Saturation Pressure Lab v3c

8/19/2019 Saturation Pressure Lab v3c

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Chapter 6

Saturation Pressure & Vapor Quality

Liquid-vapor phase change (evaporation and condensation) are extremely important to many, manyindustries. Processes such as distillation and separation in petroleum refineries, electrical powergeneration in steam power plants, and refrigeration cycles all depend upon control of evaporationand condensation.

6.1 Background

Evaporation (and boiling) is the process in which liquid becomes vapor and in doing so absorbs ameasure of thermal energy known as latent heat. As an example, to maintain a constant temper-ature the human body requires cooling to offset the thermal energy released during the metabolicprocess. Perspiration, consisting primarily of salt water, evaporates thereby cooling the surface of the skin. The process of evaporation occurs at a constant temperature. The cooling effect arisesfrom the loss of thermal energy; that is, the transfer of latent heat. The temperature at which evap-oration and condensation occurs is known as the saturation temperature. The correspondingpressure is known as the saturation pressure. The temperature at which evaporation or boilingoccurs varies with pressure. It is a common observation that water boils at a temperature less than

100 ○

C at a high altitude, such as encountered on mountains, because the atmospheric pressure isless at these elevations.

Figure 6.1. General pressure-temperature relationship.

Figure 6.1 illustrates the relationship between pressure and temperature for the solid, liquid,and vapor phases of a substance. The triple point is the temperature and pressure at which all threephases can coexist. The line separating the solid-liquid regions represents a set of temperatures


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38 CHAPTER 6. SATURATION PRESSURE & VAPOR QUALITY

and pressures at which the solid and liquid phases (ice and water) may coexist. Similarly, theline separating the liquid-vapor regions represents a set of temperatures and pressures at whichthe liquid and vapor phases (water and steam) may coexist. The critical point is the pressure-temperature state beyond which there is no distinction between liquid and vapor phases.

6.1.1 Quality of VaporThe thermodynamic state of a single phase fluid (gas or liquid) can be determined if two propertiesare known. So, if the pressure and temperature are measured and the system is in thermal equilib-rium, then all of the other properties at this state can be determined. If two phases are present (va-por and liquid), then three thermodynamic states must be known. For

example, consider a liquid is inequilibrium with its vapor in aclosed system at some tempera-ture and pressure as illustrated.Since the two phases coexist inequilibrium, the temperature is

the saturation temperature, T

sat.The exact same saturation tem-perature and pressure can be ob-tained with less liquid in the sys-

tem. In fact, the exact same temperature and pressure can be obtained without any liquid in thesystem. Just knowing the temperature and pressure is insufficient to determine the system’s statebecause the mass, density, and specific volume are not a unique to this temperature and pressure.

Any three properties may be used in specifying the thermodynamic state of a two-phase mixture.One property typically used, in addition to temperature and pressure, is quality. Quality, x, isthe ratio of vapor mass, mg, to mixture mass, mg +mf :

1

x =mg

mg +mf (6.1)

Therefore, x1 < x2 < x3 = 1. The quality of saturated liquid is 0 an the quality of saturatedvapor is 1. The thermodynamic properties of the mixture which are dependent upon mass can beexpressed using quality. The specific volume (volume per mass) of the systems in the illustration isv = (1 − x)vf + xvg. Other properties dependent upon mass such as internal energy, enthalpy, andentropy can be determined in a similar manner.

6.1.2 Pressure, Temperature and Density of a Saturated Mixture

Three properties are required to specify the thermodynamic state of a two-phase mixture. Of the numerous fluid properties, there are three which are relatively easy to determine; pressure,temperature, and density. The specific volume, v, is an intensive property which is the inverse of density, v = 1ρ.

Figure 6.2 illustrates the relationship between pressure, temperature and specific volume for aliquid-vapor system. The diagram is of pressure versus specific volume (P -v diagram) and lines of constant temperature (isotherms) are shown. The saturated state, that is the state at which vaporand liquid coexist, is defined by the saturation curve. The region to the right of the saturationcurve is superheated vapor and the region to the left of the saturation curve is subcooled liquid. In

1 By convention, a subscript f is used to denote the liquid phase and a subscript g to denote the vapor phase.

The subscript f g denotes the difference between the vapor and liquid, i.e. hfg = hf − hg.


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6.1. BACKGROUND 39

Figure 6.2. Pressure vs Specific Volume (P-v) diagram for a fluid illustrating the relationship betweenthe saturation curve, isotherms (T 2 > T 1), and regions of subcooled liquid and superheated vapor.

order to condense superheated vapor at a constant pressure, the temperature must be reduced untilthe vapor reaches the saturation curve. Similarly, evaporation of a subcooled liquid at a constantpressure requires increasing the liquid temperature until the saturation curve is reached.

At a saturation temperature of T 1 and saturation pressure of P 1, the liquid specific volume isv1f and the vapor specific volume is v1g. The specific volume of the mixture is a ratio of the liquidand vapor specific volumes based on the mass ratio of liquid and vapor as defined by the quality.

v1 = (1 − x)v1f + xv1gNote, however, that there is no saturated fluid, vapor or liquid, which has a specific volume betweenthese two values. All of the liquid is at v1f and all of the vapor is at v1g. When a portion of theliquid evaporates, the specific volume immediately jumps to v1g. There is no stable thermodynamicstate under the saturation curve. The saturation curve delineates the stable liquid thermodynamicsstates from the stable thermodynamic states of the vapor.

6.1.3 Thermodynamic Property Data

The relationship between saturation pressure, saturation temperature and other thermodynamicproperties such as specific volume, internal energy, enthalpy, specific heats, and entropy for waterand common refrigerants can be found in most standard thermodynamic textbooks [ 1, 10]. Moreextensive property data bases for a wide variety of fluids is available in software programs [ 9] and

online data bases such as that provided by the National Institute of Standards and Technology(NIST). The saturation tables generally list temperature, pressure, and then saturated liquid andvapor values for specific volume (vf , vg), internal energy (uf , ug), enthalpy (hf , hg), and entropy(sf , sg). The specific volume, internal energy, enthalpy and entropy of the liquid-vapor mixturecan only be determined once the quality is known.

If the calculated quality is greater than 1, then the fluid is not in a saturated state. Thereis no liquid present and the thermodynamic state is that of superheated vapor. A separate settof property tables and data bases are required to determine the properties of superheated vapor.Likewise, if the quality is calculated to be less than 0, then there is no vapor present and the system


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is a subcooled liquid. Still another property table or data base is required for subcooled liquid.Quality is only a property of saturated liquid-vapor and must have a value between zero and one(0 ≤ x ≤ 1).

6.1.4 Measuring Quality

Measuring quality directly is extremely difficult, especially in an open system where fluid is flowingin and out of a process. To measure quality, a two-phase mixture with two known properties suchas pressure and temperature is passed through a constant temperature process where all of theliquid evaporates so that only vapor exists. This is known as throttling a mixture.

Figure 6.3 illustrates the process. Saturated liquid and vapor at high pressure (P sat) is allowedto expand through a flow restriction resulting in a sharp decrease in pressure. If the temperaturecan be held constant and the pressure is decreasing, then the vapor moves from a saturated stateto a superheated state. This process can be seen in Fig. 6.2. Starting with saturated vapor at T 1,P 1, and v1g, if the pressure drops but the temperature remains constant then the vapor will traveldownward on the isotherm T 1 into the superheated region. As this occurs, any liquid present will“flash” to vapor in order to follow the drop in pressure. If the process illustrated in Fig. 6.3 can be

thoroughly described, then there should be sufficient information to determine the quality of theliquid-vapor mixture prior to throttling.

Figure 6.3. Throttling process for a liquid-vapor mixture.

The throttling process can be analyzed by applying Conservation of Energy (the First Law of

Thermodynamics) to a Control Volume surrounding the throttle in Fig. 6.3. There will be flowacross the control surface – into the left side and out of the right side – so this is considered anopen system. A number of simplifying assumptions are appropriate for this control volume:

steady flow ⇒ there is no accumulation of energy or mass within thecontrol volume

uniform flow ⇒ there is no variation in properties over the flow areas;there is no velocity profile to the inlet or outlet flow soit is not necessary to integrate the property variationover the flow area.

With these assumptions the Conservation of Energy for the control volume is reduced to:

Q̇− Ẇ = exits

ṁe he + V 2e2 + gze −

inlets

ṁi hi + V 2i2 + gzi (6.2)

where Q̇ is the transfer of heat across a control surface, Ẇ is the transfer of work across a controlsurface, ṁ is the mass flow rate across a control surface and (hi+V 22+gz) is the energy associatedwith the mass flow with the terms representing enthalpy, kinetic energy and potential energy,respectively. If the throttle is well insulated, then there will be no heat transfer (adiabatic) andthere is no work which crosses the control surface. The change in kinetic energy and potential


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6.1. BACKGROUND 41

energy across the throttle is nearly always negligible. Finally, since there is no accumulation of mass (steady flow), ṁe = ṁi. Thus, equation (6.2) for the throttling process reduces to

hi = he (6.3)

The enthalpy at the exit, he, can be determined if the pressure and temperature are known because

the exit condition is superheated vapor. This is a single phase so only two properties need to bemeasured to define the thermodynamic state. The value of the enthalpy at the inlet, hi, is definedby the amount of fluid in the liquid state and vapor state.

hi = (1 − x)hf + xhg (6.4)The saturation enthalpies, hf and hg, can also be determined if the pressure and temperature areknown. Thus, by combining equations (6.3) and (6.4), the quality can be found:

x =he − hf

hg − hf (6.5)

6.1.5 Empirical Correlation for Saturation Pressure and Temperature

There are times when tables of numbers for saturation properties are not convenient to use; suchas with spreadsheet programs like Excel, Lotus123, and Quattro. An empirical correlation be-tween saturation pressure and temperature could be useful. When plotted on a graph of absolutetemperature, T abs, against absolute pressure, P abs, the result is a smooth curve (Fig. 6.4). Thesaturation curve is not described completely by any single, simple equation, but over a limitedrange of pressure it is possible to obtain a good fit using:

P abs = b eaT abs (6.6)

where a and b are empirically determined coefficients. This equation is not derived from any theory

or underlying physical laws. It only approximately describes the relationship between saturationtemperature and pressure. For any particular range of pressures, there will be specific values of the coefficients a and b which minimize the differences between the measured values and the curvedescribed by equation (6.6). These differences arise both through experimental errors (random,scale and zero errors) and because the real behavior does not perfectly match the equation.

Attempting to fit experimental data to equation (6.6) is extremely difficult and likely to resultin very large discrepancies in the calculated coefficients. A more accurate approach would be tolinearize equation (6.6) using logarithms.

lnP abs = ln b + a 1T abs

(6.7)Thus, plotting lnP vs T (semilog plot) results in a straight line and standard least squares methodsmay be used to determine accurate values for the coefficients a and b which are the slope and theintercept, respectively, of the plot of lnP abs vs 1T abs. Rearranging equation (6.7) reveals that b isa reference pressure and a is a reference temperature.

lnP absb

= aT abs

(6.8)

Holman [11, §3.17] provide a more detailed discussion on plotting data.


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Figure 6.4. Saturation Temperature Plot for Water

6.1.6 Atmospheric Pressure

The pressure gauge you will be using in the saturation pressure and throttling experiments readsa gauge pressure; that is, a differential pressure relative to the local atmospheric pressure measure-ment. As such, you must add atmospheric pressure to the pressure reading in order to developan accurate correlation between saturation temperature and pressure. It is not sufficient to add astandard sea-level value of atmospheric pressure. You must measure the local atmospheric pressure.

Mercury Barometer

A barometer is a well-type manometer used to measure atmospheric pressure. The measurementtube is sealed so that the pressure at the top of the liquid column is the vapor pressure. The heightof the liquid column is balanced by the difference between the vapor pressure in the measurementtube and atmospheric pressure at the well. Mercury is used in barometers because of its highdensity (SG = 13.58) and because its vapor pressure is extremely low.


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6.2. OBJECTIVES 43

at 0 ○C (32 ○F) P v = 0.0247 Pa (3.58 × 10−6 psia)

at 20 ○C (68 ○F) P v = 0.16 Pa (2.32 × 10−5 psia)

The vapor pressure of mercury is so low that it canbe neglected in the calculation of atmospheric pressure.

P atm = (ρHg,liq − 0ρHg,vap)gh (6.9)An accurate measure of atmospheric pressure requires useof the local value of the gravitational acceleration and themercury density at the current temperature. If the localgravitational acceleration and/or the density of mercuryare not known, then standard values for both may be usedwith correction factors added to the height:

P atm = (ρHg at 0○C)(gstd) (h + ∆hg + ∆hT ) (6.10)where ∆hg is the correction to the gravitational accelera-

tion based on latitude. The standard gravitational acceleration is gstd = 9.80664 m/s2 (32.124 ft/s2)

at 45.5○ latitude. Houghton is at a latitude of 47○ 7.5’. The temperature correction, ∆hT , correctsthe observed height, h, to both the standard temperature of the measurement scale of 16.7 ○C(62 ○F) and the standard density of mercury at 0 ○C (32 ○F) which is ρHg = 13595.5 kg/m

3 = 26.35slug/ft3. Correction tables for ∆hg and ∆hT are available in the laboratory.

6.2 Objectives

The objectives of this laboratory exercise are to:

• study the relationship between saturation pressure and temperature of a water-steam mixture,

• use property tables (steam tables) to determine the thermodynamic state of a liquid-vapormixture,

• use linearization methods to obtain best fit correlations to non-linear data,

• measure the quality of a liquid-vapor mixture via throttling, and

• determine the atmospheric pressure using a mercury barometer.


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6.3 Experiment

The saturation and throttling experiments will be conducted on the Armfield TH3 SaturationPressure Units. Figure 6.5 is a schematic of the basic system. Refer to the Fig. 6.6, 6.7, and 6.8and Table 6.1 for location and description of the part numbers.

Figure 6.5. Schematic of Saturation Pressure Rig.

The saturation pressure apparatus consists of a fluid loop with an insulated cylindrical boiler (2)in one of the vertical lines. Distilled water in the boiler is heated to the boiling point using a pair of cartridge heaters (11) that are located near the bottom of the boiler. A sight glass (10) on the frontof the boiler allows the internal processes to be observed, namely boiling patterns at the surface

of the water while heating or reducing the system pressure and cessation of boiling/condensationduring cooling. The sight glass also allows the water level in the boiler to be monitored. Saturatedsteam leaving the top of the boiler passes around the loop before condensing and returning to thebase of the boiler for reheating. The operating range of the boiler and loop is 0 to 8 bar gauge.A pressure relief valve (5) is set to open at 8 bar. NEVER lean over or place your handabove the pressure relief valve! The top line of the loop incorporates an platinum RTD (3)and a pressure transducer (9) to measure the properties of the saturated steam. A Bourdon tubepressure gauge allows for monitoring of the boiler pressure even when there is no power to the unit.A fill/vent tube (38) connected to the fill/vent valve (4) on the line allows the loop to be filledwith distilled water and allows all air to be vented safely before sealing the loop for pressurizedmeasurements. The bottom of the fluid loop has a drain valve (39).

A throttling valve (6) and a throttling calorimeter (7) are attached to the vapor line, thepurpose of which is to demonstrate the measurement of steam quality, x. The steam expandsto atmospheric pressure as it passes through the throttling calorimeter. A platinum RTD (14)measures the temperature of the superheated vapor. A container (15) below the calorimeter collectscondensing vapor and allows it to be drained safely from the apparatus.

6.3.1 Procedures

Review all of the experiment procedures prior to starting this experiment. Refer to theFig. 6.6, 6.7, and 6.8 and Table 6.1 for location and description of the part numbers.


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6.3. EXPERIMENT 45

Startup

1. Verify proper water level in the sight glass (10) of the boiler (2).

2. Verify that the fill/vent valve (4), the throttling valve (6), and the drain valve (39) are closed. Thethrottling valve is closed when the valve handle is perpendicular to the tube; for this apparatus, thevalve is closed when the handle is vertical.

Saturation Pressure Experiment

3. Switch the heaters (36) ON and turn the heater power control (37) to MAXIMUM. Verify that thethrottling valve closed (6).

4. Observe the appearance of the fluid in the boiler (2) through the sight glass (10) as the temperatureincreases.

5. Record in the saturation curve data table the pressure and temperature at approximately every 1 bar(100 kPa) increment until the boiler reaches the maximum working pressure of 7 bars gauge. Thepressure can be read from the sensor readout display (26) on the console (20). The sensor selectorswitch (27) on the console may be used to toggle the readout between the platinum RTD sensor,PT100(1), and the pressure transducer. The pressure reading is gauge pressure so the atmosphericpressure will have to be measured in order to convert the transducer reading to absolute pressure. The

temperature reading is the resistance of the RTD. The resistance can be converted to temperatureusing Table 6.2.

Throttling Experiment

6. When a pressure of 7 bar gauge has been reached, turn off the heaters (36) and reset the heater powercontrol (37) to zero.

7. OPEN the throttling valve (6).

8. As the pressure decreases, record in the throttling process data table the pressure and both RTDreadouts at every 100 kPa decrement until the boiler reaches zero pressure. The pressure decreasesrapidly so plan in advance who will be switching the display and who will be recording each of thesensor readouts. Note that since the throttling calorimeter insulation has been removed, the firstfew seconds of throttling is not adiabatic. Heat is being transferred from the fluid to the throttlingcalorimeter (7). Therefore, the assumption that the process is adiabatic is incorrect and equation (6.3)is invalid. The temperature of the throttling calorimeter will increase quickly and after a few secondsthe process becomes adiabatic and equation (6.3) will be valid.

Shutdown

9. After the last set of readings SWITCH OFF the unit. LEAVE THE THROTTLING VALVEOPEN to bleed some steam. Leaving the valve closed when the system is at high temperature mayproduce a partial vacuum upon cooling which could damage the apparatus.


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Figure 6.6. Top view of Armfield TH3 Saturation Pressure Rig.

Figure 6.7. Side view of Armfield TH3 Saturation Pressure Rig.


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6.3. EXPERIMENT 47

Figure 6.8. Front and back panels of experiment control console.

Table 6.1. Component Description for the Armfield TH3 Saturation Pressure Apparatus

1 frame2 boiler3 temperature probe, PT100 (1)4 fill/vent valve

5 pressure relief valve6 throttling valve7 throttling calorimeter8 Bourdon tube pressure gauge9 pressure transducer

10 sight glass11 cartridge heaters12 shield1314 temperature probe, PT100 (2)15 condenser cup16 RTD connector, PT100 (1)17 RTD connector, PT100 (2)

18 pressure transducer connector19 cartridge heater connector20 TH3 control console

2122 console power breaker, CONT23 cartridge heater breaker, HEAT24 auxiliary power breaker, O/P

25 power input26 sensor readout27 sensor selector switch28 input/output data port, IFD329 power cable30 power switch31 heater connector32 pressure transducer connector33 PT100 (2) RTD connector34 PT100 (1) RTD connector35 auxiliary 120 A/C power36 heater switch37 heater power control

38 fill/vent tube39 drain valve4041 pressure relief line


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Name:

Date:Data Sheet for Saturation Curve

P atm: mm Hg

kN/m2

R1 T 1 T abs P 1,gauge P abs

Ω ○C K 1/T abs kN/m2 kN/m2 ln(P abs)

Data Sheet for Throttling Process

P atm: mm Hg

kN/m2

R1 T 1 T 1 R2 T 2 T 2 P 1,gauge hf hg h2 quality

Ω ○C K Ω ○C K kPa KJ/kg KJ/kg KJ/kg x

LEAVE THE CALORIMETER VALVE OPEN when the lab is completed.


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6.3. EXPERIMENT 49

T a b l e 6 . 2 .

R T D

R e s i s t a n c e – T e m p e r a t u r e C o n v e r s

i o n T a b l e


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6.4 Measuring Atmospheric Pressure

During this experiment you will determine the local value of the barometric pressure using a Fortinbarometer. Record all data in the table provided in §6.4.1. The basic procedures are as follows:

1. Set the fiducial point: The lower mercury surface in a Fortin barometer hasto be set to a datum level before adjusting its vernier and the accuracy of pres-sure measurement depends crucially upon proper setting. The mercury surfaceshould first be lowered until it is clearly below the fiducial point (F). Tap thebarometer lightly to stabilize the meniscus. Then very slowly turn adjustingknob (A) until the gap between fiducial point and the reservoir mercury surface just disappears when viewed horizontally. The point should make no more thanthe slightest dimple in the mercury surface. If the mercury surface is brightand the level correct, the tip of the fiducial point will coincide with the reflectedimage on the mercury surface. The setting will only be correct if the mercurysurface is raised to the fiducial point, not lowered. If while raising the surfacethe fiducial point penetrates the surface, the mercury level should be loweredand the procedure restarted. A dirty mercury surface, poorly shaped fiducial

point or a partially clogged porous plug (P) can make proper and repeatablesetting very difficult.

2. Setting the Vernier: The vernier (V) should be lowered until both the frontand back edges of the vernier coincide with the apex of the mercury meniscus when viewingexactly horizontal.

3. Reading the Vernier: There are two measurement scales (S); an Englishunit scale (inches) and a SI unit scale (mm). The vernier has two gradationscorresponding to each scale. After setting the vernier, read both scales simul-taneously.

4. Measure the Barometer’s Temperature: A thermometer is attached tothe barometer for measuring the temperature.

5. Apply the Gravitational and Temperature Corrections to the Ob-served Height: The barometer manual contains both English and SI correc-tion factors for latitude and temperature.


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6.4. MEASURING ATMOSPHERIC PRESSURE 51

6.4.1 Data Log for Atmospheric Pressure Measurement

Name:

Date:

Lab Partners:

Complete the table for both sets of units.

SI Units English Units

Room Temperature ○C ○F

Mercury Density (std) kg/m3 slug/ft3

Mercury Height (observed) mm in

temperature correction mm in

latitude correction mm in

atmospheric pressure mm Hg in Hg

kPa psia

National Weather Service mm Hg in Hg

kPa psia

Notes and Calculations:


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Saturation Pressure Lab v3c