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					                                           TENTAMEN ae3-235




Faculty of Mechanical Engineering and Marine
Technology

TENTAMINATION THERMODYNAMICS AND GAS TURBINES - (ae3-235)
English Version

23-08-2006, 9:00 – 12:00 h                                 4 pages + formula sheet + answering sheet

REMARKS:
1    Please fill in the answers on the answer-sheet. Also, the calculations have to be handed in.
     The grade will be determined on both the answers and calculations.
2    Please fill in your name and students-number on both the answer-sheet and calculations.
3    Except from the formula sheet included, it is not allowed to use other information!
4    Please take into account that the sequence of the questions does not always determine the
     sequence in which the answers can be found!
5    For the multiple-choice questions only one answer is correct.


Please observe the rules above very carefully. Non compliance will result in lower or no grade!




TASK I

1.    Consider a low bypass twin spool mixed turbofan military engine similar to the GE F110, the
     power plant of the F-16 fighter aircraft. Assume standard take-off ambient conditions:

     - Flight Mach number                                         0.0
     - Ambient temperature                                        288.15 K
     - Ambient pressure                                           101.325 kPa



                                                                                  Mixing
                        F                                                         Zone



                  2          2.5      3                  4 4.5       5      6                   8

     The mixing zone starts at the exit of the fan duct and at the exit of low pressure turbine and it
     lasts until station 6, where uniform values of the thermodynamic variables are achieved. A
     simplified approach to the mixing process can be based on the following assumptions:

         −   Mixing does not entail losses (p05(exit LPT) = p06(after the mixing process)).
         −   The temperature pattern after mixing is completely uniform across the flow area (the heat
             exchange between both flows is ideal and complete)
         −   The flow of the mixer until the exhaust is completely adiabatic (no heat losses)
                                                                                   (cont’d on next page)


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                                           TENTAMEN ae3-235


     The fan (F) is driven by the low pressure turbine and the compressor is driven by the high
     pressure turbine. A convergent nozzle is considered.

     At the conditions as mentioned above, the following data apply for this engine:
     - inlet air mass flow                                      90 kg/s
     - total pressure at fan inlet                              100 kPa
     - bypass ratio                                             0.6
     - fan pressure ratio (inner annulus)                       3
     - fan pressure ratio (outer annulus)                       3.2
     - fan isentropic efficiency (inner annulus)                0.81
     - fan isentropic efficiency (outer annulus)                0.80
     - fan duct pressure loss                                   1%
     - compressor pressure ratio                                8
     - compressor isentropic efficiency                         0.82
     - turbine inlet temperature                                1650 K
     - HP turbine isentropic efficiency                         0.89
     - LP turbine isentropic efficiency                         0.90
     - mechanical efficiency of HP and LP turbine               0.99
     - combustion efficiency                                    0.99
     - pressure loss of the combustor                           4%
     - nozzle isentropic efficiency                             0.97

     Calculate the following parameters:
     a) compressor exit total pressure
     b) compressor exit total temperature
     c) low pressure turbine (LPT) delivered power
     d) power absorbed by compressor
     e) fuel flow
     f) low pressure turbine exit pressure
     g) exit mixing total temperature
     h) exit mixing total pressure
     i) critical pressure ratio
     j) exit nozzle cross sectional area
     k) net thrust

2.   The turbofan of the previous point has a special device, so called “afterburner”, which can be
     used in case of military operations if the pilot needs it.


                                                       Mixing Zone
                                                                                       afterburner
                         F

                    2        2.5       3                   4 4.5      5      6 6’                8

     Assume exactly the same take-off conditions of the previous point and take into account also the
     afterburner, which significantly increases the gas temperature between stations 6 and 6’ up to
     1650 K. The variable exhaust nozzle increases the exhaust area A8 in order to maintain total
     pressure at station 6 unchanged and to leave gas generator conditions fixed as they have been
     evaluated in the previous point. Assuming the same conditions at station 6 as calculated in
     Task1.1, pressure loss of 1.5% and combustion efficiency 0.98 for the re-heating process,
     evaluate:

     a) afterburner fuel flow
     b) exit nozzle cross sectional area
     c) net thrust


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                                                    TENTAMEN ae3-235


TASK II


The Mollier Diagram and description of the different phases of a substance have been presented
separately in the course. The relationship between pressure, specific volume and temperature of any
medium can be presented on a three-dimensional surface. Because of the difficulty of visualizing and
drawing these surfaces, it is customary to depict the data of the 3D phase diagram on projections in
2D. An example of the qualitative 2D diagram (T,p) of the water is given:

 p

                                                        S = Solid Phase

         S                                              L = Liquid Phase
                          L
                                                        V = Vapor Phase



                               V




                                                    T

Considering the phase diagram above, indicate the states as a,b and c according to the questions
below, and answer the question in text

     a) where is the triple point and which condition it describes
     b) where are the saturation states and which conditions they describe
     c) where is the critical point and which condition it describes



TASK III
                      0             1                                      2




                          Primary       Secondary       Dilution
                           Holes          Holes          Holes




      Mixture         Primary           Secondary
  Preparation Unit     Zone               Zone



                     Figure 3.1: Combustor Cross Section


The Figure above depicts an annular combustor of an aero-derivative engine (such an engine,
derived from a jet engine, can be used for industrial purposes) fueled by natural gas (natural gas is to
be considred as pure methane). The fuel flow is 2.5 kg/s. The air flows into the liner are as follows:
                                                                                    (cont’d on next page)



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                                            TENTAMEN ae3-235


     -                                                   &
          Air flow through the mixture preparation unit, ma
                                                                   MPU
                                                                           : 30 kg/s;

     -                                        & PH
          Air flow through the primary holes, ma :                              30 kg/s;

     -                                          &
          Air flow through the secondary holes, ma :
                                                      SH
                                                                                20 kg/s;

     -                                         &
          Air flow through the dilution holes, ma
                                                 DH
                                                      :                         45 kg/s.


1.   Find the stoichiometric fuel-to-air ratio (by mass) for natural gas (methane), assuming the
     following reaction of ideal combustion:

                             CH 4 + 10 ( 0.2O2 + 0.8 N 2 ) → 2 H 2O + CO2 + 8 N 2 .
     The molecular weights of the chemical elements can be assumed as:
     C:        12 kg/kmol;
     H:        1 kg/kmol;
     O:        16 kg/kmol;
     N:        14 kg/kmol.


2.   a) What is the fuel-to-air equivalence ratio for the mixture preparation unit (station 0)?
     b) What is the fuel-to-air equivalence ratio at the outlet of the primary zone (station 1)?
                                                   & PH
                                       & MPU , and ma is perfect.
     The mixing between the fuel flow, ma

     c) What is the overall fuel-to-air equivalence ratio,                 ϕoverall   (at combustor outlet, station
                                           &
     2)? The mixing between the fuel flow, m
                                                MPU
                                                a
                                                            &
                                                            PH
                                                          , m
                                                            a
                                                                     &
                                                                   , m
                                                                           SH
                                                                           a
                                                                                     & DH
                                                                                 and ma is perfect.


3.   If the combustor shown in Fig. 3.1. is properly designed, the flame will stabilize in the primary
     zone.
     It is customary to describe combustion stability
                                                                                                              T3=const
     by a range of ϕoverall , fuel-to-air equivalence
                                                                                                              p3=const
     ratios, that shape the combustor stability loop.           ϕoverall
     Such a loop is obtained during combustor
     development testing: After turning on the fuel
     and igniting the mixture, the fuel supply is
     gradually reduced until “lean” flame extinction
                                                                       1
     occurs. After noting the ϕoverall of extinction,
     combustion is re-established. The fuel flow is
     now slowly increased until “rich” extinction
     takes place. This process is repeated at
     increased levels of air mass flow.
     Show a generic form of the combustor
     stability loop on the coordinate system
     given in Fig. 3.2. Indicate the regions of
     stable and unstable combustion. For
     unstable combustion, clearly indicate the                                                             Air Mass Flow
     regions of blow-off (also known as “blow
     out”)            and             flashback.                           Figure 3.2: Combustor Stability Loop




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                                                TENTAMEN ae3-235


FORMULAS

1         Assumptions.


Unless noted in the tasks, the following values and equations are valid.
1          the process in inlet, compressor, turbine and in the jet are adiabatic.
2          the contribution of the fuel mass flow to the total mass flow through the combustion
           chamber can be neglected, but through the turbine it cannot be neglected. The mass flow
           through the turbine is thus equal to the mass flow of the compressor air plus the mass flow
           of the fuel.
3          the contribution of the fuel mass flow to the total mass flow during the re-heat process can
           be neglected, but through the nozzle it cannot be neglected.


2          Physical Constants, etc.


Gas constant R                                                               287          J/kg.K
Specific heat of hot air cp                                                  1000         J/kg.K
Specific heat of flue gases cpg                                              1150         J/kg.K
Specific heat of gases after the mixer of the turbofan cpm                   1050         J/kg.K
Isentropic coefficient air γl                                                1,4
Isentropic coefficient of flue gases γg                                      1,33
Isentropic coefficient after the mixer of the turbofan γg                    1,38
Heating value fuel LHVfuel                                                   4,32.107 J/kg


3          total pressures and temperatures.



                        C
                           2
                                      γ -1 2
           T0 = T +          = T (1 +     M)
                        2 cp           2

                      T0 γ γ- 1
           p0 = p (     )
                      T


4          compression.


(index 1: initial conditions, index 2: end conditions)


           Isentropic efficiency:                                  Polytropic efficiency:
                                  γ -1                                             γ -1
           T 2 = 1 + 1 [( p2 )     γ                               T 2 = ( p2 )γ η pol
                                         - 1]
           T1       η is p1                                        T1      p1

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5        expansion.


(index 1: initial conditions, index 2: end conditions)


          Isentropic efficiency:                                              Polytropic efficiency:
                                      γ -1                                                   γ -1
                                                                                                  η pol
           T 2 = 1 - [1 - ( p2 )       γ                                      T 2 = ( p2 )    γ
                    η is                     ]
           T1               p1                                                T1      p1


Critical Pressure Ratio:


                    p1              1               γ
           ε kr =      =[                         ]γ - 1
                    p2               γ -1
                          (1 -                )
                                 η is (γ + 1)

6         compressors and turbines.


Relations of angles:         compressor                    tan α 1 + tan β 1 = tan α 2 + tan β 2


                             turbine                       tan α 2 - tan β 2 = tan β 3 - tan α 3


                                                                 Ca
Degree of reaction:          compressor                    Λ=       (tan β 1 + tan β 2)
                                                                 2U


                                                                 Ca
                             turbine                       Λ=       (tan β 3 - tan β 2)
                                                                 2U


7       simplified combustion chamber heat balance

                                 mair ⋅ c pg ⋅ ∆TCC = ηCC ⋅ m fuel ⋅ LHV fuel
                                 &                          &




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