Cold Room Refrigeration Load: Method

Cold Room Refrigeration Load

The tool adds up the heat that enters a walk-in cooler, a freezer or a cold store in 24 hours and sizes the refrigeration to remove it in the hours the plant runs. The procedure is the daily heat balance of the "Heat Load Calculation" section of USDA Agriculture Handbook 66 (2016, pages 19 to 21), whose pear-storage example is the default case; the doorway equation, the respiration table and the equipment relations are described below. Quantities owned by a copyrighted handbook or by a manufacturer (air changes against room volume, doorway flow factor, effectiveness of door protection, product thermal properties, coil ratings, compressor COP) are entered inputs.

Units

Room volume, surface areas, door size, product mass, powers and altitude carry unit dropdowns and are converted when the unit system is switched. The other inputs are plain numbers in the unit named on the form and are not converted by the switch: temperatures in °C (SI) or °F (USCS); U in W/m²·K or Btu/h·ft²·°F; R in m²·K/W or h·ft²·°F/Btu; insulation thickness in mm or inches; conductivity in W/m·K or Btu·in/h·ft²·°F; specific heat in kJ/kg·K or Btu/lb·°F; latent heat in kJ/kg or Btu/lb; respiration heat in W per tonne or Btu per short ton per day; air heat in kJ/m³ or Btu/ft³; evaporator TD and sun allowance in K or °F. Results are in kJ and kW (SI) or Btu and Btu/h (USCS); the capacity is always given in kW, Btu/h and tons of refrigeration (1 ton = 12,000 Btu/h = 3.517 kW).

Transmission

For each surface q = U A (T_far + ΔT_sun − T_room), carried for 24 hours. U is entered, or taken as 1/R, or as k divided by the insulation thickness; surface films and the panel skins are not added (their resistance is small against the insulation; include them in R when wanted). The far-side temperature is the outside design temperature unless one is entered for the surface (an adjoining room, the ground under the floor). The sun allowance is a temperature added to the far side of a roof or wall in the sun; the refrigeration handbooks tabulate such allowances by orientation and surface color, and the value is entered here.

Infiltration

Air changes. Load per 24 hours = room volume × air changes per 24 hours × heat removed per unit volume of the entering air. The heat per unit volume is computed from the moist-air states, q_v = (h_o − h_r) / v_r per cubic meter of room air, or entered. The handbook example uses 74.5 kJ/m³ for air at 30 °C and 50 % brought to −1.1 °C, and 15.3 kJ/m³ for 7.2 °C and 70 %; the psychrometric relations give 74.3 and 15.1 kJ/m³ with a room at 90 % relative humidity. The number of air changes falls with room volume and rises with traffic; the tables of average air changes in the refrigeration handbooks are entered values here (the example uses 6 per day while the room is being loaded and 1.8 in storage).

Doorway equation. Cold room air flows out through the lower part of an open doorway and warm air flows in above it. With an orifice-type velocity profile on each side of the neutral level and equal mass flows in and out, the volume of room air leaving is

Q = 0.221 A (1 − ρ_i/ρ_r)^0.5 (g H)^0.5 F_m, F_m = [2 / (1 + (ρ_r/ρ_i)^1/3)]^1.5

with A the doorway area, H its height, ρ_r and ρ_i the densities of the room air and of the entering air (Gosney and Olama 1975). The neutral level sits at H / (1 + (ρ_r/ρ_i)^1/3) above the floor, and 0.221 is one third of the flow coefficient 0.663. The load while the door stands open is q = (Q / v_r)(h_i − h_r). The average over the day is q D_t D_f (1 − E) for each doorway, where D_t = (passages × seconds per passage + 60 × minutes standing open) / 86,400 is the open-time fraction, D_f the doorway flow factor (the flow does not establish itself fully during short openings; the refrigeration handbooks use about 0.8 for temperature differences above 11 K and up to 1.1 for small ones) and E the effectiveness of a strip curtain, air curtain or vestibule (0 for an open doorway). A secondary printing of the equation gives the ratio in F_m the other way up; the form above is the one that satisfies the mass balance, which the test script verifies by integrating the two velocity profiles numerically.

Sensible and latent parts. The enthalpy difference of the two air states splits exactly into a sensible part (1.006 + 1.86 W_r)(t_o − t_r) and a latent part (W_o − W_r)(2501 + 1.86 t_o), in kJ per kg of dry air; the infiltration load is divided in that ratio. The moisture carried in per day, dry-air mass × (W_o − W_r), is what the coil collects as condensate or frost. The heat of fusion of the frost is not added to the load (the usual practice; the defrost heat is entered separately).

Product

Each row is a lot: product, packaging, bins or pallets. Above freezing Q = m c (T₁ − T₂). With "Cooling and freezing", a lot taken below its freezing point T_f gives Q = m [c_a (T₁ − T_f) + h_f + c_b (T_f − T₂)]. Thermal properties are entered; for foods they follow closely from the water fraction w (Siebel's relations: c_a ≈ 0.837 + 3.349 w and c_b ≈ 0.837 + 1.256 w kJ/kg·K, h_f ≈ 334 w kJ/kg). A lot cooled within 24 hours puts all of Q into the day; a lot with a longer cooling time t puts 24 Q / t. The handbook example cools each day's intake in two days, so the peak day carries the first-day cooling of one lot and the second-day cooling of the lot before it.

Respiration. Fresh fruits and vegetables give off heat as they respire: load = mass × rate × 24 hours, with the rate at the mean temperature of the lot. The rate is entered in W per tonne (Btu per ton per day), or left blank to take it from Table 1 of USDA Agriculture Handbook 66, which lists the carbon dioxide production in mg per kg per hour at 0, 5, 10, 15 and 20 °C; the handbook's conversion is 61 kcal per tonne per day (220 Btu per ton per day) for each mg/kg·h, that is 2.955 W per tonne. Thirty commodities whose rows carry no footnoted values are offered. Between printed temperatures the tool interpolates on the logarithm of the rate; outside them it holds the end value, so a room below 0 °C takes the 0 °C rate. Pears are not in the summary table; the default rows carry the rates of the handbook example (12,206, 1,741 and 812 kJ per tonne per day at 13, 1.7 and −1.1 °C).

Internal loads and defrost

Lights, motors, fork trucks and fans: power × quantity × hours per day × fraction released in the room. For a motor inside the room enter its input power (shaft power divided by efficiency). People: the heat given off rises as the room gets colder; a blank entry uses 272 − 6 T watts per person with T the room temperature in °C, which gives 279 W at −1.1 °C against the 1,000 kJ/h (278 W) of the handbook example. Defrost: heater power × defrosts per day × minutes × the fraction of the heat that stays in the room, an entered estimate.

Summary and equipment

The categories are summed, the safety factor is added, and the required capacity is the total divided by the run time (16 to 20 hours per day leaves time for defrost; 18 in the handbook example). The evaporating temperature is the room temperature less the evaporator temperature difference TD, and the coil rating wanted is capacity / TD, the form in which coil capacities are listed. A small TD keeps the room humid, which fresh produce needs; a large TD dries the air. The compressor power is capacity / COP with the COP entered, or estimated as a fraction η of the Carnot value T_e / (T_c − T_e) in absolute temperatures between the evaporating and condensing temperatures. The compressor energy per day is the load without the safety factor divided by the COP; the fans, lights and defrost heaters draw their own energy besides.

Pull-down check. The steady loads (everything except product cooling, as a 24 hour average) plus the cooling rates Q / t of the lots give the demand while every lot is being cooled; the installed capacity (or the required one) is compared with it, and the time to remove all the product heat with the plant running continuously is Σ Q / (capacity − steady loads).

Checks and limits

The test script reproduces every printed line of both handbook examples (cooling and filling: 12,539,232 kJ per day, 55 tons; storage: 757,895 kJ per day, 3.3 tons), compares each shipped respiration rate with the handbook text, and runs 20 randomly generated rooms against a separately written numpy and scipy reference. The handbook's summary prints the transmission line as 519,149 where its own arithmetic and subtotal use 591,149, writes the ton as 12,660 kJ "per 24 h" where it is per hour, and quotes an insulation conductivity (1.3 kJ per m² per cm per °C) that does not agree with its U of 1.1 kJ/h·m²·°C; the tool follows the U-value.

Not covered: solar gain through glass doors, heat of fusion of frost, moisture loss of the product, transient cooling of the product by its size and packaging (the cooling time is entered), a table of air changes by room volume, selection of actual coils and condensing units, and the energy of fans and defrost in the cost. The method is a design-day estimate, not an hourly simulation.