Mechanical Engineers Data Handbook Episode 6 ppsx

THERMODYNAMICS AND HEAT TRANSFER 115 Velocity compounded impulse turbine One row of nozzles is followed by two or more rows of moving blades with intervening rows of fixed blades of the same type which alter the direction of flow. Two-row wheel Assume PI = P2, k = 1 and that all blades are symmetrical. c, (exit velocitv) Maximum efficiency vmax =cosz a (at p = y) in which case the steam leaves the last row axially. 3.7.2 Impulse-reaction turbine In this case there is ‘full admission’, i.e. e= 360”. Both nozzles and moving blades are similar in shape and have approximately the same enthalpy drop. Referring to the figure: Enthalpy drop = (h, - h,) (for the fixed blades) = (h, -h2) (for the moving blades) Ce.A Mass flow rate m=- Area of flow A=2nRmh V \Maximom efficiency diagram 50% reaction (Parson’s) turbine In this case the velocity diagram is symmetrical. 2nR,hC sin a Mass flow rate m= V where: a= blade outlet angle. Enthalpy drop per stage Ahs = C’p(2 cos a - p) Cb where: p=- and Cb=2nR,N. Stage power P,=mAh, C 2p(2 cos a - p) 1 +p(2cosa-p) Stage efficiency q, = 2 cos2 a (1 + cos2 .) Maximum efficiency qmX = (when p =cos a) 116 MECHANICAL ENGINEER’S DATA HANDBOOK 3.7.3 Reheat factor and overall efficiency Referring to the ‘condition curve’ on the h-s diagram: AhA =available stage enthalpy drop Ah, = isentropic stage enthalpy drop AhoA = available overall enthalpy drop Aho, = isentropic overall enthalpy drop Stage efficiency qs=- Ah, Ah, Overall efficiency qo = - Ah01 v Reheat factor RF=2 ?, h 3.8 Gas turbines The gas turbine unit operates basically on the con- stant-pressure cycle, particularly in the case of the ‘closed cycle’. In the ‘open cycle’ air is drawn in from the atmosphere, compressed and supplied to a com- bustion chamber where fuel is burnt with a large amount of ‘excess air’. The hot gases drive a turbine which drives the compressor and also provides useful work. The efficiency increases with compression ratio. The output power increases with both compression ratio and turbine inlet temperature. The effect of losses and variation in fluid properties is shown on the basic cycle. The efficiency of the basic cycle can be greatly increased by incorporating a heat exchanger between the compressor outlet and the combustion chamber inlet. It uses the exhaust gases from the turbine to preheat the incoming air. 117 THERMODYNAMICS AND HEAT TRANSFER T I // ~ . P1 P4 (cP = specific heat for turbine cccp = specific heat for combustion chamber yc = ratio of specific heats for compressor yl =ratio of specific heats for turbine qc = isentropic compressor efficiency ql = isentropic turbine efficiency J 1 3.8.1 Simple cycle Pz P3 Comnrensinn rg tin r = - = - s Heat supplied Q =c,T,(t-c) per kg of air Work done =Turbine work out -Compressor work in 1 4. I I 1 C =compressor CC = wmbustion chamber tubine Simple cycle with isentropic eficiencies and variable specijc heats W=cpT1 [I( 1 -f)-( l)] 1 Efficiency 9 = 1 C I s Work done = Turbine work out - Compressor work in Heat supplied Q = ==cP T3 - TI - ~ (Tz-T1)] per kg of air vc W lcp( T3 - T,)ql - Net work out Gross work Work ratio= - W Efficiency q = - Q 118 MECHANICAL ENGINEER’S DATA HANDBOOK 3.8.2 Simple cycle with heat exchanger T Heat supplied Q=c,T,t 1 ( 3 Work done W=c,T, t 1 -(c-1) [( :> 1 C Efficiency q = 1 t cc 6 C =compressor T =turbine CC = combustion HE = heat exchanger W = work done n 3 S r 3.9 Heat engine cycles 3.9. I Carnot cycle The ideal gas cycle is the Carnot cycle and, in practice, only about half of the Carnot cycle efficiency is realized between the same temperature limits. 4 T2 Efficiency q = 1 TI P4 TI Pz T2 (sl - s4) = R In - -c, In - V THERMODYNAMICS AND HEAT TRANSFER 119 Work done (per kg) W= (T, - T2)(s1 -s4) Heat supplied (per kg) Q = T, (s, - s4) 3.9.2 Constant pressure cycle In this cycle, heat is supplied and rejected at constant pressure; expansion and compression are assumed to take place at constant entropy. The cycle was once known as the Joule or Brayton cycle and used for hot-air engines. It is now the ideal cycle for the closed gas turbine unit. I V 1 P ( p 1 PI Efficiency '1 = 1 - -, where r = 2 w= Cp(T3 - T4) - cp( r2 - T,) Ti T3 Work ratio = 1 - - r 3.9.3 Otto cycle (constant-volume cycle) This is the basic cycle for the petrol engine, the gas engine and the high-speed oil engine. Heat is supplied and rejected at constant volume, and expansion and compression take place isentropically. The thermal efficiency depends only on the compression ratio. 1 Efficiency q= 1 rY-l 3 V 3.9.4 Diesel cycle (constant-pressure combustion) Although this is called the 'diesel cycle', practical diesel engines do not follow it very closely. In this case heat is added at constant pressure; otherwise the cycle is the same as the Otto cycle. P I V 120 MECHANICAL ENGINEER’S DATA HANDBOOK (IY- 1) (/3-1)yrY-l Efficiency = 1 - V V where: r=A and /3=”. (‘cut-off ratio) 02 02 W=c,(T,- T2)-c,(T4- T,) Q = cp( T3 - TZ ) 3.9.5 Dual combustion cycle Modern diesel engines follow a similar cycle to this ideal one. In this case combustion takes place partly at constant volume and partly at constant pressure. (kPY - 1 ) C(k-l)+(B-l)yk]rY-l Efficiency q = 1 - V 3.9.6 Practical engine cycles In actual engines the working substance is air only in the induction and compression strokes. During expan- sion and exhaust the working substance consists of the products of combustion with different properties to air. In addition, the wide variations in temperature and pressure result in variation in the thermal proper- ties. Another factor is ‘dissociation’ which results in a lower maximum temperature than is assumed in elementary treatment of the combustion process. 3.10 Reciprocating spark ignition internal combustion engines 3. IO. I Four-stroke engine The charge of air and fuel is induced into the engine cylinder as the piston moves from top dead centre (TDC) to bottom dead centre (BDC). The charge is then compressed and ignited by the sparking plug before TDC producing high pressure and temperature at about TDC. The gas expands and work is produced as the piston moves to BDC. A little before BDC the exhaust valve opens and the gases exhaust. The process is completed during the next stroke. A typical ‘timing diagram’ (section 3.10.3) and the p-v diagram are shown. Formulae are given for power, mean effec- tive pressure, efficiency and specific fuel consumption. Pressure-volume (p-v) diagram: A=area of power loop B=area of pumping loop L, = length of diagram K =indicator constant Indicated mean effective pressure K pi = (A - B) - (N mm - ’) Ld n 2 Indicated power Pi =piApLN - (watts) THERMODYNAMICS AND HEAT TRANSFER 121 Coding water jacket Crank angle, e Typical timing diagram where: N =number of revolutions per second, n =number of cylinders, A, =piston area (m'), L = stroke (m) Torque T=FR (Nm) where: F=force on brake arm (N), R= brake radius (m). Brake power Pb=2nNT (watts) 7f/m7n3r Brake Friction power P, = Pi - P, Mechanical efficiency )I,,, = - 'b Pi 4n T Brake mean effective pressure (BMEP) pb=- ALn =constant x T(N m ~ *) 'b Brake thermal efficiency 9 -~ ,-mLCV I Cooling water- Piston- Cylinder - jackel zmiw-I - Combustion chamber Push md where: m=mass flow rate of fuel (kgs-I), LCV= lower calorific value of fuel (J kg-'). Specific fuel consumption SFC =- (kg s- ' W- ') m Pb Volume of induced air at NTP Swept volume of cylinder Volumetric efficiency )I,, = where: NTP = normal temperature and pressure. Sump Four-stmke engine 3.10.2 Two-stroke engine In an engine with crankcase compression, the piston draws a new charge into the crankcase through a spring-loaded valve during the compression stroke. Ignition occurs just before TDC after which the working stroke commences. Near the end of the stroke the exhaust port is uncovered and the next charge enters the cylinder. The exhaust port closes shortly after the transfer port, and compression begins. The piston is shaped to minimize mixing of the new charge with the exhaust. (See section 3.10.3) Pressure-volume (pu) diagram: A =area of power loop B = area of pumping loop K Indicated mean effective pressure (IMEP): pi = (A - B) - L* V 122 MECHANICAL ENGINEER'S DATA HANDBOOK Crankcase diagram where: K =indicator constant. Indicated power P,=p,A,LNn 271 T Brake mean effective pressure (BMEP) p b-ALn Other quantities are as for the four-stroke engine. TDC BOC Compression-ignition engines Two-stroke engine Both four-stroke and two-stroke engines may have compression ignition instead of spark ignition. The air is compressed to a high pressure and temperature and the fuel injected. The high air temperature causes combustion. 3.10.3 Timing diagrams Four-stroke engine IO =inlet valve opens IC =inlet valve closes EO=exhaust valve opens EC = exhaust valve closes S =spark occurs I =inlet angle (approx. 80') E =exhaust angle (approx. 120") T= transfer angle (approx. 100") TDC BDC 3.10.4 Performance curves for internal combustion engines Typical curves are shown for mechanical efficiency versus brake power, BMEP versus torque, and vol- umetric efficiency versus speed. The effect of mixture strength on the pv and pS diagrams is shown and curves of power and MEP against speed are given. The curve of specific fuel consumption versus brake power, known as the 'consumption loop' shows the effect of mixture strength on fuel consumption. THERMODYNAMICS AND HEAT TRANSFER 123 Mechanical efliclency ' s brake power BMEP vs toque N VOlUmenie efficiency vs speed V Effect of mixture strength M p - vdisgram ,Rich Crank angle, e Elfa 01 mixture strength MI p -e -am 4 P 1 speed. N Power, MEP, mechanical efficiency vs speed Max. '\i power Max. economy 124 MECHANICAL ENGINEER'S DATA HANDBOOK 3. I I Air compressors The following deals with positive-displacement-type compressors as opposed to rotodynamic types. The reciprocating compressor is the most suitable for high pressures and the Roots blower and vane compressor are most suitable for low pressures. 3. I I. I Reciprocating compressor This consists of one or more cylinders with cranks, connecting rods and pistons. The inlet and outlet valves are of the automatic spring-loaded type. Large cylinders may be water cooled, but small ones are usually finned. Air is drawn into the cylinder at slightly below atmospheric pressure, compressed to the required discharge pressure during part of the stroke, and finally discharged at outlet pressure. A small clearance volume is necessary. The cylinders may be single or double acting. Symbols used: pi =inlet pressure p2 =discharge pressure P2 r =pressure ratio = - P1 T= free air temperature T, =inlet air temperature T2 =discharge temperature V, = swept volume Vc =clearance volume Va - Vd =induced volume R = gas constant for air n =index of expansion and compression y = ratio of specific heats for air rit = air mass flow rate Q = free air volume flow rate N = number of revolutions per second Z = number of effective strokes per revolution (= 1 for single acting; 2 for double acting) q =efficiency W=work done per revolution Pi = indicated power S=number of stages p = free air pressure (atmospheric conditions) v, = V, + Vc TP Tl P Freeair flow Q=(V,-V,) NNZ where: V,=(V,+ VJ. "1 c TZ b "a V n Indicated power Pi=-mR(T2- T,) (n- 1) vc Volumetric efficiency qv = 1 - - (14 - 1 ) Vs Clearance ratio CR = - vc VS 'd ' Also =re VC [...]... coeffieients (W tn-l K-') at W C and 1 bar Metals Aluminium Antimony Brass (60 /4Q) Cadmium Chromium Cobalt Constantan Copper Gold Inconel Iron, cast Iron, pure Lead Magnesium Molybdenum Monel Nickel Platinum Silver Steel: mild stainless Tin Tungsten Uranium Zinc Liquids 239 18 96 92 67 69 22 3 86 310 15 55 80 35 151 143 26 92 67 419 50 25 67 172 28 113 Benzene Carbon tetrachloride Ethanol (ethyl alcohol) Ether... Methanol (methyl alcohol) Oil: machine transformer Water Plastics 0. 16 0.11 0.18 0.14 0.29 0.15 8.80 0.21 0.15 0.13 0.58 Gases Air Ammonia Argon Carbon dioxide Carbon monoxide Helium Hydrogen Methane Nitrogen Oxygen Water vapour 0.024 0.022 0.0 16 0.015 0.023 0.142 0. 168 0.030 0.024 0.024 0.0 16 Acrylic (Perspex) Epoxy Epoxy glass fibre Nylon 6 Polyethylene: low density high density PTFE PVC 0.20 0.17 0.23... 12 (112°C) Freon 22 (97°C) Sulphur dioxide (157.2") 0.049 0.095 0.0 76 0.10 0.0087 Insulating materials Asbestos cloth Balsa wood (average) Calcium silicate Compressed straw slab Corkboard Cotton wool Diatomaceous earth Diatomite Expanded polystyrene 0.13 0.048 0.05 0.09 0.04 0.029 0. 06 0.12 0.03/0.04 132 MECHANICAL ENGINEER’S DATA HANDBOOK Thermal conductivity coefficients (W m - K - ’) at 20°C and... foam Rock wool Rubber, natural Sawdust Slag wool Urea formaldehyde Wood Wood wool slab 1. 26 0.17 0.10.20 0 .6- 1 o 1 .6 1.7 0.1-0.3 0.4-0.7 1Sb1.8 1 1.05 0.84 1.30 2.18 1.10 0.75 1.01 0.25 1.05 0. 06 3.00 2.01 Asphalt Bitumen Breeze block Brickwork: common dense Carbon Concrete: lightweight medium dense Firebrick (60 0°C) Glass: crown flint Pyrex Ice Limestone Mica Cement Paraffin wax Porcelain Sand Sandstone... ) ~for ’ ~ GrPr= lo5 to lo8 N ~ = 0 1 4 ( G r P r ) ’ for GrPr> lo8 ~~ 49 4 134 MECHANICAL ENGINEER'S DATA HANDBOOK Horizontal plate facing downwards N ~ = 0 2 5 ( G r P r )for ~ ~ ~ GrPr> lo5 In-line pipes 3.14.9 Forced convection Laminar flow in pipe staggered pipes k Turbulentflow over flat plate Nu=3 .65 and h=3 .65 d -c t d Let: L = the distance from the leading edge over which heat is transferred... Turbulent flow over cylinder Nu =0.332Re0.5Pr0.33 Generally: Nu = 0.26Re0.6Pr0.3 For gases: Nu =0.24Re0 .6 +L- For a large temperature difference: (2°"77 N ~ = 0 3 3 2 R e ~ ~ J?~ ~ ~ Pr where: T, =plate temperature, T,=mean fluid temperature Turbulentflow over banks of pipes Generally: Nu = 0.33C,Re0.6Pr0.3 For gases: Nu =0.30C,Re0 .6 In-line pipes: C , N 1.O Staggered pipes: C,? 1.1 Turbulentflow in... The operating cycle is the reverse of that for the reciprocating compressor p 6 Referring to the p V diagram: [ Power P = N pI(Vl- V 6 ) + (P1v1- Pz VZ) n- 1 -p3(v3v4)- (J'5v5 P4v'J] - n- 1 where n =index of expansion and compression 4 V Mass flow rate of air m = N where: "=(?r z=(?Y and P4 1 ' Cut-off ratio = - 3 ' - '6 - '6 v 5 Clearance ratio =- v -v 5 3 127 THERMODYNAMICS AND HEAT TRANSFER 3 I 3... surroundings (K) A, =area of radiating body (mZ) Interchange factor f This takes into account the shape, size and relative positions of bodies H (1) Large parallel planes: f = 9 el% e, +e,-e,e, 1 36 MECHANICAL ENGINEER'SDATA HANDBOOK Parallel surfaces with intermediate wall Let: T = wall temperature e-emissivity of wall (2) Small body enclosed by another body: f=e, (3) Large body (1) enclosed by body (2): e1ez... following formulae give the heat transferred, the logarithmic mean temperature difference and the ‘effectiveness’ e l = l t , - l t , ; e,=,t,-,t, Parallel flow 61 -02 Logarithmic mean temperature difference Om =0 In 2 02 138 MECHANICAL ENGINEER'S DATA HANDBOOK 2 Cold fluid c ab 4 Heat transferred q= UAB, 1 Overall coefficient u = 1 1 -+- hll 3.15.2 Multi-pass and mixed-flo w heat exchangers ha Heat-exchanger... p , Condenser 2 Compressor Throttle Evaporator Refrigeration effect RE = h , - h, RE Coefficient of performance COP = W h 3.13.3 Gas refrigeration cycle Referring to the T-s diagram: 128 MECHANICAL ENGINEER'S DATA HANDBOOK Refrigeration effect RE =cp(TI - T 3 ) cpq,( - T,) + T3 Work in W=cp (T2- cpqt(T3- T,) V C RE Coefficient of performance COP = W ( )~ I, qt =turbine isentropic effi( T T, where: . mild Tin Tungsten Uranium Zinc stainless 239 18 96 92 67 69 22 3 86 310 15 55 80 35 151 143 26 92 67 419 50 25 67 172 28 113 Liquids Benzene Carbon tetrachloride. volume between vanes as the 1 26 MECHANICAL ENGINEER'S DATA HANDBOOK 3.12.1 Power and flow rate Referring to the pV diagram: Power P=N pI(Vl- V6)+ (P1 v1- Pz VZ) [ n-. 0.33 0.50 0.25 0.19 0.049 0.095 0.0 76 0.10 0.0087 0.13 0.048 0.05 0.09 0.04 0.029 0. 06 0.12 0.03/0.04 132 MECHANICAL ENGINEER’S DATA HANDBOOK Thermal conductivity coefficients