notes grit removal

November 2013, CHEN64301 Alastair D. Martin

Environment and Sustainable Technology

Solid-Liquid Separations:

De-gritters Contents

Introduction 2

De-gritting technology 2

Design principals for the CV channel 3

Gradient of the CV channel 5 CV channel profile 6 Grit hopper 6

Rectangular channel and Sutro weir 7

Design of the rectangular CV channel 7 Design of the Sutro weir 8

Parabolic channel and hydraulic jump flume 10

Design of the parabolic CV channel 11 Design of the hydraulic jump flume 12

Bendy Channel 14

Aerated grit box 14

Detritor 15



Introduction

In this section we shall consider the separation of “large”, dense mineral solids from the aqueous solution. In the terminology of wastewater treatment this operation is one of three classed as preliminary treatment. The other two are screening and storm water management.

Grit removal is merely a special case of sedimentation which is dealt with in more detail in the sections covering sedimentation and thickening tanks. The fundamental theory is also shared with cake filtration. Sedimentation theory is however dramatically simplified when applied to grit removal. Grit particles are considered to settle as individual isolated particles and in the rare event that a bed of grit is permitted to develop the bed is considered to be incompressible. Grit removal equipment is normally operated with a high cross flow velocity i.e. the bulk stream velocity is large and at right angles to the nominal direction of the settling grit.

De-gritting technology

There are five commonly employed technologies which can be classified according the primary and secondary flow patterns and the relative directions of flow of the two phases. All the devices considered here may be regarded as cross flow sedimentation technology. This terminology informs us that the water flow is horizontal whilst the grit falls vertially through the depth of the water stream.

The first classification is the constant velocity (CV) channel. In this class there are two common designs:

Rectangular channel Parabolic channel

Each comprises three principal components: the CV channel itself, a grit hopper and discharge system, and a flow control device. The type of flow control device dictates the cross sectional shape of the CV channel. The two common arrangements are defined as follows:

Rectangular channel, Sutro weir controlled Parabolic channel, hydraulic jump flume controlled

Both these devices employ the primary (axial) flow to partially re-entrain settled grit to “roll” the particles along the bottom of the channel into the grit hopper. In more sophisticated installations a mechanical scraper may be fitted to draw larger particles of settled grit along the floor of the channel into the hopper.

Two further devices operating on a similar principal are:

Bendy channel Aerated grit box



Both these devices set up secondary helical flow patterns to sweep the grit across the floor of the device. The bendy channel, as its name suggests, uses a curved channel to set up the secondary flow. As the primary flow negotiates the bend circumferentially, the secondary flow travels approximately radially across the bottom of the channel towards the centre of curvature sweeping the grit towards the inner wall of the channel and the entrance to grit hopper which is found close to the apex of the bend. By contrast the aerated grit chamber utilises an oblique feed pipe to establish a helical flow pattern along the length of the chamber. The flow pattern is stabilised through the action of an asymmetrically positioned aerator which produces a “curtain” of rising bubbles to entrain water. The helical secondary flow rolls settled grit towards an axial grit removal device.

The final commonly employed grit removal device is the detritor. It comprises a relatively wide, shallow circular “basin”. The gritty water enters through the circumference of one quadrant and exits over a weir mounted in the circumference of the opposing quadrant. Settled grit is mechanically raked towards and then around the circumference to the entrance of the grit hopper. The detritor operates in a manner more similar to the conventional sedimentation tanks than do the various grit channels and boxes.

Design principals for the CV channel

The aim of grit removal is to remove the majority of dense inert solids entrained in the waste water flow. In designing grit removal equipment the choice of “cut diameter” is crucial. The “cut diameter”, , is the Stokes diameter of the largest entrained particle. The choice of a suitable diameter is guided by the particle size distribution of the entrained solids and is chosen in order to minimise the mass of solids carried forwards into the subsequent process units.

The horizontal flow component of velocity in the de-gritter is critical as its magnitude determines the size of particles entrained from the floor of a flow channel. It is the vector sum of the horizontal components of the primary and secondary flows and is termed the cross flow velocity. If this velocity is too high the settling grit particles remain entrained in the flow and pass through the device and into the remainder of the treatment plant causing problems in the sedimentation tanks and sludge handling processes. The critical cross flow velocity above which a particle of a given settling velocity

becomes entrained is termed the scour velocity, and is given by equation 1, below.

l

ls

DW

scf

kgdv

8 - 1

where

= Nominal diameter of the largest entrained particle = Darcy-Weisbach friction factor

= Camp-Shields coefficient

= Scour velocity



For a representative, municipal waste water the Darcy-Weisbach friction factor is 0.02 whilst the Camp-Shields coefficient varies between 0.04 and 0.06. Given the cut diameter, the desired scouring velocity can be established. Once this has been done grit channel design becomes the design of a channel in which the scouring velocity is not exceeded and sufficient residence time is provided for particles to descend from the liquor surface to the floor of the device. The discharge of grit to a water course is rarely permitted even under conditions of extreme flow. This means the device is usually designed to pass the maximum, recorded or predicted flow for the catchment. The required cross section is readily determined from the maximum flow and the scour velocity using equation 2.

- 2

The proportions of the channel are determined by the detailed choice of technology. Design in which the depth of water at maximum flow, , is

approximately equal to the top surface width, , at the same

conditions are preferred for their economy of materials usage. In addition maintenance access to moderately deep channels is more readily achieved if the design width, , is greater than approximately 700 mm. Once the

depth of the channel has been determined the required residence time can be calculated from the settling velocity of the largest entrained particle.

- 3

Finally the length can be determined from the residence time and the scour velocity.

- 4

The sedimentation of grit is considered to occur as if each grit particle was discrete and isolated from its neighbours. Under these conditions the terminal sedimentation velocity of a particle is characterised by three different flow regimes: laminar also known as Stoke’s flow

, transitional and turbulent . There

are many equations available to describe the different regimes of which three are shown below.

- 5

- 6

- 7

Where

- 8



When the particle is falling at its terminal velocity, it is possible to equate the drag coefficient to the buoyancy of the particle:

- 9

By substituting for in equations 5, 6 or 7 it is possible to calculate the

settling velocity of the grit particles.

Gradient of the CV channel

For an open channel the flow regimes are more complex to characterise than for full pipe flow. For an open channel we need to take account of the free surface of the fluid. We do this be replacing the pipe diameter, , in the

conventional Renolds number with the hydraulic radius, . The hydraulic radius of a channel is defined as the cross-sectional area divided by the

wetted perimeter of the channel and can be shown to be equal to for a circular section pipe. Hence the key transitions occur at different Renolds

numbers. Laminar flow is characterised by whilst turbulent flow becomes established when . Given the size of typical constant velocity channels the flow is almost inevitably turbulent. Thus we will not consider the laminar case.

In uniform flow the gravity force in the channel is exactly balanced by the frictional or shear forces. Thus we can write the following force balance for the CV channel.

- 10

Where is the wetted perimeter of the CV channel. Rearranging and substituting in favour of the hydraulic radius at maximum flow, yields

the following equation for the gradient of the channel in terms of the wall

stress, .

- 11

In turbulent flow the following approximate relationship can be used to describe the wall stress in the constant velocity channel.

- 12

Substituting into equation 11 yields

- 13

The first group on the right hand side is nominally constant and is equal to the reciprocal of the Chezy constant, . ,however varies with

Reynolds number as does the hydraulic radius, . Manning and a

number of other authors observed that can be described to a

satisfactory degree of precision by the following relationship



- 14

Where is known as “Manning’s ”. Finally substituting for Chezy’s

constant in equation 13 yields the following relationship for the gradient of an arbitrary cross-section channel in uniform flow.

- 15

Wall material Manning’s n,

Concrete 0.012 – 0.017

Mortar 0.011 – 0.013

Perspex 0.009

Table 1 Manning’s values for a small selection of materials

The walls of a new, “well finished”, CV channel will typically fall into the “Mortar” range above.

CV channel profile

A number of possible profiles can be used however designs are dominated by the rectangular and parabolic sections. Here we will only consider these two configurations.

Rectangular channel Parabolic channel

The particular cross section chosen must be combined with a suitable flow control devise to ensure that the CV channel velocity does indeed remain constant over the desired range of flows.

Grit hopper

The grit hopper is a volume provided at the discharge end of the CV channel to enable grit to be directed towards the discharge device and to store quantities of material which have arrived at a higher rate than can be discharged. Typically the sides of the grit hopper will be very steep in order to help the material slide into the base and the inlet of the removal device such as an auger or classifier rake. Occasionally a high velocity jet is used to re-entrain the grit which is subsequently lifted onto an appropriately specified screen.



Rectangular channel and Sutro weir

In order to achieve the constant velocity objective the rectangular CV channel requires a particular flow control devise to be fitted to the discharge. The Sutro weir is such a device. The discharge flow from the weir is directly proportional to the height of the water above the sill.

Design of the rectangular CV channel

In the design of the CV channel we are free to choose the width. However it can be shown that the minimum channel wetted wall area, is given by the following relationship.

- 16

This dimension however turns out to be of little relevance to the design of a rectangular CV channel as the width of the sill of the associated Sutro weir is impractically wide. A secondary optimum can be found in the square cross section CV channel. From a construction objective the truly square cross section channel is impossible to construct. A cross section that is slightly taller than it is wide (high aspect ratio) leads to Sutro weir designs that are easier to construct and less prone to blockage. For maintenance

feed flow

grit hopper

Sutro weir

excess flow

weir or “benching”

inclined constant

velocity channel

Figure 1 Rectangular section constant velocity grit channel with associated Sutro

weir flow control.



access purposes it is also desirable for to be greater than approximately 700 mm.

- 17

The height of the water above floor of the CV channel is then fixed by the required area at maximum flow.

- 18

The hydraulic radius is given by

- 19

The floor of the rectangular section channel is designed to be parallel to the liquor surface to ensure “uniform” flow and to promote the travel of grit to the hopper situated up stream of, “behind”, the weir itself. The channel may be periodically cleaned either mechanically with a suitably profiled scraper or manually.

Design of the Sutro weir

The Sutro weir has a “roughly key hole” section and is illustrated in figure 1, over leaf. The weir comprises 2 sections a lower rectangular section known as the base and an upper curved section known as the complimentary weir. The detail of the curve of the complimentary weir is quite subtle. The profile is designed to ensure that the depth of fluid over the weir is directly proportional to the flow rate. This design characteristic ensures that the velocity in the rectangular section channel immediately upstream of the weir is constant regardless of flow rate.

The shape of the weir was developed by Sutro in 1908 as a practical version of the linear proportional weir previously described by Stout in 1897. Stout’s weir suffered from the requirement for an infinitely wide sill. Sutro, by sacrificing the proportionality at low flows was able to propose a considerably more practical alternative.

The discharge over a Sutro weir in its controlled flow range is given by the

following relationship for

- 20

When the height over the Sutro weir, linear flow regulation is not achieved and the discharge is described by the relationship for a rectangular weir.

- 21



When designing a Sutro weir to regulate the velocity in a grit removal channel it is necessary to match the constant of proportionality of the weir to that of the channel. The constant of proportionality is simply related to the dimensions of the CV channel. To design the weir we must determine

and the constant of proportionality, .

Figure 2 Sutro weir

- 22

Where is given by the discharge equation for a rectangular sharp

edged weir with .

- 23

To solve for both and we require a further equation. The additional relationship is derived from the need to match the derivative of discharge

equation at the top of the base when

- 24

- 25

Substituting into equation 22 and eliminating with equation 23 yields

the following.

Datum2s/3

s

hshHd3

2

H

s

yWx 1tan

21

x axis

ya

xis

0

Crest or sill

excess flow

bench

W



- 26

Equation 26 is cubic in and as such potentially hard to solve. However it can be simply rearranged to make the subject as follows.

- 27

Equation 27 can be readily solved for using a simple direct substitution

method. Since for linear control cannot be achieved it is desirable to arrange for this height to be achieved at minimum flow. It is simultaneously desirable to ensure that is greater than approximately 50 mm to avoid

blockages arising from MiS which may have passed the screens. Hence;

- 28

Since Sutro weirs are “sharp crested” they are typically manufactured from stainless steel sheet. The sheet is then bolted to the concrete structure of the CV channel. This requires the crest of the weir to be approximately 50mm narrower than the channel itself.

The discharge from the Sutro weir must be “free”. This means that the level of water in the down stream channel must never be higher than the sill or crest of the weir. The consequence of this requirement is that the head loss must be greater than . Thus the Sutro weir as a flow control device

is regarded as a high head loss option. This may be energetically satisfactory on a sloping site but may lead to problems of odour release as the flow in the discharge is highly turbulent and “churning”. This means that there is excellent mass transfer for the disengagement of odorous compounds.

Parabolic channel and hydraulic jump flume

The parabolic channel, figure 3, delivers the constant velocity objective via a different combination. The flume creates a “hydraulic jump” in the flow. The height of this jump is a rather complicated function of the flume geometry and the flow rate. The actual dimensions of the hydraulic jump are however not relevant to the operation of the flume. Its presence is all that is required. A hydraulic jump in the “recovery” section down stream of the throat indicates that super critical flow has been achieved in the throat section. Once this condition has been achieved the flow through the flume becomes a function of the depth of the liquid in the approach channel over

the sill, . Under these conditions the flow is proportional to

. When

combined with a parabolic profile in the channel upstream of the flume a constant velocity regime is set up. The mechanical design of the grit channel is similar to the rectangular channel i.e. the apex of the parabolic section is graded slightly downward toward the grit hopper, parallel to the liquid surface. This keeps the wetted cross-section and therefore the liquor velocity constant.



Design of the parabolic CV channel

The profile of a parabolic channel as a function of the height above the bottom or invert of the channel is given by the following relationship

- 29

Where

= the height above the bottom or invert of the channel and = the width of the channel at the height.

Here the width is a fixed function of the height whereas in the case of the rectangular channel it is independent of the height. The cross sectional area of a parabolic CV channel at full flow is simply found from the integral of equation 29 between the limits of and .

- 30

- 31

For an arbitrary parabolic section of width, at the maximum

controlled flow, the constant of proportionality, , is given by the

following relationship

- 32

Substituting for in equation 31 leads to the following relationship between the cross sectional area, liquid height and liquid surface width.

- 33

feed flow

grit hopper

Parshall flume

inclined

parabolic

channel

Figure 3 Parabolic section grit channel with associated Hydraulic jump flume

flow control.



As with the rectangular channel there are various optimisation strategies to guide the design of a suitable value for . Here we shall illustrate the

process based on the “right” parabola. This is a parabolic cross section channel for which the width of the liquid surface at maximum flow is equal to the depth of liquid over its invert, . Substituting for

in equation 33 yields the following relationship for the surface width

at maximum flow

- 34

Substituting for in equation 32 yields the following relationship for

the proportionality constant for a “right” parabolic section channel, .

- 35

Returning to the general parabolic section the flow area as a function of height over the invert is given by equation 36

- 36

and the hydraulic radius is given by equation 37

- 37

Design of the hydraulic jump flume

Plan and elevation diagrams of a hydraulic jump flume are shown in figure 4 over leaf.

The design of a hydraulic jump flume is based on an energy analysis of the flow. This is simply the application of Bernoulli’s theorem to the geometry of the flow. The specific energy or head in the approach section above a datum of the channel bottom in the approach section is given by equation 38

- 38

Where is the potential energy or static head and the second term on the right is the kinetic energy or velocity head. The term is commonly characterised as the “mechanical energy” or the “total head” simply to distinguish it from the thermal energy that the flow might possess. It is usual to assume that the flume is frictionless in this analysis. Thus there is no exchange between mechanical and thermal energy and it can be stated that mechanical energy is conserved. Using this assumption it is possible to write equation 39 for the mechanical head in the flume itself, , in terms of

the flow and flume dimensions and volumetric flow.



- 39

To achieve critical flow in the throat of the flume it is necessary to minimise the total head. The conditions at the minimum total head can be found by first differentiating equation 39 with respect to , the depth of water over

the sill or crest of the flume.

- 40

Setting this equal to zero and rearranging produces the following expression for the dimensions of the flume throat required to achieve minimum specific energy in the throat

- 41

This result can now be substituted into the equation 39 to yield the following relationship for the total head in the throat.

- 42

It is necessary to match height of the base (invert) of the parabolic channel to the height of the sill. Failure to do this results in significant degradation of the constant velocity properties of the channel.

Under these circumstances equation 38 can be rewritten in terms of the depth of water in the parabolic CV channel.

Ha

hcv

s

hf

EaEf

wfwcv

Sill or Crest

Throat

Approach

section

Recovery section

or

Apron

a. Plan view

b. Side elevation

Grit hopper

Figure 4 Plan and sectional elevation views of a typical hydraulic jump flume flow

control flume.



- 43

These last three equations can be combined to yield a relationship between the width and sill height of the flume. In order to specify a weir for flow control over the desired range a pair of energy balances are required one for max controlled flow the other for minimum. The resultant pair can be solved iteratively for the width and height of sill.

Bendy Channel

The bendy channel, figure 5, and the aerated grit box, described in the next section, function by setting up a secondary, helical flow pattern. In the bendy channel this is achieved by exploiting the Dean effect. As a fluid passes round a bend a secondary motion is imparted to the flow due to the action centripetal forces. These are the same forces, which cause rivers to excavate deep channels on the outsides of bends whilst depositing alluvium on the inner sides. The bendy channel is no more than a rectangular cross section channel with a carefully engineered bend and strategically placed hopper. The secondary motion sweeps the grit to the hopper from where it is recovered. The bendy channel has a significant advantage over all other devices discussed here and that is the absence of any mechanical intrusions into the flow path. This means that grit removal can be positioned ahead of screening, hence minimising the grit content of the PSS captured on the screens. This advantage may seem trivial however in the context of waste water treatment the cost of disposal of PSS is high, as it is classed as hazardous waste, and charged per unit mass. Grit on the other hand can be washed and sold.

Aerated grit box

The aerated grit box develops the secondary helical flow pattern by careful orientation of the inlet. The feed typically enters near and parallel to the floor of the box. The flow is also directed at a large angle relative to the box’s longitudinal axis. The helical motion is then sustained by asymetric

feed flow

grit

discharge

Figure 5 Schematic plan of a bendy channel.



aeration on the “rising” side of the chamber. The floor of the box slopes towards an axially orientated trough positioned directly below the aerator. The trough itself is fitted with an auger or similar equipment to convey the grit to one end of the chamber and eventually out of the process flow. Additional part height baffles within the tank control the flow pattern and minimise bypassing.

Detritor

Figure 6 Schematic plan of a detritor.

feed flow

grit hopper

air

feed flow

De-gritted

flow

grit

discharge

flow

straignteners

grit rake

grit hopper

discharge weir

rake

rotation

Figure 7 Schematic diagram of aerated grit box.



The detritor, figure 5, is a small sedimentation tank which operates in a mixture of cross flow and up flow. The flow enters the vessel through a wide circumferential inlet which extends the full depth of the device. The inlet is partially occluded by a set of vanes, which attempt to straighten the incoming flow and distribute it evenly across the device. Under the more quiescent conditions of the main vessel grit settles to the floor. The floor is provided with a heavy duty rake to draw the settled grit progressively toward the circumference of the vessel and thence to the grid hopper. The de-gritted water is then discharged over a partial weir to the remaining processes.

notes grit removal

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