calculation wind

7/31/2019 Calculation Wind

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Background

The air flow equation is the building block of air infiltration and ventilation calculations. Every

opening in the building fabric must be accurately represented by such an equation. Essentially there

are two types of opening. The first are the random gaps and cracks that appear at construction joints

or through porous material. These are ill defined and their geometry is rarely directly measurable.The second are essentially 'purpose provided' openings such as vents and windows. These are usually

clearly defined in terms of geometry, location and flow characteristics. Openings in the former

category require either measurement or implied knowledge about their characteristics. The

necessary flow characteristics of the second type of opening can be inferred from the geometry of

the opening and, therefore are easier to determine. The mathematical representation of these two

types of opening is described in this tutorial. It is also shown that, by algebraic manipulation, both

types of opening can be represented by an equation of identical structure. This considerable eases

the calculation of total air flow into and out of a space.

Volume vs. Mass Flow

Flow rate can be expressed either in terms of 'volume' flow (e.g. m3/s, l/s, cfm) or 'mass' flow (e.g.

kg/s). Most often fan capacity is expressed as a volume flow ,whereas calculations involving heat

loss, for example, require that flow be expressed as a mass flow. In fundamental terms, it is more

accurate to express flow rate as a mass flow. This is because, for a given mass of air, its volume varies

with temperature. The Law of Continuity demands that the mass flow rate of air entering a building

must match the mass leaving the building. Thus, in theory, a balance in mass flow does not

necessarily mean that there is a balance in volume flow. Notwithstanding this situation, our air

infiltration tutorials will be based on volume flow analysis. This is because for 'mild' climate

temperature differences, where temperature differences between inside and outside peak at no

more than 25 - 30C for a few hours at most in the year, any error will be marginal and because the

'iterative' approach that will be introduced to calculate infiltration and ventilation rate is much more

stable for volume flow. Any error could also be minimised by selecting an air density (to convert to

mass flow) that is midway between the outside and inside air temperature. However, switching to

mass flow is very straightforward (as presented at the end of this tutorial). Also 'multi-zone' models

such as Contam96 are structured in mass flow and can be downloaded and used for precision

analyses if needed.

Cracks and Gaps

Air flow through general cracks and gaps in the building fabric is a function the size and structure of

the opening and the pressure difference acting across it. The simplest representation of a crack is

presented in the equation below.


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This equation gives the volume flow rate (e.g. m3/s).

'C' is defined as the 'Flow Coefficient'. This is related to the size and structure of the opening. Typical

flow coefficients are given in theAIVC Numerical Data Guide.

'n' is the flow exponent and indicates the degree of turbulence. An 'n' value of 0.5 represents fullyturbulent flow and '1.0' represents fully laminar flow. The typical 'n' value for whole buildings is 0.66.

'Orifice' Openings

Clearly defined openings such as vents or windows are frequently represented as 'flat plate orifices'

in which the volume flow is represented in the equation:
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Thus flow can be determined directly from a geometric analysis of the opening. In the absence of

other information, the 'discharge coefficient' is usually based on a value of 0.61. Air flow through an

orifice is assumed to be turbulent, thus the flow exponent 'n' = 0.5.

Making an Orifice Flow Equation Look Like a Crack Flow Equation

For ease of infiltration and ventilation calculations it is important that the above two equations take

on the same form. This is achieved by making the orifice equation look like a power law crack flow

equation. To achieve this:

Exercise: Manipulate the orifice flow equation to achieve the above 'C' and 'n' values.

Changing to Mass Flow

Volumetric flow is changed to mass flow by multiplying by the air density. Since density is dependent

on air temperature, it is not a constant. Therefore, if this approach is used, it needs to be expressed

as a function of temperature. This will be covered in a future tutorial.

Quadratic Formulation of the Air Flow Equation

Some authorities prefer to express air flow in the form of a quadratic equation of the form:

This is perceived to be dimensionally correct since the laminar and turbulent components of flow are

separated. In essence, all the arguments and processes applied to the Power Law approach can be

applied to the quadratic approach. In fact the single zone model, to be developed in these tutorials,

will run just as easily in quadratic form. Again, at a later date, an equivalent analysis will beattempted.


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The Next Steps

So far we have established the Power law Equation of flow through an opening as a building block

towards infiltration and ventilation analysis. We have also shown that the flow characteristics of

purpose provided opening can be approximated by the geometry of the opening. We now have to:

Introduce a method to determine the pressure difference across openings;

Establish a 'flow network' that represents the openings in the building;

Find 'missing' data (primarily the 'C' and 'n' values of cracks and gaps).

Develop a mathematical model that enables us to calculate the total flow into and out of the

building and to calculate the flow rate and flow direction through individual openings.

Incorporate mechanical ventilation systems.

Introduce the concept of multi-zone or multi - room networks.

These steps will provide you with a basic design and ventilation evaluation tool that can be quickly

established to solve 95% of pre-design and basic design steps. It will also give you the skills to apply

more complex modelling tools that are available through the internet.

1. The Wind Pressure Equation

Wind striking an object induces, on that object, a spatially distributed pressure pattern (Figure

2.1).

Figure 2.1. Wind striking a building induces a wind induced pressure distribution.

The value of the induced pressure at any particular point can be described by the following equation:


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Equation 2.1. Wind Pressure Equation.

A typical pattern of pressure distribution is illustrated for a simple, essentially cubed shaped building,in Figure 2.2 below.

Figure 2.2. Example Wind Pressure Distribution.

With respect to atmospheric pressure, wind induces a positive pressure on the upwind face of the

object and a negative pressure on its sides and in the wake region at the rear of the building. Thewindward roof face may also be at a negative pressure unless the pitch angle exceeds about 30.

To evaluate the wind-induced pressure, the following data are needed:

Building dimensions and shape;

Information about surrounding terrain and obstructions (both upwind and downwind);

Location (e.g. city, urban, rural);

Wind speed (and, for improved precision, direction);

Spatial distribution of wind pressure coefficient.

Building Dimensions and Shape: The pressure pattern is highly dependent on the shape of the

building. Elementary and pre-design analysis is only really possible by approximating the plan-shape


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of the building by a rectangle or a series of rectangles. Anything more complex may need to be

analysed on an individual basis in a wind tunnel. computational fluid dynamic (cfd) methods are

emerging as a potential means of analysing the pressure distribution around buildings but require

substantial computational effort, especially if several wind speeds and directions are to be analysed.

Surrounding Terrain and Obstructions: This again influences the pressure distribution considerably.

The simple approach is to describe the building as being surrounded by buildings of equal height, half

the height of completely exposed. Again, this is suitable for basic pre-design analysis. The only

practical alternative is to consider a wind tunnel study in which a scale model of the building and the

surrounding buildings is incorporated. Similarly this is an area where cfd analysis is emerging and will

probably, eventually present a practical alternative.

Location: Apart from influencing the type of surrounding obstructions, location influences the

climatic driving forces of wind and temperature. Wind strength in an urban location, for example,

may be considerably lower than that measured at a nearby open-site weather station. Similarly, air

temperature may be higher in a city environment (heat island effect). A wind correction equation is

presented below. At present a suitable temperature conversion equation is not presented but it may

be worth increasing the open-site value, taken from the nearest meteorological station, by a degree

or so.

Wind Speed and Direction: Wind induced pressure increases with the square of the wind speed,

while the upwind and downwind faces of a structure clearly depends on the direction of the wind. A

key problem is that the strength of the wind varies both with height above ground and the

intervening terrain, between the nearest meteorological station (usually located in open countryside)

and the site of the building, as illustrated in Figure 2.3.

Figure 2.3 .Impact on wind speed of terrain and height above ground level.

In many cases, within an urban environment, the wind speed at building height can be less than half

of that measured at a meteorological station. Since this value is squared, failure to make the

necessary correction to wind speed can lead to a substantial overestimate in the wind induced


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pressure. A height and terrain correction approach, described in British Standard 5925 (1991) is

presented in Table 2.1.

Spatial Distribution of Wind Pressure Coefficient: The wind coefficient is assumed to be independent

of wind speed but varies according to location on the building surface, the shape of the building and

the nature of obstructions surrounding the building. Face averaged values[see Important Notes]for

simple calculations have been tabulated (e.g. BS5925:1990 [expose buildings], Guide to Energy

Efficient Ventilation [various degrees of shielding and two plan area aspect ratios]. Bowen and Wiren

have both published comprehensive, spatially distributed data for various building shapes and

shielding, based on wind tunnel studies Much of the information published in the Guide to

Ventilation are derived from these latter sources.

Table 2.1. Wind speed correction approach as used in BS5925.

These datasets are suitable for more complex calculations in which faced average values do not

provide a sufficient level of detail but where the cost of wind tunnel studies is prohibitive. Some

illustrative, simplistic example data is presented in Figure 2.4.
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Figure 2.4 . Example faced averaged wind pressure coefficient data. This data was

based on averaging and amalgamating measurement data of Bowen and Wiren. See The

Guide to Energy Efficient Ventilationfor more data.

A checklist summary of, and the approximations needed, for basic calculations is presented in Table

2.2.

Table 2.2. Checklist for simple pre design or elementary calculations.

Parameter Simple DesignAnalysis

(e.g. methods as described in

the AIVC Guide to Energy

Efficient Ventilation)

Detailed DesignMethods andMeasurements

(e.g. wind tunnel, cfd, specific

local environmental

measurements etc.)Building Shape Represent as a rectangle or

a series of rectangles.

Complex: Circular building,

sections at different heights,

courtyards etc.

Surrounding Obstructions Represent as uniformly

distributed equal to the height

of the surrounding structure,

half the height or no

obstructions

Complex: Not uniformly

distributed

Location Specify as city, urban,

rural, open country. Use

simple correction methods for

wind speed and air

temperature.

Specific detail needed (e.g.

about degree of urbanisation,

heat islands, street canyons

etc.).

Weather Data Taken from nearest weather

station (should be based on

hourly records).

(Wind speed corrected for

terrain and building height)

Specific on-site data needed.

Wind Pressure Coefficient

Data

Tabular data for simple

building shapes or, for

slightly more complex

structures, spatially

distributed data as published

by Bowen and Wiren.

Wind tunnel data from

individual scale model of the

building and its surroundings.

2. The Stack Pressure Equation

Stack flow is driven by the difference between the inside and outdoor air temperature. Assuming

that the indoor temperature is above the outdoor value, the inside air is less dense and therefore

lighter than the outside air. As a consequence, the vertical pressure gradient, exerted by the indoor

air, is steeper, resulting in a pressure imbalance. If the enclosed space is penetrated by openings at

different heights, air flows through openings at the lowest level and escapes through the upper
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openings (Figure 2.5). This flow process is reversed if the indoor temperature is less than the outdoor

temperature. The location at which the indoor and outdoor pressures are in balance is called the

neutral pressure plane. If an opening were present at this opening, there would be no airflow

through it.

Figure 2.5. The principle of stack flow.

Stack pressure is calculated directly by the application of the Ideal Gas Laws. The temperature

difference or stack induced pressure at an opening with respect any arbitrary datum height (e.g.surface level) is given by Equation 2.2, where h is the height of the opening above (or below) the

chosen datum. Usually, the datum is taken as the surface or floor level of the building. With basic

hand calculations, or very elementary networks, however, there can be an advantage in taking the

datum as the level of the lowest open. This is because the relative stack pressure at this level will be

zero, thus saving the effort of a calculation for each opening assigned to this level. In applying the

stack flow equation, it must be remembered that the temperature is given in Kelvins (degrees

absolute) and not in Centigrade.


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Equation 2.2. The stack flow equation.

3. Combining Wind Pressure with Stack Pressure

The pressures calculated using Equations 2.1 and 2.2 are additive (Figure 2.6) i.e. they can be

summed directly together. This is not the same, however, as adding together the airflow rates

calculated individually for wind and stack pressure.

Figure 2.6. Combining wind and stack pressure.

Introduction

In Tutorial 1, the various formulations of airflow equations were introduced. This was followed, in

Tutorial 2, by the formulation of the wind and stack pressure equations. In this tutorial, the flow

network, i.e. the system of openings in the building fabric, through which air exchange between the

inside and outside of a building takes place, is described.

The flow equation of Tutorial 1 must be applied to every opening in the building envelope. If any are

ignored (e.g. unidentified cracks and gaps in the building fabric) then the calculations will be in error.

Typically, the number of leakage openings is underestimated because openings are unwittingly

ignored. This results in underestimating the potential air change rate and, almost certainly,incorrectly predicting airflow patterns. The leakier the building, the more likely underestimates will


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occur. It should also be noted that a building is leaky unless specific measures have been introduced

during the construction to ensure that it is not. Usually, only if required by legislation of if specified

by the building owner, will the building be anything other than leaky. The only possible exception

might be poured concrete structures with few junction elements.

Incorporating all openings is usually undertaken by defining:

A network to represent background or air infiltration paths;

A network of purpose provided openings such as windows, air vents etc;

A network of mechanical ventilation fans.

A Network to Represent Background Openings

Figure 3.1. Background leakage networks.

Networks representing background leakages are illustrated in Figure 3.1. The basic procedure is as

follows:

Determine the total surface area of exposed building surface (m2);

Separate into the area of each face and the roof (or ceiling) area;

Separate each face into a lower half and an upper half (single storey) or upper and lower half

for each storey (multi storey building);

Identify the C value of each of each path by multiplying its area by the building porosity (as

determined by pressurisation test or as specified in design);

Check that units are set to a common value (e.g. L/s or m3/s at 1 Pa).

A Network to Represent Purpose Provided Openings

This is determined by identifying for each opening:

The face of the building in which it is located;


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The height of opening;

Its dimensions;

For large openings (e.g. open windows) divide the area into an upper and lower section so

that two way flow can be simulated.

A Network to Represent Mechanical Ventilation Fans

A simple representation of mechanical ventilation can be achieved by establishing a constant flow

path for each fan. This is only permissible if the induced flow has no more than a few Pascals

influence on pressure drop. The easiest method is to set the flow exponent to the value 1 and the C

value to the desired ventilation flow rate (in L/s or m3/s).

The flow network comprises the location and flow characteristics of ALL the above openings.

Assuming a total of j openings, the flow rate through each opening is solved by determining theinternal pressure of the space or (in the case of a multi-zone building) each internal zone. This is

determined by applying the Law of Conservation of Mass (i.e. the mass of flow into the building

equals the mass of flow out or the sum of the flow equals zero). Thus the mass balance equation (and

volume flow approximation) for j flow paths is given by:

These generally have to be solved by iteration using a model such a s PHPAIDA. The user must

supply the pressure (due to stack and wind) for each flow path and the flow coefficient and flow

exponent for each path. This leaves the internal pressure as the only unknown.

Direct solution is possible for very simple networks. Examples are given in Tutorial 5.
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This completUse the tutorials to calculate the ventilation rates for the configurations shown below.

These may all be calculated by hand. Once completed usePHPAIDAto verify the calculated values.

The Building Volume is 250 m3

The size of each opening is 1000 cm2 The wind speed at a nearby met station is 4.5 m/s

The outside air temperature is 0 Deg C

The inside air temperature is 20 Deg C

For each of the above figures calculate by hand:

Ventilation Rate (L/s);

Air Change Rate;

For:

Open Terrain;

Shielded (Urban Terrain).

Compare the results using .
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IntroductionPHPAIDA may be accessed at the link below:

http://phpaida.veetech.org.uk/phpaida.php

The purpose of this tutorial is to highlight the powerful solutions that can be achieved. This

algorithm is intended as an early stage tool for sizing natural ventilation openings and basic

mechanical systems. It can also be used in the development of control systems to adjust ventilation

openings according to weather conditions.

Starting ConditionsFor simplicity consider a building such as a dwelling in which the inside air is well mixed (e.g. open

plan space or internal doors open). Assume that good air quality is needed and that there are 4

occupants. Based on a ventilation rate of 15 Litres/s (L/s) for each occupant the required ventilation

rate is 60 L/s.

Assume the following building dimensions and weather conditions:

Urban Location

Building Height = 8 m

Building Volume = 240 M3

Outdoor Temperature = 0 C

Indoor temperature = 20 C

Windspeed from a nearby met station = 3 m/s

Sizing Openings for Natural VentilationBy entering the above data into PHPAIDA the opening areas of the 9 available flow paths can be

varied to obtain a ventilation rate of approximately 60 L/s. There is no unique solution but the
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following is an example:

Flow Path Height (m)Opening

Area (cm2

)

1 - 4 1.5 50

5 - 8 5.0 100

9 8.0 550

The opening areas were quickly derived in three manual iterations and gave a total ventilation flow

rate of 59.6 L/s combined with a fairly uniformly inflow through openings 1 to 8 combined with

extract from the chimney opening. This approach can be applied to a variety of weather conditions,for example to derive a control strategy for openings to provide a uniform ventilation rate over a

wide range of conditions.

Extract Only and Supply Only Mechanical VentilationAn alternative approach is to consider a mechanical extract or mechanical supply system. By keeping

the same openings as above, the result using PHPAIDA is:

Extract at 60 L/s gives a total ventilation rate of: 85.27 L/s

Supply at 60 L/s gives a total ventilation rate of: 90.61 L/s

Although the weather conditions and opening areas are the same as for the natural ventilation case,

it is seen that the total ventilation rate is less than the sum of the natural and mechanical rates. This

is an advantage of mechanical extract or supply only systems. The natural openings are actually

needed to provide the supply air for an extract system or to provide an exhaust route for a supply air

system. It is possible to reduce the opening sizes so that weather has a much reduced impact. This

means that a certain amount of building leakage can be accommodated. However, when the

opening size is reduced, the pressure difference between the inside and outside of the building

increases. This means that the mechanical system has to work harder, resulting in higher energy use.Also the fan must be capable of overcoming any increased pressure difference while providing the

required airflow rate.

Under many instances, natural driving forces tend to be in the low Pascal range, thus an optimum

internal pressure to overcome the influence of weather would be:

-10 Pa (i.e. 10 Pa below atmospheric) for extract systems;

+10 Pa (i.e. 10 Pa above atmospheric for supply systems.


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For low rise buildings this will result in a uniform ventilation flow rate over a wide range of normal

weather conditions.

A solution can be found by adjusting the opening areas in PHPAIDA until the internal pressure is

approximately 10 Pa. A suitable solution is:

Flow PathOpening

Area (cm2

)

1-8 40

9 0

Differential areas between the upper and lower openings are no longer important because flow wasdominated by the mechanical ventilation rather than natural forces. Also the roof stack is not

required.

For extract ventilation this gave an under pressure of: -9.13 Pa.

For supply ventilation this gave an over pressure of ; +2.98 Pa.

In both cases the flow rate was exactly 60 L/s (i.e. flow is dominated entirely by the mechanical

system.)

Of course it is possible to reduce the opening area further for the supply approach since the 10 Pa

target has not been reached. This is left as an exercise along with explaining why the pressures for

the extract and supply systems are numerically different.

Balanced VentilationBalanced Ventilation consists of mechanically providing both Supply and Extract Ventilation to the

space. Thus the design ventilation rate of 60 L/s must be applied to both the Extract and Supply

inputs of the PHPAIDA data input section.

When entering the mechanical balanced data to the original natural ventilation example, the over all

ventilation rate becomes:

Balanced at 60 L/s gives a total ventilation rate of: 119.59 L/s.

This is exactly the sum of the natural ventilation rate and the mechanical ventilation rate. Thus to

avoid over ventilation the building must be completely airtight. This is the major disadvantage of

balanced systems.

ConclusionsBy understanding and experimenting with these simple examples, the potential of PHPAIDA can be


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quickly understood. It is not possible to guarantee any results but PHPAIDA enables basic design

guidance to be obtained to assist in more advanced design tools.

calculation wind

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