Co-current Validation¶
Overview¶
This page presents two co-current (parallel flow) test cases. Co-current exchangers are limited by the thermodynamic constraint that both outlet temperatures must converge toward the mean — for balanced flow (\(C_r = 1\)), effectiveness cannot exceed 50 %. The analytical \(\varepsilon\)-NTU formula for co-current flow is:
For \(C_r = 1\) the theoretical maximum is:
Both tests verify that the DWSIM solver respects this fundamental limit and that co-current effectiveness is always lower than the counterflow effectiveness at the same operating conditions.
Test 4: Balanced Flow — Co-current¶
Configuration: 50 plates, 3 mm spacing, 500 x 1000 mm, chevron angle 60°, \(\varphi = 1.17\), \(\dot{m}_{hot} = \dot{m}_{cold} = 1.0\) kg/s, \(T_{h,in} = 80\) °C, \(T_{c,in} = 20\) °C.
| Check | DWSIM | \(\varepsilon\)-NTU Ref | Error (%) | Status |
|---|---|---|---|---|
| Heat duty \(Q\) (kW) | 125.3 | 125.3 | 0.00 | PASS |
| Hot outlet \(T_{h,out}\) (°C) | 50.02 | 50.02 | 0.00 | PASS |
| Cold outlet \(T_{c,out}\) (°C) | 49.98 | 49.98 | 0.00 | PASS |
| Effectiveness \(\varepsilon\) (%) | 49.97 | 49.97 | 0.00 | PASS |
| Overall \(U\) (W/(m²·K)) | 545.6 | 545.6 | 0.00 | PASS |
| MITA (°C) | 0.04 | — | — | PASS |
Thermodynamic Limit: \(\varepsilon \leq 50\%\) for Co-current with \(C_r = 1\)
With balanced flow in co-current arrangement, both outlet temperatures must converge to the arithmetic mean of the two inlet temperatures:
The DWSIM result of \(T_{h,out} = 50.02\) °C and \(T_{c,out} = 49.98\) °C confirms this behaviour. The effectiveness of 49.97 % is just below the theoretical ceiling of 50 %, as expected for a finite-area exchanger. The MITA of only 0.04 °C shows that the exchanger is operating very close to its thermodynamic limit.
Comparison with Counterflow
At identical conditions (Test 1), the counterflow arrangement achieves \(\varepsilon = 82.38\%\) compared to \(\varepsilon = 49.97\%\) for co-current — a 65 % relative improvement. This confirms the well-known advantage of counterflow and validates that the DWSIM solver correctly distinguishes between the two flow configurations.
Test 5: Small Exchanger — Co-current¶
Configuration: 10 plates, 3 mm spacing, 152.4 x 406.4 mm, chevron angle 60°, \(\varphi = 1.17\), \(\dot{m}_{hot} = \dot{m}_{cold} = 0.315\) kg/s, \(T_{h,in} = 40\) °C, \(T_{c,in} = 25\) °C.
| Check | DWSIM | \(\varepsilon\)-NTU Ref | Error (%) | Status |
|---|---|---|---|---|
| Heat duty \(Q\) (kW) | 8.23 | 8.23 | 0.00 | PASS |
| Effectiveness \(\varepsilon\) (%) | 41.69 | 41.69 | 0.00 | PASS |
| Overall \(U\) (W/(m²·K)) | 1623.8 | 1623.8 | 0.00 | PASS |
| \(Re_{hot}\) | 1021 | — | — | PASS |
| \(Re_{cold}\) | 1064 | — | — | PASS |
Key Findings — Test 5
This test uses a physically small exchanger (152.4 x 406.4 mm plates, 10 plates only) at moderate temperatures (40 / 25 °C). Despite the compact geometry, the Reynolds numbers exceed 1000 on both sides, producing a high overall coefficient of 1623.8 W/(m²·K) — near the upper end of the typical water-water PHE range. The effectiveness of 41.69 % is well below the \(C_r = 1\) co-current limit of 50 %, consistent with the small heat transfer area.
Summary¶
| Metric | Test 4 | Test 5 | Max Error (%) |
|---|---|---|---|
| \(Q\) (kW) | 125.3 | 8.23 | 0.00 |
| \(\varepsilon\) (%) | 49.97 | 41.69 | 0.00 |
| \(U\) (W/(m²·K)) | 545.6 | 1623.8 | 0.00 |
Aggregate Statistics
Both co-current tests pass with 0.00 % error on all thermal metrics. The results confirm that:
- The \(\varepsilon \leq 50\%\) thermodynamic ceiling for \(C_r = 1\) is respected (Test 4: 49.97 %).
- Both outlet temperatures converge toward the mean temperature as required by co-current theory.
- Co-current effectiveness is always lower than counterflow at the same conditions (49.97 % vs. 82.38 %).
- The overall coefficient range of 545.6 -- 1623.8 W/(m²·K) is consistent with published water-water PHE data (Perry and Green, 2008).