Reference ID: MET-51BD | Process Engineering Reference Sheets Calculation Guide
Introduction & Context
Flame sterilization is a high-intensity thermal processing method used primarily in the canning industry to achieve commercial sterility. Unlike conventional steam retorts, flame sterilization utilizes direct gas flame impingement to rapidly elevate the temperature of the container surface. This process is critical in Process Engineering for its ability to achieve high lethality in short residence times, particularly for liquid or semi-liquid food products. It is typically employed in continuous production lines where rapid heating is required to minimize the total thermal exposure of the product, thereby preserving organoleptic properties while ensuring food safety.
Methodology & Formulas
The thermal profile of a rotating can is modeled using the lumped capacitance method for well‑mixed liquid packs. The system is divided into three distinct thermal zones: the Flame Zone, the Holding Zone, and the Cooling Zone. The core of the calculation relies on the thermal time constant, which dictates the rate of temperature change based on the product mass, heat capacity, and the overall heat transfer coefficient, as well as the can rotation speed.
The thermal time constant \(\tau\) (in seconds) is defined as:
\[ \tau = \frac{m \cdot C_{p}}{U \cdot A} \]
For calculations in minutes, divide the result by 60: \(\tau_{\text{min}} = \tau / 60\).
The temperature profile \(T(t)\) within any zone is governed by the transient heat transfer equation:
The lethality of the process, expressed as the \(F_{0}\) value, is calculated by integrating the time-temperature history relative to the reference temperature of \(121.1^\circ C\) with a standard \(z\)-value of \(10^\circ C\):
\(300^\circ C \leq T_{\text{flame}} \leq 400^\circ C\)
Product Degradation
Maximum Hold Temperature
\(T_{\text{hold}} \leq 140^\circ C\)
Thermal Time Constant
Validity Check
\(\tau > 0\)
Cooling Lethality
Integration Limit
\(T(t) > 100^\circ C\)
Calculation Steps:
Step 1: Flame Zone Exit: Calculate the bulk temperature at the end of the flame impingement period using the initial product temperature.
Step 2: Holding Zone Iteration: Determine the required hold time by numerically integrating the lethality until the cumulative \(F_{0}\) reaches the target value, accounting for the lethality accumulated in the flame zone.
Step 3: Cooling Zone Tail: Integrate the residual lethality during the cooling phase, considering only the time intervals where the product temperature remains above the threshold of \(100^\circ C\).
In flame sterilization of canned liquid products, the flame zone typically operates between \(300^\circ C\) and \(400^\circ C\) to achieve rapid surface heating without scorching. The product bulk temperature should be kept below \(140^\circ C\) to prevent thermal degradation. The holding zone maintains a constant elevated temperature (e.g., \(130^\circ C\)) to accumulate the required lethality.
The residence (dwell) time in each zone directly influences the temperature profile and the accumulated \(F_0\) value:
Flame zone: A short dwell time (1–2 min) rapidly raises the product temperature; insufficient time may not bring the bulk temperature high enough.
Holding zone: The required dwell time is determined iteratively to achieve the target lethality; longer times increase sterility but risk over-processing.
Cooling zone: Significant lethality continues until the product temperature drops below \(100^\circ C\); the cooling dwell time must be long enough to safely handle the product.
Process deviations can arise from variations in:
Can rotation speed: Affects mixing and the overall heat transfer coefficient \(U\).
Product fill volume and viscosity: Alter the thermal time constant \(\tau\).
Flame stability and gas supply pressure: Change the heat input to the can surface.
Ambient conditions in the holding and cooling zones: Affect the effective zone temperatures.
These factors shift the temperature profile and must be monitored to ensure the target \(F_0\) is achieved.
Worked Example: Flame Sterilization of a Liquid Product in a Rotating Can
A low-viscosity liquid product (e.g., evaporated milk) in a 307×409 can is sterilized using a flame sterilizer with a pre-heating flame zone, a hot air holding zone, and a water cooling zone. The product is well-mixed due to continuous rotation, allowing the use of a lumped capacitance model. The target lethality is \(F_0 = 6.0\) minutes. The process parameters and computed results are given below.
Known Input Parameters
Initial product temperature: \(T_{\text{init}} = 25.0\) °C
Flame zone temperature: \(T_{\text{flame}} = 400.0\) °C
Hold zone temperature: \(T_{\text{hold}} = 130.0\) °C
Cooling zone temperature: \(T_{\text{cool}} = 25.0\) °C
Residence time in flame zone: \(t_{\text{flame}} = 1.0\) min
Residence time in cooling zone: \(t_{\text{cool}} = 5.0\) min
Overall heat transfer coefficient: \(U = 200.0\) W/(m²·K)
Product mass: \(m = 0.5\) kg
Product specific heat: \(C_p = 4000.0\) J/(kg·K)
Can surface area: \(A = 0.04\) m²
Reference temperature: \(T_{\text{ref}} = 121.1\) °C
Thermal death time z-value: \(z = 10.0\) °C
Target lethality: \(F_{0,\text{target}} = 6.0\) min
With \(\Delta t = 0.01\) min and the temperature history \(T_b(t)\) from the lumped capacitance model, the result is \(F_{0,\text{flame}} = 0.001\) min (the exact value is approximately \(1.4 \times 10^{-3}\) min).
Find the hold time required to achieve the target total lethality.
The remaining lethality needed from the hold zone is
The hold zone is simulated by integrating the lethality from the start of holding until the accumulated lethality reaches this target. The simulation uses the bulk temperature evolution:
The iteration finds that when \(F_{0,\text{hold}}^{\text{accumulated}} = 5.999\) min, the required hold time is \(t_{\text{hold}} = 6.89\) min. At this moment the bulk temperature at the exit of the hold zone is \(T_{\text{hold,exit}} = 125.219\) °C.
Compute the lethality contributed by the cooling zone.
The cooling zone model uses the same lumped capacitance approach with initial temperature \(T_{\text{hold,exit}}\) and final ambient \(T_{\text{cool}}\). The lethality integral is evaluated until the bulk temperature falls below 100 °C. The result is \(F_{0,\text{cool}} = 0.499\) min.
Sum the component lethalities to obtain the total process lethality.
Rounding to three decimal places gives \(F_{0,\text{total}} \approx 6.500\) min.
Final Answer
The calculated total process lethality is \(F_{0,\text{total}} = 6.500\) min for a flame zone residence time of 1.0 min, a hold zone time of 6.89 min, and a cooling zone time of 5.0 min. The exit temperature from the flame zone is 105.015 °C, and the exit temperature from the hold zone is 125.219 °C.
"Un projet n'est jamais trop grand s'il est bien conçu."— André Citroën
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