Inlet mass flow rate ratio

[Necolatis]

I need to calculate some numbers, and I am a little unsure on how to do it.

Mass flow rate through inlet. (turbine engine)
Speed of free flow air (not sure which speed to use here)

I need to get ratio of what is sucked into the inlet compared to what would be pushed into it if it was just a hollow tube.

[erik]

I think what you're looking for is called Overall Pressure Ratio:
https://en.wikipedia.org/wiki/Overall_pressure_ratio

[Necolatis]

Isn't OPR a constant for an engine?

What I am looking for, will for example at low speed typically be higher than 1 since the engine sucks in more air than would be pushed in by the air if the engine inlet would just be a hollow tube with no engine.
At higher speeds this value would typically be lower, as the air tries to push more air into the inlet than what the engine is actually sucking in.

[jam007]

I have also been thinking about this as I read of the interesting pitching effect of the airflow in Aerodynamics of Viggen (p. 61-62) recently.
To calculate the airflow through the engine based on thrust setting you would need to know how much of the air that is used for combustion and how much is used for cooling or bypass. I have not found good data on that. One source said that the RB.146 Mk.301 used in English Electric Lightning and J35 Draken uses 35% of the air for combustion and the rest cools the engine. That would mean that it uses 45 times , 1/(0.0633*0.35), as much air than fuel. But for bypass? Is the bypass ratio excluding the internal cooling air or not?

There must be a lessening of the pitching effect at very low speeds not mentioned in the document. Anyone who knows more about this.

[erik]

Reading this again I think you are referring to the compressibility of the air intake:
https://en.wikipedia.org/wiki/Compressible_flow

The air intake always makes sure the airflow entering the turbine is subsonic even when the aircraft flies faster than mach 1.

Erik

[jam007]

What I am looking for, will for example at low speed typically be higher than 1 since the engine sucks in more air than would be pushed in by the air if the engine inlet would just be a hollow tube with no engine.

I think I have a reasonable idea on this math.

The flow through the motor and intake velocity

The mass flow of air through the engine:
f= 45*(1+b)*ff
where b is the bypass ratio, ff the fuel flow and 45 comes from the reasoning above.

The inlet velocity:
vi= f/(r*A)
r is the air density and A is the area of the inlet(s).

For the pitching effect I get:

Force due to air inertia:

F=f*v0*sin(a) ~ f*v0*a (a<pi/6)
v0 is the free flow velocity and a is the angle of attack

But we want to calculate the extra force compared to a hollow tube model. So:
free flow through motor f0=V0*A*r

DF=F - f0*v0*a=a*f*v0-a*A*r*v0^2=a*(vi*r*A*v0-A*r*v0^2)=a*r*A*(vi*v0 - v0^2)

using qbar= r*S*v0^2/2 where S is the wing surface area, kA=A/S and the flow ratio CA= vi/v0 gives

DF=2*a*kA*qbar*(CA-1)

The moment are then

DF*R=2*R*kA*qbar*(CA-1)
R is the distance from the inlet to CG

Using the span as standard for moment arm
kR = R/B where B is the wing span

M= a*2*kA*kR*B*qbar*(CA-1)
M is the force moment

Combining 2*kR*kA into one coefficient Cm gives the formula:

M=a*Cm*qbar*B*(CA-1)


This agrees, as far as I can see, with the text and figures in the JA37 document.

Hope it helps!

*Edited due to missing factor (ff) in first formula

[Necolatis]

Thanks for the replies. I will look closer at this later today.

[jam007]

A small correction. The Cm in the Viggen document is a function of alpha and CA so it is different from the Cm I used in the last formula.

The last formula could be rewritten as

M=a*Cmi*qbar*B*(CA-1)
Where Cmi denotes pitch moment from intake per radian at CA=2

[Necolatis]

Very nice formulas. However the factor 45 could be different for this engine.

I therefore inspired by your equations, and that air sucked in probably is proportional to the thrust (if fuel is), did a reverse test to figure out from the graph of CA how to compute how much air the engine is sucking in:

Code: Select all

<fcs_function name="propulsion/engine/intake-flow-number-factor">
            <description>
                         mil*factor
                CA = ____________________________
                     rho*intakeArea*freeflowspeed

                     For mach 0.4 (AJ37):
                CA = 1.3
                intakeArea = 0.6 m^2 / 6.46 ft^2
                freeflowspeed = velocities/uBody-fps
                rho = atmosphere/rho-slugs_ft3
                mil = propulsion/engine/MilThrust

                          CA*rho*area*speed
                factor = __________________
                                mil


                Test:
                  fly 0.4M
                  full mil thrust
                  0m alt
                  ISA conditions
            </description>
            <function>
                <quotient>
                    <product>
                        <value>1.3</value>
                        <value>6.46</value>
                        <property>atmosphere/rho-slugs_ft3</property>
                        <property>/velocities/uBody-fps</property>
                    </product>
                    <property>propulsion/engine/MilThrust</property>
                </quotient>
            </function>
        </fcs_function>


I did 2 assumptions: that the graph is for 0m altitude, and that the atmosphere is ISA. The latter is pretty safe I think, the first seems likely.

The factor was 10.143

I then did this to get the CA factor:

Code: Select all

<function name="aero/function/CA-intake-flow-number">
        <description>
                     mil*factor
            CA = ____________________________
                 rho*intakeArea*freeflowspeed

            intakeArea = 0.6 m^2 / 6.46 ft^2
            freeflowspeed = velocities/uBody-fps
            rho = atmosphere/rho-slugs_ft3
            mil = propulsion/engine/MilThrust
            factor = 10.142755

            The limitation of this is that it wont work with idle thrust,
            as it depend on mil thrust. So the factor will be too large
            when running with idle thrust.
        </description>
        <quotient>
            <product>
                <property>propulsion/engine/MilThrust</property>
                <value>10.142755</value>
            </product>
            <product>
                <value>6.46</value>
                <property>atmosphere/rho-slugs_ft3</property>
                <property>/velocities/uBody-fps</property>
            </product>
        </quotient>
    </function>


Assuming I did that correct, I then now have to figure out how much the thrust depends on MilThrust and how much on IdleThrust.

As for the pitch moment, I think I will try your equations, and see if they match up with the Cm_CA coefficient in the document. Else I will just use the graph of the coefficient in the document.

[jam007]

Very nice formulas. However the factor 45 could be different for this engine.

I therefore inspired by your equations, and that air sucked in probably is proportional to the thrust (if fuel is),

yes. It depends on how much cooling air that is going through the engine. But if you have kg air to kg fuel (or lb air to lb fuel) it should not go under 1/0.063=16 as this is the stoichiometric ratio for combustion.

I have thought about how linear the thrust to fuel flow is in real life and how that is modelled in jsbsim. To avoid complications I think it might be better to use the fuel flow property directly rather than recalculating thrust.

As for the pitch moment, I think I will try your equations, and see if they match up with the Cm_CA coefficient in the document.

That will be interesting. I have not quantitatively tested the formula against the graph.

[Necolatis]

The fuel flow should be linear proportional to thrust in JSBSim, as its given in lbm/hr/lbf.

[jam007]

The fuel flow should be linear proportional to thrust in JSBSim, as its given in lbm/hr/lbf.

Hm.
looking at thesource code I'm not totally convinced:

Code: Select all

  N2 = Seek(&N2, IdleN2 + ThrottlePos * N2_factor, spoolup, spoolup * 3.0);
  N1 = Seek(&N1, IdleN1 + ThrottlePos * N1_factor, spoolup, spoolup * 2.4);
  N2norm = (N2 - IdleN2) / N2_factor;
  thrust = idlethrust + (milthrust * N2norm * N2norm);
  EGT_degC = TAT + 363.1 + ThrottlePos * 357.1;
  OilPressure_psi = N2 * 0.62;
  OilTemp_degK = Seek(&OilTemp_degK, 366.0, 1.2, 0.1);

  if (!Augmentation) {
   correctedTSFC = TSFC * sqrt(T/389.7) * (0.84 + (1-N2norm)*(1-N2norm));
    FuelFlow_pph = Seek(&FuelFlow_pph, thrust * correctedTSFC, 1000.0, 10000.0);
    if (FuelFlow_pph < IdleFF) FuelFlow_pph = IdleFF;
    NozzlePosition = Seek(&NozzlePosition, 1.0 - N2norm, 0.8, 0.8);
    thrust = thrust * (1.0 - BleedDemand);
EPR = 1.0 + thrust/MilThrust;

The line: correctedTSFC = TSFC * sqrt(T/389.7) * (0.84 + (1-N2norm)*(1-N2norm));
doesn’t this give a non-linear fuel consumption as N2norm changes with thrust setting?

[jam007]

Just saw that I had forgotten to multiply with fuel flow in the first calculation! Edited.

[Necolatis]

doesn’t this give a non-linear fuel consumption as N2norm changes with thrust setting?

Don't think N2 is linear with thrust.

[jam007]

Don't think N2 is linear with thrust.

CorrectedTSFC seems to non linear with thrust and thrust setting. Therefore I assume that airflow is non linear with thrust. Assuming that the engine is run close to optimum fuel/air ratio for different thrusts then makes the fuel flow a good start for calculating the intake flow of air.

I just created a function and is testing it (after struggling with the ... US units):

Code: Select all

 <function name="aero/function/CA-1">
           <description>Quotient of inlet velocit and air velocity minus one</description>
           <sum>
             <quotient>
               <product>
                 <value>0.252</value>
                 <min>
                   <property>propulsion/engine/fuel-flow-rate-pps</property>
                   <value>13000</value> <!-- Afterburner does not increase airflow -->
                 </min>
               </product>
               <product>
                 <property>atmosphere/rho-slugs_ft3</property>
                 <property>velocities/u-aero-fps</property>
               </product>
             </quotient>
             <value>-1.0</value>
           </sum>
         </function>

The 0.252 value is 45 (lb/s per lb/s fuel) divided with intake area (ft^2) and converted to slugs/s/ft^2

noticed that EngineSim gives 47 times the fuel flow for the pure turbo jet at 0 altitude and full thrust. So it seems that the 45 number has some merit. But the airflow seems to be almost constant with thrust setting. This is a bit strange as CA then would be constant... More exploring to do.

I found that the airspeed at mil thrust is approx 110 m/s for this intake and engine.