Boundary conditions based on flow elements
Often the flow from a diffuser is deter-mined by small details in the design. This means that a numerical prediction method should be able to handle small details in dimensions of one tenth of a millimeter, as well as dimensions of several meters.
This wide range of the geometry necessitates a large number of cells in the numerical scheme, which increases the prediction cost and computing time to a rather high level.
The very fine details in the flow profiles that are generated by a diffuser are also very difficult to measure and to specify.
In this chapter some special issues concern-ing computational fluid dynamic (CFD) predictions of the air flow in and close by diffusers are discussed. More information about CFD approaches for room airflows are presented in the REVHA Guidebook 10
“Computational Fluid Dynamics in Ventila-tion Design” (Nielsen et al. 2007).
Simplified boundary conditions Various simplifications can be applied dur-ing CFD predictions. The most obvious simplification is to replace the actual dif-fuser with one of less complicated geome-try that supplies the same momentum of air flow to the room. This may be obtained from a single opening with a height to width ratio similar to that of the diffuser and with an area equivalent to the total effective supply area of the diffuser. The flow from the opening is specified to be in the same direction as in the actual diffuser (Topp et al. 2001).
Using the same inlet area and inlet veloci-ty insures conservation of inlet momen-tum. Because of the very different geome-tries the flow field close by the diffuser is not represented in detail.
Figure 5.1. Wall mounted diffuser and outline of two different geometric specifications of CFD boundary conditions. Inlet area is the same in all three diffuser models.
Figure 5.1 shows as an example a wall mounted diffuser for mixing ventilation and two simplified boundary conditions for the simulation of the flow. The development and selection of the boundary conditions (A or B) is based on comparison with meas-urements (Topp et al. 2001).
The box method. The so called box meth-od is based on the specification of wall jet flow (or free jet flow) or using measured data in a region close to the diffuser (Niel-sen, 1973).
Figure 5.2 shows the location of the boundary conditions around a diffuser. The details of the flow in the immediate vicinity of the supply opening are ignored, and the supply jet is described by values along the surfaces a and b.
Two advantages are obtained by using such boundary conditions. First, it is not required to use a grid as fine as that needed for full
Diffuser A Diffuser B
0.71 m 0.68 m 1.02 m
numerical prediction of the wall jet devel-opment. Second, it is possible to make two-dimensional predictions for supply open-ings that are three-dimensional, provided that the jets develop into a two-dimensional wall jet or free jet at a given distance from the openings.
Figure 5.2. Location of boundary conditions around the diffuser, as used in the Box Method.
The prescribed velocity method The prescribed velocity method has been successfully used in the numerical predic-tion of room air movement. Figure 5.3 shows details of the method. The inlet profiles are given as boundary conditions at the diffuser in the usual way (simplified boundary conditions), although they are represented by a few grid points only. All of the variables, except the velocity profile for u at the inlet boundaries, are calculated in a volume close to the diffuser (xa, yb), as well as in the rest of the room. The ve-locity, u, is prescribed for the volume in front of the diffuser as the analytical val-ues obtained for a wall jet from the diffus-er, or it is given as measured values in front of the diffuser (Gosman et al., 1980 and Nielsen, 1992).
The data for velocity distribution in a wall jet (or a free jet) generated by available
commercial diffusers may in some cases be obtained from diffuser catalogues or they can be obtained from design guide books.
Figure 5.3. Prescribed velocity field close to the supply opening.
The momentum method
The momentum method is a method where the momentum and mass flow are decou-pled in the CFD simulation of the diffuser, and the initial momentum and mass flow rate from the diffuser are used as the boundary conditions. Chen and Srebric (2001) discussed in detail the simplified diffuser boundary conditions applied for numerical room air flow models. They recommended the box method and the mo-mentum method.
Fully resolved diffusers
Continuous development of computational capacity and speed will undoubtedly make the direct methods with local grid refine-ments or multi grid solution possible. The diffuser in Figure 5.4 consists of 12 small slots which can be adjusted to different flow directions. The diffuser is mounted in a wall below the ceiling. It is a complicated geometry generating an asymmetrical three-dimensional flow in the room and it can be introduced in the CFD predictions by making a detailed description of the boundary conditions corresponding to a fully resolved diffuser.
Figure 5.4. Air supply diffuser with unsymmetrical adjusted nozzles.
Comparisons between measurements and predictions using the diffuser in Figure 5.4 show that predictions based on 250,000 cells are sufficient to obtain a grid inde-pendent solution with both rectangular cells, Figure 5.5, as well as with unstruc-tured grid, Figure 5.6 ( Szczena et al.
2005).
Figure 5.5. Representation of the air supply diffuser in Figure 5.4 using embedded grid refinement.
Figure 5.6. Representation of the air supply diffuser in Figure 5.4 using unstructured grid.
CFD predictions of the room air flow pat-tern based on simplified boundary condi-tions should be used very carefully. If no detailed measurements are available, it will be very difficult to estimate the accuracy of the calculated flow fields.
CFD Modeling of Complex Air Diffusers
Real swirl diffusers are often complex in geometry, including guide vanes, perforat-ed plates and curvperforat-ed surfaces all with the intention of creating and maintaining ther-mal comfort for the occupants. The perfo-rated plate is often used to ensure an equal air distribution. Figure 5.7 shows all differ-ent parts of a typical swirl diffuser and the integration of such a perforated plate for homogenizing the air distribution.
Figure 5.7. Explodes view of a complex air diffuser.
Using CFD calculations of the internal and external flow field allows a detailed analy-sis of the diffuser geometry. The stream lines mapped in Figure 5.8 indicate the strong influence of the perforated plate on the performance of the guide vanes. Using a front plate without a suitable junction box will lead to uneven flow distributions and higher sound power levels.
Figure 5.8. Stream lines resulting from CFD calculations.
Comparing the CFD calculation of complex air diffusers to velocity measurements of the flow field in the region behind the vanes indicates too low velocities predicted by CFD. All measurements are taken with a laser-doppler-anemometry (LDA) (Stre-blow et al. 2007).
Figure 5.9. Radial velocity component, comparison of measurements and numerical results.
One of the main reasons for these discrep-ancies is the simplified model of the perfo-rated plate. Modeling of perfoperfo-rated plates in detail is still not feasible because they con-sist of thousands of small holes. Due to the small scale of the holes each hole cannot be calculated separately using a fully resolved geometry. Figure 5.10 shows an example of a perforated plate.
Figure 5.10. Perforated plate and geometry measures in mm.
One method to model the perforated plate is treat it as a porous zone which is imple-mented by adding a source term to the mo-mentum equation. For example an isotropic loss approach as defined in equation (5.1) can be applied:
i
i K u u
K u
S
loss 2
perm M
(5.1),
where Kperm is the permeability and Kloss is the loss coefficient. In equation (5.1) the linear term represents the viscous losses and the quadratic term represents the iner-tial losses. The isotropic loss model can be enhanced by using direction dependent source terms. This directional loss model accounts for flow angle dependent obstruc-tion of the flow by the perforated plate. The two momentum loss models for a perforat-ed plate have been testperforat-ed in a channel flow set-up. In this set-up a centered air jet hits the perforated plate mounted at the channel walls. In Figure 5.11 the flow visualization with smoke of perforated plate (45°) is presented. The picture shows the defection of the jet into the upper channel region behind the perforated plate.
Figure 5.11. Flow visualization of the jet deflection by a perforated plate.
Using this set-up for a CFD benchmark for the two momentum loss models leads to the flow field displayed in Figure 5.12. The isotropic loss model is not able to predict the upwards bending of the jet. The direc-tional loss model is able to reproduce this basic behaviour of the jet-perforated plate interaction but it fails to reproduce the very strong jet bending effect. It was not possi-ble to improve the directional model by tuning the different loss coefficients.
Figure 5.12. Velocity distribution of a jet hitting a perforated plate in a channel flow setup predicted by CFD calculations using a isotropic and directional loss model.
This example shows that it is still very dif-ficult to predict the internal and external flow field of a complex diffuser. Up to now all kind of CFD simulations should be sup-ported by experimental data (Schmidt et al.
2009).
Mixing ventilation benchmark tests It is a useful routine to test and adjust CFD software by comparing results in a bench-mark test before it is used for design of air distribution systems. The benchmark test can either be used as a test of a new pro-gram, but it can also be used to work with different details as e.g. the development of a virtual person (Computer Simulated Per-son - CSP) to be situated in a ventilated room. Three benchmark tests will be men-tioned:
Two-dimensional flow in a room with slot inlet and mixing ventilation.
Three-dimensional flow around a per-son in mixing and displacement venti-lation.
Computer simulated person - Thermal comfort.
The benchmark tests are defined on the web page: www.cfd-benchmarks.com
Two-dimensional flow in a room with slot inlet and mixing ventilation The two-dimensional benchmark test of the flow in a room with slot inlet, also called the “IEA 2D test case” was defined in 1992 to be used in the IEA Annex 20 work (Le-maire et al. 1993), but there have been large number of papers that describe this geome-try in other CFD work. The geomegeome-try is illustrated in Figure 5.13.
It is attractive for a new user to select a geometry used by a number of other re-searchers. It is possible to compare the results with other authors’ results (other turbulence models, other numerical schemes, etc.). The basic knowledge behind the benchmark test has expanded during the years and it has been addressed in numer-ous publications.
Figure 5.13. Room with slot inlet .(Nielsen 1990)
Three-dimensional flow around a person in mixing ventilation
For many years thermal manikins have been used in full-scale experiments con-cerning indoor environment problems. CFD is an alternative to full-scale measurements.
Research centers around the world have therefore developed different configura-tions (subroutines) to represent a Computer Simulated Person (CSP). The CSPs can be very different in respect to size, form
(rec-tangular grid or body-fitted grid), heat emission details, turbulence models, etc.
The variations may reflect the different possibilities of the software, but they may also be caused by different standards for persons from country to country.
A benchmark tests is introduced to test a CFD manikin in mixing ventilation.
The idea behind the benchmark tests is to test different concepts under the same boundary conditions. It is possible to make comparisons and decisions on e.g. details of the design, new boundary conditions around the manikin, etc. The tests of differ-ent manikins may improve the design of a CSP leading to new standards.
The CSP in the mixing ventilation case is seated, facing a unidirectional flow field that may be considered similar to the flow field a person is exposed to in a mixing ventilated room, as illustrated in Figure 5.14 (right).
The mixing ventilation benchmark test is therefore defined as a uniform flow in a tunnel. Both the CSP and the exhaust open-ings are centered on the x-axis. Ceiling, side wall, floor and end wall should be simulated as solid surfaces. See the right sketch in Figure 5.14.
Figure 5.14. A person exposed to a flow field in a mixing ventilated room that locally may be considered as a uniform flow (Nielsen et al.
2003)
H L W
h t
Computer simulated person - Thermal comfort
New development of computer simulated persons will not only focus on air quality problems but also on thermal comfort. The home page therefore shows a benchmark test which work with the heat loss from a manikin with the aim to predict how hu-mans will react to different climatic situa-tions.
The thermal comfort benchmark test (man-ikin heat loss benchmark test) is based on thermal manikin measurements in a mixing ventilation case. It can be used as calibra-tion of a virtual manikin posicalibra-tioned in a CFD simulated environment. The results are presented not only as whole body influ-ence, but also with local information on how the climate varies over the human body.