MTF 171 – Gas turbine technologyExam - 2007-03-10

Allowed exam aids: Any calculator allowed (no lap-top computers)

Unclear matters: 031-7721409, 0704-923339

Problem 1 (5+8 credits) GE Energy has recently introduced the LMS100TM engine to the gas turbine market, as depicted in Figure 1 and Figure 2 below. The engine is a 1380 °C firing temperature class design. The exact definition of firing temperature depends on manufacturer. Here you may approximate the firing temperature as equal to the turbine entry temperature. The pressure ratio for this cycle is given as 42:1. The mass flow of the cycle is given at 209 kg/s. An output power of 98.7 MW will be delivered by the unit with a thermal efficiency of 45%. A typical power turbine exit temperature is 440 °C.

Figure 1 - LMS100TM configuration

Figure 2 - LMS100TM schematic with station numbering

Problem 1a (5 credits)Estimate the total power required by the LPC and the HPC (the sum of the HPC and LPC powers). Assume that 12% of the total turbine power (HPT and IPT) is lost due to cooling.

Problem 1b (8 credits)Assume that the intercooler has water available for cooling. Make realistic assumptions on cooling effectiveness and cooling water temperature. Compute the pressure ratio on the LPC and HPC respectively.

7

654

3

2b

2a

1

Problem 2 (5+5 credits)A customer is interested in buying a number of the LMS100 units. However, the 98.7 MW is considered insufficient and you are asked to come up with some solutions on how the power of the unit could be increased. One suggestion that comes up is the possible use of reheat at station 5 or station 6.

Problem 2a (5 credits)The customer has a good financial condition, and worries little about plant costs. Neither is the fuel efficiency of the plant critical. However, power density is very important. Where would you introduce reheat; at station 5 or station 6 in order to maximize power output from the plant? Which station would produce the highest thermal efficiency? Make an argument on the selection based on ideal cycle analysis.

Problem 2b (5 credits)Estimate the increase in power that the added re-heat may allow for.

Problem 3 (4+3 credits)Problem 3a (4 credits)Formation of NOx is highly dependant on the flame temperature. The trend in aero engine design is to develop engines with higher and higher OPR (overall pressure ratio) to reduce fuel consumption. How does the increase in OPR impact the flame temperature?

Problem 3b (4 credits)Explain the concept of combustion stability. What does the concepts rich and lean limits mean? What does a flame-out mean? Relate this concept to the knowledge you have about combustion stability.

Problem 4 (10 credits)Show that the corrected mass flow of a turbojet can be written as:

where station 01 is at the compressor entrance and rc is the compressor pressure ratio. State clearly the assumptions under which this is true.

Problem 5 (5 credits)During lectures the Breguet range formula was derived:

where ρ is the density, SFC is the specific fuel consumption, S is the aircraft reference area, CL is the lift coefficient, CD is the drag coefficient, WSTART is the mass at start of the cruise phase and WEND is the mass at the end of the cruise phase. A typical cruise altitude for a civil aircraft is around 10000.0-12000.0 meter and a cruise Mach number of 0.77-0.83. Use the equation above to explain why this is an appropriate altitude. What would be difficult or at least less optimal with a cruise altitude of 5000 meter or 20000.0 meter? What about reducing the time required for the flight mission by increasing the cruise Mach number to 0.90?

Problem 6 (6+6 = 12 credits)

Problem 6a (6 credits)A typical range of the turbine blade loading coefficient, ψ, for aero engines is 3-5. Use this range and what you know about differences in design requirements for stationary and aero gas turbines to guess a ψ for the turbine.

Knowing that the LMS100 will be able to run on the 60Hz USA power grid, estimate the mid radius on the first PT rotor. You must use data given in Problem 1 specification as input together with your guess on ψ. If you have failed to solve problem 1 you may use

Problem 6b (6 credits)Assume that the first stage stator hub tip ratio is 0.8, and compute the axial Mach number at the power turbine entrance. Estimate the axial Mach number after re-heat.

Problem 7 (3 credits)How would you select cycle parameters for a business jet? What kind of technologies would such parameter selection involve?

Good luck – Tomas

Grading:

Complete set of hand in tasks gives 10 bonus points.

0-23 point = Failed24-35 = Grade 336-47 = Grade 448-60 = Grade 5

Grade the exam:How would you grade the exam – does it reflect the course?

1 = 2 = 3 = 4 = 5 =

Additional comments on exam:

Some useful expressions

(2.7) (2.8)

        

    

,

(Stanitz formula – slip factor)