Design procedure
1.​ Define entering and leaving air conditions for an evaporator, and air flow through both
evaporator and condenser coil.
2.​ Select a fan based on designed air flow rate with some allowance for pressure loss.
3.​ Determine cooling load and apparatus dew point (ADP) from psychrometric analysis.
4.​ Select a refrigerant and a compressor based on its cooling capacity near ADP.
5.​ Define design conditions as evaporating temperature equals to or less than ADP,
condensing temperature of your choice, and ARI rating values for superheating,
subcooling, and ambient temperature for the compressor.
6.​ Determine refrigerant flow rate, cooling capacity, compressor power consumption,
and total heat rejection from the compressor performance curves. Make sure that
cooling capacity is greater than cooling load.
7.​ Design a capillary tube to match the refrigerant flow rate at design conditions.
8.​ Design a condenser with sufficient surface area to ensure proper heat rejection at
design conditions, including discharge gas superheating and liquid subcooling.
9.​ Design an evaporator with sufficient surface area to meet rated cooling capacity at
design conditions, including suction gas superheating.
10.​Build a system prototype and charge the refrigerant until the designed evaporating
temperature is reached.
Design example
Step 1: Define entering air conditions and air flow for both evaporator and condenser coils,
and leaving air conditions for the evaporator.
Evaporator
Air flow = ……450…… CMH = ……0.125…… CMS = ……0.144…….. kg/s
𝑇𝑑𝑏( 𝐶)
RH (%)
W (g/kg)
h (kJ/kg)
Entering air
27
60
13.48
61.52
Leaving air
10
6.65
26.80
𝑜
Condenser
Air flow = ……450…… CMH = ……0.125…… CMS = ……0.144…….. kg/s
𝑜
𝑇𝑑𝑏( 𝐶)
Entering air
10
Leaving air
N/A
RH (%)
N/A
W (g/kg)
h (kJ/kg)
7.25
28.33
N/A
N/A
Step 2: Select a fan based on designed air flow rate with some allowance for pressure loss.
Fan model: ……………………………...
●​ Manufacturer: …………………..
●​ Rated airflow: …………………..
●​ Electrical: ……………………….
●​ Voltage: ………. V
●​ Power: ……….. W
●​ Phase: ………..
Fan performance curves
Step 3: Determine cooling load and apparatus dew point (ADP) from psychrometric analysis.
Evaporator cooling load = ……4650….. W = ……16000….. btu/h
𝑜
Apparatus dew point (ADP) = ……5…. ( 𝐶)
Step 4: Select a refrigerant and a compressor based on its cooling capacity near ADP.
Compressor model: …………RN220VHSMT………………
●​ Manufacturer: ………SCI…………..
●​ Refrigerant: …………R410a…………..
●​ Frequency: …50… Hz
●​ Voltage: …220……. V
●​ Current: ……….. A
●​ Phase: ……1…..
Step 5: Define design conditions as evaporating temperature equals to or less than ADP,
condensing temperature of your choice, and ARI rating values for suction gas superheating,
liquid subcooling, and ambient temperature for the compressor.
𝑜
Evaporating temperature = …2….. ( 𝐶)​
𝑜
Condensing temperature = …50….. ( 𝐶)
𝑜
𝑜
Suction gas superheating = …11.1…. ( 𝐶)​ Liquid subcooling = ………8.4…….. ( 𝐶)
𝑜
Ambient temperature = ……35….. ( 𝐶)
Step 6: Determine refrigerant flow rate, cooling capacity, compressor power consumption,
and total heat rejection from the compressor performance curves. Make sure that cooling
capacity is greater than cooling load.
Refrigerant flow rate = ……105…. (kg/h)
Cooling capacity = ……4800…… (W) = ……16400……. (btu/h)
Power consumption = ……1750…. (W)
Total heat rejection = ……6550….. (W) = ……22350……. (btu/h)
Step 7: Design a capillary tube to match the refrigerant flow rate at design conditions.
Target refrigerant flow rate = ……105…….. (kg/h)
𝑜
Liquid subcooling ∆𝑡𝑠𝑐 = …8.4….. ( 𝐶)
𝑜
Capillary tube inlet temperature = Condensing temp. - Liquid subcooling = …41.6….. ( 𝐶)
From the Saturation Properties Table for Refrigerant ……R410a…. , at the inlet temperature:
𝑃𝑠𝑎𝑡 (𝑃𝑎)
3
3
ν𝑓 (𝑚 /𝑘𝑔) ν𝑔 (𝑚 /𝑘𝑔) ℎ𝑓𝑔 (𝐽/𝑘𝑔)
𝑐𝑝𝑓 (𝐽/𝑘𝑔. 𝐾) µ𝑓 (𝑃𝑎. 𝑠)
µ𝑔 (𝑃𝑎. 𝑠)
2.50 E+6
0.001034
1970
14.71 E-6
0.00929
156280
95.90 E-6
Select capillary tube diameter 𝑑𝑐 = ……1.77…. mm = …0.00177…. m = ……0.07…. inch
Select capillary tube length 𝐿𝑐 = ……500…. mm = …0.500……. m = ……20….. inch
Calculate capillary tube dimensionless parameters as follows:
Dimensionless parameter
Definition
Value
Geometry effect
π1 = 𝐿𝑐 / 𝑑𝑐
2.94 E+02
Vaporization effect
π2 = 𝑑𝑐 ℎ𝑓𝑔 / ν𝑓 µ𝑓
Bubble formation
π3 = 𝑑𝑐σ / ν𝑓µ𝑓
Inlet pressure
π4 = 𝑑𝑐 𝑃𝑠𝑎𝑡 / ν𝑓µ𝑓
Inlet subcooling
π5 = 𝑑𝑐 𝑐𝑝𝑓∆𝑡𝑠𝑐 / ν𝑓 µ𝑓
4.86 E+12
Density effect
π6 = ν𝑔 / ν𝑓
8.99 E+00
Viscous effect
π7 = (µ𝑓 − µ𝑔)/ µ𝑔
5.52 E+00
Mass flow rate
π8 = 𝑚 / 𝑑𝑐µ𝑓
To be calculated
2
2
4.60 E+13
2
N/A
2
2
2
2
2
7.60 E+11
2
Calculate dimensionless mass flow rate from
−0.484
π8 = 1. 8925 × π1
−0.824
π2
1.369
π4
0.0187
π5
0.773
π6
0.265
π7
= ……182100……. (dimensionless)
Predicted mass flow rate 𝑚 = π8 𝑑𝑐µ𝑓 = ……0.0297……. (kg/s) = ……107……. (kg/h)
(Repeat the previous calculations with new combinations of capillary tube diameter and
length until the predicted mass flow rate is approximately equal to the target mass flow rate.)
Step 8.1: Condenser design (calculate film coefficient)
Operating conditions
Total condenser heat load = ………. W
Air flow rate through the condenser = ………. CMH = ……….. CMS = ……….. kg/s
Design condenser geometry
●​ Number of rows = 4
●​ Vertical tube spacing = …25.4….
●​ Horizontal tube spacing = …15.88…
●​ Tube outer diameter = …9.53…..
●​ Fin pitch = …….
●​ Fin thickness = …0.11…
●​ Gap between fins = …2.01….
●​ Finned length = …350….
●​ Finned height = …406.4….
●​ Fin depth = …47.63….
●​ Face area = …0.142….
Entering air conditions
●​ Temperature = …19….
●​ Face velocity = …1.76…. m/s
From the Ideal Gas Properties Table for air, at mean air temperature and 1 atm pressure:
ρ (𝑘𝑔/𝑚 )
𝑐𝑝 (𝐽/𝑘𝑔. 𝐾)
µ (𝑃𝑎. 𝑠)
Pr (dimensionless)
1.184
1.009
1.85 E-05
0.7296
3
Calculate dimensionless parameters for condenser as follows:
Dimensionless term
Definition
Value
Reynolds number
𝑅𝑒𝐷 = ρ𝑉𝐷 / µ
1072
Colburn j-factor for 3
or more tubes
𝑗 = 0. 163𝑅𝑒𝐷
Stanton number
𝑆𝑡 = 𝑗 / 𝑃𝑟
−0.369 𝑆𝑡 0.106
𝑠 0.0138 𝑆𝑡 0.13
(𝑆 )
(𝐷)
(𝐷)
𝑙
2/3
Calculate mass velocity 𝐺𝑐 = ρ𝑉 = ………..
Air-side film coefficient 𝑓𝑎 = 𝐺𝑐𝑐𝑝 × 𝑆𝑡 = ……37.60…….W/m2.K
Step 8.2: Condenser design (calculate fin efficiency)
Fin depth 𝐿𝑑 = …47.63…. mm​
Fin thickness 𝑌𝑓 = …0.11…. mm
Fin height 𝐿𝑓 = …406.4…. mm​
Fin thermal conductivity 𝑘𝑓 = ……200….. (𝑊/𝑚. 𝐾)
Calculate the following fin parameters:
𝑥𝑒 =
𝐿𝑓𝐿𝑑/π = 11. 33 𝑚𝑚​ ​
𝑥𝑏 = 𝐷𝑜/2 = 4. 76 𝑚𝑚​
𝑈𝑏 = 𝑤 2𝑓𝑎/𝑘𝑓𝑌𝑓 / (𝑥𝑒/𝑥𝑏 − 1) = 0. 393​
​
β1 = 𝐼1(𝑈𝑒)/𝐾1(𝑈𝑒) = 0. 772​ ​
ϕ=
​
𝑤 = 𝑥𝑒 − 𝑥𝑏 = 6. 57 𝑚𝑚
𝑈𝑒 = 𝑈𝑏(𝑥𝑒/𝑥𝑏) = 0. 935
𝐼 (𝑈 )−β 𝐾 (𝑈 )
2
2
𝑈𝑏(1−(𝑈𝑒/𝑈𝑏) )
× 𝐼1(𝑈𝑏)−β1𝐾1(𝑈𝑏) = 0. 870
0
𝑏
1 0
𝑏
Design number of tubes and fins for the condensing section
●​ Finned length of this coil = ………350……. mm
●​ Number of fins per unit finned length = ………12……. FPI
●​ Total number of fins for this coil = ……165……. fins
●​ Total number of tubes for this coil = ……48….. tubes
Summary of operating conditions for the condensing section
𝑜
●​ Effective surface temperature = …55….. ( 𝐶)
𝑜
●​ Entering air temperature = …19….. ( 𝐶)
●​ Air flow through this coil = ……900…. CMH = …0.25…. CMS = …0.296…. kg/s
Capacity verification for the condensing section
2
●​ Total external tube surface area = π𝐷𝑜 (𝐿𝑡𝑢𝑏𝑒 − 𝑁𝑓𝑖𝑛𝑌𝑓𝑖𝑛)𝑁𝑡𝑢𝑏𝑒 = 0.637 m2
2
●​ Total fin surface area = (𝐿𝑓𝑖𝑛𝐻𝑓𝑖𝑛 − π𝐷𝑜 /4) × 2𝑁𝑓𝑖𝑛 = = 7.011 m2
●​ Total effective surface area = 𝐴𝑡𝑢𝑏𝑒 + ϕ𝐴𝑓𝑖𝑛 = = 6.740 m2
●​ Number of transfer units 𝑁𝑇𝑈 = 𝑓𝑎𝐴𝑒𝑓𝑓 / 𝑚𝑎𝑐˙𝑝 = 0.848
●​ Air-side effectiveness ϵ = 1 − 𝑒𝑥𝑝(− 𝑁𝑇𝑈) = 0.572
●​ Leaving air temperature = 𝑡𝑎1 + ϵ(𝑡𝑠 − 𝑡𝑎1) = 37.9 C
●​ Sensible heat transfer 𝑄𝑠 = 𝑚˙ 𝑎𝑐𝑝(𝑡𝑎2 − 𝑡𝑎1) = 6833 W
●​ (Repeat the previous calculations with new coil geometry until the calculated sensible
heat transfer is equal to or greater than the condenser heat load.)