F2) CFD Simulation and Experimental Study of Flow
Characteristic of Siphon Drainage System
R.Kajiya(1), K.Sakaue(2), T. Mitsunaga(3), K.Sakai(4)
(1)[email protected]
School of Science and Technology, Meiji University, Japan
(2)[email protected]
School of Science and Technology, Meiji University, Japan
(3)[email protected]
Yamashita Sekkei, Inc., Japan
(4)[email protected]
School of Science and Technology, Meiji University, Japan
Abstract
This study adopts Computational Fluid Dynamics (CFD) analysis to elucidate the
fundamental characteristics of siphon flow in a siphon drainage system. A relationship
determined between the outflow head and horizontal pipe length is necessary to assure
an effective equipment mean drain flow rate (qd = 0.5 l/s) as transport capacity from the
result. Moreover, a fundamental calculation equation of the pipe internal velocity that is
necessary for designing this system is proposed using this result.
Keywords
Siphon drainage system,
Discharge flow, Terminal velocity ,
Experiment,
CFD
1. Introduction
In a siphon drainage system, a drain flows according to the siphon principle through
small diameter fixture drain pipe in a filled flow condition. This system, unlike a gravity
drainage system, permits non-slope drainage and a small diameter, which drastically
reduces piping space compared to conventional drainage piping. Moreover, it enables
free piping design. However, siphon drainage systems have remained under
development; various basic data have yet to be accumulated. Accordingly, this study
adopts CFD analysis to elucidate the fundamental characteristics of siphon flow in a
siphon drainage system. Its applicability is investigated through comparison with
experimental results related to the trend of pipe internal velocity, the terminal velocity
and terminal length in the outflow pipe of a siphon line.
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2. Experiment and CFD analysis of the terminal velocity in a vertical
outflow pipe
2.1 Objective
The terminal velocity and terminal length of a vertical outflow pipe are determined as a
fundamental characteristic of a 20A rigid polyvinyl chloride (PC) pipe used for siphon
drainage piping. The CFD analysis is also applied simultaneously; its reproducibility is
verified. Results will indicate whether the CFD analysis is effective as an analytical tool
of the two-phase flow of water-air.
2.2 Experiment
2.2.1 Outline of experiment
Figure 1 schematically depicts the terminal velocity experimental apparatus and an
experimental model. The theoretical terminal velocity at the coefficient of velocity C =
150 was computed using Eq. (1), the Hazen-Williams equation. The vertical outflow
pipe length necessary to reach terminal velocity was obtained using Eq. (2).
C=Q/(1.6712×i0.54×D2.63×104) --------- (1)
Lt=0.1444vt2 --------- (2)
C: the coefficient of velocity, Q: flow rate [m/s], i:hydraulic gradient [mAq/m],
D: pipe diameter [m], Lt: terminal length [m], vt: terminal velocity [m/s]
This yields a terminal length of about 3m. The vertical outflow pipe length used for this
experiment was set as 4.5 m in consideration of a safety factor of 1.5. A transparent
plastic case of 395mmL×585mmW×300mmH was used as a water tank. The water
storage height was 200mm from its bottom. The total head was 4,700mm as the sum of
the water storage height and the vertical outflow pipe length. The outflow head pipe was
filled with water in its open end, so that the terminal velocity was reached promptly
after the start of measurement, thereby shortening the CFD analysis computation time.
The pipe internal velocity was determined according to the water level change in the
water tank, as measured using an ultrasonic water level sensor.
2.2.2 Experimental results and discussion
Figure 2 depicts the pipe internal velocity fluctuation (ve), which indicates that terminal
velocity was reached within about 2s after the start of measurement. The maximum pipe
internal velocity was 4.70m/s; the mean velocity was 4.15m/s. The coefficient of
velocity C = 138 was at that time.
2.3 CFD analysis
2.3.1 Outline of CFD analysis
CFD analysis conditions are shown in table 1. An analytical model was created
according to the configuration and dimensions of the experimental model, as in Figure 1.
The cross sectional cell of the vertical outflow pipe was divided into 80 meshes. The
pipe was partitioned at an interval of 10mm in the height direction, so that was divided
into 450 divisions. Regarding the water tank, the grid was finely divided gradually
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toward the unification section with the outflow head pipe, from a large 10mm cube
mesh near the outer wall to a 2.5mm cube at the unification section. The total mesh
number is 91,540. A dynamic model was constructed as a multi-phase flow of water-air,
and the Volume-of-Fluid (VOF) method, an Euler-type method, was adopted as the
computational method of a free surface in this analysis. Because the Reynolds number
(Re) was anticipated as 104 ~ 105, within the turbulence region, the standard k-ε model
was adopted as a turbulence model. As a general-purpose fluid analysis tool, software
(STAR-CD ver. 3.24) was used.
.
Table 1- CFD analysis conditions
water level sensor
300
free surface flow(VOF method)
the first fluid : air 、the second fluid : water
standerd k-ε2-equations model
PISO,maxcimam number of collectors:50
solution
relaxation coefficient：0.8
CICS,upwind difference(advective term),
difference scheme
central difference(other terms)
wall degree of roughness 2×10-6[m],
boundary condition
experimental fixed number of Nikuradse
time step
2ms(500Hz)
5
4,800
velocity[m/s]
5,700
4,500
4,800
900
380
water tank
（395×585×300）
calculation method
fluid
turbulent model
4
max. v e = 4 .7 m / s
3
mean ve = 4.15 m / s
2
1
vertical outflow pipe 20A
Figure 1- Experimental
Apparatus for terminal velocity
ve
va
0
0
5
10
ve
15
20
time[s]
Figure 2- Analytical velocity va and
experimental velocity ve
2.3.2 CFD analysis results and discussion
Terminal velocity was reached within about 2s after the inflow start in the experiment;
in the CFD analysis, it was reached within about 1s, as depicted in Figure 2. Although
the mean terminal velocity was 4.15m/s in the experiment, it was 4.43m/s in the
analysis, some discrepancy arose.
2.4 Comparison of experimental and CFD analysis results
Figure 2 presents a comparison of the temporal variation of the pipe internal velocity in
the terminal velocity experiment (ve) and CFD analysis (va). The terminal velocity in the
vertical outflow pipe was about 4.2 ~ 4.4 m/s, with the coefficient of velocity C=140;
the terminal length was about 2.7m. Although comparison between the experiment and
CFD analysis revealed some differences in velocity variation from the outflow start to
attainment of terminal velocity, and the values of terminal velocity themselves,
sufficient agreement was observed in general. Therefore, the effectiveness of the CFD
analysis was also verified.
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3. Experiment and CFD analysis of the flow characteristics in siphon
drainage piping
3.1 Objective
This experiment is intended to establish a method of evaluating the pipe internal
velocity from piping configurations such as vertical and horizontal pipe lengths. For that
purpose, a basic piping model without a trap or crossover piping is prepared indoors,
and the flowing characteristic of siphon drainage piping is verified. Results verify
whether the siphon phenomenon by a filled flow drain peculiar to a siphon drainage
system is reproducible using the type of CFD analysis. A multi-phase flow of water-air
with clean water containing no solid matter was assumed.
3.2 Outline of experiment and CFD analysis
3.2.1 Experiment
Figure 3 portrays a schematic drawing of the experimental apparatus. The line has no
crossover piping or trap, which are indispensable in actual application, with minimal g
water flow resistance as an elementary experiment. The open end was open to the
atmosphere, also the confluence joint was not installed in drainage stack. A 20A rigid PC
pipe was used for siphon drainage piping and a bent pipe of R4D was used for the
curved sections. Table 2 presents the line dimensions and configuration used for the
experiment.
The experiment proceeded as follows. First, the water discharger was flooded so that the
inflow head (Hi) was set to 700mm. Then, after checking that the predetermined water
level was reached, the discharger plug was opened and water flow was released. For an
experiment with horizontal pipe length (Lh) of 4,000mm, which was used for the
comparison with the CFD analysis, the siphon drainage piping was also flooded to make
the pipe internal velocity promptly steady and to shorten the analysis time. Pressure
sensors were installed near the vertical and horizontal elbows, as portrayed in Figure 3,
where deflection is remarkable. A water pressure sensor was installed in the drain
characteristic measurement basin to determine the drain flow rate and flow velocity.
3.2.2 CFD analysis
The piping model of this analysis was created along with a siphon drain basic piping
model without a trap or crossover piping used in the experiment. Calculation regions
ranged from the free surface of the water discharger that was flooded initially in Figure
3 to the open end of the outflow head.
The structure meshes of the cross section of siphon drainage piping were 132. Figure
4-a schematically depicts the cross-sectional grid of the analytical model. Figure 4-b
portrays the grid outline of the junction of the analytical model. The total mesh numbers
are, respectively 144,128 and 157,592 at the minimum and maximum.
CFD analysis conditions are shown in table 1. This analysis assumed a multi-phase flow
of water-air in an isothermal and transient flow field, and the Volume-of-Fluid (VOF)
method, an Euler-type method, was adopted as the computational method of a free
surface. Transient analysis was conducted using the Pressure Implicit with Splitting of
Operators (PISO) algorithm, in which the windward difference of primary accuracy was
330
used for the advective term as the difference scheme because the flow was one way. The
generalized log law was applied to the wall surface boundary condition. The
computational time unit was 2ms. Computation for 5.0s in the actual time was carried
out.
3.3 Results and discussion
3.3.1 Experiment
The pipe internal velocity was minimal at EX 80-5 and maximal at EX 40-15. The pipe
internal velocity was 1.20 ~ 2.08m/s. The qd value was ca. 0.5 l/s. Results verified that
the flow rate varied according to the change in the pipe length (Lh) and outflow head
(Ho).
3.3.2 CFD analysis
The maximum Courant number was about 4.0 or less in all CFD analytical models.
Furthermore, y+ (=u*∆y/ν) of the first cell on the wall surface was about 150. Therefore,
it is considered that computation on this analysis was performed satisfactorily. Table 4
presents CFD analysis results and experimental results of the pipe internal velocity and
pipe internal pressure in all piping configurations. The velocity and pressure values
were on the stationary state. The pipe internal velocity evaluated in the CFD analysis
C
drainage fixture
B
A
Table 2- Pipe length and
configuration for experiment
Hi
experiment No. Ｈ o [mm]
EX40- 5
4000
EX40-10
EX40-15
EX60- 5
6000
EX60-10
EX60-15
EX80- 5
8000
EX80-10
EX80-15
Lh
Ho Hi ：inflow head
Ho ：outflow head
Lh ：horizontal length
：measuring point
of pressure
Figure 3- Experimental apparatus
a
ｂ
Lh [mm]
500
1000
1500
500
1000
1500
500
1000
1500
n. of bend
2
2
2
2
2
2
4
4
4
10 ㎜ cube
5.0 ㎜ cube
2.5 ㎜ cube
Table 3- Pipe length and
configuration for CFD
Lh [mm]
4,000
（ a：section, b：junction ）
Figure 4- Cells of CFD model
Ho [mm]
500
1,000
1,500
Lt [mm]
5,200
5,700
6,200
n. of bent
2
2
2
differ from experimental values respectively by about 5% and the pipe internal pressure
evaluated about 500Pa at the maximum. This is considered a satisfactory result
considering the resolution of the pressure sensors.
Figure 5 depicts the transient distribution of mean pipe internal velocity and pipe
331
internal pressure at the Ho: 1,500 mm. The mean velocity distribution was different
between the experimental and analysis values by 0.5 m/s at the maximum for 1 ~ 2s
after the outflow start. However, mean pipe internal velocity agreed well with the
experiment shown since 2.5s after the outflow start, when flow velocity settled into a
constant value. A rapid pipe internal negative pressure by a siphon phenomenon was
also reproduced in a satisfactory manner. Furthermore, the mean pipe internal velocity
was compared with the theoretical value obtained using the flow velocity theoretical
equation derived from experimental values at the pipe length (Lh) of 4,000mm and the
kinetic energy conservation law. Each parameter used for these analytical conditions (λ
= 0.024, d = 0.02m, ζ = 0.5）is substituted for the theoretical equation Eq(3). The
hydraulic gradient is assumed as I = Ht / Le (where Le =1.2l + 0.5). Consequently, the
relationship between the flow velocity and hydraulic gradient can be expressed as Eq
(4).
vt = 2 gH t (λ
l
+ ∑ ς + 1) --------- (3) ,
d
vt = 4043 I -------------- (4)
v t : velocity of theory[m/s], Ht: total water head[m], l:equivalent pipe length [m],
λ : friction factor [-], d: diameter [m], ς : loss coefficient[-], I:hydraulic grade [-]
Table4-CFD analysis and experiment results of velocity and prwssure
Ho
method
velocity[m/s]
A
B
C
pressure[Pa]
500[mm]
analysis
experiment
1.59
1.67
2,567
2,478
245
56
-3,594
-3,954
1,000[mm]
analysis
experiment
1.89
1.81
1,403
1,602
-1,791
-1,956
-7,206
-7,770
1,500[mm]
analysis
experiment
2.1
2.02
358
191
-3,160
-3,188
-10,306
-1,088
velocity [m/s]
2.5
2.0
1.5
0.5[m/s]
1.0
ve
va
0.5
0.0
0
1
2
3
4
5
12000
A-experiment
B-experiment
C-experiment
A-analysis
B-analysis
C-analysis
pressure [Pa]
8000
4000
0
-4000
-8000
-12000
0
1
2
3
4
5
time ［s］
Figure 5- Comparison of CFD and experiment on velocity, pressure
(Lh = 4,000mm, Ho = 1,500mm)
332
2.5
2
2
1.5
1.5
vt [m/s]
ve [m/s]
2.5
1
y = 1.011x
0.5
1
y = 0.986x
R2 = 0.985
0.5
2
R = 0.955
0
0
0
0.5
1
1.5
2
2.5
0
0.5
1
1.5
2
2.5
va [m/s]
va [m/s]
Figure 7- Comparison of va of vt
Figure 6- Comparison of va of ve
Figures 6 and 7 respectively represent the correlation of pipe internal velocity between
the CFD analysis values and the experimental and theoretical values. The CFD analysis
values exhibited a high coefficient of determination. They very closely approximated
the experimental and theoretical values. Consequently, the CFD analysis was verified as
effective for these analysis conditions.
4. Flow characteristic of siphon drainage basic piping model
4.1 Objective
In response to the satisfactory analysis results obtained using CFD in the preceding
section, a piping configuration for which it is difficult to conduct an indoor experiment
is analyzed. Flow characteristics for diverse piping are investigated in this section.
4.2 Outline of CFD analysis
The inflow head (Hi) of the piping configuration of this analysis was identical to that
used in the preceding section. In all, conditions of 24 types were assumed from four
types of the horizontal pipe length (Lh) ––2,000, 4,000, and 8,000 or 12,000 mm––and
six types of the outflow head (Ho)––0, 500, 1,000, 1,500, 2,000 or 2,500 mm.
The configuration of the cross sectional grid and analysis conditions were the same as
those reported in the preceding section. The total mesh numbers are, respectively,
111,392 and 274,412 at the minimum and maximum.
4.3 Results and discussion
Table 5 presents the pipe internal velocity for all piping configurations. Figure 8 shows
the relationship between the horizontal pipe length (Lh) and the pipe flow rate from the
CFD analysis result. Therefore, it is assumed that the equipment mean drain flow rate is
qd = 0.5 l/s, which assures that no problem in a common residence when the following
conditions are met when the inflow head (Hi) is 700mm: the horizontal pipe length of
2,000mm, and 0mm of the minimum of outflow head (Ho) is allowable; when the
horizontal pipe length is 12,000mm, the minimum of outflow head (Ho) is 2,000mm.
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This engenders the following argument: the horizontal pipe length (Lh) that is not
shorter than 15m renders it difficult to acquire sufficient drain capacity merely by the
siphon force of the outflow head according to the floor height of one story. Therefore, it
is likely that no conveying force other than the siphon force is necessary.
Figure 9 compares the square root of hydraulic gradient (I) with flow velocity from the
CFD analysis (va), the theoretical flow velocity (vt) derived from the kinetic energy
preservation law, and flow velocity from the experiment (ve). The regression coefficient
in the CFD analysis was 4.33, which very closely approximates to 4.43, the
proportionality factor of the theoretical equation, and 4.22, the regression coefficient by
experiment. Furthermore, the flow velocity from CFD analysis was compared to the
experimental and theoretical values shown in Figures 10 and 11. High coefficients of
determination in both cases prove the propriety of the analysis.
Table 5- Velocity for all piping configurations
velocity
Ho ［㎜］
[m/s]
Ｌｈ ［㎜］
0
500
1,000
1,500
2,000
2,500
2,000
1.6
1.98
2.28
2.51
2.69
2.84
4,000
1.24
1.59
1.9
2.1
2.28
2.43
8,000
0.94
1.25
1.51
1.7
1.87
2.02
12,000
0.75
1
1.21
1.41
1.61
1.73
flow rate[l/s]
1.0
Ho :[mm]
0.8
0
500
1000
1500
2000
2500
0.6
0.4
0.2
0.0
0
2000
4000
6000
8000
Lh[mm]
10000
12000
14000
Figure 8- Flow rate with Ho and Lh
3.0
velocity [m/s]
2.5
vt = 4.43
2.0
va = 4.33
I
va
ve
vt
I
R2 = 0.988
1.5
va regression line
ve regression line
1.0
0.5
0.0
0
0.1
0.2
0.3
I
0.4
0.5
0.6
0.7
Figure 9 - Comparison of square root ( I ) and va, ve, vt
334
3
2.5
2.5
2
2
vt [m/s]
ve [m/s]
3
1.5
1
1
y = 0.988x
R2 = 0.960
0.5
1.5
y = 0.978x
R2 = 0.988
0.5
0
0
0
0.5
1 1.5 2
va [m/s]
2.5
3
0
Figure 10- Comparison of va of ve
drainage fixture
Lh
1
1.5 2
va[m/s]
2.5
3
Figure 11- Comparison of va of vt
L
C
B
0.5
Hi
A
S
Lht
Ho
S
L
S
riser
pipe of drip trap
S
L
to drainage stack
Hi : inflow head
Ho : outflow head
Lh : horizontal pipe length
Lht : pipe length of water
flow
: pressure measuring point
Figure 12- Siphon drainage piping trap
2.5
velocity[m/s]
2.0
1.5
1.0
ve
0.5
va
0.0
0.0
8000
pressure[Pa]
1.0
1.5
2.0
2.5
pressure[Pa]
12000
0.5
4000
0
A-experiment_
B-experiment
C-experiment
A-analysis
-4000
B-analysis
-8000
C-analysis
-12000
0.0
0.5
1.0
1.5
2.0
2.5
time[ｓ]
Figure 13- Comparison of CFD and experiment on velocity, pressure
(Lh = 4,000mm, Ho = 1,500mm)
335
3.0
2.5
velocity [m/s]
2.0
1.5
vt = 4.43
va = 4.26
I
va
ve
vt
I
R2 = 0.988
1.0
va = 4.27
0.5
va regression line
ve regression line
I
R2 = 0.991
0.0
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
I
Figure 14- Comparison of square root ( I ) and va, ve, vt
5. Flowing characteristics of a piping trap drainage piping model
5.1 Objective
The flow characteristics of a piping model with a piping trap installed are investigated
presuming a real application, which identifies the effectiveness of the CFD analysis in
a piping model with many elbows. At the same time, this investigation aims at
expanding the comprehension of the flow characteristics of siphon drainage piping
considering local resistance.
5.2 outline of CFD analysis
This analysis considers a siphon drainage piping trap model with a line trap (water flow
length 500mm, seal depth 50mm), with Hi of 700mm and Lh of 4,000mm, using six
outflow head types with Ho of 0, 500, 1,000 and 1,500, and 2,000 or 2,500mm. Figure
11 schematically depicts the siphon drainage piping trap model.
The calculation region is initially a flooded region. The standup section of the trap was
equipartition of the longitudinal direction using an interval of 8mm, and was slightly
more finely divided compared with 10 mm of the straight section. The configuration of
the cross sectional grid (see Figure 4), analysis conditions (see Table 1), and the
calculation method of pipe internal velocity were the same as those described in the
preceding section. The total mesh numbers are, respectively, 146, 372 and 179, 900 at
the minimum and maximum. Computations for 2.5s in actual time were carried out.
5.3 Results and discussion
The maximum Courant number was about 6.0 or less for all analytical models: y+ was
about 140. Figure11 presents the hourly variation of pipe mean velocity and pipe
internal pressure at outflow head (Ho) 1,500mm. The analytic values of pipe mean flow
velocity were greater by about 0.2 m/s compared to experimental values terminal. An
almost identical tendency in velocity distribution confirms a satisfactory CFD analysis
result. Moreover, the reproducibility of the pipe internal pressure is as satisfactory as the
CFD analysis in the preceding section.
336
Figure 12 compares the CFD analysis result, experimental values, and theoretical values
on the siphon drainage piping trap model. This yields a regression coefficient in CFD
analysis of 4.26, which differs from the constant of proportion of the theoretical
equation by about 4%. However, it was very close to the regression coefficient obtained
through experimentation. The regression coefficient in the CFD analysis was 4.33 in the
siphon drainage basic piping model; it was 4.26 in the siphon drainage piping trap
model. A slight decrease in the regression coefficient was observed for the relationship
between pipe internal velocity and the square root of a hydraulic gradient with and
without a piping trap. This is the result of some deviation from the proportionality factor
of the theoretical equation. It is considered to occur because only six piping patterns
were used in these CFD analysis models. It is necessary to increase piping patterns in
the siphon drainage piping trap model and to carry out data expansion and accumulation
in the future.
6. Conclusion
Analyses of the flow characteristics of siphon drainage piping and the pipe internal
velocity equation were carried out using CFD, which provided the following knowledge
based on those results.
The CFD analysis was verified with excellent reproducibility in the siphon drainage
basic piping model for an isothermal and transient flow field and for the multi-phase
flow of water-air. Moreover, the analysis of various piping configurations demonstrated
the effectiveness of the pipe internal velocity equation derived from the kinetic energy
preservation law.
Furthermore, for the siphon drainage piping trap model, by adding the loss resistance
for a piping trap to the equivalent pipe length, it was identified that the flow velocity
equation using the view of a hydraulic gradient is effective. However, the regression
coefficient in the CFD analysis resulted from the proportionality factor of the theoretical
equation, although only slightly. This is considered to occur because only a few piping
patterns were used in the analysis model. Consequently, expansion of piping patterns is
a pressing need for further investigation.
This study investigated the flow characteristics with clean water (water-air two-phase
flow) using the CFD. It is expected however, that introduction of solid matter contained
in drainage and the viscosity change of water in an actual wastewater would degrade
flow characteristics. Accordingly, the flow characteristics of wastewater (water-air
miscellaneous matter three-phase flow) close to the actual draining state must also be
investigated, and flow characteristics and the trend of pipe stagnation of solid matter are
expected to be investigated as subjects of future studies.
7. References
1) Mitsunaga, T., Sakaue, K., Tsukagoshi, N., Yanagisawa, Y., Kodera, S. (2007),
Experimental Studies on the Siphon Drainage system (Part. 2), Technical papers of
meeting, SHASE, (pp.715-718)
2) Joel H. Ferziger, Milovan Peric (2003), Computational Methods for Fluid Dynamics,
Springer-Vertag Tokyo (pp.377-394)
337
3) S. Murakami, (2000), Computational Environment Design for Indoor and Outdoor
Climates, University of Tokyo Press
8. Presentation of Author
Ryoichi Kajiya is Lecturer at Meiji University, Dept. of Architecture,
School of Science and Technology. His specializations are Building
Equipment and Air Conditioning Systems. Recently he has researched
on siphon drainage system, airflow and thermal environmentin a room.
338