Calculation Methodology

ExCoil implements a comprehensive thermal analysis engine for finned-tube heat exchangers commonly used in HVAC&R systems. The calculation methodology follows the ε-NTU (effectiveness-NTU) method as described in the ASHRAE Handbook of Fundamentals [14], combined with detailed correlations for heat transfer coefficients and pressure drop on both the air side and the fluid side.

The software supports five types of heat exchangers, each with specific correlations tailored to their operating conditions:

The overall heat transfer rate is determined by the thermal resistance network:

The air-side heat transfer coefficient is calculated using the Colburn j-factor method, based on the work of Wang, Chi & Chang (2000) [1] and Kim, Youn & Webb (1999) [2]. These correlations were developed from extensive experimental data on plain fin-and-tube heat exchangers with staggered tube arrangements, covering a wide range of geometric parameters.

The maximum velocity V_max is calculated from the face velocity divided by the free area ratio σ, which accounts for the blockage caused by tubes and fins. The Reynolds number is based on the collar diameter D_c = D_o + 2t_fin.

The air-side pressure drop is calculated using the Fanning friction factor approach from Wang et al. (2000) [1], combined with entrance contraction and exit expansion losses from Kays & London (1984) [8]. The total pressure drop consists of three components:

Fin efficiency is calculated using the Schmidt (1949) [7] approximation for annular fins. This method provides an accurate estimate of the temperature distribution along the fin, accounting for the fin's thermal conductivity, thickness, and the air-side heat transfer coefficient.

The external surface area is calculated from the actual tube count and geometry, considering both the fin surface area (both sides of each fin) and the prime tube surface between fins:

For DX evaporators and condensers, the two-phase heat transfer coefficient is calculated using a simplified Chen (1966) [11] correlation approach. The method combines the liquid-only forced convection contribution with an enhancement factor that accounts for the nucleate boiling and convective boiling mechanisms.

For the superheated vapor region (in evaporators) and the subcooled liquid region (in condensers), the Dittus-Boelter (1930) [10] correlation is used:

The two-phase pressure drop is one of the most critical parameters in heat exchanger design. ExCoil uses the Müller-Steinhagen & Heck (1986) [3] correlation, which has been cited over 1,400 times and is widely recognized for its accuracy across a broad range of fluids and conditions. The total two-phase pressure drop consists of three components: frictional, acceleration, and return bend losses.

6.1 Frictional Pressure Drop — Müller-Steinhagen & Heck (1986)

The liquid-only and gas-only pressure drops are calculated using the Darcy-Weisbach equation with the Churchill (1977) [4] friction factor, which is valid for all flow regimes (laminar, transitional, and turbulent):

6.2 Acceleration Pressure Drop

During evaporation, the fluid accelerates as it changes from liquid to vapor (increasing specific volume). This momentum change creates an additional pressure drop. During condensation, the opposite occurs, partially recovering pressure.

6.3 Total Two-Phase Pressure Drop

For chilled water and hot water coils, the internal heat transfer coefficient is calculated using the Gnielinski (1976) [12] correlation for turbulent flow in smooth tubes, which is more accurate than Dittus-Boelter for the transition region (2300 < Re < 10,000):

The water-side pressure drop includes straight tube friction (Darcy-Weisbach with Churchill friction factor) and return bend losses:

Return bends (U-bends) in heat exchangers contribute significantly to the total pressure drop, typically adding 30-50% to the straight-tube friction losses. ExCoil calculates return bend losses using the methodology of Geary (1975) [5]for single-phase flow and Padilla et al. (2009) [6] for two-phase flow.

Steam coils operate under condensation conditions on the tube side. The internal heat transfer coefficient is calculated using the Nusselt film condensation theory, which assumes a thin laminar film of condensate flowing along the inner tube wall under gravity.

Steam properties (saturation temperature, latent heat, density) are calculated from the steam pressure using polynomial fits derived from the IAPWS-IF97 steam tables. The air-side calculations follow the same Wang et al. (2000) methodology as the other calculator types.

ExCoil includes a comprehensive refrigerant property database covering the most commonly used refrigerants in HVAC&R applications. Properties are calculated using polynomial curve fits derived from NIST REFPROP data, ensuring accuracy across the operating range of each refrigerant.

For each refrigerant, the following thermodynamic and transport properties are available as functions of temperature and/or pressure:

ExCoil includes built-in validation checks to ensure calculations remain within the valid range of the underlying correlations. When parameters fall outside recommended ranges, the software generates warnings to alert the engineer.

The energy balance error is calculated for every simulation to verify thermodynamic consistency. A converged solution typically achieves an energy balance error of 0.00%, confirming that the heat rejected/absorbed on the air side matches the heat absorbed/rejected on the fluid side within numerical precision.