Engineering task and calculation objective
This module calculates heat transfer in regenerators according to the VDI Heat Atlas (VDI-Wärmeatlas, 12th edition 2019). Regenerators transfer heat not continuously through a dividing wall but with a time offset via a storage mass: during the warm period, the hot gas gives up heat to the checkerwork (plates, cylinders, packed beds of spheres or shaped bricks); during the cold period, the cold gas takes this heat up again. The calculation follows the classical regenerator theory of Hausen with the concept of the real (effective) overall heat transfer coefficient.
In practice, this calculation is needed for hot blast stoves (Cowpers) at blast furnaces, regenerative chambers of glass melting furnaces, rotary air preheaters in power plants (Ljungström), regenerators in cryogenic and Stirling processes, and regenerative thermal oxidizers. Unlike a recuperator, the process is unsteady and periodic: to calculate a regenerator, the design must account not only for heat transfer but also for the storage capacity of the mass and the period durations.
Standard and calculation basis: VDI-Wärmeatlas, 12. Auflage 2019
Calculation workflow
- Define periods and gas flows: The inputs are the durations of the warm and cold periods, the mass flows of both periods with their mean specific heat capacities, and the inlet temperatures of the hot and cold gas. From these follow the heat capacity flows of both sides.
- Describe the storage mass and geometry: The checkerwork is characterized by hydraulic diameter, free flow cross-section, specific heating surface per m³ and the equivalent wall thickness; for the storage mass, density, heat capacity, thermal conductivity and thermal diffusivity are entered.
- Determine heat transfer in both periods: The real heat transfer coefficients are determined for the warm and cold periods. In addition to convection at the surface, they account for the unsteady heat conduction into the storage mass, which depends on the equivalent wall thickness and the thermal diffusivity.
- Form the real overall heat transfer coefficient: Following Hausen's theory, the period-related transfer coefficients are combined with the period durations into a real overall heat transfer coefficient, which allows the regenerator to be treated computationally like a continuously operating counterflow heat exchanger. Auxiliary ratios (e.g. the ratio from figure 12 of the Heat Atlas) correct for the influence of finite storage capacity.
- Calculate duty and temperatures: Using the real overall heat transfer coefficient, the heat transfer surface and the logarithmic temperature difference, the time-averaged outlet temperatures of both gases and the heat transferred per full period are determined.
Input quantities
| Quantity | Symbol | Unit |
|---|---|---|
| Length of the warm period | t1 = | s |
| Length of the cold period | t2 = | s |
| Real heat transfer coefficient | α1 = | W/(m²·K) |
| Real heat transfer coefficient | α2 = | W/(m²·K) |
| Hydraulic diameter of the flow channel | dh = | m |
| Part of the free flow cross-section | φ = | - |
| Specific heating surface per m3 checkerwork | fV = [1] | m²/m³ |
| Equivalent wall thickness δeq | = [2] | m |
| Heat transfer surface of the storage matrices | A = | m² |
| Volume of solids of the storage matrices | VS = | m³ |
| Thermal conductivity of the storage matrices | λS = | W/(m·K) |
| Density of the storage matrices | ρS = | kg/m³ |
| Specific heat capacity of the storage matrices | cp,S = | J/(kg·K) |
| Heat capacity of the storage matrices | CS = | J/K |
| Thermal diffusivity of storage matrices | a = | m²/s |
| Mass flow in the warm period | M1 = | kg/s |
| Mean specific heat capacity | cp,1 = | J/(kg·K) |
| Heat capacity flow 1 | W1 = | W/K |
| Mass flow in the cold period | M2 = | kg/s |
| Mean specific heat capacity | cp,2 = | J/(kg·K) |
| Heat capacity flow 2 | W2 = | W/K |
| Mean heat capacity of both gas flows | CPer = | J/K |
| Overall heat transfer coefficient basic oscillation | k0 = [6] | W/(m²·K) |
| Ratio (figure 12) | k/k0 = | - |
Frequently asked questions
How does a regenerator differ from a recuperator?
In a recuperator, both media flow simultaneously and exchange heat through a dividing wall — the process is steady. In a regenerator, the media flow through the same storage mass one after the other in time; here the wall is not a separating surface but a heat store. As a result, the outlet temperatures fluctuate periodically, and the design is carried out with time-averaged quantities. Regenerators achieve very large specific heating surfaces and are particularly suitable for high temperatures and dust-laden gases.
What is the real heat transfer coefficient, and why is the convective value not enough?
The convective heat transfer coefficient describes only the transfer from the gas to the surface of the storage mass. During the period, however, the heat penetrates the mass in an unsteady manner; the surface temperature runs ahead of the core temperature. The real heat transfer coefficient according to Hausen therefore contains an additional term involving the equivalent wall thickness and the thermal conductivity of the storage mass — it is always smaller than the purely convective value, especially for thick bricks and short periods.
What does the equivalent wall thickness of the checkerwork mean?
The equivalent wall thickness is the ratio of the solid volume to the heat transfer surface of the storage mass. It converts arbitrary brick shapes (plates, cylinders, spheres, honeycomb bricks) into an equivalent plane wall for which the unsteady penetration calculation is performed. Shape factors account for the fact that cylinders and spheres heat through faster than plates at the same equivalent wall thickness.
What role do the period durations play in the design?
Long periods exploit the storage mass deeply, but lower the real overall heat transfer coefficient and increase the temperature fluctuation of the exiting gas. Short periods keep the outlet temperature more uniform, but increase switching losses and valve wear. The calculation with this module shows how period duration, storage mass and the heat transferred per full period influence one another — the choice is always a compromise.