Engineering task and calculation objective
Module BIER provides the temperature-dependent physical properties of wort and beer — the basis of every thermal calculation in the brewery. The data source is the revised and extended property series by R. Wasmund (Berlin 1975), which cover the temperature range from 0 to 75 °C relevant to brewing processes.
The mechanical and thermal properties are determined: density, dynamic viscosity, specific heat capacity, thermal conductivity, thermal diffusivity, thermal expansion and Prandtl number. These properties differ markedly from pure water — dissolved extract (original gravity) increases density and viscosity and lowers the heat capacity — so designs based on water properties produce systematic errors.
The properties of wort and beer are needed wherever heat exchangers, wort coolers, plate units, mashing and CIP processes are calculated or pumps and piping are sized in beverage and food engineering: heat transfer coefficients, pressure drops and heating or cooling times depend directly on the density, viscosity, thermal conductivity and Prandtl number of the product.
Standard and calculation basis: R. Wasmund, "Überarbeitete und erweiterte Reihen der mechanischen und thermischen Stoffwerte von Würze und Bier..", Berlin 1975
Calculation workflow
- Select product and concentration: It is defined whether wort or beer is considered, together with the associated concentration (original gravity or extract content). Besides temperature, the extract fraction is the governing influence on all properties.
- Specify the temperature: The operating temperature is set within the validity range of 0 to 75 °C — from the fermentation and lagering cellar near 0 °C through cooling and heat exchanger processes up to the hot wort at the end of cooling.
- Evaluate the properties: From the stored Wasmund series, density, viscosity, heat capacity, thermal conductivity, thermal diffusivity and thermal expansion coefficient are interpolated as functions of temperature; the Prandtl number is formed from viscosity, heat capacity and thermal conductivity.
- Transfer the values into the process calculation: The determined properties feed into downstream calculations: Reynolds and Nusselt numbers for the heat transfer in the wort cooler, pressure drop and pump sizing, heating and cooling times of tanks. For averaging over a temperature range, the properties are evaluated at the mean fluid temperature.
Input quantities
| Quantity | Symbol | Unit |
|---|---|---|
| Temperature | ϑ | °C |
| Temperature | ϑ | °C |
| Pressure | p | Pa |
| Pressure | p | Pa |
| Density | ρ | kg/m³ |
| Density | ρ | kg/m³ |
| Specific heat capacity | cp | J/(kg·K) |
| Thermal conductivity | λ | W/(m·K) |
| Thermal diffusivity | a | m²/s |
| Kinematic viscosity | ν | m²/s |
| Dynamic viscosity | η | mPa·s |
| Prandtl number | Pr | - |
| Specific heat capacity | cp | J/(kg·K) |
| Thermal conductivity | λ | W/(m·K) |
| Thermal diffusivity | a | m²/s |
| Kinematic viscosity | ν | m²/s |
| Dynamic viscosity | η | mPa·s |
| Prandtl number | Pr | - |
| Sorte | Sorte | – |
| Coefficient of thermal expansion | β | 1/K |
| Coefficient of thermal expansion | β | 1/K |
Calculation options
Sorte
Wort · Beer
Frequently asked questions
Why can't I simply calculate with the properties of water?
Depending on the original gravity, wort contains 10 to 20 % dissolved extract. This increases the density by several percent and the viscosity considerably, while the specific heat capacity drops compared with water. In heat exchanger design, these deviations act directly on the heat transfer coefficient via the Reynolds and Prandtl numbers — with water properties, a wort cooler is systematically designed too optimistically.
For which range are the Wasmund property series valid?
The validity range extends from 0 to 75 °C and thus covers fermentation, lagering, filtration and the usual cooling and heating processes. Boiling wort (100 °C) or processes above 75 °C lie outside the range; extrapolating the series is not permissible — other data sources must be used there.
What role does the Prandtl number play in practice?
The Prandtl number links momentum and heat transport and enters practically all Nusselt correlations for forced and free convection. Since the viscosity of wort and beer rises sharply with falling temperature, the Prandtl number also grows considerably in the cold — the heat transfer in cold wort or beer cooling is therefore noticeably poorer than on the warm side of the same unit.
Does the module also account for dissolved CO2 in the beer?
The Wasmund series describe the liquid phase; the influence of carbonation on the single-phase properties is small and is contained within the data accuracy or negligible. However, as soon as CO2 comes out of solution — for example on pressure relief or in filling processes — a two-phase flow develops that can no longer be described with single-phase properties.