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TRANSPIRATION COOLING

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Transpiration cooling is one way of active heat protection (see Heat Protection) during which a coolant in the course of passing through the wall of a body absorbs a part of the internal energy of a body requiring cooling, and simultaneously actively affects the convective heat flux going into a body from the surrounding space. This method of cooling may be realized in the form of porous, perforated, film or obstructing cooling (Figure 1).

Forms of transpiration cooling.

Figure 1. Forms of transpiration cooling.

During injection of cold gas or liquid into a boundary layer of an incoming flow there occurs driving back of hot gas from the body surface, as a result of which the heat transfer rate decreases due to the so-called thermal blowing effect (see Heat protection.) The more effective coolants are those substances possessing the maximal specific heat and producing gaseous products with the minimal molecular mass. Table 1 presents properties of coolants used in systems of transpiration cooling.

Table 1. Coolants used in transpiration cooling

The advantage of this heat protection method over others is the possibility of maintaining the surface temperature at the desired level by controlling the coolant flow rate. In some applications, the chemical composition of the injected gas is very important. Thus, for wings and wheels of supersonic aircraft the danger is not only thermal heating, but also oxidation of the surface by the incoming flow. If we apply ammonia in the system of transpiration cooling, which has good specific heat capacity and the relatively low values of molecular mass, then in the high-temperature air flow it interacts with oxygen

The reaction products resulting in this case (water and nitrogen) are practically inactive to the metals, used in the aircraft construction. The most effective variant of the transpiration cooling is porous cooling. The mechanism of porous cooling is a combination of two processes: internal heat transfer (Figure 2), when the coolant takes away heat from the porous matrix during filtration in the direction of the outer surface (see Porous Medium), and external heat transfer, when the gaseous coolant, leaving the wall, diffuses through a boundary layer, diluting and driving back the high-temperature incoming flow from the surface (see Heat Protection). It is precisely this second process that provides the higher efficiency of porous cooling. As an example, we determine the required flow rate for blade cooling in a gas-turbine power plant. Denote the temperature of the flow before entrance into the turbine as Te, the coolant temperature at the inlet into the porous wall T0, and the coolant flow rate Gw. Assume that inside the porous matrix the gas exists in the temperature equilibrium with porous walls, while its specific heat capacity cρ,0 is approximately equal to specific heat capacity of the gas mixture before the turbine . The thermal balance on the turbine blade surface can be written in the form:

Hence, it is not difficult to obtain an equation for the cooling depth or the temperature drop ratio inside the porous wall (Tw − T0) and in the external flow (Te − T0):

In this case, = Gw/(α/cp)0 is the dimensionless flow rate of a coolant. γ is the blowing coefficient depending on the flow mode and on the coolant type (see Porous media). The dimensionless coolant flow rate is associated with the relative flow rate Gweue through the Stanton number, St = (α/cp)0eue. Even at the temperature Te = 1900 K for conservation of the blade temperature at the level of Tw ≤ 1100K it is sufficient to have a coolant flow rate Gw not more than 3% of the flow rate of the working body in the turbine. One must bear in mind that during operation of such a system it is necessary to keep the coolant clean to avoid breakage of the pores.

Figure 2. 

One of the varieties of the porous cooling is the so-called self-cooling or sweating. Its idea is borrowed from the nature, however, the practical realization is very peculiar. For example, nozzle blocks of solid-fuel rocket engines are manufactured from porous tungsten, impregnated by silver, copper, zinc or lithium hydride. Evaporating at the low temperature, these metals absorb a considerable amount of heat. Gradually departing inside the coating, the evaporation front becomes a source of formation of gaseous products, which filter through the porous layer and are blown into the boundary layer.

The requirement to the coolant purity for perforated walls is much less severe. However, in this case the internal heat absorption is not as effective as in the porous matrix. Therefore gas, leaving the wall, has a low temperature. The blocking effect of discretely blown-in jets is also less than that of uniform porous blowing; this leads, finally, to the onset of the considerable temperature "roughness" of the wall being cooled and to its splitting.

Film cooling is the other variant of transpiration cooling. Through the system of holes or gaps the liquid coolant is supplied onto the external body surface, which under the action of friction and the pressure gradient of an incoming flow is converted into a thin film, covering the whole body surface (at least, up to the next succession of holes). In this case the surface temperature nowhere will exceed the liquid boiling temperature.

The efficiency of film cooling depends on the method coolant supply, its feed angle, the presence of roughness and contamination on the surface, and on the coolant properties. With increasing number of gaps and holes, the wall temperature becomes more uniform.

Film cooling is used as additional means for protecting walls of combustion chambers and rocket engine nozzles in those cases when convective cooling does not provide the required thermal mode. The conservation of the steady-state laminar film flow without formation of waves or spraying remains a serious problem (see Film cooling).

Obstructing cooling may be considered as a variety of film cooling (Figure 1). Here, cold gas is discharged through slits or holes in the wall located at a certain distance one from another. It is desirable to realize the coolant ejection into the flow at the minimal angle to the wall. This delays the mixing process and provides the greatest heat-protecting effect. The length of the protected plate surface during the coolant supply over the normal to it is in some times smaller than over the tangent.

An interesting combination of various methods for heat protection is realized in solid-fuel rocket engines for protecting the critical nozzle cross-section. It is known that even the 5 percentage increase of the critical cross-section diameter leads to a pressure drop in the combustion chamber of 15–20%; this fact significantly decreases the engine thrust. The necessary for the obstructing cooling gas with the relatively low temperature is produced during burning of "collars" fabricated of low-calorie fuel, placed in the subsonic nozzle zone at its boundary with the combustion chamber. With this purpose one may arrange inserts made of high-melting metals, saturated by readily sublimating components.

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HEAT PROTECTION

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FILM COOLING

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