Heat Transfer Analysis

In actual rocket development not only is the heat transfer analyzed but the rocket units are almost always tested to assure that heat is transferred satisfactorily under all operating and emergency conditons. Heat transfer calculations are useful to guide the design, testing, and failure investigations. Those rocket combustion devices that are regeneratively cooled or radiation cooled can reach thermal equilibrium and the steady-state heat transfer relationships will apply. Transient heat transfer conditions apply not only during thrust buildup (starting) and shutdown of all rocket propulsion systems, but also with cooling techniques that never reach equilibrium^ such as with ablative materials.

Sophisticated finite element analysis (FEA) programs of heat transfer have been available for at least a dozen years and several different FEA computer programs have been used for the analysis of thrust chamber steady-state and transient heat transfer, with different chamber geometries or different materials with temperature variant properties. A detailed description of this powerful analysis is beyond the scope of this book, but can be found in Refs. 8-10 and 8-11. Major rocket propulsion organizations have developed their own ver-

Gimbal mount

Controller

Regeneratively cooled chamber and nozzle

Propellant coo Id own lines

Movable nozzle extension

Oxidizer-LOj inlet

Fuel-LHj inlet Turbo pump

Turbine discharge line

Fixed nozzle extension

(a) Half section of nozzle extension in stowed position

Nozzle

Nozzle extension parameters:

Height: 2.5 m (all 3 segments) Max. diameter: 2.1 Material thickness: 2.3 to 3.0 mm Mass: 92 kg

(b) Nozzle extension in deployed position

FIGURE 8-19. The RL-10B-2 rocket engine has an extendible nozzle cone or skirt, which is placed around the engine during the ascent of the Delta III launch vehicle. This extension is lowered into position by electromechanical devices after the launch vehicle has been separated from the upper stage at high altitude and before firing. (Courtesy of Pratt & Whitney, a division of United Technologies.)

extension device (motors)

Two-piece nozzle extension. Exit segment (carbon-carbon)

Regeneratively cooled chamber and nozzle

One of several pushing members to move nozzle into position

Fixed nozzle extension (carbon-carbon)

Joint and seal sions of suitable computer programs for solving their heat transfer problems. This section gives the basic relationships that are the foundation for FEA programs. They are intended to give some understanding of the phenomena and underlying principles.

General Steady-State Heat Transfer Relations

For heat transfer conduction the following general relation applies:

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