Designing an Actual Vapor-Compression Refrigeration Cycle

[Satonam]

TL;DR Summary

I'd like to understand the real-life designing process for these systems. When you search for actual components in the market, how do you tie-in the data in the spec sheet (which may have different terminology) with the values you calculated?

Greetings!

I'm a recent ME grad and I'm trying to design a refrigeration system for the first time. I understand most of the theory and calculations (I guess not, cause I wouldn't be here otherwise), but I'm having difficulty applying it to the real world. Homework problems in college often prescribe initial conditions, however, in the real world we have to determine what those conditions are before starting the problem! College never explicitly shows us how to do these things...

Anyway, after solving a problem I created with conditions I thought made sense based on research, I've decided that it might be easier if I just selected an arbitrary compressor for my calculations and see what happens. Here is the compressor I'm looking at: https://www.grainger.com/product/EMBRACO-Refrigeration-Compressor-5AHA1

At the moment, I'm mostly confused about the "Evaporating Temp" and the "Condensing Temp" listed on their webpage. Is it a limitation of the compressor? Recommendation? It doesn't even state a pressure to go with those numbers...

In my latest analysis, I have 29.75 F @ 0.28MPa going through the evaporator and into the compressor inlet. At the compressor outlet, assuming isentropic compression, I have 106.16 F @ 0.7MPa. (I converted celsius to fahrenheit in this post to be consistent with the units reported by Grainger)

A Little Bit About The Values I Calculated:

I began constructing my analysis at the Compressor Inlet as State 1 of the Vapor-Compression Refrigeration Cycle. I know that, to avoid air leaking into the system, the pressure in the system must be greater than 1 atm at all times; therefore, I arbitrarily chose a starting pressure of 0.28MPa due to ignorance of possibilities. I expect to lower this pressure to a more realistic value as I learn more through the design process. Naturally, assuming an ideal system without superheating, the temperature at State 1 is taken at the saturation temperature of R-134a vapor.

The pressure at State 2 was chosen as 0.7MPa. I did light research to conclude that the hottest temperature of my currently location throughout the year is 30 C. So I chose 0.7 MPa because it was the lowest convenient pressure in the superheated charts that provided a temperature above 30 C with the same entropy of State 1, which will enable heat rejection to environment at the condenser. (Specifically, 41.2 C / 106.16 F)

Using an expansion valve, the enthalpy is assumed to be constant as the pressure drops from the condenser exit to the evaporator inlet. No subcooling.

Of course, the pressures chosen don't take into account whether a compressor exists in the market that can actually perform the task specified, this was just a dry run to get my feet wet. If I have done this correctly, the work input for this hypothetical situation is 0.9 kW / 1.2 HP with a COPr of 8.9. (Assuming an arbitrarily chosen mass flow rate of 0.05 kg/s) The ideal COPr,carnot calculated was 9, using TL = 10 C and TH = 30 C. The fact that the COPr is so close to ideal indicates I'm very skeptical of results. Haha...

With that said, I used exergy to determine the theoretical minimum power input required to remove heat at calculated rate and reject it to the environment at To = TH. The value I got was 16 kW / 21 HP, which is considerably higher than the 1.2 HP quoted earlier. Very confusing.

 

[BvU]

At the moment, I'm mostly confused about the "Evaporating Temp" and the "Condensing Temp" listed on their webpage. Is it a limitation of the compressor? Recommendation? It doesn't even state a pressure to go with those numbers...

did you look at the physical properties of R134a, e.g. in the back of Çengel ?

 

[Satonam]

Are you saying I should infer the pressure from the saturation tables? I still don't understand why it's listed as a spec on their page. It is my understanding that the engineer determines what the evaporating and condensing temperatures should be and selects the compressor that can pressurize the refrigerant to cover the spread, no?

I was told recently by another person who read the section about how I came out my numbers and they said "You can't just choose a suction pressure, it depends on the room temperature and metering device." Would you be able to elaborate this for me?

Thanks for your response.

 

[BvU]

I should infer the pressure from the saturation tables?

Yes. What did you find ?

and selects the compressor

Sure, but you have already done that, haven't you ? And it's a pretty specific device for a very narow operating range !

 

[russ_watters]

Summary:: I'd like to understand the real-life designing process for these systems. When you search for actual components in the market, how do you tie-in the data in the spec sheet (which may have different terminology) with the values you calculated?

Greetings!

I'm a recent ME grad and I'm trying to design a refrigeration system for the first time. I understand most of the theory and calculations (I guess not, cause I wouldn't be here otherwise), but I'm having difficulty applying it to the real world. Homework problems in college often prescribe initial conditions, however, in the real world we have to determine what those conditions are before starting the problem! College never explicitly shows us how to do these things...

Anyway, after solving a problem I created with conditions I thought made sense based on research, I've decided that it might be easier if I just selected an arbitrary compressor for my calculations and see what happens...

Hi, welcome to PF!

I'm not completely sure what you are after here, but you may be jumping ahead of yourself. You've attempted to design the cycle for an air conditioner based on local weather, but without connection to a real-world problem/requirement. And your process doesn't really match how real-world HVAC engineering is done. You've basically just done a modified homework problem. So let me discuss how some real-world HVAC engineering is done and see if that's what you're after.

There's many different types of jobs for an HVAC engineer, but three main/relevant ones associated with design are:

Consulting Design Engineer (Me)
[simplified version - in reality the steps overlap and even loop]
A client calls my company, and says they want to build a building, and gives us the requirements. Architects design it, then hand the drawings over to me/my team and we calculate the cooling requirements based on the space size, building envelope/insulation, local weather, occupancy, use, etc. This is done with spreadsheets and load calculation software. Then we decide what style of system we want (constant volume, VAV, DX, chilled water, indoor, rooftop, etc.). Then we pick the unit out of a catalogue (for a simple/off the shelf unit) or talk to a vendor sales engineer about selecting or custom-building one. We usually don't have access to their proprietary selection/design software. We don't do refrigerant cycle calculations. We may concern ourselves with refrigerant pollution/global warming considerations and specify a refrigerant.

Vendor Sales Engineer
This person selects/designs the AC unit based on the requirements we give them, using proprietary selection software. There's a back-and forth discussion about features and pros/cons of different choices. S/he is an expert in their system capabilities so I don't have to be. I recently asked one for 44F air, and he said their system can only give me 45F, is that good enough? Sure. But he's not doing refrigerant calcs either; the selection software does that work.

Vendor Product Development Engineer
These guys would likely do refrigerant/cycle calcs, but I've rarely interfaced with them, so I don't know exactly how they work - they likely have software tools too. They don't necessarily start from scratch, but rather have existing product offerings that need to be refined/updated. Refrigerant environmental impact is a big problem right now for the industry (google: "refrigerant transition"). That's where the refrigerant/cycle calcs matter a lot, and some of the problems are unsolved. The goal is to design/pick/blend new refrigerants and cycles/systems that are more environmentally friendly while maintaining the same capacity, efficiency and safety of the existing cycles/systems.

With that said, I used exergy to determine the theoretical minimum power input required to remove heat at calculated rate and reject it to the environment at To = TH. The value I got was 16 kW / 21 HP, which is considerably higher than the 1.2 HP quoted earlier.

How exactly did you calculate that? Also, I don't see where you calculated or specified a required cooling capacity?

 

[Satonam]

Yes. What did you find ?

For R134a as a saturated mixture going through the evaporator at 45 F, the pressure is 54.787 psia.
For R134a as a saturated mixture going through the condenser at 130 F, the pressure is 213.53 psia.

Sure, but you have already done that, haven't you ? And it's a pretty specific device for a very narow operating range !

Well, I chose the compressor arbitrarily. It's not based on any qualifying metrics. I'm just confused that they're specifying an evaporating and condensing temperature.

 

[Satonam]

Thanks for your response! Very informative. My approach was to design a working model and then source components to fit the roles. For example, if my calculations required a 1.2 HP compressor, then I would find an adequate compressor and adjust my calculations based on what is readily available. Based on what you've said, it appears I'm attempting to fulfill the role of a Consulting Design Engineer.

A client calls my company, and says they want to build a building, and gives us the requirements. Architects design it, then hand the drawings over to me/my team and we calculate the cooling requirements based on the space size, building envelope/insulation, local weather, occupancy, use, etc.

By cooling requirements, you mean the rate of heat the system needs to remove from the environment, yes? In other words, after taking into account the amount of heat leaking in (or out) of the control volume, heat sources (people and electronics), etc, we can determine how much heat needs to be removed in order to maintain a target room temperature. Therefore, the design of an AC system starts by determining the required heat absorption rate at the evaporator, correct?

However, based on what you've said, you don't even have to go that far. You just tell vendors that you need an AC that provides air at a specific temperature? What if you're a start up and you're trying to design an AC system that doesn't exactly exist in the market? In this case, you need to find the components of an AC -such as the compressor, evaporator, condenser, throttling device, etc. Which sounds like the Product Development Engineer that you mentioned.

With that said, allow me to be more specific with my intent. I want to design an AC system from scratch by selecting components readily available in the market to service... let's say, my room. Even if I don't actually build it, this is meant as an exercise to give myself experience and apply what I've learned in college.

How exactly did you calculate that? Also, I don't see where you calculated or specified a required cooling capacity?

In my textbook, Cengel 7E pg. 621, it defines the minimum power input (Xq) required to remove heat at a rate Q from a low temperature medium at TL and reject it to an environment at temperature T0. The equation goes as follows:

Xq = Q * (T0 - TL)/TL

Instead of a cooling capacity (which may have been a mistake), I chose the temperature of the cooled environment that I wanted. In this case, 10 C. In other words, I wanted the heat absorption rate of refrigerant at -1.25 C in the evaporator to produce 10 C wind as a fan blows over the evaporator and into the air conditioned room.

 

[russ_watters]

Thanks for your response! Very informative. My approach was to design a working model and then source components to fit the roles. For example, if my calculations required a 1.2 HP compressor, then I would find an adequate compressor and adjust my calculations based on what is readily available. Based on what you've said, it appears I'm attempting to fulfill the role of a Consulting Design Engineer.
[snip]
With that said, allow me to be more specific with my intent. I want to design an AC system from scratch by selecting components readily available in the market to service... let's say, my room. Even if I don't actually build it, this is meant as an exercise to give myself experience and apply what I've learned in college.

It looks to me like you're trying to do all three at once. It's fine for a learning exercise.

By cooling requirements, you mean the rate of heat the system needs to remove from the environment, yes? In other words, after taking into account the amount of heat leaking in (or out) of the control volume, heat sources (people and electronics), etc, we can determine how much heat needs to be removed in order to maintain a target room temperature. Therefore, the design of an AC system starts by determining the required heat absorption rate at the evaporator, correct?

Exactly. Note though, that we're focusing on one of the jobs of an A/C coil and skipping the other one. Know what it is? (I'll give it away later...).

However, based on what you've said, you don't even have to go that far. You just tell vendors that you need an AC that provides air at a specific temperature?

No. Cooling capacity is airflow times temperature difference (times specific heat). You need a specific temperature and airflow. Note: your supply air temperature is not your room temperature --- your return temperature is your room temperature.

Note, though, that you have three variables, so you need to pin down two of them and solve for the third. Load is calculated - it's a requirement. The other one that is usually specified is supply air temperature, because it determines the humidity of the room. Then you solve for airflow.

What if you're a start up and you're trying to design an AC system that doesn't exactly exist in the market? In this case, you need to find the components of an AC -such as the compressor, evaporator, condenser, throttling device, etc. Which sounds like the Product Development Engineer that you mentioned.

Yep. If your intent is to design the equipment, that's product development. One big difference is your design constraints get broader. Say, for example, you want to serve the North American market. That means you need to design systems that can operate in Florida/Texas or Maine/Edmonton. Or make a conscious choice to limit your markets.

These days, there are some commodity/off the shelf components and there are components that manufacturers will make themselves. As you say, for a startup, unless there is something proprietary you are inventing, you'd start with off the shelf components. For example, if you haven't found them yet, Copeland is probably the most common compressor manufacturer.

In my textbook, Cengel 7E pg. 621, it defines the minimum power input (Xq) required to remove heat at a rate Q from a low temperature medium at TL and reject it to an environment at temperature T0. The equation goes as follows:

Xq = Q * (T0 - TL)/TL

Instead of a cooling capacity (which may have been a mistake), I chose the temperature of the cooled environment that I wanted. In this case, 10 C. In other words, I wanted the heat absorption rate of refrigerant at -1.25 C in the evaporator to produce 10 C wind as a fan blows over the evaporator and into the air conditioned room.

I'm still not following. You have T0 = 10C and TL = -1.25C. (10- -1.25)/(-1.25+273) = 0.04. What is Q?

That equation is the inverse of COP, times Q. COP is the ratio of work into heat transfer, and you're looking for work in. It's pretty obvious that your work in should be a small fraction of heat transfer.

Also, in the prior calculation, I'm getting a 14 COP, not a 9 COP. But without seeing your actual math, I can't be sure what you're doing or if I'm really duplicating it.

 

[Satonam]

I'm still not following. You have T0 = 10C and TL = -1.25C. (10- -1.25)/(-1.25+273) = 0.04. What is Q?
[snip]
Also, in the prior calculation, I'm getting a 14 COP, not a 9 COP. But without seeing your actual math, I can't be sure what you're doing or if I'm really duplicating it.

Sorry, I wasn't clear. T1 = -1.25C is the temperature of R134a saturated vapor at the compressor inlet. Which was determined after arbitrarily choosing an inlet pressure of P1 = 0.28MPa.

TL = 10C is the target temperature of the refrigerated room, it's the temperature of the medium where heat is absorbed at the evaporator.

TH = 30C is the maximum/highest temperature of the outside environment from where I currently reside (according to a light google search).

Using TL and TH to calculate the COP of a reverse carnot cycle yields 0.5
If I use TH = 27C as the lowest environment temperature throughout the year, I get 9

In image 1, please ignore the T-s curve in the top corner. I originally wanted to implement superheating in my calculations, but opted for keeping it simple to make sure I'm doing everything properly. At the bottom of the page, you can see equation (11-4) which is the reversed carnot COP and the values yielded as I described above.

Spoiler: Image 1

Image 2 shows my process and how I arrived to my values. The mass flow rate indicated at the bottom was taken from a homework problem. I figured I could just replace it once I figured out how to get an actual number.

Spoiler: Image 2

In Image 3 I used the equation for calculating the COP of refrigeration cycles, which as you stated, is the ratio between the heat removed from the refrigerated environment and the power input. I then used the exergy equation at the bottom which, as you have noticed, is the rate of heat removal divided by the reversed carnot COP. I used google to convert kW to HP.

Spoiler: Image 3

Note, though, that you have three variables, so you need to pin down two of them and solve for the third. Load is calculated - it's a requirement. The other one that is usually specified is supply air temperature, because it determines the humidity of the room. Then you solve for airflow.

In other words, here is what I think I must do in steps to solve the problem, according to what you've said:

1. Determine heat load of the room.
   1. Research how to quantify heat loss in a room, consult a professional to determine the heat loss for me, or assume proper insulation.
   2. Determine heat released from household components, such as a TV. I'm assuming I can determine this value with the electronic power requirements, or consult manufacturers.
   3. Research average heat released by humans of different weight and sizes.
2. Choosing a target temperature for the room. In this case, TL = 10C would be the lowest temperature I want the system to achieve.
   1. Assuming excess heat accumulation in the room (after all, the goal is to cool the room), to achieve the target temperature, the system must supply cool air which is able to absorb the excess heat + however much heat removal is required to drop the room temperature from x to 10C.
   2. The temperature of the air supply will be a function of: room volume, room average temperature, and the speed at which the system is required to achieve target room temperature.
3. Review heat transfer textbook to determine:
   1. Required air supply temperature to satisfy statements 2.1 and 2.2
   2. Appropriate fan speed which will optimize heat transfer between refrigerant and fan air at the evaporator to achieve target air supply temperature. (However, doesn't this also depend on the geometry and surface area of the evaporator? In other words, I have to choose an evaporator at this stage?)
4. We can determine the maximum refrigerant temperature at the evaporator to be less than the pre-cooling fan air.
   1. However, how low the temperature needs to be is a function of the fan speed and target air supply temperature, which have already been determined at this point.
   2. After determining R134a T_evap, P_evap can be taken from saturation tables.
5. So, looking at the flow chat in Image 1,
   1. T4 = T-evap and P4 = P_evap, which have been determined.
   2. P4 = P1
   3. T1 can be determined with T4 and QL.
   4. S1 can be determined.
   5. Now, we want a second fan to absorb heat from the condenser. QH = QL + Win
   6. This is the part where I start doubting myself, however, this is what I think the process looks like:
      1. At the condenser, knowing TH and assigning QH = QL, I should be able to determine an optimal fan speed and T2.
      2. Knowing T2, I know P2.
      3. Now I can find a compressor that can take me from P1 to P2_min. Win is now known.
      4. Redo calculation for QH = QL + Win
      5. This assumes that the added Win needed to reach P2_min doesn't dramatically change it. In other words, P2_min ~= P2
      6. I'm surprised entropy isn't needed here. Maybe that's a sign that my reasoning is flawed?
   7. T3 can be determined with QH and T2.
   8. P3 = P2
6. Now I need to research thermal expansion valves to understand how the throttling from T3 to T4 works. I'm assuming that, whenever we interact with an air conditioner to change the room temperature, it's actuating the thermal expansion valve to control T4.
7. At this point I have designed a vapor-compression refrigeration cycle, and probably understand how to modify it to apply superheating and subcooling.
   1. I should probably redo calculations for different settings, Room Temperatures: 10C to 25C

If you have read this far, I'm very grateful for your time!