Sunday, July 28, 2013

Revisiting Dan's PA greenhouse

Daniel Baker <baker_daniel@...> wrote:

>... the calculations don't support what I was hoping to accomplish.
> Is that about right?

I think so. For starters, it seems to me that the greenhouse needs more insulation at night and on cloudy days, and the heat store needs to move more heat into greenhouse air at night.

Filling the space between 2 layers of polyethylene film with R20 soap bubble foam at night would reduce a 500 ft^2 cover conductance to 25 Btu/h-F, so the greenhouse would only need (64-26.6)25 = 935 vs 18.7K Btu/h to stay 64 F on a 26.6 F night, or 5x24x935 = 112.2K Btu for 5 cloudy days in a row.

This could come from N 55 gallon drums with 25N ft^2 of surface and a 1.5x25N Btu/h-F conductance to slow-moving air and a Tm = 64+935/(1.5x25N) F minimum water temp.

Drums in an insulated box (a solar closet (tm)) with an R1 transparent south wall over an insulated south wall (a passive thermosyphoning air heater) under a bench that gain and lose 0.9x0.8x830 = 598 Btu/ft^2 = 6h(Ta-82)1ft^2/R1 in a greenhouse that's 82 F for 6 hours on an  average December day would have temperature Ta = 182 F.

A 55 gallon drum has 55x8.33 = 458 Btu/F of thermal capacitance. Storing 112.2K Btu = (182-Tm)458N = (182-64-24.93/N)458N makes N = 2.28. N = 4 makes Tm = 70.2 F, storing 205K Btu, enough heat for 219 cloudy hours, ie 9.1 days, with an approximate 1-2^-9.1 = 0.998 solar heating fraction.

If the drum tops and bottoms are not exposed to air, that lowers the heat transfer surface to about 75 ft^2, with a 1.5x75 = 112 Btu/h-F airfilm conductance, which raises Tm to 64+935/112 = 72.3 F. And the drum box needs a 62 F thermostat and a fan, eg a 665 cfm fan, which further raises Tm to 64+935/(1/112+1/665) = 73.7 F. And with finite insulation, the box will lose some heat at night, making the water cooler than the surrounding air during the day, which lowers Ta.

And a 9'x10' tomato greenhouse needs about 0.4x9'x10' = 36 lb/day of winter dehumidification, which normally comes from daytime ventilation with dry outdoor air, which precludes beneficial CO2 enrichment with compost, which can also generate heat. Air at 82 F and 70% RH has vapor pressure Pa = 0.7e^(17.863-9621/(460+82)) = 0.783 "Hg and humidity ratio wa = 0.62198/(29.921/Pa-1) = 0.01671 pounds of water per pound of dry air.

NREL's Blue Book says an average 33.6 F December day in Harrisburg has a 26.6 low and a 40.6 high, with 520 Btu/ft^2 of sun on the ground and 830 on a south wall. The average December humidity ratio wo = 0.0028, and air weighs about 0.075 lb/ft^2, so we can remove 36 pounds of water vapor in 6 hours if 6hx60m/hxCx0.075lb/ft^3(wa-wo) = 36lb, with a C = 96 cfm fan. With an average (33.6+40.6)/2 = 37.1 F daytime temp, this costs about 6h(82-37.1)96 = 25.9K Btu/day of heat.

The dew point of 82 F (542 R) air at 70% RH is approximately 542/(1-542ln(0.7)/9621)-460 = 71 F. If we cool it to Tg < 71 (F) with condensation, it will have vapor pressure Pg = e^(17.863-9621/(460+Tg)) "Hg at 100% RH and humidity ratio wg = 0.62198/(29.921/Pg-1). For example, cooling it to 43 F makes Pg = 0.282 "Hg and wg = 0.0059, so we can remove 36 pounds of water vapor in 6 hours if 6hx60m/hxCx0.075lb/ft^3(wa-wg) = 36lb, with a C = 124 cfm fan, at a cost of about 6h(82-43)124 = 29K Btu of sensible heat + 36K Btu for the latent heat of condensation, totaling 65K Btu/day.

If the condensation happens on the inside of 500 ft 2 of outer glazing film with a 3 Btu/h-F-ft^2 conductance to 37.1 F outdoor air, the glazing temp Tg will be 37.1+65K/6h/500/3 = 44.3 F, which is warmer than 43 F, so let's try cooling the air to (44.3+43)/2 = 43.7. Then Pg = 0.290 "Hg and wg = 0.0061 and C = 1.33/(0.01671-0.0061) = 125.4 cfm and the glazing gains 6h(82-43.7)125.4+6K = 64.8K Btu and Tg = 37.1+64.8K/6h/500/3 = 44.3 F. That's closer.

With tall indeterminate tomato plants and an 8' height and 80% solar transmission, the greenhouse could gain 0.8x10'(9'x520+8'x830') = 90.6K Btu/day. Dehumidifcation with 64.9K Btu/day leaves 90.6K-64.9K = 25.7K Btu for 18 hours of nighttime heat and more efficient dehumidification by night ventilation. With 18h(64-33.6)(500ft^2/R20+C) = 25.7K, C = 22 cfm, which can remove 18hx60x22x0.075(0.01671-0.0028) = 25 lb/day of water vapor. We could reduce the dew point of
greenhouse air to 64 F by condensation before night ventilation to avoid dripping water on plants.

Meanwhile, page 1 of says "on average, yields of crops should increase by 33% with a doubling of C02 concentration in the earth's atmosphere," ie 700 vs 350 ppm, and page 549 of Joe Hanon's Greenhouses book (CRC, 1998) says a 1 kg dry weight compost loss can provide 1.5 kg of CO2 and suggests 7-14 kg/m^2 of wet compost to provide sufficient CO2 for 20 days, eg 88 kg (193 lb) for a 9'x10' 8.4 m^2 greenhouse. Some growers spread straw between crops in windrows and keep it moist and turn it every 2-3 days, but it seems more efficient to keep compost in a closed and insulated container with an oxygen sensor and a blower to maintain at least 1% O2 and a humidity sensor and a solenoid valve to maintain a 50% moisture content, or less, if less CO2 is required. says:

>... about 0.50–0.60 kg of CO2/hr/100 m2 must be added in a ‘standard’ glass greenhouse to maintain 1,300 ppm. For double-polyethylene houses supplementation is 0.25–0.35 kg of CO2/hr/100 m2. For glass houses, supplementation is primarily used to offset the dilution due to air infiltration, while for double-poly houses the amount of CO2 required is about equal for the natural air exchange and photosynthesis.

Years ago, I visited a prizewinning orchid grower in Pennsylvania. He was a retired chemist. His greenhouse was rather dark and completely closed in, with a huge air conditioner and a natural gas heater with a thermostat and mister nozzles with a humidistat and a solenoid valve to maintain 90 F at 90% RH for 24 hours per day and alcohol lamps for CO2 enrichment and powerful fans to make plants move for better gas diffusion absorption by stomata...


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