Consider a normally-aspirated, four-stroke, spark-ignition, 1.8 L four-cylinder engine with a compression ratio of 10. The induction system uses a single throttle body, and the diameter of the throttle body is 42 mm. The air will enter the throttle body at P = 80 kPa and T = 290 K. The air will be throttled from the 80 kPa ambient pressure down to P = 30 kPa in the intake manifold while the engine's crankshaft speed is 4200 rpm. Model the air as an ideal gas having constant specific heat, using 300 K values from Cengel's tables posted on Canvas. a) Find the temperature of the air in the intake manifold after the air is throttled from P = 80 kPa to P = 30 kPa (answer: T = 288.91 K). b) Find the density and mass flow rate of the air in the intake manifold (answers P = 0.3618 kg/m" and m = 0.02533 kg/s). The volume of air in a cylinder at the start of the compression process is , which is the largest volume in a cylinder. The compression ratio, r, is the ratio of the largest volume in the cylinder to the smallest volume in the cylinder. r= + x+ max min min The displacement in each cylinder of this four-cylinder engine is -0.0018/4=.00045 m=* 1-p *=*** min An ideal four-stroke cylinder-piston engine behaves like constant volume-rate-of-flow device when it runs at a fixed speed. The crankshaft must make two revolutions in order for a cylinder to execute the Otto cycle. RPM 1 minute 2 60 seconds The volume rate of flow through one cylinder after the air passes through the throttle body is # * take = 4+=4xx. = .00050 m. where is in m/s if is in m. The total volume rate of flow of the air through the intake manifold for this four- cylinder engine at 4200 rpm is RPM 1 -X 2 60 4x0.00050x- 4200 1 -= 0.070 m/s. 2 60 The mass flow rate of the air through the engine is m = ptake, where is the density of the air in the intake manifold after it has been throttled from the ambient pressure and temperature to P = 30 kPa and T. The ideal gas equation of state may be used to compute the density of the air in the intake manifold: P P P=1 R_T R.T air m= intake The speed of the air after it passes through the throttle body is V intake, where A is A the cross-sectional area of the throttle body. Conservation of mass requires V P.VA= PVA and the first law of thermodynamics requires -+cT = + c T. V 2 2 Conservation of mass may be used with the ideal gas equation of state to express in terms of unknown temperature T: P.VA=PVA- V= P.V. P.V. T T P V VVP 2 2 Now the first law of thermodynamics becomes a third-order polynomial in T: T," =0 2 V V P VP 2 P :) ( 7 ) + , T = [ + cT = V + 0,T, cT + ( _T]}T -(V)(A) 2 2 2 V 2 cen1939 ch16-ap01.qxd 0/11/08 1:21 PM Page 936 936 I Thermodynamics TABLE A-17 Ideal-gas properties of air h P. 887.8 1.55848 808.0 1.59634 738.0 1.63279 706.1 1.65055 23.13 481.01 81.89 24.46 488.81 78.61 25.85 496.62 75.50 27.29 504.45 72.56 28.80 512.33 69.76 30.38 520.23 67.07 32.02 528.14 64.53 33.72 536.07 62.13 35.50 544.02 59.82 37.35 551.99 57.63 39.27 560.01 55.54 43.35 576.12 51.64 } U kJ/kg P kJ/kg kJ/kg 200 199.97 0.3363 142.56 1707.0 1.29559 580 586.04 14.38 419.55 115.7 210 209.97 0.3987 149.69 1512.0 1.34444 590 596.52 15.31 427,15 110.6 220 219.97 0.4690 156.82 1346.0 1.39105 600 607.02 16.28 434.78 105.81 230 230.02 0.5477 164.00 1205.0 1.43557 610 617.53 17.30 442.42 101.2 240 240.02 0.6355 171.13 1084.0 1.47824 620 628.07 18.36 450.09 96.92 250 250.05 0.7329 178.28 979.0 1.51917 630 638.63 19.84 457.78 92.84 260 260.09 0.8405 185.45 640 649.22 20.64 465.50 88.99 270 270.11 0.9590 192.60 650 659.84 21.86 473.25 85.34 280 280.13 1.0889 199.75 660 670,47 285 285.14 1.1584 203.33 670 681.14 290 290.16 1.2311 206.91 676.1 1.66802 680 691.82 295 295.17 1.3068 210.49 647.9 1.68515 690 702.52 298 298.18 1.3543 212.64 631.9 1.69528 700 713.27 300 300.19 1.3860 214.07 621.2 1.70203 710 724.04 305 305.22 1.4686 217.67 596.0 1.71865 720 734.82 310 310.24 1.5546 221.25 572.3 1.73498 730 745.62 315 315.27 1.6442 224.85 549.8 1.75106 740 756.44 320 320.29 1.7375 228.42 528.6 1.76690 750 767.29 325 325.31 1.8345 232.02 508.4 1.78249 760 778.18 330 330.34 1.9352 235.61 489.4 1.79783 780 800.03 340 340.42 2.149 242.82 454.1 1.82790 800 821.95 350 350.49 2.379 250.02 422.2 1.85708 820 843.98 52.59 608.59 44.84 360 360.58 2.626 257.24 393.4 1.88543 840 866.08 57.60 624.95 41.85 370 370.67 2.892 264.46 367.2 1.91313 860 888.27 63.09 641.40 39.12 380 380.77 3.176 271.69 343.4 1.94001 880 910.56 68.98 657.95 36.61 390 390.88 3.481 278.93 321.5 1.966331 900 932.93 75.29 674.58 34.31 400 400.98 3.806 286.16 301.6 1.99194 920 955.38 82.05 691.28 32,18 410 411.12 4.153 293.43 283.3 2.01699 940 977.92 89.28 708.08 30.22 420 421.26 4.522 300.69 266.6 2.04142 960 1000.55 97.00 725.02 28.40 430 431.43 4.915 307.99 251.1 2.06533 980 1023.25 105.2 741.98 26.73 440 441.61 5.332 315.30 236.8 2.08870 1000 1046.04 114.0 758.94 25.17 450 451.80 5.775 322.62 223.6 2.11161 1020 1068.89 123.4 776.10 23.72 460 462.02 6.245 329.97 211.4 2.13407 1040 1091.85 133.3. 793.36 23.29 470 472.24 6.742 337.32 200.1 2.15604 1060 1114.86 143.91 810.62 21.14 480 482.49 7.268 344.70 189.5 2.17760 1080 1137.89 155.2 827.88 19.98 3.05608 1100 1161.07 167.1 845.33 18.896 3.07732 1120 1184.28 179.7 862.79 17.886 3.09825 1140 1207.57 193.1 880.35 1160 1230.92 207.2 897.91 16.064 3.13916 1180 1254.34 222.2 915.57 15.241 3.15916 1200 1277.79 238.0 933.33 14.470 3.17888 1220 1301.31 254.7 951.09. 13.747 3.19834 1240 1324.93 272.3 968.95 13.069 3.21751 47.75 592.30 48.08 2.71787 2.84856 2,87324 2.89748 2.92128 2.94468 2.96770 2.99034 3,01260 3,03449 16.946 3.11883. T K 490 492.74 7.824 500 503.02 8.411 510 513.32 9.031 520 523.63 9.684 530 533.98 10.37 540 544.35 11.10 550 555.74 11.86 560 565.17 12.66 570 575.59 13.50 0 kJ/kg V kJ/kg. K 352.08 179.7 2.19876 359.49 170.6 2.21952 366.92 162.1 2.23993 374.36 154.1 2.25997 381.84 146.7 2.27967 389.34 139.7 2.29906 396.86 133.1 2.31809 404.42 127.0 2.33685 411.97 121.2 2.35531 T K V. 5 kJ/kg K 2.37348 2,39140 2.40902 2,42644 2.44356 2.46048 2.47716 2.49364 2.50985 2.52589 2.54175 2,55731 2.57277 2.58810 2.60319 2.61803) 2.63280 2.64737 2.66176 2.69013 2.74504 2.77170 2.79783 2.82344 ++