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Energy Simulation in Building Design ForKathryn, Fiona, Karen and Andrew with much appreciation and love Energy S. 𝗣𝗗𝗙 | The energy consumption of a building is a complex function of a vast number of interrelated processes. Some of these processes are weather dependent. PDF | On Jul 1, , Tudor Baracu and others published Energy simulation of Energy consumption for heating and cooling in relation to building design /.

A flexible software TERMOLOG is a comprehensive software suite providing access to many applications of building energy performance such as calculation of heat losses, energy requirements and consumption of buildings. The software calculates the energy performance indexes of winter heating, domestic hot water production, summer air conditioning, ventilation, lighting and transport, either for buildings with a central heating or composed of several autonomous units. It proves to be an effective and flexible support to model and design high performance buildings e. TERMOLOG easily creates your realistic 3D model detecting orientation, surfaces arrangement, shadings by vertical and horizontal projections and by neighbouring buildings. TERMOLOG automatically calculates thermal bridges due to the presence of corners, balconies and windows and combines discontinuities with opaque structures. IFC technology helps multiple team members work on a project using a shared model, comparing energy and structural building performances. Working on one unified platform definitely reduces the risk of data translation errors and improves the whole design process.

Energy demand, indoor environmental quality incl.

The core tools in the field of BPS are multi-domain, dynamic, whole-building simulation tools, which provide users with key indicators such as heating and cooling load, energy demand, temperature trends, humidity, thermal and visual comfort indicators, air pollutants, ecological impact and costs. Advanced whole-building simulation tools are able to consider almost all of the following in some way with different approaches. Optimizing control strategies: Controller setup for shading, window opening, heating, cooling and ventilation for increased operation performance.

History[ edit ] The history of BPS is approximately as long as that of computers. The very early developments in this direction started in the late 50's and early 60's in the United States and Sweden. During this period, several methods had been introduced for analyzing single system components e. The energy crisis also initiated development of U. Over the past decades the building simulation discipline has matured into a field that offers unique expertise, methods and tools for building performance evaluation.

Several review papers and state of the art analysis were carried out during that time giving an overview about the development. Hensen Hensen, J. Building performance simulation for better design: some issues and solutions.

In Wit, M.

Eindhoven: Technische Universiteit Eindhoven. Building performance simulation is ideal for this. This paper discusses some issues that hinder the routine use of simulation in building design. In particular, the paper discusses the issues of quality assurance, the relative slow software developments and the limited use usability of building performance simulation during the total life cycle of a building.

Possible solutions are also discussed by introducing our current research. Conference Topic: 2 Design strategies and tools Keywords: building performance simulation, building design support, distributed computing processes which lead to innovative, elegant and 1. Building performance simulation can help in reducing emission of greenhouse gasses and in providing substantial improvements in fuel consumption. More importantly it can help in achieving high level of health, comfort and productivity.

Those achievements are possible only by treating buildings and the systems which service them as complete optimized entity, not as the sum of a number of separate entities sub-systems or components which are individually designed and optimized. It is only by taking into account dynamic interactions, as indicated in Figure 1, that a complete understanding of building behavior can be obtained.

For more than a quarter of a century, building performance simulation programs have been developed to undertake non-trivial building design analysis and appraisals [1]. The techniques of Figure 1: Dynamic interacting sub-systems in a building performance simulation are undergoing rapid building context change. Dramatic improvements in computing power, algorithms, and physical data make it possible to simulate physical processes at levels of detail and time scales that were not feasible only a few years ago.

An important international effort in this area This paper discusses each of these four main is the BESTEST initiative [11—12], which is now barriers and describes our current work in this area. It is based on providing a Furthermore, there are two additional elements facility to simulate different sub-domains within the which are often underestimated when using computer same program. An integrated program supports simulation in the context of building design: information exchange throughout a simulation.

For thermal, ventilation, air quality, electrical power and example: lighting calculations; e. There have been — and are — many research projects in this area. Examples lower resolution method would be quite that are based on a general simulation environment sufficient and much more efficient. Matlab—Simulink are Simbad and Climasim.

In addition, particular environment or program, which is there are now many modeling approaches where developed by single research unit or a small group of a user should also decide which model to use.

From the developer point of view, it is This is specifically the case in many open not very attractive for other researchers to join in a simulation environments e.

Matlab toolboxes later phase. Another serious problem is how to and in higher resolution approaches think of wall ensure the long-term maintenance of the software functions and turbulence models in CFD, and the and associated libraries.

In the long run it is 3. A frequently encountered problem by engineers who would like to perform a simulation is that there is 3. Data model interoperation no single simulation environment that can cover the whole range of problems at hand.

Certain In this approach, interoperability between performance aspects are available in one package programs is achieved on the level of the product i. Two approaches may package. Similar problems occur when we consider be distinguished. Therefore, it has data management system that holds both the been suggested that sharing software developments geometrical and physical parts of the model. However, this other stakeholders producers, re-sellers, etc who method does not entirely prevent inconsistency could provide models as additional product and still requires an important data management documentation as opposed to only by software system.

To understand the simulation approach, it is useful to visualise such a system as an electrical network of time dependent resistances and capacitances subjected to time dependent potential differences. The currents to result in each branch of the network are then equivalent to the heat flows between the building's parts.

Constructional elements, room contents, glazing systems, plant components, renewable energy devices etc may be treated as network 'nodes' and characterised by capacitance, with the inter-node connections characterised by conductance.

Nodes possess 'variables of state' such as temperature and pressure analogous to voltage. Since nodes have different capacitances, the problem is essentially dynamic: It is this distributed dynamic behaviour, along with the non-trivial nature of the branch flows and network parameters, that imparts complexity to the building modelling task. The resolution of the modelmthat is the number of nodesmis a function of the analysis objectives.

Clearly, an early design stage estimation of summertime temperatures will require a lower level of discretisation than a detailed study of indoor air quality. From a mathematical viewpoint, several complex equation types must be solved to accurately represent such a system and, because these equations represent heat transfer processes that are highly inter-related, it is necessary to apply simultaneous solution techniques if the performance prediction is to be both accurate and preserve the spatial and temporal integrity of the modelled system.

Once established, a simulation program can be applied throughout the design process, from the early concept stage through detailed design. Building energy flowpaths. Consider the following application scenario. It is possible to use simulation at an early design stage to determine the optimum combination of zone layout and constructional scheme that will provide a climate responsive solution and so minimise the need for mechanical plant. Some simulations might focus on the choice of constructional materials and their relative positioning within multi-layered constructions so that good temperature and load levelling is attained.

Also, alternative daylight capture and shading strategies might be investigated to ensure glare avoidance, excess solar gain control and minimum luminaire usage. After a fundamentally sound design has emerged, well tested in terms of its performance under a range of anticipated operating conditions, a number of alternative control scenarios can be simulated. Further analysis might focus on 'smart' control by which the system is designed to respond to occupancy levels or indoor daylight illuminance.

Yet further simulations might be undertaken to ensure acceptable indoor air quality or explore the feasibility of deploying local renewable energy conversion devices such as photovoltaic cells. Introduction 7 As the underlying relationships emerge, the designer is able to assess the benefits, or otherwise, of any given course of action before it is implemented. The appraisal permutations are essentially without limit. Simulation allows users to understand the interrelation between design and performance parameters, to identify potential problem areas, and so implement and test appropriate design modifications.

The design to result is more energy conscious with better comfort levels and air quality attained throughout. To this end, a building should be regarded as being systemic many parts make the whole , dynamic the parts evolve at different rates , non-linear the parameters depend on the thermodynamic state and, above all, complex there are myriad intra- and inter-part interactions. To achieve high modelling integrity, a simulation program aims to preserve these intrinsic characteristics.

Underlying the flowpaths of figure 1. Many excellent texts exist that cover the fundamentals of heat transfer e. Kreith , Ozisik , Incropera and DeWitt and no attempt is made here to provide a similar treatment of the subject. Instead, specific mathematical models are derived for each flowpath and, as the book develops, these models are combined to form a unified representation of the building and its environmental control systems.

Transient conduction This lies at the heart of the building model. It is the process by which a fluctuation of heat flux at one boundary of a solid material finds its way to another boundary, being diminished in magnitude and shifted in time due to the material's thermal inertia. Within the building fabric, transient conduction is a function of the temperature and heat flux excitations at exposed surfaces, the possible generation of heat within the fabric, the temperature- and moisture-dependent and 8 Introduction therefore time-dependent hygro-thermal properties of the individual materials, and the relative position of these materials.

With the external weather excitations declared as known timeseries data, the modelling objective is to determine the intra-fabric temperature and moisture distribution and hence the dynamic variation of heat flux at the exposed surfaces.

In many situations it is important to consider heat flow in more than one direction, for example in cases where thermal bridging might be expected to occur or where corner and edge regions are large relative to the planar area of a wall. In some applications such dependencies may be ignored and the thermophysical properties assumed constant. Appendix A lists the thermal properties of some common building materials. Such properties can be combined to give simple indices for use at an early design stage to differentiate construction performance.

Traditionally, designers have relied on this simple steady state concept to assess the heat loss characteristics of the building fabric. In addition to ignoring the dynamic aspect of fabric behaviour, the approach does not preserve spatial integrity since different constructional arrangements will perform differently even though each may have the same U-value.

As an example, if insulation is located at the innermost position of a wall then any shortwave solar radiation penetrating windows and striking that internal surface cannot be readily stored in the construction since the insulation will act as a barrier. Instead, the solar energy will cause a surface temperature rise which, in turn, will increase the rate of energy release to the adjacent air by the process of natural convection.

A space experiencing high solar energy penetration is therefore likely to overheat if cooling is not introduced. Conversely, if the insulation is relocated externally, with capacity elements exposed to the inside, then internal surface shortwave gain can access capacity to be stored.

By proper design this stored energy can later be harnessed passively rather than by mechanical means to minimise heating requirements and avoid overheating. On the other hand, internal capacity may give rise to increased peak plant demand due to the initial high rate of transfer of energy to capacity at plant start-up in an intermittent scheme. With continuous operation, capacity can help to minimise the peaks and maximise the troughs of plant demand and so promote good load levelling.

This, in turn, will give a stable environment and encourage efficient operation by allowing plant to operate consistently at or near full load. The risk of interstitial condensation is greater in the case of internally located insulation since a portion of the construction may fall below the dew point temperature of moist air permeating through the construction in the absence of an effective vapour barrier.

In summary, transient conduction will affect energy requirements, load diversity, peak plant demand, load levelling, plant operating efficiency and condensation potential. Unfortunately, there is no simple design paradigm that can be used to select an optimum construction.

From these data it is clear that there is a need to utilise dynamic models to determine the performance of alternative constructions on a case-by-case basis: Effect of construction and plant operation on fabric performance.

Energy Load levelling LL Construction? The specifications are all inside to outside and all constructions have the same U-value. Materials with high a values transmit boundary heat flux fluctuations more rapidly than do materials with correspondingly low values, while materials with high e values will more readily absorb a surface heat flux. These parameters can be usefully applied to real constructions by reducing the multiple layers to an equivalent homogeneous layer Mackey and Wright If the second term on the right-hand side of this equation becomes negative i.

Chapter 2 describes models of transient conduction while Appendix C outlines the use of the technique to estimate a construction's time constant. Surface convection This is the process by which heat flux is exchanged between a surface opaque or transparent and the adjacent air layer. In building modelling it is usual to differentiate between external and internal exposures.

Several researchers e. Alamdari and Hammond , Halcrow , Khalifa and Marshall , Fisher , Awbi and Hatton have addressed the specific needs of building simulation by producing hc correlation equations for typical configurations. Forced convection is a function of the prevailing fluid flow vector. Typically, for external building surfaces, wind speed and direction data are available for some reference height and techniques exist to estimate non-reference height values in terms of characteristic vertical velocity profiles.

Forced convection estimation for internal surfaces is more problematic, requiting knowledge of the distribution and operation of air handling equipment. Natural convection is an easier problem to study and many formulations have emerged which give convection coefficients as a function of the surface-to-air temperature difference, surface roughness, direction of heat flow and characteristic dimensions. Chapter 7 describes approaches to the modelling of surface convection, forced and buoyant, at surface layers associated with the building fabric.

Internal surface Iongwave radiation exchange In most simplified methods, surface heat transfer coefficients are treated as combinations of convection and longwave radiation although the values used are often dubious. In reality, the two processes are related by the fact that they both can raise or lower surface temperatures and so influence each other.

Inter-surface longwave radiation is a function of the prevailing surface temperatures, the surface emissivities, the extent to which the surfaces are in visual contact, referred to as the view factor, and the nature of the surface reflection diffuse, specular or mixed.

The flowpath will tend to establish surface temperature equilibrium by cooling hot, and heating cold, surfaces. It is an important flowpath where temperature asymmetry prevails, as in passive solar buildings where an attempt is made to capture solar energy at some selected surface. A standard energy efficiency measure is to upgrade windows with glazings incorporating a low emissivity coating.

This increases the reflection of longwave radiation flux and so acts to break inter-surface heat exchange. The mathematical representation of the flowpath is non-linear in the temperature term and this introduces modelling complications as discussed in chapters 3 and 7. External surface Iongwave radiation exchange The exchange of energy by longwave radiation between external opaque and transparent surfaces and the sky vault, surrounding buildings and ground can result in a substantial lowering Introduction 11 of surface temperatures, especially under clear sky conditions and at night.

This can lead to sub-zero surface temperatures, especially with exposed-roofs, and can become critical in cases of low insulation level. Conversely, the flowpath can result in a net gain of energy, although under most conditions this will be negligible. The adequate treatment of this flowpath will require an ability to estimate several contributing factors: Shortwave radiation In most buildings, the gain of energy from the sun constitutes a significant portion of the total cooling load.

The method of treatment of the shortwave flowpaths can therefore largely determine the accuracy of the overall predictions. Some portion of the shortwave energy impinging on an external surfacemarriving directly from the sun or diffusely after atmospheric scatter and terrain reflectionsmmay, depending on subsequent temperature variations affecting transient conduction, find its way through the fabric where it will contribute to the inside surface heat flux at some later time.

Some simplified methods utilise the 'sol-air' temperature concept to handle fabric solar gain. This corresponds to a suitably elevated ambient temperature for use in fabric conduction calculations. This is clearly inadequate on two counts: Unless the solar contribution to the sol-air temperature is determined on the basis of time-dependent surface properties relating to shading and convection, then a difference will prevail between actual solar absorption and that predicted.

In such cases it is important to model the intra-construction shortwave absorptions. In the case of completely transparent structures, the shortwave energy impinging on the outermost surface is partially reflected and partially transmitted. Within the glazing layers and substrates of the system many further reflections take place and some portion of the energy is absorbed within the material to raise its temperature.

This temperature rise will augment the normal transient conduction process and, thereby, help to establish innerside and outerside surface temperatures which, in turn, will drive the surface convection and longwave radiation flowpaths. Thus, in effect, absorbed shortwave radiation penetrates the building via convection and longwave radiation. The component of the incident beam which is transmitted will strike with no perceptible time lag some internal surface s where it behaves as did the external surface impingement: Accurate solar irradiation modelling therefore requires methods for the prediction of surface position relative to the solar beam, and the assessment of the moving pattern of insolation of internal and external surfaces.

The thermophysical properties of interest include shortwave absorptivity for opaque elements and absorptivity, transmissivity and reflectivity for transparent elements Appendix A. The magnitude of these properties is dependent on the angle of incidence of the shortwave flux and on its spectral composition.

With regard to the latter, it is common practice to accept properties that are averaged over the entire solar power spectrum. Shading and insolation These factors control the magnitude and point of application of solar energy and so dictate the overall accuracy of any solar processing algorithm. It is usual to assume that facade shading caused by remote obstructions such as buildings and trees will reduce the magnitude of direct insolation, leaving the diffuse beam undiminished.

Conversely, shading caused by facade obstructions such as overhangs and window recesses should also be applied to the diffuse beam since the effective solid angle of the external scene, as subtended at the surface in question, is markedly reduced. At any point in time the shortwave radiation directly penetrating an exposed window will be associated with one or more internal surfaces, depending on the prevailing solar angle and the internal building geometry. The receiving surface s may be opaque, a window in another wall connecting the zone to another zone or back to ambient conditions , items of furniture or special surfaces included in the model to represent occupants or sensors.

While it has been observed that disregarding the apportioning of window transmitted shortwave flux between the associated receiving surfaces can have a significant effect on thermal predictions, the smearing of the portion received by one surface over its entirety will have minimum effect if the surface has a uni-directional conduction heat flow representation Robinson Air flow Within buildings, three air flow paths predominate: These flowpaths give rise to advective fluid-to-fluid heat exchanges.

Each are vector quantities in that only air flow into a region is considered to cause the thermal loading of that region, any loss being the driving force for a corresponding replacement to maintain a mass balance. Infiltration is the name given to the leakage of air from outside and can be considered as comprising two components: Zone coupled air flow, as with infiltration, is caused by pressure variations and by buoyancy forces resulting from the density differences associated with the temperatures of the coupled air volumes.

Mechanical ventilation is the deliberate supply of air to satisfy a fresh air requirement and, perhaps, heat or cool a space. Notwithstanding the stochastic nature of these occurrences, air flow models of varying complexity can be constructed. Such models will span the spectrum from whole building predictors, based on regressions applied to measured data, to the numerical solution of equations representing the conservation of mass, momentum and energy. Introduction 13 At a level appropriate to building energy modelling, air movement is often represented by a nodal network in which nodes represent fluid volumes and inter-nodal connections represent the distributed leakage paths connecting these volumes and through which flow can occur.

Numerical techniques are then applied to this network to establish the mass balance corresponding to any given nodal temperature field and boundary pressure condition. Such a method is well suited to the determination of the contribution of air movement to energy requirements.

A more comprehensive approach involves the solution of the energy, continuity mass and momentum Navier-Stokes equations when applied to a finely discretised flow domain. In addition to supporting energy analysis, such a method will also provide information on the spatial variation of indoor air quality and thermal comfort levels.

Chapter 5 describes these two approaches and elaborates a technique for their conflation with the building, HVAC and renewable energy system models derived in chapters 3 and 6 respectively. Casual gains In most non-domestic buildings, the effects of the heat gains from lighting installations, occupants, small power equipment, IT devices and the like can be considerable. It is important therefore to process these heat sources in as realistic a manner as possible.

Typically, this will necessitate the separate processing of the heat radiant and convective and moisture emissions, and the provision of a mechanism to allow each casual source to change its value by prescription or via control action.

It is usual to assume that the convective heat emission is experienced instantaneously as an air load whereas the radiant portion, behaving in a manner similar to shortwave radiation penetrating the building envelope, is apportioned between the internal opaque and transparent surfaces according to some distribution strategy. Because of the inherent relationship with the construction capacity, the radiant component will experience a time lag before it can contribute to the cooling load or elevate the internal air temperature.

Some casual gain sources, such as luminaires and IT equipment, will require the elaboration of a model of their electrical behaviour in order to modulate heat emission as a function of the electrical power usage.

For example, this would be required in the case of daylight responsive luminaire dimming. The problem of predicting energy consumption has traditionally been divided into two distinct stages.

As shown in figure 1. This is found by modifying the various instantaneous heat gains and losses as a function of the distributed thermal capacities. In the second stage, these energy requirements are modified by the operating characteristics of the plant to give the energy actually consumed. The first stage is concerned with the design of the building to reduce the energy requirements, whilst the second stage is concerned with the design of the installed plant to best match these requirements and minimise consumption and thereby the resulting gaseous emissions.

Because the building and its plant are strongly coupled, accuracy considerations dictate that they be handled simultaneously. One approach, as demonstrated in w is to incorporate plant characteristics within control statements which are then embedded within the solution of the building-side equations or used to influence their formulation.

Alternatively, and more accurately, dynamic plant system models Lebrun can be established for solution in tandem 14 Introduction Figure 1. Some possible HVAC systems. The traditional role of building and plant models. Introduction 15 with the building model so that the spatial and temporal interactions are fully respected. Such an approach is demonstrated in chapter 6 where selected plant systems are combined with the building model established in chapter 3.

Control To direct the path of a simulation, the combined building and plant model is subjected to control action. This involves the establishment of several control loops, each one comprising a sensor to measure some simulation parameter or aggregate of parameters , an actuator to receive and act upon the controller output signal and a regulation law to relate the sensed condition to the actuated state.

These control loops are used to regulate HVAC components and manage building-side entities, such as solar control devices, in response to departures from desired environmental conditions. Control loops can also be used to effect changes to the active model at run-timene. This is a useful feature where there is insufficient information to allow a detailed plant model to be established. Section 6. Moisture Dampness and mould growth are recognised as major problems affecting a significant proportion of houses throughout the world.

Approximately 2. Singh has estimated the cost of repairing the damage caused by timber decay in the UK housing stock to be approximately s per annum. Apart from aesthetic considerations, there is now considerable epidemiological evidence to support the view that mouldy housing has a detrimental effect on the physical and mental health of occupants Paton High levels of airborne spores may occur due to the growth of fungi on walls and furnishings.

Data from the Scottish housing condition survey Scottish Homes indicate that around Fluctuations in moisture levels within the building's fabric can also be problematic, leading to interstitial condensation or causing variations in a material's thermophysical properties and, thereby, adversely affecting its thermodynamic performance. Approaches to the modelling of airborne moisture transport are described in w while w describes a procedure for the modelling of the moisture flows within porous media and w describes the conditions required for the proliferation of mould growth.

Passive solar elements Many designers have come to favour the use of the so-called passive solar features. These act to capture and process solar radiation passively and without recourse to mechanical systems. Consider figure 1. In each case certain factors can be identified which, in particular, will impose technical complexity on any modelling exercise: Passive solar elements in architectural design. Introduction 17 b Diffusing direct gain systems will require solar energy apportioning to the various internal surfaces.

Thermosiphon systems will require buoyancy driven air flow modelling. Double envelopes will require sophistication on the part of solar algorithms since radiation may penetrate the external skin to cause 'deep' construction heating. Induced ventilation schemes will require accurate modelling of buoyancy and pressure induced air flows.

P q Movable insulation implies a time-dependent system definition. Selective thin films will require detailed spectral response modelling.

Advanced modelling systems seek to include these and other energy flowpaths while respecting the inevitable interactions and underlying complexities. New and renewablo energy systoms Future cities are likely to be characterised by a greater level of new and renewable energy RE systems deployment.

Traditionally, such deployment has occurred at the strategic level with the grid connection of medium-to-large scale hydro stations, bio-gas plant and wind farms. This limitation is due to the intermittent nature of RE sources, requiring controllable, fast responding reserve capacity to compensate for fluctuations in output, and energy storage to compensate for non-availability.

To attain higher levels of new and RE systems penetration, alternative approaches will be required, including the deployment of micro power systems at the local level e.

Furthermore, by utilising energy efficiency and passive solar measures, a building's energy demand may be reduced and the profile of this demand reshaped to accommodate the low power densities of RE components such as photovoltaic panels and ducted wind turbines.

Any energy deficit may then be met from the public electricity supply PES or small scale co-generation plant operating co-operatively with the local RE systems. Section 8. A significant additional energy consumption is associated with the production and transportation of construction materials.

Associated with these consumptions are gaseous emissions that can contribute to global warming CO2 , acidification SOx and ozone depletion NOx. For a succinct review of the nature of the environmental impacts associated with building construction, operation and demolition, and a simulation embedded approach to the quantification of these impacts, the reader is referred to the work of Citherlet Uncertainty Since all design parameters are subject to uncertainty, programs need to be able to apply uncertainty bands to their input data and automatically use these bands to determine the impact of uncertainty on likely performance.

Programs so endowed will be able to assess risk, rather than merely presenting performance data to their users. Surely it is better to give the probability of overheating than to output an operative temperature profile and trust to the user's interpretive skill. Indeed, the trade-off between accuracy and flexibility is itself a dynamic concept that will vary according to the modelling task in hand.

Nevertheless, it is important to differentiate between simplified models and comprehensive models which are capable of simplified model emulation. Invariably, some flowpaths are crudely approximated or omitted entirely.

The model to result is then valid only when applied to problems that embody the same simplifications. In the latter case, a comprehensive model is designed to operate on input data ranging from simplified to detailed. This is achieved by incorporating context specific defaults to allow the inclusion of any flowpath not explicitly addressed in the input data set. This approach is substantially more flexible, with the accuracy level changing as a function of the quality of the design information supplied.

To illustrate the problems associated with the former approach, Appendix B presents the results from several methods when applied to the same problem. Introduction 19 As a general strategy, it would seem reasonable to aim for a high level of accuracy combined with a model structure that is capable of adapting to the information available at any design stage. It is likely that a truly simple model, as perceived by a user, will be internally comprehensive in its treatment of the energy flowpaths, relying on the proper design of the interface for its operational flexibility.

This is the philosophy underlying the modelling approach promoted in this book. The three pole axiom of conservation of energy, conservation of integrity and conservation of flexibility is the essential goal of the integrated modelling approach.

The former method is appropriate for the solution of systems of linear differential equations possessing time invariant parameters. In use, it is usual to assume a high degree of equation decoupling. Numerical methods, on the other hand, can be used to solve time varying, non-linear equation systems without need to assume equation decoupling as a computational convenience.

Numerical methods are favoured for a number of reasons. First, to ensure accuracy it is essential to preserve the spatial and temporal integrity of real energy systems by arranging that whole system partial differential equation-sets be solved simultaneously at each computational time step. Second, numerical methods, unlike their response function counterpart, can handle complex flowpath interactions.

Third, time varying system parameters can be accommodated. Fourth, processing frequencies can be adapted to handle so-called 'stiff' systems in which time constants vary significantly between the different parts of the problem building fabric, HVAC components, fluid flow domains, control system elements etc. Chapter 2 details the response function method in its time and frequency domain forms and subsequent chapters introduce the universally applicable numerical approach.

Gough provides a succinct overview of contemporary programs and discernible development trends. Systems Simulation Liege: University of Strathclyde, Dept. Building Simulation '97 Prague: Advantages and Drawbacks Proc. Centraalbureau voor Schimmelcultures 2 Integrative modelling methods This chapter describes the theoretical basis and development background of the much popularised response function method. Both branches of the methodmtime and frequency response--are derived for the case of transient conduction and intra-zone energy flowpaths and, in each case, use in practice is described.

The elements of a more flexible modelling approach, based on a finite volume conservation method, are then presented as the essential introduction to chapters 3 and 4 where a building model is formulated and solved respectively. Finally, w introduces the criteria on the basis of which an answer might be obtained to the question, 'which method is best? Each of the methods provide a solution to the differential equations that govern the flow of heat in solids, heat transfer at surface layers and heat exchange between connected fluid volumes.

The response function approach is usually applied to differential problems of low order with time-invariant parameters whereas the numerical method is also suited to time varying problems of high order. A homogeneous, isotropic element.

An analytical approach to the solution of these equations involves the use of the Laplace transformation Carslaw and Jaeger , Churchill , Davies This is essentially a three stage procedure as follows.

The given equation in the time domain is transformed into a subsidiary equation in an imaginary space. This subsidiary equation is solved by purely algebraic manipulations. An inverse transformation is applied to this solution to obtain the solution in the time domain of the initial problem. The interesting feature of the method is that in many cases ordinary differential equations are transformed into purely algebraic equations and partial differential equations are transformed to ordinary differential equations.

Table 2. Some common Laplace transform pairs. A number of theorems accompany the transform of which two are relevant here: If 0 x, p is found in a table of transforms then the solution for O x, t may be determined immediately. If no such transform exists then O x, t is determined from 0 x, p by the inversion theorem: In the terminology, M is the transmission matrix and its entries are the transfer functions. For composite constructions, 0 q L, p C p D p Lq o, p where the value of the elements A p , B p , C p and D p of the overall transmission matrix will depend on the properties of the component elements of the multi-layered construction and the order in which the individual element transmission matrices are combined.

For a multi-layered construction with homogeneous elements e 1, e2, e3. Eqn 2. For the former method a rearrangement of eqn 2. In this way, the problem complexity is reduced. In some applications the technique can match the numerical technique although it can only be applied to an equation system which is both linear and invariable. While Mitalas has stated that such a requirement need not impose severe restrictions in a building design context, the complexity of contemporary building related issues will severely limit the method's applicability.

That said, the method is t The sign convention has first been changed by transposing L and 0 in eqn 2. This is done to maintain consistency with the published literature. This means that the elements of the overall transmission matrix will differ between the two equations. A unit excitation function has a value of unity at its start and zero thereafter i. The response of a linear, invariant equation system to this unit excitation function is termed the unit response function URF and the time-series representation of this URF, that is the individual terms of the series, are the response factors.

The number of URFs considered in any problem will depend on the number of combinations of excitation function for solar radiation, dry bulb temperature, sky longwave radiation etc and responses of interest cooling loads, internal temperatures etc. Figure 2. Time 5 6 Figure 2. Unit excitations and response functions.

In general terms there are three steps inherent in the method after the various URFs have been determined. First, the actual excitation functions are resolved into their equivalent timeseries.

This can be achieved by triangular or rectangular approximation, contemporary systems favouring the former. Second, the URFs are combined with a corresponding excitation function to determine the system response.

This is achieved by application of the convolution theorem, which states that the response of a linear, invariant system is given by the products of the response of the same system to a unit excitation the URF and the actual excitation given that the appropriate time adjustments are made.

Stated mathematically: Finally, the individual responses from the different excitation functions are superimposed to give the overall response.

Integrative modelling methods 27 URFs are only dependent on design parameters and assumptions regarding thermophysical properties and therefore, if assumptions of time invariance are acceptable, need only be determined once for any given design. This is one of the main attractions of the method over the more generalised numerical methods where a computational exercise, equivalent to URF computation, must be implemented at each time-step as a simulation proceeds.

However, should system properties vary with time, requiring that the URF be computed anew, then this computational distinction will disappear. Rectangular and triangular pulse representation of a continuous function. Pratt and Ball were among the earlier workers in the field of response function modelling. They developed a method for the calculation of room loads and temperatures using URFs derived for multi-layered constructions of up to three homogeneous elements.

Stephenson and Mitalas a are largely responsible for the present day form of the method. Their formulation builds on the earlier work of Brisken and Reque , who were among the first to consider response factors as a set of numbers denoting the time-series values of a URF at equally spaced intervals of time.

A triangular pulse representation technique was developed in which each term in some continuous excitation function is considered as the magnitude of a triangular pulse centered at the particular time in question and with a base equal to twice the selected time-step. The summation of such overlapping triangles is equivalent to a trapezoidal approximation and represents a continuous function comprised of straight line segments. Although for most applications triangular approximation gives a good fit, Gupta et al have pointed out that switched inputs such as lighting loads would be better treated by the rectangular method.

Many subsequent enhancements have been made to the response factor technique. These include the derivation of additional equations for the evaluation of interfacial temperatures and heat fluxes within multi-layered constructions Kusuda ; the concept of whole building response functions Muncey ; and an approach to the calculation of wall response based on an eigenfunction representation which is computationally efficient Gough In most response factor implementations, the overall response is conveniently considered in two stages: Overall zone responsemsequence of steps.

In other words, the first stage is concerned with the effect of heat flow across the system boundary and subsequent internal flowpath interaction to produce a design condition plant demand. The second stage addresses the operational strategy of the installed plant. The URF for such an element represents the heat flux at the innermost or outermost surfaces as caused by a unit triangular excitation applied to the other surface whilst the surface in question is held at a constant temperature.

Recall eqn 2. In this case three URFs will result: It follows from eqn 2.

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