CHAPTER 3 Experimental Procedures and Uncertainty Analysis…
3.4 Uncertainty Analysis
3.4.3 The Experimental Repeatability
ε = emissivity of the thermocouple
σ = Stefan Boltzmann constant
h= convection heat transfer coefficient at thermocouple wire surface
Now, the analysis method of uncertainty can be utilized to obtain the uncertainty in the flame temperature from the correlation associated with h, Tt, and ε. The relationship between temperature and error is shown in Fig. 3-1.
3.4.3 The Experimental Repeatability
In order to confirm the accuracy and coincidence of the experiment, selecting one test under the specified mixing fuel, pressure and flow rate of the fuel has executed at three times to ensure the experimental repeatability. The following examples are illustrated to show the creditability in the previous statement. The volume flow rates for four different low heating value fuels and several different RPMs are selected to demonstrate the experimental repeatability. It recorded three measured data of volume flow rate and made an average value for each test. The three measured data, their averaged value, and the standard deviation are
difference value between the three volume flow rates and the coefficient of variation are also listed in Tables 3-1~3-4. The coefficient of variation (C.V.) is defined as the ratio of the standard deviation s to the meanX, where the standard deviation s is calculated as:
∑
The coefficient of variation is a dimensionless number that allows comparison of the variation of data points in a data series around the mean. The averaged values are represented by curves. It can be seen in Figs. 3-2a~3-2d that in general the errors are within the acceptable range (<3%) and the repeatability shown in Figs. 3-3a~3-3d are really good.
The volume flow rate, pressure and their corresponding characteristics will be discussed in detail in the next chapter.
CHAPTER 4
RESULTS AND DISCUSSION
The original MGT, whose fuel was liquid, was modified for using gaseous fuel. Therefore, the original pipes were also adjusted accordingly.
In addition, the lubricant for bearings in original MGT was pre-mixed with oil fuel, now its supply system should be separated from the fuel pipes after modification.
In the experiment, the idling rpm, 45,000 rpm, was reached at first.
In order to increase the efficiency of fuel usage, the data were acquired continuously for the rpm that was increased 5000 rpm at each step. And each step was maintained for about 10 seconds to ensure the engine can achieve a stable condition within that duration so the measured output data at each step were meaningful. Otherwise, the stop-and-run experiments would consume a lot of amount of gases that the time was consuming and the expense was not able to be handled.
In order to let the MGT be capable of working with the low-heating-value fuel, the fuel supply system needed to take enough pressure to ensure that it would have ample fuel density. For example, when the fuel with 100% C3H8 was applied, MGT would only need 3bar fuel pressure for idling, on the other hand, it would require 8bar fuel pressure to achieve the condition when using 60% CH4 with 40% CO2 as the low-heating-value fuel. In reality, MGT does not need such high pressure. What it needs is to provide a higher volume flow rate with the low-heating-value fuel. Unfortunately, the original fuel supply pipes in
the present study were too narrow to be able to reach the proper fuel supply rate. In other words, when low-heating-value fuel was at a low pressure, the MGT could not have enough fuel to burn. So the fuel’s pressure was expected to reach a maximum of 12bar for top performances.
In the condition when the diameters of the fuel pipes were increased, the MGT could obtain enough fuel at low pressure. Besides, adding new fuel pipes from the fuel tank directly to the combustion chamber could achieve better fuel-efficiency. In such way, MGT could be modified more easily instead of changing all the fuel pipes.
Then, the corresponding sensors and actuators for the micro gas turbine system were also established. The temperatures were acquired by K-type thermal couples from four different parts of the MGT. There were compressor inlet, compressor outlet, turbine inlet, and turbine outlet.
Besides, there were two tachometers. One indicated the rpm of MGT, and another measured the rpm of generator. The measurements, which could indicate the engine performance, would be analyzed and evaluated by changing the low-heating-value fuel (CH4 mixed with CO2) with various fuel flow rate.
As the design procedure was completed, the fabrication, component tests, and operation of the developed gas turbine engine system were performed for parametric study to establish the start-up (idling) and operation procedure. All of them will be discussed in details in Sections 4.1 and 4.2.
4.1 The tests with different fuels with no load
In this section, the MGT without load was testing. There were various low-heating-value fuels with different mixture ratios of methane (CH4) and Carbon dioxide (CO2). The concentrations of CH4 in fuel were changed from 90% to 50%, and the ones of CO2 increase from 10% to 50%, correspondently. The test conditions are summarized in Table 4-1.
The temperatures of major parts of MGT were measured under the given fuel and fuel flow rate, a function of gauge pressure of cylinder. The corresponding thermal efficiency was calculated accordingly. Finally, a performance comparison was given.
4.1.1 The pressures and volume flow rate of fuel at MGT with no load The pressure of fuel was the pressure of cylinder (bottle), which could be adjusted by a control valve, and it determined the fuel volume flow rate. The measured volume flow rates for each low-heating-value fuels as a function of pressure are listed in Table 4-2, and the volume flow rate is calculated from the mass flow rate. (CH4 density is 0.7168 g/L at 0
℃, 1 atm) It can be seen that the volume flow rate for each fuel almost is linearly proportional to the pressure. The resultant rotational speeds as a function of pressure for various low-heating-fuels are shown in Figs. 4-1a and 4-1b.
In the test of fuel using 90% CH4 with 10% CO2, it can approach 85,000 rpm when the pressure reaches the maximum of 12bar, whereas in the test of using 60% CH4 with 40% CO2 can only reach 47,000 rpm at
50% CO2 can reach as low as 24,000 rpm as shown in Fig. 4-1b. It is because the test in Fig. 4-1b was carried out in the path from higher pressure to lower one, whereas the other tests in Fig. 4-1a were taken from the reverse order.
Obviously, the performance of MGT is influenced by combustible fuel concentration contained in the low-heating-value fuels. From Fig.4-1a, as expected, the higher heating-value fuel will have better performance because the fuel can supply more energy to MGT. Also, the lower heating-value fuel should have higher pressure in order to approach idle at 45,000 rpm.
Since the narrow fuel’s pipes, originally used for oil fuel, were not modified, the gas pressure was needed to increase to enhance the volume flow rate of low-heating-value gaseous fuel. As shown in Figs. 4-2a and 4-2b, they indicate that the MGT performance is proportional to the concentration of CH4 in fuel and the volume flow rate. Therefore, if the volume flow rate can be increased, the MGT will be expected to have better performance. Moreover, there are some difficulties to using low-heating-value fuel. The maximum rotational speed may be reached at a low rate which produces choking conditions at some point in the MGT.
The choke may occur in the nozzle throats or in the annulus at outlet from the turbine depending on the design. If the rotational speed increases to higher rpm (>85,000 rpm), the choke phenomenon may have more affection to limit the rotation speed of turbine wheel. It is because the rotational speed is increasing with flow rate increasing, but the maximum pressure of fuel is reached first. Hence, the choke does not occur at
present tests. When choking occurs at the higher rotational speed, the turbine can be modified by increasing the gap between the turbine blades in order to let more mass flow through the turbine to increase the rotational speed and thrust. In the other hand, a large gap between the turbine blades may cause low efficiency. In this research, the equivalent ratio is calculated from:
The air mass flow rate at primary zone that evaluates from the compressor map at 45,000rpm is 321.12g/min, and the fuel mass flow rate is 26.87g/min. The A/F is 16.7 less than the equivalent ratio 18.1, but at 80,000rpm the A/F is 22.5 more than the equivalent ratio 18.1. Hence, the A/F increases when the rotational speed increases at 45,000~80,000rpm.
Besides, since the volume flow rate is proportional to the cylinder pressure as mentioned previously, both Figs.4-1 and 4-2 are expected to be similar, and the relationship between pressure and fuel volume flow rate is described by the linear regression equation.
5.54 4.2 (4.2) Now, the volume flow rates of low-heating-value fuel are replaced by the ones of CH4, and the corresponding results are shown in Fig. 4-3.
From this figure, it can be seen that under the given compressor rotational speed, the volume flow rates of CH4 from different low-heating-value fuel are almost the same, indicating the stable combustions occur in this MGT even the different fuels are supplied.
4.1.2 The temperature of MGT without load
There are four temperatures measured, the acquisition positions are at compressor inlet (T1), compressor outlet (T2), turbine inlet (T3), and turbine outlet (T4). The histories of all the temperatures and corresponding rotational speeds for 5 different fuels are shown in Figs.
4-4~4-8. In each figure, the upper is rotational speed, whereas the lower is the 4 measured temperatures. Note that in Figure 4-4 (50% CH4 with 50% CO2), the experiments were carried out from higher rotational speed to lower one, whereas In Figs. 4-5~4-8, they were taken in reverse order.
In general aspect, these figures show the same trend that both the inlet and outlet temperatures (T3 and T4) of turbine decrease with the increase of rpm. It is because when the rpm of compressor increases, it brings more air to combustion chamber, and the temperature of turbine is cooled by this excess air. Liou and Leong [24], who used the same MGT but with an application of oil fuel, also found the same phenomena between 40,000 to 120,000rpm. However, when the MGT was over 120,000 rpm,
the temperature would increase with an increment of rpm in their work.
Figures 4-4~4-8 show that the turbine inlet temperatures (T3) vary slightly with different concentrations of CH4 in fuels. So do the turbine outlet temperatures (T4). Also, the temperature differences between T3 and T4 for all of low-heating-value fuels are more or less the same. The reason can be attributed to the results of Fig. 4-3 that under the same compressor rotational speed, the amounts of CH4 burned are the same for these fuels. Besides, T3 and T4 perturb very much at the beginning of
operation because the blower and fuel are controlled by human hands. If the flow rate of air was supplied excessively, T3 and T4 would decrease immediately. On the other hand, if the flow rate of fuel was supplied excessively, T3 and T4 would soon increase sharply.
Figure 4-9 shows the surface (case) conditions of combustion chamber by using oil fuel, whereas Figure 4-10 shows the one by using gaseous fuel. Apparently, the burning damage in Fig. 4-10 is worse.
Obviously, the temperature of combustion chamber using methane is higher than that using liquid fuel, because the combustion chamber is designed to burn liquid fuel. If the gaseous fuel was used, the cooling system would not be enough. So, the cooling holes of combustion chamber should make some modifications if the high turbine efficiency is pursued.
4.1.3 Thermal efficiency
The efficiency of the air-standard Brayton cycle is found as follows:
η 1
QL According to Sonntag et al. [25], because the working fluid does not go through a complete thermodynamic cycle in the MGT, the internal combustion engine operates on the so-called open cycle. However, for analyzing internal-combustion engines, it is advantageous to devise closed cycles that closely approximate the open cycles. One such approach is the air-standard cycle, which is based on the following assumptions:1. A fix volume of air is the working fluid throughout the entire cycle, and air is always an ideal gas. Thus, there is no inlet process or exhaust process.
2. The combustion process is replaced by a process transferring heat from an external source.
3. The cycle is completed by heat transfer to the surroundings.
4. All processes are internally reversible.
5. An additional assumption is often made that air has a constant specific heat, recognizing that this is not the most accurate model.
The thermal efficiency of the MGT is obtained from the efficiency of the air-standard Brayton cycle as shown in Eq. (4.3). Figure 4-11 is the thermal efficiency verse compressor rotational speed. For the fuels of 90%, 80% and 70% CH4, the efficiency decreases with a increase of rotational speed. Based on Eq. (4.3), the thermal efficiency is influenced by T4, T3, and T2 (the outlet temperature of compressor). T2 increases with the rotational speed of compressor. As T2 increases, the thermal efficiency decreases, but if T3 and T4 decrease in higher rpm, thermal efficiency will expect to increase. Actually, thermal efficiency decreases, because the influence of increasing T2 is larger than decreasing T3 and T4 in higher rpm. It is shown in Figs. 4-11 and 4-12 that lower-heating-value fuels have more thermal efficiency than higher-heating-value fuels. Theoretically, thermal efficiency should not increase in lower-heating-value fuels. It is because the pressure and flow rate of lower-heating-value fuels are larger than higher-heating-value, and the mismatch of combustion chamber makes the flame be moved to
approach the T3 thermal couple. Hence, the T3 is increased. Besides, if there are pressures, compressor efficiency and turbine efficiency in the MGT, cycle analysis could be used to present more accurate efficiency than the air-standard Brayton cycle. The definition of the efficiency of ideal cycle is unambiguous, but is not accurate for an open cycle with internal combustion. Knowing the compressor delivery temperature, composition of the fuel, and turbine inlet temperature required, a straightforward combustion calculation yields the A/F ratio necessary;
and combustion efficiency can also be included to allow for incomplete combustion. Thus it will be possible to express the cycle performance unambiguously. The previous section dealt with the air-standard Brayton cycle, but work output and efficiency of all actual cycles are considerably less than those of the corresponding ideal cycles because of the effect of compressor, combustor, and turbine efficiencies and pressure losses in the MGT.
Assuming the compressor efficiency is ηc and the turbine efficiency is ηt, and the actual compressor work and turbine work is given by:
Wca = ma(h2-h1)/ ηc (4.4) Wta = (ma + mf)(h3a-h4) ηt (4.5) Then, the actual output work is
Wact = Wta -Wca (4.6) The actual fuel required to raise the temperature from 2a to 3a is
mf = (h3a - h2a)/ ηb(LHV) (4.7) h4a = h3 -Wca (4.8) h4 = h3 – (Wca/ηt) (4.9)
The power turbine output work is
Wa = (ma + mf)(h4a-h5) ηt (4.10) Thus, the overall adiabatic thermal cycle efficiency can be calculated from the following equation:
ηt = Wact + Wa/mf(LHV) (4.11)
4.2 The MGT tests with generator
In this section, the MGT with generator was under test, and the other test parameters were the same as those in the Sec. 4.1. However, an additional new fuel, C3H8, was used in this section. Except the temperature measurements, the electricity generated by generator is discussed as well. The test conditions are summarized in the following table (Table4-4).
4.2.1 The pressures, volume flow rate of fuel, and temperatures at MGT with generator
All the measured temperature trends of MGT with generator are similar to the ones of MGT without load. MGT does not drive the generator directly. Actually, the generator is driven by gearbox, which has a power turbine that is driven by the high temperature and pressure gas from the MGT. Apparently, generator has little influence on MGT.
The output of MGT is directly influenced by the fuel volume flow rate, which is proportional to the cylinder pressure as mentioned previously. If the volume flow increases, the performance would be better.
Nevertheless, the volume flow rate in the MGT system is limited by the
fuel pipes, whose diameters were too narrow. The achievable volume flow rate cannot be over 58L/min, even if the highest pressure (12bar) was applied in the system. The pressure cannot exceed 12 bar, to prevent the pipe of MGT system from breakage.
4.2.2 The choice of the generator system
The loads of the MGT system are represented by two tungsten lights.
When they operate in series, the resultant resistance is greater than the ones operated in parallel, and the current intensity becomes smaller. In other words, if the current is increased in circuit, the coils of generator will make more loading to MGT. Therefore, the series arrangement of load can be driven by the MGT with the low-heating-value fuels of 60%
and 70% CH4. On the other hand, the parallel arrangement of load can only be driven by the MGT using the low-heating-value fuels of more than 80% CH4.
The choice of generator that can fit the MGT is really important. If the power of generator is too large, it will make excessive loading, and cannot be operated in suitable range. On the contrary, if the power generator is too low, it cannot supply enough loading, and the best performance cannot be measured. The worst condition is that the gear box of MGT system may be broken when it exceeds the limiting rotational speed.
4.2.3 Output of electric power
Because of the limit of volume flow rate, the MGT cannot generate
full power. Figures 4-13~4-17 are the power generations as a function of rotational speed of generator by using different low-heating-value fuels and 99.5% C3H8. In Fig.4-13, output by using 90% CH4 fuel reaches about 170W, the maximum of generator. At the same time, output of generator has been controlled to maintain an output of 170W. Thus, if the MGT can be improved to have a better performance, the generator should be changed also in order to facilitate the maximum output. As the CH4 concentration is lowered to 80%, as shown in Fig. 4-14, its heating value cannot support the generator to generate 170W output because the resultant rotational speed cannot reach the critical value of 85000rpm.
Similar behaviors are expected to observe for further lower concentrations of CH4, such as 70% and 60%, which are presented in Figs.
4-15 and 4-16. Fig. 4-16 is the power output by using low-heating-value fuel of 60% CH4. The power is extremely low because MGT’s rpm is too low to drive the generator. For the fuel of 50% CH4, the MGT can reach the idle without load, but the generator cannot operate steadily.
Thus, the output of using 50% CH4 fuel is not presented.
Finally, a case by using 99.5% C3H8 as the fuel is added. However, as shown in Fig. 4-17, the resultant output is not better than one using the low-heating-value fuel of 90% CH4. It is because C3H8 can be liquefied at
Finally, a case by using 99.5% C3H8 as the fuel is added. However, as shown in Fig. 4-17, the resultant output is not better than one using the low-heating-value fuel of 90% CH4. It is because C3H8 can be liquefied at