Non Clogging Centrifugal Pump

Final Year

Project Proposal

Abdul Hannan

To design and develop a non-clogging pump for the sewage system with improved energy efficiency.

Group # 01

Abdul Hannan

Hassan Mahmood

Taha Mustahsan

Fakhar Anwaar

Adnan Ali

DESIGN PROCEDURE

Many design procedures are available for the calculations of impeller and volute but the widely acceptable is the one mentioned in “Impeller Pumps by Stephen Lazarkiewicz and Adam T. Troskolanski”, the details of which have been completely given below.

IMPELLER DESIGN

From Euler’s fundamental equation it follows that the total head generated by a pump depends on many variables such as the peripheral velocity u2 and the meridional velocity cm2 at the impeller outlet, the blade angle β2, the number of blades z, the ratio cu2/cu3

and the ratio d1/d2.

The same total head may be attained with a smaller peripheral velocity u2, by using an impeller of smaller diameter (keeping the same rotational speed n) but having a greater angle β2 and a eater number of blades z. Evidently, the problem of calculating the dimensions of an impeller and hence of the whole pump for a given total head may have several solutions but they are not likely to be of equal merit when considered from the point of view of efficiency and production costs.

There is only Euler’s equation to help in solving this problem so it is necessary to assume the values of some of these variables. Optimum results are most likely to be obtained for given operating conditions when the variables are chosen on the basis of experimental tests on existing pumps which have given high efficiencies. Their values depend on the specific speed ns and the spouting velocity corresponding to the total head H (as in design of water turbines). The meridional velocities for the impeller inlet and outlet may be chosen with the formulae

Cm1=K cm 1√2gh ................................................................................ (i)

Cm2=K cm 2√2gh .................................................................................. (ii)

Where K cm 1and K cm 2 are the respective velocity coefficients.

The velocities given by this method should not be regarded as final, they only serve as a guide. If more recent date is known to give better results, these should be used.

Calculation of the dimensions of pumps may also be based on the results of tests on model pumps.

Impellers with blades of single curvature are among the simplest .They are used in pumps with low specific speeds ns<30 and discharges of up to app. 500 m3/h.

CALCULATIONS OF THE DIMENSIONS OF THE IMPELLER.

IMPELLER INLETa) Impeller eye inlet diameter do.

The diameter of the shaft dsh is required before the diameter of the hub dh can be determined.

The shaft diameter depends on the power it transmits and also on the value of the critical speed and the maximum permissible deflection of the shaft, which intern is connected with the type and construction of the pump.

The diameter of the hub on the inlet side is made as small as possible. So that the flow into the impeller eye is restricted as little as possible.

Usually the hub diameter is chosen according to

dh = (1.3-1.4) dsh...............................................................................................................................(iii)

The part of the hub at the back of the impeller is usually made somewhat larger in diameter, viz

dh’= (1.35-1.5)dsh.............................................................................................................................. (iv)

After determining the hub diameter the inlet diameter of the impeller eye Do can be chosen.

The free area at the eye is given by Ao= Q’/co, where Q’=Q/nv is the impeller flow including any internal leakage through the neck rings on the suction side of the impeller and through the balance holes in the back impeller shroud.

The total cross-sectional area of the inlet A’o exceeds the free area Ao by the cross-sectional area of the hub

ah=πdh2

4.............................................................................................................. (v)

so that

A’o= Ao+ ah.............................................................................................................. (vi)

The inlet diameter

do=√ 4 Ao

π..................................................................................................................

(vii)

b) Velocity of the impeller inlet

The values of the axial velocity co usually lies within the limits 1.5 to 6 m/sec although it can be as high as 12m/sec in pumps with high positive heads in their suctions. A more definite value is obtained by comparing the value co, with the value of the meridioanl component of the absolute velocity cm1, given by formula

Cm1=K cm 1√2gh

Where K cm 1is a velocity cofficient taken from the curve K cm 1=f (ns )

Graph of velocity coefficients Kcm1 and Kcm2 in relation to ns (A.J. Stepanoff)

For end suction pumps co = (0.9-1.0) Cm1. In pumps with an inlet elbow or suction chamber, through which the shaft passes, a somewhat lower value of co is used because of the disturbance of the flow caused by the rotating shaft and hence c 0= (0.8-0.9)cm1.

In U.S.S.R the inlet diameter is calculated from the empirical formula

don=(4.0−4.5) 3√ Qn

..............................................................................................(viii)

Where dondenotes the net inlet diameter in meters, without taking into account any

obstruction by the hub, Q discharge in m3

sec and n the rotational speed in r.p.m.

If the impeller inlet is restricted by a hub of diameter dh and area ah, the calculated diameter don should be increased accordingly.

c) Blade inlet angle 1 and width of the impeller at inlet b1.

Having obtained the inlet diameter d0, the diameter d1 is given according to the position and shape assumed for the blade inlet edge.

The peripheral velocity u1 for the diameter d1 is found from the formula

u1=π d1n/60......................................................................................................... (ix)

Assuming α1=90o the blade angle is calculated from the formula

tan1 =cm1/ u .......................................................................................................... (x)

Measurements carried out on centrifugal pumps have repeatedly shown that the discharge Qopt at the best efficiency point is less than that corresponding to the velocity of cm=u1tan1. This phenomenon is particularly marked when the diameter ratio d2/d1 is less than 2.0, i.e. with relatively short blades and large angles of 1.

In order to attain the required discharge it is found necessary to increase the blade angle 1 calculated from equation 6 by the angle of incidence (attack) 1=2-6o. Larger values of 1 are taken for smaller ratios of d1/d2 and larger calculated angles of 1 i.e. for shorter blades. Apart from this, it has been confirmed that exaggerating the inlet angle 1 improves the suction capacity of the pump and increases its efficiency. The angle of inclination of the blade is therefore chosen according to

1’= 1 + 1............................................................................................................................... (xi)

The inlet angle 1’ usually lies between 15o and 30o but in particular cases it may be as great as 45o.

After carrying out calculations, the inlet velocity triangle may be drawn. The area of the impeller inlet at entry to the blades is

A1=1Q '

cm1...............................................................................................................(xii)

Where 1 is a cofficient of constriction accounting for the reduction of the inlet area by the blades.

The breadth of the impeller at inlet is

b1=A1

π d1.............................................................................................................. (xiii)

The breadth b1is the diameter of the circle whose centre lies on the inlet edge of the blade at the diameterd1.

IMPELLER OUTLETa) Meridional velocity at impeller outletcm2.

The velocity at the outlet cm2 is taken as being somewhat less than the velocity at the inlet

cm2= (0.7−0.75)cm1

The value of velocity cm2 may be found by the equation

cm2=K cm 2√2gh

Where the velocity cofficientK cm 2 is taken from the graph.

b) Blade outlet angle 2.

The inclination of the blade at the outlet 2 is assumed to lie within the limits of 15o to 35o, usually of the order 25o.

The lower value of 2 is used in pumps of higher specific speed.

c) Peripheral velocity at the impeller outlet u2 and impeller diameter d2.

In order to determine the velocity u2, we use the fundamental equation for the impeller pumps in its general form

H th ∞=1g(u2 cu2−u1cu1)............................................................................. (xiv)

From the velocity triangle it follows that,

cu2=u2−cm2

tan❑2

............................................................................................. (xv)

Inserting this value into the fundamental equation, we obtain

gH th ∞=u2(u¿¿2−cm2

tan❑2

)¿-u1 cu1........................................................................... (xvi)

Or

u22-u2

cm2

tan❑2

=gH th∞+u1 cu1............................................................................ (xvii)

And hence

u2=cm2

2 tan❑2

±√¿¿........................................................ (xviii)

Only the positive value of the second term should be taken. Otherwise the velocity u2 will be negative.

If, as is customary, the angle α0=0 at the inlet, u1 cu1=0 ;hence

u2=c m2

2 tan❑2

+√¿¿.......................................................................(xix)

Taken into account the relations:

cu2=cu3 (1+Cp )∧H th ∞=H th (1+C p )................................................. (xx)

we obtain

u2=cm2

2 tan❑2

+√¿¿.................................................... (xxi)

Now we calculate the impeller diameter on the basis of the previously assumed value for the rotational speed , from the formula

u2=π d2n/60................................................................................................(xxii)

D2=60u2/ πn...................................................................................(xxiii)

Pfleiderer’s correction for a finite number of blades is taken as 1+C p=1.25−1.35 in preliminary calculations. After calculating D2 the assumed value of 1+C p may be checked and if necessary, a corresponding correction is made in the calculations of u2∧d2. After carrying out the calculations, we draw the outlet velocity triangle.

d) Impeller breadthb2.

We calculate the impeller outlet in a similar way to the inlet

A2=¿❑2

Q'cm2

¿..................................................................................................... (xxiv)

Where ❑2 is the outlet restriction coefficient.

The breadth of the impeller at outlet

b2=A2

π d2.............................................................................................................. (xxv)

The transition from the breadth b1 at the inlet to the breadth b2at outlet should be gradual, so that the velocity cm1 changes smoothly without any jumps.

The front shroud should be rounded to a radius of ≥ b1/2, in order to reduce the danger of flow separation.

REFERENCES

Pump theory and practice by V.K. Jain

Impeller pumps by Stephen Lazarkiewicz and Adam T. Troskolanski