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

Question 6 of 8: Two-stage R-134a plant with a flash chamber and a direct-contact intercooler

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, May 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-134a p-h diagram are appended to the paper. All eight problems are solved here, because the set is intended as a study resource rather than an examination script.

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. 10 (cooling towers), 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. 6 (heating loads and infiltration), 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. 16 (ventilation and infiltration), Ch. 18 (residential and non-residential load calculations), Ch. 21 (duct design), Ch. 30 (thermophysical properties of refrigerants).
Moran, Shapiro, Boettner & Bailey, Fundamentals of Engineering Thermodynamics, 9th ed., Wiley — Ch. 10 (vapour-compression refrigeration, multistage systems 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 heating degree-day normals; CSA B52 Mechanical Refrigeration Code; Canadian federal halocarbon regulations (SOR/2003-289) for the refrigerant discussion in Problem 7.

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-134a properties are on the IIR datum and agree with the appended p-h diagram. Problem-specific assumptions — climate data, fuel prices, emission factors, air-change rates, occupant density, duct roughness and the coil bypass factor — are stated where they are first used.

Question 6: Two-stage R-134a plant with a flash chamber and a direct-contact intercooler (20 marks)

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.

Check: the printed heading of this problem. the page is otherwise clean and the problem statement, sub-part lettering and 20-point weighting follow the pattern of the other seven problems, so it is reproduced above as "PROBLEM 6. (20 POINTS)". No numerical data is affected.

Given. A two-stage R-134a plant of 10 tons refrigerating capacity: saturated vapour leaves the evaporator at −30 °C, both the flash chamber and the direct-contact intercooler work at 4 bar, the condenser is at 12 bar, saturated liquid leaves the condenser and the flash chamber to feed the high- and low-pressure expansion valves respectively, and the isentropic efficiencies are 0.85 for the low stage and 0.88 for the high stage.

Given data and property values (IIR datum)
Quantity	Symbol	Value
Evaporating temperature / pressure	$t_1,\ p_e$	−30 $^\circ$C, 84.38 kPa
Intermediate (flash) pressure	$p_i$	4 bar ($t_{sat}=$ 8.93 $^\circ$C)
Condenser pressure	$p_c$	12 bar ($t_{sat}=$ 46.31 $^\circ$C)
Saturated vapour at −30 $^\circ$C	$h_1$	380.32 kJ/kg
Saturated vapour at 4 bar	$h_3$	403.72 kJ/kg
Saturated liquid at 12 bar	$h_5$	265.95 kJ/kg
Saturated liquid at 4 bar	$h_7$	212.11 kJ/kg
Isentropic efficiencies	$\eta_{lp},\ \eta_{hp}$	0.85, 0.88
Refrigerating capacity	$\dot Q_e$	10 tons = 35.17 kW

Find. (a) the refrigerant mass flow, (b) the power input to each compressor, and (c) the coefficient of performance.

The two-stage plant. Liquid from the condenser is throttled to 4 bar and separated in the flash chamber; the vapour fraction bypasses the evaporator and joins the low-stage discharge in the direct-contact heat exchanger, and only the liquid fraction is throttled again and evaporated.

The cycle on the R-134a p-h diagram. States 3, 9 and 2 all lie on the 4 bar line: 3 is the flash vapour, 2 the low-stage discharge, and 9 their mixture entering the high stage.

Approach. Work on a basis of unit total mass through the condenser. The quality after the high-pressure valve fixes how much of that mass short-circuits the evaporator as flash vapour; an energy balance on the direct-contact heat exchanger fixes the state entering the high stage; then the stated capacity scales the whole cycle.

Low-stage compression, 1 to 2. Isentropic compression from saturated vapour at −30 °C ($h_1=380.32$ kJ/kg, $s_1=1.7515$ kJ/kg·K) to 4 bar gives $h_{2s}=411.99$ kJ/kg. Correcting for the isentropic efficiency, $$h_2=h_1+\frac{h_{2s}-h_1}{\eta_{lp}} =380.32+\frac{411.99-380.32}{0.85}=417.58\ \text{kJ/kg}$$
Throttle to the flash chamber and find the vapour fraction. The high-pressure valve is isenthalpic, so $h_6=h_5$, and the quality at 4 bar is $$x=\frac{h_6-h_7}{h_3-h_7} =\frac{265.95-212.11}{403.72-212.11}=0.2810$$ so 28 % of the circulating refrigerant flashes to vapour at the intermediate pressure and never reaches the evaporator at all.
Mixing in the direct-contact heat exchanger. Per unit total mass, the flash vapour $x$ at $h_3$ meets the low-stage discharge $(1-x)$ at $h_2$: $$h_9=x\,h_3+(1-x)\,h_2 =0.2810(403.72)+(1-0.2810)(417.58)=413.68\ \text{kJ/kg}$$ The mixture is 417.58 − 413.68 = 3.89 kJ/kg cooler than the low-stage discharge; that desuperheating is the entire purpose of the intercooler, and it is what keeps the high-stage discharge temperature down to 63 °C.
High-stage compression, 9 to 4. Isentropic compression from state 9 to 12 bar gives $h_{4s}=437.88$ kJ/kg, so $$h_4=h_9+\frac{h_{4s}-h_9}{\eta_{hp}} =413.68+\frac{437.88-413.68}{0.88}=441.18\ \text{kJ/kg}$$
(a) Mass flows from the stated capacity. Only the liquid fraction reaches the evaporator, where the refrigerating effect per kilogram is $h_1-h_8=380.32-212.11=168.21$ kJ/kg. Hence $$\boxed{\;\dot m_{evap}=\frac{\dot Q_e}{h_1-h_8} =\frac{35.17}{168.21}=0.2091\ \text{kg/s}\;}$$ and since that stream is the $(1-x)$ fraction of the total, $$\boxed{\;\dot m_{total}=\frac{\dot m_{evap}}{1-x} =\frac{0.2091}{1-0.2810}=0.2908\ \text{kg/s}\;}$$ The difference, 0.0817 kg/s, is the flash vapour circulating between the flash chamber and the high stage.
(b) Power input to each compressor. The low stage handles only the evaporator flow, the high stage the whole flow: $$\boxed{\;\dot W_{lp}=\dot m_{evap}\,(h_2-h_1) =0.2091\,(417.58-380.32)=7.79\ \text{kW}\;}$$ $$\boxed{\;\dot W_{hp}=\dot m_{total}\,(h_4-h_9) =0.2908\,(441.18-413.68)=7.99\ \text{kW}\;}$$ The two stages come out almost equal, at 7.79 and 7.99 kW, which is the signature of a well-chosen intermediate pressure: 4 bar is close to the geometric mean of 0.844 and 12 bar, $\sqrt{0.844\times 12}=3.18$ bar, and the split of work follows.
(c) Coefficient of performance. $$\boxed{\;\mathrm{COP}=\frac{\dot Q_e}{\dot W_{lp}+\dot W_{hp}} =\frac{35.17}{7.79+7.99} =\frac{35.17}{15.78}=2.228\;}$$ A first-law check closes the cycle: the condenser must reject $\dot Q_e+\dot W_{tot}=35.17+15.78=50.95$ kW, and $\dot m_{total}(h_4-h_5)$ gives the same 50.95 kW.

The value of the arrangement is best seen by pricing the alternative. A single machine taking the same 10 tons from −30 °C straight to 12 bar at the same 0.85 isentropic efficiency, throttling from saturated liquid at 12 bar, would reach a COP of only 1.748. Two-staging with flash intercooling therefore improves the COP by 27.5 %, and it does so by two independent mechanisms. The flash chamber removes the vapour generated in the first throttling step before it can enter the evaporator, so the refrigerating effect per kilogram of evaporator flow rises from 168 to 168.21 kJ/kg; and the intercooler desuperheats the low-stage discharge so the high stage begins its compression closer to the saturation line, where the specific volume and hence the work per kilogram is lower. The practical bonus is the discharge temperature: 8.93 °C into the high stage rather than 23.9 °C, and 63 °C out of it rather than the far higher figure a single stage would produce, which is what protects the oil and the valve plates. For Canadian installations the whole assembly falls under CSA B52; R-134a is an A1 refrigerant, non-flammable and of low toxicity, so the machinery-room requirements are the ordinary ones.

Final results — Question 6
Quantity	Value
Flash-chamber vapour fraction $x$	0.2810
Low-stage discharge $h_2$	417.58 kJ/kg
Intercooler outlet $h_9$	413.68 kJ/kg
High-stage discharge $h_4$	441.18 kJ/kg
Refrigerating effect	168.21 kJ/kg
(a) Mass flow through the evaporator	0.2091 kg/s
(a) Mass flow through the condenser / high stage	0.2908 kg/s
(b) Low-stage power	7.79 kW
(b) High-stage power	7.99 kW
Total power	15.78 kW
(c) Coefficient of performance	2.228
Condenser heat rejection (first-law check)	50.95 kW
Single-stage COP for comparison	1.748 (27.5 % worse)

Topic. Multistage vapour-compression refrigeration with flash intercooling.

Key relations. Isentropic efficiency $\eta=(h_{2s}-h_1)/(h_2-h_1)$; isenthalpic throttling $h_{out}=h_{in}$; flash quality $x=(h_6-h_f)/(h_g-h_f)$; adiabatic mixing $h_9=xh_3+(1-x)h_2$; capacity $\dot Q_e=\dot m_{evap}(h_1-h_8)$; mass split $\dot m_{total}=\dot m_{evap}/(1-x)$; $\mathrm{COP}=\dot Q_e/(\dot W_{lp}+\dot W_{hp})$; optimum intermediate pressure $p_i\approx\sqrt{p_ep_c}$.

Why this works. Two separate irreversibilities grow as the temperature lift increases, and flash intercooling attacks both. The first is throttling loss: expanding saturated liquid from 12 bar to the evaporator pressure in one step would generate a large quality of vapour, and that vapour occupies evaporator volume without absorbing any latent heat. By throttling in two steps and bleeding off the vapour generated in the first, the evaporator sees liquid at a much lower quality and its effect per kilogram rises. The second is compression loss: the specific volume of superheated vapour rises with temperature, so compressing hot gas costs more work per unit mass than compressing gas near saturation. Mixing the low-stage discharge with saturated flash vapour desuperheats it before the second stage begins, which is cheaper than an external intercooler because the cooling medium is the refrigerant itself and no additional temperature difference is required. The optimum intermediate pressure is close to the geometric mean of the two extremes, which equalises the pressure ratio — and therefore roughly the work — across the two stages.

Common pitfall. Using one mass flow for the whole cycle. The evaporator, the low-stage compressor and the low-pressure valve all carry $(1-x)\dot m_{total}$, while the condenser, the high-stage compressor and the high-pressure valve carry $\dot m_{total}$; applying the total flow to the low stage overstates $\dot W_{lp}$ by 39 % here. The second pitfall is taking the high stage as beginning at state 2 rather than at the mixed state 9, which ignores the intercooler entirely. A third is computing the refrigerating effect as $h_1-h_5$ using the condenser liquid enthalpy; the evaporator is fed from the flash chamber, so the correct datum is $h_7$.

Source. Moran, Shapiro, Boettner & Bailey, Fundamentals of Engineering Thermodynamics, 9th ed., §10.5 (multistage compression with intercooling and flash chambers); Çengel & Boles, Thermodynamics: An Engineering Approach, §11-6; ASHRAE Handbook — Fundamentals (2021) Ch. 30 (R-134a property tables); CSA B52 Mechanical Refrigeration Code.

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