Engineering task and calculation objective
The SAC module calculates the properties of sucrose-water solutions based on the Zuckeratlas (Sugar Atlas) — the standard data compilation of the sugar industry. As a function of temperature and dry substance content, it delivers the density, specific heat capacity, thermal conductivity, dynamic and kinematic viscosity, surface tension, Prandtl number, thermal diffusivity, thermal expansion coefficient and the boiling point elevation of the solution.
Being able to calculate the properties of sugar solutions is a prerequisite for the thermal design of the equipment in sugar factories and in food processing: evaporator stations, vacuum pans (crystallizers), heat exchangers for thin and thick juice, as well as piping and pumps. The viscosity in particular rises by orders of magnitude with sucrose content and governs heat transfer and pressure drop at high concentrations; the boiling point elevation in turn reduces the usable temperature difference in multiple-effect evaporator plants and must be accounted for effect by effect there.
The values apply to pure sucrose-water solutions. Technical juices contain non-sugar substances that alter the viscosity and boiling point elevation in particular compared with the pure solution — in practice, purity corrections are used for this.
Standard and calculation basis: Zuckeratlas
Calculation workflow
- Specify the state of the solution: The inputs are the temperature and the sucrose content (dry substance in mass percent or degrees Brix). These two quantities span the validity range of the Zuckeratlas correlations.
- Density and caloric properties: From temperature and concentration, the density, specific heat capacity and thermal expansion coefficient of the solution are determined according to the Zuckeratlas tables; the heat capacity drops noticeably below the value for water as the sugar content increases.
- Transport properties: Thermal conductivity as well as dynamic and kinematic viscosity are calculated as functions of concentration and temperature; from these follow the thermal diffusivity and Prandtl number for heat transfer correlations.
- Boiling point elevation and surface tension: For evaporation and pan boiling processes, the boiling point elevation relative to pure water at the respective pressure and the surface tension of the solution are reported — input quantities for heating surface sizing and the vapor balance.
Input quantities
| Quantity | Symbol | Unit |
|---|---|---|
| 1 | ϑ1 | °C |
| 2 | ϑ2 | °C |
| Druck | p1 | Pa |
| Xi | c1 | kg/kg |
| 1 | ρ | kg/m³ |
| 1 | cp | J/(kg·K) |
| 1 | τ | °C |
| 1 | λ | W/(m·K) |
| 1 | σ | mN/m |
| 1 | ν | m²/s |
| 1 | η | mPa·s |
| 1 | Pr | - |
| 1 | ρ | kg/m³ |
| 2 | cp | J/(kg·K) |
| 2 | τ | °C |
| 2 | λ | W/(m·K) |
| 2 | σ | mN/m |
| 2 | ν | m²/s |
| 2 | η | mPa·s |
| 2 | Pr | - |
| 2 | p2 | Pa |
| Xi2 | c2 | kg/kg |
| 1 | β | 1/K |
| 2 | β | 1/K |
Frequently asked questions
How strongly does the sugar content affect the viscosity?
Extremely: between thin juice (around 15% dry substance) and thick juice or syrup (70% and more), the dynamic viscosity rises by several orders of magnitude, and at high concentration it is additionally strongly temperature-dependent. That is why highly concentrated streams are run hot, and heat transfer and pressure drop calculations must use the viscosity at the actual operating point — averages over wide concentration ranges are useless.
Why is the boiling point elevation so important for evaporator stations?
In each evaporator effect, the solution boils hotter than pure water at the same pressure by the amount of the boiling point elevation; but the vapor produced condenses in the following effect only at the saturation temperature of water. The boiling point elevation therefore enters each effect as a loss of driving temperature difference. In a multiple-effect station these losses add up and limit the economical number of effects.
Do the values also apply to technical juices containing non-sugar substances?
Only approximately. The Zuckeratlas describes pure sucrose-water solutions. Non-sugar substances (salts, invert sugar, organic matter) increase above all the viscosity and boiling point elevation at the same dry substance content. In practice, a correction via the purity (ratio of sucrose to dry substance) is applied; for low-purity molasses, special approaches are required.
What is the difference between dry substance mass fraction and degrees Brix?
Degrees Brix is defined as the mass percent of sucrose in a pure sucrose solution and is measured refractometrically. For pure solutions, Brix and mass fraction are identical; for technical juices, the refractometric Brix value deviates slightly from the true dry substance content because of the non-sugar substances. For the property calculation, the actual mass fraction is decisive.