On Knock Intensity and Superknock in SI Engines (2017)

&lt;div class="section abstract"&gt;&lt;div class="htmlview paragraph"&gt;Most studies on knock ignore the stochastic nature of knock and focus on the onset of knock which is determined by chemical kinetics. This paper focuses on knock intensity (&lt;i&gt;KI&lt;/i&gt;) which is determined by the evolution of the pressure wave following knock onset in a hot spot and highlights the stochastic processes involved.&lt;/div&gt;&lt;div class="htmlview paragraph"&gt;&lt;i&gt;KI&lt;/i&gt; is defined in this study as the maximum peak-to-peak pressure fluctuation that follows the onset of knock. It depends on &lt;i&gt;ξ&lt;/i&gt; = (&lt;i&gt;a&lt;/i&gt;/&lt;i&gt;u&lt;sub&gt;a&lt;/sub&gt;&lt;/i&gt;) where &lt;i&gt;u&lt;sub&gt;a&lt;/sub&gt;&lt;/i&gt; is the speed of the autoignition front and &lt;i&gt;a&lt;/i&gt; is the speed of sound. When &lt;i&gt;u&lt;sub&gt;a&lt;/sub&gt;&lt;/i&gt; is small, &lt;i&gt;KI&lt;/i&gt; can be related to the product of a parameter &lt;i&gt;Z&lt;/i&gt;, which depends on &lt;i&gt;P&lt;sub&gt;ko&lt;/sub&gt;&lt;/i&gt;, the pressure at knock onset and the square of (∂x/∂&lt;i&gt;T&lt;/i&gt;), which is the inverse of the gradient of temperature with distance in the hot spot. Both &lt;i&gt;Z&lt;/i&gt; and (∂&lt;i&gt;x&lt;/i&gt;/∂&lt;i&gt;T&lt;/i&gt;) were calculated using measured &lt;i&gt;KI&lt;/i&gt; and &lt;i&gt;P&lt;sub&gt;ko&lt;/sub&gt;&lt;/i&gt; for hundreds of individual knocking cycles for different fuels. The model for ignition delay as a function of pressure &lt;i&gt;P&lt;/i&gt; and &lt;i&gt;T&lt;/i&gt; in the hot spot and other data needed to calculate &lt;i&gt;Z&lt;/i&gt; were available from a previous study (SAE 2016-01-0702). For a given fuel and operating condition, &lt;i&gt;Z&lt;/i&gt; varies because &lt;i&gt;P&lt;sub&gt;ko&lt;/sub&gt;&lt;/i&gt; varies, because of cyclic variation of combustion - a stochastic process. (∂&lt;i&gt;x&lt;/i&gt;/∂&lt;i&gt;T&lt;/i&gt;) depends on the evolution of the hot spot during the engine cycle and depends on flow and turbulence - another stochastic process. All else being equal, &lt;i&gt;Z&lt;/i&gt; increases and hence the probability of high &lt;i&gt;KI&lt;/i&gt; increases as &lt;i&gt;P&lt;sub&gt;ko&lt;/sub&gt;&lt;/i&gt; increases, e.g., by more advanced spark timing and/or faster flame development. For a given &lt;i&gt;P&lt;sub&gt;ko&lt;/sub&gt;, Z&lt;/i&gt; is lower for a fuel with higher &lt;i&gt;RON&lt;/i&gt;. In modern turbocharged engines extremely high intensity knock, informally termed superknock is observed to occur occasionally even though operating conditions are chosen to avoid knock. Superknock is caused by developing detonation (DD) which results when the value of &lt;i&gt;ξ&lt;/i&gt; decreases and the pressure wave begins to couple with the autoignition front and gets amplified. Autoignition has to be initiated at high &lt;i&gt;P&lt;/i&gt; and &lt;i&gt;T&lt;/i&gt; for superknock to occur. At practical operating conditions, this can only happen via another abnormal stochastic phenomenon - preignition, when a flame is established before the spark plug fires. Both preignition and superknock become more likely as &lt;i&gt;P&lt;/i&gt; increases. All else being equal, the probability of superknock decreases as the fuel &lt;i&gt;RON&lt;/i&gt; is increased. However, even with high &lt;i&gt;RON&lt;/i&gt;, high &lt;i&gt;KI&lt;/i&gt; and superknock could occur with the right combination of &lt;i&gt;P&lt;/i&gt; and (∂&lt;i&gt;x&lt;/i&gt;/∂&lt;i&gt;T&lt;/i&gt;).&lt;/div&gt;&lt;/div&gt;