Hydraulic Analysis of the Urban Drain System

. Analysis efficiency operating drain sewer systems (DSS) is a part of urban water management. Two basic parameters flooding and sediment formation with average annual precipitation and with rains varying intensity are considering. Dealing with hydraulic problems, modelling focus lies on non-pressure systems with two-phase flows. The main requirement in the design of gravity collectors is the flow rate with self-cleaning velocity. The initial data for hydraulics calculation DSS is the flow rate in hole system and geometrical characteristic of the each elements. The average velocity in local tube depends on average flow rate and the cross-sectional area. For calculation, cross-section area needs to estimate depth of flow, which can be find only in situ. The average velocity was found for each element of the system by combining the two matrices. The first contains the initial data of the working collector, and the second contains all possible velocities and depth of the collector with such geometric characteristics. Verification of the proposed model was carried out using data from the standards and from engineering systems in Moscow. Maps with the coordinates of the tube outlet in the considered part of Moscow where the flooded collectors and collectors with sediment were compiled.


Introduction
The history of sewerage dates back about 3000 BC.This epoch is associated with discovery of sewage facilities of the ancient Babylon, Mesopotamia, Egypt, Assyria.The active building of sewerage in Europe started in the XIX century.By 1883, over 50 towns in Eng-land had the simplest sewer systems.Similarly, in Germany, by 1870, sewerage was available in about 50 big towns.In the U.S., about 1,000 towns were equipped with sewers by 1902.In Russia the first stage of the sewerage system was put into operation on July 30, 1898.Then it covered only 219 households, but by 1909 it was already 30 thousand.The urban sewage system played different roles in settlements.Initially, the urban drainage system was created for public hygiene to treat waste and as effective means of flood protection.
The history of four main influence factors of storm flooding is briefly reviewed by considering the urbanization process and climate change in the last few decades [1][2][3].The basis for the proposal of countermeasures for storm flooding is provided by analyzing the influence factors.As the determination of parameters and the modelling of storm flooding are very complex, it is necessary to know how the flow characteristics in the col-lector system change with significant flows rates.The analysis of the operation of the ur-ban drainage system is very important for flooding prevention [4][5][6][7].
The largest flood of the XX century occurred in Moscow in April 1908.The maximum flow rate was 2860 m³/s; the Moskva River rose by 8.9 m.Water flooded about 16 km² of the capital's territory.Almost 100 km of streets and alleys went under water.In the 1.5-million Moscow, about 200 thousand citizens suffered.25 000 buildings were destroyed and damaged.In the middle of the XX century, the Istra, Mozhaisk, Ruza and Ozerninskoye water storages built (which regulated river flows) and the collector system of the city.After that, big floods on the Moscow River stopped.
The main purpose of this research is to create a dynamic model of sediment formation in the drain sewer system (DSS).This publication implies the following main objectives: -Analyse a numerical model for flooding and solids transport; -Receive collector locations with low operation conditions based on Moscow DSS; -Investigate and analyses DSS under various flow regimes.

Materials an Methods
Sewage system collects wastewater inside a considering territory and transport them beyond.To compile a model, it needs to create a database with construction, sediment and hydraulic data (see Fig. 1).

Figure 1.
Schematic application of the modelling procedure.Construction Data should be collected regarding the existing or constructing collector system (diameter, length, cross-section shape, catchment area and etc.).Sediment Data -the nature of the sediments found in the system [8].Hydraulic Data -the in-tube hydraulics [9][10][11][12][13][14].
The dynamic model of sediment formation in the DSS describes the change in the state (weight, thickness) of solid particles at the bottom of pipelines depending on the intensity of precipitation.The volume of surface runoff (Q considering flow rate in collector system (m 3 /s)) and its distribution throughout the year is influenced by a complex of various processes that determine the flow of water into the drain.Hydraulic data is received by a hydrodynamic simulation.Collector system is complex net (network) of tubes (runoff outlet).The working array created to describe the collector system N = f (Q) and represents a matrix form with twelve columns: The main requirement in the design of gravity collectors is the flow rate with self-cleaning velocity ( ).In the UK BS 80056 (British Standard) recommends a full pipe   velocity of 1 m/s in order to ensure that a velocity of 0.75 m/s is exceeded at least once each day on average [15].In this study, we consider the following model of the collector system (Table 1 shows the working array (N) characteristics).2) Eight flow rates corresponding to different rain intensity, 20-min.duration (q20) and average frequency one time in a period of 4 month to 50 years.The difference between the regional regulations determines the rain intensity map (for Moscow region, see [23]).

Results
On the territory of Moscow, the total length of the river network is more than 600 km.About 295 km of them (more than 160 rivers) flow underground (Figure 2) in tube under industrial and civil constructions and have become part of DSS.  1 For diameter range -low limit is strict. 2This range more popular for underground rivers than DSS.
A model of sediment formation in the DSS was proposed.The model has been tested on the collectors of the Moscow DSS.Nine matrix arrays were created, consisting of 406 collectors, describing the hydraulic characteristics of the system.The model provides: -System condition analysis: analyze the flooding and self-cleaning condition (proportion of collectors in which self-cleaning and flooding will occur.
-Determination of the weight of the sediment formation formed and taken out of the system.
-Estimation of changing conditions of the DSS by rains of varying intensity.
-Receiving the location of the considering runoff outlet on the map of Moscow.

Flooding
The storm water collector is small culvert for storm water (rainwater) or for removing the river (creek, stream, flow) under ground.The capacity of a round pipeline depends on the geometric characteristics, surface roughness, and bottom slope.Since precipitation enters the collector system in proportion to the catchment area, flooding should not occur.Table 4 shows collectors with low flooding conditions. 2 Flooding analysis show that only one collectors always flooded because work on the big catchment area.The increase in the number of flooded collectors with increasing rainfall intensity is significant.Flooding of streets occurs during rains, the intensity of which is significantly less (less than 15%) [16] of the intensity of the calculated rain precipitation.The considered part of the drainage system in Moscow do not fulfill their functional purpose.The model proposed in this paper shows the location of flooded collectors on the map of Moscow (see Fig. 3).The simulated scenario is the 20-minute rain intensity in 10-year period.

Self-cleaning analysis
The self-cleaning velocity is the cross-sectional average flow velocity corresponding to the flow movement without deposition of solids.The principle of using the self-cleaning velocity is similar to the use of the critical velocity of a two-phase flow [17].The critical velocity of a two-phase flow (a term more commonly used in the calculation of pressure hydraulic transport) is the average velocity of the flow when deposition of solid particles begins.In case of self-cleaning mode, all solid particles move in the pipe.If not, they settle to the bottom and the flow with sediment formation can be defined.The self-cleaning velocity relates to the transport capacity of the two-phase flow.The transport capacity of the flow determines by a combination of certain dynamic conditions realized by the transport of solid particles.It characterizes the possibility to transport (or with a lack of energy -to create sediments) -to maintain solid particles in suspension (mobile or entailed) and transfer them to the distances.If self-cleaning conditions are not created in the pipe transporting the two-phase flow, then a sediments forms at the bottom.
It is important that the self-cleaning criterion check for each collector, not for the entire system, since the hydraulic conditions are very different.The average velocity in each collector is used for the self-cleaning criterion.At a given flow rate, it is possible to find the velocity if the cross section area through which the flow moves is known.The area of the cross section depends of the flow height in gravity flow in a round collector.The shape of the cross section is segment of the circle.The cross section area (ω i ) is calculated to the geometry through the central angle (α) (See Fig. 4) corresponded to the local height (h i ): (16) If we consider all possible depths in the collector, then we can accurately find the flow rate with the depth, and therefore the average velocity.For each diameter of the collector (see Table 4), the selected depth step is at 1 sm.For each depth, the central angle is determined (α), than we find cross-section area (7), wetted perimeter (11), hydraulic radius (10), Chezy coefficient (9), average velocity (8) and flow rate (12).The bottom slope and roughness coefficient are constant (see Table 1).The calculations of all possible velocities and flow rates in collectors are performed in Python and Visual Basic.As a result, we complete ten arrays, according to ten range collector diameters (see Table 4) Q = F (D) with eight columns: (17 The number of j lines of array Q corresponds to the depth step and for D = 3 m, is equal to 3000.The flow rate in local collector (the fifth column in array ( 1)) depends of the scenarios (see Table 3) and catchment area.Thus, having compared two arrays N = F (Q) (1) and Q = F(D) (15) for column with local flow rate, we can obtain local velocity in array N (1) and calculate self-cleaning criteria (5).In order to avoid siltation of sewer networks, according to the recommendations, the average velocity of wastewater depends on the degree of the pipes filling (h/D) and the size of solids contained in wastewater.The average velocities of wastewater movement in DSS with the highest estimated filling of pipes.The self-cleaning velocity is in range of 0.7 -1.6 m/sec [1], and detection condition for average annual flow rate (flow rate in considering system is 3.86 m 3 /s in   >   Table 5).  1 For diameter range -the low limit is strict.
At average annual flow rate, only 46 collectors out of 406 fit the condition of self-cleaning mode, which is 11.3%.The operation of the DSS is not assumed satisfactory [22].The most of the present-day drainage systems in Moscow and other cities do not fulfill their functional purpose [28].Therefore, a complete cleaning of the collector system will not occur.Figure 5 shows results of the self-cleaning analysis for considering system with average flow rate.

Sediment formation analysis
In collectors with low self-cleaning conditions, the sediments are formed at the bottom of the pipelines.The model considers these collectors in the column of the N array with   mark zero (see formula ( 1) and ( 3)).The calculation of the sediment in the system and its dynamics over time is for collectors with low self-cleaning condition.The sediment formation calculations are based on the concentration of suspended and petroleum particles in the flow.The cross-sectional distribution of the volume of solid particles in a two-phase flow is the probability of occurrence of a certain amount of particles at the points under consideration.The solid particles tend to move at the bottom of the flow, which causes an increase in consistency at the bottom [18,19].The standards regulate the values of the concentration of solid particles in storm-water and melt runoff [20,21].The proposed model calculates at a constant concentration of solid particles (Table 6).  1 For diameter range -the low limit is strict.
The largest number of pipes are with diameters less than 0.7 m (78% of the total); this is typical for the construction underground utilities in Moscow of the 20 th century.In tube with diameter range 0.7 -0.9 m forms largest volume of sediments.Collectors with 1.6 m diameter called «walk-through» because man can pass full growth (full length technological tunnel).Wastewater serviced volume distributed irregular, the largest volume passes through the 0.3 -0.5 tubes and through the collectors with diameter more than 2 m.
With rains of higher intensity, the number of collectors is steadily increasing.However, in 25 pipes, self-cleaning condition is not achieved.There are 2 tubes in range 1.15 -0.3 m, 13 in range 0.3 -0.5 m and 10 -in range 0.5 -0.7 m.Based on the analysis, it is recommended to clean the pipes at intervals indicated in Table 8.   8 shows results of the self-cleaning analysis for considering system and demonstrated location collectors without self-cleaning condition.

Collector conditions analysis
The regulations for engineering services indicate that the repair work of water outlets should be carried out at a minimum flow rate.Repair work at water outlets includes the elimination of damage to structural elements, the replacement of individual structural elements of water outlets, the strengthening of the foundation, etc.The method of work at the outlets is chosen depending on their location.Unsatisfactory operation of collectors is associated with insufficient energy of the water flow to perform the self-cleaning conditions.There is not enough water flow energy to ensure that the average flow rate is sufficient for the transport of solid particles (sludge erosion and removal of solids from pipes).Since in the design of the DSS of Moscow, the initial task was to drain the territory (to remove the maximum flow of the river into the pipes, where it interferes with urban development, and the collection of storm water during operation), the task of self-cleaning becomes secondary.For the average annual flow rate of water entering the collector system, it can be seen that the pipelines do not operate in the optimal mode for self-cleaning (depth, or filling only 5% of cases corresponds to the norm of 0.95 height).Analysis of the collector system showed (Fig. 6) that without special solutions, it is impossible to simultaneously solve the problem of transferring the maximum water flow rate (in case of flood) from the territory and ensure high speeds and costs (for self-cleaning).Analysis shows that up to 94% of the collectors will operate in self-cleaning mode.Thus, the sediment in the collector system always exists.About to 44% of collectors will be flooded.With an increase in the intensity of precipitation, the indicators increase (see Fig. 6).The entire volume of solids entering the collector system is not carried out of the outlets, but settles at the bottom, sometimes creating a layer of siltation that makes it difficult for the pipeline to operate.

Conclusions
The position analysis of flooded and silted collectors provides essential information for engineering.The task of choosing the optimal estimation approach for self-cleaning mode for urban drain system was calibrated on the part of the Moscow DSS.To select the final layout, solid transport was investigated in various regimes.Special conditions of flow rates were simulated on the base of the participation characteristics.Numerical modelling of sediment formation was proposed.The results of the research are presented in the article.

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Diameter of the local runoff outlet (m).  -Local runoff length (m).  -Local catchment area (m 2 ).  -Ratio -part of water catchment area for local runoff tube (catchment area for one tube   divided to the total considering catchment area for collector system (F)): Maximum possible flow rate in local runoff tube (m 3 /s).   -Flow rate in local runoff: The flow rate Q is the initial value for which all elements of the matrix (1) are calculated.-Average flow velocity (m 2 /s) in local runoff.  -Condition execution "one" or "zero" parameter.In current work, we used the following   condition based on state regulation: "If the flow in collectors has average velocity less than recommended self-cleaning velocity, , solid particles will settle in the bottom and the   sediment is formed": (4) -Condition execution "one" or "zero" parameter:   (5) -The latitude and longitude are the coordinates of the outlets.Weight of sediment formation (kg) in the local runoff: average annual volumes of storm (W s) , melt (W m) and irrigation water (W ir ) [m 3 ].The volume of flow entering the local pipeline (W i ) is proportional to the catchment area on which the collector operates (see Formula 2)., -Are concentration of suspended solid particles and petroleum products [kg/m 3 ].    The number of lines i of matrix N corresponds to the considering quantity of pipes in the DSS.

Figure 2 .
Figure 2. Moscow underground rivers map and modelling area of the calculation (Moskva River, left bank), blue circles show the outlet collector points.

Figure 3 .
Figure 3. Modelling area of the calculation (Moskva River, left bank), red circles show the area with flooded outlet collector points.

Figure 5 .
Figure 5. Self-cleaning analysis (the blue circles -collectors with self-cleaning velocity conditions, yellow -without).
Figure in Table8shows results of the self-cleaning analysis for considering system and demonstrated location collectors without self-cleaning condition.

Table 1 .
Condition of calculation.
For the average annual volume passing through the considering part of the MCS, 121.6 thousand m 3 is accepted in this work.Thus, average annual flow rate is Q = 3.86 m 3 /sec.The table 2 describes nine different flow rate scenarios including: 1) Average annual flow rate, estimated on the basis of standard storm, snowmelt and water used for irrigation.

Table 2 .
Flow rates incoming to the system.

Table 3 .
Modelling part of the Moscow collector system.

Table 4 .
For the 20-minute rain intensity

Table 6 .
Concentration solid particles.The estimation of the average annual weight of solid particles deposited at the bottom of the tubes in more than 114 thousand tons (based on the average annual levels).Sediment analysis for average flow rate presents in Table7.

Table 7 .
Sediment analysis for average flow rate.

Table 8 .
Recommended frequency of cleaning of pipes in the collector network.