ENERGY CONVERSION ES 832 a Eric Savory www

ENERGY CONVERSION ES 832 a Eric Savory www. eng. uwo. ca/people/esavory/es 832. htm Lecture 9 – Prime movers and turbomachinery Department of Mechanical and Material Engineering University of Western Ontario

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.

Pump classes and types Class Centrifugal (rotating impeller; increases the pressure energy of a fluid) Type Volute Diffuser Regenerative turbine Mixed flow Axial flow Rotary (positive displacement pump; produces the same volume output regardless of pressure) Gear Vane Cam and piston Screw Lobe Direct acting Diaphragm Rotary piston Reciprocating (pistons or plungers displace the fluid)

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

Pump types

Centrifugal pump cutaway schematic

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 - V 2/2 g

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:

• Power becomes: • The increase in Head is (Euler pump equation): • U 2 Vu 2 > U 1 Vu 1 – the device functions as a compressor • U 2 Vu 2 < U 1 Vu 1 – energy is extracted from the flow and the device function as a turbine

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

Centrifugalcompressor schematic and velocity triangles

• From figure (a) in previous slide, fluid enters the rotor with an absolute velocity that is completely radial (‘zero preswirl’), therefore, Vu 1 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:

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 K 2 (which depends on the exit angle 2) establishes the characteristics of the machine

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

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

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

The “Goulds 3196” family of pumps

Composite rating charts for the “Goulds 3196” family of pumps

Performance characteristics Symbol Parameter Imperial Units H Head (m) ft-lbf/lbm Q Flow rate (m 3/s) ft 3/s N Speed (rpm or rad/s) rpm η Mechanical efficiency none D Geometry (m) ft ρ Density (kg/m 3) lbm/ft 3 υ Viscosity (kg/ms) lbm/ft-s P Power (W) ft-lbf/s

Buckingham P theory A 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

Scaling relationships for turbomachines of the same geometry (=geometrical similarity) For a change in diameter only 3 5 For a rotational speed change only

Pumps in series and parallel Series Equivalent pump Parallel Equivalent pump

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.

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.

Pump-system operation System resistance (losses) curves (typically H Q 2) C = operating point

Jet propulsion

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

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

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

Jet Types and Uses Type Description Advantages Disadvantages Thermojet A piston engine is used to run the compressor. Works like a regular turbojet minus the turbines. Heavy, inefficient and underpowered Turbojet Generic term for simple turbine engine Simplicity of design Very basic. Does not take advantage of improved efficiency of other designs. Turbofan Uses an enlarged first stage compressor as a 'fan' to provide more thrust. Quieter, more efficient for subsonic airspeeds. More complex, large diameter, heavy, subject to foreign object damage. Ramjet No moving parts. Intake air is Lightweight, efficient Needs high speed to operate, only compressed by the above Mach 2. 0. efficient in a narrow speed airspeed and duct shape. range, used as accessory? Turboprop Not really a jet. A gas turbine driving a propeller. Propfan Turboprop engine with one or Very high fuel more propellers. Like a efficiency, turbofan without ducts. higher speed. Very complex, more noisy than turbofans. Scramjet Intake air is compressed but not slowed to subsonic. Intake, combustion and exhaust occur in a single constricted tube Still in development. Need to be above Mach 6 to operate. Cooling problems. High efficiency at low speed (300450 knots) Operates at very high speed (Mach 8 -15). Limited top speed, noisy, complex propeller drive and gearbox.

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

Principles - Physical • Newton’s 3 rd 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.

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/s 2. • Approximate equation for net thrust of a jet engine:

Principles - Chemical • Kerosene is usually used to power Jets in the form of Avtur, Jet-A 1, 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 C 12 to C 15 range.

Principles - Thermodynamic

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.

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.

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 – 15 W to 20 W output. • Flying humans: – Tiny jet engines combined with a wing-suit.