Validating the First Law of Thermodynamics for Unsteady Flow in a Compression Wave Using Mathcad

Abstract

Classical thermodynamics traditionally overlooks the role of quantities dependent on spatial coordinates and time, especially in the context of unsteady flows. This research introduces the first law of thermodynamics (FLT) tailored for nonstationary flow, distinguishing itself with the inclusion of terms bearing partial derivatives of pressure, <i>p(x, t)</i>, concerning coordinates and time (-ν(∂<i>р</i>/∂<i>х</i>)dx; -ν(∂<i>р</i>/∂<i>t</i>)dt). By employing this novel approach, the derived equations are validated using a centered compression wave as a representative nonstationary flow case study. A methodology is also presented for experimentally quantifying hydrodynamic energy losses in the intake and exhaust systems of internal combustion engines. Central to the exploration is the calculation of pressure forces' work (-ν(∂<i>р</i>/∂<i>х</i>)dx and -ν(∂<i>р</i>/∂<i>t</i>)dt) in the FLT equation for nonstationary flows, particularly their applicability to a centered compression wave. Moreover, a distinct procedure for discerning friction work in nonstationary flow is delineated. The research methods encompass both analytical derivation and numerical simulations leveraging Mathcad software. The bespoke Mathcad program crafted for this study can graphically represent multiple flow parameters as functions of time, proving invaluable for comprehending compression wave dynamics and evaluating friction work in diverse unsteady flows. Ultimately, the incorporation of energy equations tailored for nonstationary flows into classical thermodynamics paves the way for a more comprehensive understanding and application of thermodynamics to intricate flow scenarios.