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Tutorial (TOC) > Daemons > IC Engines >Examples |
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Ex-1 An ideal Otto cycle has a compression ratio of 9. At the beginning of compression, air is at 100 kPa, 27oC. The pressure is doubled during the constant-volume heat addition process. Determine (a) the thermal efficiency, (b) the net work output, and (c) the MEP. Assume variable c_p. (d) What-if scenario: How would the answers change if the compression ratio was increased to 10? Solution Detailed analysis of cyclic processes executed by a closed system is handled in the specific branch of the closed process daemons. Launch the closed-cycle daemon located at TEST. Daemons. Systems. Closed. Process. Specific.Cycles. IdealGas. |
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Let us set up the cycle as follows: Process-A: isentropic compression from State-1 to State-2 ; Process-B : constant volume heat addition from State-2 to State-3 ; Process-C : isentropic expansion from State-3 to State-4 ; Process-D : constant volume heat rejection from State-4 to State-1 . State-1: Enter m1 (assume 1 kg), T1, p1, and Calculate. State-2: Enter s2 ('=s1'), v2 ('=v1/9'), and Calculate. State-3: Enter p3 ('=p2*2'), v3 ('=v2'), and Calculate. State-4: Enter s4 ('=s3'), v4 ('=v1'), and Calculate. |
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| Fig. 1.1
Image of State-2. The State
and Process panels are identical to those found in closed-process daemons.
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On Process Panel, work on the four processes.
Process-A: Select Process-A . Select State-1 and State-2 as the b- and f-States , enter Q=0, and Calculate. The work is calculated as W_B=-299.5 kJ. Process-B: Select Process-B . Select State-2 and State-3 as the b- and f-States , and Calculate. The heat transfer is calculated as Q=599.7 kJ. Process-C: Select Process-C . Select State-3 and State-4 as the b- and f-States, enter Q=0, and Calculate. The work is calculated as W_B=627.3 kJ. Process-D: Select Process-D . Select State-4 and State-1 as the b- and f-States , and Calculate. The heat transfer is calculated as Q=-270.8 kJ. |
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| Fig. 1.2
Image of the Process-A. You do
not have to enter W_B as it is automatically calculated. For a known polytropic process, the polytropic coefficient n can be entered in this panel. |
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On the Cycle Panel, cycle variables are automatically calculated if the cycle
has been completed. The thermal efficiency is calculated as eta_th=54.8% . Super-Calculate to obtain
MEP=428.2 kPa.
For the parametric study, go to State Panel and change v2 to '=v1/10'. Calculate the state and Super-Calculate to update all calculations. The new answers are: eta_th=56.3% and MEP=455.5 kPa . |
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| Fig. 1.3 Image of the Cycle Panel. |
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Ex-2 An air standard Diesel cycle has a compression ratio of 15 and cut-off ratio of 3. At the beginning of the compression process, air is at 97 kPa and 30°C. Using the IG model for air, determine (a) the temperature after the heat addition process, (b) the thermal efficiency, and (c) the work output in kJ/kg. (c) What-if scenario: How would the answers change if the cut-off ratio was increased to 4? Solution Detailed analysis of cyclic processes executed by a closed system as in a Diesel cycle is handled in the specific branch of the closed process daemons. Launch the closed-cycle daemon located at TEST. Daemons. Systems. Closed. Process. Specific.Cycles. IdealGas. |
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Let us set up the cycle as follows: Process-A: isentropic compression from State-1 to State-2 ; Process-B : constant pressure heat addition from State-2 to State-3 ; Process-C : isentropic expansion from State-3 to State-4 ; Process-D : constant volume heat rejection from State-4 to State-1 . State-1: Enter m1 (assume 1 kg), T1, p1, and Calculate. State-2: Enter s2 ('=s1'), v2 ('=v1/15'), and Calculate. State-3: Enter p3 ('=p2'), v3 ('=v2*3', cut off ratio is 3), and Calculate. The temperature is calculated as T3=2266°C. State-4: Enter s4 ('=s3'), v4 ('=v1'), and Calculate. |
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On Process Panel, work on the four processes.
Process-A: Select Process-A . Select State-1 and State-2 as the b- and f-States , enter Q=0, and Calculate. The work is calculated as W_B=-415.8 kJ. Process-B: Select Process-B . Select State-2 and State-3 as the b- and f-States , and Calculate. The heat transfer is calculated as Q=2042 kJ. Process-C: Select Process-C . Select State-3 and State-4 as the b- and f-States, enter Q=0, and Calculate. The work is calculated as W_B=928 kJ. Process-D: Select Process-D . Select State-4 and State-1 as the b- and f-States , and Calculate. The heat transfer is calculated as Q=-1044 kJ. |
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On the Cycle Panel, cycle variables are automatically calculated if the cycle has been completed. The thermal efficiency is calculated as eta_th=48.86% and the net work output as W_net=998 kJ (see image of the cycle panel below).
For the parametric study, go to State Panel and change v3 to '=v2*4'. Calculate the state and Super-Calculate to update all calculations. The new answers are: T3=3112°C, eta_th=44.42% and W_net=1371 kJ/kg, which can be found on the cycle panel or the I/O panel as shown below.
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Ex-3 An ideal Stirling engine using helium as the working fluid operates between the temperature limits of 38°C and 850°C and pressure limits of 102 and 1020 kPa. Assuming the mass used in the cycle is 1 kg, determine (a) the thermal efficiency of the cycle, and (b) the net work. Solution Detailed analysis of cyclic processes executed by a closed system as in a Diesel, Otto, or Stirling cycle is handled in the specific branch of the closed process daemons. Helium being a perfect gas (constant c_p), launch the closed-cycle daemon located at TEST. Daemons. Systems. Closed. Process. Specific.Cycles. PG Model. |
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Let us set up the cycle as follows: Process-A: isothermal compression from State-1 to State-2 ; Process-B : constant volume heat addition from State-2 to State-3 ; Process-C : isothermal heat addition from State-3 to State-4 ; Process-D : constant volume heat rejection from State-4 to State-1 . Evaluate the four states as described in the TEST-codes. |
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On Process Panel, work on the four processes.
Select Process-A . Select State-1 and State-2 as the b- and f-States , and Calculate. The work is calculated as W_B=-1489 kJ. Select Process-B . Select State-2 and State-3 as the b- and f-States , and Calculate. The heat transfer is calculated as Q=2531 kJ. Select Process-C . Select State-3 and State-4 as the b- and f-States, and Calculate. The work is calculated as W_B=5375 kJ. Select Process-D . Select State-4 and State-1 as the b- and f-States , and Calculate. The heat transfer is calculated as Q=-2531 kJ. |
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On the Cycle Panel, cycle variables are automatically calculated without taking into account regeneration. To correctly specify the transfer of heat from Process-B (2-3)to Process-D (4-1), select the regeneration Donor and Receiver as shown in the image below. The thermal efficiency is calculated as eta_th=72.3% and the net work output as W_net=3886 kJ (see image of the cycle panel below).
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| Copyright 1998-: Subrata Bhattacharjee |
