Automated Design Final Algorithm Report Spring 2008

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Spring 2008 Team Members: Raul Santiago, Cherish Scott, Becky Katz, Tamar Sharabi, Sarah Long, Leslie Campbell, Rachael Moxley

The Automated Design Team is responsible for determining the best algorithms, or the basis of design, for each component of the small-scale water treatment plant. The ensemble constitutes the automated design program that will be used by the AguaClara team to quickly develop plans for new water treatment plants to be built in Honduras. Thus far this semester the team has worked hard to get the working skeleton of the code in place. Over the past couple of weeks we have made progress constructing and documenting our basis of design.

The Master; Program is the driver of the automated design program. It is the central file where values are entered, functions are called, and parameters are returned and displayed. Although work is in progress to incorporate LabView as the tool to allow access of our program to the end user, right now the master program is the main page for the design team to test and develop the automated design program. This report aims to explain both the large scale basis of design and the small scale components of the program in so far as they have been determined this semester.

The AguaClara Automated Design Master Program is rooted in many different assumptions. All detailed programs outlined in this report use the following

The Master Program calls the functions written by the Hydraulic Design and Unit Processes Teams. Important parameters for drawing the plant in AutoCAD and other important parameters are returned to the program and displayed for easy perusal in tables.

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A pipe design function was created so that all pipes could be designed quickly and corrected.In order to find the proper diameter the program iteratively solves for the flow that can fit through a pipe of a given diameter with the given headloss until a large enough diameter is found in the pipe database.

The inputs of this function are the maximum flow of the plant (Q _plant ), the pipe specification of available dimensions (PipeSpecification), the maximum headloss ( h _lmax), the sum of all the individual headloss coefficients of elbows, tees, valves, expansions and contractions (K _sum) and the length of the pipe (L _pipe).

The Q _plant , and L _pipe are assumed design values.

The PipeSpecification calls the Pipe Database, please refer to the Pipe Database section.

K _sum values equal to the number of elbows, tees, valves, expansions and contractions multipled by their corresponding K ~ values~. All corresponding K _values are given in the Basis of Design tab.

h _lmax values calculated using the following set of equations.

Re = Reynolds Number, to determine if flow is turbulent or laminar
Q = Flow Rate
D = Pipe Diameter
¿ = Kinematic viscosity of water

f = Friction factor, equation for either turbulent or laminar flow
epsilon = Roughness factor of PVC

h = Major head loss

The outputs of this function are actual pipe diameter referenced from the pipe database.

Inputs- Q _plant, PipeSpecification
Outputs- SedPipe _length , D _orifice, orifice _dist, manifold _depth

This program is used to design the manifold that will be used for transporting water from the sedimentation tank to the plant leveling tank. Given the maximum flow rate through the treatment plant, and the number of sedimentation tanks in the plant, the flow rate for each sedimentation tank is given. The length of the launder is the same as the length of the tank. Water level on the sedimentation tank, measured from the bottom, is 2m. The water height above the launder is equal to the water level in the sedimentation tank minus the height of the top of the lamella, measured from the bottom, minus half the difference between the water level in the sedimentation tank. The orifices will go parallel at each side of the launder, and they will be spaced every two lamella.
The diameter of the pipe is estimated through an iterative process, given the pipe database, the flow rate ratio, Q_ratio, and the following equation:

Later the head loss in the manifold is determined, and with it, the diameter of the orifices. Lastly, the head loss through the orifices is calculated.
To design the pipe component that transports water to the leveling tank the pipe design program is used. After setting an acceptable head loss, the diameter of the outlet pipe is determined. In case the diameter for the outlet pipe is different from the diameter determined in the launder program, then the largest one should be chosen.

Inputs- Q _plant, PipeSpecification
Outputs- waste _inr, D _orifice, orifice _dist

This program is used to design the manifold that will be used for the sedimentation tank drainage. Given the maximum flow rate through the treatment plant, and the number of sedimentation tanks in the plant, the flow rate for each sedimentation tank is given. Using the critical velocity, the plate settler's length and diagonal spacing, the upward velocity can be determined, which in turn can be used to determine the active area of the sedimentation tank. With the active area, the length of the sedimentation tank is determined, and with a constant orifice spacing of 10 cm, the exact number of orifices in the pipe can be calculated.
With the drainage time set at 30 min, the constant water level of 2m, the width and length of the sedimentation tank, the initial drain flow rate is estimated.
The diameter of the pipe is estimated through an iterative process, given the pipe database, the flow rate ratio, Q_ratio, and the following equation:

Later the head loss in the manifold is determined, and with it, the diameter of the orifices. Lastly, the head loss through the orifices is calculated.

The purpose of this function is to determine the dimensions of the channel. The channel will run along the ends of the sedimentation tanks, such that its length will be equal to the widths of the three sedimenation tanks. The dimensions of the width and depth of the channel depend on the water level in the sedtank, which should be about the same as in the channel and the flocculator, and the length of the flocculator, since water runs from the end of the flocculator through the channel.

The primary constraint for designing the channel connecting flocculation and sedimentation tanks is the depth of the channel. The channel must be designed to make sure that the transition between the two tanks does not break up the flocs formed in the flocculation tank. Therefore the average velocity gradient, (G.cell) was a key parameter in the design. G.cell is the average velocity gradient in the cell where the energy dissipation is assumed to be occurring. A G.cell of 15/s was used because it is the desired velocity gradient for the end of the flocculation tank. Anything higher could result in the breakup of flocs.

K.cell the loss coefficient for the channel transition and ¿.cell, energy dissipated were additional parameters. The factor b takes into account the flow rate of the plant, the average velocity gradient and energy dissipation.

The width and height is multiplied by 1.5 by convention. Opening of channel height determines the height for the entire channel. The width of the channel may also be based on construction constraints, such as the maximum space available between the flocculation and sedimentation tanks.

The length of the channel is a function of the number of sedimentation tanks, which is three in this design, and the thickness of the walls between the sedimentation tanks.

The purpose of this program is to design the dimensions of the grit chamber, the number of risers in the chamber through which rapid mix takes place, and the number of holes in each riser.

The first step taken to design the number of risers in the grit chamber is to create an array of available pipe sizes based on the pipe schedule or SDR specified by the engineer and call on the AvailPipeSizes1(Pipe Specification) function in the PipeDatabase.

A maximum head loss through the riser pipe is assumed to be 20 cm, and the maximum head loss though a single orifice is assumed to be 20 cm as well. A function was created (K.sum) to sum the head loss coefficients throughout the system. This function was then referenced with appropriate amount of components specified. The diameter of the riser pipe was then calculated using the fluids function that determine the diameter of the pipe based on a specified flow rate and head loss through the pipe (D.pipe). The orifice head loss coefficient was specified then used along with the flow rate through the plant and the maximum head loss through an orifice to determine the area of the orifices. The (A.orifice) fluids function was used in the calculation.

The diameter of each orifice is set to 1.5 in (3.75 cm), which was found rather arbitrarily only constrained by what sizes could be drilled. A ratio of the maximum inlet orifice area to the pipe area is set to 0.3, so that the riser pipe will not lose too much strength by having too many holes around its perimeter. It also assumes that the total pipe length between the orifices and the flocculator (rapid mix pipe) is 2 m.

The diameter of the riser is found from a specified headloss allowable through the rapid mix pipes and the flow rate into the plant. For each diameter available the program will iterate until the flow calculated through the pipe is greater than or equal to the flow through the plant.

The orifice equation:

The total area of the risers was used to design the dimension of the grit chamber. This area was found using the diameter of each riser pipe, and the (n.risers). In the final design of the plant the grit chamber should be a no smaller than the area of the chemical feed drum. This is simply a practicality constraint. If the riser.areaTotal is smaller than drum.area then the grit chamber will designed using drum.area instead. From the riser.areaTotal the grit.width and grit.length is found. The grit depth is 2 m by convention.
The outputs of the function are the grit chamber dimensions (grit.dim), the number of risers (n.risers), and n.orifice, which is an array of orifices for a specified vertical height.

The purpose of this program is to design the leveling tank that will keep a constant water level throughout the plant, which in turn will optimize the operation of the plant, as well as facilitating the monitoring of the plant. This component must maintain some dimensional consistency with the other components of the plant. It consists of having inlet pipes that connect to each sedimentation tank, and a circular weir in the center that will transport the water to the storage tank. It is in the weir where water will be chlorinated.
As specified in the assumptions, the height of the leveling tank's wall will be the same as the height, measured from the platform of the plant, as the wall for the channel and the sedimentation tank. Setting the base of the leveling tank at the same level as the center of the plate settlers, the height of the wall will be equal to the 2 m of the water level minus the height of the center of the plate settlers, measured from the bottom of the sedimentation tank, plus the freeboard of the sedimentation tank, which is 10 cm.
The height of the weir is equal to the water level of the sedimentation tank minus the height of the center of the plate settlers minus the head loss going through the launders. To determine the diameter of the weir, the weir equation is used:

q = 2/3 c_d ¿D (2 g)^1/2 h^3/2 (1)

where

q = flow rate (m³/s)

h = head on the weir (m)

D = diameter of weir (m)

g = 9.81 (m/s²) - gravity

c_d= discharge constant for the weir -0.62

The Plant Leveling Tank function determines all of the water level elevations throughout the plant first relative to the bottom of the sedimentation tank.
Any variables with HW indicate the depth of water. Any value Z indicates a height.
The program first assigns values from the inputs that are arrays to individual values so that it is easier to determine what they are based on the variable name.

The headloss through the launder is found in the launder function and the height of the water in the channel is set as a design assumption. From these the actual height of the water in the PLT is calculated from the height of the water in the channel minus three times the headloss through the launder since there are three launders.

The number of orifices in the grit chamber are calculated by multiplying the sum of number of orifices at each height per riser by the number of risers in the grit chamber.

L.sedexits is the length of the exit pipes from the sedimentation tanks to the plant leveling tank, but for now it is set as a constant until we determine how to calculate it.

The headloss through the weir, will determine the height of water in the level tank: The headloss through the weir in the plant leveling tank is calculated with the headloss equation for a weir in the fluids functions file. Headloss is also calculated through the total number of launder orifices and the headloss through the launder manifolds.

The height of the sed tank is found by the height of the water in the sed tank plus the height of the freeboard, which is a design assumption.

The height of the top of the plate settlers (lamella) in the sed tank is found by adding the height of the bottom of the plate settlers to the vertical projected height of the lamella at angle alpha.

The height of the launders centered in the water above the plate settlers is found by subtracting the height of the top of the plate settlers from water in the sed tank, dividing by two, and adding the height of the height of the top of the plate settlers back again. This may be different from how the depth of the water above the launder is calculated in the sedimentation tank function. This should be checked.

The head loss through the pipes that take the water to the level tank needs to take into account that the flow won't divide quite equally between the pipes because of different total loss coefficients. We use conservation of mass and the fact that the head loss through each of the paths is the same to determine the actual head loss. First we calculate the minor loss coefficients for the exit pipes. This is based on the number of ninety degree turns in the pipe, which is a design assumption since it depends on the plant layout, times the Kel90 added to the Kexit for each pipe. Then the function HLsedexits is called on to calculate the headlosses.

ZTsed is, I think the height of the wall in the tank, calculated from the height of the water in the sed tank plus the freeboard. this is probably the same as the height dimension calculated from the sed tank program.

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The flocculator design algorithm is actually a series of functions working together. The main function - flocculator - is sent the [required values] and called by the master program. In turn, it calls the functions, uturnhole, shortcircuit, bafflepositions, and Gθmincheck. Ultimately, the flocculator function outputs the [necessary values] for the design report and the autoCAD team. The function relies on these [assumptions] in order to create its final design.

In order to create a square or rectangular footprint, the dimensions of the flocculator must be similar to that of a sedimentation tank. In order to maximize the amount of tank used for flocculation and limit the amount of materials used unnecessarily, the width of the floc tank is half the width of a sedimentation tank. This decreases the flow area thereby allowing for higher G values with bigger baffle spacings. In our current design, the flocculator is comprised of [#two adjacent channels] where the water makes a 180 degree turn between the channels

[!Automated Design Final Algorithm Report Spring 2008^Floc Layout Pic.jpg|width=200px!|Automated Design Final Algorithm Report Spring 2008^Floc Layout Pic.jpg] The length of a channel is the same as the length of the sedimentation tank. Finally, the depth of the water at the end of the flocculator must be the same as the depth of water in the sedimentation tank. Due to headloss through the baffles, the water depth will be greater at the beginning of the tank. Additionally, the design calls for 10cm of free space between the water surface and the top of the tank.

After determining the dimensions of the flocculator, the function calculates the baffle spacing and number of baffles in each spacing. The baffle spacing is found using the following equation (link eq). In this equation G is a vector of the ideal velocity gradients at each spacing. These values were calculated based on the recommendations of Shulz and Okun. A flocculator requires a minimum amount of mixing to be effective. The degree of mixing is expressed by Gθ, a dimensionless value found by multiplying the velocity gradient by the residence time. This value must be found at low flow in order to ensure that the tank does not fail when the actual flow rate is less than the design flow rate. After finding Gmin and θmin , the function determines how significantly each baffle spacing contributes to this value. This is found by multiplying Gθmin by a ratio of the G of a given baffle spacing to the sum of all three velocity gradients. Gθmin was found based on flocculator currently in use in Ojojona. The number of baffles in a given spacing is set to guarantee that the baffle spacing has a sufficient Gθ value. (LINK eq)

Next, the function calls its first subfunction - uturnhole. For structural reasons, the wall between the two channels must extend from one side of the flocculator all the way to the other. Therefore, the water must flow though a hole in this wall to move from one channel to the next. The shear through this hole must not break up flocs and the width of this hole must not be greater than the baffle spacing at the beginning of the second channel. In order to guarantee that the hole will not break up flocs, the shear through the hole should be equal to the shear through the last baffle spacing. In other words, the area of the hole should equal the flow area (channel width * baffle spacing) at the largest spacing. The function determines the baffle spacing at the beginning of the second channel and sets the width of the hole to this value minus a safety factor (3 cm in our current design). The height of the hole must be sufficient to equate the areas. The hole is a square for ease of construction. Additionally, it is assumed that the hole will take up a significant portion of the wall and therefore it can be placed in the center of the wall, rather than up or down depending on baffle placement. Ultimately, the function returns a vector including the width and height of the hole.

The flocculator function then calls another subfunction - shortcircuit. In a typical flocculator design the free space between the end of a baffle and either the water surface or the bottom of the tank is equal to 1.5*baffle spacing. However, at large baffle spacings this constraint will likely cause short circuiting. Short circuiting occurs when adjacent baffles no longer overlap and water could flow straight through the tank rather than up and down around the baffles. Quantitatively, this occurs when 3*baffle spacing approaches the water depth. (PICTURE?) Our design demands a baffle overlap of at least 2 cm. The shortcircuit function checks to make sure this minimum value is achieved. If not, the function calculates a new ratio between baffle spacing and the height of the horizontal channel above or below a baffle. (LINK). The function than recalculates the baffle length of the baffles in this spacing section. The function returns a revised vector of baffle lengths.

The flocculator function does a series of simple calculations to determine the head loss through the tank. This is done by finding the head loss through a single baffle in each of the three baffle spacings (link eq). Multiplying this value by the number of baffles in each section and summing the results provides the total headloss for the tank. The water depth at the end of the flocculator plus head loss gives the water height at the beginning of the tank. The depth of the tank should be based on this water height plus freeboard to ensure that it will not overflow.

The flocculator function relies on its subfunction, bafflepositions, to output the position of each baffle in the tank. These values are used by the autoCAD team to draw the baffles. The function outputs a separate matrix for each channel. Each vector has three columns. The origin (0,0) is set at the beginning and top of the first channel. The first column is the x position of each baffle. The second and third columns are the endpoints of the baffle. One major weakness in the current flocculator design process is that this subfunction will only work for two channels. This should be changed to make the program more versatile.

There are two ways of calculating the length of a flocculator. We have chosen to make the length of the flocculator equal to the length of a sedimentation tank. It is also possible to determine the length simply by multiplying the number of baffles times their respective baffle spacings. It is very likely that these two lengths will not be the same. It is the responsibility of this function to settle this difference. Currently, the function immediately fails if the length required by baffle spacing*number of baffles is less than the length of a single channel. In this case, it would probably be best to simply use a single channel with the same width as the sedimentation tank.

If two channels are needed, the function first finds the x position of every baffle in the first channel. See the Flocculation Function mathCAD file for the step by step process (LINK). It checks to make sure that a baffle is not placed too close (less than the current baffle spacing) to the wall at the end of the channel. If a baffle is too close, this baffle is removed and the function begins assigning the x positions to the baffles in the second channel. The x coordinates in this vector are relative to the same datum; however the positions are found starting where the water enters the channel and working backward. Therefore, the x coordinates get smaller with each entry. Once again, the function checks to make sure that a baffle is not placed too close to the wall. If the length predicted by baffle spacing*number of baffles is less than the length of the two channels, extra baffles are added at the end of the second channel. These baffles will have the largest baffle spacing. Conversely, if the total length of the flocculator is less than the length demanded by baffle spacing*number of baffles, baffles are removed from the largest baffle spacing.

After assigning the x positions, the function adds the y coordinates to the matrices. Once again, the function assigns all the values for the first channel first. A baffle either starts at the top of the tank (y = 0) and extends downward an amount equal to the length or a baffle starts at the bottom of the tank (y = tank height) and extends upward an amount equal to its length. The first baffle in the first channels start at the beginning of the tank and extends upward. The function returns the matrix for each channel as well as the total number of baffles in the tank.

Finally, the flocculator function calls a subfunction, Gθmin.check, which calculates the Gθ value now that all the baffles have been placed. This function must recalculate the number of baffles in each spacing and the find the total Gθ for the tank. This new value is compared to the absolute minimum allowable Gθ value for the tank (4500 in our design). The function returns a 1 if the Gθ is too low and a 0 otherwise. The flocculator function returns an error message if Gθmin.check returns a 1.

This function calculates the flow rate of alum based on the design assumptions.

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