MEM311 Manual 09192014

MEM311 THERMAL & FLUID SCIENCE LABORATORY MANUAL

Edited by Brandon Terranova, Eric Wargo, Ertan Agar, Chris Dennison, Reyhan Taspinar and E. Caglan Kumbur Adopted from MEM 311 Thermal & Fluid Science Laboratory by Baktier Farouk and David Stacck

LIST OF EXPERIMENTS: EXPERIMENT 1: FLOW MEASURING DEVICES PAGE 3 EXPERIMENT 2: CONTROL VOLUME ENERGY AND ENTROPY ANALYSIS OF A VORTEX TUBE PAGE 11 EXPERIMENT 3: HEAT TRANSFER FROM A CIRCULAR CYLINDER PAGE 20 EXPERIMENT 4: PERFORMANCE ANALYSIS OF A STEAM TURBINE POWER PLANT PAGE 35 EXPERIMENT 5: LIFT CHARACTERISTICS OF AN AIRFOIL SECTION PAGE 46 LIST OF APPENDICES: APPENDIX A: MANOMETER PREPARATION AND OPERATION Page 57 APPENDIX B: FLOW MEASURING USING A ROTAMETER Page 60 APPENDIX C: ANALYSIS OF BIAS ERRORS AND EXPERIMENTAL UNCERTAINTY Page 62 APPENDIX D: FITTING CURVES TO EXPERIMENTAL DATA Page 68

MEM311: Thermal and Fluid Science Laboratory Experiment 2: Control Volume Energy and Entropy Analysis of a Vortex tube

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EXPERIMENT 1: FLOW MEASURING DEVICES by Brandon Terranova 2012, adapted from Bakhtier Farouk and David Staack A. OBJECTIVES The objective of this experiment is to determine the discharge coefficient for an orifice flow meter as a function of the Reynolds number. B. THEORY Review of Friction Factors in Pipe Flow As a fluid flows through a pipe (or any other device, for that matter), area changes, friction and heat transfer affect the properties in a flow system. By evaluating the forces acting on a control volume in a pipe flow, the pressure drop for fully developed laminar pipe flow, 'p, is related to the wall shear stress, , by the equation

(1) Where is the length of the pipe and is the equivalent hydraulic diameter defined as = 4(Cross-sectional area of flow) / (Perimeter wetted by fluid). Since the wall shear stress is a complex function of the flow velocity, viscosity, density, wall surface roughness, etc., the pressure drop, 'p, is expressed as a product of a non-dimensional friction factor, , and the dynamic pressure (

). Which includes the velocity and density of the fluid, V and U respectively. So the pressure drop for a horizontal pipe is given as:

(

)

(2) Equating Eq. (1) and (2), we obtain

(3) Therefore, the friction factor, , is a measure of the shear stress at the wall. The friction factor, or more generally, the effects of viscosity on fluid flow, can be correlated using the flow Reynolds number (ratio of inertial forces to viscous forces) given as

(4)


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where U and P are the density and absolute viscosity of the fluid, respectively, and V is the mean flow velocity. Review of Bernoullis Equation As explained above, friction forces induce an irreversible decrease in pressure. The pressure can also change in a reversible way as described by Bernoullis equation. Because the crux of Bernoullis principle is that along a streamline of flow, the increase in velocity corresponds to drop in the static pressure of the fluid. While Bernoullis equation assumes a lot of simplifications to your system (constant density (incompressible), steady flow, no friction), it produces very accurate results compared to empirical evidence at low Mach numbers. Using Bernoullis equation, the conservation of mass and the fact that mass flow rate, , is constant through the duct, we can write the pressure drop along the duct as a function of only the upstream velocity and the change in area:

( (

)

) (5) Pipe Flowrate Meters Equation 2 shows that the pressure drop through a pipe is a function of the velocity of the flow through the system along with the friction factor. In fact, one method to determine the flow rate of fluid through a piping system is to measure the pressure drop through a device for which the friction factor and other losses are precisely known. These are called obstruction flow meters. There are three basic designs used in obstruction flow meters as shown in Fig. 1. A venturi flow meter offers the highest accuracy and the lowest overall pressure drop but is more expensive to manufacture and accurately calibrate. Both the flow nozzle and the orifice configurations have larger permanent pressure drops but are relatively simple to manufacture. When an orifice flow meter is placed in a pipe, the hole in the orifice essentially forms a jet which expands to fill the whole pipe at some distance downstream of the plate. Of course, frictional forces affect the pressure as the air is forced through the hole. In the absence of viscous effects and under the assumption of a horizontal pipe, application of the Bernoulli equation between points (1) and (2) in figure 1 gives the volumetric flow rate through the orifice:

( ) ( )

(6)


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Figure 1. Schematic of three typical obstruction meters Where V2 is the velocity of the flow immediately after the obstruction meter (in the center of the

vena contracta) and D = d/D1 as labeled in figure 2.

Figure 2. Orifice meter detail

The Orifice Flow Meter In this lab we will be examining an orifice flow meter. A typical orifice meter is constructed by inserting between two flanges of a pipe a flat plate with a hole, as shown in figure 2. The pressure at point (2) within the vena contracta is less than that at point (1).1 Since the vena contracta area A2, is less than the area of the hole, Ao, and the turbulent motion near the orifice plate introduces losses


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that cannot be calculated theoretically. To take these effects into account, the orifice discharge coefficient is used. The discharge coefficient is the ratio of the mass flow rate at the discharge end of the orifice to that of an ideal orifice which expands an identical working fluid from the same initial conditions to the same exit pressure and can be determined experimentally, as the pressure difference can be measured using a manometer, a differential pressure gauge or pressure transducers. For more information on the principles of manometer function, refer to appendix A. The following equation yields the volumetric flow rate for the orifice by comparing the pressures on either side of the plate:

( ) ( )

(7) The Inlet Nozzle The flow pattern for the inlet nozzle used in this experiment is closer to ideal than the orifice meter flow. There is only a slight vena contracta and the secondary flow separation is less sever, but there are still viscous effects. These are accounted for by the use of the nozzle discharge coefficient, Cn, where

( ) ( )

(8) with , d being the inner diameter of the nozzle and E = d/D where D is the outer diameter of the nozzle. Practically identical to equation 7, note that the pressure drop here is measured across the nozzle, not the orifice. Be careful not to confuse the areas, the diameters used, the coefficients and location of pressures used to determine the respective coefficients. C. EQUIPMENT An image of the Armfield F6 Air Flow facility is shown in Fig. 3. The equipment consists of a long smooth walled pipe (diameter D = 80mm) with an orifice plate of diameter d = 50mm. One end of the pipe is connected to a centrifugal fan via a conical inlet duct while the other end (inlet nozzle) is open to the atmosphere. The inlet nozzle has an outer diameter of 120mm and the inner diameter is equal to the pipe diameter. The inlet nozzle discharge coefficient was determined previously to be . Pressure taps are located along the complete length of the pipe to allow measurement of the wall pressure as a function of length. The centrifugal fan is mounted on a floor-standing metal frame and is driven by a constant-speed meter. The fan discharge duct terminates is a flow control damper and jet dispersion orifice gate, which is easily adjustable. This flow control damper will be used to vary the airflow rate through the tube. Velocities between 0 and 35 m/s can be obtained with this apparatus by adjusting the position of the flow damper (labeled in figure 3).


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Table 1: Pressure tap distances Pressure tap Distance (cm) 1 0 2 7.5 3 31.5 4 79.5 5 137 6 148.5 7 159.5 8 183.5 9 208 10 232

Figure 1. Armfield F6 flow facility with transducer array A fourteen-tube manometer will be used to measure the pressures along the pipe. The manometer is filled with red oil for easier reading. The specific gravity of this oil is 0.86. A flow splitter (anti-vortex vanes) is fitted to the inlet of the pipe to prevent swirling of the flow. This experiment requires that the airflow rate through the pipe be determined independently of the orifice plate. To accomplish this, a pre-calibrated inlet flow nozzle is used. The pressure drop across the nozzle is calculated using equation 8.


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In addition to the manometers, the pressure taps along the tube are also connected in parallel to a transducer array. The pressure transducers convert the pressure force to an electrical voltage which is then read by a signal conditioner and then displayed as inches of water. There is one pressure transducer for every pressure tap along the tube. The first display (labeled 1 in figure 3) is not used in this experiment. The second display (labeled 2 in figure 3) reads the pressures of the pressure taps as selected by the rotary switch (all read non-zero baseline values, do not attempt to zero!) which can be used to choose between pressure taps 1-10. The last display (labeled 3 in figure 3) reads the pressure difference across the orifice plate, and is not necessary for this lab. It can be read by toggling the switch to read(pt 6 pt 5). You must have the switch toggled to the (#5, #6) position to be able to read the individual pressures on display 2 using the rotary switch. The pressure transducers have a built-in uncertainty of 1%. D. PROCEDURE Throughout this lab, the manometer and transducer measurements will be used to infer pressure differences along the pipe. A description of manometer operation is given in appendix A. 1. Using the rotary switch, record the pressure reading for each transduce under ambient pressure conditions (with the fan off). You will need these values to correctly offset, or

zero, your measurements during the data analysis portion of the lab report. Do not attempt to tare any of the transducer readings. 2. Turn on the fan and set a low airflow by closing the flow control damper almost all the way (do not ever fully close the damper!). Record the level of manometer tubes and the transducer measurements for pressure taps 1 - 10 on your data sheet. Be sure to also record the approximation error in your measurements. 3. Repeat the previous step for the remaining 9 damper settings. E. PRE-LAB 1. A 2-in. diameter orifice plate is inserted in a 3-in. diameter pipe. If the water flowrate through the pipe is 0.90 cfs, determine the pressure difference indicated by a manometer attached to the flow meter using the figure below with the calculated Reynolds number.


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2. Water flows through the orifice meter shown in the figure below at a rate of 0.10 cfs. If d = 0.1 ft, determine the value of h.

F. DATA ANALYSIS AND REPORTING REQUIREMENTS 1. Calculate the actual orifice volumetric flow rates (m3/s) for each of the 10 conditions from the manometer and transducer measurements (assume Q before the orifice is just Q after the nozzle).


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2. Calculate the orifice discharge coefficient, Co, defined by equation 7, and the Reynolds number, defined by equation 4, for each condition as measured by the manometer and transducers. Use the mean flow velocity, , to calculate the Reynolds number. 3. Write a formula for the orifice discharge coefficient Co in terms of only constants and the parameters which were directly measured. Make sure to include the measurement uncertainty from the experiment. For the transducers, there is a 1% transducer uncertainty. Considering the information in Appendix C, how would you calculate the overall uncertainty in both the manometer and transducer measurements? 4. On the same graph, plot the orifice discharge coefficient for both manometer and transducer readings, as a function of the Reynolds number. Be sure to include the uncertainty error bars in your plots. 5. Plot the manometer/transducer height as a function of distance along the duct for your 10 values of Q. You should have 10 plots for both manometer and transducer measurements (on separate graphs). In the plots, identify the curves and the location of the orifice flow meter. What does this plot tell you about the effect of an orifice flow meter on the air flow through a pipe? Why might this be an important consideration when designing a piping system? What are some explanations for the discrepancy between the manometer and transducer measurements? G. REFERENCES 1. Munson et. al (2009). Fundamentals of Fluid Mechanics, 6th Ed., Wiley. 2. R. L. Daugherty and J. B. Franzini (1965), Fluid Mechanics, 6th Ed., McGraw-Hill.


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EXPERIMENT 2: CONTROL VOLUME ENERGY AND ENTROPY ANALYSIS OF A VORTEX TUBE by Ertan Agar and Brandon Terranova 2010-2012, adapted from Bakhtier Farouk and David Staack A. INTRODUCTION AND OBJECTIVES The vortex tube also known as the Ranque-Hilsch vortex tube is a unique device which converts a flow of compressed gas into two streams one hotter and the other colder than the gas supply temperature. It contains no moving parts and the mechanism of its operation is still a subject of debate, yet the usually agreed upon explanation will be given herein. This vortex effect was discovered by G. Ranque in 1928. The United States became focused upon the vortex tube in 1947 when R. Hilsch published a technical paper reporting research on the device1. Since that time, many technical applications of vortex tubes for cooling, air conditioning, and drying have been developed2. The vortex tube is a simple mechanical device that diverts a flow of compressed gas into two separate streams, one hot and one cold relative to the gas supply temperature. They are commonly used to prevent thermal damage by providing spot cooling to complex mechanical or electrical systems. Other technical applications of this technology include air conditioning, drying, and recovering waste pressure energy from both high and low pressure sources. The general flow distribution inside a vortex tube is depicted below in Figure 1.

Figure 1: General Flow Pattern inside a Vortex Tube


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Figure 1-a shows high pressure compressed air entering the vortex tube. The compressed air accelerates to a high rate of rotation due to its tangential injection point, resulting in a strong vortex flow is produced inside the tube1. Figure 1-b shows hot air exiting the control volume on the right side of the device. The remainder of the compressed gas is forced to travel back across the high speed air stream and exit as extremely cold air as shown in Figure 1-c. Through an energy and entropy analysis of this flow pattern, the first and second laws of thermodynamics can be validated by experimentally determining the total rate of entropy creation per mass of air flowing through the vortex tube. The objective of this experiment is to apply a control volume energy and entropy analysis to a practical engineering device, a vortex tube. The energy separation phenomenon induced by the vortex fluid motion will be investigated and explained using basic thermodynamic principles. B. THEORY Principles of Operation On the basis of flow visualization studies, Hartnett and Eckert3 found that the axial velocity component (velocity component along the length of the tube) was relatively small over most of the radius of the tube. Therefore, the flow can be analyzed by evaluating one plane through the vortex tube perpendicular to the tube axis as shown in Figure 2 below.

Figure 2: Streamlines in a cross-section of a vortex Tube

Hartnett and Eckert also observed that the flow consisted of a colder region in the center of the tube that rotated as a solid body having a tangential velocity , where Z is the constant angular velocity of the fluid. In fluids, this type of rotation is called a forced vortex because it is vortical flow, which is induced by an external force, in this case, the outer stream. In the outer stream, the tangential velocity is linearly proportional to 1/r and can therefore be given by v2 = K/r where K is a constant. This type of vortex is called a free vortex, a common example of which is the


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vortical motion of water as it goes down the drain in a bath tub. In a true free vortex, the tangential velocity goes to zero as r goes to infinity. Therefore, the outside stream only approximates a free vortex because r must be less than or equal to R, the radius of the tube. A flow with a forced vortex inside and a free vortex outside is called a combined vortex and has a tangential velocity profile given by the following equations Inner vortex: (1) Outer vortex: (2) where ro is distance to the boundary of the opposing vortical flows. Given this velocity profile, we can determine why the temperature separation occurs and why the hotter outer stream surrounds the cooler inner core. We will begin this analysis by evaluating the pressure distribution from the centerline of the tube to the outer wall. Since the streamlines for the flow in the vortex tube form closed concentric circles, we can consider simple circular motion along the streamline. To determine the pressure at any point within the vortex tube, we start by evaluating F = ma on a differential element of fluid normal to a streamline as seen in figure 3,

where F is the centripetal force on the element, and a is the centripetal acceleration, directed toward the center.

(3) where V = velocity along the streamline, r = the radius to the differential element, and for our differential element, = mass density, dp = pressure, dA = area and dV = volume. Noticing that

, we can then write

Figure 3: Differential volume element within a vortex tube cross-section of thickness dr

dr dA

dr


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(4) Substituting equations 1 and 2, respectively, into equation 4 we obtain

(5) And

(6) Equations 5 and 6 show that in both the free and forced vortex regions, the pressure increases as r increases (Evaluate the second derivative to prove it to yourself!). Integrating these equations with respect to r, starting with a known pressure p = p1, we find the pressure distribution in the vortex tube to be given by

(7)

(

) (8) where po is the pressure at r = ro. The value of po is found by evaluating equation 7 at r = ro, and the pressure at the wall, pw is found by evaluating equation 8 at r = R.

The pressure and velocity profiles are plotted as a function of r in figure 4. From these plots we see that the pressure is lowest at the center of the tube and increases to a maximum at the wall. Herein lies the reason for the temperature difference between the inner and outer streams. Recall the piston-cylinder devices that were studied extensively in basic thermodynamics. The first law energy balance indicates that if a gas is adiabatically (no heat transfer) compressed in a piston-cylinder, the internal energy and hence, the temperature, must increase. As the gas enters the vortex tube, the viscosity of the fluid induces a vortical motion which creates a forced vortex at the

Figure 4: (a) Radial velocity and (b) pressure profiles in vortex tube

(a) (b)


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center of the tube. This flow produces the pressure distribution given by equations 6 and 7. The gas on the outside of the tube is adiabatically compressed resulting in an increase in temperature. This gas is also at a higher pressure so it can be drawn off at the control valve. The work to compress the outer gas came from the gas near the centerline which is adiabatically expanded and cooled. The cooler gas is confined to the inner core of the tube so it can be withdrawn from the opposite end of the tube through an orifice plate. Note that even though the pressure is lowest at the center of the tube, it is still greater than atmospheric pressure and will flow out of the orifice. Therefore, the separation of the gas into two streams having different temperature is caused by viscous forces in the gas which induces a pressure distribution in the tube. The gas in the high pressure region is compressed and heated while that in the low pressure region is expanded and cooled. This description of the operation of a vortex tube resulted only after many experimental observations and a detailed analysis. The first and second laws of thermodynamics, however, present us with a simple way to evaluate any thermodynamic system to determine whether it is thermodynamically valid. If we ever determine that a proposed process violates either the first or second law, we know that the process is impossible. In this experiment, you will perform a first and second law analysis of a vortex tube to examine its performance. First and Second Law of Thermodynamics for a Control Volume All thermodynamic analyses begin by defining the system to be evaluated. A vortex tube is an example of a steady-state, steady-flow device and is most easily represented by a control volume. Reference 6, Section 5-4 (Reference 5, Section 4.5) gives the general first law energy balance for such a control volume as

(

)

(

)

(9) where is the heat, the work, the mass flow rate in and out respectively, , the specific enthalpy of mass in and out, , the velocity of mass in and out, the elevation of mass in and out, and lastly, is gravitational acceleration. (The form of the first law of thermodynamics given in Ref. 5 is slightly different than that given in Eq. 9. Primarily, Ref. 5 defines the work done by a system as positive (ASME sign convention) whereas this work is negative in Ref. 6 (scientific sign convention). The equations are equivalent and you must be able to use both of them. The second law of thermodynamics is given by the entropy generation principle for a steady-state, steady-flow control volume (see Ref. 5, Section 6.2 or Ref. 6, Section 7-2) as

( ) ( )

(10) where

is the total rate of entropy change for the control volume, and is the rate of internal generation of entropy within the system (intrinsic entropy associated with matter,

for irreversible systems, for reversible systems, and system is impossible if ). In this experiment, pressurized air is used to drive the vortex tube. The ideal gas equations can therefore be used to evaluate equations 9 and 10. See reference 5, section 2.8 and


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section 5.9 (or reference 6, chapter 3 and section 7-4) to review the application of these equations to ideal gases. Pay particular attention to the evaluation of the change in entropy for an ideal gas. C. EQUIPMENT

Figure 5: Experimental Setup Figure 5 shows the experimental setup and all the components and measuring devices. Compressed air enters the system at the top left of the picture and goes through a de-humidifier, then a pressure control and a pressure gage. Then it passes through a mass flow meter. See Figure 6 for a close-up of the inlet setup.


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Figure 6: Inlet setup After the flow enters the system and has the properties desired, it then goes to the vortex tube and separated into a hot and cold stream. Below Figure 7 is a close-up picture of the vortex tube itself and the direction of the hot and cold streams.

Figure 7: Vortex Tube After leaving the vortex tube both streams pass through a series of measurement devices similar to the ones monitoring the inlet flow. For the cool stream there is a mass flow meter, a temperature indicator connected to a thermocouple and a pressure gage, see Figure 8. A throttle valve is used to control the cold air pressure.

Figure 8: Cold stream measuring device


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The cold stream uses a pressure gauge and a temperature indicator in conjunction with a digital mass flow meter. For the hot stream, pressure and temperature are similarly measured, but a rotameter is used to measure mass flow rate. A rotameter has a ball in between two tapered tracks and the air pressure flowing through the meter pushes the ball up to a certain height and the height markings on the vertical meter correlate to a flow rate (See Appendix B for rotameter function). A throttle valve and a muffler are also used on both outlet air streams. See Figure 9 for the layout of the hot stream measuring devices.

Figure 9: Hot stream measuring devices D. PROCEDURE 1. Familiarize yourself with the general performance of the vortex tube by manipulating the pressure regulating valve and the discharge throttling valves found on the hot and cold ends. 2. Set the inlet pressure of the main flow to 60 psi. Open the hot stream flow, establishing a constant mass flow rate (20 SCFH). Starting at 50 SLPM, take 5 readings with decreasing increments of 8 SLPM for the cold stream flow. 3. Record all temperatures, pressures, and flow rates at steady state (typically takes 3-4 minutes) for 5 evenly spaced cold mass flow rate values. 4. Open the cold stream flow, establishing a constant mass flow rate (10 SLPM). Starting at 100 SCFH, take 5 readings with decreasing increments of 10 SCFH for the hot stream flow. 5. Repeat all experiments at 80 psi. E. PRE-LAB 1. Covert 60 SLPM into kg/s at T=25qC and P=250kPa for air.

a. First SLPM to LPM b. Then LPM to kg/s

2. A vortex tube has an inlet air flow at 300 K and 5 bar. A vortex tube with 1 mole of input air, outputs 0.8 moles, 1 bar at 160 K on the cold side, and 0.2 moles, 1 bar at 310 K on the hot side. Assuming steady state conditions, calculate the total change in entropy of the gas due to the vortex tube. Assume ideal gases with a constant heat capacity of cp = 29.3 J/mol K. Are the output pressures and temperatures are consistent with the second law?


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F. DATA ANALYSIS AND REPORTING REQUIREMENTS 1. Calculate the volumetric and mass flow rates from the rotameter and mass flow-meters data. All volumetric flow rates (both cold plus main inlet flows) must be corrected to the actual pressure and temperature of the flowing gas to obtain an accurate volumetric flow rate. Hint: ideal gas state equation may be used. 2. Perform a mass balance for each set of operating conditions with using mass flow meters data to determine the flow rate of rotameter. Then compare the calculated value with the measured flow rate of rotameter obtained in the experiment. Use graph to show the relative error. 3. Perform an energy balance (Eq. (9)) to solve for the rate of heat transfer for each set of operating conditions from the control volume of the vortex tube. Discuss your result with drawing heat transfer rate graph for different conditions. 4. Evaluate the total rate of entropy generation (Eq. (10)) flowing through the control volume using your measurements and heat transfer rate calculated in 3 above. The property data required can be found in Ref. 5 and should be included in the sample calculations. Discuss your result with drawing rate of entropy generation graph for different conditions. 5. Do your results satisfy the Second Law of Thermodynamics (Increase-in-Entropy Principle)? What does this imply about the process that occurs in a vortex tube? G. REFERENCES 1. Hilsch, R., The Use of the Expansion of Gases in a Centrifugal Field as a Cooling Process, Review of Scientific Instruments 18, 1947. 2. Hartnett, J.P. and Eckert, E.R.G., Experimental Study of the Velocity and Temperature Distribution in a High-Velocity Vortex-Type Flow, Transactions of the ASME 79, 1957, pp. 751-758. 3. Eckert, E.R.G. and Drake, R.M., Jr., Analysis of Heat and Mass Transfer, McGraw-Hill, New York, 1972, pp. 427-430. 4. Munson, B.R., Young, D.F., and Okiishi, T.H., Fundamentals of Fluid Mechanics, John Wiley and Sons, 1990. 5. Black, W.Z. and Hartley, J.G., Thermodynamics (2nd edition), Harper Collins Publishers, New York, 1991. 6. Wark, Kenneth, Jr., Thermodynamics (5th edition), McGraw-Hill, New York, 1988. 7. Holman, J.P., Experimental Methods for Engineers. 3rd ed., McGraw-Hill, 1978.

MEM311: Thermal and Fluid Science Laboratory Experiment 3: Heat Transfer from a Circular Cylinder

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EXPERIMENT 3: HEAT TRANSFER FROM A CIRCULAR CYLINDER by Eric Wargo 2010, adapted from Bakhtier Farouk and David Staack A. OBJECTIVES The objective of this experiment is to determine the natural convection, forced convection and radiation heat transfer (qnatural convection + qforced convection + qradiation) from an electrically heated horizontal cylinder. These values will be compared to existing heat transfer correlations provided herein. In this experiment, you will demonstrate how heat transfer from a heated surface to a quiescent environment is a combination of several mechanism of heat loss. The relative magnitudes of the natural convection, forced convection, and radiation heat transfer coefficients depend on the surface temperature and flow velocity. Radiation becomes more important as the surface temperature increases. Forced convection becomes more important as the flow velocity increase. The problem will be analyzed using a control volume under equilibrium conditions. For equilibrium, heat input to a surface must equal the heat transferred from the surface to the surroundings. B. THEORY Natural and Forced Convection Free convection heat transfer occurs whenever a body is placed in a fluid at a higher or lower temperature. As a result of the temperature difference, heat is transferred between the fluid and the body and causes a change in the density of the fluid layers in the vicinity of the surface. This difference in density leads to an upward flow of the lighter fluid (figure 1). If the motion of the fluid is caused solely by differences in density resulting from temperature gradients, the associated heat transfer mechanism is called free or natural convection. If the fluid motion is enhanced using a fan or otherwise forced by some device, the heat transfer mechanism is called forced convection (figure 2). Because the fluid velocity is usually less in free convection than in forced convection, the rate of heat transfer from a surface is also generally less. In this experiment, you will measure and compare the magnitudes of the heat transfer rates for forced convection and free convection configurations.


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Figure 1. Cross sectional view of a heated cylinder under natural convection.

Figure 2. Cross sectional view of a heated cylinder under forced convection. The rate of heat transfer by convection (both forced and free) between a surface and a fluid may be computed using the relation

( ) (1) where is the average convective heat transfer coefficient, A is the area available for heat transfer, Ts is the surface temperature, and T is the ambient temperature. The relation expressed by equation 1 was originally proposed by the British scientist, Sir Isaac Newton in 1701. Therefore, it is sometimes referred to as Newtons law of cooling. Even though this equation has been used for many years to evaluate convective heat transfer, it is actually more a definition of than a law of convection. If the value of is known for a certain flow configuration, the evaluation of equation 1 to determine the rate of heat transfer is straightforward. However, determining the appropriate


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convective heat transfer coefficient is difficult because convection is a very complex phenomenon. The value of depends not only on the geometry of the surface of the object (both macroscopic and microscopic surface characteristics) but on the velocity and physical properties of the fluid, all of which affect the conditions on the boundary layer. Since these quantities are not necessarily constant over a surface, the heat transfer coefficient may vary from point to point. For this reason, we must distinguish between a local and average convective heat transfer coefficient. The local coefficient, hc, is defined by ( ) (2) while the average coefficient, , can be defined in terms of the local value by

(3) The primary problem in either forced or free convection is to determine the appropriate local or average heat transfer coefficient. Many experiments have been performed to measure these coefficients for a wide variety of geometries and flow configurations. Numerical calculations have only recently become sufficiently exact to calculate the heat transfer coefficients directly. However, heat transfer coefficients can be accurately calculated for relatively simple flow configurations. Complex configurations must still be determined experimentally. In this experiment, you will determine the heat transfer coefficient of free convection and forced convection from a cylinder placed within a range of flow conditions. Your results will be compared with existing heat transfer correlations. Radiation Heat Transfer Thermal radiation is heat transfer by the emission of electromagnetic waves which carry energy away from the emitting object. For ordinary temperatures (i.e. less than red hot), the radiation is in the infrared region of the electromagnetic spectrum. The relationship governing radiation from hot objects is called the Stefan-Boltzmann law. The heat transferred into or out of an object by thermal radiation is a function of several components. These include its surface emissivity, surface area, temperature, and geometric orientation with respect to other thermally participating objects. The heat loss rate caused by radiation from a heated surface to the surroundings can be calculated by

( ) (4) where is the Stefan-Boltzmann constant (= 5.67x10-8 W/ m2K4), is the emissivity of the surface, and Fsa is the view factor of the surface. The surface temperature is given by Ts, and the temperature of the body receiving the radiation (the ambient environment) is given by T. An object's surface emissivity is a function of its surface microstructure. The view factor takes into account the geometric orientation of the surface to the external environment. If all of the radiation emitted by the surface has a direct line of sight to the external environment, the view factor is equal to 1. Equation 4 can also be cast in the form of Newtons law of cooling (equation 1) as


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( ) (5) Comparing equation 4 with equation 5 we can define a radiative heat transfer coefficient as

( )( )

(6) Natural Convection, Forced Convection, and Radiation Heat Transfer If a surface is at a temperature above that of its surroundings and is located in stationary or moving air, heat will be transferred from the surface to the surroundings. This transfer of energy will be a combination of natural convection, forced convection (if there is a driven air flow) and radiation to the surroundings. As described above in natural convection, the motion of the fluid is caused solely by differences in density resulting from the temperature gradients. If the fluid motion is enhanced using a fan or otherwise forced by some device, the heat transfer mechanism is called forced convection. Radiation heat transfer generally becomes significant at surface temperatures well above room temperature. However, it does play a role at lower temperatures and should be accounted for, especially when comparing measurements with existing correlations for natural and forced convection. Heat loss by conduction would normally be included in the analysis of a real application. In this experiment, it is minimized by the design of the equipment and experimental procedures. The total heat lost by a surface can thus be presented as a linear superposition of the aforementioned heat losses:

(7) When there is no forced flow, the term can be neglected. When there is an air flow typically the heat lost due to the forced convection is significantly greater than that by natural convection; thus, the term can be neglected. Equation 7 can be written in terms of the various heat transfer coefficients: ( ) ( ) ( ) (8)

Experimental Determination of the Heat Transfer Coefficients Solving Equation 8 for the heat transfer coefficient, we obtain

( )

(9) The heat transfer coefficient can be determined by measuring all the quantities on the right hand side of equation 9 for a specific flow configuration and solving for . The temperatures Ts and T are easily measured using thermocouples. The area, A, is simply the surface area available for convective heat transfer (sometimes called the wetted area). This can be evaluated once the experimental configuration is defined. Therefore, the problem is reduced to determining the rate of


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heat transfer, . Recall that the first law of thermodynamics for a control mass can be written in infinitesimal form as (10) Recall from thermodynamics that passing an electrical current, I, through an object is a form of work given as

(11) where V is the applied voltage, and R is the resistance. The relations in equation 11 are based on Ohms laws, V = IR and P = VI, where P is the power. Substituting equation 11 into equation 10, dividing by a small increment of time t, and taking the limit as t goes to 0, we obtain

(12) Where is the rate of heat transfer and (V2/R) is the rate at which work is done. Since the heated cylinder can be considered to be an incompressible substance, the change in its internal energy is given as

(13) where m is the mass of the cylinder, and c is the specific heat. Recall that for an incompressible substance, cp = cv = c (see section 2.8 of reference [1], or sections 4-7 of reference [3] for a review of these thermodynamic relationships). Since m and c are constant, the rate of change of internal energy is

(14) If the electrical current to the cylinder is controlled so that the temperature remains constant,

, and therefore,

, is identically equal to zero. Such a situation happens in steady state operation. For this condition, Equation 12 reduces to the following form:

(15) The negative sign in equation 15 indicates that the heat transfer is out of the cylinder. Substituting equation 15 into equation 9 yields

( )

( )

(16) The surface temperature, TS, and the temperature of the cylinder, T, are interchangeable, because it is assumed that there are no temperature gradients inside the cylinder. This is true only if the cylinder is made of a material that conducts heat rapidly. The Biot number, defined as


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(17)

provides a measure of the accuracy of this assumption. In equation 17, L* is the characteristic dimension (cylinder diameter, around which the fluid is flowing) and ks is the thermal conductivity of the material. Physically, the Biot number is the ratio of the external convective heat transfer rate to the internal conductive heat transfer rate. If Bi 1, heat is conducted within the material much faster than it is convected away from the cylinder. The assumption of uniform temperature is then valid and equation 16 can be used to evaluate the overall rate of heat transfer. If Bi is greater than approximately 0.1, the non-uniformities within the material must be accounted for when determining the heat transfer coefficient. Equation 16 shows that the heat transfer coefficient can be calculated by measuring the electrical voltage and current supplied to the cylinder such that the cylinder temperature of the cylinder is constant. Comparing equation 16 and 8 we can simply write this as (18) which simply states that in steady state the heat flow out of the cylinder is equal to the energy flow into the cylinder.

Heat Transfer Correlations As shown by the equations above, the heat transfer coefficient is a dimensional number that depends on the area (size) of the object being evaluated and the temperature/properties of the fluid in which the object is immersed. When developing experimental correlations, it is convenient to non-dimensionalize so that the results are applicable to other configurations. The Nusselt number is a dimensionless heat transfer parameter defined as

(19)

where L* is the characteristic dimension of the geometry being evaluated (cylinder or sphere diameter, around which the fluid is flowing), and kf is the thermal conductivity of the fluid (air) in which the object is immersed. The Nusselt number is defined as the ratio of convective to conductive heat transfer across a boundary (the objects surface); thus, radiation effects should not be included in its calculation. The overbar on the Nusselt number indicates that it is formed from the average heat transfer coefficient and, therefore, is a measure of the average heat transfer from the object. Other dimensionless parameters are used that represent the air flow conditions. For forced convection flows, the Reynolds number is used to correlate heat transfer data. The Reynolds number is defined as

(20)


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where is the density, V is the velocity, L* is the characteristic length (cylinder diameter, around which the fluid is flowing), is the absolute viscosity of the fluid (air), and is the kinematic viscosity of the fluid (air) and is equal to /. In the case of natural convection, Nu depends on the Rayleigh number, Ra. The Rayleigh number, in turn, is frequently written in terms of two other non-dimensional numbers, namely the Grashof and the Prandtl numbers, Gr and Pr respectively. These are given by the equations:

( )

(21)

(22)

( )

(23) The new symbols in equations 21 23 are explained in table 1. Note: D is the characteristic dimension (cylinder diameter, around which the fluid is flowing).

Table 1. Symbol definitions for Equations 21 23. Symbol Definition Value and/or Units g gravitational acceleration 9.81 m/s2 volume expansion coefficient, 1/Tfilm K-1 kinematic viscosity, / m2/s cp specific heat J/kgK density kg/m3 thermal diffusivity m2/s k thermal conductivity W/mK

All of the thermophysical properties given in equations 1923 are functions of the temperature of the fluid (air). Since the temperature varies from the surface to the ambient, by convention these properties are evaluated at the film temperature

(24) Values of the thermophysical properties listed in table 1 can be found in appendix A of reference [2] or any other heat transfer textbook. At the very least, a reputable source should be utilized and properly referenced in the lab report; online calculators are convenient, but their range of accuracy may be questionable.


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These equations form the basis for the experimental method to experimentally evaluate the heat transfer coefficient. A more detailed discussion of forced and free convective heat transfer can be found in reference [2], chapters 7 and 9, respectively. Specifics regarding the heat transfer from a circular cylinder in cross flow may be found in reference [2], section 7.4 (forced convection) and section 9.6.3 (free convection). Reference [2] gives the following empirical correlation for the Nusselt number, Nu, for forced convection as a function of the Reynolds number: ( ) (25) where c and n are obtained from table 2.

Table 2. Reynolds number-Nusselt number empirical relation parameters. Re c n 1 40 0.75 0.4 40 1000 0.51 0.5 103 2x105 0.26 0.6 2x105 106 0.076 0.7 Reference [3] gives the following empirical correlation for the Nusselt number, Nu, for natural convection as a function of the Rayleigh number: ( ) (26) where c and n are obtained from table 3.

Table 3. Raleigh number-Nusselt number empirical relation parameters. Ra c n 10-10 to 10-2 0.675 0.058 10-2 to 102 1.02 0.148 102 to 104 0.850 0.188 104 to 107 0.480 0.250 107 to 1012 0.125 0.333 For a given Ra, the Nu value can be computed from equation 15 and the corresponding value from equation 9.


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There are other equations that are sometimes used to calculate the natural convection heat transfer coefficient. One simplified, analytical relation that may be used to calculate the average heat transfer coefficient from a horizontal cylinder is given by [

( )

] (27)

where D is the cylinder diameter. Equation 27 yields in W/m2K if the temperatures are in Kelvin and D is in meters. In the experiment, you will compare your experimental results with the predictions of equations 25, 26, and 27. Note: care must be take to distinguish Ra and Re. C. EQUIPMENT 1. Armfield HT14 Combined Convection and Radiation Accessory (see figure 3) 2. Armfield HT10X Heat Transfer Service Unit (see figure 3) 3. Computer on site or laptop for manual data entry (optional but highly recommended, since you will be recording the surface temperature in 30 second time intervals for durations sometimes totaling over 10 minutes). A stopwatch/timer is also helpful. The HT14 accessory consists of a centrifugal fan with vertical outlet duct at the top of which is mounted a heated cylinder. The heated cylinder has an outside diameter of 10mm, a heated length of 70mm and is internally heated throughout its length by an electric heating element. The heating element is rated to produce 100 Watts nominally at 24V DC into the cylinder. The power supplied to the heated cylinder can be varied and measured on the HT10X unit. The mounting arrangement for the cylinder in the duct is designed to minimize loss of heat by conduction to the wall of the duct. The surface of the cylinder is coated with heat resistant paint which provides a consistent emissivity close to unity. A K-type thermocouple is attached to the wall of the cylinder (T10), at mid position, allowing the surface temperature to be measured under the various operating conditions. A variable throttle plate at the inlet to the fan allows the velocity of the air through the outlet duct to be varied, and a vane type anemometer within the fan outlet duct allows the air velocity in the duct to be measured over the range 0-7 meters/sec. The inside diameter of the outlet duct is 70mm (matching the length of the heated cylinder). A K-type thermocouple is also located in the air duct (T9), allowing the ambient air temperature to be measured upstream of the heated cylinder. The HT10X unit is used to control the heating of the cylinder. The voltage is controlled by a rotary knob, and the top digital display can be used to alternatively view the voltage, current, and air velocity by using the selector knob. The temperature at the thermocouples is shown on the bottom digital display, and the thermocouple selector knob determines which temperature is displayed. Connections for additional accessories and computer data acquisition and control are available on the service unit but are not used in this experiment.


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Figure 3. Experimental set-up and schematic view of the duct.

Figure 4. Armfield HT10X Unit.


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D. PROCEDURE ***Before operating the equipment, please understand that the heated cylinder will reach temperatures above 500C. Serious skin burns will result if the equipment is mishandled. Please ask an instructor if you have any questions or concerns. Equipment Set-up Before proceeding with the exercise, ensure that the equipment has been prepared as follows: 1. Locate HT14 Combined Convection and Radiation accessory alongside the HT10X Heat Transfer Service Unit on a suitable bench. 2. Ensure that the horizontal cylinder is located at the top of the vertical metal duct with the T10 thermocouple attached. 3. Connect the thermocouple attached to the horizontal cylinder to socket T10 on the front of the service unit. 4. Connect the thermocouple located in the vertical duct to socket T9 on the service unit. 5. Set the voltage control potentiometer to minimum (counterclockwise) and the selector switch to MANUAL. 6. Connect the power lead from the heated cylinder on the HT14 to the socket marked O/P3 at the rear of the service unit. 7. Ensure that the service unit is connected to an electrical supply. Experimental Procedures You will perform 2 sets of experiments: one for natural convection, and another for forced convection. For the natural convection conditions, you will measure the steady state temperature achieved on the cylinder for 4 different heating voltages (7, 10, 13, and 16 volts). For the forced convection cases, you will measure the steady state temperature achieved on the cylinder for 5 different flow velocities (approximately equally spaced between 0 m/s and the maximum attainable by the device), all at a heating voltage of 10 volts. Perform the forced convection experiments first, as they achieve steady state more quickly. Record the temperatures at time intervals of 30 seconds to be able to identify when steady state has been achieved (steady state can be considered achieved when the surface temperature (T10) remains constant for 2 minutes or four, 30 second readings). 1. Prepare a data sheet on which to record the raw data. It is highly recommended that you record

your data directly into a Microsoft Excel spreadsheet, since you will be recording the surface temperature in 30 second time intervals for durations sometimes totaling over 10 minutes. The spreadsheet should have the following headings:


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Table 4. Variables to record in datasheet. Variable Symbol Units Time t min:sec Heater voltage V volts Heater current I amps Upstream air temperature, T9 T C or K Cylinder surface temperature, T10 Ts C or K Upstream air velocity Ua m/s 2. Turn on the front main switch (figure 3) (if the panel meters do not illuminate, check the circuit breakers at the rear of the service unit). All switches at the rear should be up. 3. Turn on the fan switch and open the throttle plate until the knob stops turning, ensuring the maximum air velocity is attained. 4. Set the heater voltage to 10 volts. 5. Record the experimental conditions as a function of time (30 second intervals) until a steady state is achieved. Steady state can be considered achieved when the surface temperature (T10) remains constant on the display for 2 minutes (four, 30 second readings). 6. When the temperature is stable, record V, I, T9, T10, and Ua. Note: the digital display outputs temperature readings in degrees Celsius. 7. Repeat steps 5 and 6 for an additional four flow velocities: 75%, 50%, 25%, and 0% of the maximum velocity (letting the heater remain at 10 volts). A flow velocity of 0% is best attained by shutting the fan off. The throttle plate should be opened completely to allow for air to flow naturally through the duct during free convection. 8. The last condition for forced convection above represents the first free convection condition. Repeat steps 5 and 6 for heater voltages of 7, 13, and 16 volts. In all you should measure 8 conditions, and if you deem appropriate you may change the order.

Suggestion: This lab can be completed the fastest if (after obtaining data for forced convection at 100% 25% flow velocity) the heated cylinder is allowed to cool back down by turning the voltage off and throttling the flow velocity back to 100% for a few minutes. Then, repeat steps 5 and 6 for heater voltages of 7, 10, 13, and 16 volts with the fan off and throttle plate open completely. This ensures that the cylinder is only ever heating up to steady state for all conditions, rather than cooling down naturally (which takes far more time). The order will be as follows: Voltage 10 10 10 10 ( ) 7 10 13 16 Flow rate 100% 75% 50% 25% 0% 0% 0% 0% 9. Return the voltage to 0 volts, and turn off the unit. Note: Do not set the heater voltage in excess of 16 volts when operating the cylinder in the natural convection mode (no forced airflow). The life of the heating element will be considerably reduced if operated at excessive temperature. If temperatures approach 550C check with an instructor, and if the temperatures exceed 600C shut off the unit.


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Use the following data for your calculations: Parameter Symbol/value Diameter of horizontal cylinder D = 0.01 m Heated length of cylinder L = 0.07 m Emissivity of surface of the cylinder = 0.75 Stefan-Boltzmann constant = 5.67x10-8 W/m2K4 View Factor Fs a = 1 E. PRE-LAB Assume an experimental setup similar to the Armfield facility and an ambient air temperature of 25C. 1. What is the proper temperature unit (C or K) to be used in equation 4? Why? 2. For a cylinder surface temperature of 500C, use equation 4 to calculate the power lost by radiative heat transfer. 3. For a cylinder surface temperature of 500C, calculate a Raleigh number using Equation 23 and appropriate properties based on the film temperature. Use this Raleigh number to calculate a Nusselt number by equation 26 and table 3. Use equation 19 and the Nusselt number to calculate a corresponding free convection heat transfer coefficient for the cylinder. Now use equation 1 to calculate the heating power which is dissipated by natural convection at this surface temperature. 4. For a cylinder surface temperature of 500C and a flow velocity of 5 m/s, calculate a Reynolds number using equation 20 and appropriate properties based on the film temperature. Use this Reynolds number to calculate a Nusselt number by equation 25 and table 2. Use equation 19 and the Nusselt number to calculate a corresponding forced convection heat transfer coefficient for the cylinder. Now use equation 1 to calculate the heating power which is dissipated by forced convection at this surface temperature. 5. Sum the powers lost by radiation, forced convection and free convection to get the total heating power required to maintain this temperature. What percentage are the various mechanisms of the total power? If there were no forced convection, how do radiation and free convection compare? Briefly discuss these results. 6. After reviewing the lab procedures, prepare a data sheet to record your experimental measurements. It is highly recommended that you create a data sheet in Microsoft Excel and bring it to lab along with a laptop, so you can quickly key in temperature readings during the lab. You will have access to a computer in the lab.


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F. DATA ANALYSIS AND REPORT REQUIREMENTS 1. For all 8 test conditions, plot the measured temperature as a function of time. How long does steady state take to attain? What conditions determine steady state? What methods could be employed to attain steady state faster? 2. For each of the four test conditions corresponding to natural convection at steady state a) Calculate and tabulate the following parameters using the raw data and provided theory. Parameter Symbol Units Cylinder temperature K Film temperature Tfilm K Rayleigh number Ra N/A Heat flow (power input) W Heat transferred by radiation W Heat transfer coefficient (radiation) W/m2K Heat transferred by natural convection W (Use equation 18 and assume that forced convection is negligible) Heat transfer coefficient (natural convection) W/ m2K Nusselt Number (natural convection) Nu N/A b. Compute the heat transfer coefficient (natural convection) and Nusselt number from the analytical relation, dquation 27. Also, compute a Nusselt number and heat transfer coefficient from the calculated Raleigh number and empirical correlation, dquation 26. Use dquation 19 to switch between h and Nu. c. Compare the analytical and empirical calculations of and obtainable from Question 2.b with the values for and calculated only from the experimental measurements (Question 2.a) and discuss any differences in them. Plot the experimental and calculated values of versus the surface temperature on a single graph. [hint: there should be 3 series on the plot] d. On a single graph plot , , and as a function of the average surface temperature . Comment on the relationship between and . Comment on the relative importance of natural convection and radiation heat transfer. At what temperature (if any) is = ? 3. For each of the test conditions corresponding to forced convection at steady state: a) Calculate and tabulate the following parameters using the raw data and equations given above. Parameter Symbol Units Cylinder temperature K Film temperature Tfilm K Rayleigh number Ra N/A Heat flow (power input) W Heat transferred by radiation W Heat transfer coefficient (radiation) W/m2K


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Heat transferred by forced convection W (Use equation 18 and assume that natural convection is negligible) Heat transfer coefficient (forced convection) W/ m2K Nusselt Number (forced convection) Nu N/A b) Compute a Nusselt number and heat transfer coefficient from the calculated Reynolds number and empirical correlation, dquation 25. Use dquation 19 to switch between h and Nu. c) Compare the correlation calculated values of and obtainable from Question 3.b with the values for and calculated only from the experimental measurements (Question 3.a) and discuss any differences in them. Plot the experimental and empirically calculated values of versus the surface temperature on a single graph. d) Plot as a function of the flow velocity. Comment on the relationship. e) Plot Nu vs. Re from dquation 25 for Re from 100 to 5000. On the same graph plot Nu vs. Re attained from the experiment (Question 3.a). How close are the experimental data points to the correlation line? Comment on the non-dimensional comparison. 4. For this lab, the surface temperature of the heated cylinder was only measured at a single point. If several temperature readings were obtained from locations around the cylinder diameter, what would you expect the circumferential distribution to look like? Comment on the effects of using an average temperature versus a single point temperature measurement on the calculations made above. G. REFERENCES 1. Holman, J. P. Experimental Methods for Engineers. 7th ed. Boston: McGraw-Hill, 2001. Print. 2. Incropera, F. P., and D. P. DeWitt. Fundamentals of Heat and Mass Transfer. 5th ed. New York: Wiley, 2002. Print. 3. Munson, B. R., D. F. Young, and T. H. Okiishi. Fundamentals of Fluid Mechanics. 4th ed. New York: Wiley, 2002. Print.

MEM311: Thermal & Fluid Science Laboratory Experiment 4: Performance Analysis of a Steam Turbine Power Plant

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EXPERIMENT 4: PERFORMANCE ANALYSIS OF A STEAM TURBINE POWER PLANT by Chris Dennison, Reyhan Taspinar, and Brandon Terranova, 2014, adapted from Bakhtier Farouk and David Staack A. OBJECTIVES The objective of this laboratory is to offer students hands-on experience with the operation of a functional steam turbine power plant. A comparison of real world operating characteristics to that of the ideal Rankine power cycle will be made. The laboratory is conducted using a miniaturized steam turbine power plant. The apparatus is scaled for educational use and utilizes components and systems similar to full-scale industrial facilities. Students will be able to operate and analyze this system in detail, allowing them to determine the efficiency of the facility and suggest possible modifications for further improvement.

Figure 1. Miniature steam turbine power plant

MEM311: Thermal and Fluid Science Laboratory Experiment 4: Performance Analysis of a Steam Turbine Power Plant

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B. THEORY One of the most important ways to convert energy from fossil fuels, nuclear, and solar radiation is through processes known as vapor power cycles. One example of the use of vapor power cycles is electrical power plants. As engineers it is important to become familiar with these types of systems. The first step in becoming familiar with these cycles is by studying the idealized cycles. The ideal cycle for vapor power cycles can be modeled using the Rankine Cycle. This cycle is composed of four components: a heater (boiler), a turbine, a condenser, and a pump. To complete the system there must be some type of fluid flowing through the components, which is called the working fluid. Most often the working fluid is water. As the working fluid passes through each of the components it undergoes a process and ends up at a new state. Keeping in mind that the ideal Rankine cycle is physically impossible, we define each process to involve no internal irreversibilities. For the following it is necessary to number each of the states. State 1 is the state at the boiler exit. State 2 is the turbine exit. State 3 is the condenser exit and state 4 is the pump exit.

Figure 2. Schematic of simple ideal Rankine cycle. Now the processes that the working fluid undergoes as it completes the cycle will be defined. First is the heater, which in most cases is a boiler. As the fluid ends the cycle, at state 4, it is pumped into the boiler. In the boiler, the working fluid is heated from sub-cooled liquid to saturated vapor. This occurs at a constant pressure and is described in the following equation:


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(1) where is the rate of heat addition relative to the mass flow rate of the working fluid passing through the boiler. The value ( ) is the difference in outlet and inlet enthalpies of the working fluid. Second is the turbine. Through the turbine the vapor leaving the boiler expands to the condenser pressure. This is said to be isentropic expansion so that no heat transfer to the surroundings is present. The equation that is used to describe this process is as follows:

(2) where is the rate of work being done relative to the mass flow rate through the turbine. Again the difference in inlet and exit enthalpies of the working fluid is required. Next the working fluid enters the condenser. At this stage heat is rejected from the vapor at a constant pressure. Ideally, this continues until all of the vapor condenses to leave nothing but saturated liquid. The equation for this is:

(3) where is the rate at which heat is transferred from the working fluid relative to the mass flow rate. The value ( ) is the difference between inlet and outlet enthalpies of the condenser. Finally, the working fluid enters the pump. The fluid goes through an isentropic compression process to reach the boiler pressure. The equation describing this is as follows:

(4) where is the rate of work being done relative to the mass flow rate through the pump. Finally the difference in pump outlet enthalpy and inlet enthalpy is needed. The efficiency of a given Rankine cycle may be computed as:

(5)


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Figure 3. P-v and T-s diagrams for the Rankine cycle. In reality, no Rankine cycle is completely ideal. In particular, the compression of the working fluid through the pump, and the expansion of the working fluid through the turbine are not actually isentropic processes. Irreversibilities in these processes lead to increased power input to the pump, and decreased power output from the turbine, both of which effectively lower the overall efficiency of the system. C. EXPERIMENTAL APPARATUS

The experimental hardware (RankineCycler) consists of multiple components that make up the necessary components for electrical power generation (utilizing water as the working fluid):

Figure 4. The RankineCycler apparatus, including the data acquisition system. [3]


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BOILER A stainless steel constructed, dual pass, flame-through tube type boiler, with super heat dome, that includes front and rear doors. Both doors are insulated and open easily to reveal the gas fired burner, flame tubes, hot surface igniter and general boiler construction. The boiler walls are insulated to minimize heat loss. A side mounted sight glass indicates water level.

Figure 5. Boiler with superheat dome [1]

TURBINE The axial flow steam turbine is mounted on a precision-machined stainless steel shaft, which is supported by custom manufactured bronze bearings. Two oiler ports supply lubrication to the bearings. The turbine includes a taper lock for precise mounting and is driven by steam that is directed by an axial flow, bladed nozzle ring. The turbine output shaft is coupled to an AC/DC generator.

Figure 6. Axial flow steam turbine wheel [1]

ELECTRIC GENERATOR The electric generator, driven by the axial flow steam turbine, is of the brushless type. It is a custom wound, 4-pole type and exhibits a safe/low voltage and amperage output. Both AC and DC output poles are readily available for analysis (rpm output, waveform study, relationship between amperage, voltage and power). A variable resistor load is operator adjustable and allows for power output adjustments.


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CONDENSER TOWER The seamless, metal-spun condenser tower features 4 stainless steel baffles and facilitates the collection of water vapor. The condensed steam (water) is collected in the bottom of the tower and can be easily drained for measurement/flow rate calculations. DATA ACQUISITION The experimental apparatus is also equipped with an integral computer data acquisition station, which utilizes National Instruments data acquisition software. The fully integrated data acquisition system includes 10 sensors: 1. Boiler pressure 2. Boiler temperature 3. Turbine inlet pressure 4. Turbine inlet temperature 5. Turbine exit pressure 6. Turbine exit temperature 7. Fuel flow 8. Generator voltage output 9. Generator amperage output 10. Generator RPM The sensor outputs are conditioned and displayed in real time on screen. Data can be stored and replayed. Run data can be copied off to a USB flash drive for individual student analysis. Data can be viewed in Notepad, Excel and MSWord (all included). A schematic of the complete system is shown in Figure below.

Figure 7. RankineCycler schematic [1]

Burner Boiler

LP Natural Gas Tank Fuel flow

Boiler pressure

Turbine Generator

Condensate Collection Tank

Turbine exit temperature and pressure Variable Load Current and voltage Condenser

Turbine inlet temperature and pressure Boiler temperature


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*Note: When compared to figure 2 (simple ideal Rankine cycle), the steam ejected from the RankineCycler turbine condenses into liquid via the condenser tower and then exits the condenser into a collecting volume at the condensers base, rather than being pumped back to the boiler. This represents the main difference between the simple Rankine cycle described in figure 2, since the liquid exiting the condenser is dispensed, rather than pumped back to the boiler. General Safety The RankineCycler operates at very high pressures and temperatures. It is essential for the safety of everyone on the lab that certain safety precautions are adhered to at all times. If these guidelines are not strictly followed, SERIOUS INJURY OR DEATH MAY RESULT. -Do not touch any of the functional components during operation. These components will be hot. -Do not open the boiler during or immediately following operation. If the pressure gauge indicates positive pressure, the boiler must remain closed. -Do not exceed 120 psig boiler pressure. -Be very careful working near the condensing tower. The steam exiting the tower is still extremely hot. Condensation drained from the bottom of the tower is also very hot. -If the scent of gas is detected at any time during operation, shut the equipment down immediately. -If any questions or concerns arise during equipment operation, notify the TA immediately.

D. EXPERIMENTAL PROCEDURE Do not begin operation without proper supervision. Prior to beginning any operation, ensure that a trained lab technician, TA, or faculty member is present. Prior to operation, familiarize yourself the following operator controls: GAS VALVE The gas valve is a simple two-position valve (On or Off). It is located on the far right side of the slanted operator control panel. It will prevent gas flow to the burner when in the off position- regardless of any other control positions/settings. KEYED MASTER SWITCH The systems electronic master switch is key operated and is located on the left side of the operator control panel. This key switch supplies power to all electronic and electrically operated components. A green indicator light, located directly above the keyed master switch,


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will light when the master switch is selected to the on position and power is available to the switch BURNER SWITCH The burner switch is labeled as such and is located next to the keyed master switch. The burner switch powers the automatic gas valve and ignition controls. A red indicator light, located directly above the burner switch, will light when the burner switch is selected to the on position and power is available to the switch. LOW WATER INDICATOR The low water indicator is a red light that blinks to indicate low water in the boiler. The system must be shut down if the indicator is active. LOAD SWITCH The load switch functions as a generator load disconnect switch. LOAD RHEOSTAT CONTROL KNOB The load rheostat control knob is connected in series with the load toggle switch and generator DC output terminals. It provides a source of variable generator load. AMP METER The amp meter indicates generator load conditions. VOLTMETER The voltmeter indicates the generator voltage output. STEAM ADMISSION VALVE The steam admission valve controls the steam flow rate to the steam turbine. PRE-START The TA will complete a pre-start procedure prior to the lab period. The pre-start procedure includes safety and operability checks to ensure that the equipment is functioning properly. BOILER FILL Fill the boiler according to the following procedure: 1. Verify that the boiler is empty. 2. Fill the graduated cylinder with 5500mL of distilled water. 3. Connect the fitting on the end of the plastic tube attached to the graduated cylinder to the port on the lower, middle, back side of the boiler (Figure 8). The fitting must snap

into place.


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Figure 8. Boiler fill connection. 4. Set the graduated cylinder on top of the condenser tower (Figure 9).

Figure 9. Boiler fill setup, with graduated

cylinder atop the condenser tower. 5. Drain 500mL of distilled water into the boiler by operating the valve at the base of the graduated cylinder.


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6. Record the water level indicated on the sight-glass attached to the boiler in Table 1. Note: The water level may not be visible for the first 500 to 1000 ml of water added to the boiler.

Table 1. Raw data correlating water volume to observed water level. To be completed by students.

Total Water Volume Added [ml]

Observed Water Level [cm] 500 1000 1500 2000 2500 3000 3500 4000 4500 5000 5500 7. Repeat steps 5 and 6 until all 5500mL of water have been drained into the boiler. Record the total volume of water within the boiler, and the corresponding water level each time. The data recorded during this step will be used to develop a correlation relating boiler water level to the remaining volume of water within the system. This correlation may be found by entering the data into Excel, and obtain a curve fit of the data. The resulting function can be used to calculate the total volume of water consumed during a steady-state run.

If the duration of the run is known, the mass flow rate can be computed.

Where [

] and duration of run .

START 1. Open liquid propane (LP) bottle gas valve all the way


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2. Turn gas valve knob CCW to "on" position 3. Turn master switch on (observe green indicator light on) 4. Turn the load switch to the "on" position. 5. Set the load rheostat to ~1/2 maximum load. 6. Turn burner switch on (observe red indicator light on) NOTE: Combustion blower starts automatically. Wait for 30 seconds. This will allow the lines to purge. Then turn the burner switch to the "off" position and immediately back on (this step can be eliminated from the start procedure if the system has previously been operated using the currently attached LP source). This resets the starting cycle and assures that the lines are purged. After approximately 20 seconds, the automatic gas valve will open and the burner will light. 7. Ensure that the steam admission valve is fully closed to allow steam pressure to accumulate in the boiler. 8. Boiler pressure indication should be observed within 3 minutes of ignition. 9. Allow the boiler pressure to increase to approximately 110 psig. NOTE: SHUT OFF BURNER SWITCH IF THE BOILER PRESSURE EXCEEDS 120 PSIG. 10. Observe the voltmeter and gently open the steam admission valve. Regulate turbine speed to indicate 7-10 volts. This will pre-heat the turbine components and the pipes. Close valve after 30 seconds and wait for boiler pressure to return to 110 psig. Very small leaks may be visible due to condensation and cold turbine bearing clearances. This is normal and will stop after normal operating temperatures are attained. 11. Repeat step 10 two more times (three times total) to completely pre-heat the

system. DATA COLLECTION The TA will create a folder for you on the data acquisition computer prior to the start of the experiment. 1. Open the RankineCycler data acquisition program on the laptop attached to the device.

Set the pressure units to PSIG, as shown in Figure 10 . Also, open a plot of Boiler Pressure vs. Time by clicking on the Plot Data button (Figs 11 and 12).


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Figure 10: Change the pressure units to PSIG.

Figure 11: Click the Plot Data button.


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Figure 12: Set the plot output to Boiler Pressure. 2. Ensure that the load switch is on, and the load rheostat is set to ~ load. 3. Allow the boiler pressure to return to 110 psig. 4. Gently open the steam admission valve, and make fine adjustments to achieve a steady-state condition at 100 psig. Each group must determine their own steady-state

tolerance. It is helpful to use the real-time boiler pressure display on the RankineCycler data acquisition program. 5. Once a steady-state has been reached, simultaneously: a) Begin data acquisition by clicking the Log Data to File button in the RankineCycler program (Figure 13). A dialog box will open asking you to specify a file name and location for the data file. Data acquisition will begin after designating the file name. b) Record the starting water level in Table 2. c) Begin timing for 3 minutes.


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Figure 13: Click the Log Data to File button to begin data acquistition. A dialog box will open, asking you

to specify a file name. During data acquisition, you may continue to make fine adjustments to the steam admission valve to maintain your desired steady state. 6. After 3 minutes have passed, stop the data acquisition by clicking the End Data Log button (Figure 14) and record the final water level in Table 2. 7. Open the Excel data file to ensure that data was recorded successfully. 8. Repeat steps 2 through 7 with the rheostat set to load. Be sure to designate a new file name for the second run, otherwise all data from the first run will be overwritten. Table 2. Water level and time data. To be completed by students.

Load Setting Initial Water Level [cm] Final Water Level

[cm] Total Run Time

[mm:ss] 50% 75%


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Figure 14: Click the End Data Log button to end data acquisition.

SHUT DOWN 1. Leave the steam admission valve open after the final data collection run. 2. Move the burner switch to the "off" position. 3. Turn gas valve off. 4. Turn LP gas bottle valve off. 5. Slowly open the steam admission valve to release the remaining pressure. Do not allow the generator voltage to exceed 12V. 6. Turn the master switch to the off position. EMERGENCY SHUTDOWN 1. Turn the master switch to the OFF position. 2. Unplug RankineCycler power cord. 3. Move to a safe distance. 4. If safety is not compromised: Turn load rheostat to maximum, open steam admission valve to obtain maximum voltage.


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E. PRE-LAB Complete the following thermodynamic problem. This is intended to provide a review of the Rankine cycle. 1. Read the entire lab procedure. You will be responsible for conducting the lab as a group, and are expected to know the procedure completely ahead of time. 2. Consider a steam power plant that operates on a simple ideal Rankine cycle and has a net power output of 30 MW. Steam enters the turbine at 7 MPa at 500C and is cooled in the condenser at a pressure of 10 kPa by running cooling water from a lake through the tubes of the condenser at a rate of 2000 kg/s. Show the cycle on a p-v, and a T-s diagram with respect to saturation lines, and the determine (a) the thermal efficiency of the cycle, (b) the mass flow rate of the system and (c) the change in temperature of the cooling water. 3. Compute the Carnot efficiency of the cycle described in part 1. Discuss the reasons for any difference between the Rankine and Carnot efficiencies. How would you increase the efficiency of the Rankine cycle? 4. The boiler used in this lab burns Liquid Propane (LP) as a fuel. What is the energy content per unit volume of gaseous LP? 5. If 6 litres/min of LP is supplied to the boiler, what is the steady-state energy consumption per hour? 6. Assuming the entire system is 35% efficient, how much electrical power (in watts) will be generated? 7. The boiler used in this lab is a shell and tube style construction. Calculate the available volume for water in the boiler given the following basic construction dimensions: Main Shell External Length = 29.65 cm Main Shell Wall Thickness = 0.64 cm End Plate Outside Diameter = 20.70 cm End Plate Wall Thickness = 0.64 cm Main Flame Tube Outside Diameter = 5.08 cm 17 Return Pass Flame Tubes Outside Diameter = 1.90 cm If 5500 ml of water is added to the boiler, how much volume will be left unoccupied in the boiler? If one or more flame tubes pass through this unoccupied space, how will this affect the system (thermodynamically)? F. DATA ANALYSIS AND REPORTING REQUIREMENTS 1. Using the boiler water level data you collected in Table 1, develop a linear correlation relating the observed water level to the volume of water in the boiler. 2. From the time-averaged data collected by the computer, calculate the values of enthalpy and entropy for the state points 4, 1 and 2. Why do we exclude state point 3? For state 4,


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assume saturated liquid at the measured boiler pressure. Why is this assumption necessary (e.g. why not use the measured temperature for state 4)? 3. Plot the state points 4, 1 and 2 (as shown in Figure 3). 4. Compute the turbine work (Watts). The water level/volume correlation, obtained in Step 1, can be used to determine the mass flow rate. 4. Compute the generator work from the measured voltage and current measurements. 5. Compute the (rate of heat addition) to the boiler from the fuel flow rate and the heating value of the fuel (propane). 6. Compute the cycle efficiency. Identify and discuss sources of inefficiency in the system. You must go beyond the obvious sources of inefficiency for this step. Pay careful attention to the raw data you obtained, and consider how it compares to an ideal Rankine cycle. Suggest modifications which would improve cycle efficiency. Complete these steps at both operating conditions ( and load). G. REFERENCES 1. RankineCycler Operations Manual, Turbine Technologies, Ltd., Chetek, WI. 2. Cengel, Y. A. and Boles , M. A., Thermodynamics, An Engineering Approach (4th Edition), McGraw-Hill, 2002 3. "Rankine Cycle." Wikipedia, the Free Encyclopedia. Web. .

MEM311: Thermal and Fluid Science Laboratory Experiment 5: Lift Characteristics of an Airfoil Section

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EXPERIMENT 5: LIFT CHARACTERISTICS OF AN AIRFOIL SECTION by Brandon Terranova 2010, adapted from Bakhtier Farouk and David Staack A. OBJECTIVES Determine lift force and coefficient for an airfoil section at different angles of attack for several tunnel velocities. B. THEORY Airfoil geometry The wing of an airplane is its primary lifting device. Lift is the force that counteracts the aircraft weight and causes flight. The simplified cross-section of an infinite wing, an airfoil, is often tested in wind tunnels to accurately and optimally design the wing of an aircraft. The study of actual wing geometries (finite wings) is built on the understanding of the idealized airfoil aerodynamics. A schematic of the airfoil geometry with associated terminology is shown in figure 1 below.

Figure 1: Airfoil geometry This experiment uses the NACA-2415 airfoil, which is one of the NACA 4-digit series standard airfoils. The National Advisory Committee on Aeronautics (NACA) studied the characteristics of airfoils to develop a database for aeronautic engineering design. Notice that this particular airf

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MEM311 Manual 09192014