Buildings.Fluid.HeatExchangers.RadiantSlabs

Package with radiant slab models

Information

This package contains models for radiant slabs with pipes or a capillary heat exchanger embedded in the construction.

Extends from Modelica.Icons.VariantsPackage (Icon for package containing variants).

Package Content

Name	Description
SingleCircuitSlab	Model of a single circuit of a radiant slab
ParallelCircuitsSlab	Model of multiple parallel circuits of a radiant slab
Examples	Collection of models that illustrate model use and test models
BaseClasses	Package with base classes for Buildings.Fluid.HeatExchangers.RadiantSlabs

Buildings.Fluid.HeatExchangers.RadiantSlabs.SingleCircuitSlab

Model of a single circuit of a radiant slab

Information

This is a model of a single flow circuit of a radiant slab with pipes or a capillary heat exchanger embedded in the construction. For a model with multiple parallel flow circuits, see Buildings.Fluid.HeatExchangers.RadiantSlabs.ParallelCircuitsSlab.

The figure below shows the thermal resistance network of the model for an example in which the pipes are embedded in the concrete slab, and the layers below the pipes are insulation and reinforced concrete.

The construction con_a computes transient heat conduction between the surface heat port surf_a and the plane that contains the pipes, with the heat port con_a.port_a connecting to surf_a. Similarly, the construction con_b is between the plane that contains the pipes and the surface heat port sur_b, with the heat port con_b.port_b connecting to surf_b. The temperature of the plane that contains the pipes is computes using a fictitious resistance RFic, which is computed by Buildings.Fluid.HeatExchangers.RadiantSlabs.BaseClasses.Functions.AverageResistance. There is also a resistance for the pipe wall RPip and a convective heat transfer coefficient between the fluid and the pipe inside wall. The convective heat transfer coefficient is a function of the mass flow rate and is computed by Buildings.Fluid.HeatExchangers.RadiantSlabs.BaseClasses.InternalFlowConvection.

This resistance network is instantiated several times along the flow path. The parameter nSeg determines how many instances are used. However, all instances connect to the same surface temperature heat ports surf_a and surf_b.

The material layers are declared by the parameter layers, which is an instance of Buildings.HeatTransfer.Data.OpaqueConstructions. The first layer of this material is the one at the heat port surf_a, and the last layer is at the heat port surf_b. The parameter iLayPip must be set to the number of the interface in which the pipes are located. For example, consider the following floor slab.

  Buildings.HeatTransfer.Data.OpaqueConstructions.Generic layers(
        nLay=3, 
        material={
          Buildings.HeatTransfer.Data.Solids.Generic(
            x=0.08,
            k=1.13,
            c=1000,
            d=1400,
            nSta=5),
          Buildings.HeatTransfer.Data.Solids.Generic(
            x=0.05,
            k=0.04,
            c=1400,
            d=10),
          Buildings.HeatTransfer.Data.Solids.Generic(
            x=0.2,
            k=1.8,
            c=1100,
            d=2400)}) "Material definition for floor construction"; 

Note that we set nSta=5 in the first material layer. In this example, this material layer is the concrete layer in which the pipes are embedded. By setting nSta=5 the simulation is forced to be done with five state variables in this layer. The default setting would have led to only one state variable in this layer.

Since the pipes are at the interface of the concrete and the insulation, we set iLayPip=1.

Initialization

The initialization of the fluid in the pipes and of the slab temperature are independent of each other.

To initialize the medium, the same mechanism is used as for any other fluid volume, such as Buildings.Fluid.MixingVolumes.MixingVolume. Specifically, the parameters energyDynamics and massDynamics on the Dynamics tab are used. Depending on the values of these parameters, the medium is initialized using the values p_start, T_start, X_start and C_start, provided that the medium model contains species concentrations X and trace substances C.

To initialize the construction temperatures, the parameters steadyStateInitial, T_a_start, T_b_start and T_c_start are used. By default, T_c_start is set to the temperature that leads to steady-state heat transfer between the surfaces surf_a and surf_b, whose temperatures are both set to T_a_start and T_b_start.

The parameter pipe, which is an instance of the record Buildings.Fluid.Data.Pipes, defines the pipe material and geometry. The parameter disPip declares the spacing between the pipes and the parameter length, with default length=A/disPip where A is the slab surface area, declares the whole length of the pipe circuit.

The parameter sysTyp is used to select the equation that is used to compute the average temperature in the plane of the pipes. It needs to be set to the following values:

Limitations

The analogy with a three-resistance network and the corresponding equation for Rx is based on a steady-state heat transfer analysis. Therefore, it is only valid during steady-state. For a fully dynamic model, a three-dimensional finite element method for the radiant slab would need to be implemented.

Implementation

To separate the material declaration layers into layers between the pipes and heat port surf_a, and between the pipes and surf_b, the vector layers.material[nLay] is partitioned into layers.material[1:iLayPip] and layers.material[iLayPip+1:nLay]. The respective partitions are then assigned to the models for heat conduction between the plane with the pipes and the construction surfaces, con_a and con_b.

Extends from Buildings.Fluid.HeatExchangers.RadiantSlabs.BaseClasses.Slab (Base class for radiant slab), Buildings.Fluid.FixedResistances.BaseClasses.Pipe (Model of a pipe with finite volume discretization along the flow path).

Parameters

Connectors

Modelica definition

Buildings.Fluid.HeatExchangers.RadiantSlabs.ParallelCircuitsSlab

Model of multiple parallel circuits of a radiant slab

Information

This is a model of a radiant slab with pipes or a capillary heat exchanger embedded in the construction. The model is a composition of multiple models of Buildings.Fluid.HeatExchangers.RadiantSlabs.SingleCircuitSlab that are arranged in a parallel.

The parameter nCir declares the number of parallel flow circuits. Each circuit will have the same mass flow rate, and it is exposed to the same port variables for the heat port at the two surfaces, and for the flow inlet and outlet.

A typical model application is as follows: Suppose a large room has a radiant slab with two parallel circuits with the same pipe spacing and pipe length. Then, rather than using two instances of Buildings.Fluid.HeatExchangers.RadiantSlabs.SingleCircuitSlab, this system can be modeled using one instance of this model in order to reduce computing effort. See Buildings.Fluid.HeatExchangers.RadiantSlabs.Examples.SingleCircuitMultipleCircuit for an example that shows that the models give identical results.

Since this model is a parallel arrangment of nCir models of Buildings.Fluid.HeatExchangers.RadiantSlabs.SingleCircuitSlab, we refer to Buildings.Fluid.HeatExchangers.RadiantSlabs.SingleCircuitSlab for the model documentation.

Implementation

To allow a better comment for the nominal mass flow rate, i.e., to specify that its value is for all circuits combined, this model does not inherit Buildings.Fluid.Interfaces.PartialTwoPortInterface.

Extends from Modelica.Fluid.Interfaces.PartialTwoPort (Partial component with two ports), Buildings.Fluid.HeatExchangers.RadiantSlabs.BaseClasses.Slab (Base class for radiant slab), Buildings.Fluid.Interfaces.LumpedVolumeDeclarations (Declarations for lumped volumes), Buildings.Fluid.Interfaces.TwoPortFlowResistanceParameters (Parameters for flow resistance for models with two ports).

Parameters

Connectors

Modelica definition