Residencial

Quite obviously, the design and off design performance of the fan, compressor, and turbine have a significant ef-fect on the overall performance of the engine. Steady state operation demands flow continuity and a power balance between components on the same shaft. Changes in engine inlet conditions and power settings produce migrations on component maps so that the performance characteristics of the turbine and compressor (or fan) must be very carefully matched, or else the engine will suffer from poor off design performance. The designers will try to match components so that the fan and the compressor are operating near their peak efficiency throughout the entire range of operation. This is accom-plished by running the steady state operating line through the centers of the efficiency islands (so long as surge margin considerations allow). A great deal of ex-perience and results from previous studies are needed to proceed quickly to a reasonable design, through a gener-alized method can be outlined to provide exposure to some of the complexities and constraints that are en-countered in a typical design cycle.

The results from preliminary cycle studies will yield the inlet and exit flow conditions and the work requirements of the respective components, although these values are subject to change as the design is iterated. For turboma-chinery preliminary analysis very often begins with a flow averaged radius analysis, after which radial varia-tions are considered. The work coefficient, which char-acterizes the work interaction for rotating components, is used as a first order aerodynamic loading parameter.

4> = gJAH/2U² (turbines)

$ = 2gJAH/U: (compressors)

where AH = change in total enthalpy across the stage and U = wr or the linear velocity of rotation at radius r.

Thus, the work coefficient is the ratio of work per unit mass flow divided by the wheel speed squared. Using

1-30 PREUMINARY ENGINE DESIGN

Mechanical Constraint Cycle Parameter Pressure and temperature extremes for engine inlet and casing

(defined from flight envelope and inlet recovery)

T1 (min, max) P1 (min, max) Compressor casing AP limit PS3(max), PS14 Compressor casing and cooling flow maximum temperature T3 (max)

HPT and LPT average gas temperature limit at rotor inlet T41 (max), T49 (max) Augmentor liner temperature limit T6 (max), T8 (max)

All rotor speeds N (max)

Augmentor liner buckling load limit APS (max) Maximum pressures and loadings on nozzle plugs, flaps, and

reverse rs

P8-PAMB (max)

Exhaust nozzle area ratio limits for actuator and flap design A9/A8 (min, max) Minimum combustor pressure drop for backflow margin in

turbine cooling circuits

(P3-P4)/P3 (min)

Combustor and afterburner fuel flows for control design and fuel/oil heat exchanger temperature limits

WF3 (min, max) WF6 (min, max) Gearbox and shaft torque limits for power turbine output and

customer power extraction

PWX (max)

Customer bleed rate, temperature and pressure limits WB (max) TB (max) PB (min, max) Table 1.3 Mechanical Design Limits

the Euler equation, which give the work input for a ro-tating blade row;

gJAH = A(UCu)

where Cu is the tangential component of the fluid veloc-ity.

In axial compressors and turbines it can be assumed that the radial shift in the streamline between the inlet and exit of a blade row is small, so mat the change in the blade rotational speed along a streamline is negligible.

The work coefficient becomes

^ = ACu/2U (turbines) 4* = 2.iCu/U (compressors)

Typical values of turbine work coefficient are around unity. Counter-rotating vaneless turbines are a factor of two higher. The same set of design rules apply to a counter-rotating design, but since the loss associated with the vane is absent, a higher work extraction and ro-tor loss can be tolerated without a reduction in the over-all efficiency. Alternately, a low work extraction may be employed to achieve a higher efficiency. A representa-tive value of compressor work coefficient is 0.8.

With the specific work established from the cycle, the designer selects the work coefficient and calculates the required wheel speed. The rotational speed of the spool is limited by the thermal environment of the turbine, and practical upper limits on turbine blade wheel speeds are 2,000 ft/sec at the blade tip.

PRELIMINARY ENGINE DESIGN 1-31

Aerothermodynamic Constraint

Maximum corrected speed and flow of each compression component

Stall pressure ratio on each compression component for stall margin stack on operating line

Combustor and augmentor fuel flows for burner smoke, emissions and stability limits and augmentor thrust jumps Combustor and augmentor blowout parameter

Turbine flow function limits which establish turbine area requirements

Turbine corrected speed, work and pressure ratio limits

Turbine exit Mach number limit Augmentor inlet Mach number limit

Exhaust nozzle area requirements for complete expansion and nozzle stability

Duct Mach limits for sizing ducts

Cycle Parameter Table 1.4 Aerothermodynamic Design Limits

Turbine rotational speed constraints are usually ex-pressed as the product of the annulus area and the square of the speed AN2. The actual limiting value of AN2 will depend upon the turbine inlet temperature and the blade material. The numerical value of AN² rarely exceeds 5 x 10⁹, where the annulus area is expressed in inches squared. (An annulus area of 500 in2 and an RPM of 10,000 yields AN2 = 5 x 109.) Another rotational speed limiting parameter is bearing DN, where D is the bearing race inner diameter in millimeters. DN then is simply a way of referring to the bearing peripheral sur-face speed. DN values are restricted to 2.2 x 106, and it is usually only in small machines where this becomes a limiting parameter.

Once the AN² limit has been established, the annulus area is selected from the turbine exit Mach number con-siderations. Selection of a higher turbine exit Mach number reduces the annulus area and tends to enable

higher loadings, but reduces the efficiency and limits power extraction at high power due to annulus choke.

Due to these considerations, axial Mach numbers at the turbine rarely exceed 0.5. With the annulus area so de-termined the spool rotational speed is calculated from the assumed value of AN². With the wheel speed and ro-tational speed known, the radial location of the turbine may be calculated using

U = T R N / 3 6 0

where U is in ft/sec, R is radius in inches, and N is revo-lutions per minute.

With the RPM of the spool determined the next step is to define the compressor configuration.The first step is to determine the annulus area at the compressor inlet. The compressor inlet corrected flow, given by the cycle, and an assumption of the inlet specific flow and radius ratio

1-32 PRELIMINARY ENGINE DESIGN

determines the inlet dimensions from the following rela-tionship:

A = T R:( 1 - rJ)

where R is the inlet tip radius and r is the inlet radius ra-tio.

Using the rotational speed determined by the turbine, compressor blade speeds are calculated to check the rea-sonableness of the assumptions. Limiting values of com-pressor tip speeds are 1800 ft/sec at the inlet. Typical maximum rim speeds are 1200 ft/sec at the compressor exit where the gas temperatures are the highest, and a practical upper limit on the exit radius ratio is 0.92. Re-ducing the inlet radius ratio reduces the inlet tip radius and speed. Reductions in the rotational speed may also be employed to lower tip speeds but only at the expense of increasing turbine radius to achieve the necessary tur-bine wheel speed and loading. Generally speaking, the compressor inlet radius ratio needs to be increased until a limit on die inlet tip speed, exit rim speed, or exit ra-dius ratio is encountered.

Axial compressor designs generally fall between two ex-tremes; constant tip radius and constant hub radius. Con-stant tip configurations maximize the average wheel speed, which tends to reduce the stage count. Constant hub configurations maximize blade height, which tends to increase efficiency. For a given annulus area, clear-ance to blade height ratio decreases as blade height in-creases so that a smaller portion of the blade is subject to end wall effects. However, as blade height is increased, larger clearances are necessary to protect from rubs.

Constant tip configurations require smaller clearances, but tolerances are harder to maintain at the larger diame-ters. Clearly, the problem is very complex. The applica-tion will ultimately determine which configuraapplica-tion is more suitable. Where weight and size are the primary

consideration, the stage count must be kept to a mini-mum; which suggests a constant tip configuration. When fuel economy and efficiency are the principle concerns, me design will tend toward a constant hub configuration.

The GE25 (a turbojet) is an example of a near constant tip design, while die CFM56 is an example of a near constant hub design. The CF6, on the other hand, is an example of a near constant pitch design, the pitch line being the arithmetic average of the hub and tip radius.

Additional complexities arise for multiple spool designs, compressor flow extractions, and turbine cooling flows.

Transition ducts require common interfaces, create pres-sure losses, and may require cooling. Close coupling of components may also restrict the work potential of com-ponents. When cooling the combustor liner and high pressure turbine, compressor discharge air is the only source of internal engine air with a high enough pressure to avoid hot gas backflow into the cooling circuit. (Com-pressor interstage bleed may be used for low pressure turbine cooling.) Therefore, the temperature of the com-pressor discharge air must be restricted to increase the effectiveness of die coolant flow. The coolant flow is a penalty to the cycle because only a portion or, in the limit, none of the energy invested in pumping this flow up to pressure is extracted in the turbine. The compro-mises are many and varied, and numerous trade-offs must be performed before a final configuration is de-fined.

Figures 1.27 and 1.28 are cross-sections of advanced turbofan engines superimposed on their contemporary counterparts. These engines will have higher pressure ratios, higher turbine inlet temperatures, and fewer tur-bomachinery stages. In addition, composite materials will be used extensively in the low temperature areas of the engine. These next generation engines will have higher thrust to weight ratios and improved installed per-formance and efficiency.

PRELIMINARY ENGINE DESIGN ^1-33

Figure 1.27 Comparison of an Advanced High Bypass Ratio Turbofan Engine with a CF6-50C Engine

tj;ff5,'*f'i*fl K-iifS

~0

m r

>

so m z o tn

a m

CO

a

Figure 1.28 Comparison of an Advanced Military Fighter Engine with a F110-GE-100 Engine

T R E U M I N I ^ Y E N G I N E T E ^

1-36

Chapter 2