2.3 Thermal Simulation
2.3.4 Space Heating Distribution System
Within a dwelling, a space heating distribution system (SHDS) is utilised to distribute thermal energy from a central heat generator, to the individual rooms. In the UK, the dominant SHDS is a wet central heating system [39], in which a volume of water is pumped through pipework to a series of heat emitters (typically radiators).
The effect of using a SHDS is to introduce thermal lag between heat generation and heat delivery to the dwelling airspace. Initial development work on the BIM-G model omitted a SHDS. When BIM-G results were compared against internal air measurements recorded by the author in several dwellings, several features of the resulting temperature profiles were skewed. Without a SHDS, the internal air temperature fell sharply on cessation of heat generation, which in practice does not occur due to residual thermal energy stored in the volume of space heating water (SHW) and metal of the radiators and pipework, which gradually transfers to the air mass over time. Similarly, internal air temperature rose sharply when the heat generator was activated, whilst in practice the increase is much more gradual, as the SHW acts as a buffer.
In order to increase the accuracy of thermal simulation, a simplified space heating distribution system was devised. To work within the limits of a single zone, 1-D model, simplifications were necessary, yet worthwhile, as they would serve to introduce an indicative thermal lag term to the thermal demand estimation routine. The SHDS has four sections; a heat emitter (i.e. radiator), a heat exchanger (HX) within the heat generator, a flow pipe (from heat generator HX to emitter), and a return pipe (from emitter to heat generator HX). This arrangement is displayed in Figure 2.5. Each section contains a volume of SHW, where flow between the sections is simulated every time-step by calculating the average temperature for each element based on a single flow volume (at the previous temperature of that element) being replaced with a flow volume of the preceding element (at the previous temperature of that element). The emitter and pipes are defined with a surface area, for which the heat transfer to the internal air volume is calculated based on temperature differential. The energy transfer into the heat generator’s HX is determined by the heat output of the heat generators under simulation. If a thermal store is specified for a particular demand scenario, then the HX volume considered is that of HX within the thermal store, and not of the heat generator.
Figure 2.5: Schematic of Space Heating Distribution System (SHDS) concept used in BIM-G model, where each section of the SHDS relates to a volume of water whose temperature is calculated each time-step based on flow between each section and indicated heat flows
It may be argued that a full heat and mass flow model of the SHDS for a given dwelling should have been implemented. This would have involved further division of the SHW into smaller elements, and a heat transfer characteristic dictated by the position of the element within the SHDS and the temperature of surrounding elements. The increase in simulation accuracy that this approach would have offered would have been attained if the exact geometry of the SHDS was known. To have done so would have required specifying a discrete system for each dwelling considered, which was considered beyond the scope of this investigation. The major drawback of the simplified approach is that the temperature within each section is representative of the average across the section, and hence the extremes of temperatures entering and leaving the sections are not calculated.
In the end, the complex approach was considered impractical within the constraints of the BIM-G Model, as it would require full geometric and technical specification of the SHW distribution system, including pumps, pipework, heat emitters and expansion vessels. The resources required for such development, as well as the intrinsic binding of any results to that particular system design, were deemed inappropriate, especially as the rationale of the BIM-G model was to remain generic.
The design of the SHDS was undertaken using a domestic wet central heating design guide [17], published by an industry body, the Heating and Ventilation Contractors’ Association (HVCA). Using the SHDS design methodology described in the guide [17], the rated emitter thermal output was derived, and from numerical analysis of typical emitter characteristics, the associated SHW volume and emitter surface area was calculated. From pipework layout estimations, undertaken using a floor plan of the dwelling, and numerical analysis of typical pipework lengths per radiator from the HVCA guide, the surface areas and volumes of both pipes were calculated. If the SHDS is specified with a thermal store, the HX volume is calculated from a relationship with store volume, as derived from the HVCA guide [17]. If the SHDS is specified with no thermal store, the heat generator HX volume is taken as the HVCA guide’s typical value.
When the SHDS circulation pump is activated, the BIM-G model simulates the flow of SHW by volume-averaged recalculation of SHW temperatures in each section of the SHDS. The rate at which the SHW circulates was chosen using the HVCA design guide [17], with supporting information from the relevant British Standard [18].
In the HX section of the heat generator, any temperature rise is calculated from heat generator output acting on the volume of water in the section. If a thermal store is specified, the input energy flow to the SHDS (QSHDSIn) from the thermal store to the HX section (of the SHDS) is calculated from the temperature difference between the SHW in the thermal store HX and water in the thermal store itself, using equation (2.15).
()
*
*c T t T t
m
QSHDSIn SHWFlow Water Store PipeF
(2.15)
Heat transfer between the heat emitter and internal air was calculated using the “characteristic equation” of a typical radiator, as defined by the relevant British Standard [19] and the HVCA guide [17]. This “characteristic equation” quantifies the heat transfer due to convection and radiation, for radiators of an assumed height, in relation to the temperature difference between the SHW in the emitter and internal air. The characteristic equation is applied in the BIM-G model using equation (2.16),
where KMRadiator is the characteristic heat output, and nRadiator the radiator constant. These values were derived by performing a power-type regression on data from the HVCA guide [17], which related the temperature difference between the radiator water and surrounding air to radiator thermal output.
nRadiator In Radiator Radiator Radiator KM T t T t Q * ( ) (2.16)Equation (2.16) is also used to calculate the heat loss from the flow (QPipe-Flow) and return (QPipe-Return) pipework sections of the SHDS, using values for KMPipe and nPipe again derived by regression from data in the HVCA guide [17], and the pipe water temperatures, TPipe-Flow & TPipe-Return. The water temperature in the return pipe is used as a control signal for the SHDS circulation pump, as discussed in Section 2.3.6. The heat loss from the pipework is assumed to split between heated and unheated portions of the dwelling, i.e. some of the heat of the heat quantified by QPipe-Flow &
QPipe-Return enters the dwelling’s heated airspace, and the remainder is immediately lost
to the environment under suspended floors and in unheated loft spaces. The BIM-G model uses a 50:50 split, as no definitive information was available to the contrary. The heat loss is based on heat transfer from the exterior surface of the pipes, using the minimum pipe insulation standard quoted by industry guidance material [17].
The final heat input to the dwelling’s internal airspace, QSHDS, is calculated using equation (2.17).