Energy Input Calculation 1

[purplehaze2004]

hi guys,

I can't seem to find the calculation for this scale-up.

If I have a lab-top KITCHEN AID mixer (0.5HP) mixing dough using the following mixing profile,
Agitator (mixing tool)
Low speed 107 rpm
Med speed 198 rpm
Mixing for one min on low, followed by 20 sec on medium speed


I want to scale up to an existing industrial sized mixer, similar mixing tool design. ~60HP,
how do I calculate the RPM/time required to achieve the same energy input?
Basically, I want to achieve the same dough consistency on the big mixer.
any help is appreciated.

 

[kingnero]

Will you be using the same (evenly scaled up) type agitator?

I do not believe that you can scale up the rpm's evenly, as you'll beat up the batter too much.

Trial and error is no option?
Or searching for a similar installation?

 

[purplehaze2004]

yes - same mixing tool (just larger).

trial and error is an option, but wanted to somehow calculate a starting point.

 

[drawoh]

purplehaze2004,

It sounds like you are assuming that the power at 107rpm equals the power at 198rpm equals 0.5hp. I would not assume that.

Your motor is capable of 0.5hp, probably at some specific RPM. What knows what it actually is doing? If you know the type of motor and you know its power characteristics, you can monitor voltage and current. Otherwise, you might have to replace it with a motor you have specifications for and test that.

I agree with kingnero's point about scaling. Probably, you want a bigger mixer that works at the same speed as your current one.

JHG

 

[TenPenny]

If I recall correctly, when agitating, power is related to the cube of the speed change or impeller diameter change. But that's more applicable to agitating a tank of liquid. In your case, you're mixing dough, which is a different kettle of fish (or kettle of dough, as the case may be). I think that what you need to look at is the power that you are inputting into the dough.

You'll probably want the same energy density in the larger batch, so the power that you want will be proportional to the ratio of the mass of the full batch to the test batch.

You'll probably want to keep a similar speed for the blade, because you don't usually want to mix too quickly. So what I would do is work out the ratio of the masses, use that to work out your power requirement, and then try to find a mixing element that will let you put that much power into the mixing at a similar speed.

As a rough starting guide, I would work from the starting point that the power draw ratio is likely near the cube of the blade size ratio, as it is with a pump, so if your full batch is 2x the size of your test batch, you'll want 2x the power, so use a blade that is 1.26 times the size of the test one. Start with that concept, and be prepared to modify it as required.

Making some wild assumptions with your numbers, if the full batch is 120 times the test batch (you tossed out 60 hp and .5 hp), use a full size mixing element just under 5 times the size of your test one.

Disclaimer - I am not a food scientist, so this is only my thought process off the top of my head while I'm eating pizza.

 

[dvd]

I do not know anything about mixing...

Seems to me that the path traveled by the dough would be a good point to scale to. The smaller beater has a smaller radius and slower "tip speed". Look at the total distance traveled at the tip speed and time and have the larger mixer perform similarly.

Horsepower, to me, would be a function of how many lbs/minute are being moved at some velocity against some frictional resistance.

 

[dvd]

fan laws?

 

[MintJulep]

Measure the power draw of the mixer - volts x amps.

Energy is power x time.

Divide by the weight of the dough. This gives you a specific energy input per weight of dough.

That's your scaling factor.

 

[zekeman]

I found this very good summary for mixers.

http://www.haywardgordon.com/documents/Mixing_Fundamentals.pdf

But you must be careful in the scaleup. I read somewhere you should, where possible use similar geometry and keep the tip speed of the dcaled up version the same as the prototype

 

[IRstuff]

You should be using the same speed, but at a higher torque capacity.

TTFN

FAQ731-376
Chinese prisoner wins Nobel Peace Prize

 

[rb1957]

how are you scaling the load (ie how much more dough) ? 30x ??

i thought beating dough was about adding air into the dough.

i liked the point above that your .5hp motor doesn't have to be producing .5hp ... can you measure the electrical work being done ?

my initial thought was the same as IR's (use the same speed), but i'd consult Zeke's reference.

 

[TheTick]

Your question imposes a lot of assumed linear relationships where non really exist. Consider that dough is a non-newtonian fluid and the problem gets even stranger.

 

[geesamand]

"If I recall correctly, when agitating, power is related to the cube of the speed change or impeller diameter change. But that's more applicable to agitating a tank of liquid. In your case, you're mixing dough, which is a different kettle of fish (or kettle of dough, as the case may be). I think that what you need to look at is the power that you are inputting into the dough."

Power draw follows speed cubed and diameter to the 5th power in liquids. Doughs can be non-newtonian and may be very sensitive to the proportions of tank vs. impeller.

Whether to scale on torque / vol, power / vol, turnover, etc all depends on the process. I do not know offhand how to scale using dough.