(a) In a cogeneration plant, the net power output is 6 MW and the heating load is 1·5 MW. Steam is generated at 40 bar and 500 °C, and is expanded isentropically through a turbine to a condenser at 0·1 bar. The heating load is supplied by extracting

Question

(a) In a cogeneration plant, the net power output is 6 MW and the heating load is 1·5 MW. Steam is generated at 40 bar and 500 °C, and is expanded isentropically through a turbine to a condenser at 0·1 bar. The heating load is supplied by extracting steam from the turbine at 2 bar, which is condensed in a process heater to saturated liquid at 2 bar and then pumped back to the boiler. Draw the schematic and T-s diagram. Determine (i) the steam generation capacity (in kg/s) of the boiler and (ii) mass flow rate (in kg/s) of the steam through the heating load.
The steam properties at 40 bar, 500 °C are h = 3445·21 kJ/kg, s = 7·09 kJ/kg-K.
Use steam tables given at the end to get other properties.

For Question No. 7(a) :
Saturated Water Pressure Entry

Press. (kPa) | Temp. (°C) | Enthalpy (kJ/kg): Sat. Liquid h_f | Evap. h_fg | Sat. Vapour h_g | Entropy (kJ/kg-K): Sat. Liquid s_f | Evap. s_fg | Sat. Vapour s_g
0·6113 | 0·01 | 0·00 | 2501·30 | 2501·30 | 0 | 9·1562 | 9·1562
1·0 | 6·98 | 29·29 | 2484·89 | 2514·18 | 0·1059 | 8·8697 | 8·9756
1·5 | 13·03 | 54·70 | 2470·59 | 2525·30 | 0·1956 | 8·6322 | 8·8278
2·0 | 17·50 | 73·47 | 2460·02 | 2533·49 | 0·2607 | 8·4629 | 8·7236
2·5 | 21·08 | 88·47 | 2451·56 | 2540·03 | 0·3120 | 8·3311 | 8·6431
3·0 | 24·08 | 101·03 | 2444·47 | 2545·50 | 0·3545 | 8·2231 | 8·5775
4·0 | 28·96 | 121·44 | 2432·93 | 2554·37 | 0·4226 | 8·0520 | 8·4746
5·0 | 32·88 | 137·79 | 2423·66 | 2561·45 | 0·4763 | 7·9187 | 8·3950
7·5 | 40·29 | 168·77 | 2406·02 | 2574·79 | 0·5763 | 7·6751 | 8·2514
10 | 45·81 | 191·81 | 2392·82 | 2584·63 | 0·6492 | 7·5010 | 8·1501
15 | 53·97 | 225·91 | 2373·14 | 2599·06 | 0·7548 | 7·2536 | 8·0084
20 | 60·06 | 251·38 | 2358·33 | 2609·70 | 0·8319 | 7·0766 | 7·9085
25 | 64·97 | 271·90 | 2346·29 | 2618·19 | 0·8930 | 6·9383 | 7·8313
30 | 69·10 | 289·21 | 2336·07 | 2625·28 | 0·9439 | 6·8247 | 7·7686
40 | 75·87 | 317·55 | 2319·19 | 2636·74 | 1·0258 | 6·6441 | 7·6700
50 | 81·33 | 340·47 | 2305·40 | 2645·87 | 1·0910 | 6·5029 | 7·5939
75 | 91·77 | 384·36 | 2278·59 | 2662·96 | 1·2129 | 6·2434 | 7·4563
100 | 99·62 | 417·44 | 2258·02 | 2675·46 | 1·3025 | 6·0568 | 7·3593
125 | 105·99 | 444·30 | 2241·05 | 2685·35 | 1·3739 | 5·9104 | 7·2843
150 | 111·37 | 467·08 | 2226·46 | 2693·54 | 1·4335 | 5·7897 | 7·2232
175 | 116·06 | 486·97 | 2213·57 | 2700·53 | 1·4848 | 5·6868 | 7·1717
200 | 120·23 | 504·68 | 2201·96 | 2706·63 | 1·5300 | 5·5970 | 7·1271
225 | 124·00 | 520·69 | 2191·35 | 2712·04 | 1·5705 | 5·5173 | 7·0878
250 | 127·43 | 535·34 | 2181·55 | 2716·89 | 1·6072 | 5·4455 | 7·0526
275 | 130·60 | 548·87 | 2172·42 | 2721·29 | 1·6407 | 5·3801 | 7·0208
300 | 133·55 | 561·45 | 2163·85 | 2725·30 | 1·6717 | 5·3201 | 6·9918
325 | 136·30 | 573·23 | 2155·76 | 2728·99 | 1·7005 | 5·2646 | 6·9651
350 | 138·88 | 584·31 | 2148·10 | 2732·40 | 1·7274 | 5·2130 | 6·9404
375 | 141·32 | 594·79 | 2140·79 | 2735·58 | 1·7527 | 5·1647 | 6·9174
400 | 143·63 | 604·73 | 2133·81 | 2738·53 | 1·7766 | 5·1193 | 6·8958
450 | 147·93 | 623·24 | 2120·67 | 2743·91 | 1·8206 | 5·0359 | 6·8565
500 | 151·86 | 640·21 | 2108·47 | 2748·67 | 1·8606 | 4·9606 | 6·8212
550 | 155·48 | 655·91 | 2097·04 | 2752·94 | 1·8972 | 4·8920 | 6·7892
600 | 158·85 | 670·54 | 2086·26 | 2756·80 | 1·9311 | 4·8289 | 6·7600
650 | 162·01 | 684·26 | 2076·04 | 2760·30 | 1·9627 | 4·7704 | 6·7330
700 | 164·97 | 697·20 | 2066·30 | 2763·50 | 1·9922 | 4·7158 | 6·7080
750 | 167·77 | 709·45 | 2056·98 | 2766·43 | 2·0199 | 4·6647 | 6·6846
800 | 170·43 | 721·10 | 2048·04 | 2769·13 | 2·0461 | 4·6166 | 6·6627

KVMS–B–MCH/7        15        [ P.T.O.

[Table printed on page 14]
For Question No. 7(a) :
Saturated Water Pressure Entry

Press. (kPa) | Temp. (°C) | Specific Volume (m³/kg): Sat. Liquid v_f | Evap. v_fg | Sat. Vapour v_g | Internal Energy (kJ/kg): Sat. Liquid u_f | Evap. u_fg | Sat. Vapour u_g
0·6113 | 0·01 | 0·001000 | 206·131 | 206·132 | 0 | 2375·3 | 2375·3
1·0 | 6·98 | 0·001000 | 129·20702 | 129·20802 | 29·29 | 2355·69 | 2384·98
1·5 | 13·03 | 0·001001 | 87·97913 | 87·98013 | 54·70 | 2338·63 | 2393·32
2·0 | 17·50 | 0·001001 | 67·00285 | 67·00385 | 73·47 | 2326·02 | 2399·48
2·5 | 21·08 | 0·001002 | 54·25285 | 54·25385 | 88·47 | 2315·93 | 2404·40
3·0 | 24·08 | 0·001003 | 45·66402 | 45·66502 | 101·03 | 2307·48 | 2408·51
4·0 | 28·96 | 0·001004 | 34·79915 | 34·80015 | 121·44 | 2293·73 | 2415·17
5·0 | 32·88 | 0·001005 | 28·19150 | 28·19251 | 137·79 | 2282·70 | 2420·49
7·5 | 40·29 | 0·001008 | 19·23674 | 19·23775 | 168·76 | 2261·74 | 2430·50
10 | 45·81 | 0·001010 | 14·67254 | 14·67355 | 191·79 | 2246·10 | 2437·89
15 | 53·97 | 0·001014 | 10·02117 | 10·02218 | 225·90 | 2222·83 | 2448·73
20 | 60·06 | 0·001017 | 7·64835 | 7·64937 | 251·35 | 2205·36 | 2456·71
25 | 64·97 | 0·001020 | 6·20322 | 6·20424 | 271·88 | 2191·21 | 2463·08
30 | 69·10 | 0·001022 | 5·22816 | 5·22918 | 289·18 | 2179·22 | 2468·40
40 | 75·87 | 0·001026 | 3·99243 | 3·99345 | 317·51 | 2159·49 | 2477·00
50 | 81·33 | 0·001030 | 3·23931 | 3·24034 | 340·42 | 2143·43 | 2483·85
75 | 91·77 | 0·001037 | 2·21607 | 2·21711 | 394·29 | 2112·39 | 2496·67
100 | 99·62 | 0·001043 | 1·69296 | 1·69400 | 417·33 | 2088·72 | 2506·06
125 | 105·99 | 0·001048 | 1·37385 | 1·37490 | 444·16 | 2069·32 | 2513·48
150 | 111·37 | 0·001053 | 1·15828 | 1·15933 | 466·92 | 2052·72 | 2519·64
175 | 116·06 | 0·001057 | 1·00257 | 1·00363 | 486·78 | 2038·12 | 2524·90
200 | 120·23 | 0·001061 | 0·88467 | 0·88573 | 504·47 | 2025·02 | 2529·49
225 | 124·00 | 0·001064 | 0·79219 | 0·79325 | 520·45 | 2013·10 | 2533·56
250 | 127·43 | 0·001067 | 0·71765 | 0·71871 | 535·08 | 2002·14 | 2537·21
275 | 130·60 | 0·001070 | 0·65624 | 0·65731 | 548·57 | 1991·95 | 2540·53
300 | 133·55 | 0·001073 | 0·60475 | 0·60582 | 561·13 | 1982·43 | 2543·55
325 | 136·30 | 0·001076 | 0·56093 | 0·56201 | 572·88 | 1973·46 | 2546·34
350 | 138·88 | 0·001079 | 0·52317 | 0·52425 | 583·93 | 1964·98 | 2548·92
375 | 141·32 | 0·001081 | 0·49029 | 0·49137 | 594·38 | 1956·93 | 2551·31
400 | 143·63 | 0·001084 | 0·46138 | 0·46246 | 604·29 | 1949·26 | 2553·55
450 | 147·93 | 0·001088 | 0·41289 | 0·41398 | 622·75 | 1934·87 | 2557·62
500 | 151·86 | 0·001093 | 0·37380 | 0·37489 | 639·66 | 1921·57 | 2561·23
550 | 155·48 | 0·001097 | 0·34159 | 0·34268 | 655·30 | 1909·17 | 2564·47
600 | 158·85 | 0·001101 | 0·31457 | 0·31567 | 669·88 | 1897·52 | 2567·40
650 | 162·01 | 0·001104 | 0·29158 | 0·29268 | 683·55 | 1886·51 | 2570·06
700 | 164·97 | 0·001108 | 0·27176 | 0·27286 | 696·43 | 1876·07 | 2572·49
750 | 167·77 | 0·001111 | 0·25449 | 0·25560 | 708·62 | 1866·11 | 2574·73
800 | 170·43 | 0·001115 | 0·23931 | 0·24043 | 720·20 | 1856·58 | 2576·79

KVMS–B–MCH/7        14 (20 marks)

(b) An R717 simple saturation cycle refrigerator operates at 40 °C condenser and –16 °C evaporator temperatures. Determine COP and power per TR. If a liquid-vapour regenerative heat exchanger is installed in the system, with the suction vapour at 15 °C, what will be the effect on COP and power per TR?
Assume specific heat of vapour at condenser temperature as 3·1 kJ/kg-K, when no heat exchanger is used, and 2·9 kJ/kg-K, when heat exchanger is used.
The properties of R717 are given in the table below :
Temperature (°C) | Enthalpy (kJ/kg) Liquid (h_f) | Enthalpy (kJ/kg) Vapour (h_g) | Entropy (kJ/kg-K) Liquid (s_f) | Entropy (kJ/kg-K) Vapour (s_g)
–16 | 126·73 | 1442·60 | 0·72511 | 5·8420
40 | 390·59 | 1490·42 | 1·64377 | 5·1558
Draw the P-h diagram also. The specific heat of vapour corresponding to evaporator temperature may be assumed as 2·38 kJ/kg-K. (20 marks)

(c) How are the ratings of SI and CI engine fuels done? Explain in brief. (10 marks)

UPSC Answer Check · Accepted Answer

(a) Cogeneration plant (20 marks)

The plant is drawn below: the boiler supplies steam at 1 (40 bar, 500 °C) to the turbine; a part ṁ_e is extracted at 2 bar (state 2) and condensed in the process heater, and the rest expands to 0.1 bar (state 3) and condenses. Both condensates are pumped back to the boiler.

Properties from the tables (h in kJ/kg, s in kJ/kg·K).
State 1: h₁ = 3445.21, s₁ = 7.09.
At 2 bar: h_f = 504.68, h_fg = 2201.96, s_f = 1.5300, s_fg = 5.5970, s_g = 7.1271, v_f = 0.001061 m³/kg.
At 0.1 bar (10 kPa): h_f = 191.81, h_fg = 2392.82, s_f = 0.6492, s_fg = 7.5010, v_f = 0.001010 m³/kg.

Isentropic expansion. Since s₁ = 7.09 is below s_g at 2 bar, the steam is wet at state 2:

x₂ = (7.09 − 1.5300)/5.5970 = 0.9934, so h₂ = 504.68 + 0.9934 × 2201.96 = 2692.08 kJ/kg.

At 0.1 bar, x₃ = (7.09 − 0.6492)/7.5010 = 0.8587, so h₃ = 191.81 + 0.8587 × 2392.82 = 2246.43 kJ/kg.

(ii) Extraction flow to the heater. The heating load is the heat given up as the extracted steam condenses to saturated liquid at 2 bar:

ṁ_e (h₂ − h_f2) = 1500 kW, so ṁ_e = 1500/(2692.08 − 504.68) = 1500/2187.40 = 0.686 kg/s.

(i) Boiler steam generation capacity. The pump work is small: w_P1 = v_f(p₁ − 0.1 bar) = 0.001010 × (4000 − 10) = 4.03 kJ/kg for the condenser stream, and w_P2 = 0.001061 × (4000 − 200) = 4.03 kJ/kg for the heater stream, so both pumps take the same 4.03 kJ/kg. With the boiler flow ṁ, the net power is

W_net = ṁ (h₁ − h₂) + (ṁ − ṁ_e)(h₂ − h₃) − (ṁ − ṁ_e) w_P1 − ṁ_e w_P2 = 6000 kW.

Substituting, with h₁ − h₂ = 753.13 and h₂ − h₃ = 445.65 kJ/kg: 753.13 ṁ + 445.65 (ṁ − 0.686) − 4.03 ṁ = 6000, that is 1194.75 ṁ − 305.6 = 6000, so

ṁ = 5.28 kg/s.

Neglecting pump work gives 5.26 kg/s, practically the same. The condenser flow is ṁ − ṁ_e = 4.59 kg/s, and the turbine develops about 6021 kW, of which 21 kW drives the pumps.

(b) R717 refrigerator with and without the heat exchanger (20 marks)

Data: T_c = 40 °C = 313.15 K, T_e = −16 °C = 257.15 K. At −16 °C: h_g = 1442.60, s_g = 5.8420. At 40 °C: h_f = 390.59, h_g = 1490.42, s_g = 5.1558. 1 TR = 3.5167 kW.

Simple saturation cycle (no heat exchanger).
State 1: saturated vapour at −16 °C, h₁ = 1442.60, s₁ = 5.8420.
State 2 (isentropic compression to 40 °C pressure): s₂ = s₁ = 5.8420, which exceeds s_g at 40 °C (5.1558), so the vapour is superheated. With c_p = 3.1: s₂ = s_g + c_p ln(T₂/T_c), so ln(T₂/313.15) = 0.6862/3.1 = 0.2214 and T₂ = 390.7 K.
h₂ = h_g + c_p (T₂ − T_c) = 1490.42 + 3.1 × 77.6 = 1730.94 kJ/kg.
State 3: saturated liquid at 40 °C, h₃ = 390.59 = h₄ (throttling).
Refrigerating effect q_e = h₁ − h₄ = 1442.60 − 390.59 = 1052.01 kJ/kg.
Compressor work w = h₂ − h₁ = 1730.94 − 1442.60 = 288.34 kJ/kg.

COP = 1052.01/288.34 = 3.65, and the power per TR = 3.5167/3.648 = 0.964 kW/TR.

Cycle with the liquid-vapour heat exchanger. The vapour leaves the evaporator at −16 °C (h_g = 1442.60) and is heated to 15 °C in the exchanger. With c_p = 2.38:
h₁′ = 1442.60 + 2.38 × 31 = 1516.38 kJ/kg.
s₁′ = 5.8420 + 2.38 ln(288.15/257.15) = 5.8420 + 0.2709 = 6.1129.
Heat exchanger balance: the liquid is cooled by the same amount, so h₄′ = 390.59 − (1516.38 − 1442.60) = 316.81 kJ/kg.
Isentropic compression from 1′, with c_p = 2.9: ln(T₂′/313.15) = (6.1129 − 5.1558)/2.9 = 0.3300, so T₂′ = 435.6 K.
h₂′ = 1490.42 + 2.9 × (435.6 − 313.15) = 1845.51 kJ/kg.
q_e = h₁ − h₄′ = 1442.60 − 316.81 = 1125.79 kJ/kg (the heat absorbed in the evaporator, from the cooled liquid at 4′ to saturated vapour at 1).
w = h₂′ − h₁′ = 1845.51 − 1516.38 = 329.13 kJ/kg.

COP = 1125.79/329.13 = 3.42, and the power per TR = 3.5167/3.420 = 1.028 kW/TR.

Effect. The heat exchanger raises the refrigerating effect by about 7%, but the compressor work rises by about 14%, since the vapour enters hotter and less dense and ammonia has a high isentropic exponent. Hence COP falls from 3.65 to 3.42 (about 6%), and the power per TR increases from 0.964 to 1.028 kW/TR (about 7%). The discharge temperature also rises from about 118 °C to about 162 °C. So for ammonia a suction-liquid heat exchanger is not beneficial (it is used for R12 or R134a, and to avoid liquid entering the compressor).

(c) Rating of SI and CI engine fuels (10 marks)

SI engine fuels: octane number (5 marks). The rating measures the resistance of a fuel to knock. Two reference fuels are used: iso-octane (2,2,4-trimethylpentane), which is highly knock-resistant and is assigned an octane number of 100, and n-heptane, which knocks readily and is assigned 0. The octane number of a fuel is the percentage by volume of iso-octane in a blend with n-heptane that matches the knock intensity of the test fuel. The test is done in the standard CFR (Cooperative Fuel Research) engine, a single-cylinder, variable-compression-ratio engine, at constant speed. The compression ratio is raised until standard knock intensity is measured with a knockmeter, and the fuel is then bracketed between two reference blends. Two conditions are used: the Research Octane Number (RON, ASTM D2699, 600 rpm, mild inlet temperature) and the Motor Octane Number (MON, ASTM D2700, 900 rpm, heated mixture), where MON is lower by about 8–10 units. Typical values are RON of about 91–95 for petrol in India, and above 100 for aviation and racing fuels, which are quoted on a performance-number scale. Tetraethyl lead was formerly used to raise it; today ethanol and aromatics are used.

CI engine fuels: cetane number (5 marks). The rating measures the ease of self-ignition, that is a short ignition delay. The reference fuels are n-cetane (hexadecane), which ignites readily and is assigned 100, and α-methylnaphthalene, which ignites poorly and is assigned 0 (now often replaced by heptamethylnonane, cetane number 15). The cetane number is the percentage by volume of cetane in the blend that has the same ignition delay as the test fuel. The test uses the standard CFR diesel engine (ASTM D613, 900 rpm), with injection fixed at 13° before top dead centre. The compression ratio is varied until ignition takes place at top dead centre for the test fuel, and it is then bracketed between two reference blends that need slightly higher and lower compression ratios. Typical values are 40–55 for automobile diesel, with a minimum of 51 for Indian BS-VI diesel; a higher value gives easier starting, smoother combustion and less diesel knock.

The two scales run in opposite senses: a good SI fuel resists autoignition, while a good CI fuel readily undergoes it, so petrol has a low cetane number and diesel a low octane number.

(a) In a cogeneration plant, the net power output is 6 MW and the heating load is 1·5 MW. Steam is generated at 40 bar and 500…

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(a) Cogeneration plant (20 marks)

(b) R717 refrigerator with and without the heat exchanger (20 marks)

(c) Rating of SI and CI engine fuels (10 marks)

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