Aeroenginetech_5_fransloekito_4776887.docx

DELFT UNIVERSITY OF TECHNOLOGY

Aero Engine Technology AE4238

Assignment 5 Subsonic Inlet Behaviour in Turbofans

Frans Loekito (4776887)

December 05, 2018

List of Symbol, Abbreviations, and Station Number

Symbol ṁ T p κ V

Table A. Symbol Explanation Mass flow Temperature Pressure Ratio of specific heat (kappa) Velocity

Station Number 0 1 2

Table B. Station numbering Location Ambient (capture) Inlet lip (throat) Fan face

Unit [kg/s] [K] [Pa] [-] [m/s]

1. Problem Recently, there is an ever increasing demand for a more efficient engine in the aviation industry. The inlet have a huge effect in the overall engine performance, therefore recent inlets are designed with 99% efficiency. Due to this recent trend, it is important to understand the effect of inlet design to flow behavior. In this assignment, we will investigate the subsonic inlet flow behavior (Mach and flow cross section area) in CFM56-5B turbofan at different stages of flight, at the inlet stations.

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2. Assumptions In analyzing this problem, several assumptions are made: Air is an ideal gas. No temperature & pressure drop due to viscous effect (in the calculation, viscous effect neglected). No spillage loss. Flow is axial. Nacelle is perfectly circular, and its length is 0.4 engine diameter. M1 = 0.75. Inlet design: inlet diameter ≈ throat diameter at critical condition. Inlet critical condition: during the flight stage with the maximum corrected mass flow rate

3. Procedure First we calculate the total temperature and pressure for each altitude from the respective static temperature and pressure. The we get the corrected mass flow rate of each flight conditions using the formula: 𝑇𝑡0 𝑚̇𝑐𝑜𝑟𝑟 √288.15 = 𝑝𝑡0 𝑚̇ 101325 Then we calculate the airspeed in each flight condition. We first find the speed of sound in each altitude and then calculate the actual airspeed from the mach number. Combined, we use the equation: 𝑉̅0 = 𝑀0 √𝜅𝑎 𝑅𝑇0

We use the airspeed to cross section area in the streamlines ahead of the inlet. Using the the mass flow relation: 𝑚̇ 𝐴0 = 𝜌𝑎 𝑉̅0 To find the throat area, we use the isentropic flow relation equation (Farokhi, 2014): 𝜅𝑎 +1

𝜅𝑎 − 1 2 2(𝜅𝑎−1) 𝐴0 𝑀1 1 + 2 𝑀0 = ( ) 𝐴1 𝑀0 1 + 𝜅𝑎 − 1 𝑀 2 1 2 The subscripts 0 and 1 is the ambient and throat station, respectively, and M1 is assumed to be 0.75 for every flight condition. After filling the equation with respective values, we can find A1 (throat area) and thus, its diameter. We can use the same equation to find Mach number at the fan face (M2). However, we use the the ratio of A0 and A2 (fan face area), and thus M2 (not M1). A2 can be found by subtracting the area of the fan by the area of the fan cone. 4. Result Table 1. Corrected mass flow, throat diameter and fan face Mach at each flight stage Corrected mass flow (kg/s) Throat Diameter (m) Mach at Fan Face 462.44 1.61 0.48 Take-off 337.44 1.38 0.43 Top of Climb 258.26 1.20 0.31 Cruise From Table 1 we can see that the most critical condition for the inlet is during the take off. This is reasonable, as the higher the altitude, the lower the static pressure and temperature. Mach number of the aircraft during take-off is also much lower than during the other two flight phase. As the aircraft goes to higher Mach number, total temperature and pressure, will be higher. However, total pressure increases more than total temperature, as the gas dynamic equation for total pressure is Mach to the order of 3.5 in this case (γ/ (γ-1), with γ = 1.4), while total temperature is Mach to the order of 1. The high total pressure and low total temperature during cruise causes the corretced mass flow rate to be small compared to that during take-off. After finding each flight stage corrected mass flow, we can see that take off is the critical flight stage, as the engine design should allow the high mass flow.

Fig 1. Schematic drawing of inlet The throat diameter of each flight stages in Table 1 shows that in higher mach number, the throat area of the engine (in this case the inlet area) decrceases. As the inlet design have to accommodate the highest mass flow rate during operation (the critical flight stage), which in

this case is the take-off, we take Dinlet to be slightly higher than throat diameter during take-off. The schematic drawing of the proposed inlet can be seen on Fig 1. We can also visualize the boundary of intake stream tube at every flight stage, as seen on Fig 2.

(a)

(b)

(c) Figure 2. Visualization of intake stream tube boundary during (a) take-off, (b) top of climb, and (c) cruise From the design we can see that during take-off, or low speed cruise, A1 < A2 < A0. During top of climb, in this case, A0 = A1 < A2. The similar value of A0 and A1 is simply because M1 is assumed 0.75, which is coincidentally similar to the flight Mach number (or ambient Mach, M0). On the other hand, during cruise, A0 < A1 < A2. These trend of area comparison is easily explained using isentropic flow relation equation, which states the higher Mach at the station, the smaller the area.

Figure 3. Flow separation at the inlet during cruise

However, the design, although can accommodate the critical condition, can cause flow separation in higher Mach number. The area inside the inlet lip that is not enclosed by the stream tube boundary, like the one present in Fig 2(b) and (c), is the area where flow separation can happen. The separation at that area may be caused by the interaction of the high pressure flow inside the stream tube with the flow at that area that have lower pressure (ambient pressure). We can see this phenomenon in Fig 3. To prevent this effect, we cannot use the throat diameter at take-off as the inlet diameter, and we have to select a larger inlet diameter. Aside from the corrected mass flow rate and throat diameter, we can also find M2. As seen on the table, M2 decrease from take off until cruise. This is, again, can be understood using isentropic flow relation equation. As A2 (fan face area) is constant, a high A0 (take-off) cause also a high M2 (the area ratio is high, hence the right hand side of the equation have to be high as well). Comparing to the typical engine mach number graph (Fig 4.)

Figure 4. Typical engine mach number graph (Farokhi, 2014, Fig.6.23) Typical engine has M2 of 0.4-0.6 (Farokhi, 2014), hence in our case, the M2 exceeds the lower values (0.31 during cruise). For the problem regarding the low mach number during cruise, it may be caused by the small cross section of streamlines in front of the engines, which in turn caused by the low mass flow rate. 5. Conclusion Based on this assignment, we can conclude several important points:  The most critical condition for the inlet is during the take off.  In higher mach number, the throat area of the engine decrceases.  During take-off, or low speed cruise, A1 < A2 < A0. During top of climb: A0 = A1 < A2. During cruise, A0 < A1 < A2.  The designed inlet can cause flow separation in higher Mach number, because of the interaction of the high pressure flow inside the stream tube with the flow at that area that have lower pressure.  To prevent this effect, we cannot use the throat diameter at take-off as the inlet diameter, and we have to select a larger inlet diameter.  In this case, the M2 during cruise exceeds these values (0.31)  It may be caused by the small cross section of streamlines in front of the engines, which in turn caused by the low mass flow rate. References Farokhi, Saaed. 2014. Aircraft Propulsion, 2nd Edition. Chichester: John Wiley & Sons, Ltd.