22-Mec-B2 Environmental Control in Buildings · December 2016

Question 2 of 8: Winter plant with preheater, furnace and steam humidifier

Nivaar worked solution (AI-drafted; not reviewed by a licensed engineer)

Notes on this paper

Paper format. Professional Engineers of Ontario / Engineers Canada annual examination 07-Mec-B2 Environmental Control in Buildings, December 2016, three hours, open book. Eight problems of 20 points each; candidates are required to solve five, and all questions carry the same value. Psychrometric charts and an R-22 p-h diagram are appended to the paper. All eight problems are solved here.

Reference texts for this subject.

W. P. Jones, Air Conditioning Engineering, 5th ed., Butterworth-Heinemann — the standard reference for this examination code; Ch. 2–3 (psychrometry), Ch. 5–6 (heating and cooling loads), Ch. 15 (fans and duct design).
McQuiston, Parker & Spitler, Heating, Ventilating and Air Conditioning: Analysis and Design, 6th ed., Wiley — Ch. 3 (moist air), Ch. 5 (heat transmission in building structures), Ch. 8 (energy estimating and the degree-day method), Ch. 12–13 (fluid flow, fans and duct design).
ASHRAE Handbook — Fundamentals (2021) — Ch. 1 (psychrometrics), Ch. 14 (climatic design information), Ch. 18 (non-residential cooling and heating load calculations), Ch. 21 (duct design), Ch. 26 (heat, air and moisture control), Ch. 30 (thermophysical properties of refrigerants).
Moran, Shapiro, Boettner & Bailey, Fundamentals of Engineering Thermodynamics, 9th ed., Wiley — Ch. 10 (vapour-compression refrigeration and heat pumps).
ANSI/ASHRAE Standard 62.1, Ventilation for Acceptable Indoor Air Quality; ANSI/ASHRAE Standard 55, Thermal Environmental Conditions for Human Occupancy.
Canadian frame: National Building Code of Canada 2020 and its Appendix C design temperatures; National Energy Code of Canada for Buildings 2020; Environment and Climate Change Canada degree-day normals for Toronto and Ottawa; CSA B52 Mechanical Refrigeration Code; Canada Green Building Council LEED Canada and the CaGBC Zero Carbon Building Standard for Problem 5.

Check: assumptions carried through this paper. Cover-page instruction 1 invites a clear statement of any assumption. Standard barometric pressure of 101.325 kPa is used throughout; moist-air properties follow the ASHRAE Handbook — Fundamentals Ch. 1 formulation (Hyland–Wexler saturation pressure, so results agree with the appended chart to chart-reading accuracy rather than being read off it); R-22 properties are on the IIR datum and agree with the appended p-h diagram. Problem-specific assumptions — the coil bypass factor, climate and degree-day data, fuel prices and equipment efficiencies, duct roughness, and the CLTD / SCL / CLF table entries — are stated where they are first used.

Question 2: Winter plant with preheater, furnace and steam humidifier (20 points)

Question text not reproduced: the examination questions are © Engineers and Geoscientists BC. Open the official past paper (linked at the top of this page) to read the question, then follow the worked solution below.

Given. Outdoor air is preheated, mixed with return air in a fixed mass ratio, heated in the furnace and humidified with steam before delivery to the space.

Given data, Problem 2
Quantity	Symbol	Value
Outdoor air at the preheater inlet	state 1	−14 °C, ≈ 0 % RH
Preheater leaving temperature	t₂	16 °C
Supply air to the space	state 5	40 °C, 30 % RH
Space condition	state R	20 °C, 30 % RH
Outdoor-air fraction of supply, by mass	x	0.25
Total space heating load	q_t	145 kW
Space sensible heat factor	SHF	0.8
Humidifying steam	—	saturated, 1.2 bar (104.81 °C, h_g = 2,683.4 kJ/kg)

Find. The plant sketch and cycle, the dry- and wet-bulb temperature at every significant state, the supply condition and supply air quantity, the temperature rise across the furnace, the steam demand, and the furnace and preheater duties.

Part (a) — plant arrangement. The preheater treats only the outdoor-air stream, so the mixing box never sees sub-freezing air; the furnace and the steam humidifier then act on the full supply stream.

Approach. Fix the space and supply states, take the air quantity from the sensible balance, mix the preheated outdoor air with the return air to find the furnace inlet, then work backwards from the supply state through the steam-injection energy balance to split the remaining heat between the furnace and the humidifier.

Check: the data are over-specified. The paper states the supply condition (40 °C, 30 % RH) and the space sensible heat factor (0.8) and the total load (145 kW). These three do not describe one room process. Sizing the air on the sensible load gives 5.621 kg/s; the latent load alone would give 1.212 kg/s and the total enthalpy rise 3.229 kg/s. A supply state on a true SHF = 0.8 line from the space would sit at 40 °C and only about 14 % RH, not 30 %. Supply air is always sized on the sensible balance, because that is the balance the thermostat closes, so 5.621 kg/s is the answer carried forward and the stated supply humidity is treated as the design maximum that the humidistat throttles back from. No part of the question needs both readings, so nothing has to be reconciled — the redundancy is declared here under cover-page instruction 1.

Fix the space and supply states. With $W=0.622\,\phi p_{ws}/(p-\phi p_{ws})$ and $h=1.006\,t+W(2501+1.86\,t)$, the space at 20 °C and 30 % RH has $W_{R}=0.004337$ kg/kg (4.34 g/kg) and $h_{R}=31.13$ kJ/kg, wet bulb 10.85 °C. The supply air at 40 °C and 30 % RH has $W_{5}=0.013900$ kg/kg (13.90 g/kg), $h_{5}=76.04$ kJ/kg and wet bulb 25.09 °C. That answers the first half of part (c): the supply condition is the stated 40 °C dry bulb, 25.09 °C wet bulb.
Size the supply air on the sensible load. The sensible and latent shares of the 145 kW load are $q_{s}=0.8\times145=116$ kW and $q_{l}=29$ kW. Supply air must make up the sensible loss across the 20 K supply-to-room difference:$$\dot{m}=\frac{q_{s}}{c_{p}\,(t_{5}-t_{R})}=\frac{116}{(1.006+1.86\times0.013900)\times(40-20)}$$$$\boxed{\ \dot{m}=5.621\ \text{kg/s of dry air}\ }$$At the supply humid volume of 0.9069 m³/kg that is 5.098 m³/s, and the outdoor-air stream is $0.25\dot{m}=1.405$ kg/s.
Mix the preheated outdoor air with the return air. The preheater raises the outdoor air from −14 °C to 16 °C at constant moisture content, so state 2 is still essentially bone dry ($W_{2}\approx0$, wet bulb 3.75 °C). Mixing 25 % of it with 75 % return air gives$$W_{M}=0.25\times0+0.75\,W_{R}=0.003253\ \text{kg/kg},\qquad h_{M}=0.25\,h_{2}+0.75\,h_{R}=27.37\ \text{kJ/kg}$$$$t_{M}=\frac{h_{M}-2501\,W_{M}}{1.006+1.86\,W_{M}}=19.01\ ^\circ\text{C}$$so the furnace sees 19.01 °C dry bulb, 9.23 °C wet bulb, at 3.25 g/kg — noticeably drier than the room, which is exactly why humidification is needed.
Split the remaining heat between furnace and humidifier. Steam injection adds moisture and enthalpy but is not the place to add most of the sensible heat, so the furnace acts first, at constant $W_{M}$, and the humidifier then carries the state to 5. Injecting $\Delta W$ of steam of enthalpy $h_{g}$ raises the air enthalpy by $\Delta W\,h_{g}$, so working back from the supply state:$$\Delta W=W_{5}-W_{M}=0.010647\ \text{kg/kg},\qquad h_{4}=h_{5}-\Delta W\,h_{g}=76.04-28.57=47.47\ \text{kJ/kg}$$The furnace outlet is therefore at $t_{4}=(h_{4}-2501W_{M})/(1.006+1.86W_{M})=38.86\ ^\circ\text{C}$, wet bulb 17.10 °C.
Temperature rise across the furnace, part (d). The air enters the furnace at 19.01 °C and leaves at 38.86 °C:$$\boxed{\ \Delta t_{\text{furnace}}=38.86-19.01=19.86\ \text{K}\ }$$The steam then carries the air the last 28.57 kJ/kg to 40 °C, which is worth about 1.1 K of dry bulb — a small but real sensible contribution that a solution ignoring it would miss.
Water vapour required, part (e). The humidifier must supply the moisture deficit of the whole supply stream:$$\dot{m}_{w}=\dot{m}\,\Delta W=5.621\times0.010647=0.05985\ \text{kg/s}$$$$\boxed{\ \dot{m}_{w}=215.5\ \text{kg/h of steam}\ }$$carrying 160.6 kW of enthalpy with it — a reminder that in a cold, dry climate the humidification duty is not a trivial addition to the boiler.
Furnace and preheater capacities, part (f). The furnace heats the full supply stream from M to 4, while the preheater heats only the outdoor-air quarter from −14 °C to 16 °C at $W=0$:$$\dot{Q}_{\text{furnace}}=\dot{m}\,(h_{4}-h_{M})=5.621\times(47.47-27.37)$$$$\boxed{\ \dot{Q}_{\text{furnace}}=113.0\ \text{kW}\ }$$$$\dot{Q}_{\text{preheat}}=0.25\,\dot{m}\,c_{pa}\,(16-(-14))=1.405\times1.006\times30$$$$\boxed{\ \dot{Q}_{\text{preheat}}=42.4\ \text{kW}\ }$$A whole-plant energy balance closes the answer: the preheater, furnace and steam together add exactly the enthalpy difference between the supply stream and the two entering streams, to within rounding.

Parts (a) and (b) — the winter cycle. 1–2 is the preheat at constant moisture, 2 and R mix to M, M–4 is the furnace, 4–5 is the steam humidifier (nearly vertical, with a slight rightward lean from the steam superheat), and 5–R is the room process.

Part (b) — the significant state points
Point	Description	Dry bulb, °C	Wet bulb, °C	W, kg/kg	h, kJ/kg
1	outdoor air, preheater inlet	−14.00	3.75 at state 2	0.000000	−14.08
2	preheater outlet	16.00	3.75	0.000000	16.10
M	mixed air, furnace inlet	19.01	9.23	0.003253	27.37
4	furnace outlet, humidifier inlet	38.86	17.10	0.003253	47.47
5	supply air to the space	40.00	25.09	0.013900	76.04
R	space and return air	20.00	10.85	0.004337	31.13

Problem 2 — results
Quantity	Value
(c) Supply condition	40.00 °C dB, 25.09 °C wB, 13.90 g/kg
(c) Supply air quantity	5.621 kg/s dry air = 5.098 m³/s
(d) Temperature rise in the furnace	19.86 K (19.01 → 38.86 °C)
(e) Water vapour required	0.05985 kg/s = 215.5 kg/h
(f) Furnace (heating coil) capacity	113.0 kW
(f) Preheater capacity	42.4 kW
Mixed-air state at the furnace inlet	19.01 °C dB, 9.23 °C wB

Topic. The winter preheat–mix–heat–humidify plant, and steam injection as an energy as well as a moisture input.

Key relations. Sensible sizing $\dot{m}=q_{s}/[c_{p}(t_{S}-t_{R})]$ with $c_{p}=1.006+1.86\,W$; adiabatic mixing on $W$ and $h$; steam injection $h_{\text{out}}=h_{\text{in}}+\Delta W\,h_{g}$; sensible heating $\dot{Q}=\dot{m}\,\Delta h$ at constant $W$.

Why this works. Each device changes the air state in exactly one simple way, so the cycle decomposes into segments that can be walked in either direction. Heating is horizontal on the chart, mixing lands on the straight line between the two streams at the mass ratio, and steam injection is very nearly vertical — very nearly, because the steam arrives at 104.81 °C and carries 2,683.4 kJ per kilogram, which tilts the line slightly to the right and is worth about a kelvin here. Preheating only the outdoor-air branch, rather than the mixed stream, is the standard arrangement in a Canadian climate: it protects the mixing box and any downstream coil from freezing while heating only a quarter of the mass flow.

Common pitfall. Treating steam humidification as though it were adiabatic (an air washer), which puts state 4 at the wrong temperature and mis-splits the furnace and humidifier duties. The other trap is trying to force the stated supply state, the stated SHF and the stated total load to agree; they cannot, and the professional response is to say which balance governs and why, not to invent a reconciliation.

Source. W. P. Jones, Air Conditioning Engineering, 5th ed., Ch. 3 and Ch. 5; McQuiston, Parker & Spitler, 6th ed., Ch. 3; ASHRAE Handbook — Fundamentals (2021), Ch. 1 and Ch. 22 (humidifiers).

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