2-Stream Validation¶

Reference Method¶

All 2-stream tests are validated against the e-NTU analytical method (Kays & London, 1984) with constant \(c_p = 4184\) J/(kg·K) for water.

Why Small Differences?

The MSHX solver uses DWSIM's thermodynamic engine with temperature-dependent properties (real Cp via Raoult's Law), while the e-NTU reference uses constant Cp = 4184. This accounts for the 0.1–1% differences observed — both approaches are correct within their modeling assumptions.

Test Conditions¶

Fluid: Water
Pressure: 10 atm (1,013,250 Pa) — ensures liquid phase
Property Package: Raoult's Law
Segments: 25

Test 1: Counterflow UA=1000, Balanced¶

Configuration: \(T_{h,\text{in}}\) = 75°C, \(T_{c,\text{in}}\) = 25°C, \(\dot{m}_h = \dot{m}_c\) = 1 kg/s, UA = 1000 W/K

Check	DWSIM	e-NTU	Error	Status
\(T_{h,\text{out}}\) (°C)	65.58	65.35	0.35%	PASS
\(T_{c,\text{out}}\) (°C)	34.74	34.65	0.27%	PASS
Q (kW)	40.40	40.35	0.11%	PASS
UA (W/K)	999.3	1000.0	0.07%	PASS

Test 2: Co-current UA=1000, Balanced¶

Configuration: Same as Test 1 but co-current flow direction.

Check	DWSIM	e-NTU	Error	Status
\(T_{h,\text{out}}\) (°C)	65.71	65.50	0.33%	PASS
\(T_{c,\text{out}}\) (°C)	34.60	34.50	0.30%	PASS
Q (kW)	39.83	39.75	0.22%	PASS
UA (W/K)	1000.4	1000.0	0.04%	PASS

Counterflow vs Co-current

Test 1 (counterflow) transfers slightly more heat (40.40 kW) than Test 2 (co-current, 39.83 kW) for the same UA — consistent with theory.

Test 3: Counterflow UA=1000, Unbalanced (Cr=0.5)¶

Configuration: \(\dot{m}_h\) = 1 kg/s, \(\dot{m}_c\) = 2 kg/s (Cr = 0.5)

Check	DWSIM	e-NTU	Error	Status
\(T_{h,\text{out}}\) (°C)	65.10	64.88	0.34%	PASS
\(T_{c,\text{out}}\) (°C)	30.12	30.06	0.20%	PASS
Q (kW)	42.45	42.36	0.23%	PASS
UA (W/K)	1000.0	1000.0	0.00%	PASS

Test 4: Counterflow UA=100, Small Exchanger¶

Configuration: UA = 100 W/K (small exchanger, low NTU)

Check	DWSIM	e-NTU	Error	Status
\(T_{h,\text{out}}\) (°C)	73.87	73.83	0.05%	PASS
\(T_{c,\text{out}}\) (°C)	26.18	26.17	0.05%	PASS
Q (kW)	4.88	4.88	0.01%	PASS
UA (W/K)	100.0	100.0	0.04%	PASS

Test 5: Counterflow UA=10000, Large Exchanger¶

Configuration: UA = 10,000 W/K (large exchanger, high NTU)

Check	DWSIM	e-NTU	Error	Status
\(T_{h,\text{out}}\) (°C)	40.02	39.75	0.69%	PASS
\(T_{c,\text{out}}\) (°C)	60.41	60.25	0.26%	PASS
Q (kW)	148.12	147.49	0.43%	PASS
UA (W/K)	9987.1	10000.0	0.13%	PASS

Higher Error at High NTU

The slightly larger discrepancy (0.69%) at UA=10,000 is expected: at high NTU, the outlet temperatures are more sensitive to the Cp model (real vs constant), and the difference between DWSIM's temperature-dependent Cp and the constant Cp=4184 becomes more significant.

Test 6: Counterflow MITA=10K, Balanced¶

Configuration: MITA = 10 K, counterflow, balanced streams

Check	DWSIM	e-NTU	Error	Status
\(T_{h,\text{out}}\) (°C)	35.34	35.00	0.96%	PASS
\(T_{c,\text{out}}\) (°C)	65.00	65.00	0.00%	PASS
Q (kW)	167.66	167.36	0.18%	PASS
MITA (K)	10.00	10.00	0.02%	PASS

Test 7: Co-current MITA=15K, Balanced¶

Configuration: MITA = 15 K, co-current, balanced streams

Check	DWSIM	e-NTU	Error	Status
\(T_{h,\text{out}}\) (°C)	57.73	57.50	0.40%	PASS
\(T_{c,\text{out}}\) (°C)	42.74	42.50	0.56%	PASS
Q (kW)	73.75	73.22	0.73%	PASS
MITA (K)	14.99	15.00	0.06%	PASS

Test 8: Counterflow U×A Mode (U=500, A=2)¶

Configuration: U = 500 W/(m²·K), A = 2 m² → effective UA = 1000 W/K

Check	DWSIM	e-NTU	Error	Status
\(T_{h,\text{out}}\) (°C)	65.58	65.35	0.35%	PASS
\(T_{c,\text{out}}\) (°C)	34.74	34.65	0.27%	PASS
Q (kW)	40.40	40.35	0.11%	PASS
UA (W/K)	999.3	1000.0	0.07%	PASS

U×A Consistency

Results are identical to Test 1 (UA=1000 direct), confirming that the U×A input mode correctly computes the effective UA product.

Summary¶

2-stream validation error distribution — **Figure 1.** Distribution of errors across all 2-stream test cases. All temperature and heat duty errors are below 1%, with most under 0.4%.

Statistic	Temperature Error	Heat Duty Error	UA Error
Maximum	0.96%	0.73%	0.13%
Average	0.31%	0.25%	0.05%
All PASS	Yes	Yes	Yes