Problems

1. How much total heat per second can be absorbed in a thrust chamber with an inside wall surface area of 0.200 m2 if the coolant is liquid hydrogen and the coolant temperature does not exceed 145 K in the jacket? Coolant flow is 2 kg/sec. What is the average heat transfer rate per second per unit area? Use the data from Table 7-1 and the following:

Heat of vaporization near boiling point 446 kJ/kg

Thermal conductivity (gas at 21 K) 0.013 W/m-K

2. During a static test a certain steel thrust chamber is cooled by water. The following data are given:

Average water temperature 100°F

Thermal conductivity of water 1.07 x 10~4 Btu/sec-ft2-°F/ft

Gas temperature 4500°F

Viscosity of water 2.5 x 10~5 lbf-sec/ft2

Specific heat of water 1.0 Btu/lb-°F

Cooling passage dimensions | x j in.

Water flow through passage 0.585 lb/sec

Thickness of inner wall | in.

Heat absorbed 1.3 Btu/in. -sec

Thermal conductivity of wall material 26 Btu/hr-ft2-°F/ft Determine (a) the film coefficient of the coolant; (b) the wall temperature on the coolant side; (c) the wall temperature on the gas side.

3. In the example of Problem 2 determine the water flow required to decrease the wall temperature on the gas side by 100°F. What is the percentage increase in coolant velocity? Assume that the various properties of the water and the average water temperature do not change.

4. Express the total temperature drop in Problem 2 in terms of the percentage tem-preature drops through the coolant film, the wall, and the gas film.

5. Determine the absolute and relative reduction in wall temperatures and heat transfer caused by applying insulation in a liquid-cooled rocket chamber with the following data:

Tube wall thickness 0.381 mm

Gas temperature 2760 K

Gas-side wall temperature 1260 K Heat transfer rate 15 MW/m2

Liquid film coefficient 23 kW/m2-K

Wall material Stainless steel AISI type 302

A 0.2 mm thick layer of insulating paint is applied on the gas side; the paint consists mostly of magnesia particles. The conductivity of this magnesia is 2.59 W/m2-K/m. The stainless steel has an average thermal conductivity of 140 Btu/hr-ft2-°F/in.

6. A small thruster has the following characteristics:

Propellants Nitrogen tetroxide and monomethyl hydrazine

Injection individual hole size Between 0.063 and 0.030 in.

Injection hole pattern Unlike impinging doublet

Thrust chamber type Ablative liner with a carbon-carbon nozzle throat insert

Specific gravities: 1.446 for oxidizer and 0.876 for fuel

Impingement point 0.25 in. from injector face

Direction of jet momentum Parallel to chamber axis after impingement r = 1.65 (fuel rich) ('Actual = 251 sec

Determine the number of oxidizer and fuel holes and their angles. Make a sketch to show the symmetric hole pattern and the feed passages in the injector. To protect the wall, the outermost holes should all be fuel holes.

7. A large, uncooled, uninsulated, low carbon steel thrust chamber burned out in the throat region during a test. The wall (0.375 in. thick) had melted and there were several holes. The test engineer said that he estimated the heat transfer to have been about 15 Btu/in.2. The chamber was repaired and you are responsible for the next test. Someone suggested that a series of water hoses be hooked up to spray plenty of water on the outside of the nozzle wall at the throat region during the next test to prolong the firing duration. The steel's melting point is estimated to be 2550°F. Because of the likely local variation in mixture ratio and possibly imperfect impingement, you anticipate some local gas regions that are oxidizer rich and could start the rapid oxidation of the steel. You therefore decide that 2250°F should be the maximum allowable inner wall temperature. Besides knowing the steel weight density (0.284 lbf/in.3), you have the following data for steel for the temperature range from ambient to 2250°F: the specific heat is 0.143 Btu/lbm-°F and the thermal conductivity is 260 Btu/hr-ft2-°F/in. Determine the approximate time for running the next test (without burnout) both with and without the water sprays. Justify any assumptions you make about the liquid film coefficient of the water flow. If the water spray seems to be worth while (getting at least 10% more burning time), make sketches with notes on how the mechanic should arrange for this water flow so it will be most effective.

8. The following conditions are given for a double-walled cooling jacket of a rocket thrust chamber assembly:

Rated chamber pressure

210 psi

Rated jacket pressure

290 psi

Chamber diameter

16.5 in.

Nozzle throat diameter

5.0 in.

Nozzle throat gas pressure

112 psi

Average inner wall temperature at throat region

110°F

Average inner wall temperature at chamber region

800°F

Cooling passage height at chamber and nozzle exit

0.375 in.

Cooling passage height at nozzle throat

0.250 in.

Nozzle exit gas pressure

14.7 psi.

Nozzle exit diameter

10 in.

Wall material

1020 carbon steel

Safety factor on yield strength

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