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"The grooves, tubes, or coolant passages in liquid propellant rocket chambers are often of complex cross section. The equivalent diameter, needed for fluid-film heat transfer calculations, is usually defined as four times the hydraulic radius of the coolant passage; the hydraulic radius is the cross-sectional flow area divided by the wetted perimeter.

"The grooves, tubes, or coolant passages in liquid propellant rocket chambers are often of complex cross section. The equivalent diameter, needed for fluid-film heat transfer calculations, is usually defined as four times the hydraulic radius of the coolant passage; the hydraulic radius is the cross-sectional flow area divided by the wetted perimeter.

boiling region shifts to the right, to B'-C'. This boiling permits a substantial increase in the heat transfer beyond that predicted by Eq. 8-25. This phenomenon often occurs locally in the nozzle throat area, where the heat flux is high.

3. As the heat transfer is increased further, the rate of bubble formation and the bubble size become so great that the bubbles are unable to escape from the wall rapidly enough. This reaction (shown as C—D in Fig. 8-22) is characterized by an unstable gas film and is difficult to obtain repro-ducibly in tests. When a film consisting largely or completely of gas forms along the hot wall surface, then this film acts as an insulation layer, causing a decrease in heat flux and, usually, a rapid increase in wall temperature, often resulting in a burnout or melting of the wall material. The maximum feasible heat transfer rate (point C) is indicated as qmax in Table 8-5 and appears to be a function of the cooling-fluid properties, the presence of dissolved gases, the pressure, and the flow velocity.

4. As the temperature difference across the film is further increased, the wall temperatures reach values in which heat transfer by radiation becomes important. Region D—E is not of interest to rocket designers.

Cooling can also be accomplished by a fluid above its critical point with coolants such as hydrogen. In this case there is no nucleate boiling and the heat transfer increases with the temperature difference, as shown by the supercritical (dashed) line in Fig. 8-22. Liquid hydrogen is an excellent coolant, has a high specific heat, and leaves no residues.

Chemical changes in the liquid can seriously influence the heat transfer from hot walls to liquids. Cracking of the fuel, with an attendant formation of insoluble gas, tends to reduce the maximum heat flux and thus promote failure more readily. Hydrocarbon fuel coolants (methane, jet fuel) can break down and form solid, sticky carbon deposits inside the cooling channel, impeding the heat transfer. Other factors influencing steady-state coolant heat transfer are gas radiation to the wall, bends in the coolant passage, improper welds or manufacture, and flow oscillations caused by turbulence or combustion unsteadiness. Some propellants, such as hydrazine, can decompose spontaneously and explode in the cooling passage if they become too hot.

To achieve a good heat-absorbing capacity of the coolant, the pressure and the coolant flow velocity are selected so that boiling is permitted locally but the bulk of the coolant does not reach this boiling condition. The total heat rejected by the hot gases to the surface of the hot walls, as given by Eq. 8-15 must be less than that permitted by the temperature rise in the coolant, namely qA = Q = mc{T\ - T2) (8-26)

where m is the coolant mass flow rate, c the average specific heat of the liquid, T\ the initial temperature of the coolant as it enters the cooling jacket, and T2

its final temperature. Q is the rate of heat absorption per unit time; q is this same rate per unit heat transfer area. A. T2 should be below the boiling point prevailing at the cooling jacket pressure.

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