Contrails !

Contrails ! The Meredith Effect


Meredith's note
Coll GTH


Note On The Cooling Of Aircraft Engines With Special Reference To Ethylene Glycol Radiators Enclosed In Ducts
By F. W. Meredith, B.A.

Communicated by the Director of Scientific Research, Air Ministry Reports and Memoranda No. 1683

14 August, 1935


Some excerpts of F.Meredith's note



  • (a) Introductory (Purpose of investigation). --The recent increase in the speed of aeroplanes has brought the question of cooling drag into prominence and forced the application of the principle of low velocity cooling. An analysis of the performance of a cooling system enclosed in a duct is required to guide further research and design.
  • (b) Range of investigation. -- The theory of the ducted radiator is developed and a basis of calculating the drag is provided.
  • The effects of compressibility are also investigated.

  • (c) Conclusions. -- It is shown that the power expended on cooling does not increase with speed for a properly designed ducted system but that, owing to recovery of waste heat, a thrust may be derived at speeds of the order of 300 m.p.h.

    Attention is drawn to the importance of the momentum of the exhaust gases at high speeds of flight.

  • Introductory. -- Cooling of aero engines involves the exposure of a large heated surface to a stream of air, a process which involves the expenditure of power owing to the viscosity of air. Until recently, it appeared that this fact imposed an intractable limit to the speed of aircraft since, whereas the heat transfer only varies directly as the speed of the air over the surface, the power expenditure varies as the cube. Thus even though the exposed surface be adjusted until only the required heat transfer is effected, the power expenditure increases as the square of the speed.

    The advent of wing surface cooling appeared, at one time, to offer a solution of this difficulty by effecting the cooling without any additional surface. There is, however, reason to believe that the heat transfer necessarily increases the drag of the wing. Apart from this, the Supermarine S 6 B utilised practically the entire exposed surface for cooling and additional surface inside the wing. Further advance in speed appeared to depend upon raising the temperature of the surface.

    It is the purpose of the report to show that, by correct design of low velocity cooling systems, in which the surface (whether in the form of honeycomb radiator or of fins on the cylinder heads and barrels) is exposed in an internal duct, the power expended on cooling does not increase with the speed of flight, but that, on the contrary, it should diminish to vanishing point at a practicable speed beyond which the cooling system contributes to the propulsion.


  • Effects of compressibility of the air. -- These effects are four.

  • (1) The effective temperature of the air is raised by the kinetic energy of the main stream.

  • (2) The drop in pressure across the radiator is increased for the same mass flow by the reduction of density resulting from heating the stream.
  • (3) At altitude, the power necessarily expended in the radiator varies inversely as the square of the density and inversely as the cube of the available temperature difference.
  • (4) The available energy of the cooling stream is increased by the expansion after the addition of heat.
  • [...]
  • Effect of the momentum of the exhaust gases on the drag of an engine installation. - Various proposals have been made to utilise the energy of the exhaust gases to assist the induction of the cooling stream, although design to date has apparently been little affected by consideration of the momentum of the issuing gases.

    Broadly it may be stated that the effect of the momentum is the same whether it be diffused with the cooling stream or not. It should be noted, however, that some of the benefit in thrust will be lost by a consequent increase of skin friction drag if the exhaust gases scrub an appreciable surface at high velocity. For this reason diffusion of momentum inside the duct my be desirable and this may be convenient method of diffusing the exhaust heat.

    The thrust derivable from the rearward direction of the exhaust gases is given by the product of the mass flow and the velocity of exit and the latter quantity depends upon the internal design of the exhaust system. The thrust power is, however, also proportional to the speed of flight. Thus it becomes increasingly important to utilise this thrust as the speed of flight increases.

    No attempt is here made to asses the power which may be available from this source. It is suggested, however, that if by the use of suitable deflectors for guiding the exhaust gases round the necessary bends and by the avoidable of excessive unguided expansions, an appreciable proportion of the original energy of the exhaust gases can be preserved, this will provide an appreciable increment to the thrust horse power of a high speed aeroplane.

  • Conclusions. -- The employment of the principle of low velocity cooling avoids the necessity for an increasing expenditure of power with increasing speed provided the exit conditions are adjusted to suit the speed.

    Further the combined effects of compressibility and heat transfer from the radiator may reduce the power consumption to nothing if the size of the radiator is adequate. By the use of the heat of the exhaust, in addition, and appreciable thrust may be expected from the presence of the cooling stream.

    Finally, attention is drawn to the importance of the momentum of the exhaust gases for a high speed aeroplane, although no attempt is made to deal with this point quantitatively.


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