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VI.3 Application of Computational Fluid Dynamics to Simulate the Behaviour of Fluids inside Vertical Stack of Building Drainage System

Eric Wai Ming Lee

ericlee@cityu.edu.hk

Department of Building and Construction, City University of Hong Kong,

Tat Chee Avenue, Kowloon Tong, Hong Kong (SAR), People’s Republic of China.

Abstract

A numerical method is presented to simulate nonlinear free surface flow in a vertical stack building drainage system by computational fluid dynamics (CFD). The volume of fluid (VOF) method is adopted to track the air/water interface, and the effect of the interfacial surface tension is simulated by the continuum surface force (CSF) model. The numerical results are validated against full-scale experimental data. The results demonstrate the behaviour of the air pressure and the annular drain flowing along the vertical stack. They also show the reduction in air pressure when the air flow passes through the branch inlet and the existence of positive air pressure at the base of the vertical drainage stack. The CFD simulation results are similar to the experimental results.

Keywords

Building Drainage; Computational fluid dynamics; Continuum surface force; Drainage stack; Multiphase flow; Volume of fluid

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1. Introduction

Since the outbreak of severe acute respiratory syndrome (SARS) in 2003, the vertical drainage pipe system that connects with the ventilation system within a building has been postulated as a possible channel that facilitates the cross contamination of this deadly disease [1]. To minimise the risk of the disastrous spread of SARS, much attention has been directed towards better understanding the free surface flow structure to improve the existing design of building drainage ventilation systems. Conventionally, design guidelines that are formulated based on statistical theories are used in the design of practical drainage systems [2, 3]. However, because these guidelines do not address the interior nonlinear free surface flow structure, they are inadequate for the design of complex drainage systems in super-high-rise buildings. A numerical model (AIRNET) was developed by Jack and Swaffield [4] in their pioneering work in building drainage simulation. However, the model is a one-dimensional unsteady flow model, and the nonlinear interactions between the air and liquid phases inside the drainage pipes are not described in detail. This paper presents a detailed methodology to investigate the free surface flow behaviour in a vertical pipe system using the volume of fluid (VOF) method. The model predictions are compared against the experimental data of a single vertical stack system that are obtained from Lu [5]. Particular attention is directed towards the visualisation of the complex flow structure.

2. Mathematical Modelling

The air flow in a vertical stack is initiated by the shear between the annular water film and the air core [6]. To resolve the hydrodynamics of air and water, which travel at different velocities, an inhomogeneous two-fluid model that consists of two sets of conservation equations is adopted. Appropriate inter-phase constitutive relationships are applied to close the inhomogeneous two-fluid model for the air and water flow. These inter-phase constitutive relationships represent the drag and non-drag forces that act on such a flow. The non-drag forces are modelled according to the virtual mass, lift, wall lubrication and turbulent dispersion.

The interface between the air and water is tracked using the volume of fluid (VOF) method. This method uses a volume fraction function to define the volume portion of one particular fluid inside a cell volume. As the sum of the volume fraction is equal to one and has no inter-phase mass transfer, a transport volume fraction conservation

equation is given by the following equation where is the density and is the travelling velocity vector of phase .

1· 0

This equation represents the advection algorithm to advance the interface, which simultaneously conserves the volume fraction. To account for the effect of the

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interfacial surface tension, the continuum surface force (CSF) model is adopted. By combining the surface force with the volume force that is concentrated at the interface, the surface tension force is expressed as of which

σ and , is the surface tension coefficient, is the normal vector that

goes from phase to phase , is the surface curvature of the interface and is the gradient operator at the interface. The turbulence of the air and water flow is simulated

by the inhomogeneous shear stress transport (SST) model, which incorporates the k-

model for the flow within the boundary layer and the k- model for the flow in the free stream.

3. Numerical Results and Validation

The numerical simulations were carried out using the generic CFD code ANSYS CFX 10. The predictions of the numerical models were then validated against the measurements of the full-scale single-pipe system of Lu [5]. The experiment was performed on an experimental tower attached to a building 40 m in height. In the tower, a main vertical stack 100 mm in diameter was installed and connected with branches (75 mm in diameter) to each floor and the building’s drain pipe (125 mm in diameter). The average air pressure was measured at each floor using small diffuse semiconductor air pressure transducers. Water flow was discharged at the ninth floor (i.e., 27 m above ground level) at a flow rate of 2.0 l/s. Figure 1 is a schematic diagram of the experimental setup.

Figure 1: Schematic of the Experimental Setup

2m 

2m

12m 

27m 

75mm 

Horizontal

100mm 

Vertical Stack 

125mm 

Horizontal

2.0 lit/s

Outflow

 

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under-predicted. This could be attributed to the uncertainty in the drag force calculation, in which the air entrainment may be underestimated because of the shear of water. It will be further investigated in future.

Figure 3: Air pressure profile along the height of the vertical drainage stack.

Figure 4 shows the free surface flow structure at the branch/stack junction. The free surface is highlighted in blue. As the figure shows, water discharging from the branch becomes annular flow at the downstream of the junction. The air is drawn by the annular drain from top of the drainage stack to the core of the drainage stack by the shear at the interface between water and air of the annular drain. Figure 5 depicts the flow structure at the base of the vertical drainage stack. It shows that the annular drain from the vertical stack forms a water curtain at the base of the stack. The water curtain causes an occlusion of the air. When the air at the upstream of the curtain (i.e. 0 to 5m high of the stack) gains sufficient positive pressure, it blows through the curtain and reach the horizontal drain at which the air pressure is close to atmospheric pressure.

+

+

+

+

+

+

+

+

+

+

+

+

+

+

x

x

x

x

x

x

x

x

x

x

x

x

x

x

AIR PRESSURE (mm H2O)

HE

IGH

TA

BO

VE

ST

AC

KB

AS

E(M

)

-20 -10 0 10 200

5

10

15

20

25

30

35

40

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Figure 4: Detailed flow structure at the branch/stack junction

Figure 5: Isometric view on detailed flow structure at the base of the vertical stack

100 Vertical 

Drainage Stack

X

Z

Y 

Water curtain 

covers the drain 

100 Horizontal 

Drain Pipe 

Annular 

drain

Flow of branch 

inlet occupies 

a portion of 

the cross‐

sectional pipe 

Vertical 

drainage 

stack

Air is drawn from 

atmosphere to the 

stack by the shear of 

the annular drain

Branch 

inlet

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4. Conclusion

A detailed methodology for solving the complex nonlinear free surface flow in a vertical stack building drainage system is presented. The numerical results are validated against the full-scale experimental data of Lu [5]. Comparison of the predicted and the measured results shows that they are in good agreement. Also, the simulation results capture the following 5 important observations of vertical drainage stack flow as follows.

a) Annular drain is formed at the downstream of a branch inlet.

b) The annular drain draws air from atmosphere to the stack by the shear at the interface of air and water of the annular drain.

c) Air pressure is reduced at the immediate downstream of the branch inlet due to the orifice effect.

d) Water curtain forms at the base of the vertical stack.

e) Air pressure becomes positive at the immediate upstream of the water curtain.

This study demonstrates the advantage of using the volume of fluid (VOF) method to investigate the free surface flow behaviour in a vertical drainage stack. The visualisation of three-dimensional flow that is realised by the VOF method offers a great way to improve the existing design of building ventilation drainage systems, which may effectively prevent cross contamination of fatal diseases via the building drainage ventilation systems of high-rise buildings.

Acknowledgements

The work described in this paper was fully supported by a grant from the Research Grants Council of the Hong Kong Administrative Region, China [Project no. CityU 115507].

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5. References

1. WHO (2003). Risk factors involved in the possible environmental transmission of severe acute respiratory syndrome (SARS) in specified residential buildings in the Special Administrative Region of Hong Kong, World Health Organisation Report, World Health Organisation.

2. Whitehead A. (2002). Plumbing engineering services design guide. The Institute of Plumbing, Hornchurch, Essex, UK.

3. BS EN 12056:2 (2000). Gravity drainage systems inside buildings – part 2: sanitary pipework, layout and calculation, UK, British Standard Institute.

4. Jack, L. B. and Swaffield J. A. (1999). Developments in the simulation of the air pressure transient regime within single stack building drainage system. Proceedings - 25th International Symposium of Water Supply and Drainage for Buildings CIB W062 (pp. 1-11). Edinburgh, UK: Heriot-Watt University.

5. Lu, W. H. (2005) Prediction method of air pressure on two-pipe stack building drainage system, PhD thesis, National Taiwan University of Science and Technology.

6. Gormley, M. (2007) Air pressure transient generation as a result of falling solids in building drainage stacks: definition, mechanisms and modelling, Building Services Engineering Research and Technology (pp. 55-70).

6. Presentation of Author

Eric Lee is an assistant professor at City University of Hong Kong in the Department of Building and Construction. He is specialized in plumbing and drainage system design. He is also the designer of the plumbing and drainage system of Two-International-Financial-Center which is the highest existing building in Hong Kong.