MECH 351 Lab 2

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Apr 3, 2024

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Lab Report on Experiment 2 DWSIM MECH-351 Lab Section WI-X Group B February 19th, 2024 Dr. Lyes Kadem & Dr. Charles Kiyanda Concordia University Montreal, QC, Canada

SECTION 1 Figure 1: Rankine Cycle Diagram from Experiment 1

Figure 2: Results from Experiment 1 A) Compute the actual Carnot and thermal efficiencies a.1.) Carnot efficiency: 50.98% a.2.) Thermal efficiency: 29.20% B) Plot the T-S diagram for the actual Rankine cycle

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C) Plot the variations for the following Inlet Turbine Temperatures: Figure 3: Diagram Containing Variations for Inlet Turbine Temperatures

Temperature (Celsius) 450 500 550 600 Carnot Efficiency 50.98% 54.15% 56.94% 59.40% Thermal Efficiency 29.20% 30.05% 30.94% 31.86% Steam Quality 0.9219 0.9450 0.9667 0.9873 Table 1: Table Containing Variations for Inlet Turbine Temperatures DISCUSSION: Both the Carnot and Thermal efficiencies of the system increases with the increase of heat at the turbine inlet. This can be explained by the formulas 1-(Tc/Th) (Carnot) and W/Qin (Thermal). Both efficiencies generally increase with an increase in the heat supplied to the turbine inlet, but the Carnot efficiency benefits from the increase in temperature difference between the heat source while the thermal efficiency benefits from the increased net work output. The steam quality inches closer to the saturated vapor line (x= 1) with the increase of heat because more heat entails that the quality of the water at the same given pressure will come closer to dry vapor and further away from the saturated vapor line (x=0).

D) Plot the variations for the following Condenser Pressures: Figure 4: Diagram Containing Variations for Condenser Pressures

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Condenser Pressures (kPa) 50 40 30 20 10 Carnot Efficiency 50.98% 51.74% 52.67% 53.92% 55.89% Thermal Efficiency 29.20% 30.07% 31.14% 32.57% 34.83% Steam Quality 0.9219 0.9121 0.9000 0.8838 0.8582 Table 2: Table Containing Variations for Condenser Pressures DISCUSSION: As the pressure of the condenser decreases, the efficiencies increase. By decreasing the pressure at the condenser, the condenser temperature decreases. This, in turn, increases the temperature difference between the boiler and the condenser. According to the Carnot efficiency formula, a larger temperature difference leads to higher efficiency. When the pressure at the condenser decreases, the pressure difference decreases as well, resulting in reduced pump work. This reduction in pump work improves the overall efficiency of the cycle.The steam quality is also reduced because lower pressures yield lower temperatures which in turn, yield steam that is less “dry”.

E) Plot the variations for the following Condenser Exit Temperatures: Figure 5: Diagram Containing Variations for Condenser Exit Temperatures

Figure 6: Diagram Containing Variations for Condenser Outlet Temperatures Back Work Ratio

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Temperature (Celsius) 80 70 60 50 20 Carnot Efficiency 51.17% 52.55% 53.93% 55.31% 59.46% Thermal Efficiency 29.15% 28.75% 28.36% 27.98% 26.90% Back Work Ratio (work pump / Work turbine) 3.45e-3 3.43e-3 3.41e-3 3.40e-3 3.36e-3 Table 3: Table Containing Variations for Condenser Exit Temperatures DISCUSSION: By decreasing the condenser exit temperature, the temperature difference between the boiler and the condenser increases. According to the Carnot efficiency formula, a larger temperature difference leads to a higher Carnot efficiency. Therefore, lowering the condenser exit temperature would increase the Carnot efficiency. The thermal efficiency on the other hand, is determined by the ratio of net work output to the heat input. Decreasing the condenser exit temperature can reduce the temperature at which heat is rejected from the cycle. As a result, the heat rejected in the condenser decreases. However, the work output from the turbine remains relatively constant, leading to a reduction in the ratio of work output to heat input and thus a decrease in thermal efficiency. The work of the pump in this ideal rankine cycle is negligible. The average value of percentage of work in, in comparison with that of the value of work out, is less than 1%.

F) Plot the variations for the following Turbine Pressures : Figure 7: Diagram Containing Variations for Turbine Inlet Pressures

Pressure (MPa) 2 5 10 15 20 Carnot Efficiency 50.98% 50.98% 50.98% 50.98% 50.98% Thermal Efficiency 27.18% 31.65% 34.65% 36.09% 36.82% Steam Quality 0.9528 0.8812 0.8199 0.7770 0.7402 Table 4: Table Containing Variations for Turbine Pressures DISCUSSION: Increasing the inlet turbine pressure doesn't directly impact the Carnot efficiency, as long as the temperatures of the heat source (boiler) and the heat sink (condenser) remain the same. Higher turbine inlet pressure means higher enthalpy of the steam entering the turbine. This results in more work output for the same mass flow rate of steam passing through the turbine, increasing the cycle's efficiency. With increased turbine inlet pressure, the turbine expands the steam to a lower pressure, which can lead to increased expansion work output. This is because the larger pressure drop across the turbine results in more work extracted from the steam. Additionally, higher turbine inlet pressure can allow for a reduction in the amount of superheating needed in the boiler, reducing energy losses associated with superheating and improving overall efficiency. The quality of the steam inevitably inches closer to x=1 due to the increase in pressure which in turn, increases temperature. The quality will always inch closer to x=1 (saturated vapor line) as temperature increases.

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SECTION 2 Figure 2: Ideal Regeneration Rankine Cycle on DWSIM Thermal Efficiency Feed Water Heater Pressure (kPa) 30.00% 200 29.84% 400 29.73% 600 29.65% 800 29.59% 1000 Table 2: Thermal Efficiency Vs Feed Water Heater Pressure for an Ideal Regeneration Rankine Cycle Data

Figure 3: Thermal Efficiency Vs Feed Water Heater Pressure for an Ideal Regeneration Rankine Cycle Question 2 Discussion

As seen above, the thermal efficiency decreases as the feed water heater (FWH) pressure increases. Mathematically, this can be seen from the data in the appendix. As FWH pressure increases, the “Q_in” value decreases and the “Q_out” value remains stable, while thermal efficiency can be calculated as: ղ Th = 1 - Q_out/Q_in showing that the ratio “Q_out/Q_in” increases. The same can be said for the ratio “Net Work/Q_in”. Both values decrease with the increased pressure of the FWH, but the “Net Work” decreases at a higher rate than “Q_in”. However, theoretically this does not make sense as a FWH should increase the efficiency of a rankine system as the FWH temperature approaches closer to the average of the outlet temperature of the boiler and the outlet temperature of the condenser. The FWH being at a higher pressure means the temperature should be higher as well. Looking at the data, the expected outcome would be an increase in thermal efficiency from 200 kPa to 600 kPa and then a decrease until 1000 kPa as temperature starts to become further from the average. This discrepancy with the expected trend may be due to many factors. One factor may be the fraction split between the FWH and the second turbine. No fraction was specified and so only 5.00% of the mass flow went to the FWH. Another issue may be that the mass split was done after the turbines work whereas, generally, FWH’s take some of the flow directly from the turbine, before the work is finished, as it allows for it to use higher pressure steam while also allowing the first turbine to complete more work. This however, should not be the issue as the calculations were done under the assumption of ideal parameters with 100% efficiency. Although the values were not as expected, the FWH still increased the efficiency of the system compared to if no FWH was involved. The thermal efficiency at 200 kPa without a FWH would have been: ղ Th = 1 - Q_out/Q_in → ղ Th = 1 - 2124.7946kW/3001.1445kW = 0.2920 = 29.20% compared to the 30.00% that was calculated instead. SECTION 3 a)

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Figure 4: Three Turbine, Reheat and Regeneration Cycle b) Choice 1 : We need the pressure at point 16, which is where the steam is extracted for the water heating. Choice2 : We need the temperature at point 14. This is right after the throttling process and before the open feedwater heater. c) Choice 1 (Pressure at Point 4): This pressure is typically chosen to maximize the efficiency of the turbine cycle while still providing sufficient energy for the extraction process. Since the steam is being extracted for feedwater heating, the pressure should be high enough to ensure a significant temperature difference between the extracted steam and the feedwater. However, it shouldn't be too high to avoid excessive energy loss in the extraction process. A reasonable range for the pressure at point 4 could be between 0.7 MPa to 1 MPa {0.7, 0.8, 0.9, 1.0}. Choice 2 (Temperature at Point 8): This temperature is typically slightly above the saturation temperature corresponding to the pressure at point 4, as it is right after the throttling process. The throttling process results in a small decrease in temperature due to the Joule-Thomson effect, but it should remain close to the saturation temperature. A reasonable range for the temperature at point 8 could be 350ºC to 400ºC {350, 375, 400, 425, 450}. d)

Figure 5: Thermal Efficiency vs Pressure for Three Turbine Cycle The parameter we chose is Pressure. There are 3 stages to what we observe: 1. When the steam is bleeding at a low pressure, it has a low thermal efficiency, as we can see on the graph, if we plot a value of low pressure, the thermal efficiency will be Thermal efficiency P

low. We can also say that there is very low heat sent to the feed water heater, so the thermal efficiency is low. 2. When pressure is bleeding at a high pressure, it has a high thermal efficiency because the heat required by the boiler is less, so the thermal efficiency increases. 3. When the pressure starts being too high, the thermal efficiency decreases because the work output of the turbine will be less. 4. Values: At 0.6MPa: Thermal efficiency is 28.87% At 0.7MPa: Thermal efficiency is 31.83% At 0.8MPa: Thermal efficiency is 34.66% At 0.9MPa: Thermal efficiency is 36.37% At 1.0MPa: Thermal efficiency is 34.98%

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