Turbofan model results and validation
3.2 Off-design performance results
analysis: setting the specific thrust at its maximum and simultaneously keeping fuel consumption as low as possible. It is also possible to understand the effect different levels of technology have in specific thrust, although it shows mainly in specific fuel consumption.
There is a good agreement between the results obtained usingGasTurbR and those obtained here.
The existing differences can be traced back to the fact thatGasTurbR software implements a model that is more robust than the one used here. Thus, it contains less simplifications. On the other hand, several components of the engine are there characterized differently.
Figure 3.7 shows the results obtained for specific thrust, specific fuel consumption, engine mass flow and maximum thrust, respectively, as a function of flight Mach number and flight altitude. It is possible to observe the influence of flight Mach number in such properties: specific thrust decreases with increased flight velocity, and, consequently, with greater flight Mach number, while specific fuel consumption in- creases. With increased flight altitude, these performance parameters decrease; however at higher flight altitudes the differences become smaller. Engine mass flow as a function of flight Mach number is also plotted. The dependence is clear: there is a continued increase in total engine mass flow as flight Mach number gets larger, accentuated fromM0 = 0.3 to near supersonic values. By combining specific thrust with total engine mass flow, it is possible to visualize variations of thrust: it can be seen that an increase in flight Mach number and flight altitude led to a significant decrease in thrust force;
furthermore, with the increase of flight altitude, changes in flight Mach number produce a smaller effect in thrust (ath = 12 kmthrust is almost constant). In this last chart, for each flight altitude there is a specific value of flight Mach number where a breakpoint (e.g. forh= 3kmthe value isM0 = 0.6) can be detected. This breakpoint appears due to the fact that all constraints functions exhibited in Figure 3.8 have reached their design value, and are maintained there by engine control.
(a)Ψas a function ofM0 (b)Sas a function ofM0
(c)m˙ as a function ofM0 (d)Fas a function ofM0
Figure 3.7: Off-design results forΨ,S,m˙ andF as a function of flight Mach numberM0
Figure 3.8 shows the variation of bypass ratio, fan pressure ratio and high-pressure compressor pressure ratio with flight Mach number and altitude. Bypass ratio shows a constant increase in value with the increase of flight Mach number as well as a constant decrease with increased altitude. On the other hand, fan pressure ratio decreases with the increase of the Mach number, but increases with flight altitude. The high-pressure compressor pressure ratio presents the same trend as the fan pressure ratio.
(a)Bas a function ofM0 (b)πfas a function ofM0
(c)πcHas a function ofM0
Figure 3.8: Off-design results forB,πf andπcH as a function of flight Mach numberM0
Figure 3.9 shows the variation of thermal, propulsive and overall efficiency with flight Mach number at several flight altitudes. It can be seen that thermal efficiency decreases with Mach number, and until M0 = 0.5 it stays pretty much independent of altitude. On the other hand, propulsive efficiency shows a clear increase with increasing flight Mach number, and, in addition, flight altitude does not affect sig- nificantly the efficiency values. In terms of overall efficiency, it can be noted an increase with increasing Mach number until it reaches its maximum (aroundM0= 0.65) and then a decrease while approaching supersonic conditions.
(a)ηthas a function ofM0 (b)ηpas a function ofM0
(c)ηoas a function ofM0
Figure 3.9: Off-design efficiencies results as a function of flight Mach numberM0
In parallel to what was done with design point performance results, in off-design analysis the results obtained are also compared with those obtained by using similar software recognized by the scientific and academic communities. In Figure 3.10 three charts are plotted where specific thrust, specific fuel consumption and engine mass flow results obtained with the present model are compared with results obtained by usingGasTurbR andPERFR. These results are for an operating condition ath= 10km.
It can be seen that there is a good overall agreement between the several models; furthermore, all methods display exactly the same trend. Only at specific thrust results, PERFR model exhibits some discrepancies when compared with the other models.
Once again, there is a good agreement between the results obtained using GasTurbR, PERFR and those obtained here. The existing differences can be traced back to the fact that GasTurbR and PERFR software implement a model that is more robust than the one used here. Thus, it contains less simplifications. On the other hand, several components of the engine are there characterized differently. The mean relative errors between the results presented here and those produced by the packageGasTurbR for specific thrust, specific fuel consumption and engine mass flow are 4.5%, 2.9%
and 2.4 %, respectively. The same relative errors for the case of thePERFR software for specific thrust, specific fuel consumption and engine mass flow are 15.2%, 4.8% and 5.8%, respectively.
(a)Ψas a function ofM0: software comparison (b)Sas a function ofM0: software comparison
(c)m˙ as a function ofM0: software comparison
Figure 3.10: Off-design software comparison results as a function of flight Mach numberM0
As previously mentioned, the present model contains an option allowing the iteration process to finish only when, besidesτtL, alsoB,τcH,τcLandτfhave to reached a difference between successive values that is smaller than the tolerance (set here to 0.0001). This was a recommendation from [38]. However, as can be seen in Figure 3.11, the variation in performance results is negligible for subsonic conditions.
Only for greater values of flight Mach number does the different iteration process show a slightly different performance result; however, supersonic range is out of the range of operating conditions studied in this work.
(a)Ψas a function ofM0: iterations process comparison (b)Sas a function ofM0: iterations process comparison
(c)m˙ as a function ofM0: iterations process comparison
Figure 3.11: Off-design iteration comparison results as a function of flight Mach numberM0