Environmental Thermal Engineering Lecture # 13 Min soo Kim Mechanical & Aerospace Engineering

Space Heating load

The types of heat loads ㅊ 20℃ 5℃ Through the sealing Through the window Through the wall Through the sealing Through the shared wall Through the floor

The kinds of heat loads The kinds of heat loads ① conducted heat by the temperature difference - through the window - through the wall, roof - through the shared wall ② leaking air - by infiltration ③ entering air - by ventilation Entering air Conducted heat by temperature difference humidification Leaking air

Categories of heating and cooling loads exfiltration infiltration Transmission internal Solar Categories of heating and cooling loads

Design Criteria External condition Building structure / Insulation Degree of exposure / Airtightness Area of window Hours of use / Occupied room characteristic Temperature drop condition Daily temperature range / Lowest Auxiliary heating system Economic feasibility

Internal condition Purpose of building Occupied room characteristic Legal validity

Calculating heating loads Heat Loss by Conduction Heat loads Setting up external design criteria Determine internal temperature Calculating overall heat transfer coefficient Calculating areas of control spaces Leaking Air Σ Load due to Entering Air

1. Heat loss through external wall, roof, floor, and window q : Heat loss through external wall, roof, floor, and window [W] A : Area of wall, roof, floor, and window [㎡ ] U : Overall coefficient of heat transfer [W/㎡ K] : Indoor air temperature [K] : Outdoor air temperature [K]

- Heat loss through underground wall 2. Heat loss through underground wall and floor - Heat loss through underground wall - Heat loss through underground floor - Heat loss through floor on the surface of the earth

2-1 Path of heat loss through underground (without insulator) Heat flux Radial isothermal line

2-2 Path of heat loss through underground (with partial insulator) Air temperature +1 +2 +3 +4 +5 +6 +7 +8 +9 +10 +11 +12 Indoor temperature

Heat loss coefficient, W/( K) Minimum width of the building, m 6 7.3 2-3 Heat loss through underground floor Underground wall height Heat loss coefficient, W/( K) Minimum width of the building, m 6 7.3 8.5 9.7 1.5 0.18 0.16 0.15 0.13 1,8 0.17 0.14 0.12 2.1

1) Sensible heat loss 3. Heat loss due to outdoor air infiltration mo : Mass flow rate of outdoor air cp : Specific heat of air Q : Volume flow rate of outdoor air vo : Specific volume

2) Latent heat loss - Humidification load to maintain optimum humidity level ql : Required heat to increase humidity from Wo to Wi [W] Q : Volume flow rate of outdoor air infiltration [L/s] Wi : Absolute humidity of indoor air Wo : Absolute humidity of outdoor air hfg : Latent heat of vapor

- Empirical prediction of air change rate 4. Outdoor air infiltration prediction 1) Method of air change - Empirical prediction of air change rate - ACH (Air Change per Hour) range : 0.5 ~ 2.0 (fresh outdoor air) ex) Modern office building 0.1 ACH Outdoor air requirements per person = 36 CMH/person (ASHRAE)

- Prediction using pressure difference between indoor & outdoor 2) Cracking method - Prediction using pressure difference between indoor & outdoor and characteristics of window, wall, and door Q : Volume flow rate of outdoor air infiltration A : Valid leaking area of the crack C : Flow factor depending on crack shape and flow characteristics ΔP: Pressure difference between indoor & outdoor n : Flow characteristic factor at the crack (0.4 ~ 1.0)

Outdoor air characteristic at door and window

Window category Wood Double-hung (Locked) Other types Tight-fitting window K = 1.0 Weatherstripped average gap (1/64”. Crack) Wood casement and awning windows; weatherstripped Metal casement windows; weatherstripped Average-fitting window K = 2.0 Non- weatherstripped average gap (1/64”. Crack) All types of vertical and horizontal sliding windows; weatherstripped. Note: If average gap (1/64”. Crack) this could be tight-fitting window Weatherstripped large gap (3/32”. Crack) Nonweatherstripped. Note: If large gap (3/32”. Crack) this cuold be a loose-fitting window Loose-fitting window K = 6.0 weatherstripped large gap (3/32”. Crack) Vertical and horizontal sliding windows; nonweatherstripped Reference : ASHRAE Cooling and Heating Load Calculation Manual, 2nd ed., 1992.

Door category Tight-fitting door K = 1.0 Very small perimeter gap and perfect fit weatherstripping - often characteristic of new doors Average-fitting door K = 2.0 Small perimeter gap having stop trim fitting properly around door and weatherstripped Loose-fitting door K = 6.0 Larger perimeter gap having poor fitting stop trim and weatherstripped or Small perimeter gap with no weatherstripping Reference : ASHRAE Cooling and Heating Load Calculation Manual, 2nd ed., 1992.

: Pressure difference due to wind ----- (a) : Pressure difference due to chimney effects ----- (b) : Pressure difference due to pressurizations ----- (c) * Pressure differences are positive values when they make air flow into the building

(a) Pressure difference due to wind (pressure difference when Vf =0) Vw : Speed of wind Vf : Final speed of wind at the border of the building Cp : Pressure coefficient

- Pressure coefficient ( ) Depend on direction and shape of the building * Average pressure coefficient of low-rise building

Average pressure coefficient of high-rise building Reference : ASHRAE Handbook, Fundamentals Volume, 1989

Theoretical pressure difference without internal barriers (b) Pressure difference due to chimney effects - Chimney effects : Occurs when indoor & outdoor air densities are different - Neutral pressure height : Height where pressure difference is zero when only chimney effect is considered Theoretical pressure difference without internal barriers Po : Outdoor pressure [Pa] h : Vertical distance from neutral pressure height [m] To : Outdoor temperature [K] Ti : Indoor temperature [K] Ra : Gas constant of air

Pressure difference due to chimney effects * Ventilation coefficient Pressure difference due to chimney effects Po : Outdoor pressure [Pa] h : Vertical distance from neutral pressure height [m] To : Outdoor temperature [K] Ti : Indoor temperature [K] Ra : Gas constant of air

* Pressure difference due to chimney effects Reference : ASHRAE GRP 158, Cooling and heating Load Calculation Manual, 2nd ed., 1992

5. Heat loss through the duct system U : Overall heat transfer coefficient : Exterior surface area of duct : Mean temperature difference between air inside duct and surrounding

= The outside temperature – Air temperature inside the duct Example ⊙ Calculate the heat loss for circular duct when air flows 1000 cfm at 120 F. The length and diameter of duct are 25 ft and 16 in respectively. The insulator of duct is 1 in fiber glass and overall heat transfer coefficient is 0.2 Btu/(hr- -F). The outside temperature is 12F. Sol) = The outside temperature – Air temperature inside the duct : Surface area of duct( )

Bin method ⊙ Method to calculatee heating load with the outdoor temperature changes within a certain period, energy consumption of building depends on outdoor temperature, and occurrence (hours) Heating load Heating load to maintain proper indoor temperature (Q) Outdoor temperature (to) Balance point : (tb) Point which heating & cooling are not required

⊙ It is required to consider a case that people are inside the building (occupied) to compute heating load of the building. Heating load d Occupied Unoccupied Internal load Outdoor temperature

⊙ Partial Load Factor (PLF) ※ : Performance degradation coefficient

⊙ Occupied run time (Hr) ⊙ Unoccupied run time (Hr)

⊙ Occupied Electrical resistance Input (kW) ⊙ Unoccupied Electrical resistance Input (kW) ⊙ Total Energy (kWh)

⊙ Sequence of Bin method Set building load using load curve Set unit capacity Calculate theoretical operating time as ratio of building load and unit capacity Calculate partial load ratio Calculate real operating time ratio Calculate real operating time (Bin hour * Real operating time ratio) Calculate power consumption of unit Calculate energy required (Power consumption of unit * Real operating time) Set the cost of unit energy Calculate energy cost of a single bin (Cost of unit energy * Energy required ) Repeat 1~10 for all the other bins

# Example ⊙ Consider a building in the state of Oklahoma. The curve of system load is expressed as follow. Load curve of residential hours (Group A) = 267,000 – 4860×to [kW] Load curve of nonresidential hours (Group B) = 316,000 – 4860×to [kW] Use performance curve of heat pump, and assume degradation factor is 0.25. All bins in table is happened in cold whether. Calculate necessary energy of heating building to keep 70 F for residential and nonresidential group. ♣ Appendix 1 : transfer of bin hours of group A and B. ♣ Appendix 2 : Ratio of bin hours at each times ♣ Appendix 3 : Bin hours for in the state of Oklahoma yearly ♣ Appendix 4 : Calculate bin hours for groups at each hours ♣ Appendix 5 : Operation curve of heat pump ♣ Appendix 6 : Heating capacity of heat pump at 6000 CFM ♣ Appendix 7 : Solution

♣ Appendix 1

Table. Bin hour ratio of time shifts ♣ Appendix 2 Table. Bin hour ratio of time shifts Time Group Hours in Shift A in Each Group Days in Shift A in Each Group Total Occupied Hours in Each Group Total Hours in Each Group Shift A Fraction in Each Group Shift B Fraction in Each Group I 28 0.0 1.0 II 1 5 0.18 0.82 III 4 20 0.71 0.29 IV V 2 10 0.36 0.64 VI

Table. Annual bin hour of Oclahoma ♣ Appendix 3 Table. Annual bin hour of Oclahoma Bin Temperature (F) Shift A Hours Each Time Group Total Hours 1-4 I 5-8 II 9-12 III 13-16 IV 17-20 V 21-24 VI 102 2 97 5 70 29 104 92 55 153 88 296 87 116 145 120 24 407 82 20 33 148 168 96 618 77 121 93 132 115 144 171 776 72 229 221 138 118 117 186 1009 67 161 98 136 747 62 99 95 135 642 57 105 108 81 601 52 103 137 94 133 684 47 100 66 122 569 42 150 91 140 667 37 89 54 76 621 32 107 74 40 50 504 27 63 51 22 36 41 23 17 31 19 1 16 12 7 3 18

Table. Bin hours of time shifts ♣ Appendix 4 Table. Bin hours of time shifts Bin Temperature (F) Shift A Hours Each Time Group I (0.00”) II (0.18”) III (0.71”) IV (0.71”) V (0.36”) VI (0.00”) 102 1 97 4 50 10 92 39 109 32 87 82 103 43 6 105 60 77 17 94 52 72 40 98 84 42 67 29 70 33 62 18 96 35 57 19 75 48 47 71 31 22 37 28 63 38 27 25 53 9 7 16 12 8 2

Characteristics of heat pump ♣ Appendix 5 Characteristics of heat pump

Table. Heating capacity of heat pump where air flow rate is 6000 CFM ♣ Appendix 6 Table. Heating capacity of heat pump where air flow rate is 6000 CFM Outdoor temperature (F) Heating Capacity, Btu/hr x 1000 at Indoor Dry Bulb Temperature (F) Total Power Input (kW) at Indoor Dry Bulb Temperature (F) 60 70 75 80 -3 70.5 68.8 68.0 67.2 12.9 13.3 13.5 13.7 2 78.7 76.9 75.9 75.0 13.4 13.8 14.0 14.2 7 87.0 84.9 83.9 82.9 14.5 14.7 12 95.2 93.0 91.8 90.7 14.3 14.9 15.2 17 103.0 101.0 99.8 98.6 15.4 15.7 22 111.0 109.0 108.0 106.0 15.0 15.5 16.0 27 120.0 117.0 115.0 114.0 15.3 15.8 16.3 32 128.0 125.0 123.0 121.0 16.6 37 140.0 136.0 135.0 133.0 16.8 17.1 42 158.0 154.0 152.0 150.0 16.9 17.4 17.7 18.0 47 176.0 172.0 170.0 168.0 18.3 18.6 18.9 52 188.0 184.0 182.0 179.0 18.2 19.1 19.4 57 201.0 196.0 193.0 191.0 18.7 19.3 19.7 20.0 62 213.0 208.0 205.0 202.0 19.2 19.9 20.2 20.5 67 225.0 219.0 217.0 214.0 20.4 20.7 21.0 * Correction factor – Value with different air flow rate – (Value with 6000 CFM air flow x Correction factor)

Solution ♣ Appendix 1

Table. Bin hour ratio of time shifts ♣ Appendix 2 Table. Bin hour ratio of time shifts Time Group Hours in Shift A in Each Group Days in Shift A in Each Group Total Occupied Hours in Each Group Total Hours in Each Group Shift A Fraction in Each Group Shift B Fraction in Each Group I 28 0.0 1.0 II 1 5 0.18 0.82 III 4 20 0.71 0.29 IV V 2 10 0.36 0.64 VI X axis value of appendix 1 1-shift A fraction in Each Group Y axis value of appendix 2 Total hours in each group Total Occupied Hours in Each Group Total Hours in Each Group

Table. Annual bin hour of Oclahoma ♣ Appendix 3 Table. Annual bin hour of Oclahoma Bin Temperature (F) Shift A Hours Each Time Group Total Hours 1-4 I 5-8 II 9-12 III 13-16 IV 17-20 V 21-24 VI 102 2 97 5 70 29 104 92 55 153 88 296 87 116 145 120 24 407 82 20 33 148 168 96 618 77 121 93 132 115 144 171 776 72 229 221 138 118 117 186 1009 67 161 98 136 747 62 99 95 135 642 57 105 108 81 601 52 103 137 94 133 684 47 100 66 122 569 42 150 91 140 667 37 89 54 76 621 32 107 74 40 50 504 27 63 51 22 36 41 23 17 31 19 1 16 12 7 3 18

Table. Computing bin hours for each time group ♣ Appendix 4 Total hours – Shift A hours Table. Computing bin hours for each time group Bin Temperature (F) Shift A Hours Each Time Group Shift A Hours Shift B Hours I (0.00”) II (0.18”) III (0.71”) IV (0.71”) V (0.36”) VI (0.00”) 102 1 97 4 50 10 64 40 92 39 109 32 179 117 87 82 103 43 229 178 6 105 60 280 338 77 17 94 52 244 532 72 98 84 42 264 745 67 29 70 33 202 545 62 18 96 35 216 426 57 19 75 212 389 48 230 454 47 71 31 166 403 22 172 495 37 28 63 38 27 156 465 25 53 124 380 9 54 175 7 16 12 8 44 127 2 21 74 3 15 Total 2861 5899 “ Ratio of occupied time shift (shift A)

♣ Appendix 6 Table. Heating capacity of heat pump where air flow rate is 6000 CFM Outdoor temperature (F) Heating Capacity, Btu/hr x 1000 at Indoor Dry Bulb Temperature (F) Total Power Input (kW) at Indoor Dry Bulb Temperature (F) 60 70 75 80 -3 70.5 68.8 68.0 67.2 12.9 13.3 13.5 13.7 2 78.7 76.9 75.9 75.0 13.4 13.8 14.0 14.2 7 87.0 84.9 83.9 82.9 14.5 14.7 12 95.2 93.0 91.8 90.7 14.3 14.9 15.2 17 103.0 101.0 99.8 98.6 15.4 15.7 22 111.0 109.0 108.0 106.0 15.0 15.5 16.0 27 120.0 117.0 115.0 114.0 15.3 15.8 16.3 32 128.0 125.0 123.0 121.0 16.6 37 140.0 136.0 135.0 133.0 16.8 17.1 42 158.0 154.0 152.0 150.0 16.9 17.4 17.7 18.0 47 176.0 172.0 170.0 168.0 18.3 18.6 18.9 52 188.0 184.0 182.0 179.0 18.2 19.1 19.4 57 201.0 196.0 193.0 191.0 18.7 19.3 19.7 20.0 62 213.0 208.0 205.0 202.0 19.2 19.9 20.2 20.5 67 225.0 219.0 217.0 214.0 20.4 20.7 21.0 * Correction factor – Value with different air flow rate – (Value with 6000 CFM air flow x Correction factor) Linear interpolation Linear interpolation  C = 2367to + 60,767  P = 0.103to + 13.4

Characteristics of heat pump ♣ Appendix 5 Characteristics of heat pump

Power consumption can be calculated as below by same way. ♣ Appendix 7 Given load curve is suitable for applying bin method. For each shifts, it is possible to calculate balance point by set and zero. Occupied case  to=267,000/4860 = 55 F Unoccupied case  tuo=316,000/4860 = 65 F Therefore, we don’t need to consider temperature bins higher than 65 F. Steady state performance of heat pump can be computed as below with appendix 6. Choose two heating capacity and temperature (17 F, 101.0 Btu/hr and 47 F, 172.0 Btu/hr) and suppose heating capacity is linearly dependent to outdoor temperature(aX+b=Y). The result is shown below.  C = 2367to + 60,767 Btu/hr Power consumption can be calculated as below by same way.  P = 0.103to + 13.4 kW

Equipment Capacity (J/K) # Calculate sequence of example prob. (1-1) Bin Temperature Occupied Hours Unoccupied Hours Occupied Load (Btu/hr) Unoccupied Load (kW) Equipment Capacity (J/K) Occupied PLF 1 Table 5-6 2 3 4 Given Eq. 5-26 5 Given Eq. 5-27 6 Given Eq. 5-28 7 Eq. 5-24, Dc=0.25 62 216 426 14,680 207,521 0.75 57 212 389 38,980 195,686 52 230 454 14,280 63,280 183,851 0.77 47 166 403 38,580 87,580 172,016 0.81 42 172 495 62,880 111,880 160,181 0.85 37 156 465 87,180 136,180 148,346 0.90 32 124 380 111,480 160,480 136,511 0.95 27 54 175 135,780 184,780 124,676 1.00 22 127 160,080 209,080 112,841 17 21 74 184,380 233,380 101,006 12 15 208,680 257,680 89,171 From appendix 4 From load curve From interpolation

# Calculate sequence of example prob. (1-2) Unoccupied PLF Occupied Run Time (Hr) Unoccupied Run Time (Hr) Power Input (kW) Occupied Electrical resistance Input (kW) Unoccupied Electrical resistance Input (kW) Total Energy (kWh) 8 Eq. 5-24 Dc = 0.29 9 4x2/(6x7) 10 5x3/(6x8) 11 Given Eq. 5-29 12 4-6 13 5-6 14 9x(11+12)+ 10x(11+13) 0.77 0.0 39.3 19.8 776.7 0.80 96.9 19.3 1,867.0 0.84 23.2 186.9 18.8 3,941.1 0.88 46.2 233.9 18.2 5,108.8 0.92 79.6 373.9 17.7 8,039.4 0.98 102.2 435.8 17.2 9,259.8 1.00 106.1 446.7 16.7 7.0 12,368.6 58.8 259.4 16.2 3.3 17.6 9,908.6 62.4 235.3 15.7 13.8 28.2 12,168.8 38.3 171.0 15.2 24.4 38.8 10,741.5 43.3 14.6 35.0 49.4 3,123.8 Total 77,301.1 From interpolation