Ventilation Energy and Environmental Technology
                                     from VEETECH Ltd. 
             Updated 12th April 2013

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Tutorial  1    Calculating Flow Rate Through Openings:- 
The Flow Equations
  

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CLICK HERE for PHPAIDA The Interactive Ventilation Calculator Based on Opening Area combined with Wind, Stack and Mechanical Ventilation

This tutorial covers:

- Background;
- Volume Flow vs. Mass Flow:
 

- The 'Crack Flow' Power Law Equation;
- The 'Flat Plate' Orifice Equation;
- Making an Orifice Equation look like a Power  Law Equation;
- Changing to Mass Flow;
- Quadratic Flow Representation;
- The Next Step.

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.

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 the Guide to Energy Efficient Ventilation. 

'n' is the flow exponent and indicates the degree of turbulence. An 'n' value of 0.5 represents fully turbulent 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: 

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 be attempted.

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.

Tutorial 2 - Determining the natural driving forces (wind and temperature) ;

Tutorial 3 - Establishing a flow work - air leakage data and flow paths;

Tutorial 4 - AIDA a Single Zone Air Infiltration and Ventilation  Model;

Tutorial 5 - Incorporating mechanical ventilation;

Tutorial 6 - Calculating pollutant concentration and energy impact.

Tutorial 7 - Towards multi-zone modelling.

This completes Tutorial 1

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Guide to Energy 
Efficient Ventilation
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