Film vs Flooded Configurations for Food Applications

Reference ID: MET-2874 | Process Engineering Reference Sheets Calculation Guide

Introduction & Context

In process engineering, particularly within the food and beverage industry, the selection of an evaporator configuration is critical for maintaining product quality. The choice between Falling Film, Climbing Film, and Flooded (Forced Circulation) configurations is primarily driven by the rheological properties of the fluid, the heat sensitivity of the product, and the required residence time.

Falling film evaporators are preferred for heat-sensitive liquids (e.g., fruit juices, milk) due to their low residence time and high heat transfer coefficients at low temperature gradients. Conversely, flooded configurations are utilized for high-viscosity products where gravity-driven flow is insufficient to maintain a stable film. Understanding the transition between these regimes is essential for preventing thermal degradation, fouling, and dry-out conditions.

Methodology & Formulas

The following calculations determine the hydraulic and thermal performance of a vertical falling film evaporator. The logic relies on the film Reynolds number to characterize the flow regime and the Nusselt film thickness to estimate the heat transfer coefficient.

1. Hydraulic Parameters

The film load Γ represents the mass flow per unit wetted perimeter, which dictates the film Reynolds number Re_δ:

\[ \Gamma = \frac{\dot{m}}{N_{\text{tubes}} \cdot \pi D_{\text{tube}}} \] \[ Re_{\delta} = \frac{4\Gamma}{\mu} \]

2. Film Thickness and Residence Time

The film thickness δ is calculated based on the laminar Nusselt theory, assuming gravity-driven flow. The average velocity v_avg and residence time τ are then derived:

\[ \delta = \left( \frac{3 \mu \Gamma}{\rho^2 g} \right)^{1/3} \] \[ v_{\text{avg}} = \frac{\Gamma}{\rho \delta} \] \[ \tau = \frac{L_{\text{tube}}}{v_{\text{avg}}} \]

3. Heat Transfer and Overall Coefficient

The film heat transfer coefficient h_f is determined using the wavy‑laminar correlation, and the overall heat transfer coefficient and boiling mechanisms are then calculated by summing the individual thermal resistances.

\[ h_{f} = \frac{k}{\delta} \cdot 0.606 \cdot (Re_{\delta})^{0.11} \cdot (Pr)^{0.5} \] \[ \frac{1}{U} = \frac{1}{h_{f}} + R_{\text{foul}} + R_{\text{wall}} + \frac{1}{h_{\text{steam}}} \]

Operational Regimes and Constraints

Parameter	Constraint / Threshold	Engineering Implication
Film Reynolds (Re_δ)	30 ≤ Re_δ ≤ 1800	Below 30 risks dry spots; above 1800 indicates turbulent transition.
Film Thickness (δ)	δ ≤ 0.002 m	Exceeding 2 mm indicates poor wetting and high fouling risk.
Residence Time (τ)	τ ≤ 300 s	Exceeding 5 minutes risks thermal damage to heat-sensitive food products.
Viscosity (μ)	μ ≤ 0.2 Pa·s	High viscosity requires forced circulation or scraped surface designs.
Temperature Gradient (ΔT)	ΔT ≤ 20 K	High gradients trigger uncontrolled nucleate boiling within the film.

Film evaporators offer superior heat transfer coefficients for heat-sensitive food products because they minimize residence time and hydrostatic head pressure. In contrast, flooded configurations provide:

Higher thermal stability for large-scale batch processing.
Better handling of viscous fluids that might otherwise foul a thin-film surface.
Reduced risk of dry-out zones during fluctuations in feed rate.

For heat-sensitive applications, the falling film configuration is generally preferred. This choice is driven by the following process requirements:

Lower operating temperatures to preserve nutritional integrity and flavor profiles.
Short contact time with the heating surface to prevent thermal degradation.
Lower pressure drop across the heat exchanger, which is critical for vacuum-based concentration processes.

CIP protocols vary significantly based on the internal geometry of the evaporator:

Falling film units require precise liquid distribution at the top of the tubes to ensure full wetting during the cleaning cycle.
Flooded systems often require higher flow velocities or specialized chemical circulation to ensure that stagnant zones within the shell side are fully sanitized.
Both systems must be validated for the removal of proteinaceous or sugary residues common in food production.

Worked Example: Falling Film Evaporator for Orange Juice Concentration

A falling film evaporator is designed to concentrate orange juice from 11°Brix to 66°Brix. The feed rate is 0.278 kg/s, with an evaporation rate of 0.231 kg/s. Saturated steam at 70 °C provides a temperature difference of 20 K. The tube geometry is 0.04 m diameter and 6.0 m length. Product properties: density 1050 kg/m³, viscosity 0.002 Pa·s, thermal conductivity 0.6 W/(m·K), Prandtl number 3.4. Steam-side coefficient 6000 W/(m²·K), fouling resistance 0.0002 m²·K/W, wall resistance 0.0001 m²·K/W. An initial target overall coefficient of 2000 W/(m²·K) required 18 tubes, but film hydraulics proved this unachievable; the design was iterated to 42 tubes. The following calculations verify performance.

Knowns (input parameters):

Feed mass flow rate, \(\dot{m}_{\text{feed}} = 0.278\) kg/s
Evaporation rate, \(\dot{m}_{\text{evap}} = 0.231\) kg/s
Temperature difference, \(\Delta T = 20.0\) K
Tube diameter, \(D_{\text{tube}} = 0.04\) m
Tube length, \(L_{\text{tube}} = 6.0\) m
Density, \(\rho = 1050.0\) kg/m³
Dynamic viscosity, \(\mu = 0.002\) Pa·s
Thermal conductivity, \(k = 0.6\) W/(m·K)
Prandtl number, \(Pr = 3.4\)
Latent heat, \(\lambda = 2.38 \times 10^6\) J/kg
Steam-side coefficient, \(h_{\text{steam}} = 6000.0\) W/(m²·K)
Fouling resistance, \(R_{\text{foul}} = 0.0002\) m²·K/W
Wall resistance, \(R_{\text{wall}} = 0.0001\) m²·K/W
Number of tubes, \(N_{\text{tubes}} = 42\)

Step-by-step calculation:

Thermal duty: \(\dot{Q} = \dot{m}_{\text{evap}} \cdot \lambda = 0.231 \cdot 2.38 \times 10^6 = 549780\) W.
Total wetted perimeter: \(W_{\text{perimeter}} = N_{\text{tubes}} \cdot \pi \cdot D_{\text{tube}} = 42 \cdot 3.1416 \cdot 0.04 = 5.278\) m.
Film load: \(\Gamma = \dfrac{\dot{m}_{\text{feed}}}{W_{\text{perimeter}}} = \dfrac{0.278}{5.278} = 0.0527\) kg/(m·s).
Film Reynolds number: \(Re_{\delta} = \dfrac{4\Gamma}{\mu} = \dfrac{4 \cdot 0.0527}{0.002} = 105.4\) (valid wavy‑laminar regime: 30–1800).
Nusselt film thickness: \(\delta = \left( \dfrac{3 \mu \Gamma}{\rho^2 g} \right)^{1/3} = \left( \dfrac{3 \cdot 0.002 \cdot 0.0527}{1050^2 \cdot 9.81} \right)^{1/3} = 3.08 \times 10^{-4}\) m (0.308 mm).
Average film velocity: \(v_{\text{avg}} = \dfrac{\Gamma}{\rho \delta} = \dfrac{0.0527}{1050 \cdot 3.08 \times 10^{-4}} = 0.163\) m/s.
Residence time: \(\tau = \dfrac{L_{\text{tube}}}{v_{\text{avg}}} = \dfrac{6.0}{0.163} = 36.8\) s (well below the 5‑minute limit).
Film Nusselt number (wavy‑laminar correlation): \(Nu_{\delta} = 0.606 \, Re_{\delta}^{0.11} Pr^{0.5} = 0.606 \cdot (105.4)^{0.11} \cdot (3.4)^{0.5} = 1.865\).
Film heat transfer coefficient: \(h_f = \dfrac{k}{\delta} \cdot Nu_{\delta} = \dfrac{0.6}{3.08 \times 10^{-4}} \cdot 1.865 = 3633\) W/(m²·K).
Overall heat transfer coefficient: \(\dfrac{1}{U_{\text{real}}} = \dfrac{1}{h_f} + R_{\text{foul}} + R_{\text{wall}} + \dfrac{1}{h_{\text{steam}}} = \dfrac{1}{3633} + 0.0002 + 0.0001 + \dfrac{1}{6000} = 0.000742\) m²·K/W. Therefore, \(U_{\text{real}} = \dfrac{1}{0.000742} = 1348\) W/(m²·K).

Final Answer: With 42 tubes, the falling film evaporator achieves \(U_{\text{real}} \approx 1348\) W/(m²·K) and a residence time of 36.8 seconds. This confirms the configuration is suitable for heat-sensitive orange juice; the initial target of 2000 W/(m²·K) was unrealistic for a gravity‑driven film without boiling.

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