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This paper reviews the correlation concepts and tools available, with the emphasis on their historical origins, mathematical properties and applications. Two of the most commonly used statistical correlation indicators, i.e., modal assurance criterion (MAC) for structural deformation pattern identification/correlation and the coefficient of determination (R2) for data correlation are investigated. The mathematical structure of R2 is critically examined, and the physical meanings and their implications are discussed. Based on the insights gained from these analyses, a data scatter measure and a dependency measure are proposed. The applications of the measures for both linear and nonlinear data are also discussed. Finally, several worked examples in vehicle dynamics analysis and statistical data analyses are provided to demonstrate the effectiveness of these concepts.

Stringent global emissions legislation demands effective NOx reduction strategies, particularly for the aftertreatment, and current typical liquid urea SCR systems achieve efficiencies greater than 90% [1]. However, with such high-performing systems comes the trade-off of requiring a tank of reductant (urea water solution) to be filled regularly, usually as soon as the fuel fillings or as far as oil changes. Advantages of solid reductants, particularly ammonium carbamate, include greater ammonia densities, enabling the reductant refill interval to be extended several multiples versus a given reductant volume of urea, or diesel exhaust fluid (DEF) [2]. An additional advantage is direct gaseous ammonia dosing, enabling reductant injection at lower exhaust temperatures to widen its operational coverage achieving greater emissions reduction potential [3], as well as eliminating deposits, reducing mixing lengths, and avoiding freeze/thaw risks and investments.

Diesel exhaust after treatment solutions using injection, such as urea-based SCR and lean NOx trap systems, effectively reduce the emission NOx level in various light vehicles, commercial vehicles, and industrial applications. The performance of the injector is crucial for successfully utilizing this type of technology, and a simulation tool plays an important role in the virtual design, that the performance of the injector is evaluated to reach the optimized design. The virtual test methodology using CFD to capture the fluid dynamics of the injector internal flow has been previously developed and validated for quantifying the dosing rate of the test injector. In this study, the capability of the virtual test methodology was extended to determine the spray angle of the test injector, and the effect of the manufacturing process on the injector internal nozzle flow characteristics was investigated using the enhanced virtual test methodology.