1. Turbomachines are fluid machines that are based on a spinning rotor
[ physical interpretation: what are we doing today? ]
Turbomachines are fluid machines that are based on a spinning rotor
The rotor will typically have blades, deflectors, or buckets on it to effect interaction with the fluid
We can loosely divide turbomachines into two categories, pumps and turbines
Pumps add energy to the fluid and turbines remove it
Fluid Mechanics

2. Who cares? TURBOMACHINES
[ physical interpretation: what are we doing today? ]
Who cares?
Fluid Mechanics

3. radial flow turbomachine axial flow turbomachine
TURBOMACHINES
[ radial, mixed, and axial flow machines ]
Turbomachines can be further subdivided into three other categories depending on whether they are radial, mixed flow, or axial flow configurations
This is defined by the manner in which the flow moves relative to the machine rotor
radial flow turbomachine
axial flow turbomachine
In radial flow machines, there exists a significant radial flow component at the inlet, exit, or both -- in mixed (not pure radial) machines, the flow can have some radial and axial components through the rotor row
Fluid Mechanics

4. TURBOMACHINES
[ centrifugal pumps ]
Centrifugal 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
Fluid Mechanics

5. TURBOMACHINES
[ centrifugal pumps ]
As 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 kinetic energy of the flow, converting this to a gain in pressure energy
a centrifugal pump
Pumps can be single or double suction (double suction reduces inlet velocity)
Pumps can also be single or multistage --- discharge from the first impeller flows into the eye of the second stage, each stage augments the pressure
Fluid Mechanics

6. TURBOMACHINES
[ centrifugal pumps: theory ]
For analysis, we simplify the three dimensional, unsteady flow in a pump to a steady (in the mean) one dimensional flow
We consider simple vector triangles to resolve the velocity directions and magnitudes at pump inlet and outlets
a centrifugal pump
Fluid Mechanics

7. here 1 denotes entrance conditions and 2 denotes exit
TURBOMACHINES
[ centrifugal pumps: theory ]
The absolute velocity, V, of the flow entering or leaving the passage is a vector sum of the blade velocity, U, and the relative velocity W
V = W + U
- [1]
where:
U1 = r1w
- [2]
U2 = r2w
- [3]
here 1 denotes entrance conditions and 2 denotes exit
Fluid Mechanics

8. TURBOMACHINES
[ centrifugal pumps: theory ]
We know from the moment of momentum equation that the torque required to rotate the pump impeller is given by
- [4]
- [5]
here the Vq1 and Vq2 are the tangential components of the absolute velocities V1 and V2
Fluid Mechanics

9. subbing in our expression [5] for Tshaft
TURBOMACHINES
[ centrifugal pumps: theory ]
Quantification of the power added to the fluid by the pump can be easily had by examining the following
We know
- [6]
subbing in our expression [5] for Tshaft
- [7]
which we can write (employing U = wr)
- [8]
[8] shows us how power is transferred to the fluid
Fluid Mechanics

10. combining [9] with [8] we can write
TURBOMACHINES
[ centrifugal pumps: theory ]
It is also important for us to quantify the head a pump supplies to a fluid, this can be had via [9]
- [9]
combining [9] with [8] we can write
- [10]
[10] represents the ideal head rise a fluid experiences in passing through a pump
We realize that this amount will be ultimately compromised by the head losses through the pump components
Fluid Mechanics

11. Pressures can become very low on the suction side of a pump
TURBOMACHINES
[ centrifugal pumps: theory: net positive suction head (NPSH) ]
Pressures can become very low on the suction side of a pump
In some situations pressures can drop to below the vapor pressure of the fluid, at this pressure bubbles will form in the liquid and the liquid will effectively “boil” at the current temperature
Cavitation can significantly reduce efficiency and cause the pump structural damage
It is the difference between the total head on the suction side near the pump impeller inlet, ps/g + V2s/2g, and the liquid vapor pressure head, pv/g that characterizes the potential for cavitation
This difference is called the NPSH, where
- [11]
There are two types of NPSH, the NPSH required, NPSHR and the NPSH available, NPSHA
Fluid Mechanics

12. Therefore, the head available at the inlet is
TURBOMACHINES
[ centrifugal pumps: theory: net positive suction head (NPSH) ]
The NPSHR refers to that amount of head that must be maintained or exceeded to avoid cavitation
The NPSHA refers the head that actually occurs for the entire hydraulic system, we can determine this value by calculation if the system parameters are known, otherwise it is determined from experiment
If we apply the energy equation between the liquid free surface and suction side of the impeller, we get
- [12]
Where ShL represents the losses from the free surface to the impeller inlet
Therefore, the head available at the inlet is
- [13]
Fluid Mechanics

13. Then we can say that to successfully avoid cavitation
TURBOMACHINES
[ centrifugal pumps: theory: net positive suction head (NPSH) ]
Then we can say
- [14]
Then we can say that to successfully avoid cavitation
- [15]
We learn from [14] that as the pump elevation, z, or hL increase, the NPSHA decreases, thus there is always a finite height (above some datum) at which the pump will not operate
Fluid Mechanics

14. TURBOMACHINES
[ centrifugal pumps: theory: net positive suction head (NPSH): example ]
GIVEN:
Water is pumped at 0.5 cfs, at this flowrate the NPSHR is 15 ft, water temperature is 80oF and atmospheric pressure is 14.7 psi
REQD:
Determine the max height above the water free surface, z1 that the pump can be situated to avoid cavitation – the only loss to be considered is the inlet filter that has a loss coefficient KL=20
Fluid Mechanics

15. 1. We know the available NPSH can be computed
TURBOMACHINES
[ centrifugal pumps: theory: net positive suction head (NPSH): example ]
SOLU:
1. We know the available NPSH can be computed
- [E1]
2. Our max elevation will occur when the limiting condition of NPSHA=NPSHR
- [E2]
3. The only headloss we have to consider is the minor loss, so let us pick up the velocity
- [E3]
Fluid Mechanics

16. SOLU: 4. The velocity then - [E4] 5. Now we can solve for hL - [E5]
TURBOMACHINES
[ centrifugal pumps: theory: net positive suction head (NPSH): example ]
SOLU:
4. The velocity then
- [E4]
5. Now we can solve for hL
- [E5]
6. Now we pick up the vapor pressure and specific weight at 80oF from tabulated values, and solve for z1max
- [ans]
Fluid Mechanics

17. TURBOMACHINES
[ centrifugal pumps: theory: pump parameters and similarity laws ]
We have learned that the principal dependent pump variables are the actual head rise, ha, the shaft power, Wdotshaft, and of course the pump efficiency, h
It is reasonable to expect that these variables will depend on the geometrical configuration which we would typically represent by a characteristic diameter, D, and other relevant lengths, li; other important variables would include the flowrate, Q, the shaft rotational speed, w, the fluid viscosity, m, and finally, the fluid density, r
The results of dimensional analysis, show us that three primary parameters will emerge from the variables mentioned above, CH, CP, and h
Fluid Mechanics

18. TURBOMACHINES
[ centrifugal pumps: theory: pump parameters and similarity laws ]
Where
- [16]
- [17]
- [18]
CH is deemed the head rise coefficient, CP is the power coefficient, and of course, h represents the efficiency
Fluid Mechanics

19. This said, we can say that the similarity laws may be expressed as
TURBOMACHINES
[ centrifugal pumps: theory: pump parameters and similarity laws ]
We observe from the preceding expressions [16-18], that the typically high Reynolds 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 expressed as
- [19]
Here, we call the bracketed term, the flow coefficient, CQ
- [20]
- [22]
- [21]
Fluid Mechanics

20. Here, subscripts 1 and 2 refer to two geometrically similar pumps
TURBOMACHINES
[ centrifugal pumps: theory: pump parameters and similarity laws ]
Now we can say that if two pumps are operated at the same flow coefficient
- [23]
Here, subscripts 1 and 2 refer to two geometrically similar pumps
then
The existence of these pump scaling laws allow us to utilize laboratory data to predict different operating conditions
- [24]
- [25]
- [26]
Fluid Mechanics

21. TURBOMACHINES
[ centrifugal pumps: theory: pump parameters and similarity laws ]
Pictured above we have typical performance data for a 12 inch impeller centrifugal pump (left) and dimensionless characteristic curves that represent a family of geometrically similar pumps
Fluid Mechanics

22. TURBOMACHINES
[ centrifugal pumps: theory: pump parameters and similarity laws: example ]
GIVEN:
An 8 inch centrifugal pump operating at 1200 rpm is geometrically similar to the 12 inch pump depicted in the performance characteristic curves shown in the figure below. Assume the 12 inch pump is operating at 1000 rpm and water is the working fluid at 60oF
REQD:
For peak efficiency predict the discharge, actual head rise, and shaft horsepower for the smaller pump
Fluid Mechanics

23. 2. So, at peak efficiency, CQ=0.0625, therefore for our 8 inch pump
TURBOMACHINES
[ centrifugal pumps: theory: pump parameters and similarity laws: example ]
SOLU:
1. Now, we have learned, for a geometrically similar family of pumps, the flow coefficient will have the same value for the same efficiency
2. So, at peak efficiency, CQ=0.0625, therefore for our 8 inch pump
- [E1]
- [ans]
Fluid Mechanics

24. TURBOMACHINES
[ centrifugal pumps: theory: pump parameters and similarity laws: example ]
SOLU:
3. Now, we can pick up the actual head rise and shaft horsepower following the same methodology, as at peak h, CH=0.19, and CP=0.014
thus
- [ans]
- [ans]
Fluid Mechanics

25. TURBOMACHINES
[ centrifugal pumps: theory: pump parameters and similarity laws: example ]
SOLU:
4. We just solved for shaft horsepower (supplied to the shaft), now we seek to determine the power actually acquired by the fluid
- [E2]
5. From this we can compute the pump’s efficiency, h
- [E3]
thus, this corroborates our graphical finding earlier in the solution !
Fluid Mechanics

26. This dimensionless parameter, Ns, is called the specific speed
TURBOMACHINES
[ centrifugal pumps: theory: pump parameters and similarity laws: specific speed ]
The diameter, D, can be eliminated when the flow coefficient and head rise coefficient are combined
- [26]
This dimensionless parameter, Ns, is called the specific speed
It is customary to specify a value of specific speed at the flow coefficient corresponding to peak efficiency
Pumps with low flows and high heads will have lower specific speeds
Pumps with high flows and low heads will have higher specific speeds
The specific speed, Ns, is used to help determine which pump type is most appropriate for a given application
Fluid Mechanics

27. TURBOMACHINES
[ centrifugal pumps: theory: pump parameters and similarity laws: specific speed ]
- [26]
If the flowrate, head, and speed are specified, Ns can be computed and appropriate pump type can be selected
Fluid Mechanics

28. TURBOMACHINES
[ turbines: a brief look ]
Most turbines are classified as either “impulse” or “reaction” turbines
An impulse turbine is driven by a tangential inflow, the total head of this flow (elevation, pressure, velocity), is converted to velocity head at the exit of the flow supply nozzle
There is no pressure drop across the rotor in an impulse turbine (all of the pressure drop occurs at the nozzle)
A reaction turbine is driven by an axial flow, the rotor in a reaction turbine experiences a large static pressure drop
impulse turbine
reaction turbine

29. intercooled, double stage compressor
TURBOMACHINES
[ turbines: a brief look ]
A Pelton Wheel is an example of an impulse turbine, you can find one in your lawn sprinkler
An automotive turbocharger is an example of a reaction turbine (gas compressor)
single stage turbo
intercooled, double stage compressor