1 ROCKET PROPULSION LECTURE 2 ROCKET NOZZLES AND

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1 ROCKET PROPULSION LECTURE 2: ROCKET NOZZLES AND THRUST Propulsion 2011 Lecture 2 –

1 ROCKET PROPULSION LECTURE 2: ROCKET NOZZLES AND THRUST Propulsion 2011 Lecture 2 – ROCKET NOZZLES AND THRUST

2 Propulsion 2011 Lecture 2 – ROCKET NOZZLES AND THRUST Contents • Rocket thrust

2 Propulsion 2011 Lecture 2 – ROCKET NOZZLES AND THRUST Contents • Rocket thrust equation • Energy balance and nozzle efficiency • Effect of stagnation enthalpy non-uniformities Rocket thrust equation Energy balance and nozzle efficiency Effect of stagnation enthalpy non-uniformities

3 Propulsion 2011 Lecture 2 – ROCKET NOZZLES AND THRUST Rocket thrust equation(1) •

3 Propulsion 2011 Lecture 2 – ROCKET NOZZLES AND THRUST Rocket thrust equation(1) • Remember the turbojet thrust equation: • For a rocket: • But taking into account the nozzle geometry: Effective velocity: where Effective pressure: Transversal area: Rocket thrust equation Energy balance and nozzle efficiency Effect of stagnation enthalpy non-uniformities

4 Propulsion 2011 Lecture 2 – ROCKET NOZZLES AND THRUST SPIKE NOZZLE AXISIMETRIC 2

4 Propulsion 2011 Lecture 2 – ROCKET NOZZLES AND THRUST SPIKE NOZZLE AXISIMETRIC 2 D NOZZLE Rocket thrust equation(2) Rocket thrust equation § Cylindrical surface of radius R. § Uniform Ue and Pe. ue § Spherical wedge with revolution profile. § 2 D strongly flow. § Analytical treatment exists. §Prandtl-Mayer expansions. Energy balance and nozzle efficiency Effect of stagnation enthalpy non-uniformities

5 Propulsion 2011 Lecture 2 – ROCKET NOZZLES AND THRUST Energy balance and nozzle

5 Propulsion 2011 Lecture 2 – ROCKET NOZZLES AND THRUST Energy balance and nozzle efficiency • Total specific enthalpy at combustion chamber: • Along the flow expansion in the nozzle, ht. C is conserved for each streamline: • Related with these, the nozzle efficiency is defined by: Rocket thrust equation Energy balance and nozzle efficiency Effect of stagnation enthalpy non-uniformities

6 Propulsion 2011 Lecture 2 – ROCKET NOZZLES AND THRUST Energy balance and nozzle

6 Propulsion 2011 Lecture 2 – ROCKET NOZZLES AND THRUST Energy balance and nozzle efficiency • Using the total enthalpy, the exhaust velocity can be described as: • Adding the nozzle efficiency: • Thus, the jet power is the kinetic energy flow out of the nozzle: Rocket thrust equation Energy balance and nozzle efficiency Effect of stagnation enthalpy non-uniformities

7 Propulsion 2011 Effect of stagnation enthalpy non-uniformities Lecture 2 – ROCKET NOZZLES AND

7 Propulsion 2011 Effect of stagnation enthalpy non-uniformities Lecture 2 – ROCKET NOZZLES AND THRUST • Then, a comparison about two different flows is done in order to evaluate them. The following flows will be compared: Thrust § Matched nozzle § Uniform flow Power § Matched nozzle § Non-Uniform flow Thrust Power Rocket thrust equation Energy balance and nozzle efficiency Effect of stagnation enthalpy non-uniformities

8 Propulsion 2011 Effect of stagnation enthalpy non-uniformities Lecture 2 – ROCKET NOZZLES AND

8 Propulsion 2011 Effect of stagnation enthalpy non-uniformities Lecture 2 – ROCKET NOZZLES AND THRUST • Defining an “efficiency” for a given thrust: ▫ Chemical rockets ~ 90 -95% • Thus, we can consider, with an acceptable error, the next expression as valid for the rest of the course:

9 Propulsion 2011 Lecture 2 – ROCKET NOZZLES AND THRUST Bibliography • 16. 512,

9 Propulsion 2011 Lecture 2 – ROCKET NOZZLES AND THRUST Bibliography • 16. 512, Rocket Propulsion. MARTINEZ-SANCHEZ, Manuel. Rocket thrust equation Energy balance and nozzle efficiency Effect of stagnation enthalpy non-uniformities