Predictability of Exergy Destruction in Helically Coiled Tube Heat Exchangers: Global, Pitch-Specific and Hierarchical Correlations

Purpose: To quantify second-law performance in a vertically oriented helically coiled tube heat exchanger (HCTHEX) and to develop predictive correlations for the dimensionless exergy-destruction fraction ϕ_D=E ̇_D/E ̇_(in,total)across a matrix of operating conditions and coil pitches. Methodology: A steady, real fluid-to-fluid CFD model was used with water on both shell and coil sides and laminar (or weakly transitional) treatment over the stated Reynolds-number range. Exergy rates at shell/coil inlets and outlets were computed for a heat-exchanger control volume and used to evaluate E ̇_Dand ϕ_D. Predictability was assessed via (i) global (non-pitch-specific) regressions including pitch as an explicit predictor, and (ii) pitch-specific regressions trained separately at each pitch; all models were trained in log space and evaluated using five-fold cross-validation. Findings: The global baseline power-law regression ϕ_D=A" " Re_shell^a Re_coil^b p^cyields statistically significant dependence on pitch and Reynolds numbers (e.g., for the D_h-based case: A=0.2238, a=0.04885, b=0.04982, c=0.7507). However, cross-validation shows limited predictive fidelity for the baseline (for D_h: R_(CV,log⁡)^2=0.1687, RMSE_(CV,log⁡)=0.1402). Among advanced surrogates, LogLog–GPR–ARDSE provides the best global performance for both characteristic-length definitions (for D_h: R_(CV,log⁡)^2=0.7171, RMSE_(CV,log⁡)=0.08181), representing a substantial reduction in prediction error relative to the baseline. Pitch-specific analysis demonstrates that the best advanced model depends on pitch: GPR–ARDSE is selected at p=1.80, 1.85, and 2.00, while bagged trees slightly outperform GPR at p=1.90and 1.95 under the minimum RMSE_(CV,log⁡)criterion. limitations: The reported correlations are calibrated to the simulated geometry family and operating ranges examined (including the pitch range studied) and should not be extrapolated beyond these conditions without additional verification. Practical implications: The resulting correlations enable rapid estimation of ϕ_Dfrom readily available nondimensional inputs (Re_shellⓜ,Re_coilⓜ,p), reducing the need for repeated full exergy accounting during design screening and operating-map exploration. Originality: This work couples a full fluid-to-fluid CFD exergy framework with systematic, cross-validated benchmarking of baseline power-law, advanced surrogate, and pitch-conditioned predictive models for ϕ_Din HCTHEX geometries, explicitly quantifying how model form and pitch conditioning affect predictive accuracy.