Counterflow Validation¶
Overview¶
This page presents three counterflow test cases that cover balanced flow, unbalanced flow (\(C_r = 0.5\)), and a reduced-plate geometry matching MATLAB Simscape reference dimensions. All tests use water-water duty and compare DWSIM outputs against the analytical \(\varepsilon\)-NTU counterflow formula:
For the special case \(C_r = 1\):
Test 1: Balanced Flow — Counterflow¶
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) | 206.6 | 206.6 | 0.00 | PASS |
| Hot outlet \(T_{h,out}\) (°C) | 30.57 | 30.57 | 0.00 | PASS |
| Cold outlet \(T_{c,out}\) (°C) | 69.43 | 69.43 | 0.00 | PASS |
| Effectiveness \(\varepsilon\) (%) | 82.38 | 82.38 | 0.00 | PASS |
| Overall \(U\) (W/(m²·K)) | 695.8 | 695.8 | 0.00 | PASS |
| LMTD (°C) | 10.57 | 10.57 | 0.00 | PASS |
| MITA (°C) | 10.57 | — | — | PASS |
| \(\Delta P_{hot}\) (bar) | 0.00149 | — | — | PASS |
| \(\Delta P_{cold}\) (bar) | 0.00166 | — | — | PASS |
| \(Re_{hot}\) | 274 | — | — | PASS |
| \(Re_{cold}\) | 239 | — | — | PASS |
Key Findings — Test 1
With balanced flow (\(C_r = 1\)), the DWSIM solver produces an effectiveness of 82.38 %, which matches the analytical \(\varepsilon\)-NTU prediction exactly. The LMTD and MITA coincide at 10.57 °C, which is expected for a balanced counterflow exchanger. Both Reynolds numbers are in the laminar regime, and the overall heat transfer coefficient of 695.8 W/(m²·K) falls within the typical water-water PHE range of 500 -- 1600 W/(m²·K) (Perry and Green, 2008).
Test 2: Unequal Flow — Counterflow (\(C_r = 0.5\))¶
Configuration: 50 plates, 3 mm spacing, 500 x 1000 mm, chevron angle 60°, \(\varphi = 1.17\), \(\dot{m}_{hot} = 2.0\) kg/s, \(\dot{m}_{cold} = 1.0\) kg/s, \(T_{h,in} = 80\) °C, \(T_{c,in} = 20\) °C.
| Check | DWSIM | \(\varepsilon\)-NTU Ref | Error (%) | Status |
|---|---|---|---|---|
| Heat duty \(Q\) (kW) | 243.3 | 243.3 | 0.00 | PASS |
| Hot outlet \(T_{h,out}\) (°C) | 50.90 | 50.90 | 0.00 | PASS |
| Cold outlet \(T_{c,out}\) (°C) | 78.21 | 78.21 | 0.00 | PASS |
| Effectiveness \(\varepsilon\) (%) | 97.02 | 97.02 | 0.00 | PASS |
| Overall \(U\) (W/(m²·K)) | 848.0 | 848.0 | 0.00 | PASS |
| MITA (°C) | 1.79 | — | — | PASS |
| \(Re_{hot}\) | 640 | — | — | PASS |
| \(Re_{cold}\) | 258 | — | — | PASS |
Key Findings — Test 2
When the capacity ratio drops to \(C_r = 0.5\), effectiveness rises to 97.02 % — substantially higher than the balanced case (82.38 %). This is consistent with the theoretical result that counterflow effectiveness increases as \(C_r\) decreases, reaching 100 % in the limit \(C_r \to 0\). The MITA narrows to only 1.79 °C, confirming that the cold outlet closely approaches the hot inlet. The higher hot-side Reynolds number (640 vs. 274) reflects the doubled hot-side mass flow rate and produces a higher overall \(U\) of 848.0 W/(m²·K).
Test 3: 25 Plates — MATLAB Simscape Geometry¶
Configuration: 25 plates, 5 mm spacing, 500 x 1000 mm, chevron angle 60°, \(\varphi = 1.17\), \(\dot{m}_{hot} = \dot{m}_{cold} = 2.0\) kg/s, \(T_{h,in} = 80\) °C, \(T_{c,in} = 20\) °C.
| Check | DWSIM | \(\varepsilon\)-NTU Ref | Error (%) | Status |
|---|---|---|---|---|
| Heat duty \(Q\) (kW) | 306.8 | 306.8 | 0.00 | PASS |
| Hot outlet \(T_{h,out}\) (°C) | 43.30 | 43.30 | 0.00 | PASS |
| Cold outlet \(T_{c,out}\) (°C) | 56.70 | 56.70 | 0.00 | PASS |
| Effectiveness \(\varepsilon\) (%) | 61.16 | 61.16 | 0.00 | PASS |
| Overall \(U\) (W/(m²·K)) | 978.5 | 978.5 | 0.00 | PASS |
| LMTD (°C) | 23.30 | 23.30 | 0.00 | PASS |
| \(Re_{hot}\) | 1262 | — | — | PASS |
| \(Re_{cold}\) | 847 | — | — | PASS |
Key Findings — Test 3
Halving the plate count from 50 to 25 reduces effectiveness from 82.38 % to 61.16 % for the same flow arrangement, as expected from the lower NTU. Despite the lower effectiveness, the overall coefficient is higher (978.5 vs. 695.8 W/(m²·K)) because the wider 5 mm channel spacing at doubled flow rate pushes both Reynolds numbers into a higher range (Re up to 1262), enhancing convective heat transfer. This geometry matches the MATLAB Simscape Plate Heat Exchanger (TL-TL) reference configuration.
Summary¶
| Metric | Test 1 | Test 2 | Test 3 | Max Error (%) |
|---|---|---|---|---|
| \(Q\) (kW) | 206.6 | 243.3 | 306.8 | 0.00 |
| \(\varepsilon\) (%) | 82.38 | 97.02 | 61.16 | 0.00 |
| \(U\) (W/(m²·K)) | 695.8 | 848.0 | 978.5 | 0.00 |
| LMTD (°C) | 10.57 | — | 23.30 | 0.00 |
Aggregate Statistics
All three counterflow tests pass with 0.00 % error on heat duty, effectiveness, overall coefficient, and LMTD. The \(\varepsilon\)-NTU method and the \(Q = UA \cdot \text{LMTD}\) formulation produce identical results in every case, confirming internal consistency of the DWSIM solver. Reynolds numbers span the range 239 -- 1262 and overall coefficients span 695.8 -- 978.5 W/(m²·K), all within expected bounds for water-water plate heat exchangers.