ENERGY CONVERSION MME 9617A Eric Savory www.eng.uwo.ca/people/esavory/mme9617a.htm Lecture 9 – Prime movers and turbomac

1. ENERGY CONVERSION MME 9617A Eric Savory www.eng.uwo.ca/people/esavory/mme9617a.htm Lecture 9 – Prime movers and turbomachinery Department of Mechanical and Material Engineering University of Western Ontario

2. Definition • Turbomachinery describes machines that transfer energy between a rotor and a fluid, including both turbines and compressors. • A turbine transfers energy from a fluid to a rotor, a compressor transfers energy from a rotor to a fluid. • The two types of machines are governed by the same basic relationships including Newton's second law of motion and Euler's energy equation. • Centrifugal pumps are also turbomachines that transfer energy from a rotor to a fluid, usually a liquid. • Energy is converted from kinetic to potential and vice versa with the ‘aid’ of mechanical energy.

3. Pump classes and types

4. Positive displacement pumps: External gear pump Reciprocating piston Double screw pump Sliding vane Three-lobe pump (left) Double circumferential piston (centre) Flexible tube squeegee (peristaltic)

5. Pump types

6. Centrifugal pump cutaway schematic

7. Formulation of the concept • We will focus on the ‘centrifugal pump’. However, the principles are the same for compressors and turbines with a geometry change and appropriate boundary conditions. • The dominant direction of the flow during the energy transfer process is radial. • Rotor (impeller) – rotating element where the energy transfer process occurs. • Diffuser – stationary element which is responsible for the transformation of the velocity head into static pressure. • Velocity head - V2/2g Centrifugal pump with volute and diffuser

8. Energy transfer mechanism • The energy transfer mechanism results from the change in angular momentum of the fluid: • The torque on the shaft is: • Where Vu denotes the component of the vector V in the direction of U, the tangential wheel speed (at a given U=rw), assuming steady-state frictionless flow. • Further assumptions of uniform flow at the inlet and outlet and an ‘effective’ mean radius, give:

9. Power becomes: • The increase in Head is (Euler pump equation): • U2Vu2 > U1Vu1 – the device functions as a compressor • U2Vu2 < U1Vu1 – energy is extracted from the flow and the device function as a turbine

10. The velocity triangle • V - absolute velocity • U - tangential velocity • Vr - relative velocity

11. Centrifugal-compressorschematicandvelocitytriangles

12. From figure (a) in previous slide, fluid enters the rotor with an absolute velocity that is completely radial (‘zero pre-swirl’), therefore, Vu1 is zero. The increase in Head is: • Denoting the radial component of the exit velocity as Vm, then: • And from the exit velocity triangle fig. (c): • For an impeller of width w, the volume flow rate is:

13. Head (H) versus Volume flow rate (Q) relationships • The increase in Head is a function of the volumetric flow rate, Q: • Defining: • We obtain: • The sign on K2 (which depends on the exit angle 2) establishes the characteristics of the machine

14. H - Q characteristics Three separate cases can be considered: (1) Radial exit blades (b2 = 90o) (2) Backward-curved blades (b2 < 90o) (3) Forward-curved blades (b2 > 90o) “Ideal” H versus Q curves

15. Actual H - Q relationships Losses inside pump (e.g. friction and turning losses) Head H Volume flow rate Q

16. Manufacturer’s pump characteristics Index of pumps from Goulds Pumps Inc

17. The“Goulds 3196”family of pumps

18. Composite ratingcharts for the“Goulds 3196”family of pumps

19. Performance characteristics

20. Buckingham P theoryA dimensional analysis of all the variables involved yields a number of non-dimensional groups called  parameters: Note that although the viscosity  is an appropriate parameter to include and it yields the Reynolds number (4), in practice this is not a dominant parameter for turbomachine scaling analysis

21. Scaling relationships for turbomachines of the same geometry (=geometrical similarity) 3 5

22. Pumps in series and parallel Series Equivalent pump Parallel Equivalent pump

23. Pumps in Series Add the heads (H) at each flow rate (Q) For example, for two identical pumps the head will be double that of a single pump.

24. Pumps in Parallel Add the flow rates (Q) at each head (H) For example, for two identical pumps the flow rate will be double that of a single pump.

25. Pump-system operation System resistance (losses) curves (typically H  Q2) C = operating point

26. Jet propulsion

27. History – Before Turbojets Thermojet Henri Coandă 1910 Aeolipile Hero of Alexandria 75 A.D. Rocket Chinese Taoist Chemists 1st Century

28. History – The First Jets Hans Von Ohain Frank Whittle Test engine - 1937 Test engine - 1935 W.1 Turbojet - 1939 He S-3 - 1938

29. History – More Modern Jets Centrifugal Compressor Turbojet - Used by Whittle & Ohain - Short and fat - Must bend the airflow • Axial Flow Compressor Turbojet • Introduced by Anselm Franz • (Junkers' Engine Div.) ~ 1944 • Long and thin • - Improved airflow

30. Jet Types and Uses

31. Principles - Physical Major Components of a Jet Engine • Fan • Compressor • Combustor • Turbine • Mixer / Nozzle

32. Principles - Physical • Newton’s 3rd Law of Motion: • For every action there is an equal and opposite reaction. • Boyle’s Law: • there is a relationship between the pressure of a fixed amount of air and its volume.

33. Principles - Physical • Power is measured in pounds (lb) of thrust (or Newtons of thrust: 4.45 N=1 lb). • 1 lb of thrust means that the engine will be able to accelerate one pound of material at 32 ft/s2. • Approximate equation for net thrust of a jet engine:

34. Principles - Chemical • Kerosene is usually used to power Jets in the form of Avtur, Jet-A, Jet-A1, Jet-B, JP-4, JP-5, JP-7, or JP-8. • Kerosene is obtained from the fractional distillation of petroleum at 150°C and 275°C • Kerosene consists of carbon chains from the C12 to C15 range.

35. Principles - Thermodynamic

36. Efficiency • Thermal Efficiency: • 45% - 50% for today’s best engines. • Propulsive Efficiency: • About 47% for low by-pass turbojets. • About 80% for high by-pass turbofans. • Overall Efficiency: • About 40% for modern jets at cruise speed.

37. Future of Jets ? • Small, personal jet aircraft using highly efficient jet engines. • High speed, high altitude jet aircraft. • Engines to be cooled by new coal derived jet fuel.

38. Future of Jets ? • MEMS Turbines (Power on a Chip): • Turbine blades span an area smaller than a dime. • Run for 10+ hrs on a container of diesel fuel about as big as a D battery. • Also could be used to power tiny planes for the military • 15W to 20W output. • Flying humans: • Tiny jet engines combined with a wing-suit.