Cooling Load Calculation for Cold Rooms

Cooling Load Calculation for cold rooms. In this article we’ll be looking at how to calculate the cooling load for a cold room. We’ll first look at the heat sources and then we’ll look at a worked example of how to perform a cold room cooling load calculation in a simplified example.

What is a Cold Room?

A cold room is used to store perishable goods such as meat and vegetables to slow down their deterioration and preserve them as fresh as possible for as long as possible. Heat accelerates their deterioration so the products are cooled down by removing the heat.

To remove the heat we use a refrigeration system as this allows accurate and automatic control of the temperature to preserve the goods for as long as possible.

To remove the heat we need to know what the cooling load will be. The cooling load varies throughout the day so in most cases the average cooling load is calculated and the refrigeration capacity is calculated to suit this.

Cold Room Heat Sources

Where does all the heat come from that we need to remove?

Typically 5-15% is through transmission loads. This is the thermal energy transferred through the roof, walls and floor into the cold room. Heat always flows from hot to cold and the interior of the cold room is obviously a lot colder than its surroundings, so heat is always trying to enter the space because of that difference in temperature. If the cold store is exposed to direct sunlight then the heat transfer will be higher so an additional correction will need to be applied to allow for this.

Then we have Product loads which account for typically 55-75% of the cooling load. This accounts for the heat that is introduced into the cold room when new products enter. Its also the energy required to cool, freeze and further cool after freezing. If you’re just cooling the products then you only need to consider the sensible heat load. If you’re freezing the product then you need to account for the latent heat also as a phase change occurs. During this time energy is used but you will not see a temperature change while the product changes between a state of liquid and ice. There is additional energy required to further chill this food down below the freezing point which is again sensible heat. You also need to account for the packaging as this will inherently be cooled also. Lastly if you’re cooling fruit and vegetables then these products are alive and they will generate some heat so you’ll need to account for the removal of this too.

The next thing to consider is the internal loads which account for around 10-20%. This is the heat given off by people working in the cold room, the lighting and equipment such as fork lifts trucks etc. So for this you’ll need to consider what equipment will be used by the staff members in order to move the products in and out of the store, how much heat will they and the equipment give off and the daily duration.

Then we need to consider the refrigeration equipment in the room which will account for around 1-10% of the total cooling load. For this we want to know the rating of the fan motors and estimate how long they will run for each day, then we want to also account for any heat transferred into the space from defrosting the evaporator.

The last thing we need to consider is infiltration which again adds 1-10% to the cooling load. This occurs when the door opens so there is a transfer of heat into the space through the air. The other consideration is ventilation. Fruit and vegetables give off carbon dioxide so some stores will require a ventilation fan, this air needs to be cooled down so you must account for this if it’s used.

Cooling Load Calculation – Cold Room Worked Example

Transmission Load

• The dimensions of our cold store are 6m long, 5m wide and 4m high.
• The ambient air is 30°c at 50% RH, The internal air is 1°C at 95% RH
• The walls, roof and floor are all insulated with 80mm polyurethane with a U value of 0.28W/m².K
• The ground temperature is 10°C.

Just to note the manufacturer should tell you what the u value is for the insulation panels, if not, then you will need to calculate this.

To calculate the transmission load we will be using the formula

Q = U x A x (Temp out – Temp in) x 24 ÷ 1000.

• Q= kWh/day heat load
• U = U value of insulation (we already know this value) (W/m².K)
• A = surface area of walls roof and floor (we will calculate this) (m²)
• Temp in = The air temperature inside the room (°C)
• Temp out = The ambient external air temperature (°C)
• 24 = Hours in a day
• 1000 = conversion from Watts to kW.

To calculate “A” is fairly easy, its just the size of each internal walls, so drop the numbers in to find the area of each wall, roof and floor.

Side 1 = 6m x 4m = 24m²
Side 2 = 6m x 4m = 24m²
Side 3 = 5m x 4m = 20m²
Side 4 = 5m x 4m = 20m²
Roof = 5m x 6m = 30m²
Floor = 5m x 6m = 30m²

Then we can run these numbers in the formula we saw earlier, you’ll need to calculate the floor separately to the walls and roof as the temperature difference is different under the floor so the heat transfer will therefore be different.

Walls and Roof

Q = U x A x (Temp out – Temp in) x 24 ÷ 1000
Q = 0.28W/m².K x 113m² x (30°C – 1°C) x 24 ÷ 1000
Q = 22 kWh/day

[113m² = 24m² + 24m² + 20m² + 20m² + 30m² + 30m² ]

Floor

Q = U x A x (Temp out – Temp in) x 24 ÷ 1000
Q = 0.28W/m².K x 30m² x (10°C – 1°C) x 24 ÷ 1000
Q = 1.8 kWh/day

If the floor isn’t insulated then you will need to use a different formula based on empirical data.

Total daily transmission heat gain = 22kWh/day + 1.8kWh/day = 23.8kWh/day

Remember if your cold room is in direct sunlight you’ll need to account for the suns energy also.

Product Load – Product Exchange

Next we will calculate the cooling load from the product exchange, that being the heat brought into the cold room from new products which are at a higher temperature.

For this example we’ll be storing apples, we can look up the specific heat capacity of the apples but do remember if you’re freezing products then the products will have a different specific heat when cooling, freezing and sub cooling so you’ll need to account for this and calculate this separately, but in this example we’re just cooling.

There are 4,000kg of new apples arriving each day at a temperature of 5°C and a specific heat capacity of 3.65kJ/kg.°C.

We can then use the formula

Q = m x Cp x (Temp enter – Temp store) / 3600.

• Q = kWh/day
• CP = Specific Heat Capacity of product (kJ/kg.°C)
• m = the mass of new products each day (kg)
• Temp enter = the entering temperature of the products (°C)
• Temp store = the temperature within the store (°C)
• 3600 = convert from kJ to kWh.

Calculation

Q = m x Cp x (Temp enter – Temp store) / 3600
Q = 4,000kg x 3.65kJ/kg.°C x (5°C – 1°C) / 3600.
Q = 16kWh/day

Product Load – Product Respiration

Next we calculate the product respiration, this is the heat generated by living products such as fruit and vegetables. These will generate heat as they are still alive, that’s why we’re cooling them to slow them down their deterioration and preserve them for longer.

For this example I’ve used 1.9kJ/kg per day as an average but this rate changes over time and with temperature. In this example we’re using a rules of thumb value just to simplify the calculation since this cooling load is not considered critical. If you were to calculate for a critical load you should use greater precision. In this example the store maintains a hold of 20,000kg of apples.

To calculate this we’ll use the formula

Q = m x resp / 3600

• Q = kWh/day
• m = mass of product in storage (kg)
• resp = the respiration heat of the product (1.9kJ/kg)
• 3600 = converts the kJ to kWh.

Q = m x resp / 3600
Q = 20,000kg x 1.9kJ/kg / 3600
Q = 10.5kWh/day

For the product section we’ll sum together the product exchange of 16kWh/day and respiration load of 10.5kWh/day to get a total product load of 26.5 kWh/day.

Internal Heat Load – People

Next we’ll calculate the internal loads from people working in the cold room, as people generate heat and we need to account for this.

We’ll estimate 2 people working in the store for 4 hours a day and we can look up and see at this temperature they will give off around 270 Watts of heat per hour inside.

We’ll use the formula:

Q = people x time x heat / 1000

• Q = kWh/day
• people = how many people inside
• time = length of time they spend inside each day per person (Hours)
• heat = heat loss per person per hour (Watts)
• 1,000 just converts the watts into kW

Calculation:

Q = people x time x heat / 1000
Q = 2 x 4 hours x 270 Watts / 1000
Q = 2.16 kWh/day

Internal Heat Load – Lighting

Then we can calculate the heat generated by the lighting, this is fairly simple to do and we can use the formula

Q= lamps x time x wattage / 1000

• Q = kWh/day,
• lamps = number of lamps within the cold room
• time = hours of use per day
• wattage = power rating of the lamps
• 1000 = converts the Watts to kW.

If we have 3 lamps at 100W each, running for 4 hours a day, the calculation would be:

Q= lamps x time x wattage / 1000
Q= 3 x 4 hours x 100W / 1000
Q= 1.2kWh/day

For the total internal load we then just sum the people load (2.16 kWh/day) and lighting load (1.2kWh/day) to get a value of 3.36kWh/day.

Equipment Load – Fan Motors

Now we can calculate the heat generation of the fan motors in the evaporator. For this we can the use the formula of:

Q = fans x time x wattage / 1000

• Q = kWh/day
• fans = the number of fans
• time = fan daily run hours (hours)
• wattage = the rated power of the fan motors (Watts)
• 1000 = convert from watts to kw.

In this cold room evaporator we’ll be using 3 fans rated at 200W each and estimate that they will be running for 14 hours per day.

Calculation:

Q = fans x time x wattage / 1000
Q = 3 x 14 hours x 200W / 1000
Q = 8.4kWh/day

Equipment Load – Fan Motors

Now we will calculate the heat load caused by defrosting the evaporator. To calculate this we’ll use the formula:

Q = power x time x cycles x efficiency

• Q = kWh/day,
• power = power rating of the heating element (kW)
• time = defrost run time (Hours)
• cycles = how many times per day will the defrost cycle occur
• efficiency = what % of the heat will be transferred into the space.

In this example our cold room uses an electric heating element rated at 1.2kW, it runs for 30 minutes 3 times per day and the estimate that 30% of all the energy it consumes is just transferred into the cold room.

Q = power x time x cycles x efficiency
Q = 1.2kW x 0.5hours x 3 x 0.3
Q = 0.54kWh/day

The total equipment load is then the fan heat load (8.4kWh/day) plus the defrost heat load (0.54kWh/day) which therefore equals 8.94 kWh/day

Infiltration Load

Now we need to calculate the heat load from air infiltration. I’m going to use a simplified equation but depending on how critical your calculation is then you may need to use other more comprehensive formulas to achieve greater precision. We will use the formula:

Q = changes x volume x energy x (Temp out – Temp in ) / 3600

• Q = kWh/d
• changes = number of volume changes per day
• volume = the volume of the cold store
• energy = energy per cubic meter per degree Celsius
• Temp out is the air temperature outside
• Temp in is the air temperature inside
• 3600 is just to convert from kJ to kWh.

We’ll estimate that there will be 5 volume air changes per day due to the door being open, the volume is calculated at 120m³, each cubic meter of new air provides 2kJ/°C, the air outside is 30°C and the air inside is 1°C

Q = changes x volume x energy x (Temp out – Temp in ) / 3600
Q = 5 x 120m³ x 2kJ/°C x (30°C – 1°C ) / 3600
Q = 9.67 kWh/day

Total Cooling Load

To calculate the total cooling load we will just sum all the values calculated

Transmission load: 23.8kWh/day
Product load: 26.5 kWh/day
Internal load: 3.36kWh/day
Equipment load: 8.94 kWh/day
Infiltration load: 9.67 kWh/day
Total = 72.27 kWh/day

Safety Factor

We should also then apply a safety factor to the calculation to account for errors and variations from design. Its typical to add 10 to 30 percent onto the calculation to cover this, I’ve gone with 20% in this example so well just multiply the cooling load by a safety factor of 1.2 to give us our total cooling load of 86.7 kWh/day

Refrigeration Cooling Capacity Sizing

The last thing we need to do is calculate the refrigeration capacity to handle this load, a common approach is to average the total daily cooling load by the run time of the refrigeration unit. For this I’m estimating the unit to run 14 hours per day which is fairly typical for this size and type of store. Therefore our total cooling load of 86.7kWh/day divided by 14 hours means our refrigeration unit needs to have a capacity of 6.2kW to sufficiently meet this cooling load.

Source: theengineeringmindset.com

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