Internal Validation¶

Summary¶

Metric	Value
Total Tests	10
Passed	10
Failed	0
Pass Rate	100%

Test Methodology¶

Each test case is validated against independent calculations using:

Psychrometric properties: ASHRAE correlations for saturation pressure, humidity ratio, and moist air enthalpy
Merkel integration: 4-point Chebyshev quadrature (CTI standard) as an independent reference
Energy balance: Q_water = mw * Cpw * Range vs. Q_air = ma * (h_a,out - h_a,in)

Test Cases¶

Case 1: Design/Poppe — Classic (L/G = 1.0)¶

Parameter	Value
Tw,in / Tw,out	40 / 30 °C
Tdb / Twb	25 / 20 °C
L/G	1.0
mw	0.278 kg/s

Results: Tw,out = 30.00 °C, Q = 11.60 kW, KaV/L = 0.8144, Evap = 0.00393 kg/s

Case 2: Design/Merkel — Classic (L/G = 1.0)¶

Same inputs as Case 1, but using Merkel method.

Results: KaV/L = 0.8030 (1.4% lower than Poppe — expected due to Le_f assumption)

Case 3: Rating/Poppe — Round-Trip from Case 1¶

Using KaV/L = 0.8144 from Case 1 as input.

Results: Tw,out = 30.00 °C (0.00 K deviation — perfect round-trip)

Case 4: Rating/Merkel — Round-Trip from Case 2¶

Using KaV/L = 0.8144 as input.

Results: Tw,out = 29.93 °C, Q = 11.68 kW

Case 5: Design/Merkel — High L/G = 2.0¶

Parameter	Value
Tw,out target	32 °C
L/G	2.0

Results: KaV/L = 0.7166

Case 6: Design/Merkel — Low L/G = 0.5¶

Parameter	Value
Tw,out target	28 °C
L/G	0.5

Results: KaV/L = 0.9767

Case 7: Design/Poppe — Narrow Approach (2 K)¶

Parameter	Value
Tw,in / Tw,out	35 / 22 °C
Twb	20 °C
Approach	2 K

Results: KaV/L = 6.9055 (very high — extreme condition)

Case 8: Design/Merkel — Wide Range (20 K)¶

Parameter	Value
Tw,in / Tw,out	50 / 30 °C
Tdb / Twb	30 / 25 °C
L/G	1.5

Results: KaV/L = 2.7417

Case 9: Rating/Poppe — Higher Flow (1 kg/s)¶

Parameter	Value
Tw,in	40 °C
KaV/L	1.5
L/G	1.0

Results: Tw,out = 27.11 °C, Q = 53.84 kW

Case 10: Design/Merkel — Flow Consistency Check¶

Same conditions as Case 1 but with mw = 1.0 kg/s to confirm the KaV/L is flow-independent.

Cross-Validation: Poppe vs Merkel¶

Poppe vs Merkel comparison — **Figure 1.** Comparison of KaV/L values from Poppe (RK4) and Merkel (Simpson) methods across different L/G ratios. The Poppe method consistently predicts slightly higher KaV/L due to the Lewis factor correction.

Comparison	Poppe	Merkel	Difference
KaV/L (L/G=1.0)	0.8144	0.8030	+1.4%
Q rejected	11,602 W	11,602 W	0.0%
Air outlet T	32.35 °C	25.28 °C	+7.1 K
Air outlet w	0.02693	0.02904	-7.3%

Expected Differences

The Poppe method predicts higher air outlet temperatures because it properly accounts for the Lewis factor, resulting in a more accurate air-side energy balance. The Merkel method, by assuming Le_f = 1, overestimates the humidity ratio increase and underestimates the temperature rise.

Energy Balance Verification¶

For all 10 test cases, the energy balance was verified:

\[ \left| \frac{Q_{water} - Q_{air}}{Q_{water}} \right| < 5\% \]

where:

\( Q_{water} = \dot{m}_w \cdot c_{pw} \cdot (T_{w,in} - T_{w,out}) \)
\( Q_{air} = \dot{m}_a \cdot (h_{a,out} - h_{a,in}) \)

All cases passed this criterion.

Design-Rating Round-Trip¶

The round-trip test (Design produces KaV/L, Rating uses it to recover Tw,out) was verified with 0.00 K deviation for both methods.