Traditional Generator

Built-in heat exchanger type · Version 1 · 15 October 2026 · Case study: Yang Yanyan (2013), single-effect LiBr–water chiller

Generator and condenser in a sealed shell — The generator and the condenser share one shell; the refrigerant vapour crosses above the partition. Rich solution enters at the upper left and is sprayed over the heated tube bundle; weak solution leaves at the lower left; the vapour flow from generator to condenser is ṁ_v,gc.

Trial calculation: from generator outlet back to inlet

Given the outlet solution (sgp) concentration and flow and the outlet vapour flow, back out the inlet rich-solution flow and concentration; the condensing temperature T_cond fixes the high-side pressure P_gen (pure-water saturation pressure, Wagner equation); T_sgp then follows from P_gen and ξ_sgp, and Q_g from the inlet/outlet enthalpies, with a binary choice of vapour-enthalpy booking. Assumption: the outlet vapour carries no absorbent (true for LiBr–water).

Working pair

ξ_sgp outlet solution concentration (%)ṁ_sgp outlet solution flow (kg/s)ṁ_v,gc outlet vapour flow (kg/s)T_cond condensing temperature (°C)T_sgr inlet rich-solution temperature (°C)

Vapour enthalpy in Q_g

ṁ_sgr inlet rich-solution flow = 1.100 kg/s; ξ_sgr rich-solution concentration = 55.00 %; T_sgp outlet weak-solution temperature = 86.35 °C; P_gen = 0.00739 MPa

Q_g generator heat input = 284.1 kW (solution-side balance)

Specific enthalpies: h_sgr(T_sgr, ξ_sgr) = 166.9 kJ/kg; h_sgp(T_sgp, ξ_sgp) = 206.3 kJ/kg; h_v,gc (vapour, selected booking) = 2613.5 kJ/kg

ṁ_sgr = ṁ_sgp + ṁ_v,gc; ξ_sgr = ξ_sgp·ṁ_sgp / ṁ_sgr; T_sgp from inverting Psol(T_sgp, ξ_sgp) = P_gen; Q_g = ṁ_v,gc·h_vap + ṁ_sgp·h(T_sgp, ξ_sgp) − ṁ_sgr·h(T_sgr, ξ_sgr), with t_vap = (T_cond + T_sgp)/2 on the superheated booking. On the other booking (saturated vapour enthalpy) Q_g = 279.8 kW. Properties from the same set as this site’s trial-calculation library (Patterson solution model, Wagner pure-water line).

1. The balance: three equations side by side

The worked example is the lumped component model of Yang Yanyan's 2013 Dalian University of Technology master's thesis on a single-effect LiBr–water chiller. The generator is one control volume; its energy balance (Eq. 2.30 of the thesis) books the heat on both sides of the wall in a single line — heating-water side on the left, solution side on the right:

Q_gen = ṁ_h c_p,h (t_h1 − t_h2) = (ṁ_a − ṁ_r) h₆ + ṁ_r h₁₀ − ṁ_a h₅ (2.30)

with the heat-transfer equation and the mean temperature difference:

Q_gen = K_gen F_gen Δt_m (2.31)

Δt_m = t_h1 − t₁₀′ − 0.35 (t_h1 − t_h2) − 0.65 (t₆ − t₁₀′) (2.32)

Here ṁ_a is the rich (dilute) solution entering, ṁ_r the refrigerant vapour raised, (ṁ_a − ṁ_r) the weak (concentrated) solution leaving; h₅, h₆, h₁₀ are the specific enthalpies at the state points of the cycle diagram — inlet solution, outlet solution, outlet vapour. LiBr mass conservation (Eq. 2.33) closes the set. The mean difference is not the logarithmic one: it is a weighted form, 0.35/0.65, taken from the source book below.

2. Provenance

Component model (the three-equation set): transcribed from reference [47] of the thesis — Dai Yongqing (ed.), Lithium Bromide Absorption Refrigeration Technology and Applications, China Machine Press, 1996.
Solution properties: Jia Mingsheng (2002) polynomial set for LiBr–water; its enthalpy carries a +418.6 kJ/kg reference offset.
Water/steam properties: the set transcribed from Wagner, Properties of Water and Steam.

3. The vapour enthalpy: saturated or superheated?

The vapour leaves in contact with boiling solution, at solution temperature — well above the saturation temperature at condenser pressure. Yang's model therefore treats the exit vapour as superheated: its temperature is defined as the mean solution temperature of the generator,

t₁₀ = (t₁₀′ + t₆) / 2 (2.36)

and its enthalpy is computed as saturated-vapour enthalpy plus a mean-specific-heat superheat term,

h = h″(t_s) + c̄_p,m (t − t_s) (2.17)

What is the choice worth? Recomputed with IAPWS water/steam properties, the difference Δh = h_superheated − h″ between the two bookings is:

t_s (condensing)	t₁₀ (vapour)	h″	h superheated	Δh
35 °C	80 °C	2564.5	2650.1	85.5
40 °C	80 °C	2573.5	2649.8	76.3
40 °C	90 °C	2573.5	2668.8	95.3
40 °C	100 °C	2573.5	2687.8	114.3
45 °C	100 °C	2582.4	2687.5	105.1
40 °C	110 °C	2573.5	2706.8	133.3

Over the full grid (t_s = 35/40/45 °C × t₁₀ = 80/90/100/110 °C) Δh runs from 67 to 142 kJ/kg. Two observations:

The approximation in Eq. (2.17) is itself accurate: its Δ agrees with the IAPWS values within 0.3–0.9 kJ/kg. What matters is not the approximation but whether superheat is booked at all.
Per kilogram of refrigerant vapour, Q_gen differs between the two bookings by exactly Δh. With Q_gen/ṁ_r ≈ 2800–3200 kJ/kg for a single-effect machine, that is 3–5%, and COP moves by the same relative amount in the opposite direction — a COP of 0.688 computed on saturated vapour reads about 0.66 on superheated vapour. A paper that does not state this choice carries a 3–5% systematic uncertainty in its COP.

The same superheated construction appears in Liu Jinliang (2007) — h′_v = h_v + C_pg(t − t₁) with C_pg = 1.8543 + 5.7221×10⁻⁴ t — and in Fu Mengxian's double-effect ejector-absorption study, whose steam specific heat is the same polynomial, digit for digit. Most other generator balances in the survey book the vapour term without stating which enthalpy was taken; one (Shen, 2005) uses the saturated value h″_g explicitly.

4. Accounting notes for this model

COP = Q_eva/Q_gen, solution-pump work excluded (design point 0.6879).
Heat loss of the generator is neglected by a stated global assumption.
No rectification heat is booked: in a LiBr–water machine the vapour is pure water.
Both sides of Eq. (2.30) are carried in the same line, so the water-side and solution-side accounts cross-check each other by construction.

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