THE PROBLEM OF HEAT ADDITION IN DUCTS

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Abstract
The one-dimensional problem of heat addition in a duct with friction losses is examined.The variation of the total head temperature and pressure ratio, as well as the static ones, have been obtained as functions of the Mach number and the frictional coefficient. It is shown that an extreme value of the total head temperature and pressure ratio is obtained when the Mach number equals unity. An extreme value of the static temperature is obtained at Mach numbers smaller or larger than unity, depending on the form of the duct.It is concluded that when the total head pressure losses are to be kept low, a diverging duct must be used. The frictional losses have a convergence effect on the flow. When the friction losses are disregarded, no total head pressure loss will result if the area variation of the duct is such as to ensure a constant Mach number.The results and conclusions found may be useful in the design of combustion chambers for gas turbines, propulsive ducts, and rockets.

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