a2gemini - Let us know how that griddle does. I need one, too.

You have to call in scientists from CERN to analyze your "boil patterns."

Your Gramma's old cast-iron griddle shrieks in horror on pancake day.

You honestly know what Sil-Pat is.

And, to be fair:

You have the most efficient, most responsive and temperature-steady means of cooking known to human-kind short of psychic barbecue which is not widely available.

(I did broil some peppers today, for the soup, and they did get charred, though not as thoroughly as on a flame. As Westsider said, that's what the rest of the appliances are for...)

... you use a Bic for Flambe's.

... you gave your mom all the ceramic cookware.

... your MIL says "I'll let you cook since you seem to enjoy it more than me."

You have mastered the technique of "Flambe of the Mind."

Your old "Visions" cookware dies of loneliness.

Your Mother in law calls you at the theater to announce that the burners on your stove won't get hot.

Gary

Further, the CFM calculated above should be the actual CFM achieved. Hood and duct transitions, baffle friction, duct friction, house negative pressure due to imperfect MUA will cause the hood blower to move less air than it is rated for. People who have lived with recirculating hoods, or OTR microwave oven ventilation, or the poser kitchens widely published in the media that have no ventilation, will be able to get away with less flow and still be ahead of where they were.

The aperture has to be large enough to capture the expanding uprising effluent. Expansion half angle varies around 22.5 degrees from every point on the pan surface hot enough to cook and generate water and grease vapor. The hood aperture should overhang the locus of these projected points at the planned height of the hood.

kas

The hood system has to capture, contain, and evacuate. Capture requires that the hood overhang the expanding effluent plume, which expands at about a 7-degree half angle. Contain means that the stuff not curl in the hood and come back out. That is partly determined by hood design, but also by air velocity keeping the effluent velocity from being redirected. Having a cfm high enough that the air velocity at the entrance to the hood be as high as that of the effluent velocity should be plenty, possibly overkill unless the airflow is easily disturbed from movement in the room or replacement air velocity being too high near the hood. Flow around the edges of the hood vs. the lower effluent velocity at the edges of the plume can be a factor in adjusting the velocity requirement. And evacuation results from having a cfm at least that of the effluent and generally more to meet the containment velocity requirement.

kas

We next consider using a 34-inch by 48-inch Wolf hood to provide adequate overlap of the plume to handle expansion in the hood and plume deviations due to air disturbances in the kitchen. The diameter of the plume at one meter is shown in the papers to be under 34 inches.

The actual entrance area of the Wolf Pro Island Hood of these dimensions is unknown to this author. There appears to be a slight return on the edges of the hood, and there are switches inside one edge. We guess that the actual entrance area is 10 square feet. (32 in by 46 in is 10.22 sq.ft.)

300 cfm divided by 10 sq. ft. leads to an average air velocity at the hood entrance of 30 ft/min. However, interpolating the results for the induction range in the part 2 article, the peak velocity of the plume studied was 0.66 m/s or 130 ft/min. This will vary with cooking temperature, but we are using a average over the cooktop so it shouldn't be too far off.

What happens when a plume with a nominal Gaussian velocity distribution and central velocity of 130 ft/min enters a hood with an average intake velocity of 30 ft/min? The plume reaches to top of the hood and the higher velocity part spills downward. It is unlikely it will all reach 30 ft/min and be perfectly captured before some of it spills out.

If the entire hood entrance were provided an average airflow of 130 ft/min to ensure capture without any roiling, then the cfm required would be 1300 at the hood entrance. The roof fan that could achieve this would likely be rated 2000 cfm at zero static pressure. Probably (we hope), 1300 cfm is overkill because much of the plume is well under 130 ft/min.

[handwaving begins]
If we assume that the baffle entrances are 40% of the hood aperture, and consider that the roiling plume has to pass close to baffle entrances with airflows thus 2.5x that of the average, then a 600 cfm average airflow would yield baffle edge air velocities of 2.5 x 60 or 150 ft/min. This might be enough for sufficient capture. Here we are hoping that spilling effluent is slowed down and is drawn into the higher speed baffle entrances before any can leak out of the hood and contribute to kitchen odor.
[end handwaving]

Wolf recommends for a 36-inch induction cook-top a 600 cfm fan. This is fan cfm at zero static pressure, so they are likely actually expecting somewhat less at the hood, maybe 400.

We would choose 600 real cfm for this case to be safe and use a nominal 900 cfm roof fan to obtain it (pending analysis of all the pressure losses involved). This rate will be higher than needed for many cooking conditions, but the roof fan can always be turned down. Running at reduced power reduces noise, and beats kicking oneself for not having enough power when the need arises.

Schlieren photography of this hood and cook-top combination (or a very elaborate computational fluid dynamics analysis) would be needed to determine the true minimum cfm that ensures full capture and containment.

kas

PART 1

We need two conversion factors:

To get ft/min from m/s, multiply by 197
To get cfm from m^3/s, multiply by 2119

First, we look at what the induction cook-top effluent plume characteristics are.

We assume that the entire 9.6 kW maximum power output of the Diva 36-inch cook-top is being used, and that the pan configuratin is such that the heated surfaces have the same area as the cook-top. The first assumption is unlikely and hance conservative, and the second has only a second order effect on the result.

Using the methods of the referenced papers, we can find that the hydraulic diamter D_h is 0.64m. We want a hood that is over our head, so we choose 1-m height about the cook-top. (Higher means larger cfm.) Of the 9.6 kW output by the Diva, only 6% heats the air per the referenced experiments. Hence the convective heating is 0.576 kW.

We use the equation:

q_v = 0.05*((z + a D_h)^5/3 * phi^1/3)

where a is 1.7, z is 1m, and phi is 0.576 kW

(The papers use a coefficient of 0.05 in one place, and 5 in another, and claim phi is in watts but their tabulated results require phi to be in kW.)

Solving the equation and converting to cfm leads to 300 cfm in the convective plume from all 5 hobs.

continued below

kas

The supplier granite yard is out of business and the fabricator although it was one of their suppliers says there is nothing they can do about it.

The only reason we are looking at replacing is that we have the problem with shedding, the awful feel of this stone that feels dirty and like it is covered with tiny pepper grains no matter how many times I wipe it down. It snags my dish cloth and the sink recently cracked and has to be replaced. The sink is a mystery as to why that happened.

Thank you so very much I will check in to the Hydro Shield and hopefully it will make it more tolerable. The island is the worst thank goodness since we could just replace that to keep down the cost. I really wasn't planning on an expense like this coming up this soon! It hasn't even been a year yet. The granite fabricator gave me a replacement price for new granite of $4500 which is the same as we paid for the original granite and it was supposed to be their super discounted price ....sigh. Live and learn, thank you very much again.