WHOLE BUILDING HAM SIMULATION WITH A MULTIZONE AIR FLOW MODEL Karl Grau 1 and Carsten Rode 2 1 Danish Building Research Institute 2 Technical University of Denmark ABSTRACT BSim is a whole building thermal simulation tool, which is able to predict indoor humidity conditions using a transient model for the moisture conditions in the building envelope. The simulation tool has recently been extended with a multizone model for air flow between zones in the building which makes it possible to predict the air flows between zones and through openings in the building enclosure. The model applies loop equations, which is a simpler and more efficient paradigm for continually predicting the interzonal airflow, than for instance paradigms of COMIS/TRNSYS. The new air flow model has been developed and used for analysis of hybrid ventilation. The paper will present a case of calculating whole building heat air and moisture conditions using as well the transient moisture model of the program and the new model for interzonal air flow. INTRODUCTION In multizone air flow simulation the common way to calculate the airflow is to set up a system of equations linking the pressure at each zone through airflow components (e.g. windows, doors and cracks) and solve for the internal pressure. Loop equations have been widely used in water distribution network and related fields to resolve the flow of water and other fluids (Savic and Walters, 1996). When the airflow is solved by use of loop equations all the driving pressures (wind and stack) and pressure losses for the flow components are summed around the loop starting at an arbitrary node and following the loop back to the same node. Since returning to the same node the sum of all the pressure changes must be zero. The mass flow is then determined so this is fulfilled. The theory of establishing the loops is based on graph theory. An idealised control is implemented which controls the opening degree of the windows and doors ( windoors ). The windoors have a finite number of opening positions, which can be specified by the user. At each time step the control is allowed to change the opening positions of the windoors a finite number of times in an attempt to obtain the desired airflow needed to match the set-points of indoor air temperature and CO 2 level. BSIM The new model is integrated into an ISO STEP based, integrated building design tool, BSim (Wittchen, Johnsen and Grau, 25). The core of the design tool is a common building data model shared by the different design tools, and a common database with typical building materials, constructions, windows and doors. Figure 1 illustrates the user interface of BSim. Figure 1 SimView, the user interface of BSim for editing and viewing the layout of the building Applications integrated in BSim are: SimView for editing and visualisation of the building model geometry. XSun for analyses of solar distribution and shadows in and around buildings. tsbi5 for thermal simulations. The program is based on the finite control volume method. It has been widely validated and employed in several international research projects, e.g. EU COMBINE (Augenbroe, 1995). The program includes a model for synchronous calculation of transient hygrothermal conditions (Rode and Grau, 23). SimLight is a simple tool for estimation of the daylight conditions in concave [car1]spaces.
SimPv is a tool for calculation of the potential electrical production from building integrated PV-systems (Wittchen, 23). SimDB is the user interface for the common database with building materials, constructions etc., including moisture properties. The multizone airflow model is fully integrated into the graphical user interface of BSim and requires only a few extra user data compared to the thermal model it self. At this time the airflow model includes only the orifice flow model. DATA MODEL A building in BSim is represented as a collection of one or more rooms. A room is defined by the plane faces that separate the rooms from each other and from the outdoors. The faces define the geometry, and represent the location of constructions that are defined by their thermophysical properties of their materials. A face may include a number of windows, doors and openings. One or more rooms can be included in a so-called thermal zone (or just "zone"), indicating that the rooms take part in a thermal simulation. To a zone can be attached different systems that have an influence upon or control the indoor climate. A "system" is a general concept, and not just a mechanical system like ventilation, lighting or heating and cooling systems, but may also represent the heat and moisture load from people, or air exchange with the outside or neighbor zones. In Figure 2 the data model for a building is shown as a NIAM diagram (Nijssen and Halpin, 1989). MULTIZONE AIRFLOW MODEL In the following is a short description of the theoretical basis for the multizone airflow model based on loop equations to account for the coupled thermal/airflow in natural and hybrid ventilated buildings. The model was developed as part f a Ph.D. study by Jensen (25). The principle of the loop equations is to calculate the air flow between zones based on closed loops that pass through zones which are connected by openings. The flows are calculated by ensuring that the mass balance is kept for each zone, and that the total pressure loss will add up to zero for every loop. Conservation of mass in every zone m & in m& out = m& mech, removed m& mech, supplied & in m m& out m& mech, removed m& mech, supplied Conservation of energy in loops Mass flow into the zone through openings [kg/s] Mass flow out of the zone through openings [kg/s] Mass flow removed by mechanical ventilation [kg/s] Mass flow supplied by mechanical ventilation [kg/s] For the loops the energy must be kept, i.e. the loss of energy caused by friction (resistance) is equal to the energy supplied by wind and thermics. Ploss = Pbuoyancy + Pwind = ci P Pressure loss in the loop from the loss openings [Pa] Pbuoyancy Driving force from thermics [Pa] Pwind Driving force from wind [Pa] Pressure drop of opening i [Pa] c i The demands of conservation of mass and energy can be expressed in a common linear equation system [ M ][ Q ] = [ P ] Figure 2 BSim data model of a building The common data model for BSim consists of eight separate, but interrelated models of different aspects, e.g. a model for 3D geometry and topology. The models are defined as EXPRESS files, which have been automatically converted to C++ classes, on which the implementation of the program is based (Rode and Grau, 1996). Where the matrix M consists of two parts: One for conservation of energy, and one for conservation of mass. The vector Q represents the volume flows, and in energy conservation, the vector P represents the pressure difference. For the mass balance the vector on the right hand side ( P ) should either be zero or it should represent a gain or sink of mass. Equation system The following gives a description of how the equation system is set up for a simple building. The
building (see Figure 3) consists of two thermal zones TZ1 and TZ2. Both zones have an opening facing outdoors. The separating wall has two openings allowing air to move between the zones. m V p p d T Mass [kg] Volume [m³] Partial pressure [Pa] Vapor pressure [Pa] Air temperature [K] The density differences are converted to pressure differences assuming hydrostatic pressure distribution. z ( Z ) ge( z) P j e i, j = z i dz P Pressure difference [Pa] g z Acceleration due to gravity [m/s²] Height [m] Figure 3 Simple building with nodes and branches The equation system for this case will be the following: c1 out c c TZ1 4 4 TZ1 c 7 TZ 2 TZ 2 c 1 out Q1 Pa Q4 Pb = Q 7 Q1 The first two rows is the expression for conservation of energy, and the last two rows is the expression for conservation of mass. The resistance for each opening in the loop is calculated by the following formula, and the sign reflects the direction of the airflow: V& i ci = 2 2 2 2 C d Ai c i Resistance of opening i [Pa] Air density [kg/m³] V & Volumetric air flow through the i opening [m³/s] C d Discharge coefficient [-] A i Area of the opening [m²] When the temperature is constant, the formula can be expressed as: Pe ( Z ) = eg zi j i, j, The linear equation system is solved and the resulting Q is the signed mass flow through the openings. EXAMPLE An existing BSim model of the BESTEST case has been taken as starting point for illustrating the capabilities of the multizone airflow model (mzm). The original model consists of just one thermal zone. Two thermal zones have been added representing a bathroom and a kitchen, and the original thermal zone representing a living room (see Figure 4). The model is developed as an extension to the DTU solution for Common Exercise 1 B of IEA Annex 41, Subtask 1 (CE1B). Inspired by Woloszyn et al. (25) has been added a bathroom and a kitchen within the BESTEST building, while keeping the same materials for the exterior building envelope as in CE1B monolithic constructions of aerated concrete. m p p = =.34837.13169 d V T T Density [kg/m³]
Taking moisture absorption and desorption into account gives a lower moisture content in the bathroom of around 7 8 % relative humidity, and with peaks when the moisture is produced (see Figure 6). Week 23 25 1 9 8 Figure 4. BESTEST model with bathroom and kitchen The bathroom and kitchen have a door facing the living room. The doors have been split up in two parts allowing the airflow to be in different directions for the lower and upper parts. Windows facing outdoors have been added allowing venting with outdoor air. The inner walls are made of.2 m lightweight concrete. The living room has heat production of.8 kw during daytime (9-18) and moisture supply on.2 kg/h during nighttime (18-9). The bathroom and kitchen have moisture production.2 kg/h at 7-8 hour, and 19-21 hour. All the rooms has an infiltration rate of.5 pr hour. The setpoint for the operative air temperature is 2 C for the entire thermal zone. A simulation with no venting in the bathroom, and without taking into account moisture absorption and desorption in constructions shows a relative humidity in the bathroom of up to 1% when the moisture is produced (see Figure 5). Week 23 25 7 6 5 Figure 6. Relative humidity, no venting in bathroom, and with moisture absorption and desorption in constructions Absorption and desorption in constructions and furniture in a bathroom is not very realistic. Instead venting with outdoor air is activated through the window (see Figure 7). Venting is activated during the time the moisture is produced, and for the following hour. The relative humidity in the bathroom has been stabilized to around 65 7 %. 1 9 8 7 6 Week 23 25 5 1 9 8 7 6 Figure 7. Relative humidity, venting in bathroom through the window In Figure 8 can be seen when the window is opened, and the opening fraction. 5 Figure 5. Relative humidity, no venting in bathroom and no moisture absorption and desorption in constructions
Week 23 25 Thursday 9.6.25 1 * VentOfrac(Opening Bath)- VentSpeed(Opening Bath)m/s VentSpeed(Door Bath Top)m/s VentSpeed(Door Bath)m/s VentSpeed(Win1)m/s 8 6 4 2,4,2, -,2 -,4 -,6 9 1 11 12 13 14 15 16 17 18 19 2 21 22 23 24 Hour Figure 8. Opening fraction of the window when venting the bathroom through the window To take into account opening of the door to the living room, the multizone airflow model is activated (see Figure 9). 1 9 8 7 6 Week 23 25 5 Figure 9. Relative humidity, multizone airflow taking into account natural ventilation between bathroom and living room Mixing the air between the bathroom and living room brings the relative humidity further down to around 65%, but the relative humidity in the living room is slightly raised. The air flow direction and amount is dependent on the outdoor conditions, i.e. the wind speed and the wind direction (see Figure 1). Figure 1. Wind speed and direction through openings by natural ventilation The air flow direction can change during a day dependent on the wind direction, and the air flow direction can be different for the lower and upper part of an opening, as can be seen for the bathroom door. CONCLUSION An existing whole building thermal simulation tool has been extended with a multizone model for calculation of the airflow between thermal zones in the building. It makes it possible to predict the airflow through openings between zones and through openings in the building enclosure. The model is based on the loop equation method, which has been widely used to resolve the flow of water in water distribution networks, and related fields. The paper gives a short introduction to the thermal simulation program, to the theory for the multizone model, and finally gives an example of use of the model to predict the humidity conditions for a bathroom in a dwelling. ACKNOWLEDGMENT The theory for the multizone airflow model has been developed by Rasmus Lund Jensen, Aalborg University, Center for Hybrid Ventilation, Denmark (Jensen, 25). REFERENCES Augenbroe, G.L.M. (Editor). 1995. Computer Models for the Building Industry in Europe, Final Report, Delft University of Technology, Netherlands. Grau, K., Wittchen, K.B. 1999. Building Design System and CAD Integration, Proceedings of IBPSA Building Simulation '99, Kyoto, Japan. Jensen, R.L. 25. Modellering af naturlig ventilation og natkøling - ved hjælp af ringmetoden (Modeling of natural ventilation and night cooling using the Loop Equation Method) (in
Danish). Aalborg University, Department of Civil Engineering. Nijssen, G.M. and T.A. Halpin. 1989. Conceptual Schema and Relational Database Design, Prentice Hall. Rode, C., Grau, K. 1996. Pragmatic Implementation of an Integrated Building Design System, Proceedings of CIB Workshop: Construction on the Information Highway, Bled, Slovenia. Rode, C., Grau, K. 23. Whole Building Hygrothermal Simulation Model, American Society of Heating, Refrigriation and Air-conditioning Engineers. Recent Advances in Energy Simulation: Building Loads, Symposium CH- 3-9, Chicago, USA. Savic, D., Walters, G. 1996. Integration of a Model for Hydraulic Analysis of Water Distribution Networks with an Evolution Program for Pressure Regulation, Microcomputers in Civil Engineering, 11, Blackwell Publishers, USA. Wittchen, K.B. 23. Building Integrated Photo Voltaic in a Thermal Building Simulation Tool, Proceedings of IBPSA Building Simulation 23, Eindhoven, Netherlands. Wittchen, K.B., Johnsen, K., Grau, K. 25. BSim - User s Guide, Danish Building Research Institute, Hørsholm, Denmark. Woloszyn, M., Shen, J., Mordelet, A. and Brau, J. 25. Numerical Simulations of Energy Performance of a Ventilation System Controlled by Relative Humidity. AIVC Conference Ventilation in relation to the energy performance of buildings, Brussels, September 21-23, 25 INTERNET SOURCES Danish Building Research Institute: www.sbi.dk Bsim: www.bsim.dk