FOOD3801/8801 2025 assignment two: evaporation
Due date: Wednesday, 16/07/2025 (Week 7), 7 p.m. AEST
Submission via Moodle workshop tool and completion of quiz
Introduction to assignments for FOOD3801/8801
The assignments for this course have been designed to enhance your learning of important unit operations in the food industry. These assignments will complement the material presented in the lectures and give you an opportunity to practise and develop your problem-solving and critical-thinking skills.
Whilst the assignments may seem quite long and in-depth, you certainly have the skills and knowledge that you need to solve them. In most of the problems, the questions have been set up in a way to guide you through the problem. Again, these assignments have been designed to help you learn and to develop your problem-solving skills. We suggest you work through the example problems in the lectures, and tackle some of the problems in the prescribed textbook, as they will be of help.
It is true that you may find some parts of the assignment challenging, and some answers will not be immediately obvious, particularly for questions that require analysis and/or solving of potential real-life industry issues. However, the reason for their inclusion is to give you an experience of the types of real-life challenges that you may face as a food scientist or food technologist working in the food industry. How do you handle issues like a malfunctioning cool room, or a dryer making a product that is too high in moisture, or your packaged food product still becoming spoiled quickly? These are the types of challenges we hope to expose you to throughout the Term to enhance your skills to become confident food scientists and food technologists!
The questions of this second assignment are on the topic of evaporation. In this assignment, you have been given a “design brief”, where you will need to make a recommendation to your company for the purchase of a new evaporator. You will solve problems based on given specifications and analyse the options, before making a final recommendation to the company.
Project brief
A company needs to buy a new single-effect evaporator to concentrate 40,000 kg/h of a juice from 4% to 40% solids. The juice will enter the evaporator at 45 °C as it will be preheated with residual hot water streams via heat exchangers already available in the company. The evaporation chamber can perform the evaporation at a maximum temperature of 45 °C for two reasons: 1) to avoid externally high costs of higher vacuum pressures, which will be needed to reduce the temperature below 45 °C; and, 2) to minimise the damage of heat-sensitive compounds and the loss of volatile flavour compounds, which will be exacerbated for temperatures above 45 °C. The evaporator needs to be operated with saturated steam at 120 °C, which is already produced at this temperature in other food manufacturing processes in the company.
The properties of the juice, which are independent of temperature, are approximated as follows:
• Density = 1,020 kg/m3
• Viscosity = 0.0035 Pa.s
• Thermal conductivity = 0.5 W/(m.K)
• You can estimate the specific heat capacity of the feed and the concentrated product with the Siebel (1892) model below, where the specific heat is a function of the concentration of solids as:
CP = 0.837 + 3.349(1 — xS)
After looking into several types of evaporators and contacting different manufacturers, the company was able to narrow down their options to two evaporators (whose specifications are described in more detail below):
1. A forced recirculation evaporator with an external calandria.
2. A falling film evaporator with an external calandria.
Which evaporator do you recommend the company to purchase, based on cost and the quality constraints of the juice? Give reasons for your recommendation.
Hint: Please carefully study the lecture notes “11_Heat exchanger for evaporation”, which explains in detail how to solve problems on forced recirculation and falling film evaporators. Please pay close attention to examples 1 to 4.
Note: you are advised to make all calculations in Excel. This series of calculations are greatly affected by rounding in errors, which are minimized (or eliminated) by calculating everything in a spreadsheet.
Option 1: forced recirculation evaporator
The first option, the forced recirculation evaporator, has its pressure maintained in the heat exchanger, such that no boiling occurs in the tubes of the calandria; all the evaporation takes place at the evaporation chamber because of flash. The recirculation is achieved with a pump that recirculates the juice from the evaporation chamber to the calandria and back to the recirculation chamber. The pump creates a strong recirculation and raises the pressure of the juice in the calandria to avoid evaporation. The calandria rises the temperature of the juice from 45 °C to 83 °C before being released into the evaporation chamber. In the evaporation chamber, the pressure is reduced, allowing for flash evaporation at 45 °C (temperature on the evaporation chamber). The strong recirculation introduced by the pump ensures that the concentration of solids of the liquid juice inside the evaporator, including the juice passing through the calandria, is the same of that of the concentrated product, i.e., the concentration of solids of the juice in the evaporator and through the calandria is that of the final product. The tubes of the calandria have the following properties:
• Pipe inner diameter (I.D.) = 60 mm
• Pipe outer diameter (O.D.) = 62 mm
• Length of the tubes = 25 m
• Pipe material: stainless steel
• Thermal conductivity of steel = 15 W/(m.K)
The overall cost of this evaporator can be roughly correlated with the price of the number of tubes in the calandria plus the cost of the recirculation pump. The cost per tube is $2,000 and the cost of the pump is $30,000.
Option 2: falling film evaporator
The second option, the falling film evaporator, has the following properties:
• Pipe inner diameter (I.D.) = 360 mm
• Pipe outer diameter (O.D.) = 364 mm
• Length of the tubes = 12 m
• Pipe material: stainless steel
• Thermal conductivity of steel = 15 W/(m.K)
The overall cost of this evaporator can be roughly correlated with the price of the number of tubes in the calandria plus the cost of the flow distribution system into the tubes. The cost per tube is $7,000 and the cost of the flow distribution system is $30,000.
Question 1
This question will be based on the first option of evaporator, the forced recirculation evaporator.
1) Briefly explain how a forced recirculation evaporator works. 2
2) What are some advantages of using a forced recirculation evaporator? 2
3) Draw a diagram of the evaporation process, making sure that you include the calandria (vertically orientated), the evaporation chamber, and the recirculation pump. Add the data you know into the diagram. 2
Estimate the enthalpies for the flow components in the process (this will be used later on the energy balances).
4) Calculate the enthalpy of the feed juice Hf using 0 °C as the reference temperature. 1
5) Similarly, calculate the enthalpy of the concentrated product juice Hc using 0 °C as the reference temperature.
Using the steam table provided, estimate the enthalpy of the vapour Hv1 . 1
9) Calculate the enthalpy of the juice at the outlet of the calandria HRo . 1
In the diagram, add the enthalpy data and identify the unknow variables. Some of the unknown mass flowrates can be calculated with mass balances.
10) Perform a mass balance of solid components. 2
11) Hence, use this equation to calculate the mass flowrate of the product m.p (i.e., concentrated juice after evaporation). 2
12) Perform a mass balance of the food product. 2
13) Hence, use this equation to calculate the mass flowrate of the released vapour from the juice m.v1 . 2
After completing the two mass balances above, we can now proceed with the energy balances.
14) Perform an energy balance on the full evaporator. 2
15) Hence, by solving this equation, calculate the mass flowrate of steam required to perform the specified evaporation process m.s . 2
16) Hence, calculate the steam economy of this evaporation process. 2
Now, we can look at the recirculation for this evaporator. We will need to perform an energy balance on the heat exchanger (calandria) only. In this heat exchanger, the heat from the condensation of steam is used to heat the juice prior to evaporation in the evaporation chamber. In other words, the heat lost by the steam is gained by the juice. Note that the mass flowrate of the recirculated juice (m.R ) in the heat exchanger is unknown.
17) Perform an energy balance on the heat exchanger.
Hint: write this equation by equating the heat loss by the steam to the heat gained by the juice. This results in an equation written in terms of the mass flowrates and enthalpy values of each component entering and leaving the heat exchanger, and where the only unknown is the mass flowrate of recirculated juice (m.R ).
18) Hence, by solving this equation, calculate the mass flowrate of recirculated juice in the calandria m.R . 2
19) Hence, calculate the recirculation rate of the juice RR (ratio of mass flowrate of recirculated juice to feed juice). 2
From here, we can now analyse the evaporator equipment itself based on our calculated rates of heat transfer in the calandria between the steam and the juice. We will firstly determine the heat transfer coefficient of the heat exchanger. For simplicity, neglect the resistance by convection outside the tubes and by conduction through the tubes. Hence, the overall heat transfer equation U is equal to the inner heat transfer coefficient (hi) ( U = hi)
For forced circulation evaporators, hi is calculated with the Dittus-Boelter equation (the viscosity correction term in this equation can be ignored). hi is calculated first by assuming that the flow is passing through a single tube. Then, for multiple tubes, use the equation below:
U = hiN-0.8 (1)
where N is the number of tubes in the exchanger.
The Dittus-Boelter equation estimates the Nusselt number as function of the Reynolds and Prandt numbers. To calculate Reynolds number, you need to calculate the velocity, which can be done as follows:
20) Calculate the cross-sectional area of flow of a tube in the calandria. 1
21) Calculate the volumetric flowrate (m3/s) of the juice in the calandria. 1
22) Hence, calculate the velocity of flow of the orange juice (i.e., in units m/s). 1
Now you can proceed to estimate hi:
23) Calculate the Reynolds number of the orange juice recirculated through the calandria. Remember that this value should be unitless (i.e ., check that your units cancel). 2
24) Calculate the Prandtl number of the juice (use the specific heat capacity of the concentrated juice). This value should also be unitless. 2
25) Hence, calculate the Nusselt number of the orange juice heat transfer by using the Dittus-Boelter equation (remember neglecting the viscosity correction term in this equation). 2
26) Now, from the definition of the Nusselt number, determine the inner heat transfer coefficient (hi) (c.f. Equation 11.15 from the lecture notes). 2
Now equation 1 (U = hiN!0.8 ) gives you an expression for the overall heat transfer coefficient U as function of the number of tubes. This is an expression because the total number or tubes is still unknown.
The energy balance on the heat exchanger, done in part 17, can also be written as:
UAΔTln = m.SHvS — m.SHcS (2)
where the right-hand and left-hand side terms represent the heat lost by the steam and the heat transferred through the walls of the heat exchanger (which is then absorbed by the juice), respectively. This equation will be used to estimate the number of tubes.
27) Draw a rough diagram and write an equation to define the log-mean temperature difference (LMTD, or ΔTln ) for two counter-current fluids. 2
28) Hence, calculate the log-mean temperature difference in the calandria (ΔTln ). 2
29) Hence, calculate the number of tubes required in the heat exchanger. 2
Now that we know the number of tubes, we can calculate the total cost to purchase this evaporator.
30) By multiplying the number of calandria tubes by the cost per tube, and adding the cost of the recirculation pump, calculate the total capital cost of this evaporation system. 3
Question 2
This question will be based on the second option of evaporator, the falling film evaporator.
1) Briefly explain how a falling film evaporator works. 2
2) What are some advantages of using a falling film (as opposed to rising film) evaporator? 2
3) Draw a diagram of the evaporation process, making sure that you include the calandria (vertically orientated), and the evaporation chamber. 2
Similar to question 1, you need to estimate enthalpies. Because both evaporators are being evaluated to perform the juice concentration process outlined on the project brief, the enthalpies estimated in sections 4 to 8 of question 1 apply here (there is no need to calculate them again as they are estimated at the same temperatures and concentration of solids).
Then you need to perform the two mass balances: 1) a mass balance of solid components, and 2), a mass balance of the food product. If you perform. those balances, you will notice that they yield the same equations of the forced circulation evaporator. The same applies for the energy balance on the full evaporator. Both evaporators are being evaluated to perform the same juice concentration process outlined on the project brief. Hence, the evaporation parameters and conditions are the same. Consequently, the mass flowrate of the product m.p , the mass flowrate of the released vapour from the juice m.v1 , the mass flowrate of steam required to perform the specified evaporation process on the juice m.S , and the steam economy, will be the same. Hence, those values will be taken from the results of question 1. You can verify all of this by doing those balances.
We can now analyse the falling film evaporator by focusing specifically on the heat exchange between the steam and the juice in the calandria. Note that for this evaporator, there is no increase in the temperature of the juice and evaporation occurs at the same temperature of the feed.
Firstly, we will determine the heat transfer coefficient of the heat exchange.
4) Calculate the Reynolds number of the orange juice flow (c.f. equation 11.21 of the lecture notes). Remember that this value should be unitless (i.e., check that the units cancel). 2
5) Calculate the average specific heat capacity of the juice (average between feed and product). We need to calculate this average since the evaporation occurs within the heat exchanger which changes the concentration of solids during the evaporation process, which will change the specific heat capacity. 2
6) Hence, calculate the Prandtl number (use the average specific heat capacity). This value should also be unitless. 2
7) Calculate the value φ (c.f. equation 11.22 of the lecture notes) using the density, velocity, and thermal conductivity of the juice. Assume that the gravitational force is 9.8 m/s2 . 2
8) Hence, calculate the heat transfer coefficient for the falling film in this heat exchanger (hi ) (c.f. equation 11.20).
As mentioned, the temperature of the juice will remain constant at its feed inlet temperature (°C) throughout the process.
9) Calculate the temperature difference between the steam and the juice in the calandria. 2
Note that you do not need to calculate the ΔTln , as these temperatures stay constant
(the liquid juice evaporates at constant temperature from the inlet to the outlet of the calandria). Instead, you should just calculate ΔT.
The resistance by convection outside the tubes and by conduction through the tubes were neglected.
Hence, the overall heat transfer equation U is equal to the inner heat transfer coefficient (hi) (U = hi) hi was calculated above assuming that the flow is passing through a single tube. Then, for multiple tubes, use the equation:
U = hiN-1/3 (3)
where N is the number of tubes in the exchanger. Like in question 1, the energy balance on the heat exchanger can be written as:
UAΔT = m.SHvS — m.SHcS (4)
where the right-hand side term represents the heat lost by the steam and the left-hand side the heat transferred through the walls of the heat exchanger (which is then absorbed by the juice).
10) Use the above equation to calculate the number of tubes required in the heat exchanger. 2
Now that we know the number of tubes, we can calculate the total cost to purchase this evaporator.
11) By multiplying the number of calandria tubes by the cost per tube, and adding the cost of the flow distribution system, calculate the total capital cost of this evaporator. 3
Question 3
Write a final recommendation to the company of which evaporator to buy – this should include considerations of cost and the quality of your product. This justification should be 2–3 paragraphs. 15
Total available marks: 90