3. METHODOLOGY
3.2 Preliminary Design and Tool Development
3.2.1 Ventilation model calculation method
This involves determining the sizes and positions of external and internal openings.
The way chosen here is an originally compiled electric analogy model, which defines the ventilative driving forces as voltage source, the openings as resistances, and the volumetric airflow as current. By knowing the positions of the openings and their ext. temp. at inlet height internal air temperature EN15251 category II chimney air temp.
mean radiant temp. operative temperature air change rate
conditions are important for strategies involving night cooling and free-running systems, dynamic thermal modelling is required as described in § 3.2.2.
3.2.1.1 Driving forces
As described in § 2.2.1, the driving forces for natural ventilation in rooms and buildings are pressure differences caused by buoyancy and wind. Ventilation rates are dependent on the magnitude and direction of these forces, and flow resistance of the flow path. The magnitudes of driving forces change with atmospheric variation over height.
Wind pressure difference
The pressure distribution around the building depends on pressure coefficients (see
§ 2.2.1.2), and the local wind speed and direction at the height of the openings. The pressure on the building at a certain height and orientation due to wind forces is:
= 0,5 ∙ c∙ ∙ (3.1)
Within the preliminary approach developed in the context of this thesis and in EnergyPlus simulations, the ASHRAE power law estimation [27] calculates the local wind speed depending on the height of the opening, the terrain roughness, and the meteorological wind speed. This is of special importance in high-rise buildings, where the wind speed significantly changes depending on the local height level of the openings.
With this approach, local wind velocities are derived from the local opening height (centroid), the wind profile coefficients δ and β (terrain characteristics), and wind speed [27,122], where 10 m is the assumed height of the meteorological station:
+t- = f +t- ∙ .mf 10m5
opqr
∙ . s m 5
oturq
(3.2)
Table 3.1: Terrain-dependent coefficients [27].
terrain exponent β Layer thickness δ in m
ocean 0,10 210
flat, open country, meteorological station 0,14 270
rough, wooded country, urban, industrial, forest 0,22 370
towns and cities 0,33 460
Figure 3.6: Local wind speed profiles depending on terrain, meteorological wind speed, and height.
The wind pressure difference between two façade orientations at different height levels is (see also § 2.2.1.2):
∆ = 0,5 ∙ "∙ " ∙ ,"− 0,5 ∙ ∙ ∙ , (3.3) Stack pressure difference
Stack pressure differences due to buoyancy forces depend on the magnitude of density and height differences:
∆ ?= ∆ v∙ ∙ ∆s (3.4)
The density differences are mostly affected by temperature differences. In the context of office building ventilation, the humidity ratio in kg water per kg air (HR), both outside and inside the building, can be assumed to be relatively constant.
Nevertheless, a comprehensive method for determining the air density was chosen including humidity and barometric pressure.
The density of air is dependent on temperature, moisture content, and barometric pressure. The moist air density may be calculated by [123]:
c, = xy ∙? w, , ∙ 1 + [x
1 + [x ∙ xx (3.5)
0 20 40 60 80 100 120 140 160 180 200
0 1 2 3 4 5
z in m
v in m/s meteorological station
open country urban city
The barometric pressure is calculated at the start height of the building segment. The external temperature at local height is calculated at the height level of the openings.
Including the gas constant of air and water vapour (Ra = 286,9 J kg-1 K-1 and
For simplicity of the model, it is assumed that the humidity ratio of the external air is equal to the humidity ratio of the internal air (only sensible internal heat gains).
Then, the internal air density becomes:
v = ? w,
286,9 Jkg ∙ K ∙ v
∙ 1 + [x
1 + [x ∙ 1,609 (3.7)
As mentioned before in § 2.2.1.1, for flow rate calculations or the sizing of opening areas it is important to use a relatively accurate value for the density difference Δρ.
The absolute value for the density is less important. Therefore, it is practicable to assume dry air conditions whenever the humidity level is unknown.
According to the U.S. Standard Atmosphere model, the external air temperature decreases with height at a rate of approximately 1 °C per 150 m. In the pre-design stage, this is of minor importance when considering relatively lower height building segments. But as a side note, it should be also mentioned that 1°C lower supply air temperature will make a difference in thermal comfort aspects.
At altitude z above ground, according to the U.S. Standard Atmosphere model the With an assumed height of the meteorological station at 1,5 m:
c, = f – 0,0065 K
where 6,36·106 m is the radius of the earth and -0,0065 K/m is the air temperature gradient in the troposphere.
Figure 3.7: Local external temperature profiles depending on the height.
The local barometric pressure above sea level can be calculated as [122,124]:
? w, = 101325 ∙ •1 − 2,25577 ∙ 10i€∙ +s + s -•€, €€‚ (3.10) where 101 325 Pa is the reference pressure, which is the standard atmospheric pressure at sea level.
Figure 3.8: Local atmospheric pressure profiles depending on the height.
The buoyancy pressure difference between two height and temperature levels is (see also § 2.2.1.1):
Steady state boundaries
For the design of natural ventilation strategies, it is common practice to first design and size the system by fixed boundary conditions depending on the climate and the building location.
The wind velocity passive cooling design condition chosen is the climate specific, average wind velocity in the hottest 91 days of the year (see § 5.3.3). The local wind speed is then calculated according to the terrain and the local height of the openings.
The temperature difference chosen is 3 °C between inside and outside, which is the value recommend by CIBSE [26] for the minimum hygienic air change and for passive cooling in summer.
Optionally the chimney temperatures may be adapted. Additional chimney heats gains (to cell B Figure 3.9), usually from solar radiation or from internal heat sources, lower the chimney air density, and therefore increase the upward buoyant flow. Additional chimney heats loss (from cell A Figure 3.9), usually from mechanical cooling but could also be considered from evaporation cooling or due to underground ducts, increases the chimney air density, and in turn increases the upward buoyant flow due to higher temperature differences.
Pressure differences on each storey
Total pressure drop from the chimney inlet to the outlet (for the whole flow path):
∆ A = ∆ ?,"+ ∆ ?, + ∆ ?, + ∆ (3.12)
Pressure differences due to buoyancy forces, exemplary for the 3rd storey (F) of the building segment:
∆ ?,"= + ƒ− „- ∙ ∙ +s‚− s"- (3.13)
∆ ?, = + ƒ− …- ∙ ∙ +s""− s‚- (3.14)
∆ ?,P= + ƒ− †- ∙ ∙ +s − s""- (3.15) Pressure difference due to wind forces:
∆ = 0,5 ∙ c∙ " ∙ ,"− 0,5 ∙ c∙ ∙ , (3.16)
Figure 3.9: Pressure drops across the whole flow path from the supply inlet to the exhaust outlet.
3.2.1.2 Electric airflow analogy model
The building ventilation model is based on a set of resistances, generators, and flows.
Pressure is analogous to voltage, electrical current is analogous to volumetric airflow rate, and electrical resistance is analogous to airflow resistance [125]. Potential differences can be generated by sources like mechanical fans or by the natural forces of wind and buoyancy.
Figure 3.10: Electric circuit (a) and airflow analogy (b).
This approach provides a useful framework when developing computer software for calculating airflow through complex networks with multiple inlet and outlet openings and when internal flows occur through a network of flow paths. Models, among others, are based on electrical circuit analogies such as Kirchhoff's first and second laws, and Atkinson's equation originally published in 1886 for mine ventilation [126]. Concerning airflow circuits, Kirchhoff's first law states that the quantity of air leaving a node must be equal to the quantity of air entering the node. The second law
w ≤ 5,0·h
states that the sum of pressure drops around any closed path must be equal to zero.
Atkinson's equation relates the pressure losses at an orifice at which turbulent airflow occurs proportionally to the square of the volume flow.
The use of a solver goal seeking values as available in MS visual basic integrated in Excel 2010, is very convenient for this purpose because it allows equations not to be written in an explicit form.
Model components
As described before, pressure supply sources in natural ventilation systems are buoyancy and wind:
∆ A = ∆ ?+ ∆ (3.17)
The laminar-flow pressure losses are linear and analogous to the electric potential difference between two points according to the Ohm’s law. Unlike in electrical engineering, for turbulent airflows through orifices, the Atkinson's equation relates the pressure losses in an airway proportionally to the square of the volumetric airflow rate through the airway, with the constant of proportionality being the resistance of the airway:
∆ = x ∙ 9: (3.18)
Figure 3.11: Pressure head at differently sized openings (Cd=0,61) depending on the volume flow according to Atkinson's equation for turbulent flow [126].
Thus, the volumetric airflow rate through an orifice such as a wall opening or
pressue loss at the opening in Pa
volume flow in m³/s
Resistors are used to model pressure drops due to an orifice. The airflow resistance of orifices can be expressed in terms of their discharge coefficients, the density of air, and the effective area of the opening:
x = 2 ∙ ; ∙ ( %% (3.20)
When airflow passes through a number of sequential openings with resistances, the equivalent resistance for all the openings in series can be calculated by the sum of the individual resistances:
xA = x"+ x + xP+. . . +x (3.21)
When airflow passes through a number of parallel connected openings with resistances, the reciprocal of the equivalent resistance for all the openings in parallel can be calculated by the sum of the reciprocal individual resistances:
1 xA = 1
x"+ 1 x + 1
xP+. . . + 1
x (3.22)
Considering air change rates necessary to meet the comfort criteria, the opening areas are defined according to the design air volume flow rate, the orifice resistance, the pressure drop at the opening, and the air density:
( = 9:
;,M2 ∙ |∆ |
B
(3.23)
Flow path specifications
Exemplary, for a five-storey per segment scenario, some specifications are necessary to properly size the natural ventilation system. The specifications aim to achieve a uniform airflow throughout the building and a constant cross-sectional area of the central chimney. The following rules are implemented in the ventilation model of the pre-design tool based on electric analogy:
1) The air volume flow rate on each storey of the building segment is defined to be equal:
9:ˆ= 9:‰ = 9:Š= 9:‹= 9:Œ (3.24)
2) Due to the conservation of mass (Kirchhoff’s first law analogy), and not modelling the infiltration, the total mass flow rate through the chimney inlet and outlet is the sum of the mass flows through each storey:
9:•∙ • = 9:ˆ∙ ˆ+ 9:‰∙ ‰+ 9:Š∙ Š+ 9:‹∙ ‹+ 9:Œ∙ Œ= 9:Ž∙ Ž (3.25) 3) The chimney’s vertical cross-sectional area is defined to be constant
throughout the building segment. This is realised by keeping all inlet areas from the chimney to the offices of a specific storey equal to the outlet area from the offices to the chimney. For example:
(P = (€ (3.26)
4) Moreover, the chimney’s air inlet from and outlet to the environment are initially defined to be equally sized as the sum of the office inlets and outlets, and is therefore equal to the internal vertical chimney’s cross-section - but can be adapted by a sizing factor k. With a sizing factor other than 1, the chimney’s supply opening area and exhaust opening area will be sized as bigger and smaller than the internal chimney cross-sectional area, respectively:
• ∙ (" = (P+ (~+ (‚+ (" + ("€= (€+ (•+ (""+ ("Q+ ("Q= • ∙ ( (3.27) 5) Finally, to reduce the internal flow resistance, the area of the internal
overflow openings from the offices to the core are initially set twice (factor K = 2) the area of storey outlets to the chimney. A high value of K will increase the overflow opening area and therefore decrease the internal flow resistance. For example:
‘ ∙ (Q = (€ (3.28)
The schematic in Figure 3.12 shows the arrangement of the openings and the flow path arrangement as specified before.
Figure 3.12: Schematic overview of the exemplary 5 storey per segment for volume flow calculations.
Flow path dimensioning / system sizing
The openings in the flow path are sized according to pressure differences, target air change rates, and flow path resistances. Planners can simply dimension openings, chimneys, and overflow air vents for the provision of fresh air and passive cooling in office buildings.
Although the tool developed can handle one to ten storeys per building segment, equations are exemplarily derived for the five-storey base-case scenario shown in Figure 3.13. This scenario is an eight-cell model with a well-mixed air assumption in each cell. The internal openings divide the envelope into seven internal cells.
Overflow openings from the offices to the core area only represent an additional resistance. Cell A and Cell B can be considered as two conical stacks, one for fresh air supply and one for exhaust. The airflow rates satisfy the continuity equation for each cell and for the total envelope.
The model developed in the context of this thesis differs significantly from the envelope flow model developed by Etheridge [26]; the notation used is loosely based on that used by his models, i.e., the openings in the external envelope are denoted by lower number subscripts, the internal openings by higher numbers, and the segment cells by capital letter indices.
Figure 3.13: Configuration for applying the electric analogy method to upward flow ventilation of a seven-cell model of a five storey building segment.
The wind pressure share of the original equations integrates the ‘local wind speed’
(see § 3.2.1.1) on inlet and outlet opening heights instead of a constant value (without wind profile) for all openings as in the approach developed by Etheridge [26]. The external barometric pressure, the air temperature, and the density for moist air are calculated at start height of each building segment (see Figure 3.13) instead of a fixed reference external air density and temperature.
Integrating the design specification into the electric analogy model developed before, the resulting flow circuit model for an exemplary five-storey per building segment can be summarised as shown in Figure 3.14.
The resistance of flow paths for each storey is dependent on the openings’ flow resistances in series. Upon starting the iterating solvers described below, the
‘HighVent’ tool then automatically adapts the opening areas according to the design specifications to maintain the intended flow rates.
w ≤ 5,0· h
Figure 3.14: Fixed sizing boundary conditions natural ventilation model exemplarily for a segment including two chimney and five storey cells.
The solver seeks for a solution for each storey of the segment to fulfil Kirchhoff’s 2nd law and the sizing specification defined before. Because each storey also influences the other storeys, the procedure is looped five times.
For the five-storey example of Figure 3.14, the changing parameters are the opening areas A3, A6, A9, A12 and A15; the other areas and all pressure drops change accordingly.
1st storey: ∆ ’ = ∆ "+ ∆ + ∆ P+ ∆ Q+ ∆ € (3.29) 2nd storey: ∆ ’ = ∆ "+ ∆ + ∆ ~+ ∆ j+ ∆ • (3.30) 3rd storey: ∆ ’ = ∆ "+ ∆ + ∆ ‚+ ∆ "B+ ∆ "" (3.31) 4th storey: ∆ ’ = ∆ "+ ∆ + ∆ " + ∆ "P+ ∆ "Q (3.32) 5th storey: ∆ A = ∆ "+ ∆ + ∆ "€+ ∆ "~+ ∆ "j (3.33)
suppy chimney ~ cell A exhaust chimney ~ cell B
external environment ~ cell E
where for upward flow direction, the reference density ρ0 for the calculation of the pressure drop at the openings is
for Δp1: B = c (3.34)
for Δp2: B = Ž (3.35)
for Δpi=[3,6,9,12,15]: B = • (3.36)
for all other Δpi: B = v (3.37)
where ρI is the density of specific office cells.