Calculation of Thrust and Wing Area

[roldy]

I posted I question in regards to shock angles on this very same problem earlier but now I have a new problem. I need to calculate the heat rate required in the combuster in order to ensure that the vehicle will cruise (delta z=0). I also need to find the mass flow rate of the fuel. h for the fuel is 1.2*10⁸ J/kg.

Along with this, I need to find the area of the wing required to ensure constant altitude.
Attached is a crappy drawing of the hypersonic vehicle.

I have found all the forces for C, D, E, and for the wing I found the forces F and G in terms of the area.

The x forces resulting from the pressures on the different surfaces would hinder the movement of the vehicle. Thus they are the drag forces.

The y forces are the lift forces. And to maintain a constant altitude they must equal the weight of the vehicle.

Solving the y forces equation for area of wing( this term was included in the top and bottom forces of the wing...F=P/Area), I got a value of about 1.002 m^2

Plugging into the x forces for area, I got the thrust to be 19915.11 N

One thing that I'm not positive on is point e. How do I go about computing values for Mach, Pressure, Temperature, Total Pressure, Total Temperature, and Velocity if I can't get from ce to e due to lack of data (none) at ce?

So now I believe I can solve for the mass flow rate of the fuel and the heat rate required but I am not sure how to arrive at this point. I believe it involves the conservation of energy and conservation of mass.


mdot₁+mdot_fuel=mdot₂

Qdot -Wdot +mdot₁(h¹+1/2U₁²)=mdot₂(h₂+1/2U₂²)

There is no work being done. Substitution for mdot₂ and simplifying yields:

Qdot +1/2mdot₁h₁(U₁²-U₂²)=mdot_fuel(h₂+1/2U₂²)

This seems right but for some reason I believe I missed something here. There is no h_fuel.

My professor pointed out to me that the prerequisite course for this class dealt with this kind of stuff albeit on a easier level. However, I did not take that course because I came from another university. The course there didn't cover much of this, just theory. So I am at a bit of a disadvantage. Sorry for the long post and crappy drawing. I really want to understand this (being that I spent 9 hours studying on the internet and solving for the various items). Any help would be awesome.

 

[Navin A S]

To calculate the heat rate required in the combustor and the mass flow rate of the fuel, you need to use the energy balance equation. The energy balance equation states that the total energy input into a system is equal to the total energy output from the system. In this case, the total energy input is the heat rate and the mass flow rate of the fuel, while the total energy output is the thrust of the vehicle. Therefore, the equation can be written as:Qdot + mdotfuel*h = Thrust where Qdot is the heat rate, mdotfuel is the mass flow rate of the fuel, h is the enthalpy of the fuel and Thrust is the thrust of the vehicle. By substituting the values for Thrust and h, you can solve for the heat rate and mass flow rate of the fuel.