2 Dynamic Behaviour of Buildings

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1 2 Dynamic Behaviour of Buildings Handouts: Building for Energy Conservation by Burberry P (section 3.3) Cibse Guide Section A: Admittance Technique Steady-State Analysis This traditional analysis was undertaken for plant sizing assuming typical indoor and design external conditions. For buildings which have high levels of thermal mass, low solar gains, and constant internal temperatures (e.g. old hospitals), the steady state method can give an indication of energy consumption. For this analysis, fabric heat losses are controlled by conductivity and thickness of the external construction and surface resistances. U= 1/R tot (W/m 2 K) R tot = R si + (t/k) + R so (m 2 K/W) Dynamic Behaviour For calculation of dynamic behaviour, it is necessary to take heat storage (thermal capacity) into account: specific heat capacity: C (J/kgK) density: ρ (kg/m 3 ) volumetric heat capacity = ρc (J/m 3 K) Steady state analysis is often not sufficient because: Thermal properties of newer buildings tend towards a lightweight constructions which have lower thermal capacity, faster response to heat inputs and therefore much greater temperature swings. Even heavyweight buildings will act as lightweight buildings if the walls are lined with some insulation. Improved heating systems have faster response (e.g. gas-fired boilers) and better controllers, which enable heat to be input when required. Intermittent occupancy patterns are more common in the domestic sector: this requires rapid warming up of the building in the morning and again in the evening.

2 Table IV in the handout shows the thermal capacity of different materials having the same U-value. Clearly, surface temperatures of constructions with high thermal mass would take a long time to increase after a period of no heating (e.g. in an office after a weekend) and would contribute to poor thermal comfort conditions in a room until the heating had been on for several hours. Figures 3.11 to 3.13 in the handout show how different wall constructions react to intermittent heating. As can be seen, a wall with high thermal mass can have large differences between internal air temperature and wall surface temperature: this can lead to condensation problems as well as poor thermal comfort. Transient Conduction This is controlled by the Fourier Equation, which for 1 dimensional conduction is: ρ ϑ 2 ϑ C = k t x 2 An important property is the ratio of thermal conductivity to volumetric heat capacity, known as the diffusivity: α = k / ρc This has units of m 2 /s and it indicative of the rate at which a heat pulse will propagate through a solid. The time constant (t c ) is related to the response of a construction to a step change: T Heavyweight constructions have long time constants, lightweight constructions have short time constants. t c t

3 Response of Heavyweight and Lightweight Buildings The building response will differ according to whether the building is lightweight or heavyweight. The following figure illustrates this. Heating curves for heavyweight and lightweight buildings Fabric Performance and Fuel Consumption Figure 3.14 in the handout shows how thermal capacity affects fuel consumption in lightweight and heavyweight buildings. For intermittent heating, lightweight buildings offer significant potential fuel savings, unlike heavyweight buildings. For example, the following table shows the heat required to raise fabric temperature. Material Drop in temperature ( o C) Heat required to return to ambient temperature (kj/m 2 ) 100mm brick mm fibreboard Although a fibreboard-lined room will show a greater drop in temperature when heating is off, less heat is required to get back to temperature. Also less time is required (see Figure above). During the heating off period, the fibreboard-lined room would be colder and in practice it may be necessary to have a lower limit, below which heating is switched on, to prevent condensation risk.

4 Figure 3.15 in the handout shows how the use of steady state analysis and design temperatures instead of more realistic boundary conditions can lead to incorrect conclusions on potential for fuel saving. Summer conditions In hot climates with intermittent active cooling, lightweight buildings offer the same advantages for heating as discussed above. However, for buildings that are not actively cooled, heavyweight constructions are best because they reduce peak daily temperatures. Additional cooling of the thermal mass at night ( night purging ) can assist in reducing peak daytime temperatures. Effect of solar gains on heavyweight and lightweight buildings Prediction Techniques

5 Figure 3.16 shows more realistic variation in internal and external conditions. Three methods of predicting such dynamic variations in temperature are: Analogue method: superseded by numerical techniques. Admittance technique: developed by CIBSE, used in particular for calculating peak summertime temperatures. Solution of Fourier Equation: computer programs based on a variety of numerical methods are used; some examples are covered later in the course. Analogue Method There exist a clear analogy between electrical flow and heat flow. Formerly, this analogy was the basis for constructing electrical analogue devices (sometimes incorporated in analogue computers) which were used in the study of complex heat flow phenomena. Thermal Electrical Resistance Resistance Capacity Capacitance Temperature Voltage Heat flow Current Thermal/electrical analogy The following figure shows the electrical network used to generate Figure 3.16 in the handout.

6 Electrical representation of thermal properties Different heating options and insulation levels can be tested by altering current and resistance values in the analogue model. Figure 3.19 and Tables VI and VII in the handout show how energy consumption varies. Such analyses were very time consuming to set up and only used for research. Admittance Procedure This was developed by CIBSE to give a prediction method for dynamic thermal performance. It takes into account: both air and radiant temperature for achievement of thermal comfort conditions; the modifying effect on temperature fluctuations of the materials used for internal room surfaces; solar heat gain; cyclic variations in ventilation, internal gains and external temperature: steady state and cyclic variations (and any associated time lag) are treated separately and then combined.

7 Temperatures Inside air temperature (t ai ): this is the volume averaged air temperature in the room. Mean surface temperature (t m ): The mean surface temperature is the area-weighted average temperature of the internal surfaces of the room. t m = ( At ) s ( A) Mean radiant temperature (t r ) This is a function of areas, shapes and surface temperatures as viewed from a specific point in the room; it varies according to view factors between the object and room surfaces. It is equal to the mean surface temperature at the centre of a cubical room in which all surfaces have the same emissivity. It is often used as a good approximation for other room shapes. Inside environmental temperature (t ei ) This is used to calculate the heat exchange between a surface and an enclosed space. It is a combination of the mean surface temperature and air temperature. The combination will depend on the relative magnitudes of the radiant and convective heat transfer coefficients, but typically the following equation is used: t ei = 1/3 t ai + 2/3 t m Dry resultant temperature (t c ) In cases where air movement is low, the dry resultant temperature is used as an index of thermal comfort. In such cases: t c = 1/2 t ai + 1/2 t m where t m is used as an approximation for t r at the centre of the room.

8 Outside air temperature (t ao ) This is the bulk air temperature of the air surrounding the building Sol-air temperature (t eo ) and sol-air excess temperature difference Sol-air temperature is that temperature which, in the absence of solar radiation, would give the same rate of heat transfer through the wall or roof as exists with the actual outdoor air temperature and incident solar radiation. It is effectively the outside environmental temperature. It is given by: t eo = t ao + R so (α I t + ε I l ) where I t is the total intensity of solar radiation on the outside surface and I l is the net longwave radiation exchange between a black body at outside air temperature and the outside environment. The sol-air temperature is approximately equal to the external air temperature under overcast conditions. The sol-air excess temperature difference is the quantity that must be added to or subtracted from the outside air temperature in order to calculate the heat transfer through opaque external surfaces resulting from the radiation exchange between those surfaces and the sun and the sky. t eo = R so (α I t + ε I l ) Non-Steady State Thermal Characteristics The admittance, decrement factor and surface factor are functions of the thickness, thermal conductivity, density and specific heat capacity of each of the materials used within a construction, as well as the relative positions of those materials. Energy inputs are assumed to be cyclic, usually with a 24 hour period. Admittance

9 The admittance of a construction is the rate of heat flow between its internal surface and the space temperature, for each degree swing in space temperature about its mean value. It determines the storage of energy in the room surfaces following fluctuations in internal temperature. It is related to the diffusivity and thickness of materials. It has the same units as U-value (W/m 2 K) and can be considered as a cyclic U- value. Q ~ y θ ~ = (AY)( t ) (AY)(tei tei) ϑ+ω = where the tilde indicates the cyclic component and the bar indicates the mean value. Y is the admittance. For thin constructions, the admittance equals the U-value. Admittance is greater for higher thermal mass. Examples are given in Table A3.16 in the handout (from the CIBSE guide). ei ϑ+ω Decrement Factor Decrement Factor is the ratio of the rate of heat flow through the structure to the internal space temperature for each degree of swing in external temperature about its mean value, to the steady state rate of heat flow or U-value. It is the attenuation of a wave travelling through an element of the building structure. For thin structures of low thermal capacity, the decrement factor =1; it decreases with increasing thickness and capacity. For fabric transfer due to external fluctuations: ~ Q ~ f θ = (fau)(teo teo) ϑ ϕ = (fau)( teo) where f is the decrement factor and ϕ is the time lag. Surface Factor Surface Factor is the ratio of the variation of heat flow about its mean value readmitted to a space from the surface, to the variation of heat flow about its mean value absorbed in the surface. The surface factor decreases and its time lag increases with increasing thermal capacity and they are almost constant with thickness. It is used when allowing for solar radiation and the radiative component of internal gains on internal surfaces. ϑ ϕ

10 Calculation of Peak Summertime Temperatures Application of the admittance technique requires the following calculations: (a) Mean heat gains from all sources. (b) Mean internal environmental temperature. (c) Swing (deviation), from mean-to-peak, in heat gains from all sources. (d) Swing (deviation), from mean-to-peak, in internal environmental temperature. (e) From (b) and (d), the peak internal environmental temperature. Intermittent Heating For intermittent heating, additional plant capacity (above steady state requirements) is required to bring the building up to temperature after overnight or weekend cooling. In such cases it is recommended by CIBSE that the total output under boosted intermittent operating conditions, Q pb, is calculated by Q pb = F 3 Q p where Q p is the design load for continuous heating and F 3 is the plant size ratio (the factor for intermittent heating). F 3 can be calculated from F 3 = Hf r 24f r + (24 H) where H is the total hours of heating including pre-heat, and f r is the thermal response factor (the thermal weight of the building). The thermal response factor is given by f r = (AY) + 1 3NV (AU) + 1 3NV The thermal response factor is less than 4 for a lightweight (fast-response) building, and greater than 4 for a heavyweight (slow-response) building. If the calculated value of F 3 is <1.2, a value of 1.2 is taken (to give a safety margin of 20%).

11 Example: 15m 7.5m Small factory building Height=5m 12 windows, each 4m 2 Doors 6m 2 Volume = 562.5m 3 Air infiltration = 0.5 ac/h Surface Area (m 2 ) U-value (W/m 2 K A x U (W/K) Y-value (W/m 2 K A x Y (W/K) ) ) Ext wall Doors Floor Roof Windows Sum Σ(AU) is calculated over surfaces through which heat flow occurs. Assume the heating plant operates for 8 hours with a pre-heat time of 3 hours, and that the total heat loss = 8.72kW for continuous heating (for an internal dry bulb temperature of 19 C and an external design temperature of -1 C). Calculate the plant capacity for intermittent operation. Ventilation conductance = 1/3 N V = (0.5 x 562.5)/3 = W/K. The thermal response factor f r = ( ) / ( ) = 3.49 Therefore the correction factor for intermittent heating F 3 = (24 x 3.49) / ((11 x 3.49) + (24 11)) = 1.63 Therefore the calculated plant capacity for intermittent operation is Q pb = 8.72 x 1.63 = kw

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