Engineering guide
This module calculates the stirring power in stirred vessels according to Section N3.3 of the VDI-Wärmeatlas (VDI Heat Atlas: Heat transfer and power consumption in stirred vessels, 12th edition, 2019). The power consumption of the impeller is a fundamental quantity in every stirred vessel design: it determines the sizing of drive and gearbox, enters the heat balance of the vessel as dissipated power, and is the reference quantity for scale-up criteria such as the power input per unit volume.
The core of the calculation is the Newton number (power number): it links the stirring power to density, rotational speed and impeller diameter and depends on the impeller Reynolds number, the impeller type (e.g. disc, pitched-blade, propeller or anchor impeller), the geometric installation ratios and the baffling of the vessel. In the laminar regime the Newton number falls in inverse proportion to the Reynolds number; in the fully turbulent regime it is an impeller-specific constant in the baffled vessel.
The required fluid properties – density and dynamic viscosity at the mean temperature of the vessel contents – are provided by the module; with them, both single-phase approaches and the effects of gassed or two-phase operation on the power consumption can be evaluated.
Scope
- Heat transfer and Power consumption in stirred vessels: Stirring Power
Typical workflow
Define impeller geometry and installation
Impeller type, impeller diameter, mounting height, ratio of impeller to vessel diameter and the baffling (number and width of the baffles) are entered – they determine the Newton number characteristic of the system.
Determine fluid properties at the mean temperature
Density and dynamic viscosity of the vessel contents are evaluated at the mean temperature; for non-Newtonian media, a representative apparent viscosity from the mean shear rate in the impeller region must be used.
Form the impeller Reynolds number
From rotational speed, impeller diameter, density and viscosity, the Reynolds number of the impeller is calculated; it decides whether the laminar, transition or turbulent regime applies.
Read the Newton number from the power characteristic
For the chosen impeller type and installation, the power characteristic yields Ne = f(Re): in the laminar regime Ne ~ 1/Re, in the turbulent regime in the baffled vessel a constant, impeller-specific value; in the unbaffled vessel the co-rotating vortex reduces the power consumption.
Calculate and assess the stirring power
The power follows from P = Ne · ρ · n³ · d⁵. It is carried into the drive sizing with margins for start-up, level fluctuations and, if applicable, gassing (reduced power consumption in the gassed state), and is accounted for as dissipated power in the heat balance.
Frequently asked questions
Why does the impeller diameter enter the power with the fifth power?
From dimensional analysis: power is torque times angular velocity; in the turbulent regime the torque scales with the dynamic pressure (ρ·(n·d)²) times blade area (d²) times lever arm (d). In practical terms: enlarging the impeller diameter by just 15 % roughly doubles the power consumption at the same speed – the impeller diameter is the strongest lever in drive sizing.
What role do baffles play for the power consumption?
Without baffles the liquid co-rotates and forms a vortex; the relative velocity between impeller and fluid decreases, and with it the Newton number and the power consumption. Fully baffled vessels (typically four baffles with a width of about one tenth of the vessel diameter) suppress the rotation, maximize the power input and improve mixing. Newton number data always apply to a defined baffling.
How does gassing affect the stirring power?
In gassed operation, gas cavities collect behind the impeller blades; the effective density and the form drag decrease, so that the power consumption can fall to about 40 to 70 % of the ungassed value, depending on the gas flow rate. The drive must nevertheless be sized for the ungassed state, since the full power applies if the gas supply fails.
What must be considered for non-Newtonian media?
The viscosity depends on the local shear rate, which is high in the impeller region and low near the wall. Following the Metzner and Otto concept, a mean shear rate proportional to the rotational speed is applied, and the Reynolds number is formed with the resulting apparent viscosity. In strongly shear-thinning or viscoelastic media, cavern formation and dead zones can significantly alter the actual power consumption and mixing.
Worked example
In a fully baffled stirred vessel (four baffles), a six-blade disc impeller (Rushton turbine) mixes water at 20 °C. This worked example calculates the Reynolds number and the stirring power.
Given
| Impeller diameter d | 0.50 m |
|---|---|
| Rotational speed n | 2.0 1/s (120 min⁻¹) |
| Density of water ρ | 998 kg/m³ |
| Dynamic viscosity of water η | 1.0 · 10⁻³ Pa·s |
| Newton number Ne (Rushton, turbulent, baffled) | ≈ 5.0 |
Solution
Impeller Reynolds number
Re = n · d² · ρ / η = 2.0 · 0.50² · 998 / 0.001
Re ≈ 5.0 · 10⁵
Re lies far above 10⁴ – the flow is fully turbulent, so the Newton number in the baffled vessel is constant.
Stirring power
P = Ne · ρ · n³ · d⁵ = 5.0 · 998 · 2.0³ · 0.50⁵
P = 5.0 · 998 · 8.0 · 0.03125 W ≈ 1,248 W ≈ 1.25 kW
For the drive sizing, margins for start-up, gearbox efficiency and motor reserve are added.
Result
| Reynolds number Re | ≈ 5.0 · 10⁵ (fully turbulent) |
|---|---|
| Stirring power P | ≈ 1.25 kW |
Technical content source: LV-Solved-Problems-Content 628d313247e7