Calculation of Optimal Heat Release Rates under Constrained Conditions
The work extends a methodology, for searching for optimal heat release
profiles, by adding complex constraints on states. To find the optimum heat
release profile a methodology, that uses available theory and methods, was
developed that enables the use of state of the art optimal control software
to find the optimum combustion trace for a model. The methodology is here
extended to include constraints and the method is then applied to study how
sensitive the solution is to different effects such as heat transfer,
crevice flow, maximum rate of pressure rise, maximum pressure, knock and NO
generation. The Gatowski single zone model is extended to a pseudo two zone
model, to get an unburned zone that is used to describe the knocking and a
burned zone for NO generation. A modification of the extended Zeldovich
mechanism that makes it continuously differentiable, is used for NO
generation. Previous results showed that the crevice effect had a
significant influence on the shape for the unconstrained case where a two
mode combustion was seen, one initial pressure rise and one constant
pressure phase. Here it is shown that it still has a significant influence
on the appearance until the maximum pressure limit is reached and becomes
the dominating constraint. In the unconstrained case no conditions had
combustion before TDC all started after, but when limitations are considered
and come into play the combustion can now start before TDC to avoid
excessive losses during the expansion. When introducing constraints on the
NO formation through the extended Zeldovich mechanism the combustion takes
the shape of a three mode combustion, one initial rapid burning, one later
rapid burning and a constant pressure phase. In summary it is shown that the
methodology is able to cope with the introduced constraints.
Lars Eriksson and Martin Sivertsson
2016
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