Anastasios I. Stamou, Ioannis Katsiris
Department of Civil Engineering
National Technical University of Athens
Iroon Polytechniou 5, 15780 Athens, Greece
Tel: 0030-1-7722809, Fax: 0030-1-7722814
E-mail: stamou@central.ntua.gr
Stefanos Georgiadis, Sofia Kanellopoulou and Filippos Tzoumerkas
Department of Coordination, Design and Operation
Direction of Water Supply Network
Water Supply and Sewerage Corporation of Athens (Eydap)
Tel: 0030-1-2144301, Fax: 0030-1-2144290
Abstract: The Terpsithea tank in Athens (Greece) is used for water balancing
and emergency chlorination. The tank shows a very poor hydraulic performance
with dead spaces, which results in insufficient chlorination and high dosages of
chlorine. To improve the hydraulic efficiency of the tank, the use of a
deflector (which consists of three sides) is examined. Flow Through Curves (FTCs)
are used to investigate the effect of this modification. To derive a FTC, a
known mass of tracer is injected instantaneously at the inlet of the tank. The
resulting plot of the tracer concentration vs. time at the outlet is the FTC.
The shape of the FTC and its characteristics provide information on the
hydraulic efficiency of the tank. In the present work, the FTCs are not derived
experimentally, but are calculated with a mathematical model. Calculated flow
fields are used as input to the FTC calculations. The calculation of the FTCs
and their characteristics permits the correlation of FTCs with the flow fields.
The comparison of the flow fields and the FTCs for the initial and the modified
geometry leads to the following conclusions: (1) The flow for the initial
geometry is characterized by a high level of short-circuiting and two main
re-circulation regions. Due to the large size of these regions, a high degree of
mixing occurs. (2) The flow for the modified geometry shows limited
short-circuiting. Two main re-circulation regions are formed, which occupy
significantly less volume than the corresponding for the initial geometry and
thus create less mixing. In a significant portion of the tank flow resembles to
“plug flow”. Therefore, the use of the deflector improves dramatically the
hydraulic efficiency of the tank.
Keywords: Flow Through Curves (FTCs),
mathematical models, hydraulic efficiency
The design of water tanks is performed to achieve the required efficiency (disinfection, removal of suspended or organic matter etc.) of the process. The process efficiency depends on the hydraulic efficiency, which is determined by the flow field. The experimental derivation of the flow field is a very difficult and expensive task. Alternatively, a simple tracer technique, which is called the Flow Through Curve (FTC) experiment, can be used to determine the main convective and diffusive characteristics of the flow. A known mass of tracer is injected instantaneously at the inlet of the tank. The resulting plot of the tracer concentration vs. time at the outlet is the FTC. The shape of the FTC and its characteristics provide information on the hydraulic efficiency of the tank (Stamou and Noutsopoulos, 1994).
The tank of Terpsithea is a main component of the water supply network of the city of Athens (Greece), used for balancing and emergency disinfection. The tank shows a very poor hydraulic performance, which results in insufficient disinfection and high doses of chlorine. To improve the hydraulic and chlorination efficiency, a modified geometry with the use of a deflector is proposed. This geometry is expected to create a flow, which approaches the desired Plug Flow (PF). To assess and quantify the effect of this modification, the FTCs of the initial and modified geometries are compared. The FTCs are not derived experimentally, but computationally with a mathematical model. The shapes and the characteristics of the FTCs are compared and correlated to the calculated flow patterns.
The horizontal
section of the tank of Terpsithea is a square with sides equal to 57.9 m. The
water depth is H=5.0 m and the volume is equal to V=16762 m3. The
average flow rate is Q=20.8 m3/min and the theoretical detention time
is calculated equal to Tth =16762/20.8=805 min. The water flows into
the tank with a 900 mm inlet pipe (which is placed on the bottom of the tank)
and exits via a pipe of diameter 900 mm, located in a hopper at the bottom of
the tank (see Fig. 1a). This geometry is expected to create significant
short-circuiting and large volumes of re-circulation regions. A significant part
of the flow is expected to leave the tank in a much lower time than Tth.
Practically speaking, a large part of the tank remains unused as “dead space”,
leading to a significant deterioration of the disinfection process. To minimize
dead spaces the initial geometry has been modified with the use of a deflector,
consisting of three sides, as shown in Fig.1b.
The computer code CFX-5 (CFX, 1999) has been used, which calculates the 3-D flow field using the continuity and momentum equations. In the present calculations turbulence is described with the standard k-ε model (Rodi, 1980). The code employs an automatic, unstructured hybrid element mesh generator with an adaptive mesh refinement algorithm, which permits a very accurate representation of the boundaries. In the present work a numerical grid with 300000 cells has been used, with grid refinement in the inlet and outlet regions. For the solution of the equations, a scalable and fully implicit coupled solver (accelerated using algebraic multi-grid with linear performance characteristics in parallel computing environments) is used. FTC is calculated from the solution of a non-steady, convection-diffusion tracer concentration equation.
Despite the strong 3-D nature of flow in some parts of the tank, the flow has the general features, which are shown in the calculated velocity vectors of Figures 1a and b (at a horizontal plane located 3.0 m above the bottom of the tank).
(a)
(b)
Fig. 1 Velocity vectors at a horizontal plane, located at a distance 3.0 m from the bottom.
(a) Initial geometry and (b) modified geometry (with deflector).
In the initial geometry (see Fig.1a) the incoming flow strikes on the sides of the tank and is divided into 3 parts. The first, main part is directed to the right side of the inlet pipe, flowing parallel to the sidewalls and exits via the outlet, forming a massive re-circulation region, which occupies almost 70% of the tank volume. The second part of the flow is directed to the left side of the inlet pipe, forming a second, large re-circulation region. A third, small eddy is formed over the exit of the inlet pipe, due to the upward movement of the third part of the incoming flow. High velocities are observed in the inlet region and in the peripheries of the re-circulation regions. Very low velocities are found in the central regions of the re-circulation regions, where deposition of solids is expected to occur.
In the modified geometry (see Fig.1b) the sides of the deflector form the boundaries of an “inlet region”, which covers 23% of the volume of the tank. In this region, where the inlet kinetic energy is dissipated, the flow forms a main re-circulation region, which occupies almost 70% of the “inlet region”. After leaving this region, the flow enters into the “main tank”. There, it follows a “plug flow” parallel to the walls, forming a long re-circulation region along the first and second side of the deflector and finally exits via the outlet pipe.
The following data have been used for the simulation of the FTC experiment: Tracer injection time Tin= 3.0 min, injected mass of tracer Μin =6246.6 kg and duration of experiment Texp= 1449 min. The average tracer concentration in the tank is calculated equal to Co= 6246.6/16762=0.37 kg/m3.
Calculated FTCs have been normalized following the procedure described in Stamou and Noutsopoulos (1994); i.e. tracer concentrations (C) are divided by the average concentration (Co), times (T) by the theoretical detention time (Tth), while the area below the FTC is set equal to unity (after division with tracer recovery). The normalized FTC, E(t), represents the pdf (probability density function) of the detention times (t) in the tank. From E(t), the cumulative FTC, F(t), is constructed. F(t) values represent the probability that a part of the water in the tank has a detention time less or equal than t. The simulated FTCs, E(t) and F(t), for the initial and modified geometries are shown in Fig.2.
Fig. 2 FTC, E(t), and cumulative FTC, F(t), for the initial and modified geometry.
The FTC characteristics, which can be used as “indicators of the flow” are critically presented and analyzed in Stamou and Noutsopoulos (1994). In the present work only 10 characteristics are used. These are grouped into 4 broad categories of indicators: (1) short circuiting, (2) mixing-dispersion, (3) type of flow and (4) efficiency. (1) Short-circuiting indicators are the initial arrival time, t0, and the time at which 10% of the tracer has passed the outlet, t10. (2) Mixing indicators are measures of the width of the FTC. These are the time differences t75-t25 and t90-t10, the time ratio t90/t10 and the (statistical) variance of E(t), Var. (3) Type of flow indicators attempt to establish effective fractions of the PF (p) and CM (Completely Mixed) conditions (1–p) according to the theory of Rebhun and Argaman (1965). (4) The characteristic times, which are used as indicators of the efficiency, are the most probable time, tmax, and the time at which 50% of the tracer has passed, t50. The FTC characteristics for the initial and modified geometry are shown in Table 1.
Table 1 FTC characteristics
|
Indicator |
Initial geometry |
Modified geometry |
|
(1) Short circuiting t0 t10 |
0.02 0.06 |
0.35 0.53 |
|
(2) Mixing-dispersion t75-t25 t90-t10 t90/t10 Var |
0.74 1.30 22.60 0.35 |
0.42 0.82 2.54 0.08 |
|
(3) Type of flow p (fraction of PF) 1-p (fraction of CM) |
0.14 0.86 |
0.50 0.50 |
|
(4) Efficiency tmax t50 |
0.05 0.47 |
0.59 0.76 |
The FTC for the initial geometry consists of 3 parts. The first part, from t=0.02 to 0.09 is a relatively symmetrical curve with a rising and a declining part. This part represents the volume of tracer (calculated equal to 14%) leaving the tank via a short-circuiting path. The second part from t=0.09 to 0.30 represents the volume of tracer (36%), which exits the tank after following a series of paths, imposed by the flow field of Fig. 1a. The third part (t>0.30) is the “tail” of the FTC. It represents the volume of tracer (50%), which exits the tank after remaining in the relatively slow regions in the tank.
The FTC characteristics of the initial geometry (see Table 1) indicate (1) very high short-circuiting (extremely low values of t0=0.02 and t10=0.06), (2) very intense mixing (high values of mixing indicators), (3) low fraction of PF (p=14%) and high fraction of CM (86%) and (4) low efficiency (very low values of tmax=0.05 and t50=0.47).
The FTC for the modified geometry consists of two parts. The initial part, which represents short-circuiting and has been observed in the FTC for the initial geometry, does not exist. This is due to the fact that the use of the deflector does not permit the creation of a significant short-circuiting route in the tank. Furthermore, the FTC is shifted to the right, i.e. the detention times have been significantly increased. Thus, the first part of the FTC (t/T=0.35 to 0.85) represents the volume of tracer (60%), which exits the tank after following a series of paths, imposed by the flow field of Fig. 1b. The last part (t>0.85) represents the volume of tracer (40%), which exits the tank after remaining in the relatively slow regions in the tank.
The FTC characteristics of the initial geometry (see Table 1) indicate (1) very low short-circuiting (relatively high values of t0=0.35 and t10=0.53), (2) moderate mixing (medium values of mixing indicators), (3) equal fractions of PF (p=50%) and CM (1-p=50%) and (4) relatively high efficiency (high values of tmax=0.59 and t50=0.76).
The comparison of the flow fields and the FTCs for the initial and the modified geometry leads to the following conclusions:
(1) The flow for the initial geometry is characterized by a high level of short-circuiting and two re-circulation regions. Due to the large size of these regions, a high degree of mixing occurs.
(2) The flow for the modified geometry shows limited short-circuiting. Two main re-circulation regions are formed, which occupy significantly less volume than the corresponding for the initial geometry and thus create less mixing. In a significant portion of the tank flow resembles to “plug flow”. Therefore, the use of the deflector improves dramatically the hydraulic efficiency of the tank.
The author would like to thank (a) EYDAP for the financial support, (b) the personnel of EYDAP for providing the required information and data, (c) Dr. G. Theodoridis for the setup of the computer code CFX and the performance of the initial calculations.
[1] CFX-5 (1999). “Reference Manual”, AEA Technology, http://www.aeat.com/cfx.
[2] Rebhun, M. and Argaman, Y. (1965). “Evaluation of Hydraulic Efficiency of Sedimentation Basins”, J. of the San. Eng. Div., ASCE, 91, 37-45.
[3] Rodi, W. (1980).”Turbulence Models and Their Application in Hydraulics ‑A State of the Art Review”, IAHR, Delft, The Netherlands.
[4] Stamou, A. I. and Noutsopoulos, G. (1994). “Evaluating the Effect of Inlet Arrangement in Settling Tanks Using the Hydraulic Efficiency Diagram”, Water SA, 20(1), 77-83.