Question

A large, uncooled, uninsulated, low-carbon-steel thrust chamber burned out at the throat

region during testing. 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 thrust chamber was repaired, and assume that 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 2150 ∘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 2150 ∘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. If the water spray
seems to be adequate (getting at least 10% more burning time), make sketches with
notes on how the mechanic should arrange for this water flow during testing so it will be
most effective.

Answer 1

To prevent burnout of a steel thrust chamber during testing, heat transfer rate, specific heat, and thermal conductivity are used to calculate the safe test duration. Introducing water sprays can significantly prolong this duration by increasing heat loss. An effective water spray arrangement is key for optimal cooling.

Step-by-step explanation:

To solve this engineering problem related to heat and heat transfer methods, we need to consider thermal properties such as specific heat capacity and thermal conductivity. When a material is subject to a heat source, its temperature will rise until the heat input is equal to the heat loss. By coating the thrust chamber with water, the goal is to increase the heat loss through evaporation and convection, thus keeping the temperature below the steel's maximum allowable temperature of 2150 ℉.

The heat flux is given as 15 Btu/in.2, and we aim to calculate how quickly this translates to the steel reaching its limit of 2150 ℉. Using the specific heat capacity (0.143 Btu/lbm-℉) and the thermal conductivity of steel (260 Btu/hr-ft2-℉/in), we can determine the rate at which the steel's temperature will rise. Furthermore, by introducing water spray, we can estimate the increased test duration based on the efficacy of water in absorbing and carrying away heat.

To give a practical recommendation, assuming a 10% increase in burning time with water sprays, it's important to position the water hoses to ensure the water is evenly distributed over the nozzle's external throat region without hindering the test observation and data collection.

Without Water Spray

1. Estimate the initial temperature of the steel.
2. Calculate the rate of temperature increase based on heat flux, specific heat, and steel weight density.
3. Determine the time to reach 2150 ℉.

With Water Spray

1. Estimate cooling effect of water based on heat absorption and evaporation.
2. Adjust the rate of temperature increase to account for cooling.
3. Recalculate the time to reach 2150 ℉ and compare with the unsprayed scenario.