Lecture_11__Turbomachines-2.ppt

TURBOMACHINES [ physical physical interpretation: what are we doin today! today! "



Turbomachines Turbo machines are fluid machines that are based on a spinning rotor 



The rotor will typically have blades deflectors or buc!ets on it to effect interaction with the fluid



"e can loosely divide turbomachines into two categories pumps and turbines



#umps add energy to the fluid f luid and turbines remove it

TURBOMACHINES [ physical physical interpretation: what are we doin today! today! "



"ho cares$

TURBOMACHINES [ radial# $i%ed# and a%ial &low $achines "



Turbomachines can be further subdivided into three other categories depending on whether they are radial mi%ed flow or a%ial flow configurations



This is defined by the manner in which the flow moves relative to the machine rotor  radial flow turbomachine



a%ial flow turbomachine

&n radial flow machines there e%ists a significant radial flow component at the inlet e%it or both -- in mi%ed 'not pure radial( machines the flow can have some radial and a%ial components through the rotor row

TURBOMACHINES [ centri&'al p'$ps "



)entrifugal pumps represent one of the most common radial flow turbomachines



There are two main components to the machine a rotating impeller and a stationary housing or *volute+ a centrifugal pump

TURBOMACHINES [ centri&'al p'$ps "





 ,s the impeller rotates it pulls fluid in through the eye at its centre and then is thrown radially outward to the walls of the casing The casings are generally shaped to reduce the velocity and !inetic energy of the flow converting this to a gain in pressure energy a centrifugal pump



#umps can be single or double suction 'double suction reduces inlet velocity(



#umps can also be single or multistage --- discharge from the first impeller flows into the eye of the second stage each stage augments the pressure

TURBOMACHINES [ centri&'al p'$ps: theory "



For analysis we simplify the three dimensional unsteady flow in a pump to a steady 'in the mean( one dimensional flow



"e consider simple vector triangles to resolve the velocity directions and magnitudes at pump inlet and outlets a centrifugal pump

TURBOMACHINES [ centri&'al p'$ps: theory "



The absolute velocity  of the flow entering or leaving the passage is a vector sum of the blade velocity . and the relative velocity " /"0.

- 12

where



.1 / r 1ω

- 42

.4 / r 4ω

- 32

here 1 denotes entrance conditions and 4 denotes e%it

TURBOMACHINES [ centri&'al p'$ps: theory "



"e !now from the moment of momentum euation that the torue reuired to rotate the pump impeller is given by - 62

- 52



here the θ1 and θ4 are the tangential components of the absolute velocities 1 and 4

TURBOMACHINES [ centri&'al p'$ps: theory "



uantification of the power added to the fluid by the pump can be easily had by e%amining the following



"e !now - 2



subbing in our e%pression 52 for Tshaft - 72



which we can write 'employing . / ωr( - 82



82 shows us how power is transferred to the fluid

TURBOMACHINES [ centri&'al p'$ps: theory "



&t is also important for us to uantify the head a pump supplies to a fluid this can be had via 92 - 92



combining 92 with 82 we can write - 1:2



1:2 represents the ideal head rise a fluid e%periences in passing through a pump



"e reali;e that this amount will be ultimately compromised by the head losses through the pump components

TURBOMACHINES [ centri&'al p'$ps: theory: net positi(e s'ction head )N*SH+ "



#ressures can become very low on the suction side of a pump



&n some situations pressures can drop to below the vapor pressure of the fluid at this pressure bubbles will form in the liuid and the liuid will effectively *boil+ at the current temperature



)avitation can significantly reduce efficiency and cause the pump structural damage



&t is the difference between the total head on the suction side near the pump impeller inlet ps?γ  0 4s?4g and the liuid vapor pressure head p v?γ  that characteri;es the potential for cavitation



This difference is called the  where - 112



There are two types of  the reuired @ and the available  ,

TURBOMACHINES [ centri&'al p'$ps: theory: net positi(e s'ction head )N*SH+ "







The @ refers to that amount of head that must be maintained or e%ceeded to avoid cavitation The  , refers the head that actually occurs for the entire hydraulic system we can determine this value by calculation if the system parameters are !nown otherwise it is determined from e%periment &f we apply the energy euation between the liuid free surface and s uction side of the impeller we get - 142



"here ΣhA represents the losses from the free surface to the impeller inlet



Therefore the head available at the inlet is

- 132

TURBOMACHINES [ centri&'al p'$ps: theory: net positi(e s'ction head )N*SH+ "



Then we can say - 162



Then we can say that to successfully avoid cavitation - 152



"e learn from 162 that as the pump elevation ; or h A increase the  , decreases thus there is always a finite height 'above some datum( at which the pump will not operate

TURBOMACHINES [ centri&'al p'$ps: theory: net positi(e s'ction head )N*SH+: e%a$ple "

,I-EN: "ater is pumped at :B5 cfs at this flowrate the @ is 15 ft water temperature is 8: oF and atmospheric pressure is 16B7 psi

RE./:

Cetermine the ma% height above the water free surface ;1 that the pump can be situated to avoid cavitation D the only loss to be considered is the inlet filter that has a loss coefficient EA/4:

TURBOMACHINES [ centri&'al p'$ps: theory: net positi(e s'ction head )N*SH+: e%a$ple "

SO0U: 1B "e !now the available can be computed

- 12

4B Gur ma% elevation will occur when the limiting condition of  ,/@ - 42

3B The only headloss we have to consider is the minor loss so let us pic! up the velocity - 32

TURBOMACHINES [ centri&'al p'$ps: theory: net positi(e s'ction head )N*SH+: e%a$ple "

SO0U: 6B The velocity then - 62

5B  is deemed the head rise coefficient ) P is the power coefficient and of course η represents the efficiency

TURBOMACHINES [ centri&'al p'$ps: theory: p'$p para$eters and si$ilarity laws "



"e observe from the preceding e%pressions 1-182 that the typically high @eynolds numbers that are associated with pumped flows will render the last pi term negligible and relative roughness pi term will also be neglected on the basis of the highly irregular shape of the pump casing being the governing geometric factor 



This said we can say that the similarity laws may be e%pressed as

- 192

- 4:2

- 412



>ere we call the brac!eted term the flow coefficient ) - 442

TURBOMACHINES [ centri&'al p'$ps: theory: p'$p para$eters and si$ilarity laws "



ere subscripts 1 and 4 refer to two geometrically similar pumps



The e%istence of these pump scaling laws allow us to utili;e laboratory data to predict different operating conditions

TURBOMACHINES [ centri&'al p'$ps: theory: p'$p para$eters and si$ilarity laws "



#ictured above we have typical performance data for a 14 inch impeller centrifugal pump 'left( and dimensionless characteristic curves that represent a family of geometrically similar pumps

TURBOMACHINES [ centri&'al p'$ps: theory: p'$p para$eters and si$ilarity laws: e%a$ple "

,I-EN:

RE./:

,n 8 inch centrifugal pump operating at 14:: rpm is geometrically similar to the 14 inch pump depicted in the performance characteristic curves shown in the figure belowB ,ssume the 14 inch pump is operating at 1::: rpm and water is the wor!ing fluid at : oF

For pea! efficiency predict the discharge actual head rise and shaft horsepower for the smaller pump

TURBOMACHINES [ centri&'al p'$ps: theory: p'$p para$eters and si$ilarity laws: e%a$ple "

SO0U:

1B