CHAPTER 4 AIR FLOW THROUGH OPENINGS

Transcription

1 CHAPTER 4 AIR FLOW THROUGH OPENINGS Learning Objectives This chapter introduces the equations that describe airflow through openings. After you have studied this chapter and completed the personal feedback form you should be able to: 1. Identify the parameters that describe airflow; 2. Understand how airflow through openings can be approximated by a general mathematical equation; 3. Understand what is meant by flow parameters and pressure drop. The Calculation methods precented in Chapters 4, 5 and 6 are based on material published in the AIVC Air Infiltration Calculation Techniques Guide, the AIVC Guide to Ventilation and the CIBSE Guide A Handbook (Liddament 1986, 1996, CIBSE 2006). Introduction Natural ventilation is governed by the amount and distribution of openings in the envelope of the building, the internal pattern of flow paths and the pressure generated by the natural driving forces. This Section is concerned with outlining the flow characteristics of openings and explaining how the flow rate can be estimated from the pressure drop across each opening. Because the variability of climate is so high and the mechanics of flow is so complex, natural ventilation is often treated in very simplified or empirical terms. This includes treating components individually or making generalisations about flow patterns. Often such rule of thumb approaches are all that can be accomplished. At the other end of the spectrum increasing use is being made of computational fluid dynamics to predict natural ventilation performance. While results can be obtained, there is much uncertainty about the necessary approximations needed to reflect the driving parameters. This course follows a theoretical approach that can enable good calculations to be performed. It too, however is restricted by the following: Wind Induced Flow through Openings: Classical natural ventilation theory is based the assumption that wind induced pressure is developed from the transfer of kinetic energy of the wind when it strikes a solid body. However, if an opening is large, kinetic energy is not fully converted to induce a surface pressure. Instead the wind simply drives air under its own momentum through the opening. Some research suggests that this breakdown occurs immediately an opening is present but a porosity figure of up to 30% of the wall surface area has been suggested as satisfactory for classical theory to be acceptable. Discharge Coefficient: A discharge coefficient is frequently used to describe the flow characteristics if an identifiable opening. This coefficient will depend on many factors including the geometry of the opening and the direction of attack of the wind. The value suggested in this the theoretical sections is a guideline figure within the classical range for an orifice opening in which wind is normal to the opening. The literature reveals an increasing amount of discharge coefficients for a wider range of conditions. As yet no further practical guidance on these issues can be given other than the need to carry out specific tests on components, including wind tunnel analysis, for critical design. Further guidance on ventilation calculations, based on a component basis, is given in CEN Standard /TC 156 Ventilation for buildings Calculation methods for the determination of air flow rates in buildings including infiltration.

2 4.1 FLOW THROUGH PURPOSE DESIGNED OPENINGS For a given applied pressure, the nature of airflow is dependent on the dimensions and geometry of the opening itself. For well-defined, purpose provided openings such as vents, airflow is usually assumed to be turbulent and is often approximated by the orifice equation given by: Ø2 ø Q = Cd AŒ Dp r œ º ß 1 2 (m 3 /s) (4.1) Where: Q = air flow rate (m 3 /s) C d = discharge coefficient, ρ = air density (kg/m 3 ); Δp = pressure difference across opening (Pa); A = area of opening (m 2 ). In this instance the area, A, is the net physical openable area. This is usually much less than the dimension of the vent itself because a significant part of the vent area is taken up with insect screen or loose filling. The Discharge Coefficient The discharge coefficient is dependent on the opening geometry and also on the direction of approaching flow (e.g. wind direction). For a flat plate orifice in which the air stream is directed at right angles to the opening, it typically has a value of approximately Such a range is widely used in preliminary design calculations. However for practical components the actual value will be dependent on the component itself and on wind direction. For more detailed analysis, therefore, the compentent should be tested to obtain its actual flow characteristics. 4.2 FLOW THROUGH GAPS AND CRACKS AIR INFILTRATION A particular type of opening is the adventitious construction crack that appears at each joint in the building envelope or at each service penetration. Formerly such openings represented a significant component of the overall porosity of the building which resulted in high and uncontrollable air change rates. In modern buildings much effort goes into minimising such openings and airtightness requirements are included in the building regulations of a number of countries. Despite increasing levels of airtightness it is still important to incorporate the impact of air infiltration on natural ventilation design. For very narrow cracks with relatively long flow paths, such as may be found in mortar and between tight fitting components, the nature of flow at ambient flow is altogether very different and is dominated by the effects of viscosity. Airflow through such openings is closer to laminar in which the flow rate and becomes proportional to the applied pressure difference. Often the flow rate through less well defined openings such as infiltration openings is represented by the Power Law Equation: Where: C = flow coefficient; n = flow exponent; Δp = pressure difference across the opening. Q = C( D p) n m 3 /s (4.2) The Coefficient, C, is related to the size of the opening (i.e. it increases with opening size) while the exponent, n, characterises the flow regime and varies in value between 0.5 (fully turbulent flow) to 1.0 (fully laminar flow).

3 This power law is an approximation but is an approach that is most widely used in building airflow analysis. This is because laminar, turbulent and intermediate flow characteristics can all be represented by the same equation thus simplifying calculation techniques. Sometimes a quadratic equation is recommended in which the laminar and turbulent terms are separated. This form of the equation is given by: 2 D p = aq+ bq (4.3) Where α and β are constants Unlike the power law, this equation is dimensionally correct and is often thought to represent flow at low driving pressures much more accurately. However despite these benefits, use of the quadratic equation has not yet been popular. 4.3 A GENERAL FLOW EQUATION FOR OPENINGS In undertaking design calculations it is important to be able to express the flow through openings, regardless of type, by a general equation. In this case the power law equation (Equation 4.2) represents the most general case and can be applied to the various types of opening as follows: Purpose Provided Ventilation Openings: Infiltration Openings 0.5 Ø2 ø C = Cd AŒ ; n= 0.5 r œ º ß (4.4) C = C; n» 0.6 (4.5) 4.4 PARAMETERS NEEDED TO DETERMINE AIRFLOW RATE Thus to determine the flow rate through an opening it is necessary to know: The flow characteristics of the opening (either in relation to its area for well defined orifices or by measuring its flow characteristics through the process of laboratory or site testing to obtain its C and n value. The pressure drop, Δp, across the opening. Flow Characteristics: In early design sizing calculations, based on defined openings, C and n can be based on the orifice equation as outlined in Equation 4.4 above While an allowance for infiltration openings can be made using Equation 4.2 directly. It is imperative that every opening is accounted for. More detailed analysis should then be based on the measured flow characteristics of the intended devices. These characteristics should be represented in terms of the C and n values (or of the quadratic exponents if the quadratic equation (much rarer) is used). Pressure Drop: The pressure drop across openings is developed by the driving forces of wind and temperature as well as that induced by mechanical fans. The calculation of pressure drop forms the basis of natural ventilation design since this defines the necessary openable area needed to achieve the required airflow rate. Guidance in calculating the pressure distribution is covered in the following sections.

4 4.5 QUESTIONS Answers: 1. An air vent has a dimension of 30 cm x 3 cm and is fitted with a gauze insect screen that reduces the effective area of the opening by 40%. Based on the orifice flow equation, calculate the airflow rate through the opening at a pressure drop of 5 Pa. Gross area of vent = 0.30 * 0.03 m 2 = m 2 The area is reduced by 40% therefore the net area of opening is m 2 Assume an air density of 1.21 kg/m3 (20 C) Flow Equation: Ø2 ø Q = Cd AŒ Dp r œ º ß 1 2 Thus Q = 0.61* * (2*5/1.21) 1/2 = m3/s = 9.5 L/s Note: answer will vary according to density chosen 2. How could the estimate of flow rate vs pressure drop be improved? By measuring the actual flow performance of the vent rather than relying on orifice assumptions. 3. For the same pressure drop, what is likely to happen to the flow rate over an extended period of installation (e.g. over several years)? The flow performance will reduce over time because the insect screen will steadily trap material thus reducing the area of opening.

5 CHAPTER 5 WIND DRIVEN VENTILATION Learning Objectives This chapter outlines the principles of wind driven ventilation. After you have studied this Chapter and completed the personal feedback form you should be able to: 1. Understand how wind creates a driving pressure across a building opening; 2. Understand how the pressure is influenced by shelter; 3. Use equations and data to approximate the value of wind pressure acting at an opening on the surface of a building. Introduction Wind provides one of the key driving forces for natural ventilation. It is harnessed in many ways varying from purpose designed wind towers or wind catchers to reliance on ventilation grilles and openable windows. To size a system correctly it is important to understand the wind pressure mechanism and to be able to estimate the pressure induced at an opening by wind. This Section covers the development of wind pressure and outlines simple calculation techniques that can be used to give an approximate estimate of wind induced pressure. More detailed calculation methods may require wind tunnel analysis, computational fluid dynamics and an understanding of how the size of the opening itself modifies the flow characteristics. 5.1 WIND INDUCED PRESSURE DISTRIBUTION Wind within the lower regions of the earth's atmosphere is characterised by random fluctuations in velocity which, when averaged over a fixed period of time, possess a mean value of speed and direction. The strength of the wind is also a function of height above ground, this function being dependent on surface or terrain roughness, and on the thermal nature of the atmosphere (thermal stability). On impinging the surface of an exposed building, wind induces a pressure distribution on the building as shown in the examples illustrated in Figure 5.1 Wind deflection occurs which induces a positive pressure on the upwind face. The flow separates at the sharp edges of the building, giving rise to negative pressures along the sides. Negative pressures are also experienced within the wake region on the leeward face. The pressure distribution on the roof varies according to pitch, with negative pressures being experienced on both faces for roof pitches of less than approximately 30 º. Above this angle, positive pressures are experienced on the leading face Wind incident to the corner of the building will induce a net positive pressure on both upwind faces but, as flow veers towards a particular side, the remaining face will undergo a transition from positive to negative pressure. The angle at which this transition occurs is dependent on the side ratio of the building. For buildings with ventilated roof spaces, wind will directly affect the ceiling pressure distribution.

6 Figure 5.1. Wind pressure distribution for various building shapes and orientations. Other considerations include protrusions from roofs such as chimneys and flues. The pressure due to wind acting on the mouths of such components is a function of position, roof pitch and height of protrusion.

7 5.2 ESTIMATING WIND INDUCED PRESSURE In general it is observed that relative to the static pressure of the free wind, the time averaged pressure acting at any point on the surface of a building may be represented by the equation: Where: p w = wind induced pressure; ρ = air density; C p = wind pressure coefficient; v = wind velocity at a datum level (usually building height). p r 2 2 w = Cv p (5.1) Terrain and Shielding Since the strength of the wind close to the earth's surface is influenced by the roughness of the underlying terrain and the height above ground, a reference level for wind velocity must be specified for use in the wind pressure calculation. In calculating the wind impact on ventilation the wind velocity is commonly expressed as the measured speed at building height. Unfortunately, as a general rule, "on-site" wind data are rarely available and therefore data taken from the nearest climatalogical station must usually be applied. Before such data can be used, however, it is essential that such measurements are corrected to account for any difference between measurement height and building height and to account for intervening terrain roughness. By nature of the square term in Equation 5.1, wind pressure is very sensitive to the wind velocity and, as a consequence, the arbitrary use of raw wind data will invariably give rise to misleading results. This is, perhaps, one of the most common causes of error in the calculation of air infiltration rates. Suitable correction for the effects of these parameters may be achieved by using a power law wind profile equation of the form: Where: z = datum height (m); v = Mean wind speed at datum height (i.e. height of building) (m/s); v m = mean wind speed at weather station (m/s); α and γ are coefficients according to terrain roughness (see table **). V V m g = a z (5.2) This equation and the associated coefficients are taken from BS 5925:1990. Example coefficients are given in Table 5.1. Table 5.1 Terrain coefficients for use with Equation 5.2 Terrain Coefficient a g Open, flat Country with scattered wind breaks urban city Such an approach is generally acceptable for winds measured between roof height and a recording height of 10m. It is inappropriate for the reduction of wind speeds measured in the upper atmosphere. Alternative methods of wind correction are also used based on a log law profile. Pressure Coefficient The pressure coefficient, C p, is an empirically derived parameter which is a function of the pattern of flow around the building. It is normally assumed to be independent of wind speed but varies according to wind

8 direction and position on the building surface. It is also significantly affected by neighbouring obstructions with the result that similar buildings subjected to different surroundings may be expected to exhibit similar markedly different pressure coefficient patterns. Accurate evaluation of this parameter is one of the most difficult aspects of natural ventilation and air infiltration modelling and, as yet, is not possible by theoretical means alone. Although pressure coefficients can be determined by direct measurements of buildings, most information comes from the results of wind loading tests made on scale models of isolated buildings in wind tunnels. Purpose designed tests for specific buildings and shielding conditions may be performed, but this is an expensive exercise and is therefore rarely possible. For low buildings of up to typically 3 storeys, pressure coefficients may be expressed as an average value for each face of the building and for each 45 º sector, or even 30º sector in wind direction. For taller buildings, the spatial distribution of wind pressure takes on much greater significance, since the strength of the wind can vary considerably over the height range. In these instances spatial dependent data are essential. Solutions include scale wind tunnel modelling and the use of cfd to predict the surrounding pressure field. Representative pressure coefficients for open and urban environments are presented in Table 5.2

9 Table 5.2 sample face averaged pressure coefficients for low rise buildings.(based on AIVC data guide Orme ) Turbulent Fluctuations Turbulent fluctuations can provide background air change even when there is no net driving force from the mean wind speed. Various formulas exist but resultant air exchange is low and should not be incorporated into a design methodology. 5.3 QUESTIONS 1. Consider the wind pressure distribution as illustrated in the Figure below.

10 (a) If face average wind pressure coefficients were applied to describe the wind pressure in a calculation model draw, with arrows, the flow direction for openings A and B. (b) If the actual pressure distribution was applied, rather than face averaged values how would the estimate flow pattern change? Which of the two answers is most likely to represent the true situation? Face average assumption: The pressure distribution is assumed to be uniform on each wall and therefore the wind pressure at A and B are assumed to be identical. If A and B are the only openings in the building then there will be no wind driven flow when using this assumption. Actual pressure distribution: the wind pressure is more negative at A than at B. Air will enter the space via opening B and will exhaust via opening A. The actual pressure distribution answer will be the most accurate. 2. Given an open site wind speed of 10 m/s at a meteorological measurement height of 10 m above ground calculate the wind speed at a building height of 8 m for: (i) A building located on an exposed site (ii) A building located at an urban site A B 3. Use the pressure coefficient tables to assess the average pressure coefficient values at openings A1 and A2 indicated in the Figure below for: (i) An open terrain with no surrounding buildings (ii) An urban environment with surrounding buildings of equal height

11 Building Height Windspeed = 4 m/s A2 Building Height = 4.5 m 4 m A1 1 m Answers: 1. Consider the wind pressure distribution as illustrated in the Figure below. (a) If face average wind pressure coefficients were applied to describe the wind pressure in a calculation model draw, with arrows, the flow direction for openings A and B. (b) If the actual pressure distribution was applied, rather than face averaged values how would the estimate flow pattern change? Which of the two answers is most likely to represent the true situation? A Face average assumption: The pressure distribution is assumed to be uniform on each wall and therefore the wind pressure at A and B are assumed to be identical. If A and B are the only openings in the building then there will be no wind driven flow when using this assumption. Actual pressure distribution: the wind pressure is more negative at A than at B. Air will enter the space via opening B and will exhaust via opening A. The actual pressure distribution answer will be the most accurate. B

12 2. Given an open site wind speed of 10 m/s at a meteorological measurement height of 10 m above ground calculate the wind speed at a building height of 8 m for: (i) A building located on an exposed site (ii) A building located at an urban site 9.68 m/s 5.89 m/s 3. Use the pressure coefficient tables to assess the average pressure coefficient values at openings A1 and A2 indicated in the Figure below for: (i) An open terrain with no surrounding buildings (ii) An urban environment with surrounding buildings of equal height A1 =.7 A2 = -.2 A1 =.2 A2 = -.25 Building Height Windspeed = 4 m/s A2 Building Height = 4.5 m 4 m A1 1 m

13 CHAPTER 6 STACK DRIVEN VENTILATION Learning Objectives This chapter outlines the principles of stack driven ventilation. After you have studied this chapter and completed the personal feedback form you should be able to: 1. Understand how temperature difference creates a driving pressure across a building opening; 2. Understand how the pressure is influenced by the height of openings; 3. Use equations and data to approximate the value of stack pressure acting at an opening on the surface of a building. Introduction The stack effect arises as a result of differences in temperature and hence air density between the interior and exterior of a building. This produces an imbalance in the pressure gradients of the internal and external air masses, thus creating a vertical pressure difference (Figure 6.1). When the internal air temperature is higher than that of the outside air mass, air enters through openings in the lower part of the building and escapes through openings at a higher level. This flow direction is reversed when the interna1 air temperature is lower than that of the air outside. Figure 6.1. Principles of stack effect showing airflow derived from the imbalances in pressure distribution caused by internal/external temperature difference. The level at which the transition between inflow and outflow occurs is defined as the neutral pressure plane. In practice, the level of the neutral plane is rarely known although it can be predicted for straightforward leakage distributions. More generally, the stack pressure is expressed relative to the level of the lowest opening or to some other convenient datum (for example ground level).

14 For natural ventilation design, the consequences and significance of the stack effect must be considered for a number of alternative configurations. These include: Single zone uniform internal temperature distribution; Multi-zone buildings with impermeably separated vertical zones; Multi-zone buildings in which interconnected vertically placed zones are at different temperatures; Multi-zone buildings in which horizontally placed zones are at different temperatures, Large single zone structures subjected to thermal stratification; Ventilation stacks, Each of these configurations may be readily analysed and combined by consideration of the vertical pressure gradient of the respective air masses. 6.1 STACK EFFECT: SINGLE ZONE - UNIFORM INTERNAL TEMPERATURE DISTRIBUTION Assuming a uniform air temperature, the pressure of an air mass at any height z above a convenient datum level, zo, (for example ground or floor level) is given by: p = p - r gz (Pa) (6.1) z 0 Where: p z = pressure at datum level z o (Pa); g = acceleration due to gravity (m/s 2 ); z = height above dataum (m). The resultant pressure gradient is therefore: dp dz =- rg (6.2) which becomes, by consideration of the ideal (Gas Laws): dp 273 =- rog (6.3) dz q Where: ρ o = air density at 273K (kg/m 3 ); θ = absolute temperature of the air mass (K). Thus the pressure gradient is inversely proportional to the absolute temperature of the air mass. Pressure gradients and the absolute pressure distribution for a building in which two openings, hl and h2, are vertically separated a distance h apart are illustrated in Figure 6.1 above. The level of alignment of the internal and external pressures (neutral pressure plane) is a function of the overall distribution and flow characteristics of openings, and is fixed such that a mass flow balance is maintained. Knowledge of this level is not a prerequisite of natural ventilation modelling. The stack induced pressure at h2, with respect to the pressure at hl, is represented in Figure 6.1 by the net horizontal displacement of the pressure curves at these locations (A + B) and is given by: Where: Ø 1 1ø ps =-rog273( h2 -h1) Œ - œ q q º e iß (Pa) (6.4)

15 θ e = Absolute temperature of the outdoor air (K); θ i = Absolute temperature of the indoor air (K) Stack Pressures are often comparable with wind induced pressures and many ventilation designs concentrate od developing the stack pressure to drive ventilation airflow. 6.2 STACK EFFECT ADVANCED Multizone Buildings with Impermeably Separated Vertical Zones Figure 6.2 Stack induced pressure distribution in a multi-storey building in which each floor is isolated. Often it is necessary to consider the design for a multi-storey building, such as an office or an apartment block, in which each floor is essentially isolated (Figure 6.2). This isolation is usually necessary to ensure the separation of individual units and to prevent fire spread. In this instance each floor displays its own neutral pressure plane and it is possible to calculate the stack pressure distribution without reference to adjacent zones. Thus the stack pressure equation 6.4 above can be applied to each floor to estimate flow rates stack flow rates for opening configurations.

16 Multi-zone buildings in which vertically interconnected zones are at different temperatures Figure 6.3 Stack pressure distribution for vertically placed zones at different temperatures. In practice, a uniform temperature distribution may not always be possible or even desired. By design or otherwise, it may be that the internal temperature of each zone will differ. In dwellings, for example, upstairs bedrooms are frequently maintained at a lower temperature to the living area, while a roof space might not be heated at all. The resultant stack pressure may be analysed in exactly the same way as the previous example, except that the pressure gradient of each cell varies according to the zonal air temperature (Figure 6.3). The stack pressure at any level is again given by the displacement in pressure gradients. For example, the stack pressure at level h 2 with respect to level h 1 (horizontal displacement A in the diagram) is given by: Ø1 1 ø Ø 1 1 ø ps =-rog273 ( L1-h1) Œ - œ+ ( h2-l1) Œ - œ (Pa) (6.5) º q1 qeß º q2 qeß Where: L 1 = First floor level (m); θ 1 = Internal temperature of ground floor zone (K); θ 2 = Internal temperature of first floor zone (K).

17 Multi-Zone Building in which Horizontally Placed Zones are at Different Temperatures Figure 6.4. Stack pressure for horizontally spaced zones at different temperatures. This situation may occur in an office environment or multi-storey building in which the stairwell or public access areas are maintained at a lower temperature than the occupied parts of the building. Again, the temperature gradients in each of the zones are analysed as previously described with the stack pressure being expressed relative to the lowest opening. The corresponding stack pressures at other heights are then determined by the relative displacements (Figure 6.4 above). Thus the stack pressure at height h5, between zone 1 and 4 (horizontal displacement B in the Figure) is given by: Where: θ 1 = Temperature of each of the vertical zones; θ 2 = Temperature of Zone 1. Ø1 1 ø ps =-rg273( h5-h1) Œ - œ q q º 1 2ß (Pa) (6.6) 6.3 QUESTIONS 1. Calculate the stack pressure difference between openings A1 and A2 the figure below:

18 A2 θint =10 C θint =20 C Building Height = 4.5 m 4 m A1 1 m 2. For the temperatures given draw, with arrows, the direction of airflow at openings A1 and A2. 3. If the external temperature was increased from 10 ºC to 25 ºC, while the internal temperature is kept maintained at 20 ºC, how will the flow directions at A1 and A2 change. Answers: 1. Calculate the stack pressure difference between openings A1 and A2 the figure below: A2 θint =10 C θint =20 C Building Height = 4.5 m 4 m A1 1 m Stack Pressure between the two openings (3 m apart) = Pa 2. For the temperatures given draw, with arrows, the direction of airflow at openings A1 and A2. Air enters through A1 into the building and leaves through A2 3. If the external temperature was increased from 10 ºC to 25 ºC, while the internal temperature is kept maintained at 20 ºC, how will the flow directions at A1 and A2 change. They are reversed

19 CHAPTER 7 COMBINING WIND AND STACK DRIVEN VENTILATION ADDING HYBRID FANS Learning Objectives This chapter outlines the process of combining the impact of wind and stack driven pressures. It then describes how a hybrid fan can be introduced. After you have studied this chapter and completed the personal feedback form you should be able to: 1. Describe the total pressure acting on an opening; 2. Understand how a hybrid fan influences the pressure distribution. Introduction It is usually impossible to separate stack driving forces from wind driving forces. In other words both stack and wind forces are normally present at the same time. Therefore despite efforts to design a stack or wind driven concept allowance must be made for the impact of the alternative force. Unfortunately it is not possible to calculate the air change due to wind and stack pressure separately then to add the two results together. It is possible, however to add the contributions of pressure due to stack and wind at each opening to obtain a pressure acting on each opening. The calculation of air change or flow rate through each opening can then be calculated. In the case of hybrid ventilation, fans are used to enhance the driving pressure. Again it is not possible to add the flow rate developed by the fan to the flow rate calculated by wind and stack effect. Instead the change in pressure caused by the fan must be calculated. The means by which this may be achieved are described in the next section This Section describes the combining of pressures and the inclusion of hybrid fans. 7.1 COMBINING WIND WITH STACK PRESSURE The total pressure, p ti, acting at an opening, i, due to the combined impact of wind and stack effect, is given by: p = p + p ti wi si It is important to understand that summing the pressures due to stack and wind effect at each opening is not the same as summing the flow rates determined by calculating the flow rates due to wind and stack pressure separately. Summing the flow rates would lead to an erroneous result. 7.2 PRESSURE EFFECTS DUE TO HYBRID VENTILATION Mechanical ventilation may be analysed in terms of the induced flow rate and pressure imbalance created across the fan and associated ducting. The resultant pressure difference becomes another component to the total pressure equation. The additional pressure imbalance created by an extract only ventilation system is very straightforward to calculate by direct application of the Power Law equation (Equation 4.2). In this case the flow coefficient C is given by the flow rate through the fan and the flow exponent, n, is set to zero i.e:

20 Q C p = 0 ( ) n f = f D (7.1) Where: Q f = Specified flow rate through the fan; C f = Corresponding flow coefficient. This forces a constant flow condition. A check must be performed to ensure that the fan can achieve the given flow rate at the resultant induced pressure drop across the fan. In practice the resultant induced pressure created by the fan (See Section 8). 7.3 QUESTIONS 1. For the Figure below calculate the combined stack and wind pressures at each opening assuming that the building is located in an urban environment and surrounded by buildings of equal height. Building Height Windspeed = 4 m/s Building Volume =250 m³ θ ext = 10 C θ int = 20 C A2 Area of opening, A2 = 0.1 m² Building Height = 4.5 m 4 m Area of opening, A1 = 0.1 m² A1 1 m Exposure: Urban, surrounded by buildings of equal height. 2. Sketch the probable directions of airflow through openings A1 and A2. Explain your reasoning.

21 Answers: 1. For the Figure below calculate the combined stack and wind pressures at each opening assuming that the building is located in an urban environment and surrounded by buildings of equal height. Building Height Windspeed = 4 m/s Building Volume =250 m³ θ ext = 10 C θ int = 20 C A2 Area of opening, A2 = 0.1 m² Building Height = 4.5 m 4 m Area of opening, A1 = 0.1 m² A1 1 m Wind Pressure: A1 = 2.02 A2 = Exposure: Urban, surrounded by buildings of equal height. Stack Pressure A1 = 0.0 or A2 = or Note: answer depends on the datum level (e.g. base level or level of first opening). However the pressure difference will always be the same. 2. Sketch the probable directions of airflow through openings A1 and A2. Explain your reasoning. Flow through A1 into building; Flow out of building through A2; The wind pressure reinforces the stack pressure.

22 CHAPTER 8 CALCULATING NATURAL VENTILATION RATE USING THE FLOW EQUATIONS, WIND PRESSURE AND STACK PRESSURE EQUATIONS Learning Objectives This chapter combines the flow Equations developed in Chapter 4 with the pressure equations developed in chapters 5 to 7 in order to estimate the natural and hybrid ventilation flow through a building. After you have studied this Chapter and completed the personal feedback form you should be able to: 1. Understand the meaning of single and multizone models; 2. Undertake natural and hybrid ventilation flow calculations for a simple single zone building structure; 3. Introducing hybrid fans; 4. Treatment of single sided openings. Introduction The calculation of ventilation rate involves: Identifying the ventilation openings; Determining the pressures acting on each opening; Applying the flow equations at each opening; Obtaining a flow balance so that the air entering the building (and individual zones in a building) is balanced by the outgoing air. The first three steps are covered by the preceding Sections. This section is concerned with the flow balance calculation. Appropriate algorithms are presented in the common resource module. Such calculations are needed to: Size ventilation openings as part of a ventilation design; Check on the adequacy of a ventilation design; Determine the need for and develop a hybrid ventilation strategy; Suitable calculation techniques include: Single zone network models; Multi zone network models; Computational fluid dynamics (CFD). This course provides sufficient information to undertake single zone modelling. While basic descriptions are presented on multi zone and cfd technique. More details are available in the resource module. 8.1 SINGLE ZONE NETWORK MODELS This approach is used to calculate infiltration into a single enclosed space. Model parameters include: Flow path distribution:

23 Flow path characteristics (C and n values); Building height; Internal/external temperature difference; Local wind speed (or reduced from remote site); Local shielding conditions; Terrain roughness parameters; Characteristics of hybrid ventilation. Any number of flow paths, terminating within the internal zone, can be selected to represent leakage openings in each face of the building (Inset Figure). A naturally ventilated building consists of a series of openings through which air will pass. These openings include: Purpose provided openings (e.g vents and windows as described in chapter 3 ); Adventitious infiltration openings. In assessing the natural ventilation performance of a building, both types of openings must be included. Even although buildings are less leaky than in the past, gaps and cracks can still adversely add to flow rates, especially in winter when driving forces are usually higher. Single Zone Buildings: In some cases the building itself may be considered as a single open space (e.g. an open plan office, warehouse or a house in which internal doors are predominantly left open. Multi Zone Buildings: In other cases a building may be considered as a multizone building in which each room is separated form its neighbours by partitions and walls. 8.2 CALCULATING THE NATURAL VENTILATION RATE By referring to Figure 8.1 above, the calculation of naturally induced airflow through the building requires the following steps: Apply the general flow equation (chapter 4) to each path; Calculate wind pressure for each path; Calculate stack pressure for each path; Determine the total pressure (add wind +stack) for each path; Determine an internal pressure for the space such that the total airflow into a space is balanced by the total airflow out of the space. This final step is the central component of ventilation calculations. Except for very simple networks, the calculation is not direct and the process of iteration is required. It is this element that makes ventilation calculation approaches so difficult to follow. This section attempts to present a simple explanation of the process. Taking all the flow paths, the conservation of mass requires a flow balance between the ingoing and outgoing airflow. This is expressed by: j i= 1 Where: ρ i = Density of air flowing through flow path i (kg/m³); Q i = Volume airflow rate through flow path i (m³/s). rq i i = 0 (kg/s) (8.1) The air density, ρ i, of incoming air is given by that of the value for the outside air while, for outflowing air, it is given by that of the internal air density. If the density differences between the internal and external air masses are negligible in comparison to the magnitude of the overall density of air then density term may be ignored and, instead, calculation can be considered in terms of conservation of volume flow rather than mass flow.

24 Working in terms of volume flow rate rather than mass flow rate helps simplify iterative calculation and presents results in the familiar format of volume flow. Thus Equation (8.1) above is simplified to: j i= 1 Q i = 0 (8.2) To determine the flow rate through each flow path, it is necessary to express Qi by the chosen flow equation (in this module the popular power law equation is used although alternative equations such as the quadratic approach are equally applicable). The power law equation gives: Where: j i= 1 C i ( p ) n i D = 0 (8.3) C i and n i = the flow coefficient and flow exponent of the i th flow path respectively (Δp i) = the pressure difference acting across the path. The pressure difference (Δp i) is made up of the wind and stack pressure acting on the outside of the opening and the internal pressure of the space, p int. This internal pressure adjusts itself to preserve flow balance and is the unkown that must be determined in order calculate the flow through each opening. For the airflows to add up to zero therefore some flows must be positive (air coming into the building) and others must be negative (air leaving the building). This means, also, that some Δp s will be positive and some Δp s will be negative. Unfortunately it is not possible to raise a negative Δp to the power n and therefore some rearrangement of the Equation 8.3 above is needed. Incorporating this rearrangement and replacing Δp i by p i - p int gives: i j ni i int Ci pi - pint = i= 1 pi - pint p - p (Term 1) (Term 2) (Term 3) Ł ł 0 (8.4) In this rearrangement, Term 2 is always positive (and hence can be raised to the power n) while term three becomes either +1 or -1 and hence defines the flow direction. Advantages The single cell network approach offers many advantages. These include: Comparative ease of calculation; The incorporation of any number of flow paths; The inclusion of any combination of wind, stack and mechanically induced pressures; The ability to assess the effect of flow path distribution on air change rates); The ability to identify the flow direction and the magnitude of the flow rate through each of the defined openings; The calculation of internal pressure; The ability to determine the neutral pressure plane using the external and internal pressure data. Disadvantages The principle disadvantage is: Only applicable to buildings that can be approximated by a zone of single uniform pressure;

25 8.3 MULTI-ZONE NETWORK MODELS A Multizone network model is an approach in which individual rooms or zones within a space are separately divided. This approach is needed when internal partitioning presents an impedance to the movement of air. Possible exceptions to using a multizone approach may be permissible when: Only the absolute maximum air change rate for the building is required; When internal doors are very leaky or are generally left open. There are therefore many instances in which single zone approaches will be of little value and, as a result, consideration must be given to an internal flow structure. Similar model parameters to the previous network approach apply, including: Flow path distribution (internal and external); Flow path characteristics; Building height; Internal/external temperature differences and the temperature of each zone; Wind speed; Local shielding conditions; Terrain roughness parameters; Details of mechanical systems. Again, any number of flow paths, terminating within each internal zone, can be selected to represent leakage openings in the building envelope. Additionally paths are selected to represent leakage openings across internal zones. For the m'th such zone with a total of j. flow paths, the mass flow balance is given by: p - p - = 0 Ł ł jm nim im m rimkim pim pm im = 1 pim - pm (8.5) For q zones the mass balance is applied to each zone to give: p - p ( - ) = 0 Ł ł q jm nim im m rimkim pim pm m= 1 im = 1 pim - pm (8.6) Unlike the 'single zone' approach, where there was only one internal pressure to determine, there are now many values. This adds considerably to the complexity of the numerical solution method. Suitable algorithms are outlined in the resource module. 8.4 INTRODUCING HYBRID VENTILATION Hybrid fans are introduced by including in the network a fan equation of the type described in Chapter 7 Equation Treatment of Single Sided Openings There are circumstance where other mechanisms may be relevant, in particular where a space within a building has openings on one wall only and has either no flow paths to other zones or where such flow paths are considerably smaller than the area of opening on the single outside wall. This could occur for instance where offices or classrooms have one external wall and limited internal flow paths to ensure privacy or reduce disturbance from other activities within the building. Equations have been derived which allow the ventilation rate of such spaces to be determined, based upon adapting the wind and stack equations as outlined below. Wind effect: Based upon full-scale measurements and wind-tunnel studies, a simple empirical equation has been derived to predict wind driven ventilation:

26 Q = k.a.u ref (8.7) Where, A is the area of opening and U ref is the speed of the undisturbed wind at the height of the building containing the space under consideration. In practice the value of k will depend upon a number of factors, including wind direction relative to the façade containing the opening, surrounding structures and any local obstruction at the surface of the building in proximity of the opening. However, a conservative value for design purposes may be taken as Stack effect: The basic equations for stack effect set out in Section 6.1 can be applied to flow through a single opening. The neutral plane (see Figure 6.1) occurs within the opening and, if internal air temperature is higher than outside air, air flow out above the opening and in at the lower part of the opening. The position of the neutral plane is determined by the equality of the mass flow in and mass flow out. For a plane rectangular opening of height, h, and area A, the ventilation rate is given by the following equation; A Dθ.h.g Q= C d.. Ł 3 ł Łθ ł where, Δθ is the difference between internal and external air temperature θ is the mean of internal and external air temperatures g is the gravitational constant C d is the discharge coefficient of the opening (see Chapter 4) 0.5 (8.8) Wind and Stack Effect: In the case of both wind and temperature difference being present, the contribution due to wind and stack effect should be determined separately and the larger of the two values applied.

27 8.5 QUESTIONS 1. For the figure and conditions illustrated calculate the flow airflow rate through openings A1 and A2 assuming wind driven flow only. Building Height Windspeed = 4 m/s Building Volume =250 m³ θ ex = 10 C θ in = 20 C A 2 Area of opening, A2 = 0.1 m² t t Area of opening, A1 = 0.1 m² A 1 1 m Building Height = 4.5 m 4 m Exposure: Urban, surrounded by buildings of equal height. 2. For the same configuration calculate stack driven flow only. 3. Calculate the airflow rates due to the combined influence of wind and stack pressure. 4. For the combined case what is: (a) The airflow direction through openings A1 and A2? (b) The air change rate in air changes per hour (ac/h)? Answers: 1. For the figure and conditions illustrated calculate the flow airflow rate through openings A1 and A2 assuming wind driven flow only L/s 2. For the same configuration calculate stack driven flow only L/s 3. Calculate the airflow rates due to the combined influence of wind and stack pressure L/s 4. For the combined case what is: (a) The airflow direction through openings A1 and A2? (b) The air change rate in air changes per hour (ac/h)? (a) Into A1 out of A2, (b) 2.26 ac/h

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