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Fluid Bed Roaster Calculator
sahstim001
Hello all! This is my first post here.

I am planning on building a fluid bed roaster. I'm very much a "measure twice, cut once" type, so I've been doing a lot of research and thinking about everything involved. After all that, I've put together an Excel spreadsheet with the goal of shedding light on whether a given design is feasible. I hoped it might answer questions like "is this enough wattage?", "how many CFM's do I need?", "how big should the roast chamber be?", etc.

I have no clue if it's any good, or if I'm missing things, or if I've just missed the mark entirely! I've attached the spreadsheet if you want to look. There is no password to unlock the sheets. It can also change between metric and imperial units.

If anyone has knowledge of the physics involved, please have a look at my math and see if there's anything off.

If you have practical experience on roaster designs that worked / didn't work, I'm curious about if the spreadsheet would reflect your experience? Might be interesting to see.

So what do you think? Is this potentially a useful tool?

Thanks for looking!

EDIT 2/25/23
Small change to terminal velocity calculation to consider reduced hot air density. Also considers bean expansion and heat loss during roasting.
Added roast chamber height calculation.
Reorganization of tabs.

EDIT 3/3/23
Added perforated area calculation.

EDIT 5/5/23
Getting into my own build now. It seems that I need much more pressure getting the air past the heating coil is more demanding than simply pushing the beans. Not sure if it's possible to account for this using simple calcs.
sahstim001 attached the following file:
fb_roaster_calc_v3.zip [43.92kB / 193 Downloads]

Edited by sahstim001 on 05/05/2023 11:57 PM
 
renatoa
Welcome !
What an interesting introductory post !
I would love to hear some words explaining the formulas you are using for the computations, to better understand the physics behind them.
 
sahstim001

Quote

renatoa wrote:

Welcome !
What an interesting introductory post !


Haha, I've been lurking in the background for a while Grin

Here is a breakdown of the major equations involved:

How much air can the heater heat?
Q=mcΔT
Therefore:
Air Mass / Time = Heat Power / (Specific Heat x Change in Temperature)
From power and temperature rise we can get air mass/time. Then convert mass to volume to find CFM's (cold air). This is the most CFM's you can do and still hit your temperature.

How fast is the hot air moving?
The cold air expands due to heating (pressure constant):
Expanded Volume = Initial Volume x Temperature 2 / Temperature 1
Then:
Velocity = (Volume / Time) / Area
We get hot air speed based on gas expansion and chamber area.

What is the fan pressure?
Pressure = Force / Area
We get fan pressure from total roast weight and chamber area.

Is the hot air able to lift the beans?
Air must blow at the terminal velocity of the beans or greater.

What is the terminal velocity of the beans?
Vt=√(2mg/ρACd)
We get terminal velocity (minimum hot air speed) by considering the properties of a coffee bean (mass, size, drag coefficient) and air (density of air).
This number might also be estimated without all the math. Then compare with the hot air speed calculated above.

I'm sure what's actually happening is more complex than these equations make it seem, but I'm hoping doing the math can help give understanding of how the different components all work together, and if you're in the ballpark for your goals.
Edited by sahstim001 on 02/24/2023 11:40 AM
 
allenb
I second the welcome to HRO! I think this is a great idea and could be a very useful tool. One thing that unfortunately prevents most of us from being able to utilize typical engineering best practices in designing a fluidbed roaster is the inability to take reasonably accurate measurements of cfm and velocity when having to take readings in relatively tiny ducts or enclosures. Some have purchased micro sized prop style velometers but could never achieve anything approaching an accurate reading. As you have mentioned, there are ways to derive air flow by using mass and change in temperature but due to severe temperature stratification of the air leaving the heating element, achieving an accurate air temperature reading post-heater, is next to impossible without the use of good lab equipment.

Let us know if you have found a way around this problem?
Edited by allenb on 02/25/2023 1:12 PM
1/2 lb and 1 lb drum, Siemens Sirocco fluidbed, presspot, chemex, cajun biggin brewer from the backwoods of Louisiana
 
sahstim001

Quote

allenb wrote:

One thing that unfortunately prevents most of us from being able to utilize typical engineering best practices in designing a fluidbed roaster is the inability to take reasonably accurate measurements


That makes sense. I can see how it would be difficult to take performance measurements of an already-built roaster.

Do you think this would be useful when designing a new roaster from the ground up? I've seen folks posting questions on HRO asking "how much wattage do I need for xxx grams of beans? How much CFM?", etc. My hope is to remove some (not all) of the trial and error.
 
allenb
One of our members started a thread intended for collecting this kind of data which would eventually allow creation of a spreadsheet. I need to locate it. The intent was for everyone to add information when available to eventually include enough to allow one to pull values they could use for their build without having to start from scratch.
1/2 lb and 1 lb drum, Siemens Sirocco fluidbed, presspot, chemex, cajun biggin brewer from the backwoods of Louisiana
 
sahstim001
Nice! That might also be a good resource to test how valid these calculations are.
 
renatoa
This is the thread: https://homeroast...ad_id=6818
 
allenb
Thanks for tracking it down! 👍
1/2 lb and 1 lb drum, Siemens Sirocco fluidbed, presspot, chemex, cajun biggin brewer from the backwoods of Louisiana
 
sahstim001

Quote

allenb wrote:

One of our members started a thread intended for collecting this kind of data which would eventually allow creation of a spreadsheet. I need to locate it. The intent was for everyone to add information when available to eventually include enough to allow one to pull values they could use for their build without having to start from scratch.


So I went to that thread and tested the spreadsheet again those couple known-to-work examples, and the spreadsheet was in agreement that those designs are indeed valid. So the spreadsheet seems to be working properly so far.
 
btreichel
Just a reflection on the air roasting process. I ran a split fan / heater p1 many years with variacs on both fan and heat. I would routinely start the fan variac above 130 volts, and have it down to about 90 at the end of the roast to keep the beans in proper fountain motion & not blow out all of the heat. Too much air and the heat all goes up the chimney, too little, scorch and uneven. Just adjusted the heat varaic by a 'bit' if I wasn't happy with the tc reading in the bean mass with proper air flow. The beans growing by 40 to 50 % in volume, and loosing 13% mass changes the required to loft a bean by quite a bit.
 
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