Issue with Mixer Pressure

[ArnaultT]

Hi,

I've been working on building a mixed turbofan model and encountered some issues with the mixer.
While investigating the mixer module, I noticed something unusual when printing the incoming flow properties.

Consider the following test case:

def test_mix_air_with_airfuel(self):
    p = Problem()

    cycle = p.model = Cycle()
    cycle.options['thermo_method'] = 'CEA'
    cycle.options['thermo_data'] = janaf

    cycle.set_input_defaults('start1.P', 22.838, units='psi')
    cycle.set_input_defaults('start1.T', 1718.825, units='degR')
    cycle.set_input_defaults('start1.MN', 0.800)
    cycle.set_input_defaults('start1.W', 187.893, units='lbm/s')

    cycle.set_input_defaults('start2.P', 11.708, units='psi')
    cycle.set_input_defaults('start2.T', 522.821, units='degR')
    cycle.set_input_defaults('start2.MN', 0.600)
    cycle.set_input_defaults('start2.W', 66.176, units='lbm/s')

    cycle.add_subsystem('start1', FlowStart(composition=CEA_AIR_FUEL_COMPOSITION))
    cycle.add_subsystem('start2', FlowStart(composition=CEA_AIR_COMPOSITION))

    cycle.add_subsystem('mixer', Mixer(design=True, designed_stream=1))

    cycle.pyc_connect_flow('start1.Fl_O', 'mixer.Fl_I1')
    cycle.pyc_connect_flow('start2.Fl_O', 'mixer.Fl_I2')

    p.setup(force_alloc_complex=True)
    p.set_solver_print(level=-1)
    p.run_model()

    tol = 1e-6
    print(p['mixer.Fl_O:stat:area'])
    print(p['mixer.Fl_O:tot:P'])
    print(p['mixer.ER'])
    print(p['mixer.Fl_O:stat:MN'])

When printing the variables used in the MixImpulse class compute function:

def compute(self, inputs, outputs):
    outputs['impulse_mix'] = (inputs['Fl_I1:stat:P'] * inputs['Fl_I1:stat:area'] + inputs['Fl_I1:stat:W'] * inputs['Fl_I1:stat:V']) + \
                             (inputs['Fl_I2:stat:P'] * inputs['Fl_I2:stat:area'] + inputs['Fl_I2:stat:W'] * inputs['Fl_I2:stat:V'])

    print("Mix Impulse computations:")
    print('Fl_I1:stat:W', inputs['Fl_I1:stat:W'])
    print('Fl_I1:stat:P', inputs['Fl_I1:stat:P'])
    print('Fl_I1:stat:V', inputs['Fl_I1:stat:V'])
    print('Fl_I1:stat:area', inputs['Fl_I1:stat:area'])
    print('Fl_I2:stat:W', inputs['Fl_I2:stat:W'])
    print('Fl_I2:stat:P', inputs['Fl_I2:stat:P'])
    print('Fl_I2:stat:V', inputs['Fl_I2:stat:V'])
    print('Fl_I2:stat:area', inputs['Fl_I2:stat:area'])

I get the following output:

Mix Impulse computations:
Fl_I1:stat:W [85.22683118]
Fl_I1:stat:P [63282.44448509]
Fl_I1:stat:V [461.46240572]
Fl_I1:stat:area [0.43591669]
Fl_I2:stat:W [30.01692868]
Fl_I2:stat:P [63282.44448509]
Fl_I2:stat:V [198.01842072]
Fl_I2:stat:area [0.18629003]
[964.42234196]
[19.03367286]
[1.95063205]
[0.90091354]

Both incoming flows have the same pressure. I'm not sure if this is expected, but I don't fully understand the physics behind it.

Looking further into the Mixer class code, I found this:

if design:
    ...
    self.add_subsystem('Fl_I1_stat_calc', Fl1_stat,
                       promotes_inputs=[('composition', 'Fl_I1:tot:composition'), ('S', 'Fl_I1:tot:S'),
                                        ('ht', 'Fl_I1:tot:h'), ('W', 'Fl_I1:stat:W'), ('Ps', 'Fl_I2:stat:P')],
                       promotes_outputs=['Fl_I1_calc:stat*'])
    ...
else:
    ...
    self.add_subsystem('Fl_I2_stat_calc', Fl2_stat,
                       promotes_inputs=[('composition', 'Fl_I2:tot:composition'), ('S', 'Fl_I2:tot:S'),
                                        ('ht', 'Fl_I2:tot:h'), ('W', 'Fl_I2:stat:W'), ('Ps', 'Fl_I1:stat:P')],
                       promotes_outputs=['Fl_I2_calc:stat:*'])
    ...

After modifying the connections between Ps and Fl_Ix:stat:P, I obtained the following output:

Mix Impulse computations:
Fl_I1:stat:W [85.22683118]
Fl_I1:stat:P [104599.90621965]
Fl_I1:stat:V [461.46240572]
Fl_I1:stat:area [0.43591669]
Fl_I2:stat:W [30.01692868]
Fl_I2:stat:P [63282.44448509]
Fl_I2:stat:V [198.01842072]
Fl_I2:stat:area [0.18629003]
[964.42234196]
[19.03367286]
[1.95063205]
[0.90091354]

Now, the pressure of flow_1 is nearly twice that of flow_2, which matches the input values I initially set.

Is this a potential issue, or am I simply misunderstanding something?

Thanks! :)

[kavdborr]

Hello there!

I think you're indeed not fully understanding the physics at play here.
When two streams are mixed in a mixer, this is under the assumption that the static pressure of both streams are the same, called the static pressure balance. If this was not the case physically, the pressure difference would induce a flow from one inlet to the other! The static pressure balance is always be valid, both in on- and off-design.

So what does that mean? It means that for a given combination of total inlet pressures, the Mach number at the inlets will change in such a way that the static pressure balance is valid. In on-design, the area of stream 1 will change first, until the design Mach number is achieved. Then the outer Mach number is varied until there is static pressure balance. In off-design, the areas are fixed, which means that now the static pressure unbalance will become a residual equation. So the pressure unbalance needs to be driven to zero by iteration over another variable, such as bypass ratio (system dependant).

It has been a while that I used pyCycle, but this concept is generally valid for all engines with mixers.

I hope this has been of some help?

[ArnaultT]

Sorry for the late reply, and thank you very much for your clear explanation.
I understand the physical process and that, at equilibrium, the incoming flows share the same pressure. That makes sense now! If I understand the code correctly, this equilibrium state is determined using the balance equation of the mixer component, right?

I’m still struggling to balance the design. I’m trying to find the performance of an engine like the F100-PW-229, but the set of parameters I’m using makes me think that the mixer equilibrium is not being reached...

You can find a modified mixedflow_turbofan.py script that attempts to model the F100-PW-229. It’s rough, of course, as we lack a lot of information. Absolute precision is not my goal.

The output of this script give me that;

----------------------------------------------------------------------------
                              POINT: DESIGN
----------------------------------------------------------------------------
                       PERFORMANCE CHARACTERISTICS
    Mach      Alt       W      Fn      Fg    Fram     OPR     TSFC  
[0.2] [0.] [250.] [12110.6519606] [13845.78386579] [1735.13190519] [29.23822174] [1.20964498]
********************************************************************************
*           DESIGN
********************************************************************************
BPR [0.36]
W [250.]
Fnet uninst. [12110.6519606]
------------------------------------------------------------------------------------------------------------------------------------------------
                            FLOW STATIONS
------------------------------------------------------------------------------------------------------------------------------------------------
------------------------------------------------------------------------------------------------------------------------------------------------
Flow Station           |          tot:P        tot:T        tot:h        tot:S       stat:P       stat:W      stat:MN       stat:V    stat:area
------------------------------------------------------------------------------------------------------------------------------------------------
DESIGN.fc.Fl_O         |         15.112      522.821       -5.186        1.631       14.696      250.000        0.200      223.305     2108.080
DESIGN.inlet.Fl_O      |         15.096      522.821       -5.186        1.631       11.835      250.000        0.600      649.667      845.998
DESIGN.inlet_duct.Fl_O |         14.935      522.821       -5.186        1.632       11.708      250.000        0.600      649.667      855.148
DESIGN.fan.Fl_O        |         14.935      522.821       -5.186        1.632       11.708      250.000        0.600      649.667      855.148
DESIGN.bypass_duct.Fl_O|         14.775      522.821       -5.186        1.633       11.583       66.176        0.600      649.667      228.811
DESIGN.splitter.Fl_O2  |         14.935      522.821       -5.186        1.632       11.708       66.176        0.600      649.667      226.363
DESIGN.splitter.Fl_O1  |         14.935      522.821       -5.186        1.632       11.708      183.824        0.600      649.667      628.785
DESIGN.splitter_core_du|         14.863      522.821       -5.186        1.632       11.652      183.824        0.600      649.667      631.818
DESIGN.lpc.Fl_O        |         44.590      730.558       44.850        1.638       34.977      183.824        0.600      767.149      249.257
DESIGN.lpc_duct.Fl_O   |         44.139      730.558       44.850        1.638       37.227      183.824        0.500      645.790      283.987
DESIGN.hpc.Fl_O        |        441.394     1466.687      230.337        1.655      373.955      174.502        0.500      903.907       38.683
DESIGN.bld3.Fl_O       |        441.394     1466.687      230.337        1.655      415.513      162.773        0.300      549.420       54.921
DESIGN.burner.Fl_O     |        417.558     3016.174      224.719        1.893      407.037      166.843        0.200      513.314      127.769
DESIGN.hpt.Fl_O        |        139.186     2355.621       52.098        1.892       93.409      178.572        0.800     1755.125      124.762
DESIGN.hpt_duct.Fl_O   |        138.476     2355.621       52.098        1.892       92.933      178.572        0.800     1755.125      125.401
DESIGN.lpt_duct.Fl_O   |         34.249     1718.825     -110.918        1.896       22.838      187.893        0.800     1508.507      452.449
DESIGN.mixer.Fl_O      |         15.000     1430.049      -83.379        1.898        0.185      254.069    -2146.067 -2345872.564      707.364
DESIGN.mixer_duct.Fl_O |         14.839     1430.049      -83.379        1.899       11.728      254.069        0.600     1058.833     1469.402
DESIGN.afterburner.Fl_O|         14.038     1430.049      -83.379        1.902       11.094      254.069        0.600     1058.833     1553.279
DESIGN.mixed_nozz.Fl_O |         14.038     1430.049      -83.379        1.902        7.019      254.069        1.058     1765.184     1307.034
------------------------------------------------------------------------------------------------------------------------------------------------

looks like balance is not found... but BPR and W are equal to their initial values. I understood that theses quantities should be balanced. The main issue is that the flow mixer mach is inconsistent. The other values seem right.

Thanks a lot for your help

import sys
import numpy as np

import openmdao.api as om

import pycycle.api as pyc


class MixedFlowTurbofan(pyc.Cycle):

    def setup(self):
        design = self.options['design']

        USE_TABULAR = False

        if USE_TABULAR: 
            self.options['thermo_method'] = 'TABULAR'
            self.options['thermo_data'] = pyc.AIR_JETA_TAB_SPEC
            FUEL_TYPE = "FAR"
        else: 
            self.options['thermo_method'] = 'CEA'
            self.options['thermo_data'] = pyc.species_data.janaf
            FUEL_TYPE = "Jet-A(g)"

        self.add_subsystem('fc', pyc.FlightConditions())
        # Inlet Components
        self.add_subsystem('inlet', pyc.Inlet())
        self.add_subsystem('inlet_duct', pyc.Duct())
        # Fan Components - Split here for CFD integration Add a CFDStart Compomponent
        self.add_subsystem('fan', pyc.Compressor(map_data=pyc.AXI5,
                                             map_extrap=True),promotes_inputs=[('Nmech','LP_Nmech')])
        self.add_subsystem('splitter', pyc.Splitter())
        # Core Stream components
        self.add_subsystem('splitter_core_duct', pyc.Duct())
        self.add_subsystem('lpc', pyc.Compressor(map_data=pyc.LPCMap, map_extrap=True),
                                             promotes_inputs=[('Nmech','LP_Nmech')])
        self.add_subsystem('lpc_duct', pyc.Duct())
        self.add_subsystem('hpc', pyc.Compressor(map_data=pyc.HPCMap, 
                                        bleed_names=['cool1'],map_extrap=True),promotes_inputs=[('Nmech','HP_Nmech')])
        self.add_subsystem('bld3', pyc.BleedOut(bleed_names=['cool3']))

        self.add_subsystem('burner', pyc.Combustor(fuel_type=FUEL_TYPE))
       
        self.add_subsystem('hpt', pyc.Turbine(map_data=pyc.HPTMap,
                                          bleed_names=['cool3'],map_extrap=True),promotes_inputs=[('Nmech','HP_Nmech')])
        self.add_subsystem('hpt_duct', pyc.Duct())
        self.add_subsystem('lpt', pyc.Turbine(map_data=pyc.LPTMap,
                                        bleed_names=['cool1'],map_extrap=True), promotes_inputs=[('Nmech','LP_Nmech')])
        self.add_subsystem('lpt_duct', pyc.Duct())
        # Bypass Components
        self.add_subsystem('bypass_duct', pyc.Duct())
        # Mixer component
        self.add_subsystem('mixer', pyc.Mixer(design=True, designed_stream=1))
        self.add_subsystem('mixer_duct', pyc.Duct())
        # Afterburner Components
        self.add_subsystem('afterburner', pyc.Combustor(fuel_type=FUEL_TYPE))
    
        # End CFD HERE
        # Nozzle
        self.add_subsystem('mixed_nozz', pyc.Nozzle(nozzType='CD', lossCoef='Cfg'))

        # Mechanical components
        self.add_subsystem('lp_shaft', pyc.Shaft(num_ports=3),promotes_inputs=[('Nmech','LP_Nmech')])
        self.add_subsystem('hp_shaft', pyc.Shaft(num_ports=2),promotes_inputs=[('Nmech','HP_Nmech')])

        # Aggregating component
        self.add_subsystem('perf', pyc.Performance(num_nozzles=1, num_burners=2))

        # Connnect flow path
        self.pyc_connect_flow('fc.Fl_O', 'inlet.Fl_I')
        self.pyc_connect_flow('inlet.Fl_O', 'inlet_duct.Fl_I')
        self.pyc_connect_flow('inlet_duct.Fl_O', 'fan.Fl_I')
        self.pyc_connect_flow('fan.Fl_O', 'splitter.Fl_I')
        # Core connections
        self.pyc_connect_flow('splitter.Fl_O1', 'splitter_core_duct.Fl_I')
        self.pyc_connect_flow('splitter_core_duct.Fl_O', 'lpc.Fl_I')
        self.pyc_connect_flow('lpc.Fl_O', 'lpc_duct.Fl_I')
        self.pyc_connect_flow('lpc_duct.Fl_O', 'hpc.Fl_I')
        self.pyc_connect_flow('hpc.Fl_O', 'bld3.Fl_I')
        self.pyc_connect_flow('bld3.Fl_O', 'burner.Fl_I')
        self.pyc_connect_flow('burner.Fl_O', 'hpt.Fl_I')
        self.pyc_connect_flow('hpt.Fl_O', 'hpt_duct.Fl_I')
        self.pyc_connect_flow('hpt_duct.Fl_O', 'lpt.Fl_I')
        self.pyc_connect_flow('lpt.Fl_O', 'lpt_duct.Fl_I')
        self.pyc_connect_flow('lpt_duct.Fl_O','mixer.Fl_I1')
        # Bypass Connections
        self.pyc_connect_flow('splitter.Fl_O2', 'bypass_duct.Fl_I')
        self.pyc_connect_flow('bypass_duct.Fl_O', 'mixer.Fl_I2')

        #Mixer Connections
        self.pyc_connect_flow('mixer.Fl_O', 'mixer_duct.Fl_I')
        # After Burner
        self.pyc_connect_flow('mixer_duct.Fl_O','afterburner.Fl_I')

        # Nozzle
        self.pyc_connect_flow('afterburner.Fl_O','mixed_nozz.Fl_I')

        # Connect cooling flows
        self.pyc_connect_flow('hpc.cool1', 'lpt.cool1', connect_stat=False)
        self.pyc_connect_flow('bld3.cool3', 'hpt.cool3', connect_stat=False)

        # Make additional model connections
        self.connect('inlet.Fl_O:tot:P', 'perf.Pt2')
        self.connect('hpc.Fl_O:tot:P', 'perf.Pt3')
        self.connect('burner.Wfuel', 'perf.Wfuel_0')
        self.connect('afterburner.Wfuel', 'perf.Wfuel_1')
        self.connect('inlet.F_ram', 'perf.ram_drag')
        self.connect('mixed_nozz.Fg', 'perf.Fg_0')

        self.connect('fan.trq', 'lp_shaft.trq_0')
        self.connect('lpc.trq', 'lp_shaft.trq_1')
        self.connect('lpt.trq', 'lp_shaft.trq_2')
        self.connect('hpc.trq', 'hp_shaft.trq_0')
        self.connect('hpt.trq', 'hp_shaft.trq_1')
        self.connect('fc.Fl_O:stat:P', 'mixed_nozz.Ps_exhaust')

        # Add balence components to close the implicit components
        balance = self.add_subsystem('balance', om.BalanceComp())
        if design:
            balance.add_balance('W', lower=1e-3, upper=400., units='lbm/s', eq_units='lbf', rhs_name='Fn_target')
            self.connect('balance.W', 'fc.W')
            self.connect('perf.Fn', 'balance.lhs:W')

            balance.add_balance('BPR', eq_units=None, lower=0.1, val=100.0)
            self.connect('balance.BPR', 'splitter.BPR')
            self.connect('mixer.ER', 'balance.lhs:BPR')

            balance.add_balance('FAR_core', eq_units='degR', lower=1e-4, val=.017)
            self.connect('balance.FAR_core', 'burner.Fl_I:FAR')
            self.connect('burner.Fl_O:tot:T', 'balance.lhs:FAR_core')

            balance.add_balance('FAR_ab', eq_units='degR', lower=1e-4, val=.017)
            self.connect('balance.FAR_ab', 'afterburner.Fl_I:FAR')
            self.connect('afterburner.Fl_O:tot:T', 'balance.lhs:FAR_ab')

            balance.add_balance('lpt_PR', val=1.5, lower=1.001, upper=8, eq_units='hp', use_mult=True, mult_val=-1)
            self.connect('balance.lpt_PR', 'lpt.PR')
            self.connect('lp_shaft.pwr_in', 'balance.lhs:lpt_PR')
            self.connect('lp_shaft.pwr_out', 'balance.rhs:lpt_PR')

            balance.add_balance('hpt_PR', val=1.5, lower=1.001, upper=8, eq_units='hp', use_mult=True, mult_val=-1)
            self.connect('balance.hpt_PR', 'hpt.PR')
            self.connect('hp_shaft.pwr_in', 'balance.lhs:hpt_PR')
            self.connect('hp_shaft.pwr_out', 'balance.rhs:hpt_PR')
        else:

            balance.add_balance('W', lower=1e-3, upper=400., units='lbm/s', eq_units='inch**2')
            self.connect('balance.W', 'fc.W')
            self.connect('mixed_nozz.Throat:stat:area', 'balance.lhs:W')

            balance.add_balance('BPR', lower=0.25, upper=5.0, eq_units='psi')
            self.connect('balance.BPR', 'splitter.BPR')
            self.connect('mixer.Fl_I1_calc:stat:P', 'balance.lhs:BPR')
            self.connect('bypass_duct.Fl_O:stat:P', 'balance.rhs:BPR')

            balance.add_balance('FAR_core', eq_units='degR', lower=1e-4, upper=.06, val=.017)
            self.connect('balance.FAR_core', 'burner.Fl_I:FAR')
            self.connect('burner.Fl_O:tot:T', 'balance.lhs:FAR_core')

            balance.add_balance('FAR_ab', eq_units='degR', lower=1e-4, upper=.06, val=.017)
            self.connect('balance.FAR_ab', 'afterburner.Fl_I:FAR')
            self.connect('afterburner.Fl_O:tot:T', 'balance.lhs:FAR_ab')

            balance.add_balance('LP_Nmech', val=1., units='rpm', lower=500., eq_units='hp', use_mult=True, mult_val=-1)
            self.connect('balance.LP_Nmech', 'LP_Nmech')
            self.connect('lp_shaft.pwr_in', 'balance.lhs:LP_Nmech')
            self.connect('lp_shaft.pwr_out', 'balance.rhs:LP_Nmech')

            balance.add_balance('HP_Nmech', val=1., units='rpm', lower=500., eq_units='hp', use_mult=True, mult_val=-1)
            self.connect('balance.HP_Nmech', 'HP_Nmech')
            self.connect('hp_shaft.pwr_in', 'balance.lhs:HP_Nmech')
            self.connect('hp_shaft.pwr_out', 'balance.rhs:HP_Nmech')

        # Off design
        newton = self.nonlinear_solver = om.NewtonSolver()
        newton.options['atol'] = 1e-6
        newton.options['rtol'] = 1e-10
        newton.options['iprint'] = 2
        newton.options['maxiter'] = 10
        newton.options['solve_subsystems'] = True
        newton.options['max_sub_solves'] = 100
        newton.options['reraise_child_analysiserror'] = False
        newton.linesearch = om.BoundsEnforceLS()
        newton.linesearch.options['bound_enforcement'] = 'scalar'
        newton.linesearch.options['iprint'] = -1


        self.linear_solver = om.DirectSolver(assemble_jac=True)

        super().setup()


def print_perf(prob,ptName):
    print('BPR',prob[ptName+'.balance.BPR'])
    print('W',prob[ptName+'.balance.W'])
    print('Fnet uninst.',prob[ptName+'.perf.Fn'])

def page_viewer(point, file=sys.stdout):


    print(file=file, flush=True)
    print(file=file, flush=True)
    print(file=file, flush=True)
    print("----------------------------------------------------------------------------", file=file, flush=True)
    print("                              POINT:", point, file=file, flush=True)
    print("----------------------------------------------------------------------------", file=file, flush=True)
    print("                       PERFORMANCE CHARACTERISTICS", file=file, flush=True)
    print("    Mach      Alt       W      Fn      Fg    Fram     OPR     TSFC  ", file=file, flush=True)
    print(prob[point+'.fc.Fl_O:stat:MN'], prob[point+'.fc.alt'], prob[point+'.inlet.Fl_O:stat:W'], 
                    prob[point+'.perf.Fn'], prob[point+'.perf.Fg'], prob[point+'.inlet.F_ram'],
                    prob[point+'.perf.OPR'], prob[point+'.perf.TSFC'])

    flow_stations = ['fc.Fl_O', 'inlet.Fl_O', 'inlet_duct.Fl_O', 'fan.Fl_O', 'bypass_duct.Fl_O',
                     'splitter.Fl_O2', 'splitter.Fl_O1', 'splitter_core_duct.Fl_O',
                     'lpc.Fl_O', 'lpc_duct.Fl_O', 'hpc.Fl_O', 'bld3.Fl_O', 'burner.Fl_O',
                     'hpt.Fl_O', 'hpt_duct.Fl_O', 'lpt_duct.Fl_O',
                     'mixer.Fl_O', 'mixer_duct.Fl_O', 'afterburner.Fl_O', 'mixed_nozz.Fl_O']

    compressors = ['fan', 'hpc', 'lpc']
    burners = ['burner', 'afterburner']
    turbines = ['hpt', 'lpt']
    shafts = ['hp_shaft', 'lp_shaft']

    print('*'*80)
    print('* ' + ' '*10 + point)
    print('*'*80)
    print_perf(prob, point)

    pyc.print_flow_station(prob,[point+ "."+fl for fl in flow_stations])
    pyc.print_compressor(prob,[point+ "." + c for c in compressors])
    pyc.print_splitter(prob,[point+ ".splitter" ])
    pyc.print_burner(prob,[point+ "." + b for b in burners])
    pyc.print_turbine(prob,[point+ "." + turb for turb in turbines])
    pyc.print_mixer(prob, [point+'.mixer'])
    pyc.print_nozzle(prob, [point + '.mixed_nozz'])
    pyc.print_shaft(prob, [point+ "." + s for s in shafts])
    pyc.print_bleed(prob, [point+'.hpc', point+'.bld3'])


class MPMixedFlowTurbofan(pyc.MPCycle):

    def setup(self):

        self.pyc_add_pnt('DESIGN', MixedFlowTurbofan(design=True, thermo_method='CEA'))

        # self.set_input_defaults('DESIGN.balance.rhs:BPR', 0.35 ,units=None) # defined as 1 over 2
        self.set_input_defaults('DESIGN.inlet.MN',              0.6)
        self.set_input_defaults('DESIGN.inlet_duct.MN',         0.6)
        self.set_input_defaults('DESIGN.fan.MN',                0.6)
        self.set_input_defaults('DESIGN.splitter.MN1',          0.6)
        self.set_input_defaults('DESIGN.splitter.MN2',          0.6)
        self.set_input_defaults('DESIGN.splitter_core_duct.MN', 0.6)
        self.set_input_defaults('DESIGN.lpc.MN',                0.6)
        self.set_input_defaults('DESIGN.lpc_duct.MN',           0.5)
        self.set_input_defaults('DESIGN.hpc.MN',                0.5)
        self.set_input_defaults('DESIGN.bld3.MN',               0.3)
        self.set_input_defaults('DESIGN.burner.MN',             0.2)
        self.set_input_defaults('DESIGN.hpt.MN',                0.8)
        self.set_input_defaults('DESIGN.hpt_duct.MN',           0.8)
        self.set_input_defaults('DESIGN.lpt.MN',                0.8)
        self.set_input_defaults('DESIGN.lpt_duct.MN',           0.8)
        self.set_input_defaults('DESIGN.bypass_duct.MN',        0.6)
        self.set_input_defaults('DESIGN.mixer_duct.MN',         0.6)
        self.set_input_defaults('DESIGN.afterburner.MN',        0.6)
        self.set_input_defaults('DESIGN.LP_Nmech', 8000.0, units='rpm')
        self.set_input_defaults('DESIGN.HP_Nmech', 13000.0, units='rpm')

        self.pyc_add_cycle_param('balance.rhs:FAR_ab', 3400 ,units='degR')
        self.pyc_add_cycle_param('hp_shaft.HPX', 250, units='hp')
        self.pyc_add_cycle_param('inlet.ram_recovery', 0.9990)
        self.pyc_add_cycle_param('inlet_duct.dPqP', 0.0107)
        self.pyc_add_cycle_param('splitter_core_duct.dPqP', 0.0048)
        self.pyc_add_cycle_param('lpc_duct.dPqP', 0.0101)
        self.pyc_add_cycle_param('burner.dPqP', 0.0540)
        self.pyc_add_cycle_param('hpt_duct.dPqP', 0.0051)
        self.pyc_add_cycle_param('lpt_duct.dPqP', 0.0107)
        self.pyc_add_cycle_param('bypass_duct.dPqP', 0.0107)
        self.pyc_add_cycle_param('mixer_duct.dPqP', 0.0107)
        self.pyc_add_cycle_param('afterburner.dPqP', 0.0540)
        self.pyc_add_cycle_param('mixed_nozz.Cfg', 0.9933)
        self.pyc_add_cycle_param('hpc.cool1:frac_W', 0.050708)
        self.pyc_add_cycle_param('hpc.cool1:frac_P', 0.5)
        self.pyc_add_cycle_param('hpc.cool1:frac_work', 0.5)
        self.pyc_add_cycle_param('bld3.cool3:frac_W', 0.067214)
        self.pyc_add_cycle_param('hpt.cool3:frac_P', 1.0)
        self.pyc_add_cycle_param('lpt.cool1:frac_P', 1.0)

        self.od_pts = ['OD',]
        self.od_T4s = [3100,]
        self.od_alts = [0.0,]
        self.od_MNs = [0.000001, ]

        for i,pt in enumerate(self.od_pts):
            self.pyc_add_pnt(pt, MixedFlowTurbofan(design=False, thermo_method='CEA'))

            self.set_input_defaults(pt+'.balance.rhs:FAR_core', self.od_T4s[i], units='degR')
            self.set_input_defaults(pt+'.fc.alt', self.od_alts[i], units='ft')
            self.set_input_defaults(pt+'.fc.MN', self.od_MNs[i])

        # map scalars
        self.pyc_connect_des_od('fan.s_PR', 'fan.s_PR')
        self.pyc_connect_des_od('fan.s_Wc', 'fan.s_Wc')
        self.pyc_connect_des_od('fan.s_eff', 'fan.s_eff')
        self.pyc_connect_des_od('fan.s_Nc', 'fan.s_Nc')
        self.pyc_connect_des_od('lpc.s_PR', 'lpc.s_PR')
        self.pyc_connect_des_od('lpc.s_Wc', 'lpc.s_Wc')
        self.pyc_connect_des_od('lpc.s_eff', 'lpc.s_eff')
        self.pyc_connect_des_od('lpc.s_Nc', 'lpc.s_Nc')
        self.pyc_connect_des_od('hpc.s_PR', 'hpc.s_PR')
        self.pyc_connect_des_od('hpc.s_Wc', 'hpc.s_Wc')
        self.pyc_connect_des_od('hpc.s_eff', 'hpc.s_eff')
        self.pyc_connect_des_od('hpc.s_Nc', 'hpc.s_Nc')
        self.pyc_connect_des_od('hpt.s_PR', 'hpt.s_PR')
        self.pyc_connect_des_od('hpt.s_Wp', 'hpt.s_Wp')
        self.pyc_connect_des_od('hpt.s_eff', 'hpt.s_eff')
        self.pyc_connect_des_od('hpt.s_Np', 'hpt.s_Np')
        self.pyc_connect_des_od('lpt.s_PR', 'lpt.s_PR')
        self.pyc_connect_des_od('lpt.s_Wp', 'lpt.s_Wp')
        self.pyc_connect_des_od('lpt.s_eff', 'lpt.s_eff')
        self.pyc_connect_des_od('lpt.s_Np', 'lpt.s_Np')

        # flow areas
        self.pyc_connect_des_od('mixed_nozz.Throat:stat:area', 'balance.rhs:W')
        self.pyc_connect_des_od('inlet.Fl_O:stat:area', 'inlet.area')
        self.pyc_connect_des_od('fan.Fl_O:stat:area', 'fan.area')
        self.pyc_connect_des_od('splitter.Fl_O1:stat:area', 'splitter.area1')
        self.pyc_connect_des_od('splitter.Fl_O2:stat:area', 'splitter.area2')
        self.pyc_connect_des_od('splitter_core_duct.Fl_O:stat:area', 'splitter_core_duct.area')
        self.pyc_connect_des_od('lpc.Fl_O:stat:area', 'lpc.area')
        self.pyc_connect_des_od('lpc_duct.Fl_O:stat:area', 'lpc_duct.area')
        self.pyc_connect_des_od('hpc.Fl_O:stat:area', 'hpc.area')
        self.pyc_connect_des_od('bld3.Fl_O:stat:area', 'bld3.area')
        self.pyc_connect_des_od('burner.Fl_O:stat:area', 'burner.area')
        self.pyc_connect_des_od('hpt.Fl_O:stat:area', 'hpt.area')
        self.pyc_connect_des_od('hpt_duct.Fl_O:stat:area', 'hpt_duct.area')
        self.pyc_connect_des_od('lpt.Fl_O:stat:area', 'lpt.area')
        self.pyc_connect_des_od('lpt_duct.Fl_O:stat:area', 'lpt_duct.area')
        self.pyc_connect_des_od('bypass_duct.Fl_O:stat:area', 'bypass_duct.area')
        self.pyc_connect_des_od('mixer.Fl_O:stat:area', 'mixer.area')
        self.pyc_connect_des_od('mixer.Fl_I1_calc:stat:area', 'mixer.Fl_I1_stat_calc.area')
        self.pyc_connect_des_od('mixer_duct.Fl_O:stat:area', 'mixer_duct.area')
        self.pyc_connect_des_od('afterburner.Fl_O:stat:area', 'afterburner.area')
        super().setup()


if __name__ == "__main__":
    import time
    from openmdao.api import Problem

    prob = Problem()

    prob.model = mp_mixedflow = MPMixedFlowTurbofan()

    prob.setup()

    #Define the design point
    prob.set_val('DESIGN.splitter.BPR', 0.36)
    prob.set_val('DESIGN.fan.PR', 1.0)
    prob.set_val('DESIGN.fan.eff', 0.8948)
    prob.set_val('DESIGN.lpc.PR', 3)
    prob.set_val('DESIGN.lpc.eff', 0.9243)
    prob.set_val('DESIGN.hpc.PR', 10)
    prob.set_val('DESIGN.hpc.eff', 0.8707)
    prob.set_val('DESIGN.hpt.eff', 0.8888)
    prob.set_val('DESIGN.lpt.eff', 0.8996)
    prob.set_val('DESIGN.fc.alt', 0.0, units='ft') 
    prob.set_val('DESIGN.fc.MN', 0.2) 
    prob.set_val('DESIGN.balance.Fn_target', 14000.0, units='lbf')
    prob.set_val('DESIGN.balance.rhs:FAR_core', 3100, units='degR')

    # Set initial guesses for the balances
    prob['DESIGN.balance.FAR_core'] = 0.025
    prob['DESIGN.balance.FAR_ab'] = 0.0
    prob['DESIGN.balance.BPR'] = 0.36
    prob['DESIGN.balance.W'] = 250.0
    prob['DESIGN.balance.lpt_PR'] = 4.0
    prob['DESIGN.balance.hpt_PR'] = 3.0
    prob['DESIGN.fc.balance.Pt'] = 5.2
    prob['DESIGN.fc.balance.Tt'] = 440.0
    prob['DESIGN.mixer.balance.P_tot']= 15

    for i,pt in enumerate(mp_mixedflow.od_pts):

        prob[pt+'.balance.FAR_core'] = 0.025
        prob[pt+'.balance.FAR_ab'] = 0.025
        prob[pt+'.balance.BPR'] = 0.36
        prob[pt+'.balance.W'] = 250.
        prob[pt+'.balance.HP_Nmech'] = 8000
        prob[pt+'.balance.LP_Nmech'] = 13000
        prob[pt+'.fc.balance.Pt'] = 5.2
        prob[pt+'.fc.balance.Tt'] = 440.0
        prob[pt+'.mixer.balance.P_tot']= 15
        prob[pt+'.hpt.PR'] = 4.0
        prob[pt+'.lpt.PR'] = 3.0
        prob[pt+'.fan.map.RlineMap'] = 2.0
        prob[pt+'.lpc.map.RlineMap'] = 2.0
        prob[pt+'.hpc.map.RlineMap'] = 2.0

    st = time.time()

    prob.set_solver_print(level=-1)
    prob.set_solver_print(level=2, depth=1)

    prob.run_model()
    page_viewer('DESIGN')

   
    for pt in ['DESIGN']+mp_mixedflow.od_pts:
        page_viewer(pt)

    print()
    print("time", time.time() - st)

[kavdborr]

In the balance block, you are trying to vary the BPR, so the mass flow rate that is bypassed after the fan, to make the extraction ratio (ER) in the mixer equal to one. The extraction ratio is equal to the total pressure ratio of the bypass to core stream in the mixer (or visa versa, doesn't really matter). In order to arrive at the static pressure balance, this ER should be between ~0.9-1.1, otherwise, one of the two streams will reach Mach 1. As now ER is much larger, you get the weird mixer results.

So why are you not able to reach a suitable ER, as set up in the balance block? It is because the fan is not actually compressing (PR=1, as defined by you). As such, it is not extracting power from the turbine, which means it has no effect on the PR of the turbines to reach a power balance. If you have a PR_fan different from one, you should see that increasing the BPR decreases Pt_mixer_core, bringing ER closer to 1. Alternatively, you can fix the BPR to a value you want, and change the PR_fan to the same effect. You could do this last point in the balance block. Or you can remove the target ER altogether, and manually play with PR_fan and BPR until you reach sensible values for the mixer.

Mixed-flow turbofans, and how to set their design parameters sensibly is something quite tricky when you start out. For more info, you can also read the book of Halliwell and Kurzke (propulsion and power), or Mattingly.

[ArnaultT]

Ok, I tried a few things with the fan and see where I went wrong. I'm experimenting with the different PRs available in the inputs, and reaching equilibrium is quite tricky. Changing the fan PR from 2.1 to 2.11 leads to significantly different results... The minimization function seems to be very sensitive to the starting point.

I can get the mixer ER close to 1, but the mixer Mach number is still inconsistent. If I achieve a consistent ER, the BPR ends up higher than 1, whereas I'm aiming for 0.36... It's really challenging. I tried simplifying the balance problem, but I’m still struggling to reach equilibrium. I might need to use a simpler model, like a turbojet.

Thanks a lot for your advice!

[kavdborr]

In my experience, the mixer does make the whole design quite a bit more tricky. Also the convergence is more difficult. Starting with a turbojet might be a good plan indeed!