Wednesday, July 10, 2013

A tomato greenhouse in Nashville

"brad.howard308" <bradhoward@...> wrote:

>I am trying to design a solar heating system for a new 32 ft x 96 ft greenhouse on my farm.

NREL says 730 Btu/ft^2 of sun falls on the ground and 1030 falls on a south wall on an average 36.2 F January day in Nashville, with a 26.5 and 45.9 low and high and a (36.2+45.9)/2 = 41 average daytime temp and a wa = 0.0035 humidity ratio (0.0035 pounds of water per pound of dry air.) The deep ground temp is 59.1. The 30-year record low is -17 F. The average July temp is 79.3, with a 68.9 and 89.5 low and high and 1980 Btu/ft^2 of sun on the ground and 770 on a south wall and a 0.0152 humidity ratio.

>I need to try and keep temps in the greenhouse between 50F - 90F with the optimum range 60F - 80F. recommends a 70 to 82 F day temperature at 60-70% RH and a 64 F minimum night temperature, with nutritional deficiencies below 60 F and fruit damage below 57 F. says a tomato greenhouse can evaporate 0.4 lb/ft^2 per day of water vapor, about 0.4x32'x96' = 1229 lb for a 32'x96' greenhouse.

Air at 82 F and 70% RH has vapor pressure Pg = 0.7e^(17.863-9621/(82+460)) = 0.783 "Hg and humidity ratio wg = 0.62198/(29.921/Pg-1) = 0.0167, and it weighs about 0.075 lb/ft^3, so it looks like maintaining a 70% RH requires 1229/(6hx60m/h/0.075lb/ft^3(wg-wa)) = 3448 cfm of ventilation for 6 hours per day. The dew point of 82 F (542 R) air at 70% RH is approximately 542/(1-542ln(0.7)/9621)-460 = 71 F.  

>Idea 1... a south facing 4 ft x 96 ft screen collector tilted at about 50 degrees, laying on its side down the length of the greenhouse blowing into 4 inch corrugated plastic non-perforated drain pipe buried 3 ft under the green house with 2 ft perimeter insulation.

Why not omit the screen and its plant shading and just blow warm air down from the peak of the greenhouse through perforated pipes, to allow any condensation to drain from the pipes (altho there won't be any condensation if the ground is warmer than 71 F)... suggests something like this, but I'd still worry about mold and mildew in the pipes infecting the plants.

The Kissock equation says A ft^2 of soil with Rf floor insulation and Rp perimeter insulation would lose Qf = UA(Tg-Ts) Btu/h, with U = 0.11/(4+Rf+Rp)+0.89/(16+Rf), where Tg is the greenhouse air temp and Ts is the deep ground temp. With A = 32'x96' and Rf = 0 and Rp = 10 and Tg = 59.1, Qf = 205(Tg-59.1) Btu/h.

With 2 R1 polyethylene film covers, the greenhouse thermal conductance would be about 32'x96'/R2 = 1536 Btu/h-F.

With tall indeterminate tomato plants and a 12' height and 80% solar transmission, it could gain about 0.8x96'(32'x730+1030x12') = 2.74 million Btu/day.

With lots of thermal mass and airflow and a constant Tg (F) temp 24 hours per day,

2.64M = 6(Tg-41)3448+24(Tg-36.2)1536+24(Tg-59.1)205
      = 20688Tg-848208+36864Tg-1334477+4920Tg-290722

makes Tg = 83.5, but the greenhouse could be 70 F during the day and 64 at night, so there's plenty of solar heat on an average day.

Keeping the greenhouse 64 F on an average night requires (64-26.5)1536 = 57.6K Btu/h. Soil with a 32x96x1.5 = 4608 slow-moving airfilm conductance could provide this at a 64+57.6K/4608 = 76 F surface temp.

Keeping the greenhouse 64 F on a 24-hour average 36.2 F day requires (64-36.2)1536 = 42.7K Btu/h... 16 96' x 4" pipes would have 1608 ft^2 of surface with a 1608x1.5 = 2413 Btu/h-F airfilm conductance... says 55 cfm flowing through 48' of 4" duct would have a 0.1 H20 pressure drop, so 16 pipes fed from the center would have about 0.1 "H20 with a 16x2x55 = 1760 cfm flow. With a combined surface and pipe conductance of 4608+1/(1/2413+1/1760) = 5626 Btu/h-F, the soil can provide 42.7K Btu/h at a 64+42.7K/5626 = 72 F temp.

The greenhouse needs 5dx24hx57.6K = 6.9 million Btu to stay 64 F for 5 cloudy 36.2 F days in a row. This could come from 6.9M/(82-72) = 690K Btu/F of mass cooling from 82 to 72 F, eg 690K/30Btu/F-ft^3 = 23K ft^3 of soil with a 30 Btu/ft^3-F specific heat by volume, eg a 23K/32'x96' = 7.5' deep x 32'x96' greenhouse floor. That's very deep, because the temperature swing of this mass is only 10 F, and the floor probably needs more than 1 level of pipes, given the R1 per foot soil thermal resistance.

>Idea 2... a south facing 4 ft x 96 ft PEX or CPVC type collector in the same configuration but use a "tank", basically an insulated hole lined with pond liner as a heat storage tank. Use pex buried in the ground to heat the ground up and inside the greenhouse.

This seems more promising. Water has twice the thermal mass by volume of soil, and it could have a higher temp on an average day and a larger temperature swing. At 140 F, a 4'x96' water tray with an R1 cover under the ceiling would collect 4'x96'(0.8x730-6h(140-82)/R1) = 90.6K Btu/day. With 4'x96'x2x1.5 = 1152 Btu/h-F of airfilm conductance and a 10K cfm ceiling fan and a 1/(1/1152+1/10K) = 1033 Btu/h-F total conductance, tray water at 64+57.6K/1033 = 120 F could keep the greenhouse 64 F on a 26.5 F night.

That's a high minimum usable tray water temp, so the greenhouse needs a large water volume to store enough heat for 5 cloudy days in a row: 6.9M/(140-120)/62.33 = 5469 ft^3 of water, eg an 18' cube. Adding 8 1000 Btu/h-F car radiators and fans would raise the total conductance to 9033 Btu/h-F with a minimum tray water temp of 64+57.6K/9033 = 70 F and a 6.9M/(140-70)/62.33 = 1581 ft^3 tank, eg a 12' cube, but it seems more practical to fill the space between 2 poly film covers with soap bubble foam on cloudy days.

R20 foam would reduce the heat requirement to (64-26.5)32'x96'/R20 = 5.76K Btu/h on an average night, and the tray and ceiling fan could provide that with a minimum tray water temp of 64+5.76K/1033 = 70 F. The greenhouse would only need 5dx24hx5.76K = 690K Btu to stay 64 F for 5 cloudy 36.2 F days in a row, eg a 690K/(140-70)/62.33 = 158 ft^3 tank, eg a 6' cube or a 4' wide x 3' tall x 14' long plywood box with a 10'x20' folded EPDM liner under a bench.

Zelon’s Swedish patent (US No. 3672184, June, 1972) described insulating shop windows at night with soap bubble foam. Professor John Groh at U. Arizona measured US R3 per inch for soap bubble greenhouse insulation in 1968. Professor Otho Wells at U. New Hampshire did later greenhouse experiments. In 1995, Bill Sturm built a 12,000 ft^2 tomato greenhouse with a soap bubble foam roof in Calgary, Alberta and measured an 84% propane energy savings with and without foam on alternate nights at 20 F below zero.

Bill showed me a simple foam generator with a shop vac blower connected to a horizontal 2" PVC pipe full of holes in a shallow trough near the ground containing a 10% detergent solution which expands by a factor of 300 when foamed. He suggests some window screen to push on a microswitch in an air return at the top of the glazing cavity to turn off the shop vac for all but a few seconds every half-hour at night, along with a standard greenhouse inflation blower above the trough water line to fill the space between the 2 films with air during the day, with a check valve to reduce blower power...

How about summer cooling?


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