Modeling Jet Fans, Part 2: Validation using Experimental Data

In this post, we explore two approaches to modeling jet fans using FDS: (1) a velocity patch and,  (2) an HVAC duct. For the velocity patch we examine the effects of different shroud lengths and for the HVAC duct we examine the effects of a short downstream shroud. We evaluate the models using the downstream centerline velocity and flow entrainment.

In Part 1 of this series, we did a quick background review of downstream flow, including the Potential core and Axisymmetric decay regions for a free circular jet. In this post we will focus on modeling the Novenco jet fan tested by Giesen et al. (2011): diameter 290 mm, length is 2.6 m, exhaust flow rate 1.0 m3/s, exhaust air velocity 18 m/s (= 59.1 ft/s = 64.8 km/hr = 40.2 miles/hr), capacity 21 N. For flow conditions that represent this fan, Part 1 found that a mesh size of 12.5 mm was required to obtain reasonably accurate results for the first 5 m downstream of the outlet. Unfortunately, it is not feasible to simulate full scale parking garages with such a fine mesh, even if multiple meshes are used, so in this post we examine alternate approaches.

(See also Part 1: Background and Convergence StudyPart 3: Car Park Simulation.)

Background Equations for Jet Fans

In Part 1, we presented the Baturin (1972) and Kümmel (2007) equations that represent experimental data for centerline velocity downstream of a jet fan.

The Baturin equation for a circular duct is:

    \[u_{m}(x)=\frac{0.48}{ax/d_{0}+0.145}\times u_{0}\]

where: u_{m} is the centerline velocity, a is a constant (0.076 to 0.080 for cylindrical tubes and 0.12 for an axial fan with guide vanes), x is distance from the supply, d_{0} is the supply diameter, and u_{0} is the supply velocity.

The Kümmel equation for a square duct is:

    \[x_{o}=\frac{h}{m}\]

and

    \[u_{m}(x)=\frac{x_{0}}{x}\]

where:  x_{0} is the length of the potential core, h is the side length of the square duct, and m is a constant that varies between 0.12 and 0.20.

Both equations are plotted below for a square 0.25 m square duct (equivalent diameter 0.2821 m) with an initial air velocity of 18 m/s. As will be discussed below, the Kummel equation with m=0.20 provides a good match with jet fan results measured by Geisen et al. (2011).

Figure 1: Plots of the experimental correlations for the range of equation parameters.
Figure 1: Plots of the experimental correlations for the range of equation parameters.

Baturin also provides data on the spread angle for different jets. For a cylindrical tube \alpha=29 deg and for an axial fan with guide vanes \alpha=44 deg. The calculated jet diameters are shown below.

Figure 2: Plot of the jet diameter base on the Baturin equation. The value alpha is the total spread angle of the jet.
Figure 2: Plot of the jet diameter base on the Baturin equation. The value alpha is the total spread angle of the jet.

Ricou and Spalding (1961) developed the following expression for flow entrainment based on experimental measurements.

    \[Q(x)=0.32(\frac{x}{d_{0}}) \times Q_{0}\]

where: Q is the volume flow rate at distance x and Q_{0} is the supply flow rate. This is plotted below for a supply flow rate of 1 m3/s..

Figure 3: Flow entrainment based on experimental fit by Ricou and Spalding
Figure 3: Flow entrainment based on experimental fit by Ricou and Spalding

Jet Fan Convergence Study

To model a jet fan, we must couple the inlet flow to the outlet while preserving the fuel, air, and product mixture. The jet fan in this convergence study is 1 m long and is a square duct with sides s=0.25 m and an outlet air velocity of 18 m/s. This test problem is similar to that in Part 1, except now we explicitly model the fan (not just a supply vent) and the centerline distance is extended to 10 m downstream of the fan. At 0.5 m intervals we use devices to measure the velocity time history.

Figure 4: Jet fan simulation with 1 m long fan and 0.25 m sides. Distance from fan outlet to model boundary is 10 m.
Figure 4: Jet fan simulation with 1 m long fan and 0.25 m sides. Distance from fan outlet to model boundary is 10 m.

Velocity Patch Model

In the velocity patch model, the fan is represented by a region where the axial (X) velocity is specified. The lateral (Y and Z) velocities are not defined. The velocity patch approach was implemented in FDS as an approach to approximate entrainment of air in sprinkler flow.

A velocity patch can be defined with or without a shroud surrounding the patch. The shroud (a hollow tube defined by thin obstructions) changes how adjacent air is drawn into the velocity patch and also focuses the flow in the axial direction of the shroud. For the convergence study, we explored three shroud configurations: full length shroud, short shroud (1/4 length), and no shroud.

Figure 5: Velocity patch shroud configurations (flow from left to right).
Figure 5: Velocity patch shroud configurations (flow from left to right).

HVAC Model

For the HVAC model, we used a standard HVAC duct with vents and a duct in which we used both an HVAC duct and a downstream shroud. We shorten the HVAC duct to 0.5 m and add a hollow shroud (similar to the velocity patch shroud) that extends downstream of the HVAC duct 0.5 m so that the length of the HVAC duct plus the shroud is equal to the total fan length.

The reason to add a shroud is to make sure the outlet flow is in the axial direction. FDS calculates cell velocities at the center of the cell sides (staggered grid). The HVAC duct is connected to the grid at a vent and the flow boundary conditions at the vent are specified on the faces of the cells that touch the vent. As a result, the flow can expand in the first cell downstream of the vent, reducing the axial velocity. This can be seen in the convergence study of Part 1. The shroud maintains the outlet flow in the axial direction, ensuring that the one dimensional axial velocity is preserved at the fan outlet.

Results of Convergence Study

The convergence study used the two with mesh sizes of 125 mm, 62.5 mm, and 31.25 mm. Since the jet fan side is 250 mm, these correspond to 2, 4, and 8 divisions along each side.

The figure below shows typical velocity contours for the standard HVAC model with a 125 mm mesh.

Figure 6: Velocity contours for the standard HVAC duct model and a cell size of 125 mm.
Figure 6: Velocity contours for the standard HVAC duct model and a cell size of 125 mm.

And the figure below shows the measured velocities 7.5 m downstream of the outlet.

Figure 7: The measured velocity time history 7.5 m downstream for the standard HVAC duct model and a cell size of 125 mm.
Figure 7: The measured velocity time history 7.5 m downstream for the standard HVAC duct model and a cell size of 125 mm.

Results for the HVAC model are shown below. For the HVAC model without a shroud, we see the initial lateral expansion of the flow at the outlet (blue lines in charts). All the results show less flow entrainment than the experimental fit, with the finer mesh of the shroud model having the closest match.

Figure 8: Centerline velocity and flow entrainment for the convergence study using the HVAC duct model, with and without a downstream shroud. Click for a larger, clearer image.
Figure 8: Centerline velocity and flow entrainment for the convergence study using the HVAC duct model, with and without a downstream shroud. Click for a larger, clearer image.

The figure below shows the centerline velocity and flow entrainment for the convergence study for the jet fan model that used the velocity patch. For the centerline velocity, all the results approach the experimental fit at a downstream distance of 10 m. Closer to the jet fan outlet, the coarse mesh results (delx=125 mm = side/2) undershoot the data, the medium mesh results (delx=62.5 mm = side/4) with a full or short shroud overshoot the data, and the fine mesh with the full shroud (delx=31.25 mm = side/8) matches the experimental fit quite well. The flow entrainment results show that reducing the shroud increases the flow, with no shroud the entrained flow is larger than desired.

Figure 9: Centerline velocity and flow entrainment for the convergence study using the velocity patch model. Click for a larger, clearer image.
Figure 9: Centerline velocity and flow entrainment for the convergence study using the velocity patch model. Click for a larger, clearer image.

Geisen et al. Jet Fan Experiments

Geisen et al. (2011) describe jet fan experiments performed in a 34 x 32 x 6.5 m hall using a Novenco fan (diameter 290 mm, length 2.6 m, exhaust flow 1.0 m^3/s, exhaust velocity 18 m/s, and capacity 21 N). Air velocity measurements were made at distances of 0.5, 1, 2, 4, 8, 12 and 16 m from the exhaust. For the free jet experiment, the fan center was positioned 2.5 m above the floor.

The velocity profile at the exhaust from the actual fan is not uniform. An average velocity of 15.1 m/s is calculated using the stated fan diameter and flow, while a maximum centerline value of 18.9 m/s was measured in the experiments. In all the following calculations the fan outlet was assumed to be a 250 x 250 mm square with a velocity of 18 m/s (giving a flow of 1.125 m3/s).

The jet fan experiment model is shown below. As before, we model the jet fan using a velocity patch and an HVAC duct. At the fan, mesh resolutions of 125 mm and 62.5 mm were used, with 125 mm downstream and 250 mm on the sides of the fan. The upstream boundary was OPEN while the downstream boundary has a 2.3 m wall a distance of 24 m from the jet fan outlet.

Figure 10: The model used for the Geisen et al. experiment. Click for a larger, clearer image.
Figure 10: The model used for the Geisen et al. experiment. Click for a larger, clearer image.

Velocity contours for the HVAC duct with a downstream shroud and mesh size 125 mm are shown below.

Figure 11: Velocity contours for the HVAC duct with a downstream shroud and mesh size 125 mm. Click for a larger, clearer image.
Figure 11: Velocity contours for the HVAC duct with a downstream shroud and mesh size 125 mm. Click for a larger, clearer image.

First, we compare the Geisen et al. experimental measurements with the Kümmel (2007) equations. The experimentally measured centerline velocity shows good correlation with the Kümmel equation for m=0.2. The experimentally measured flow entrainment matches the Ricou and Spalding equation until a downstream distance of about 8 m. At this point the diameter of the jet expands to where it interacts with the floor (the fan was mounted 2.5 m above the floor, so at a jet diameter of 5 m it has reached the floor). Referring to Figure 2, a jet diameter of 5 m is reached between 6.7 and 10.2 m downstream, which corresponds to start of the plateau shown below.

Figure 12: Comparison of measured centerline velocity and flow entrainment for the Geisen et al. experiment with correlations. Click for a larger, clearer image.
Figure 12: Comparison of measured centerline velocity and flow entrainment for the Geisen et al. experiment with correlations. Click for a larger, clearer image.

Results for the HVAC model are shown below. In this case, the HVAC duct with a downstream shroud and mesh size of 125 mm performed quite well in both matching the centerline velocity decay and the flow entrainment. This is an improved result compared to the convergence study.

Figure 13: Centerline velocity and flow entrainment for the Geisen et al. experiment using the HVAC duct model with and without a downstream shroud. Click for a larger, clearer image.
Figure 13: Centerline velocity and flow entrainment for the Geisen et al. experiment using the HVAC duct model with and without a downstream shroud. Click for a larger, clearer image.

Results for the velocity patch model are shown below. In general, the centerline velocity decay results are satisfactory, but for the No Shroud case the flow entrainment is much larger than measured and is not satisfactory. The short shroud with the coarse mesh is larger than the experimental fit by about 20%.

Figure 14: Centerline velocity and flow entrainment for the Geisen et al. experiment using the velocity patch model. Click for a larger, clearer image.
Figure 14: Centerline velocity and flow entrainment for the Geisen et al. experiment using the velocity patch model. Click for a larger, clearer image.

Summary

There is no single model that was uniformly superior in both the convergence study and the modeling of the jet fan experiments.

Comparison with the experimental data of Geisen et al. (2011) shows that the HVAC duct with a downstream shroud and mesh size of 125 mm performed quite well in both matching the centerline velocity decay and the flow entrainment. The good news is that this is a feasible mesh size and the calculation uses the default FDS Deardorff turbulent viscosity model.

Alternately, the velocity patch model with the short shroud and mesh size of 125 mm had a better match with the flow entrainment for the convergence study and did a reasonable job for the experimental data.

In the next post, we will use both approaches to model jet fans in a parking garage.

Acknowledgements

All calculations were performed using the FDS and Smokeview software. PyroSim was used to create and run the FDS models. Discussions with NIST led to the velocity patch model which then led to the HVAC duct with shroud.

Input Files

Download the PyroSim and FDS input files here:

References

Awbi, Hazim B., (2003). Ventilation of Buildings, Second edition, Spon Press, 2003.

Baturin, V. V., (1972). Fundamentals of Industrial Ventilation, Pergamon, Oxford.

Giesen, B.J.M. v.d., Penders, S.H.A. , Loomans, M.G.L.C., Rutten, P.G.S., & Hensen, J.L.M. (2011).  “Modelling and simulation of a jet fan for controlled air flow in large enclosures,” Environmental Modelling and Software, 26(2), 191-200.

Kümmel, (2007). Technische strömungsmechanik. Technical report, B.G. Teubner, 3. Auflage, 2007. 25

McGrattan, K., McDermott, R., Weinschenk, C., Overholt, K., Hostikka, S., Floyd, J., (2013). Fire Dynamics Simulator Technical Reference Guide, Volume 2: Verification, Sixth Edition, NIST Special Publication 1018, National Institute of Standards and Technology.

Ricou, F. P. and Spalding, D. B. (1961) Measurements of entrainment by axisymmetrical turbulent jets. J. Fluid Mech., 11, 21-32.

Comments or Questions

This post was written by Daniel Swenson. For comments or questions, send email to support@thunderheadeng.com.

Update History

This post replaces a previous post that examined the options of modeling jet fans using Synthetic Turbulence or Dynamic Smagorinsky turbulent viscosity with larger mesh sizes. Neither of these approaches is currently recommended: Synthetic Turbulence requires calibration (and is not implemented in FDS for use with HVAC ducts) and Dynamic Smagorinsky does not perform well for coarse simulations of fire (based on discussions with NIST, developers of FDS).

Updates to this post include:

  • 2016/05/24 – Added results and discussion for the velocity patch case with short and no shrouds. Previously, only the velocity patch full shroud results were included.

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