Rotating Heated Cylinder Technology for Liquid/Paste Foods

Reference ID: MET-7523 | Process Engineering Reference Sheets Calculation Guide

Introduction & Context

The drum dryer is a critical unit operation in food process engineering, specifically designed for the continuous dehydration of liquid or paste-like food products. The system utilizes a steam-heated rotating cylinder where a thin film of the feed material is applied to the exterior surface. As the drum rotates, heat is transferred via conduction from the internal steam through the metal wall and the product film, resulting in rapid evaporation of moisture.

This calculation is essential for determining the production capacity and thermal requirements of the dryer. It is typically used during the design phase to size equipment based on desired throughput, or during operational optimization to ensure the film remains within stable, laminar flow regimes while achieving target moisture content.

Methodology & Formulas

The following equations define the steady-state performance of the drum dryer, assuming a thin-film approximation where the film thickness is significantly smaller than the drum diameter. The analysis assumes that the liquid feed is preheated and enters the dryer at the film boiling temperature; therefore, the energy balance includes only the latent heat of vaporization. For cold feed, an additional sensible heat term must be incorporated.

1. Rotational Kinematics and Residence Time
The angular velocity (\(\omega\)) and the residence time (\(t_{res}\)) of the product on the heated surface are defined by the drum speed (\(N\)) and the active drying arc (\(\theta\)):

\[ \omega = \frac{2\pi \cdot N}{60} \] \[ t_{res} = \frac{\theta}{\omega} \]

2. Overall Heat Transfer Coefficient
The resistance to heat flow is the sum of the internal steam condensation resistance, the conductive resistance of the drum wall, and the conductive resistance of the product film:

\[ \frac{1}{U} = \frac{1}{h_{steam}} + \frac{L_{wall}}{k_{wall}} + \frac{\delta}{k_{product}} \]

3. Heat Flux and Total Heat Transfer
The heat flux (\(q''\)) is driven by the temperature gradient between the steam and the boiling film. The total heat transfer rate (\(Q\)) is the product of this flux and the active surface area (\(A\)):

\[ q'' = U \cdot (T_{steam} - T_{film}) \] \[ A = \frac{\theta \cdot D \cdot W}{2} \] \[ Q = q'' \cdot A \]

4. Evaporation and Capacity
The water evaporation rate (\(\dot{m}_{water}\)) is derived from the latent heat of vaporization (\(h_{fg}\)). The final dry product capacity (\(\dot{m}_{product}\)) is calculated based on the mass balance of solids:

\[ \dot{m}_{water} = \frac{Q}{h_{fg}} \] \[ \dot{m}_{product} = \dot{m}_{water} \cdot \left( \frac{x_{initial}}{x_{final} - x_{initial}} \right) \]

5. Hydrodynamic Regime
To ensure film stability, the Reynolds number (\(Re_{film}\)) is calculated using the surface velocity (\(V_{surface}\)):

\[ V_{surface} = \omega \cdot \frac{D}{2} \] \[ Re_{film} = \frac{\rho \cdot V_{surface} \cdot \delta}{\mu} \]

Parameter	Operational Threshold / Regime
Film Reynolds Number	9.0 ≤ Re_film ≤ 200.0 (Laminar)
Heat Flux	5.0 ≤ q'' ≤ 50.0 kW/m²
Residence Time	10.0 ≤ t_res ≤ 30.0 s
Steam Temperature	120.0 ≤ T_steam ≤ 155.0 °C
Film Thickness	0.1 ≤ δ ≤ 2.0 mm

The system utilizes a combination of precise thermal transfer and mechanical shear to ensure uniformity. Key factors include:

Continuous surface scraping to prevent localized overheating or fouling.
Controlled rotational speed to manage the residence time of the product.
Uniform heat distribution across the cylinder wall to maintain consistent viscosity throughout the process.

Maintaining hygiene in food processing requires rigorous protocols. Process engineers should focus on:

Implementing Clean-in-Place (CIP) systems that reach all internal contact surfaces.
Verifying that the scraper blade material is compatible with standard caustic and acidic cleaning agents.
Ensuring the cylinder surface finish meets sanitary standards to prevent microbial buildup in microscopic crevices.

Optimizing thermal efficiency involves balancing several operational variables:

Adjusting the gap between the scraper blade and the cylinder wall to minimize the boundary layer thickness.
Modulating the steam pressure or thermal fluid temperature based on the specific heat capacity of the product.
Increasing the rotational frequency to reduce the product film thickness, thereby improving the overall conductive heat transfer coefficient across the film.

Worked Example: Drum Dryer Capacity Calculation for Liquid Paste Food

Consider a horizontal drum dryer used to dry a liquid paste food from 20% solids to 94% solids. The drum is steam-heated internally and rotates at constant speed. The feed is assumed to be preheated to the film boiling temperature, so sensible heating is negligible. The following scenario demonstrates the step-by-step calculation of dryer capacity using standard heat transfer and mass balance equations.

Known Input Parameters and Constants

Drum diameter, D = 1.5 m
Drum width, W = 2.0 m
Rotational speed, N = 3.0 RPM
Active drying arc angle, θ = 4.71 rad (270°)
Steam saturation temperature, T_steam = 145.0 °C
Drum wall thickness (stainless steel), L_wall = 0.012 m
Product film thickness, δ = 0.0004 m
Film temperature (boiling water at atmosphere), T_film = 100.0 °C
Feed temperature (assumed preheated to film temperature), T_feed = 100.0 °C (sensible heat neglected)
Initial solids mass fraction, x_initial = 0.20
Final solids mass fraction, x_final = 0.94
Steam condensation heat transfer coefficient, h_steam = 6000.0 W/m²·K
Thermal conductivity of wall, k_wall = 16.0 W/m·K
Thermal conductivity of product, k_product = 0.6 W/m·K
Latent heat of vaporization at 100°C, h_fg = 2257.0 kJ/kg
Product density, ρ = 1000.0 kg/m³
Product viscosity, μ = 0.01 Pa·s

Step-by-Step Calculation

Angular Velocity
\[ \omega = \frac{2 \pi N}{60} \] From the calculation, ω = 0.314 rad/s.
Residence Time
\[ t_{res} = \frac{\theta}{\omega} \] Using θ = 4.71 rad and ω = 0.314 rad/s, the residence time is 14.992 s.
Overall Heat Transfer Coefficient
\[ \frac{1}{U} = \frac{1}{h_{steam}} + \frac{L_{wall}}{k_{wall}} + \frac{\delta}{k_{product}} \] Substituting the known values:
\[ \frac{1}{U} = \frac{1}{6000} + \frac{0.012}{16} + \frac{0.0004}{0.6} = 0.001583\ \text{m}^2\cdot\text{K/W} \] Therefore, U = 631.579 W/m²·K.
Heat Flux
\[ q'' = U \cdot (T_{steam} - T_{film}) \] With ΔT = 145.0 - 100.0 = 45.0 K, we obtain q'' = 28.421 kW/m² (28421.05 W/m²).
Heat Transfer Area
\[ A = \frac{\theta \cdot D \cdot W}{2} \] Substituting θ = 4.71 rad, D = 1.5 m, W = 2.0 m gives A = 7.065 m².
Total Heat Transfer Rate
\[ Q = q'' \cdot A \] Q = 28421.05 W/m² × 7.065 m² = 200,795 W = 200.795 kW.
Water Evaporation Rate
\[ \dot{m}_{water} = \frac{Q}{h_{fg}} \] Assuming the feed enters at the film temperature, all transferred heat is used for evaporation. Using Q = 200.795 kW and h_fg = 2257 kJ/kg,
\[ \dot{m}_{water} = 0.088965\ \text{kg/s} = 320.275\ \text{kg/h}. \]
Dry Product Capacity
Solids mass balance: \[ \dot{m}_{product} = \dot{m}_{water} \cdot \frac{x_{initial}}{x_{final} - x_{initial}} \] Substituting x_initial = 0.20, x_final = 0.94, and \(\dot{m}_{water}\) = 320.275 kg/h,
\[ \dot{m}_{product} = 320.275 \times \frac{0.20}{0.74} = 86.561\ \text{kg/h}. \]
Film Reynolds Number (Verification)
\[ Re = \frac{\rho \cdot V_{surface} \cdot \delta}{\mu} \] Surface velocity V_surface = ω · D/2 = 0.314 × 0.75 = 0.236 m/s.
Re = (1000 × 0.236 × 0.0004) / 0.01 = 9.425 (laminar, within acceptable bounds).

Final Answer

The dryer produces 86.561 kg/h of product at 94% solids, with a water evaporation rate of 320.275 kg/h. The heat flux (28.421 kW/m²) and residence time (14.992 s) are within typical empirical ranges for thin-film drum dryers.

"Un projet n'est jamais trop grand s'il est bien conçu." — André Citroën

"La difficulté attire l'homme de caractère, car c'est en l'étreignant qu'il se réalise." — Charles de Gaulle