Part 1 focuses on the definitions while the Part 2 explains the k-factor and its relation to Cd. This part demonstrates a few worked examples about defining the equivalent area and choosing the right grille size with the right Cd value. Furthermore, it is explained how the volumetric loss coefficient, k-factor of a louvre, should be used in a CFD simulation and why the inlet and outlet losses should be excluded.
A car park with 100 m2 floor area is required to have openings on the walls of which the equivalent area is equal to 2.5% of the floor area. The total area of the structural openings is equal to 4 m2. A type of louvre will be installed to the openings. Define the properties of the louvre by following the questions:
- a. What is the minimum Cd value the openings (louvre assembly) should have?
- b. What is the maximum loss coefficient (k-factor) the openings (louvre assembly) can have?
- c. What is the maximum loss coefficient (k-factor) the louvre itself can have (exclude inlet and outlet losses)?
- d. What volumetric loss coefficient (zeta value or k-factor) should be used in computational fluid dynamics (CFD) model?
The required area is 2.5% of 100 m2= 2.5 m2 equivalent area
Aerodynamic area of the openings and the square edged orifice must be equal to ascertain the same flow performance as the square edge orifice.
The k-factor of an orifice which has an opening of a half size of the duct width is around 2-2.5 depending on the geometry. When an approximate k-factor of 2.25 of an orifice inserted into the previously derived equation, Cd = sqrt(1/ξ), we obtain Cd of a squared edged orifice which roughly equals to 0.67.
The minimum coefficient of discharge (answer to (a)) and the maximum k-factor of the louvre assembly (answer to (b)) are, respectively:
Note that the found values above indicate the complete assembly including the inlet loss, the louvre loss and the exit loss. We can replace the combination of the inlet and the exit losses with the approximate k-factor (i.e. 2.25 as used above) of an orifice. Therefore the k-factor of only the louvre itself is expressed as below (answer to (c) and (d)). This value should also be used in CFD calculations as a volumetric loss (1/m) coefficient.
Catalogue coefficient of discharge value of a louvre, is 0.24. What zeta (or k-factor) value should it be used for the louvre in the CFD model?
Based on the derived equations in the previous part of the blog, the k-factor can be found as:
However, depending on how the test of the grille had been executed (which is almost always described in the data sheets of the grilles, for standard test setup see also further below) the measured loss of the grille also accounts for in and/or outlet losses. In the CFD simulation the inlet and outlet losses for the air to go in and out of the grille are always modelled and therefore already accounted for. However, the grille itself is often to detailed and not fully modelled. Therefore, the inlet and/or outlet losses must be subtracted from the K-factor as obtained from the data sheet value. In our case, assuming that the test data accounted for inlet and outlet losses we subtract 2.25 from 17.36 to get to a K-factor to be applied in the CFD of 15.11.
Cd determination through standardized test of EN 13030
This part is a proof of concept that the derived equations fit the calculated CFD data.
According to test method of EN 13030 Ventilation for buildings - Terminals - Performance testing of louvres subjected to simulated rain, the Cd value is calculated based on a few parameters that involve the flow rate and a measured pressure. The pressure is measured at a specified location as shown in the figure below. It is right next below the outlet opening in the aerodynamic measurement section. The location corresponds to 310 mm above the ground and 100 mm away from the upstream wall.
To investigate the spatial dynamics in the test apparatus enclosure, we have modelled the section in CFD environment. A 3D model of the apparatus is seen in the figure below.
The pressure measurement point in CFD model is identical to the EN13030 location.
The applied volume flow through the openings is 2 m3/s. The orifice opening has dimensions of 0.85 m x 0.85 m x 0.1 m.
The result of the calculation shows that the coefficient of discharge is approximately 0.68 which is in range of the literature Cd value which is between 0.6 - 0.8 (Depending on Re number) and the assumed example case with Cd of 0.67 above. The pressure measurement point is out of the high velocity zone and is measuring the average pressure difference of around 10 Pa.
CFD is a proved tool to design, develop, verify and test the performance of louvres in any configuration. We would be happy to able to help you should you have any queries for your product. Feel free to contact us.
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