Ducted Fan Force and nozzle optimisation
Ducted Fan Force and nozzle optimisation
(OP)
I have a model aircraft ducted fan with exit velocity of 22.4m/s and area of 6221sq mm. Is there an equation I can use to estimate static thrust? Also, if I added a nozzle with exit area of 4418sq mm, what effect would that have on static thrust and is there an equation I can use to optimise the nozzle area ratio?
Any help would be much appreciated,
Andrew
Any help would be much appreciated,
Andrew





RE: Ducted Fan Force and nozzle optimisation
Adding a nozzle won't help.
RE: Ducted Fan Force and nozzle optimisation
Static Thrust= mass flow * average exit velocity.
Mass flow ~ Air density * exit area * average exit velocity
Ts = rho * Ae * Ve^2.
Thrust is zero when your your plane moves as fast forward as your exhaust is backwards.
So if you constrict the exit duct w/ a convergent nozzle, you reduce mass flow because the fan is working against a restriction, but you increase average exit velocity. This gives you less static thrust, but when properly done, a higher maximum airspeed.
RE: Ducted Fan Force and nozzle optimisation
The thrust is, without external air friction is
p1A1-p2A2+mass flow rate*(V2-V1)
p1=static pressure of air entering duct
p2= static pressure at exhaust
A1 entering duct area
A2 exhaust duct area
p1 and p2 are found from fan curves total pressure vs flow rate and the fluid flow equation (energy equation)for the duct.
V1,V2 velocity at entrance, exhaust
RE: Ducted Fan Force and nozzle optimisation
intuitively a nozzle would create a faster airflow, and more losses ... the thrust is developed by the fan blade ... the power from the engine is applied to the airflow by the blade, increasing the airflow's speed. making the airflow increase it's speed downstream (by a nozzle) doesn't sound like you've added energy to the airflow, but caused some to be wasted.
i disagree with the above post ... the exhaust velocity is the delta V imparted by the van. if the forward velocity is equal to this, i think the fan will still be producing thrust, albeit reduced, becuase the fan blade efficiency will be reduced, but not zero.
RE: Ducted Fan Force and nozzle optimisation
Um, no. Quick thought experiment: typical spacecraft launch vehicles reach velocities of some 7,000 meters/sec or more, yet have typical exhaust velocities of some 3,000 to 4,500 m/sec. Propulsive efficiency may decrease, but thrust pretty much stays constant, or even increases with forward speed for typical airbreathing engines (due to higher ram pressure on engine intakes).
RE: Ducted Fan Force and nozzle optimisation
Thrust=.5*rho*A*(Ve^2-Vo^2)
rho= air density
Ve= entry velocity
Vo= exit velocity
.5*rho*(Ve^2-Vo^2)=pressure differential
With that I agree with moon161 given the circumstances that the exit velocity will limit your top speed.
A rocket creates a large LOCAL pressure differential and thrust velocity vs vehicle velocity is marginalized
RE: Ducted Fan Force and nozzle optimisation
stationary the outflow velocity is 22.3 m/s because of the energy the blade is adding to the airflow, a deltaV of 22.3 m/s.
if the plane is moving forward the deltaV will still be there, slightly reduced from the stationary value 'cause the efficiency of the blade is slightly reduced 'cuase the AoA has increased slightly. At some speed the blade will stall and thrust produced will drop significantly but i don't think it ever becomes zero.
thought exercise ... is the slipstream velocity of a spitfire something like 400 mph, ie it's max speed ? ... again, i don't think so.
RE: Ducted Fan Force and nozzle optimisation
Not trying to say thrust is not produced once you reach an airspeed equal to the stationary outflow only that it is a limiting factor and unlikely you can surpass it by much if at all in a propeller driven aircraft.
RE: Ducted Fan Force and nozzle optimisation
thus i don't think the plane's speed is limited to 22.4 m/s 'cause that's the fan's deltaV.
it's max speed is going to be limited to it's drag (and not the fan's deltaV).
RE: Ducted Fan Force and nozzle optimisation
Apologize for a lot of over simplifications in my previous posts.
but drag alone will not determine a max airspeed
Drag, then Prop efficiency, then power curve of the engine will all be important factors in determining max airspeed.
Stationary delta V is related to the prop and engine power curves but is not directly correlated to max airspeed
RE: Ducted Fan Force and nozzle optimisation
The basic thrust equations for rockets work for ducted fans too. Thrust = (mdot)*Vexit, plus some pressure expansion terms.
RE: Ducted Fan Force and nozzle optimisation
slipstream velocity = vehicle velocity + deltaV
the OP is telling us with vehicle velocity = 0, slipstream = deltaV = 22.4 m/s
the vehicle can quite possibly travel faster than 22.4 m/s, depending on the drag of the vehicle and the efficiency of the fan producing thrust.
RE: Ducted Fan Force and nozzle optimisation
U*T
U = Air speed
T= thrust
The maximum thrust you can get would coincide with the maximum fan power that can be delivered. If you look at the fan curve, there is a point (assuming constant fan speed) that the power is maximized, at a combination of
m' and pL
m'= mass flow rate lb/hr
pL= total pressure of duct airflow=p+rhoV^2/2g
To get the maximum you have to adjust the exit area to get m' and the corresponding pL that maximizes fan power
Absent friction, I did the Bernouli equation and got
Uv1/g+v1^2/2g+pl/rho+pL/rho+pl/rho=Uv2/g+v2^2/2g+ p2/rho
Now, the left side is known= K and the RHS is a function of v2 and p2
The airframe thrust equation is
p2A2-p1A1+m'(v2-v1)
p2A1*v1/v2-p1A1+m'(v2-v1)
I maximzed this to get
-(U+v2)/g*A1*v1/v2+A1*v1/v2(K-Uv2/g+v2^2/2g)+m'/g=0
solve for v2 and from that you get A2 and v2