This study was undertaken to study the performance of the type of toilet seat by using CFD numerical methods to obtain the optimum flow rate to reduce water usage. Toilet seat has two main types which is siphon and washdown. The case is the model type of siphon and washdown, using a mixture of water and air as a medium to flush the toilet. The area is considered critical to all cases in the stagnant water inlet and outlet. The analysis result, shows that the type of siphon is better than the washdown for the both case. The comparison also show that (Siphon Type Water closet) second case has better performance than (Washdown Water Closet) the first case.

1. 1
A STUDY ON EVACUATION PERFORMANCE OF SIT TYPE WATER
CLOSET BY COMPUTATIONAL FLUID DYNAMICS(CFD)
Mohd Reza Fadhlan Bin Daud
Suhana Binti Ramli
Mukah Polytechnics
ABSTRACT
This study was undertaken to study the performance of the type of toilet seat
by using CFD numerical methods to obtain the optimum flow rate to reduce water
usage. Toilet seat has two main types which is siphon and washdown. The case is the
model type of siphon and washdown, using a mixture of water and air as a medium to
flush the toilet. The area is considered critical to all cases in the stagnant water inlet
and outlet. The analysis result, shows that the type of siphon is better than the
washdown for the both case. The comparison also show that (Siphon Type Water
closet) second case has better performance than (Washdown Water Closet) the first
case.
Key words: Computational Fluid Dynamic, Water Closet, Flush
Performance, Washdown type, Siphon Type, Numerical Method,
Inlet and Outlet, Stagnant water

2. 2
1.0 INTRODUCTION
Malaysia receives an average annual rainfall of 3000 mm. Water resources
development has been a catalyst for the socio-economic development of the country
during the past decades. Dams and kilometres of pipelines and canals divert water
from rivers to sustain domestic, industrial and agricultural needs. Lately, the water
situation for the country has changed from one of relative abundance to one of
scarcity. Population growth, urbanization, industrialization and the expansion of
irrigated agriculture are imposing rapidly growing demands and pressures on the
water resources, besides contributing to the rising water pollution. Nowadays
preserving water resources has become an important issue.
Statistic data of many researchers suggest that more than 50% of a family
water usage is spent on sanitary. There are many type of water closet in Malaysia
market. In Malaysia, there are many variant choices of sit type water closet bowl;
however Malaysian Government still allowed the usage of the 9 litre flush for water
closet, but not to western government. The maximum flush tank is not exceed 6 litre.
2.0 PURPOSE OF THE STUDY
The purpose of the present study is establish the flow pattern, to study the
optimum flow through the sit type water closet bowl design and to reduce water usage
and simulate the flow by using Computer Fluids Dynamics (CFD). This study also to
show the application of Fluid Mechanics in our life to Polytechnic Student.
3.0 RESEARCH METHODOLOGY
The CFD solver from Partial Differential Equation of Navier- Stoke to the
Ordinary Differential Equation was used to developed this study. Additionally, the
assumption has been made on the boundary condition and operating condition, to
obtain better results.

3. 3
3.2 The Derivation of Navier-Stokes Equation
This section will discuss the derivation of the Navier-Stokes Equation from
partial derivative to the first order equation.
3.2.1 Newton’s Second Law
Newton's second law states that the force applied to a body produces a
proportional acceleration; the relationship between the two is
(3.1)
Where F is the force applied, m is the mass of the body, and a is the body’s
acceleration.
In component from Eq. 3.1, can be written as:
(3.1a)
(3.1b)
(3.1c)
We also know that summation of all forces acting on a small cubical element of fluid
in terms of the stresses acting on the faces of the element in x direction is:
(3.11a)
Resultant surface forces in y directions:
(3.11b)
Resultant surface forces in z directions:
(3.11c)

4. 4
Where and the acceleration of fluid particle can be expressed as;
(3.12)
And in component form:
(3.12a)
(3.12b)
(3.12c)
Therefore, from acceleration components given by Eq. 3.12 and forces on the element
by Eq. 3.11, we have the general differential equations of motion for a fluid:
(3.13a)
(3.13b)
(3.13c)
where the element volume cancels out.
Equations 3.13 are the general differential equations of motions for a fluid. In
fact, they are applicable to any continuum (solid or fluid) in motion or at rest.
However, before we can use the equations to solve specific problems, some additional
information about the stresses must be obtained. Otherwise, we will have more
unknowns (all of the stresses and velocities and the density) than equations.

5. 5
Therefore, before proceeding it is necessary to establish a stress-deformation
relationship between the stresses and velocities.
3.2.2 Stress-Deformation Relationship
For incompressible Newtonian fluids it is known that the stresses are linearly
related to the rates of deformation and can be expressed in Cartesian coordinates for
normal stresses:
(3.14a)
(3.14b)
(3.14c)
For shearing stresses:
(3.15a)
(3.15b)
(3.15c)
For viscous fluids in motion the normal stresses are not necessary the same in
different directions, thus, the need to define the pressure as the average of the three
normal stresses. For fluids at rest, or frictionless fluids, the normal stresses are equal
in all directions.

6. 6
3.2.3 Conservation of Mass
The differential equation for conservation of mass is
(3.16)
The above equation is also commonly known as the Continuity Equation. The
continuity equation is one of the fundamental equations of fluid mechanics and also
valid for steady and unsteady flow, and compressible and incompressible fluids.
When the flow is at steady-state, does not change with respect to time;
(3.17)
this reduced the continuity equation to;
(3.18)
When the flow is incompressible, the fluid density, is constant and does not change
with respect to space. The continuity equation from Eq. 2.59 is reduced to;
(3.19)
3.2.4 The Navier-Stokes Equations
The stresses as defined in the Eq. 3.17 and 3.18 can be substituted into the differential
equations of motion (Eq. 3.16) and simplified by the continuity equation (Eq. 3.19) as
below:
(x direction)
(3.19a)

7. 7
(y direction)
(3.19b)
(z direction)
(3.19c)
Considering 2D Cartesian flow is assumed (w = 0 and no dependence of anything on
z), the above equations reduce to:
(3.20a)
(3.20b)
3.3 Problem Description
This section explains the information about the simulated model. The
information to be explained are the total mesh, boundary condition, dimensions, and
solver. This model comes from the Johsonsuisse retail catalogue (refer to Appendix
C). All sizes and shapes were taken from the catalog.
3.3.1 Model description
The first model is siphon type shown in figure 3.1. By using the full scale,
with a height of 380 mm, 40 mm inlet and outlet of 90 mm, for more information
refer to table 3.2. For the amount of mesh that has been used please refer to table 3.1.
Siphon model has been iterates with a different inlet. The first model model (siphon
type) is the use of water and air as a flushing medium. For detail refer table 3.3. Initial
conditions of the model (siphon type) show in the figure 3.3.
The second model is of a washdown type as shown in figure 3.2. By using the
full scale, with a height of 380 mm, 40 mm inlet and outlet of 90 mm, for more

8. 8
information refer table 3.5. For the amount of mesh that has been used please refer to
table 3.4.Washdown model will be iterates with a different inlet. The Second model
model (washdown type) is use of water and air as a flushing medium. For detail refer
table 3.3. Initial conditions of the model (washdown type) show in the figure 3.4.
Figure 3.1. Siphon type water closet Figure 3.2. washdown water closet
Table 3.1 Siphon type mesh data
Level Cells Faces Nodes Partitions
0 10036 20443 10408 1
Table 3.2. Siphon type dimension
Inlet Diameter Outlet diameter height Top wall length
40 mm 90 mm 380 mm 360 mm
Table 3.3. Problem specification
Run Inlet boundary condition
simulation
time
water (kg/s) air (kg/s) t (sec)
1 2 0 3
2 2 0.01 3
Table 3.4. Washdown type mesh data
Level Cells Faces Nodes Partitions
0 10876 22089 11214 1

9. 9
Table 3.5. Washdown dimension
Inlet Diameter Outlet diameter height Top wall length
40 mm 90 mm 380 mm 380 mm
3.3.2 Boundary Condition
This section will explain the information of boundary condition that includes
the parameter and value of description model of computer for the developed model.
For detail of specification of model computer parameters refer table 3.6.
Table 3.6. Specification of model computer parameters
Parameter Value of Description
Solver type Pressure Based,
Time Unsteady
Computational domain type 2d Plannar
Multiphase flow model Volume fraction (vof) implicit body force
Number of phases in the flow 2(air, water)
Air density [kg/m3] 1.225
Air viscosity [kg/ms] 1.7894·10−5
Water Density [kg/m3] 998.2
Water Density [kg/m3] 0.001003
Energy equation switched off
Turbulence model κ-ε realizable, Standard Wall Function (SWF),
Dispersed
Operational pressure [Pa] 101325
Acceleration of gravity [m/s2] 9.81
Inlet type mass flow rate
Inlet water mass flow rate
[kg/s]
2, 2
inlet air mass flow rate [kg/s] 0, 0.01
Outlet type Pressure outlet
Outlet air pressure [Pa] 0 (relative to operational pressure)

10. 10
Figure 3.3. Initial Volume Fraction (siphon-type)
Figure 3.4. Initial Volume fraction (washdown-type)
Figure 3.5. Boundary Condition of Siphon type WC and Washdown type
4.0. RESULTS AND DISCUSSIONS
Results from studies using CFD. study of the siphon type and Washdown WC
with flush air and water medium. This simulation has been set for performance at the
time of 1s, 2s and 3s.

11. 11
4.1.1 Siphon-Type Water Closet- water flush with compress air
Result obtain from discussion is the velocity and negative pressure occurs
during the flush on siphon type WC. The maximum velocity and pressure at time 1
sec, 2 sec and 3 sec clearly shows in table 4.1 (a). From the figure 4.1 and 4.2 show
the velocity at the inlet region and outlet region respectively.
Critical path of this problem is the value of pressure. Considered the outlet
region, the maximum negative pressure value, the maximum of the performance
occurs at time 2 sec. This is happened at position 66 cm (see figure 4.4) with -190 pa,
graph manners because of the effect of the inlet gravity flushing and siphon effect was
functions.
Table 4.1 (a) Run 1 result summary
Time (s)/
inlet
1 sec 2 sec 3 sec Time (s)/
outlet
1 sec 2 sec 3 sec
V (m/s) 1.38 1.34 1.4 V (m/s) 0.52 2.6 1.7
Pressure
(pa) max
1330 1320 765 Pressure
(pa) max
98 270 1250
Pressure
(pa) min
700 1030 570 Pressure
(pa) min
-96 -190 -150
Figure 4.1 Velocity vs Position at inlet stagnant water

12. 12
Figure 4.2 Velocity vs Position at outlet stagnant water
Figure 4.3 Pressure vs position at inlet stagnant water

13. 13
Figure 4.4 Pressure vs Position at outlet stagnant water
4.1.2 Washdown Type Water Closet- water flush with compress air
Result obtain from discussion is the velocity and negative pressure occurs
during the flush on siphon type WC. The maximum velocity and pressure at time 1
sec, 2 sec and 3 sec clearly shows in table 4.1 (b). From the figure 4.5 and 4.6 show
the velocity at the inlet region and outlet region respectively.
Critical path of this problem is the value of pressure. Figure 4.7 and 4.8 Show
the graph of pressure vs position. Considered the outlet region, the maximum negative
pressure value, the maximum of the performance occurs at time 3 sec. This is
happened at position 61 cm (see figure 4.20) with -12.5 pa, graph manners because of
the effect of the inlet gravity flushing and s-trap effect was functions.
Table 4.1 (b) Run 2 result summary
Time (s)/
inlet
1 sec 2 sec 3 sec Time (s)/
outlet
1 sec 2 sec 3 sec
V (m/s) 1.49 1.4 1.42 V (m/s) 2.75 2.75 2.3
Pressure
(pa) max
1220 427 2080 Pressure
(pa) max
70 112 54
Pressure
(pa) min
198 425 1440 Pressure
(pa) min
-3 -5 -12.5

14. 14
Figure 4.5 Velocity vs Position at inlet stagnant water
Figure 4.6 Velocity vs Position at outlet stagnant water

15. 15
Figure 4.7 Pressure vs Position at inlet stagnant water
Figure 4.8 Pressure vs Position at outlet stagnant water
Table 4.2 Comparison of pressure occurs at outlet region
Pressure
outlet
1sec
(pamax)
1sec
(pamin)
2sec
(pamax)
2sec
(pamin)
3sec
(pamax)
3sec
(pamin)
Siphon type 98 -96 270 -190 1250 -150
Washdown
type
70 -3 112 -5 54 -12.5

16. 16
From table 4.2 show the maximum and minimum pressure occurs at outlet
region. At this point, if the pressure is in the negative, there has been a vacuum
phenomenon. Where, this area will suck anything in this area to return to normal
conditions.
5.0 CONCLUSIONS
Based on this study, this report documents the finding of and evacuation
performance of the sit type water closet. Siphon-type model and washdown-type that
has been simulated, each model was simulated using numerical methods (Fluent),
using a 2D case. From this limited study, result show that the siphon- type
performance better than washdown- type water closet with air mass flow rate (kg/s) at
inlet.
The analysis of this study base on data from numerical analysis (fluent) but
still need further study. Findings of this study are summarized as the study on Siphon-
type versus Washdown- type by using mixture air and water as a flush medium show
the siphon- type was better performance than Washdown- type.
6.0 REFERENCES
Roger Temam(2001) Navier-Stokes equations: theory and numerical analysis
Edition3, illustrated, reprint, AMS Bookstore, Amsterdam
Jiří Neustupa, Patrick Penel (2001) Mathematical fluid mechanics: recent results and
open questions, Birkhäuser,Berlin
A.F.E. Wise and J.A. Swaffield (2002), Water, Sanitary & Waste Services for
Buildings, Butterworth-Heinemann, London (Page 190-191)
Rong Yuan and Tsan-Liang Su (2005), Hydraulic Performance Of Closet With Del
Mar“Aquamyzer” Water Conservation Flush Valve Kit, Del Mar Lighting,
LLC, Brentwood

17. 17
Matthew David Reyes ( 2004), High Volume Flush vs. Low Flush Water Closets and
Solid Waste Transport Distance: A Comparative study, Texas A&M
University
William Gauley, P.Eng. and John Koeller, P.E (2003), Maximum Performance
Testing of Popular Toilet Models, Veritec Consulting Inc, Mississauga,
Canada
Wei-Seng Cheng, Ruey-Tsung Lee, Chia-Hung Liu, Cheng-Wei Hsia (2009), A Study on
Evacuation Performance of Siphon-Type Water Closets, Lunghwa University
of Science and Technology, Taiwan
Greg White, Dr. John Bryant, Matthew Reyes, Jonathan Carrier (2005), Waste
Transport In Piping System Served By Low- Flow Water Closet, Texas A&M
Energy Systems Lab