Modeling of Turbulence in Internal Combustion Engines

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Abstract
One of the most widely used models of turbulence for the calculation of complex flows is the k-ε model. However, it has been recently pointed out by W. C. Reynolds that this model does not correctly represent the behavior of homogeneous turbulence in the special case of “rapid” spherical compression. His observation is highly relevant to flows subjected to large desity changes, in which flow compression may be considered to be very rapid, such as those generated in engines. Reynolds suggested that the dissipation equation of the k-ε model should be modified in order to represent correctly the special case of a rapid spherical compression. However, the types of compression occurring inside engine cylinders are not spherical in general; for example, piston motion generates a unidirectional (axial) compression. Because of this, the original analysis of Reynolds has been generalized and extended to more general types of compression. Sample calculations have been made of the turbulence inside a piston-engine geometry with 8:1 compression ratio. When the original model was used, a sharp increase in turbulence length was predicted, resulting in a length scale up to several times larger than the cylinder clearance height. By contrast, the modified turbulence model predicts a physically more plausible behavior.