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1
Analysisofgas‐firedNH3‐H2Ogeneratorwithcross
flowgasburner.
Marcello Aprile (1), Tommaso Toppi, Marco Guerra, Mario Motta
Department of Energy, Politecnico di Milano, 20156 Milano, Italy
Preprint
© 2015. This manuscript version is made available under the CC-BY-NC-ND 4.0 license
http://creativecommons.org/licenses/by-nc-nd/4.0/
Please cite this paper as:
M. Aprile, T. Toppi, M. Guerra, M. Motta, Analysis of gas-fired NH3-H2O generator with cross
flow gas burner, Applied Thermal Engineering 93 (2016) 1216–1227.
http://dx.doi.org/10.1016/j.applthermaleng.2015.10.088
Abstract
This paper presents a model to simulate the combined heat and mass transfer processes that occur in
a gas-fired generator of an ammonia water absorption heat pump. The model comprises three
interconnected components: the gas furnace, the distillation column and the rectifier. The furnace is
modelled like a well-stirred single volume. The distillation column and the rectifier are discretized
along their axial dimension. Several heat transfer mechanisms are simultaneously solved: radiative
and convective heat transfer between combustion products and generator finned surface, flow
1 Corresponding author. Tel.: +39 02 2399 3865; fax: +39 02 2399 3868.
E-mail address: marcello.aprile@polimi.it (M. Aprile).
2
boiling and pool boiling in the two-phase ammonia water mixture inside the distillation column.
The model is applied to operating conditions of interest in real applications. The generated outputs
provide insight on the internal gradients, the quantification of gas furnace efficiency, and
effectiveness of solution boiling and internal heat recovery. The model can be used for the
simulation of absorption heat pumps with modulating gas burners.
1. Introduction
The increasing worldwide population poses serious concerns on climate change, energy resources
depletion and environmental sustainability. In the last decades, several policies have promoted the
rational use of energy and the diffusion of renewable energy sources. Recently, the “2030
framework for climate and energy policies” has set new targets for the EU member states: 27%
energy savings, 27% share of renewable energy, 40% reduction of CO2 emissions with reference to
1990 data. The new policy addresses in particular the building sector, responsible for a large
portion of total energy consumption and associated CO2 emissions. In this context, gas-driven
absorption heat pumps can help reducing fuel consumption for space heating and sanitary hot water
demands. In recent developments of gas-fired absorption heat pumps (GAHP), seasonal fuel savings
of 30% with respect to the best condensing boilers have been demonstrated for domestic
applications [1]. It is worth mentioning that the GAHP was of the air-source type, with a nominal
heating capacity of 18 kW and connected to a radiator based heating system. Moreover, the
absorption system utilized ammonia water as working pair in a GAX (Generator-Absorber-Heat
Exchanger) cycle configuration.
The capability to model the whole GAHP system is desirable in order to understand the system
behavior at operating conditions different from design point, identify pitfalls in design and control,
and assess the feasibility of possible design improvements. In particular, the GAHP performance
degradation at large thermal lifts and at low heating loads has been experimentally observed [2] but
the margin for improvement in these challenging conditions has not been completely explored.
3
The GAX cycle has been investigated extensively in the past, both numerically [3–5] and
experimentally [6–8]. Its distinctive characteristic is to bring the rich solution above the boiling
curve by recovering part of the heat released during the absorption process by means of the
Generator-Absorber-Heat exchanger (GAX). This is beneficial because the reduced heat demand at
the generator increases cycle COP. Ideally, both absorber and desorber can be divided in three
stages, each one operating in a different temperature range. Starting from the lowest temperature
range, the first stage in the absorber is the water cooled absorber (WCA), followed by the solution
cooled absorber (SCA) and the GAX. Symmetrically, the stage at the lowest temperature in the
generator is the GAX, followed by the solution heated desorber (SHD) and the gas-fired desorber
(GFD).
In ammonia water absorption cycles, a vapor purification stage is normally needed because the
vapor desorbed at the generator is not rich enough to allow an effective operation of the evaporator.
In single effect ammonia water absorption cycles, this can be achieved with a distillation column
(DC) and a partial condenser or rectifier (REC). The distillation column comprises two sections:
stripping section (SS) at the bottom and enrichment (or rectifying) section (ES) on top. In the SS,
vapor exchanges heat and mass with the descending rich solution, externally supplied (feed). In the
ES, the vapor is purified further by contacting the condensate reflux from the REC. Another
possible configuration consists in recirculating part of the condensate after the condenser back to
the DC to increase the purification efficiency of the ES, although this trick does not bring any
benefit to cycle COP [9]. To enhance the liquid – vapor contact surface, cascade of trays or packed
beds are normally employed. In small-scale absorption systems, the tray-type DC is the preferred
choice. However, their thermal design is a complex task involving phase change in particular flow
regimes, such as turbulent froth, that are strongly influenced by the geometry of the trays. Since
robust, tray-specific, correlations are not easy to find, a conceptual approach, the Ponchon-Savarit
method, is commonly adopted [10]. Using this method, which is based on the notions of ideal tray
4
and tray efficiency, Zavaleta-Aguilar et al. [11] have carried out the thermal design of a tray-type
distillation column for an ammonia water absorption system.
One of the main problems in designing the gas-fired GAX hardware is the arrangement of the
different stages in the generator, that, as mentioned, comprises REC, ES, SS, GAX, SHD and DFG.
In commercial small-scale GAX units, the stages are not physically separated, most likely for
practical and economic reasons. In particular, DC, GFD, SHD overlaps, making difficult the
mathematical modelling of the desorption process.
Moreover, the gas furnace arrangement is another important aspect. In fact, the main figure of merit
for a GAHP is the so-called gas utilization efficiency (GUE), defined as useful heat output to gas
input ratio. The link between cycle COP and GUE is the furnace thermal efficiency, i.e. the
generator heat input to burner gas input ratio.
As both cycle COP and furnace thermal efficiency can vary with the gas input and the temperatures
at the external heat exchangers, a comprehensive model of the GAHP shall address not only the
heat and mass transfer in the ammonia water thermodynamic cycle but also the fuel combustion
process and the heat transfer mechanism in the furnace.
In this work, a mathematical model is developed for a gas-fired ammonia-water generator used in
commercial GAHP units. The model comprises the gas furnace, the distillation column and the
rectifier, which are closely interconnected and constitute one independent block that can be easily
incorporated in the model of a GAHP system. The model aims to provide insight on the partial load
behavior of the generator, including burner efficiency variations, temperature and mass fraction
gradients in the distillation column, and effectiveness of internal heat recovery under varying
operating conditions. A method to address the combined radiation and convection problem in cross-
flow configuration is proposed, since no standard way exists to treat such case. In previous works,
the interaction between heat transfer in the combustion chamber and heat transfer in the generator
was not treated. Modeling of GAX cycles either focused on thermal COP or relied on measured
values for the burner efficiency. Heat input to the generator, heat and mass transfer in the
5
distillation column, and heat recovery from the poor solution were treated as separated processes.
Moreover, since burner efficiency was derived from measurements, design parameters regarding the
furnace heat exchanger were not provided.
2. Gas-fired generator description
The gas-fired generator is schematically represented in Fig. 1. The pre-mix gas burner distributes
combustion reactants through a vertical burner pipe, in order to obtain a uniform vertical
distribution of the flame temperature. The combustion products leaving the furnace exchange heat
by radiation and convection with the bottommost section of the distillation column. A tightly
packed array of fins, welded on the external wall of the distillation column, improves heat transfer.
The distillation column is composed of a cascade of trays, whose function is to enhance heat and
mass transfer between the descending liquid solution and the rising vapor. The column comprises
four sections. Starting from the base, vapor desorbs in the gas fired generator and solution heated
desorber (GFSHD). Heat is supplied to the boiling solution from both the lateral wall of the column
and an internal heat recovery coil. The liquid residue, poor in ammonia concentration, is collected at
the bottom and rises up through the internal heat exchanger. The desorption process continues in the
solution heated desorber (SHD) by means of internal heat recovery only. The rising vapor
encounters the feed stream, rich in ammonia concentration, and adiabatically exchanges heat and
mass with the descending liquid solution in the stripping section. Finally, the rising vapor
encounters the liquid reflux from the rectifier in the enriching section.
In the rectifier, the stream of vapor crosses horizontally a packed bed of particles (e.g. pall rings),
cooled by an internal coil. Vapor partially condenses along its path towards the exit, leaving behind
a mass of condensate. The liquid that forms on the packing particles surface collects at the base by
gravity and drains back to the distillation column. The distillate vapor leaves the rectifier rich in
ammonia concentration.
6
Fig. 1. Gas-fired ammonia-water generator.
3. Mathematical model
The gas furnace is subdivided in three adjacent volumes, radiative (), radiative convective ()
and convective (), as shown in Fig 2. In volume , the predominant mechanism of heat transfer
is radiation among a portion of the insulated wall (, the fictive surface separating from ,
and the hot combustion products in volume . In volume , convection between combustion
products and the portion of load surface delimited by surface adds up to the net radiative
exchange between and . In volume , which extends within the angular sector 2
,
the temperature of combustion products is relatively low and convection with the remaining portion
of load surface becomes the predominant heat transfer mechanism.
7
Fig. 2. Gas furnace volumes.
The heat transfer to the interior of the generator is a complex mechanism that involves net radiation
heat transfer with the radiative zone, convection on the fins surface, conduction through the fins and
the generator wall, convection on the internal surface of the generator wall. A detailed analysis is
carried out by subdividing the gas-fired section of the generator in a number (
) of discretized
volumes of equal height Δ (see Fig. 3), and locally modelling the heat transfer problem as one-
dimensional in the radial direction.
Fig. 3. Discretized volume for the GFSHD section.
8
Finally, the rectifier is modelled as a series of elementary volumes of length Δ (see Fig. 4). The
liquid mass flow rates of each element, which forms by partial condensation of the vapor,
adiabatically mix at the bottom.
Fig. 4. Discretized volume for the rectifier.
3.1. Furnace radiative volume
Model hypotheses:
1. The gas furnace radiative volume is modelled as a well-stirred single volume with uniform
combustion products temperature and composition.
2. The mean radiating combustion products temperature is equal to the temperature at the exit
of the gas furnace radiative volume (
,
).
3. The wall of the insulated portion of the gas furnace (
) is assumed to be isothermal, grey
and diffuse.
4. The load fictive surface (
=
) is assumed to be isothermal and black. Its temperature
(
) can be thought as an equivalent mean radiative temperature.
5. Flames are non-luminous and combustion products can be represented as a weighted sum of
non-scattering grey gases (WSGG model).
9
A detailed description of radiation transfer within a well-stirred single volume two surface
enclosure can be found in [12]. Based on the WSGG model for emissivity and absorptivity of the
combustion products, as described in [13] and first proposed by Hottel [14], the net radiation
exchanges towards insulated wall (
), load surface (
) and combustion products volume (
) can
be expressed in terms of the directed flux areas and the blackbody emissions related the involved
isothermal zones:
,
,
,
,
,
(1)
,
,
,
,
,
(2)
,
,
,
,
,
(3)
The directed flux areas (
,
,
,
,
,
are calculated as weighted summation
of the total exchange areas (
,
,
) for each gas. In the following, combustion products
are treated as a mixture of two non-scattering grey gases plus one clear gas.
For volume-surface transfer,
,
(4)
(5)
Similar relationships hold for surface-surface transfer,
(6)
In the summations above, the weighting factors
and the mean grey gas transmittance
are
derived from the correlations of Taylor and Foster [15]:
,
,
(7)
exp
,
(8)
10
where , , , are the grey gas coefficients, reported in Table 1, and is the mean beam
length,
3.5
/ (9)
Table 1. Grey gas coefficients.
, (-) , x 105 K-1 , atm-1 m-1
1 0.437 7.13 0
2 0.39 -0.52 1.88
3 1.173 -6.61 68.8
For the considered furnace geometry, 1
/,
/,
1 and 0.
Consequently, the following expressions for total exchange areas can be derived:
/11/ (10)
/11/1
/11/ (11)
/11/1
/11/ (12)
The overall energy balance for the radiative zone, which includes also the terms related to fuel
combustion and neglects convective heat transfer between combustion products and insulated wall,
is:
,
, (13)
Finally, the energy balance at the insulated wall is given by:
, (14)
3.2. Furnace radiative convective volume
Model hypotheses:
11
1. The radiative transfer of the gas confined within the fins and the fictive surface is
assumed negligible.
2. The fins surface and the generator prime surface are black.
3. Combustion products mass flow rate distributes uniformly across the finned tube height.
3.2.1.Volumediscretization
The volume is discretized in elements, each one characterized by a single fin temperature
distribution. A detailed analysis of the radiative transfer at the load surface is necessary in order to
connect the furnace radiative volume model, which provides the overall ,, and the discretized
radiative convective volume model, which requires in input the net radiative transfer for each
volume, ,,. One can think of , as the net effect of diffuse irradiance at the fictive surface
() and the emission from an indented load surface comprising generator prime surface, fin lateral
surface and fin tip surface. The temperatures of these surfaces in each volume are
designated,,, ,,and ,,, respectively. For simplicity, they are assumed uniform and ,,is
approximated with the arithmetic mean of ,, and ,,. Under these assumptions, the emission
from the indented load surface is easily calculated. Since the ratio of fin length to distillation
column radius is small, curvature effect are negligible and the view factor for perpendicular plates
with a common edge can be used [16]. The following expressions for , are obtained:
,
(15)
,
,,
1
,,
1
,,
(16)
where is the view factor from surface to the generator prime surface (see Fig. 5):
1
//
/ (17)
and is the view factor from surface to fin lateral surface :
12
1
(18)
It follows
1
,,
1
,,
1
,,
(19)
Finally, the net radiative transfer for the volume can be expressed as follows:
,,
,,,
,,,
,,,
(20)
where
,,,
,
,,,
,
,,,
are the net radiative transfer related to the fin tip, the prime surface
and the lateral fin surface:
,,,
,,
(21)
,,,
1
,,
(22)
,,,
1
,,
(23)
Fig. 5. Fin geometry.
13
3.2.2.Heattransferthroughthefins
Heat transfer through the fins is treated as one-dimensional. In the radiative and convective zone,
the term
,,,
related to the fins lateral surface is recast as a uniform heat generation term in the
fin (
:
,
2
,,,
/
,
(24)
The analytical solution for the one-dimensional fin [17] can be extended to the case of interest by
including the generation term in the excess temperature,
,
,,
,
/2
(25)
Boundary conditions are set at fin base and tip. A uniform temperature
,,
is set at fin base,
,
,,
,,
,
/2
(26)
Neglecting convection at the tip, net radiative transfer
,,,
provides a boundary condition at fin
tip,
,,
,,,
,
(27)
Finally, the following analytical solution is obtained for the excess temperature:
,
,
(28)
where
2
/ (29)
,
,
,
(30)
,
,
,,
/
(31)
14
3.2.3.Heattransferthroughthegeneratorwall
Heat transfer through the generator wall comprises three terms: conduction at fin base, convection
at prime surface, net radiative transfer at prime surface. Therefore, the energy balance equation at
the wall yields:
,,,
,,1
,,,,
,,
,/
R
,
(32)
where R, is the thermal resistance of a wall element of height Δ extending over the sector of
angle ,
R
,ln
⁄
λ
Δ (33)
The term in square brackets in Eq. (32) is derived by integrating, over the angle , the conductive
heat flux at the fin base and the convective heat flux at the prime surface. Since combustion
products temperature changes along the integration path, the convective temperature becomes:
,,
,,
,
,,/ln,
,,/,,
,, (34)
where ,, is the combustion products temperature at
/2 within volume j.
Heat transferred by convection can be derived by difference:
,,
,,
,/
R
,
, (35)
3.3. Furnace convective volume
The previous equations for heat transfer through fins and generator wall apply also to the furnace
convective volume. In this case, radiative heat transfer is absent and the volume extends over the
angle .
Therefore, equations (28–31) hold with different boundary conditions:
,
,
,,
(36)
15
,,
0
(37)
Heat transfer through the generator wall yields:
,
,,
,,
1
,
,,
,
/
R
,
,,
(38)
Similarly to the previous case, convective temperature is calculated as
,,
,,
,,
,,
/ln
,,
,,
/
,,
,,
(39)
where
,,
is the combustion products temperature at within volume j.
3.4. Distillation column
Each section of the distillation column is discretized in vertical segments, each one comprising a
single ideal tray. The topmost segment is designated with 1, the bottommost segment with
, respectively the number of ideal trays in the enriching section, the stripping
section, the SHD and the GFSHD. The pressure is supposed uniform throughout the column.
Enriching section, stripping section and SHD can be easily derived as special cases of GFSHD.
Thus, only the latter is described in the following.
For the ideal tray of the GFSHD, mass, species and energy balance yield:
,
,
,
,
,
(40)
,
,
,
,
,
(41)
,
,
,
,
,
,
(42)
,
,
,
,
,
,
,
,
,
,
(43)
In the equations above, the liquid and the vapor leaving the tray are in thermodynamic equilibrium,
,
,
(44)
16
,
,, (45)
,
,, (46)
Moreover, it assumed that the liquid part covers the entire heat exchange surface so that heat , is
transferred to the liquid solution through the generator wall and from internal heat recovery coil,
i.e.:
,
,,
,
, Δ, (47)
where, is the partial heat transfer coefficient between wall and boiling liquid solution, ,
is the overall heat transfer coefficient of the portion of internal heat exchanger contained in volume
j and Δ, is the log mean temperature difference between the liquid leaving the tray (L) and the
rising solution (S):
Δ,
,
,
,
,/ln,
,/,
, (48)
Energy balance for the solution stream flowing inside the internal coil yields:
,
,Δ,
, (49)
Finally, energy balance through the generator wall yields:
,,
,
R
,,,
,
R
,
,,
, (50)
3.5. Rectifier
The rectifier is discretized along the axial dimension in elements of length Δ. In each element,
mass, species and energy balances are imposed, along with the equilibrium condition at liquid-
vapor interface and heat transfer to the internal cooling coil:
,
,
, (51)
,
,
, (52)
,
,
, (53)
,
, (54)
17
,
,
(55)
,
,
,
(56)
,
,
,
(57)
,
Δ
,
(58)
Due to the non-uniform void fraction in the bed, especially near the shell wall, vapor mass flow
does not distribute uniformly in the cross section. This effect is accounted for by introducing a
bypass fraction for the vapor, i.e. assuming that a portion of the vapor stream separates at the inlet
and adiabatically mixes with the vapor leaving the bed near the exit. Since the overall effect of the
bypass is to increase the vapor outlet temperature, the bypass fraction can be experimentally tuned
so that the calculated value of the vapor outlet temperature matches the measured value. Moreover,
the UA value of the heat exchanger is difficult to assess because of the complex geometry of the
bed. Therefore, an overall UA value is assigned and uniformly distributed across the segments.
Despite of the simplification introduced, the model is able to predict the state of the condensate
returned to the distillation column, by adiabatic mixing of the descending liquid streams that collect
at the bottom.
4. Properties and correlations
4.1. Fluids and materials properties
Ammonia water thermodynamic properties are derived from the Ziegler-Trepp correlations [18].
The gaseous fuel is 100% methane. Complete combustion is assumed for the combustion reactants
CH
4
and dry air (21% O
2
, 79% N
2
). The distillation column and its fins are made of carbon steel.
The combustion chamber insulation material is mineral wool. The required thermophysical
properties of the involved fluids and materials are temperature dependent.
18
4.2. Heat transfer correlations
4.2.1.Combustionproducts
Although the configuration of the cross-flow gas burner and the generator finned surface does not
exactly match any known convection heat transfer models, the heat transfer coefficient can be
predicted by the following arguments. In volume , assuming the flow is not too influenced by the
presence of the chamber external wall, a correlation for external flow and finned tube can be used to
get an estimate of the heat transfer coefficient. The correlation of McQuiston [19], valid for plane
fins, has been used. On the opposite, in volume a large portion of the flow is confined between
the fins interspace, the prime surface of the generator and the combustion chamber wall. In this
case, convection through a rectangular duct can be considered a valid approximation. Assuming
laminar flow and constant surface temperature, the Nusselt number can be determined according to
the duct base to height ratio [20].
4.2.2.Ammoniawatermixture
Ammonia water is brought to boil by two simultaneous inputs of heat, one through the wall of the
column and the other through the internal coil. Flow boiling inside a vertical tube can be considered
a suitable heat transfer model for the former, whereas boiling on horizontal plain tubes is more
adapted to the latter. No attempt is made to consider the influence of the trays, which force the
descending liquid and the rising bubbles to follow a tortuous path, since boiling models for such
specific case are not known.
The correlation of Chen [21] is used for calculating the flow boiling heat transfer coefficient inside
a vertical tube. Moreover, since ammonia water mixture is zeotropic, the nucleate boiling heat
transfer coefficient is corrected to take into account the effect of mass transfer, as proposed by
Thome [22].
19
Boiling heat transfer on horizontal plain tubes is determined by the correlations of Cooper [23],
used for calculating the heat transfer coefficients of pure components water and ammonia, and
Stephan and Körner [24], from which the heat transfer coefficient of the solution is derived.
Finally, the convective heat transfer coefficient for the liquid solution flowing inside the coil shall
be determined. Since the flow regime inside the coil is turbulent, with Re number above 104,
Seider-Tate correlation can be used.
5. Solution method
In order to solve the large system of nonlinear equations resulting from the combination of the
individual models comprising the gas-fired generator, an iterative solution scheme has been
implemented.
1. Initialize variables {,, and .
2. Guess .
3. Set = .
4. Solve Eq. (1–14) in the unknowns , and .
5. For each elementary volume of height Δ comprising the distillation column, proceeding
downward:
5.1. If volume belongs to the GFSHD section,
5.1.1. Calculate , Eq. (15), and radiative heat transfer terms, Eq. (21–23).
5.1.2. Solve heat transfer through generator wall within sector in ,,, Eq. (32).
5.1.3. Solve heat transfer through generator wall within sector in ,,, Eq. (38).
5.1.4. Solve energy balance through the generator wall in ,, Eq. (50).
5.1.5. Calculate ,, from ,,, Eq. (35), and update ,,, Eq. (34), and ,,.
5.1.6. Calculate ,, from ,,, Eq. (38), and update ,,, Eq. (39), and ,,.
5.1.7. Calculate heat transferred to boiling solution, Eq. (47)
20
5.2. If volume j belongs to SHD section
5.2.1. Calculate heat transferred to boiling solution, Eq. (47) without the first term on RHS
5.3. Solve distillation column equations (40–46), updating variables.
6. For each elementary volume of height Δ comprising the distillation column, proceeding
upward:
6.1. Solve distillation column equations, Eq. (40–46), updating and variables.
7. For each elementary volume of length Δ comprising the rectifier, proceeding in the vapor
direction:
7.1. Solve rectifier equations (51–58) providing and and variables.
8. For each elementary volume of length Δ comprising the rectifier, proceeding in the coolant
direction:
8.1. Solve rectifier equations (51–58) providing variables.
9. Calculate a new value for , Eq. (19).
10. Set ,, at the base of the distillation column,
.
11. Set variables of the rectifier equal to variables of the distillation column.
12. Set variables of the distillation column equal to the mixing state of the liquid streams leaving
each rectifier volume.
13. Update ̂ variables as the mixing state of liquid descending from tray ̂1 and feed, where ̂
designates the element containing the feed.
14. Iterate from step 3 until |–| .
Heat transfer coefficients are recalculated at the end of each iteration and the new values are under-
relaxed to strengthen numerical convergence.
6. Results and discussion
21
6.1. Parameters identification
The model is parametrized according to the characteristics of the hardware under investigation, a
commercial water-source GAHP unit of 25 kW gas input capacity (LHV) [25]. Model parameters
(see Table 2) include data that are difficult to assess: the number of ideal trays in each section, the
rectifier UA-value and the rectifier bypass fraction. Thus, these parameters are determined through
experimental identification. It is assumed that, with varying operating conditions, the number of
ideal trays in each section is constant, the rectifier UA-value varies proportionally with the 0.8
power of coolant mass flow rate (as suggested by heat transfer correlations for turbulent flow inside
plain tubes), and the bypass factor is constant.
Table 2. Model parameters.
Parameter Value Unit
Enrichment section height 120 mm
Stripping section height 50 mm
SHD section height 240 mm
GFSHD section height 480 mm
No. of ideal trays, enrichment section 2 -
No. of ideal trays, stripping section 1 -
No. of ideal trays, SHD section 4 -
No. of ideal trays, GFSHD section 5 -
Column outer diameter 158 mm
Column wall thickness 3 mm
Internal coil outer diameter 8 mm
Internal coil thickness 1 mm
Internal coil outer surface 0.316 m2
Insulation thickness 30 mm
Combustion chamber surface () 0.44 m2
Combustion chamber volume () 0.011 m3
Combustion chamber emissivity 0.7 -
Angle β 150 deg
Fin spacing 6 mm
Fin thickness 3 mm
Fin length 16 mm
Rectifier UA at nominal condition 100 W K-1
Rectifier bypass fraction 0.40 -
22
In order to perform the parameters identification, a sample GAHP unit is tested in the laboratory.
The experimental set-up and the procedure for the determination of the required mass flow rates and
thermodynamic states are discussed in Appendix A.
Simulations and experiments are run in parallel for three different operating conditions: nominal,
high temperature and partial load. The source cool water (i.e., the water stream connected to the
GAHP evaporator) is set to 10 °C inlet / 5 °C outlet for all conditions. At nominal condition, the
burner operates at the design gas input, and the hot water (i.e., the water stream connected to the
GAHP water heater loop) is set at 35 °C inlet / 50 °C outlet. At high temperature condition, the hot
water temperature is raised to 45 °C inlet / 60 °C outlet. At partial load condition, the gas input is
reduced to 50% of its design value. The measurement-based data provided in input to the model are
shown in Table 3. In addition, combustion chamber pressure and excess air are set to 101.325 kPa
and 20%, respectively.
Table 3. Measurement-based input data.
Parameter Nominal High temperature Partial load Unit
Feed temperature 107.5 122.9 87.8 °C
Feed mass fraction 0.4429 0.3852 0.3981 kg kg-1
Feed mass flow rate <151 142 99 kg h-1
Coolant inlet temperature 45.8 56.0 49.3 °C
Coolant mass fraction 0.4429 0.3852 0.3981 kg kg-1
Coolant mass flow rate <151 142 99 kg h-1
Distillation column pressure 2040 2517 1895 kPa
Fuel temperature 5.0 5.0 5.0 °C
Air temperature 5.0 5.0 5.0 °C
Gas input ratio 103 106 51 %
The unknown parameters are identified by minimizing the difference between model-based and
experiment-based output data for ,,,,,,. As shown in Table 4, the agreement is
good. Only the temperature of the flue gases does not match very well, although it shall be noticed
that a difference of 10 °C over a temperature drop of about 1000 °C is 1% error. In nominal
23
condition, the residue is subcooled in state 7. Therefore, only the maximum mass flow rate of the
feed (151 kg h-1) and the maximum mass fraction of the residue (0.1205 kg kg-1) can be derived
from the available experimental data (see Appendix A). Since the mass flow rate of refrigerant is
the most sensitive output, a value of 140 kg h-1 is set in order to match the measurement-based mass
flow rate of refrigerant.
Table 4. Model-based and measurement-based output data.
Parameter Nominal High temperature Partial load Unit
, measurement 113.0 132.8 104.6 °C
, model 112.6 131.7 107.5 °C
, measurement 103.5 120.2 97.1 °C
, model 104.8 122.2 99.6 °C
, measurement 83.0 98.2 76.5 °C
, model 83.0 99.6 77.3 °C
, measurement <0.1205 0.0716 0.2315 kg kg-1
, model 0.0830 0.0655 0.2367 kg kg-1
, measurement 193.2 204.2 135.0 °C
, model 197.7 218.6 142.1 °C
,measurement55.6 48.2 22.1 kg h-1
,model55.8 49.9 21.3 kg h-1
, measurement 22.9 22.9 11.4 kW
, model 22.7 23.1 11.3 kW
6.2. Simulation results
The temperature of the combustion products along the half-perimeter of the fin at the midpoint of
the GFSHD height is shown in Fig. 6. The variation with the different operating conditions is the
consequence of two factors: the change in average temperature of the generator and the different
input of gas.
24
Fig. 6. Variation of combustion products temperature along fins half-perimeter.
The fins and the wall temperatures along the GFSHD section height at nominal condition are shown
in Fig. 7. As expected, temperatures are higher at the bottom (z=0), due to the temperature gradient
of the solution inside the distillation column. Interestingly, the upstream tip can reach temperatures
of approximately 60 °C higher than the internal wall and 40 °C higher than the downwind tip. In
fact, only the upwind portion of the fins is irradiated by the furnace, thus reaching higher
temperatures than the downwind portion.
Fig. 7. Generator fin and wall temperature along distillation column height (nominal).
25
For each condition, temperature, mass fraction, mass flow rates and heat flux per unit length along
the distillation column height are presented in Figures 8 – 10. At nominal condition (Fig. 8), the
temperature of the descending liquid on top raises in the ES, reaching the same temperature of the
feed (represented in the diagram by a diamond indicator). The mass fraction in liquid decreases, a
sign that ammonia has been transferred to the vapor. However, the mass flow rate of the reflux is
very small, and the beneficial effect on the vapor mass fraction is hardly visible in the diagram.
After mixing with the feed, the liquid mass flow rate increases abruptly. Temperature starts to
increase at the bottom of the SHD section. It is only in the GFSHD that the liquid attains a large
temperature gradient. The liquid solution, diminished in mass fraction and mass flow rate, raises
through the internal coil. Vapor mass fraction and mass flow rate follow the same trend of the
descending liquid, but in the opposite direction. The largest share over the total heat supplied at the
boiling mixture is represented by convective heat transfer. Radiative heat transfer and heat recovery
(i.e., the heat transferred from the internal heat recovery coil to the boiling mixture) provide nearly
the same contribution, which is relevant. At the exit of the internal coil, the pinch between solution
and two-phase mixture is quite modest, about 3 °C. The vapor leaves the column with a relatively
high mass fraction, above 0.96. In order to achieve the larger mass fraction of about 0.98, partial
condensation (not shown) is necessary.
26
Fig. 8. Temperature, mass fraction, mass flow rates and heat flux per unit length along distillation
column height (nominal).
27
Fig. 9. Temperature, mass fraction, mass flow rates and heat flux per unit length along distillation
column height (high temperature).
28
Similar trends are observed for the high temperature condition (see Fig. 9). Due to the increased
temperature of the feed, higher solution temperatures are reached at the bottom of the generator. In
this case, the feed is slightly subcooled. The main consequences of that, as shown in Fig. 9, are
found in the stripping section, where the mixture temperature is higher than feed temperature and
vapor flow rate decreases. These effects are due to the rapid saturation of the feed as soon as it gets
in contact with the vapor rising through the distillation column. Heat recovery continues to
represent a large share of total heat, although the heat recovery potential between rich and poor
solution is not fully exploited. An increase of the overall heat transfer coefficient of the heat
recovery coil would not bring much benefit. In fact, the main limitation to heat recovery is the
temperature increase of the two-phase mixture due to saturation of the feed.
At partial load condition (see Fig. 10), all gradients are less pronounced. The feed is subcooled and
here its effect is even more evident than in the previous case. As soon as the liquid gets in contact
with vapor in the distillation column, saturation brings the two-phase mixture at a temperature
considerably higher than the feed temperature, from 88 °C to 107 °C. The higher temperature limits
the possibility to cool down the solution leaving the column through the internal heat recovery coil.
It shall be noticed that the insufficient cooling of the poor ammonia water solution is a problem
because, in absence of an additional solution heat exchanger, flashing might occur after the
throttling valve that separates the generator pressure from the absorber pressure. Solution flashing
causes cooling of the solution at the absorber inlet and thus further limits the heat recovery potential
between absorber and generator.
29
Fig. 10. Temperature, mass fraction, mass flow rates and heat flux per unit length along distillation
column height (partial load).
30
Fig. 11. a) combustion and thermal efficiency and b) useful heat and losses as share of gas input
(HHV) under varying loads.
Fig. 11 shows the effect of the continuous variation of the gas input from 20% to 100% on both the
combustion and thermal efficiencies, respectively defined as:
1
,
⁄ (59)
31
,
⁄1
,
⁄ (60)
Combustion efficiency (see Fig. 11-a), which takes into account only stack losses, decreases from
85% to 82%. This trend is explained by the lower generator temperatures at reduced loads, which
result in lower temperature of the flue gases. However, thermal efficiency, which includes also
jacket losses, varies very little. Its value is around 80%, with a peak of nearly 81% at about 50% gas
input. As shown in Fig. 11- b, the share of jacket losses over total gas input, based on HHV,
becomes non negligible at reduced loads. This fact suggests that a different furnace geometry or,
more simply, better insulation of the furnace, can provide benefits in terms of GUE at small partial
loads.
7. Conclusions
In this paper, a model to simulate the combined heat and mass transfer processes that occur in a gas-
fired generator of an ammonia water absorption heat pump was presented. The model comprises
three interconnected components: the gas furnace, the distillation column and the rectifier. The
furnace was modelled like a well-stirred single volume. The distillation column and the rectifier
were discretized along their axial dimension. The one-dimensional problem in the distillation
column was solved taking into account the different heat transfer mechanisms involved: radiative
and convective heat transfer between combustion products and generator finned surface, flow
boiling and pool boiling in the two-phase ammonia water mixture inside the distillation column. An
iterative algorithm for the solution of the model is proposed. The model has been successfully
applied to three different operating conditions, which are of interest in real applications, and
suitable input conditions have been derived considering experimental data. The model provided
valuable data regarding the temperature, mass fraction, mass flow rate and heat transfer rate
gradients along the distillation column height. In particular, the model outputs provided the
quantification of the effectiveness of radiative and convective heat transfer in the gas furnace,
32
solution boiling, and internal heat recovery. The distance from saturation of the feed is found
critical at partial load, leaving the possibility to explore alternative solutions for the exploitation of
the internal heat recovery potential. Combustion efficiency, based on HHV, varied with gas input
between 0.82 and 0.85, whereas thermal efficiency was not too sensibly affected by gas input, since,
at lower loads, the decrease of stack losses is compensated by a higher influence of jacket losses.
The model could be used in the future for the detailed simulation of gas absorption heat pumps with
modulating gas burner.
33
Appendix A
The scheme of the water-source GAHP is shown in Fig. A-1, where the main cycle state points are
marked from 1 to 9. Besides the distillation column (DC) and the rectifier (REC), solution cooled
absorber (SCA), water cooled absorber (WCA), condenser (COND), refrigerant heat exchanger
(RHE), evaporator (EVAP), solution pump (PMP) are also shown. The unit is hydraulically
connected to a cool water loop (i.e. the heat source) and a hot water loop (i.e., the heat sink). During
tests, gas input is electronically set by acting on the burner’s blower. The cool water and hot water
compensation systems (not shown) are controlled until the desired steady state conditions are
achieved in the corresponding hydraulic loops.
Fig. A-1 Water-source GAHP scheme.
The unit is instrumented in order to measure: gas thermal input (i.e., volume flow rate, pressure,
temperature and composition of the fuel), cooling capacity (i.e., temperatures and flow rate of the
external cool water loop), heating capacity (i.e., temperatures and flow rate of the external hot water
loop), temperature of the cycle state points 1-9, pressure of state points 3,5 and 9, and temperature
of flue gases after the generator (position 10). Measurements accuracy is shown in Table A-1.
34
Table A-1. Measurements accuracy.
measure probe range accuracy
,1..9 cycle point temperature thermocouple type T 0 - 150 °C ±0.3 °C
flue gas temperature thermocouple type T 0 - 350 °C ±0.5 °C
, hot water temperature PT100 30-70 °C ±0.1 °C
Δ hot water temperature difference calculated 10-15 °C ±0.15 °C
hot water volume flow rate magnetic flow meter 1.0-3.0 m3
h-1 1.5%
heating capacity calculated 19-45 kW 2.0%
, cool water temperature PT100 5-20 °C ±0.1 °C
Δ cool water temperature difference calculated 3-6 °C ±0.15 °C
cool water volume flow rate magnetic flow meter 1.0-3.0 m3
h-1 1.5%
cooling capacity calculated 6-18 kW 3.0%
, gas thermal input calculated (ISO 6976) 14-29 kW 2.5%
, low pressure (absolute) capacitive DP probe 3-6 bar 0.5-1.0%
high pressure (absolute) capacitive DP probe 15-30 bar 0.2-0.4%
Notes:
The values in % are applied to the value read, not to full scale.
The uncertainty includes the probe and the measurement chain uncertainty.
Mass fraction of the feed is calculated based on pressure and temperature at the inlet of the solution
pump, assuming 1.5 °C subcool at pump inlet:
,
1.5 (A-1)
The above assumption is suggested by experience and by the kind of pump used, a membrane pump
whose characteristic is to work with very little subcool at the inlet.
Mass fraction of the residue is estimated based on pressure and temperature after throttling from
state 2 to state 7:
,,,, (A-2)
Mass fraction of the distillate (), which typically achieves a high grade of purity in ammonia
concentration, is assumed equal to 0.98 kg kg-1.
The refrigerant mass flow rate is estimated based on cooling capacity and enthalpies in states 8 and
9:
/,,,, (A-3)
35
The mass and species balance for the subsystem comprising DC and REC provide the solution mass
flow rate:
(A-4)
The assumptions made about subcool at the pump inlet and mass fraction of the refrigerant do not
introduce appreciable errors. Deviations up to 0.5 °C from the assumed subcool value affect the
calculation of feed mass flow rate by about 1%. Deviations up to 0.005 kg kg-1 from the assumed
mass fraction value affect the calculation of feed mass flow rate by about 1%.
Eq. A-2 is accurate only when vapor flashing occurs in state 7. When state 7 is subcooled, the only
information provided is the upper limit for the mass fraction in state 2 and, according to Eq. A-4,
the upper limit of the solution mass flow rate in state 1.
The overall energy balance for the thermodynamic cycle, assuming negligible heat losses, provides
the useful heat input to the generator:
/,, (A-5)
36
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Nomenclature
ammonia mass fraction, kg kg-1
blackbody emission, W m-2
view factor, -
irradiance, W m-2
enthalpy, J kg-1
height, m
zero-order modified Bessel function of first kind
first-order modified Bessel function of first kind
zero-order modified Bessel function of second kind
first-order modified Bessel function of second kind
mean beam length, m
number of elements, -
mass flow rate, kg s-1
partial pressure, Pa
total pressure, Pa
heat generation per unit volume, W m-3
heat transfer rate, W
radius, m
thermal resistance, K W-1
fins spacing, m
surface, m2
39
fin thickness, m
temperature, K
heat transfer coefficient, W K-1
volume, m3
Greek symbols
heat transfer coefficient, W m-2 K-1
angle, rad
angular position, rad
Δ length of the discretized volume , m
Δ height of the discretized volume , m
emissivity, -
thermal conductivity, W m-1 K-1
excess temperature, K
reflectivity, - , density, kg m-3
Stephan-Boltzmann constant, W m-2 K-4
gas transmittance, -
Subscripts
ambient air, aperture
base, bubble
rectifier (partial condenser), convective
convective (temperature)
combustion
cool water
40
cool water inlet
cool water outlet
distillation column
enriching section
equilibrium
fuel, fin lateral surface
fin volume
GFSHD section, combustion products
hot water
hot water inlet
hot water outlet
internal heat exchanger
stack
furnace jacket
fuel gas
high heating value
input to generator
index of discretized volume (distillation column)
index of discretized volume (rectifier)
liquid
outer
SHD section, radiative
stripping section
solution, surface
tip
41
thermal
vapor
wall
