Mechanical Engineering Systems 2008 Part 4 potx

Thermodynamics 67 Types of steam Most of us see steam only when we boil the kettle, but we can learn something even from this. We observe that because it is able to lift the kettle lid, steam can do work. Because we can scald our hands with it, we know that it can transfer heat energy. Also, if we look closely at the steam coming out of the spout, we can see water droplets, or a water mist, within it, indicating it is what we call ‘wet steam’. All boilers, of whatever size, are doing the same thing as the kettle, i.e. boiling water. For low grade applications such as heating, we may need only hot water. For turbines we are interested in much higher temperatures and pressures to produce steam of the right quality. We have already said that the steam produced by a kettle is wet steam. This sort of steam is made up of water droplets and ‘pure steam’, i.e. steam which does not have water droplets. If the steam was taken away from the water from which it is produced, and more heat energy added, some of the droplets would change into pure steam, and the steam would be drier. Eventually all the water droplets would have changed state and the steam would be dry. The steam produced from the boiling water is at the same temperature as the water. This is called the saturation temperature, t s . The steam cannot rise above this temperature until all the water droplets have disappeared, because all the heat energy supplied is used to change the state of the water droplets, i.e. latent heat of vaporization. A soon as the steam has dried, and if more heat energy is supplied, the temperature of the steam will increase to produce superheated steam, i.e. steam above the saturation temperature of the water from which it was produced. Using tables of steam properties – steam tables – we can find the energy of the steam. This energy is available to do work in a turbine or to be transferred for heating purposes. The production of steam Figure 2.6.1 shows diagrammatically the production of steam. (1) Boiling water, i.e. water at saturation temperature, t s . (2) Wet saturated steam. Steam composed of water droplets and ‘pure steam’. Temperature, t s . Low dryness fraction, x. (3) Wet saturated steam. More water droplets have changed into ‘pure’ steam. Temperature, t s . Dryness fraction, x, higher. Key points ᭹ Wet steam cannot be superheated. ᭹ Steam containing water droplets is called wet sat- urated steam. ᭹ Steam not containing water droplets, but which is at saturation tempera- ture, is called dry sat- urated steam. ᭹ Steam above saturation temperature is known as superheated steam. ᭹ The degree of wetness of saturated steam is given by its dryness fraction, x. This is a value between 0 and 1. The higher the value, the drier the steam and the more heat energy the steam will contain. Dryness fraction is the ratio of the mass of pure steam to the total mass of the steam sample, and indicates what is called the quality of the steam. Key points To fix a value in the steam tables: ᭹ If the steam is wet, we need to know its pressure and its dryness fraction. ᭹ If the steam is super- heated, we need to know its pressure and its tem- perature. Figure 2.6.1 Production of steam 68 Thermodynamics (4) Dry saturated steam. No water droplets. Temperature, t s . Dryness fraction, x =1. (5) Superheated steam. Temperature above, t s . The steam temperature cannot be raised above saturation temperature, t s , until all the water droplets have gone. The temperature/enthalpy (T/h) diagram Figure 2.6.2 shows a simplified diagram of temperature against enthalpy, h. Remember to think of enthalpy as ‘total energy’ made up of internal energy and pressure energy. Values of enthalpy are used to calculate heat energy transfer and work transfer, as we see later in this chapter. On the diagram: h f : enthalpy of water at saturation temperature, t s (kJ/kg). h g : enthalpy of dry steam. (kJ/kg). h fg : h g – h f : latent heat of vaporization (kJ/kg). All these values are found in the steam tables, which use the units given. It is worth studying this diagram carefully because it gives a clear picture of what is happening alongside the associated steam table values, and shows dryness fraction and degree of superheat. The diagram can be drawn for any pressure. See Figure 2.6.3 which is an accurate plot of temperature against specific enthalpy. Figure 2.6.2 Simplified T/h diagram for a pressure of 1 bar Figure 2.6.3 Temperature/ enthalpy diagram for vapour Thermodynamics 69 Note the following: ᭹ The liquid, wet steam and superheat regions. ᭹ The saturated liquid line. ᭹ The saturated vapour line. ᭹ The lines of constant pressure. The separating and throttling calorimeter The quality (i.e. the dryness) of wet steam can be found by using a separating and throttling calorimeter. Figure 2.6.4 shows the general arrangement of the device. The separator, as its name suggests, physically separates the water droplets from the steam sample. This alone would give us a good idea of the dryness of the steam, despite that the separation is not complete, because, as we have seen the dryness fraction is the ratio of the mass of pure steam to the total mass of the steam. Having separated out the water droplets we can find their mass to give us the mass of water in the sample, m 1 . The ‘pure steam’ is then condensed to allow its mass to be found, m 2 . Then, Dryness fraction from separator, x = m 2 m 1 + m 2 A more accurate answer is obtained by connecting the outlet from the separator directly to a throttle and finding the dryness fraction of the partly dried steam. In the throttling calorimeter, the steam issuing through the orifice must be superheated, or we have two dryness fractions, neither of which we can find. Throttling improves the quality of the steam, which is already high after passing through the separator, therefore superheated steam at this point is not difficult to create. To find the enthalpy of the superheated steam, we need its temperature and its pressure. Figure 2.6.4 Separator and throttling calorimeter 70 Thermodynamics For the throttling calorimeter, Enthalpy before = enthalpy after throttling (see page 57, ‘Applications of the SFEE’) h f + x.h fg = enthalpy from superheat tables If we call the dryness from the separator, x 1 , and the dryness from the throttling calorimeter x 2 , the dryness fraction of the steam sample is x, given by, x = x 1 × x 2 Example 2.6.1 (Study next section for use of steam tables.) Steam at a pressure of 15 bar was tested by use of a separating and throttling calorimeter. The mass of water collected in the separator was 0.55 kg and the mass condensed and col- lected after the throttle was 10 kg. After the throttle, the pressure of the steam was 1 bar and the temperature 150°C. Find the dryness fraction of the steam sample. Dryness from separator = m 1 m 1 + m 2 = 10 10 + 0.55 = 0.948 = x 1 For the throttle, Enthalpy before = enthalpy after h f + x.h fg at 15 bar = h at 1 bar 150°C 845 + (x 2 × 1947) = 2777 x 2 = 2777 – 845 1947 = 0.992 Dryness of sample = x 1 × x 2 = 0.948 × 0.992 = 0.94 The steam tables Figure 2.6.5 shows a steam tables extract for a pressure of 2 bar. We are concerned at this stage only with p, t s , V g , h f , h fg and h g . Specific enthalpy, h, is the total energy of 1 kg of the steam, made up of internal energy and pressure energy. It is important because it is the energy we want to use in the steam heater or turbine. Specific volume, v, is the volume in m 3 which 1 kg of the steam will occupy. It is important because the size of the boilers and piping, etc., can be estimated using these values. Thermodynamics 71 Pressure is p, and saturation temperature (boiling point corresponding to the pressure) is t s . Once again, refer to Figure 2.6.2 for an idea of these quantities. Finding values in the saturated water and steam section ᭹ To find the enthalpy of water, look up pressure and read off h f . ᭹ To find the enthalpy of dry steam, look up pressure and read off h g . ᭹ To find the enthalpy of wet steam, look up pressure and use h = h f + x.h fg . ᭹ Similarly, to find internal energy values, use u f , u g , and u f + x.u fg . ᭹ To find the specific volume of dry steam, use v = v g . ᭹ To find the specific volume of wet steam, use v = x.v g . Superheated steam These tables are arranged differently from the saturated water and steam tables. Remember that dryness fraction, x, is not involved in these values, because steam cannot be superheated unless all the water droplets have gone. The temperature of the superheated steam must be known. Figure 2.6.6 shows an extract for the details of superheated steam at 10 bar, 350°C. The degree of superheat is the number of degrees above t s . In this case, the degree of superheat is 350 – 179.9 = 170.1°C. Note that most steam tables have a table for water between 0 and 100°C, with corresponding pressures in the second column. This is useful when finding the enthalpy of water, h f , between 0 and 100°C. Figure 2.6.5 Saturated water and steam extract for a pressure of 2 bar Figure 2.6.6 Superheated steam table extract for a pressure of 10 bar, temperature 350°C 72 Thermodynamics Example 2.6.2 Find the enthalpy of: (a) Steam at 6 bar, dry. From tables, h g = 2757 kJ/kg (b) Steam at 50 bar, dry. From tables, h g = 2794 kJ/kg (c) Steam at 12 bar, dryness, x = 0.75 h = h f + x.h fg = 798 + (0.75 × 1986) = 2287.5 kJ/kg (d) Steam at 70 bar, x = 0.9 h = h f + x.h fg = 1267 + (0.9 × 1505) = 2621.5 kJ/kg (e) Steam at 10 bar 300°C. From superheat tables, h = 3052 kJ/kg (f) Steam at 40 bar, 400°C. From superheat tables, h = 3214 kJ/kg (g) Water at 34°C. Refer to temperature only, h f = 142.4 kJ/kg (h) Water at 850°C. h f = 355.9 kJ/kg Example 2.6.3 (a) What volume does 1 kg of steam at 15 bar, x = 1, occupy? v g = 0.1371 m 3 /kg. (b) What volume does 5 kg of steam at 20 bar, x = 0.75 occupy? v g = 0.099 57 m 3 /kg, v = x.v g = 0.75 × 0.099 57 = 0.0747 m 3 /kg. This is the volume 1 kg will occupy. 5 kg will occupy 5 × 0.0747 = 0.3735 m 3 Example 2.6.4 Find the internal energy of: (a) 1 kg of dry steam at 10 bar. u g = 2584 kJ/kg. (b) 3 kg of water at 130°C. Refer to temperature only, u f = 546 kJ/kg. For 3 kg, u = 3 × 546 = 1638 kJ. (c) 1 kg of steam at 50 bar, dryness 0.8. u = u f + x.u fg Values of u fg are not listed in most steam tables, because of space limitations. u fg is the difference between u f and u g , i.e. the difference between the internal energy of the water at saturation temperature and as dry steam (also at saturation temperature by definition). u = 1149 + 0.8(2597 – 1149) = 2307.4 kJ/kg (d) 5 kg of steam at 40 bar, t = 500°C. From superheat tables, u = 3099 kJ/kg. For 5 kg, u =5 × 3099 = 15 495 kJ. Thermodynamics 73 Example 2.6.5 A boiler produces steam at 50 bar, 350°C. What is the degree of superheat of the steam? The degree of superheat is the number of degrees above saturation temperature, i.e. degree of superheat = t – t s . In this case, degree of superheat = 350 – 263.9 = 86.1°C. Example 2.6.6 A vessel of volume 0.2816 m 3 contains dry steam at 14 bar. What mass of steam does the vessel contain? Specific volume of dry steam at 14 bar = v g = 0.1408 m 3 /kg We have 0.2816 m 3 , which is twice this volume, therefore the vessel contains 2 kg. Example 2.6.7 A steam space in a boiler drum has a volume of 0.5 m 3 . If it contains steam at 10 bar, dryness = 0.75, what is the mass of steam in the drum? Specific volume of the steam, v = x.v g = 0.75 × 0.1944 = 0.1458 m 3 /kg Mass of steam in the drum = 0.5 0.1458 = 3.43 kg. Problems 2.6.1 (1) Find the specific enthalpy of the following: (a) Water at 50°C. (b) Steam at 50 bar, x = 0.9. (c) Steam at 2 bar, x = 0.76. (d) Steam at 10 bar, 500°C. (e) Steam at 20 bar, 250°C. (f) Dry saturated steam at 8 bar. (2) If steam at a pressure of 40 bar has a temperature of 450°C, what is the degree of superheat? (3) Find the volume of 6 kg of steam at 5 bar, x = 0.8. Key points ᭹ The steam tables values are specific, i.e. for 1 kg. ᭹ Values of enthalpy and internal energy are kJ/kg. ᭹ For enthalpy of water between 0 and 100°C, use the page of the steam tables where temperature is in the first column. When finding the enthalpy of water, refer to the tem- perature only, disregard- ing the pressure which makes little difference. ᭹ In the superheat tables, for convenience the sat- uration temperature is in brackets beneath the pressure. ᭹ It is necessary to inter- polate between values if a value is in between the values given. See page 86, ‘Maths in action’. 74 Thermodynamics (4) The steam drum in a boiler contains steam at 30 bar, 350°C. If the volume of the drum is 0.4525 m 3 , what mass of steam does it contain? (5) Find the internal energy of 6 kg of steam at 5 bar, dryness 0.9. (6) Steam at 6.5 bar passes from a steam main through a separating and throttling calorimeter. The condition of the steam after throttling is 1 bar, 125°C. The mass of steam condensed after throttling is 25 kg and 1.31 kg of water is collected in the separator. Calculate the dryness of the steam. It is important to have a good working knowledge of the steam tables, and be able to use them routinely for finding the values required. Steam flow processes We have already seen the application of the steady flow energy equation in gas processes. In applying the same equation to steam, instead of using the expression ␦h = m.c p .␦T which applies only to a perfect gas, we refer to steam tables and read off values of h for wet, dry or saturated steam, as required. Example 2.6.8 Determine the power output from a steam turbine if it receives steam at 40 bar, 350°C, and the steam leaving the turbine is at 15 bar, 200°C. The steam mass flow rate is 0.5 kg/s. Figure 2.6.7 shows the turbine. SFEE Q – W = ˙ m ΄ (h 2 – h 1 ) + c 2 2 –c 2 1 2 ΅ neglecting heat losses and velocity changes, W = ˙ m(h 2 – h 1 ) From steam tables, h 1 = 3094 kJ/kg h 2 = 2796 kJ/kg W = 0.5(3094 – 2796) = 149 kW Figure 2.6.7 Example 2.6.8 Thermodynamics 75 Example 2.6.9 Steam enters a heater at 3 bar, dryness fraction, x = 0.8. If the drain from the heater is steam at 1 bar, x = 0.3, what is the heat energy transferred per kg of steam, assuming no losses? Figure 2.6.8 shows the heater. From the SFEE, Q = ˙ m(h 2 – h 1 ) From steam tables, h 1 = h f + x.h fg = 561 + (0.8 × 2164) = 2292.2 kJ/kg h 2 = h f + x.h fg = 417 + (0.3 × 2258) = 1094 kJ/kg Q = 1(2292.2 – 1094) = 1198.2 kJ/kg If the mass flow rate of steam through the heater is 0.2 kg/s, what is the heater rating in kW? Q = 0.2 × 1197.8 = 239.6 kW Problems 2.6.2 (1) Determine the power output from a steam turbine if it receives 2 kg/s of steam at 50 bar, 400°C and the steam leaves the turbine at 0.5 bar with a dryness of 0.2. (2) In a steam turbine plant, the steam supply to the turbine is 44 bar dry saturated and the exhaust steam is 0.04 bar with a dryness of 0.69. Determine the power output from the turbine for a steam mass flow rate of 3 kg/s. (3) A turbo-generator is supplied with superheated steam at a pressure of 30 bar and temperature 350°C. The exhaust steam has a pressure of 0.06 bar, dryness 0.88. Find: (a) The enthalpy drop per kg of steam; (b) The power developed if the steam flow rate is 0.25 kg/s. (4) Steam enters the heating coils of an evaporator at 3 bar, 300°C and leaves as water at 25°C. How much heat energy has been given up per kg of steam to the water in the evaporator? If there are 75 kg of water at 25°C in the evaporator, to what temperature will it rise after 6 kg of steam have passed through the heating coil? Specific heat of water = 4.2 kJ/kgK. (5) Steam enters the superheaters of a boiler at a pressure of 20 bar, dryness 0.8, and leaves at the same pressure at a temperature of 300°C. Calculate the heat energy supplied per kg of steam in the superheaters and the increase in volume of the steam through the superheaters. Figure 2.6.8 Example 2.6.9 76 Thermodynamics Steam plant If we consider all the items in a simple steam plant, we have boiler, turbine and condenser. For calculation purposes it is usual to neglect the feed pump which supplies water to the boiler. Figure 2.6.9 shows the basic steam plant. Each of these items involves a steady flow process, and as we saw in Section 2.5, and in the foregoing examples, the SFEE can be reduced to a very simple form. For each item then, it is a simple matter to find the work or heat energy transfers if we know the condition of the steam or the temperature of the water as the case may be. We can then find turbine power, heat energy lost to condenser cooling, heat energy supplied to the boiler and plant efficiency. If we made the plant more sophisticated by adding feed heaters (steam heaters which pre-heat the boiler feedwater), multi-stage expansion in the turbines, de-aerators (to remove oxygen from the feed to reduce corrosion), and other refinements, we could use the simplified SFEE for these too, since they are all steady flow. It is convenient to show steam processes on axes of properties, and a complete steam plant cycle can then be seen. In the introduction to steam, we looked at a simplified temperature/ enthalpy curve as an aid to understanding the production of steam and the values shown in the steam tables. To show steam processes in steam plant, pressure/volume, temperature/entropy, enthalpy/entropy and pressure/ enthalpy diagrams can be used, but usually the T/s diagram is sufficient. The h/s diagram is available as a chart from which values can be read instead of using the steam tables. The p/h diagram is usually used for refrigerant plant. Figures 2.6.10, 11, 12 and 13 show the form of these plots for any vapour. They can be produced for water by taking values from the steam tables. For each plot note: ᭹ The saturated liquid and saturated vapour lines. ᭹ The liquid, vapour and superheat regions. ᭹ The critical point is at the turning point of the saturated liquid and the saturated vapour lines, where there is a zero value of latent heat of vaporization, and therefore boiling to produce the vapour does not occur. Figure 2.6.9 Basic steam plant Figure 2.6.10 p/V diagram for vapour [...]... Example 2.6. 14 1 kilogram of steam at 8 bar, dryness 0.9 is expanded until the pressure is 4 bar If expansion follows the law pV 1.25 = C, find the final dryness fraction of the steam V1 = x.Vg = 0.9 × 0. 240 3 = 0.2163 m3/kg p1 V n = p2 V n 1 2 Thermodynamics 85 8 × 0.26131.25 = 4 × V 1.25 2 V2 = ͱසසසසස 1.25 8 × 0.26131.25 4 = 0 .45 5 m3/kg V = x.Vg at 4 bar 0 .45 5 = x × 0 .46 23 x = 0 .45 5 0 .46 23 = 0.9 84 Example... bar, 40 0°C, h1 = 3231 kJ/kg 3231 – h2 = 947 .4, h2 = 3231 – 947 .4 = 2283.6 kJ/kg h2 = 2283.6 = hf + x.hfg at 0.05 bar, 2283.6 = 138 + x. 242 3, x = 0.886 (a) For isentropic expansion, s1 = 6.921 kJ/kgK = sЈ 2 Note that at 0.05 bar, sg = 8.3 94 kJ/kgK, which is greater, therefore the steam is wet after the expansion sЈ = sf + x.sfg , 6.921 = 0 .47 6 + x(7.918), x = 0.8 14 2 hЈ = hf + x.hfg = 138 + (0.8 14 × 242 3)... 2.6.18 shows the plant Figure 2.6.18 Example 2.6.11 80 Thermodynamics h1 = 343 3 kJ/kg h2 = hf + x.hfg at 0.2 bar = 251 + 0.92(2358) = 242 0.36 kJ/kg ˙ P = m(h1 – h2 ) = 1.5( 343 3 – 242 0.36) = 1519 kW ˙ Heat to condenser cooling = m(h2 – h3 ) = 1.5( 242 0.36 – 230.2) = 3285. 24 kW Thermal efficiency = h1 – h2 h1 – h4 = 343 3 – 242 0.36 343 3 – 230.2 = 0.316 = 31.6% Note: ᭹ ᭹ ᭹ ᭹ Condenser undercooling is ts –... 0.763(2 544 – 561) = 20 74 kJ/kg Q = W + (U2 – U1 ) = 80.35 + (20 74 – 20 74. 3)0. 346 = 80.25 kJ Example 2.6.17 0.1 m3 of steam at a pressure of 14 bar is expanded at constant volume to a pressure of 6 bar Find: (a) (b) (c) (d) the the the the mass of steam; dryness after expansion; change in internal energy; heat energy transferred Specific volume of steam at 14 bar, x = 0.9, is given by, V = x.Vg = 0.9 × 0. 140 8... expansion, sЈ = s1 = 6.029 = 0 .42 2 + x(8.051), 2 x = 6.029 – 0 .42 2 8.051 = 0.696 hЈ = hf + x.hfg = 121 + (0.696 × 243 3) = 18 14. 37 kJ/kg 2 ␩T = h1 – h2 h1 – hЈ 2 , 0.85 = 2798 – h2 2798 – 18 14. 37 h2 = 2798 – 0.85(2798 – 18 14. 37) = 1962 kJ/kg ˙ P = m(h1 – h2 ) = 2(2798 – 1962) = 1672 kW Example 2.6.13 A steam turbine expands steam from a pressure and temperature of 30 bar and 40 0°C respectively to 0.05 bar... After expansion at 6 bar, the volume is unchanged = 0.127 m3/kg V = x.Vg at 6 bar 0.127 = x.0.3156, x = 0.127 0.3156 = 0 .4 (b) u1 = uf + x.ufg = 828 + 0.9(2593 – 828) = 241 6.5 kJ/kg u2 = uf + x.ufg = 669 + 0 .4( 2568 – 669) = 142 8.6 kJ/kg Change in internal energy = U2 – U1 = ( 142 8.6 – 241 6.5)0.787 = –778 kJ/kg (c) Heat energy transferred, Q = W + (U2 – U1 ) This is a constant volume process in which W... temperature of the steam before expansion is greater than the saturation temperature corresponding to the pressure The steam is therefore superheated V1 = 0.3 94 m3/kg p1 V n = p2 V n 1 2 6 × 0.3 941 .13 = 1.5 × V 1.13 , 2 V2 = ͱසසසසස 1.13 6 × 0.3 941 .13 1.5 = 1. 344 m3 (a) Examination of the steam tables at 1.5 bar shows that this volume lies between 150°C and 200°C By interpolation, temperature after expansion... condenser undercooling Feedpump work is neglected, therefore h3 = h4 Problems 2.6.3 In each case sketch the T/s diagram (1) (2) In a steam turbine plant, the steam supply to the turbine is 44 bar dry saturated, and the exhaust steam is at 0. 04 bar after isentropic expansion Calculate the Rankine efficiency of the cycle Steam enters a turbine at 40 bar, 300°C and exhausts into the condenser at 0.065 bar,... Example 2.6.10 At 17.5 bar, 300°C, h1 = 3032 kJ/kg, s1 = 6. 843 5 kJ/kgK s1 = s2 because the expansion is isentropic 6. 843 5 = sf + x.sfg at 0.07 bar 6. 843 5 = 0.559 + x(7.715), x = 6. 843 5 – 0.559 7.715 = 0.815 h2 = hf + xhfg = 163 + 0.815( 240 9) = 2126 kJ/kg Rankine efficiency = h1 – h2 h1 – h4 = 3032 – 2126 3032 – 163 = 0.3161 = 31.6% Example 2.6.11 Steam enters a turbine at 50 bar, 500°C and exhausts into... Steam enters a turbine at 44 bar, dry, and expands with an isentropic efficiency of 0.85 to 0. 04 bar If the mass flow rate of steam through the turbine is 2 kg/s, calculate the power developed by the turbine Figure 2.6.20 shows the turbine and the process on the h/s diagram Figure 2.6.20 Example 2.6.12 82 Thermodynamics From steam tables, h1 = 2798 kJ/kg, s1 = 6.029 kJ/kgK At 0. 04 bar, for isentropic expansion, . h 2 = 947 .4 kJ/kg From the superheat tables at 30 bar, 40 0°C, h 1 = 3231 kJ/kg 3231 – h 2 = 947 .4, h 2 = 3231 – 947 .4 = 2283.6 kJ/kg h 2 = 2283.6 = h f + x.h fg at 0.05 bar, 2283.6 = 138 + x. 242 3,. 0. 240 3 = 0.2163 m 3 /kg p 1 V n 1 = p 2 V n 2 Thermodynamics 85 8 × 0.2613 1.25 =4 × V 1.25 2 V 2 = 1.2 5 ͱ සසසසස 8 × 0.2613 1.25 4 = 0 .45 5 m 3 /kg V = x.V g at 4 bar 0 .45 5 = x × 0 .46 23 x = 0 .45 5 0 .46 23 =. superheat tables, h = 3052 kJ/kg (f) Steam at 40 bar, 40 0°C. From superheat tables, h = 32 14 kJ/kg (g) Water at 34 C. Refer to temperature only, h f = 142 .4 kJ/kg (h) Water at 850°C. h f = 355.9 kJ/kg Example