Methods to Calculate Entropy Generation

Abstract

Entropy generation, formulated by combining the first and second laws of thermodynamics with an appropriate thermodynamic potential, emerges as the difference between a phenomenological entropy function and a reversible entropy function. The phenomenological entropy function is evaluated over an irreversible path through thermodynamic state space via real-time measurements of thermodynamic states. The reversible entropy function is calculated along an ideal reversible path through the same state space. Entropy generation models for various classes of systems—thermal, externally loaded, internally reactive, open and closed––are developed via selection of suitable thermodynamic potentials. Here- we simplify thermodynamic principles to specify convenient and consistently accurate system governing equations and characterization models. The formulations introduce a new and universal Phenomenological Entropy Generation (PEG) theorem. The systems and methods presented––and demonstrated on frictional wear, grease degradation, battery charging and discharging, metal fatigue and pump flow––can be used for design, analysis, and support of diagnostic monitoring and optimization.

Systems and Methods for Transformation and Degradation Analyses

“…To maintain the nonnegative inequality of Equation (4) mandated by the second law, for energy extraction/decomposition or system loading, 𝑑𝕊 𝑟𝑒𝑣 ≤ 𝛿𝕊 𝑝ℎ𝑒𝑛 < 0, and for energy addition or system formation, 0 < 𝑑𝕊 𝑟𝑒𝑣 ≤ 𝛿𝕊 𝑝ℎ𝑒𝑛 . Details of the PEG theorem, including statements and derivation, can be found in reference [26].…”

“…Similarly, deriving from first principles, a corollary of the PEG theorem asserts [19]: Given r number of active work interactions, the phenomenological entropy generation of a simple system is completely specified by r+1 independent properties. Single-variable entropy generations 𝑆′ 𝑊,𝑟 = ∑ 𝑌 𝑟 𝑑𝑋 𝑟 𝑇 𝑟 [29] govern all the r active (internal and external) work mechanisms while Microstructurothermal (MST) entropy 𝑆′ 𝜇𝑇 = −𝑆𝑑𝑇 [20,21,26] governs the accompanying coupled microstructural and thermal mechanisms:…”

“…Here, 𝑆′ 𝑊,𝑟 = 𝑆′ 𝑊 + 𝑆′ 𝑁 , where 𝑆′ 𝑊 represents all the boundary/external interactions (or work transfers) and 𝑆′ 𝑁 is the internal compositional change (including matter flow) entropy. Y is generalized force, dX is generalized displacement, dT is temperature change, and S is entropy content defined by material properties and process variables [26] as Heat and work are different manifestations of energy, represented with different terms in the energy balance. While an algebraic sum of both heat and work yields the internal energy change between two states when the end state values of the system variables are unknown, the sum does not give useful information on-for example, which mechanism dominates-the system transformation between both states.…”

“…The dissipation factor [18,26,30] which measures a non-thermal system's dissipation tendencies relative to useful work output/chemical reaction is…”

“…These and several others have presented accurate realworld results, with shortcomings attributable to assumptions. Osara and Bryant [17][18][19][20][21][22][23][24][25] directly correlated phenomenological entropy generation (PEG) [26] with a transformation/degradation measure, as prescribed by the degradation-entropy generation (DEG) theorem [27], to describe highly dissipative system-process interactions at near-100% accuracy.…”