Slides for ME 115 Steam Turbine Review Steam turbine and its representation on a T-s diagram (Thermodynamics 4th ed., Cengel and Boles, Figure 6-50) Week 2 notes Review steam turbine principles and T-s diagram Significance of pressure difference Definition and significance of isentropic turbines; Actual work and isentropic efficiency, 2nd law of thermo Shaft work (units? W, HP, Btu/hr, etc…), energy balance Superheat, saturated vapor, saturated mixture, saturated liquid, liquid T-P dependence in vapor dome What-ifs: Can exhaust be superheated, saturated, liquid?

Slides for ME 115 Basic Equations

Slides for ME 115 Engine Basics Dynamometer: Measures RPM and torque of steam turbine shaft and applies load. Torque: a force acting through a radius; common units ft lbf Brake (shaft) horsepower: derives its name from the fact that the power output of an engine can be measured using a dynamometer to apply a torque to resist the turning of a shaft What are RPM and torque? Revolutions per minute, and force x radius Shaft work has dimensions of (Power = Energy per time = Force x distance per time), RPM has dimensions of (per time), and torque (Force x distance). Therefore, shaft work is proportional to RPM x torque. The exact formula is: Shaft work = 2(rev per second) x Torque OR HP = RPM x torque/5252 Load is resistance. Changing load changes torque for a given RPM. All engines/turbomachinery exhibit their maximum power and efficiency at their optimum torque and rpm conditions.

Engine Basics Efficiency changes with bhp. Slides for ME 115 Engine Basics Efficiency changes with bhp. The maximum efficiency will occur at different bhp’s for different RPM’s. Rated power Efficiency RPM1 RPM2

Temperature and Pressure Measurements Slides for ME 115 Temperature and Pressure Measurements Temperature Thermocouples: voltage changes with temperature Thermistors and RTDs: resistance change with temperature Thermometers Pressure Manometers Transducers

Temperature Sensors Industrial thermocouples Slides for ME 115 Temperature Sensors Industrial thermocouples Various thermocouple bead styles Thermocouple probes Talk about each sensor and mechanisms for a few minutes. Thermometers Thermistors

Thermocouple Basics Seebeck effect Slides for ME 115 Thermocouple Basics Seebeck effect If two wires of dissimilar metals are joined at both ends and one end is heated, current will flow. If the circuit is broken, there will be an open circuit voltage across the wires. Voltage is a function of temperature and metal types. For small DT’s, the relationship with temperature is linear For larger DT’s, non-linearities may occur. Vertical Axis: Millivolts generated, Bottom axis: Temperature difference from 32 deg F Point out different metals and that fact that some of them generate positive or negative EMFs. Best thermocouples pair positive slope material with negative slope one for maximum resolution T: copper-constantan J: Iron-constantan K: Chromel-alumel

Slides for ME 115 Thermocouple Basics If you attach the thermocouple directly to a voltmeter, you will have problems. You have just created another junction! Your displayed voltage will be proportional to the difference between J1 and J2 (and hence T1 and T2). Note that this is “Type T” thermocouple. www.omega.com

External Reference Junction Slides for ME 115 External Reference Junction A solution is to put J2 in an ice-bath; then you know T2, and your output voltage will be proportional to T1-T2. Handheld thermocouple readers and computer data acquisition systems use something called an isothermal block instead to perform this task.

Comparison of Pressure Instruments Slides for ME 115 Comparison of Pressure Instruments Characteristics Manometer Transducer Dial gauge Overall Inherently accurate Automation friendly Poor precision Electronic output No Yes Temperature range Approx. -50°C to +50°C Approx. -200°C to +400°C Frequency response < 10 Hz < 1 MHz Cost $100-$2000 $50-$10,000 $10-$3000

Manometer Basics Pressure varies with depth for constant density fluid Slides for ME 115 Manometer Basics Pressure varies with depth for constant density fluid P2 P1 H Manometer fluid This relation holds regardless of cross-sectional area of container tube

Manometers/Micromanometers Examples Slides for ME 115 Manometers/Micromanometers Examples (b) Micromanometer (c) Inclined U-tube manometer: Measures pressure difference between pressure taps by displaying difference in fluid heights. High pressure should be connected to side with reservoir. Reservoir is of larger diameter so that its height stays relatively constant. Surface tension effects need to be accounted for in small diameter tubes. Fluid is oil or water with known density. Larger pressure differences can be measured with higher density fluids. Micromanometer: Fluid level is precisely detected via contact with low-power AC circuit mounted to a micrometer. Other styles magnify the location of the fluid level whose height is then measured using a micrometer. Can be repeatable up to 0.00025 inches water. Manufacturers include Dwyer and Combist. Inclined manometer: Height is inclined for greater resolution. Source: www.dwyer-inst.com (a) U-tube

Pressure Transducer Basics Slides for ME 115 Pressure Transducer Basics Diaphram strain Strain on a diaphram is linearly proportional to pressure difference for the following conditions: A strain gage changes in resistance with strain. This resistance change can be indicated by the voltage output of a bridge circuit. Strain gage Stress () on a diaphram meeting the above criteria is equal to the applied force difference divided by the area, or pressure difference. Strain () is defined as deflection divided by length, and is linearly proportional to stress (or pressure difference) up until its proportional limit. The governing relationship is Hooke’s Law:  = E , where E is the modulus of elasticity, aka Young’s modulus. The figure above illustrates the variation in radial and tangential strain as a function of radius on a round diaphram. The integrated strain over the total diaphram area or a subset of it is linear with pressure difference. There are many styles of strain gages. The wire strain gage was just chosen as an example. The resistance of a strain gage can be implemented in a bridge circuit. A Wheatstone bridge is shown here as an example. It requires a source current, and produces an output voltage that changes with the resistance of the strain gage. There are also strain gages that can output current instead of voltage. The output voltage can be measured with a voltmeter. Bridge circuit

Pressure Transducer Examples Slides for ME 115 Pressure Transducer Examples (c) General purpose Low pressure (Validyne DP103) Low pressure transducer appropriate for electronics cooling applications. Pressure range is appropriate for chassis impedance and velocity measurements. High performance transducer used in industrial applications with low maintenance requirements. General purpose transducer with digital readout. Miniature transducer for board level applications. Pressure transducers come in all sizes and shapes depending on application. (d) Miniature Source: www.omega.com (b) High performance

Slides for ME 115 Dial Gauges A deformable pressure sensing element is attached to a pointer which rotates against a graduated dial--like these children’s party blowouts: Sources of error include: human error, hysteresis Good for quick “sanity check” or visual monitoring type measurements Resolution often too poor for thermal-fluids research Examples from: www.omega.com