added homotopy operator.
• February 11, 2011 by Michael Wetter:
  Revised the initialization to ensure that at the nominal conditions, the amount of transferred heat is excatly the same as the specified nominal power. In the previous implementation, the UA-value was computed using a simplified expression for the temperature difference, leading to a slightly different amount of heat transfer.
• February 4, 2011 by Michael Wetter:
  Simplified implementation.
• January 30, 2009 by Michael Wetter:
  First implementation.