Engineering task and calculation objective
The module calculates pressure drop and heat transfer in plate heat exchangers with corrugated plates according to chapter N6 of the VDI Wärmeatlas (VDI Heat Atlas, 12th edition 2019). From the operating data of both sides — mass or volume flow rate, inlet pressure, inlet and outlet temperatures — and the physical properties (density, heat capacity, thermal conductivity, dynamic viscosity, Prandtl number, each also at wall temperature), the flow velocity, Reynolds number, friction factor, pressure gradient and pressure drop as well as the heat transfer and the transferable duty of both channel sides are determined.
Anyone who designs or rates compact equipment for liquid-to-liquid duties needs to calculate plate heat exchangers: district heating substations, cooling circuits, process heat recovery, food and HVAC applications. The herringbone embossing (chevron corrugation) of the plates generates turbulence-like flow even at small Reynolds numbers and thus high heat transfer coefficients in a small footprint — at the price of comparatively high pressure drops, which must always be checked as part of the design.
The calculation is based on the VDI Wärmeatlas concept for chevron plates, in which the chevron angle, amplitude and wavelength of the corrugation enter the heat transfer correlation via a generalized pressure drop relationship; fouling factors of both sides are accounted for in the overall heat transfer.
Standard and calculation basis: VDI-Wärmeatlas, 12. Auflage 2019
Calculation workflow
- Define plate geometry and pass arrangement: The plate dimensions, chevron angle, amplitude and wavelength of the corrugation, number of plates and the arrangement (single-pass or multi-pass, counter-current or co-current) are defined. From these follow the hydraulic diameter, surface enlargement factor and the number of parallel channels per side.
- Set up the balance and mean temperature difference: From the mass flow rates, inlet and outlet temperatures and heat capacities of both sides, the duty is balanced and the logarithmic mean temperature difference of the chosen arrangement is determined; the physical properties are evaluated at the mean temperatures.
- Determine the flow conditions for each channel side: From the mass flow per channel and the gap cross-section follows the flow velocity, and from it, with the hydraulic diameter, the Reynolds number. Because of the corrugation, the transition to quasi-turbulent flow occurs at very low Reynolds numbers.
- Calculate the pressure drop: The friction factor is determined as a function of Reynolds number and chevron angle from the generalized relationship for chevron plates; from this follow the pressure gradient and pressure drop per side, plus the contributions from the inlet and outlet ports and the distribution channels.
- Determine heat transfer and overall heat transfer: Using the analogy between momentum and heat transport, the Nusselt number of each side is calculated from the friction behavior, corrected with the viscosity ratio at wall temperature. With the plate thickness, wall material and the fouling factors of both sides, the overall heat transfer coefficient is obtained.
- Perform the surface area check: The available transfer surface is compared with the required surface obtained from duty, overall heat transfer coefficient and mean temperature difference; in parallel, it is checked whether the permissible pressure drops of both sides are maintained. Transfer margin and pressure drop together determine the choice of plate number and chevron angle.
Input quantities
| Quantity | Symbol | Unit |
|---|---|---|
| Wall thickness of the plates | sW | m |
| Thermal conductivity of wall material | λW | W/(m·K) |
| Amplitude | Amplitude â | m |
| Corrugation length | Λ | m |
| Angle of embossing | φ | ° |
| Angle of embossing | φ1 φ2 | ° |
| Angle of embossing | φ1 φ2 | ° |
| Number of corrugations | X | - |
| Area enlargement factor | Φ | - |
| Hydraulic diameter | dh | m |
| Empirical constants | a = b = c = | - |
| Empirical constants | a = b = c = | - |
| Empirical constants | a = b = c = | - |
| Mass flow | m | kg/s |
| Mass flow | m | kg/s |
| Inlet temperature | ϑe | °C |
| Inlet temperature | ϑe | °C |
| Outlet temperature | ϑa | °C |
| Outlet temperature | ϑa | °C |
| Wall temperature | ϑw | °C |
| Wall temperature | ϑw | °C |
| Specific heat capacity | cp | J/(kg·K) |
| Specific heat capacity | cp | J/(kg·K) |
| Density | ρ | kg/m³ |
Frequently asked questions
What role does the chevron angle of the plates play?
The chevron angle is the most important design parameter: shallow, soft corrugations give low pressure drops at moderate heat transfer, while aggressive corrugations with a large angle generate intensive swirling flow with high transfer coefficients and high pressure drops. By mixing differently embossed plates in the pack, the thermal length can be finely matched to the duty — exactly this relationship is captured by the correlations via the angle-dependent friction factor.
Why are plate heat exchangers so much more compact than shell-and-tube units?
The corrugation forces the flow into a quasi-turbulent state already at Reynolds numbers of a few hundred, so heat transfer coefficients are achieved that would require far higher velocities in a tube. Together with thin plates, small gap widths and nearly ideal counter-current flow, the required surface drops significantly; temperature approaches of 1–2 K are economically feasible.
How is fouling included in the calculation, and what must be observed?
The fouling factors of both sides are included as additional resistances in the overall heat transfer. Important: for plate units, significantly smaller fouling factors apply than the values familiar from shell-and-tube practice, because the high wall shear stress inhibits deposit formation. If shell-and-tube fouling values are adopted unchecked, the unit is heavily oversized, which lowers the flow velocity and can, paradoxically, promote fouling.
Where are the application limits of gasketed plate heat exchangers?
The limiting factor is the elastomer gaskets: depending on the material, about 150–180 °C and usually up to around 25 bar. For higher pressures and temperatures or critical media, brazed or fully welded plate units come into consideration. In addition, the narrow gaps are sensitive to solids-laden media and fibers; wide-gap plates or other designs should be chosen there.