Chapter 3 Numerical analyses
3.7 Grid-independence test
For obtaining the acceptable numerical solution, this study applied the unstructured grids produced from geometry models to carry out grid-independence test. The grid-independence test comprised combustion case.
Because the over-heating problem of liners is one of concerns in this research, the grid densities is increased especially near the liners, whose thicknesses are only 0.4mm, and the fuel tube, which is about 0.5mm in thickness. Owing to adoption of upwind numerical difference scheme, the grid amount should be dense enough to avoid the false diffusion phenomenon.
For grid test, the operating conditions are specified as that the air inflow of
m& =0.0044 kg/s is generated by compressor with a compression ratio 1.35 under the rotation rate 80000 rpm, and the fuel tube supplies a mixing fuel of methane (mass fraction 0.766) and CO2 (mass fraction 0.234) under a fixed mass flow rate (m& =3.325E-05kg/s). From the above discussion, the mass flow rate, velocity and temperature of gas mixture ejected from the rear of combustion chamber are the emphasized data
The grid numbers adopted for the grid-independence tests in this case are 477181, 717974, and 1484378. The test results are listed in Table 3.5. From the information given by the table, it can be seen that the maximum relative errors
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of various physical quantities are all less than 3%. Under such circumstance, it is naturally to select the grid number of 477181 to compromise the computational time. Pentium 4 with CPU 3.0 GHz, 2GB RAM is used to carry out the computation, and select convergence criterion as 10-3. Then the computational time for a typical simulation in the c case needs about 60 hours.
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Table 3.1: Sutherland's law coefficients of dynamic viscosity
Species Sutherland's
Law Coefficients
CH4 O2 CO2 H2O CO H2 H N2
A 1.25E-06 1.78E-06 1.50E-06 1.86E-06 1.50E-006 6.89E-007 6.89E-007 1.40E-06
B 197.4 156 222.26 708 136.35 96.69 96.69 111.5
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Table 3.2: JANNAF coefficients of gas specific heat
Species
※ These coefficients will be used at temperatures between the lower limet and the break point
a1 7.79E-01 3.21E+00 2.28E+00 3.39E+00 3.26E+00 3.30E+03 2.5 3.30E+00 a2 1.75E-02 1.13E-03 9.92E-03 3.47E-03 0.15E-02 0.82E-03 0 1.41E-03 a3 -2.78E-05 -5.76E-07 -1.04E-05 -6.35E-06 -3.88E-006 -8.14E-07 0 -3.96E-06 a4 3.05E-08 1.31E-09 6.87E-09 6.97E-09 5.58E-09 -9.48E-11 0 5.64E-09 a5 -1.22E-11 -8.77E-13 -2.12E-12 -2.51E-12 -2.47E-12 4.13E-13 0 -2.44E-12 a6 -9.83E+03 -1.01E+03 -4.84E+04 -3.02E+04 -1.43E+04 -1.01E+03 2.55E+04 -1.02E+0
3 a7 1.37E+01 6.03E+00 1.02E+01 2.59E+00 4.85E+00 -3.29E+00 -0.46E+0
0 3.95E+00
Coefficients at upper
limit
※ These coefficients will be used at temperatures between the break point and the upper limit
a1 1.68E+00 3.70E+00 4.45E+00 2.67E+00 3.02E+00 2.99 E+00
2.5 2.93E+0 0
a2 1.02E-02 6.14E-04 3.14E-03 3.06E-03 0.14E-02 0.70E-03 0 1.49E-03
a3 -3.88E-06 -1.26E-07 -1.28E-06 -8.73E-07 -5.63E-07 -5.63E-08
0 -5.68E-0 7
a4 6.79E-10 1.78E-11 2.39E-10 1.20E-10 1.02E-10 -9.23E-12 0 1.01E-10
a5 -4.50E-14 -1.14E-15 -1.67E-14 -6.39E-15 -6.91E-15 1.58E-15
0 -6.75E-1 5
a6 -1.01E+04 -1.23E+03 -4.90E+04 -2.99E+04 -1.43+04 -8.35E+02
2.55E+04 -9.23E+0 2
a7 9.62E+00 3.19E+00 -9.55E-01 6.86E+00 6.11E+00 -1.36E+00 -0.46E+0 0
5.98E+0 0
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Table 3.3: Properties of solid liner Material Density(kg/m3) Specific
heat(J/kg-K) Thermal conductivity(W/m-K)
Steel_AISI_1020 7900 470 48
Table 3.4: Boundary conditions of combustion chamber
Air Inlet Fuel Inlet
Conditions
Hydraulic diameter(Dh)=0.012 m Turbulence intensity (I )=0.04
YN2=0.768 YO2=0.232
45000 1.081 0.001765 307.8 94.80 73.60 62.58 55.30
46000 1.088 0.001800 308.5 96.20
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Table 3.5: Grid test results of different grid densities for numerical simulation 477181 grids 717974 grids 1484378 grids Maximum Relative
Error (%)
Outlet mass flow rates
(kg/s) 4.18×10-3 4.17×10-3 4.25×10-3 1.9 Outlet max.
temperature (K) 645 641 655.2 2.2
Outlet max. velocity
(z-direction) (m/s) 108.9 106 106.4 2.3
Average outlet velocity (z-direction) (m/s)
80.6 81.5 82.9 2.5
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Chapter 4
Dynamic Model of MGT for Control Strategy
This section describes the development of a dynamic model for the proposed MGT system. According to the thermal process of the MGT, different models have been developed to predict the dynamic response behaviors of gas turbine systems. The MGT’s dynamic model used in this study is adapted from that developed by Rowen [51]. This model is commonly used due to its simplicity and flexibility in adjusting to turbines with different characteristics.
An outline of the structure, including the control and fuel systems, was generated using Matlab/Simulink (Fig. 4.1); the relevant equations are
[ ]
of the fuel, Tamb is ambient temperature, Tr is the maximum exhaust temperature, Tx is predicted exhaust temperature, Torqueis predicted mechanic torque produced by the MGT, a, y and zare correlation factors, and N (p.u) is compressor rotational speed. These equations can calculate turbine torque and exhaust temperature algebraically.Signal Vfuel, which represent the volume flow rate of fuel, is the most
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important variable when operating the MGT. In numerical simulation of the dynamic model of the MGT, compressor rotational speed, exhaust temperature of the MGT, and MGT loading were functions of Vfuel. Notably, Vfuel was utilized to calculate MGT mechanic torque and exhaust temperature after the simulation signal was modulated by a time delay block generated by combustion reactions.
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Chapter 5
Results and Discussions
5.1 Experimental results and discussions
The original MGT, which was powered by liquid fuel, was modified to run on gaseous fuel. Therefore, the original pipes were changed accordingly.
Additionally, the lubricant for bearings in the original MGT was pre-mixed with oil fuel. The lubricant supply system was separated from the fuel pipes after modification. In the experiments, stable rotational speed, 45,000 RPM, was reached. To increase fuel efficiency, data were obtained at each step as the rotational speed was increased by 5000 RPM increments. Each step was maintained for approximately 10 seconds to ensure that the engine reached a stable condition such that measured output data at each step were meaningful;
otherwise, stop-and-run experiments would consume a substantial amount of gas and the time required would be excessive. Additionally, maximum exhaust temperature was set at 800°C for safety reasons.
5.1.1 Tests using various fuels with no load
The proposed MGT was tested without loading. Various fuels with LHV with various mixture ratios of methane (CH4) to carbon dioxide (CO2) were used.
The concentrations of CH4 in the fuel were in the range of 50–90%, and those of CO2 increased from 10% to 50%. The temperatures of the main components of the MGT were measured at a specified fuel and fuel flow rate against cylinder gauge pressure. Thermal efficiency was calculated accordingly. Finally, the performances of the MGT under the various test conditions were compared.
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5.1.1.1 Pressures and volume flow rates of fuel in the MGT
Fuel pressure was the pressure exerted by the cylinder (bottle); this pressure was adjusted using a control valve. Fuel pressure was determined by fuel volume flow rate. The volume flow rate of each fuel was measured as a function of pressure, and calculated from mass flow rate. (CH4 density is 0.7168 g/L at 0°C, 1 atm) The volume flow rate of each fuel was roughly linearly proportional to fuel pressure. Figure 5.1 plot rotational speeds as functions of volume flow rates for the various fuels with LHV.
In the test using fuel comprised of 90% CH4 and 10% CO2, the rotational rate approached 85,000 RPM as fuel pressure approached a maximum of 12bar.
Under the same pressure, a rate of only 47,500 rpm was reached with 60% CH4
and 40% CO2. The condition of 50% methane could not generate power when loading was applied. More specifically, the power of MGT at 40,000 RPM while applying 50% methane fuel was not able to drive the generator. The author present the results of 50% methane here were tending to offer more information for future research interest. Clearly, the combustible fuel concentration in the LHV fuels influenced the performance of MGT. According to Fig. 5.1, as expected, the fuel with the higher heating value performs better because it can supply more energy to MGT. Also, a higher pressure must be applied to the lower heating-value fuel to approach idleness at 45,000 RPM.
Since MGT performance was proportional to the CH4 concentration in fuel and volume flow rate, increasing volume flow rate increased MGT performance.
Furthermore, using a fuel with a LHV in the MGT originally designed for oil fuel may result in choking of both the turbine wheel and fuel supply pipe. This choking can occur in the nozzle throat or in the annulus at the turbine outlet. As rotational speed increases to >85,000 rpm, choking may markedly limit the
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rotational rate of the turbine wheel because the rotational speed increases as flow rate increases; however, the maximum fuel pressure reached at 85,000 rpm was 12 bar. Therefore, turbine choking did not occur during tests in this study.
Compared to the turbine choking, the choking at fuel supply pipe needs more attention. The original pipe which only have 0.5mm diameter was designed to deliver 0.05L liquid fuel per minute at 80,000 rpm. However, the experiment results showed that the volume of the fuel was 58L and the pressure was 12 bar when the maximum power was reached. Thus, in order to avoid choking condition, the fuel supply system should be modified to deliver more volume of fuel so that the pressure will be reduced and the security will be enhanced.
In this investigation, the equivalent ratio was given by O
The air mass flow rate of 321.12 g/min in the primary zone was determined from the compressor map at 45,000 RPM; the fuel mass flow rate was 26.87 g/min. The Air/Fuel ratio (A/F) was 16.7 less than the equivalent ratio of 18.1;
however, at 80,000 RPM, the A/F was 22.5, which was greater than the equivalent ratio of 18.1. Therefore, the A/F increased as rotational speed increased from 45,000 to 80,000 RPM.
Since the volume flow rate was proportional to cylinder pressure, the volume flow rate of fuel was given by the following linear regression equation (CH4 density is 0.7168 g/L at 0°C, 1 atm):
Pout
m& =5.54+4.2 (5.2)
The volume flow rates of the fuels with a LHV were then replaced by those of CH4. Figure 5.2 presents the corresponding results. At a particular compressor
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rotational speed, the volume flow rates of CH4 obtained for different fuels with LHV were almost equal, indicating that combustion was stable in the proposed MGT, even when different fuels were used.
5.1.1.2 Temperature of unloaded MGT
Temperatures were measured at the compressor inlet (T1), compressor outlet (T2), turbine inlet (T3) and turbine outlet (T4). Figures 5.3 (a-d) indicate that the histories of all temperatures and the corresponding rotational speeds for different LHV fuel. The inlet and outlet temperatures (T3 and T4) of the turbine declined as rotational speed increased because as compressor RPM increased, an increased amount of air enters the combustion chamber, and the turbine was cooled by this additional air. Liou and Leong [52], who experimented with a particular MGT using oil fuel, observed the same phenomenon at 40,000–120,000 RPM. However, when this MGT operated at >120,000 RPM, temperature increased as rotational speed increased.
Turbine inlet (T3) and turbine outlet (T4) temperatures varied slightly as the concentration of CH4 in fuels varied (Figs. 5.3(a) and (b)). This trend could influence thermal efficiency, which was discussed in Section 5.1.4. Additionally, the difference between T3 and T4 varied minimally with the fuel with a LHV because, at a given compressor rotational speed, the amounts of CH4 burned were the same for all fuels (Fig. 5.2). T3 and T4 were markedly perturbed at the start of operation because the blower and fuel were manually controlled before the MGT reached stability. Thus, a red dash line was added in Fig. 5.3 to separate an unstable duration of the MGT from the stable one. Excessively increasing the air flow rate markedly reduced T3 and T4. However, an excessive fuel flow rate rapidly increased T3 and T4.
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Figure 5.4(a) presents the surface (case) conditions of a combustion chamber using oil fuel; Fig. 5.4(b) presents those of a combustion chamber using gaseous fuel. In Fig. 5.4 (b), The surface condition (color changed) on both the primary and intermediate zones of combustion chamber have been affected by high temperature while applying the LHV fuel, whereas such phenomenon was not appeared when using liquid fuel. Clearly, combustion chamber temperature with methane exceeds that with liquid fuel because the combustion chamber was designed to burn liquid fuel. When gaseous fuel was used, the cooling system was inadequate. Moreover, this experimental conclusion can also be deduced that it is easier to burn methane than oil fuel.
Based on the schematic view of the MGT system (Fig. 3.2), the fuel pipe in the combustion chamber is close to the liner wall. Thus, the gas fuel should burn immediately after it is ejected from the fuel pipe and the temperature near the liner wall should be higher than using oil fuel. This phenomenon has been predicted from the numerical results of temperature distribution in the combustion chamber; discussed in section 5.2.
5.1.1.3 Thermal efficiency
The thermal efficiency of the proposed MGT system combined with the adiabatic efficiencies of the compressor and turbine were estimated thermodynamically by assuming a typical and simple Brayton cycle. The reason for selecting this simple Brayton cycle is that this equation is suitable for a single-shaft and low compression-ratio gas turbine that is suggested by Sonntag et al. [53]. The efficiency of the air-standard Brayton cycle is
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According to Sonntag [53], because the working fluid does not complete a thermodynamic cycle in the MGT, the internal combustion engine operates on a so-called open cycle. However, when analyzing internal-combustion engines, devising closed cycles that closely approximate open cycle is advantageous.
The thermal efficiency of the proposed MGT was derived from the efficiency of the air-standard Brayton cycle in Eq. (5.3). Figure 5.5 shows thermal efficiency versus compressor rotational speed. For the fuels with different concentration of CH4, efficiency decreased as rotational speed increased. Based on Eq. (5.3), the thermal efficiency was affected by T4, T3, and T2 (compressor outlet temperature); that is, thermal efficiency decreased because the decrease in T2 was larger than the decrease in T3 and T4 at high RPMs. Fuels with lower concentration of methane had more thermal efficiency (Figs. 5.5). Theoretically, thermal efficiency should not increase with the decrease of methane concentration in fuel. The T3 in the experiment condition of using 60% methane was larger than using 90% methane. This phenomenon could be observed in Figs. 5.3. The inferences was that the pressures and flow rates of fuels with lower concentration of methane were larger than those of fuels with higher concentration, and high inject pressure of fuel could cause major variation to temperature distribution in combustion chamber because the fuel pipe exit was very close to the front wall of chamber.
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5.1.2 Testing MGT with generator
In this section, the MGT with a generator was tested; all test parameters were the same as those used in Section 5.1.1. Temperature was measured and the amount of electricity generated by the generator was discussed. All temperatures measured in the MGT with a generator were similar to those of the unloaded MGT. Notably, the MGT does not directly drive the generator; the generator is driven by a gearbox, which has a power turbine driven by high-temperature and high-pressure gas from the MGT. The generator weakly influences MGT performance. Choosing a generator that fits the MGT is extremely important. If the generator power is too high, loading will be excessive, and the MGT cannot then be operated at a suitable range of rotational speed. If the power generated is too low, the load will be too low and optimal performance cannot be obtained.
The worst outcome is that the gearbox of the MGT system breaks when the rotational speed limit is exceeded. The power output obtained using 90% CH4
fuel was roughly 170W, which was the maximum output of the generator, and 70W at 60,000 RPM as 70% CH4 with 30% CO2 was used (Fig. 5.6). When a critical limit of 60% CH4 was used, the power output was extremely low. The output of the MGT was a function of fuel volume flow rate, which, as stated, was proportional to cylinder pressure. As volume flow increased, performance improved. However, excessively narrow fuel pipes limited the volume flow rate in the MGT system. Thus, the achievable volume flow rate did not exceed 58L/min, even when maximum pressure (12bar) was applied to the system. Thus, pressure must not exceed 12bar to prevent pipe breakage in the MGT system.
Additionally, the electric efficiency which calculated from the power output divided by the fuel release heat due to combustion shown in Eq. (5.4) was around 10%, assuming a reversible, adiabatic, steady-state process.
56 enthalpy to different species and m is mass flow rate to different species. This i considerable difference was due to the losses from the connected transmission gear box and the bridge rectifier.
5.2 Numerical Simulation results and discussions
The corresponding simulated mass flow rate of fuel could be divided into four mass-fraction conditions, that is, the highest one was 90 percent of methane and the lowest was 60 percent. All the rotation speed conditions were simulated according to the experimental works. Since a series of parametric studies was carried out, a reference case of steady state of methane concentration, 60%, at idle speed of MGT (45000 RPM) was chosen to serve as a detail illustration case [Fig 5.7 (a-d)]. Table 5.1 presented some important data of the simulation results.
Figures 5.8 to 5.11 demonstrated the simulation results of 45000 RPM condition while applying different concentration of CH4.
Figures 5.7(a) and 5.8 show simulation results of temperature distribution on the symmetric plane (0 degree cross-section) in the annular MGT combustor with different concentration of CH4, which demonstrated that with an appropriate value of air-fuel ratio, the temperature inside annular combustion chamber core reached 2106.7K (Table 5.2). Thus, combustion existed inside the combustion chamber. From the schematic view of MGT system, it can be realized that the fuel pipe in the combustion chamber is close to the liner wall.
Thus, the gas fuel ought to burn right after it ejects from the fuel pipe and the
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temperature near the front wall of the combustor is expected to be higher. The simulation results shown in Figs. 5.7(a) indicated that the high-temperature zone did concentrate at the front of the combustion chamber. The combustor chamber could be divided into three zones: primary, intermediate, and dilution zones.
They were marked according to the position of liner holes shown in Fig. 5.7(a).
The other phenomenon shown in Fig. 5.7(a) was that the cool air flows via dilution holes on liners were fully functional. The jet flow, which discharged from dilution holes, cooled down the exhaust gas temperature effectively. The average exhaust temperature of combustor outlet was below the endurance temperature 800°C (1073K). In Fig. 5.8, the high temperature zone was moved toward the outlet of combustor as the methane concentration decreased. It was because that the fuel flow velocity was increased as the methane concentration was lowered that pushes the flame more downward. Furthermore, the more scattering distributed high temperature areas were induced by the lowered methane concentration. Also, the combustor outlet temperature (T3) was increased due to the downstream-shifted high-temperature zone with the decrease of methane concentration.
The simulation results shown in Figs. 5.7(b) and 5.9 demonstrated the distribution of CH4 mass fractions in primary zone. It was realized that the inverse fuel injection system could deliver the fuel properly to ensure that the combustion reaction occurred at the front of the combustion chamber. The fuel mixture of CH4 and CO2 was injected into a mixing tube, where it mixed with the concurrent air flow from the back of combustor. Then, the premixed fuel/air was exhausted from the mixing tube and immediately met with the air supplied from the hole of liner above to enter the primary zone. In the meantime, air was also supplied via the hole on the bottom surface of liner. Since such hole in the
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primary zone was not located on the symmetric plane, it couldn’t be observed in these figures. Because the air and fuel were mixed and burn in the primary zone, the mass fraction of CH4 decreased gradually from fuel tube exit to primary zone.
Eventually, the mass fraction of CH4 was near zero in the intermediate zone due to the strong dilution from air. In Figs 5.9, the CH4 mass fraction in primary zone was increased with CH4 concentration raised. Moreover, larger CH4 mass fraction produces much more severe reaction at interface zero methane mass fraction and mass diffusion zone of methane concentration gradient.
When the function of intermediate holes was discussed, Figs. 5.7 (c) and 5.10 showed the distribution of O2 mass fraction with different concentration of CH4 and indicated that large number of compressed air was induced to the combustion chamber via the intermediate holes. Under this condition, combustion would be done more completely and less dissociated product would occur. There were fourteen air inlets in the computational domain, which can be
When the function of intermediate holes was discussed, Figs. 5.7 (c) and 5.10 showed the distribution of O2 mass fraction with different concentration of CH4 and indicated that large number of compressed air was induced to the combustion chamber via the intermediate holes. Under this condition, combustion would be done more completely and less dissociated product would occur. There were fourteen air inlets in the computational domain, which can be