{"id":105,"date":"2014-09-22T13:24:47","date_gmt":"2014-09-22T13:24:47","guid":{"rendered":"http:\/\/openwam.webs.upv.es\/docs\/?p=105"},"modified":"2014-09-22T13:25:32","modified_gmt":"2014-09-22T13:25:32","slug":"four-wiebes-simulation","status":"publish","type":"post","link":"https:\/\/openwam.webs.upv.es\/docs\/?p=105","title":{"rendered":"Four Wiebes simulation"},"content":{"rendered":"

<\/p>\n

Wiebe’s function for combustion simulation<\/h1>\n

The model used in Openwam is based on the use of Wiebe\u2019s functions. The Wiebe\u00b4s functions simulate pilot, premixed, diffusion and late combustion phases.
\nThe mathematical expression of the rate of heat release given by a Wiebe\u00b4s function is,<\/p>\n

<\/a><\/p>\n

(1) <\/span>   <\/span>\"\begin{align*}<\/p>\n

which is the derivative of the heat release:<\/p>\n

<\/a><\/p>\n

(2) <\/span>   <\/span>\"\begin{align*}<\/p>\n

In this two equations, \"\alpha\" is the crank angle; \"\Delta\alpha\" is the duration of the combustion phase \"i\" (premixed, diffusion or late combustion); \"\alpha_{0i}\" is the crank angle at which the combustion phase \"i\" stars; \"\beta\" represents the proportion of the combustion phase \"i\" with regard to the whole combustion. Hence, its value varies between 0 and 1; \"C_i\" represents the modulation parameter that controls what percentage of fuel injected is burnt within the combustion duration; and \"m_i\" is the shape parameter that controls the gradient of the combustion phase \"i\".<\/p>\n

RoHR are normalised by dividing the heat release energy by the injected fuel energy. As a consequence, the value of the area under the function is equal to 1. The reference RoHR versus crank angle comes from the combustion diagnostic code <\/span>.<\/p>\n

HRL interpolation for non-defined operating point<\/h1>\n

In some cases, mainly when in the modelling of transient operation, it is needed to predict the HRL for the engine conditions so that the prediction of the Wiebe\u2019s functions to simulate the combustion process becomes critical. The model applied in OpenWAM proposes the use of a simple technique to interpolate the RoHR versus crank angle value from an engine database of empirical results. The proposed interpolation model is supported by an engine database that represents the engine transient operation range homogeneously. It is composed by a set of parametrized RoHRs, which are obtained by using the criteria describe in <\/span>. Every RoHR is associated to the following average cycle variables, which are going to be referred as interpolation parameters:<\/p>\n