Thermodynamic optimization of Organic Rankine Cycles for low and

ultra low grade waste heat recovery applications: influence of the

working fluid on the ORC net power output

GIOVANNA CAVAZZINI SERENA BARI GUIDO ARDIZZON GIORGIO PAVESI

Department of Industrial Engineering

University of Padova

Via Venezia 1 -35131 Padova

ITALY

giovanna.cavazzini@unipd.it http://www.dii.unipd.it

Abstract: - The present work is focused on the thermodynamic optimization of Organic Rankine Cycles (ORCs)

for power generation from low and ultra low grade waste heat recovery. The paper is aimed at providing a

preference selection order of working fluids for applications characterized by low and ultra low heat source temperatures (from 80°C to 150 °C).

Among the commonly available working fluids, a selection based on environmental and technical criteria was

carried out resulting in a list of 12 working fluids: R245fa, R245ca, R1234yf, R134a, R227, R236fa, RC318, Isobutane, Butane, Isopentane, Pentane.

A model of a simple ORC cycle was developed and optimized by means of a recent evolution of the Particle

Swarm Optimization (PSO) algorithm. The evaporation pressure and the approach and pinch point temperature

differences have been chosen as decisional variables. Two refrigerants (R1234yf and R134a) were able to maintain good performance in the whole considered range

of temperature, whereas due to their thermos-fluid-dynamic properties the hydrocarbons always remained near

the bottom apart from the temperature. However, for heat source temperatures lower than 100 °C, the difference between the most and the less performing fluid in terms of net power output and system efficiency significantly

reduces, demonstrating that for ultra low waste heat recovery applications the net power output resulted not to be

a really effective selective criteria and should be combined with other environmental and/or technical criteria

(minimum costs, minimum environmental impact, maximum heat exchange efficiency…).

Key-Words: waste heat, ORC, optimization, simulation model, PSO, working fluid

1 Introduction The interest for low grade heat recovery has been

growing for the last ten years because of the

increasing concern over energy shortage and global

warming. Since conventional steam power cycles cannot give a good performance to recover low grade

waste heat, new solutions have been proposed:

among them the Organic Rankine Cycle (ORC) system seems to be the most promising process and it

is the most widely studied.

This system includes the same components as in a conventional steam power plant (a vapour generator,

an expansion device, a condenser and a pump), with

the exception that the working fluid is an organic

substance, characterized by a low ebullition temperature allowing for smaller evaporating

temperatures.

Previous papers ( [1], [2], [3], [4]) are focused on the screening of fluids following basic screening criteria

such as the slope of the saturation vapour curve, the

critical point position and other thermodynamic

properties.

Qiu [5] proposed a selection method for the working

fluid for the medium-to-low temperature ORC considering only thermo-physical characteristics of

the organic refrigerants without taking in account any

cycle parameters. Chen et al. [6] analysed the

selection criteria of potential working fluids and the influence of fluid properties on cycle performance.

Other papers performed optimization analysis ( [7],

[8], [9]) or system simulations ( [10], [11], [12]) considering a selected number of fluids. Dai et al.

[13], conducted a parametric optimization by means

of genetic algorithm using as objective function the exergetic efficiency. The heating source considered

was an exhaust gas stream at 145°C and among the

fluids taken in account R2236ea showed the higher

efficiency under the same given waste heat condition. Wang et al. [14] used a genetic optimization

algorithm to investigate the expander inlet pressure

and temperature, approach-point and pinch-point influence on the power output and the total thermal

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ISBN: 978-1-61804-346-7 32

exchange area.

The usual target for the system optimization works

are the power output ( [15]), the thermal or global

efficiency of the cycle ( [14], [16], [17],), the total exergy destruction, the heat exchangers area ( [18],)

or others parameters such as the size of the expansion

device ( [19]) or the overall cost for the entire system ( [20], [21]).

In this paper a list of nearly 50 fluids was preliminary

taken in account and was screened applying basic criteria such as the slope of the saturation curve, the

Ozone Depleting Potential (ODP) and the eventual

phasing out date of the organic fluid. Then an

optimization of the ORC parameters aimed at maximizing the net power output, was carried out by

means of a PSO-based algorithm on a selection of

working fluids at different temperatures of the heat source in order to find a preference selection order for

ultra low grade waste heat recovery applications.

2 The model A basic ORC to recover energy from a low

temperature heat source, consisting of a pump,

evaporator expander and condenser, was modeled in Matlab/Simulink environment (Fig. 1).

Figure 1 – T-s diagram of a typical simple ORC

For the heat source, a water stream entering in the evaporator at different temperatures (Tsin=80-90-

100-120-150 °C) with a mass flow rate of 5 kg/s (ṁs)

was considered. The cooling fluid in the condenser was assumed to be water, with an inlet temperature

of 10 °C (Tpin).

At the condenser exit, the fully saturated liquid

working fluid is pumped to the evaporator (process 1-2 in fig. 1) where it absorbs heat at a relatively high

pressure (2-3). Then it expands in the expander

producing useful shaft work (3-4) and rejects heat at a lower pressure (4-1) in the condenser.

The following energy balances were used to model

the different components:

PUMP:

𝜂𝑝𝑢𝑚𝑝 =ℎ2𝑖𝑠−ℎ1

ℎ2−ℎ1 (1)

𝑃𝑝𝑢𝑚𝑝 = ṁ𝑤𝑓(ℎ2 − ℎ1) (2)

EVAPORATOR:

ṁ𝑠𝑐𝑝𝑠(𝑇𝑠𝑖𝑛 − 𝑇𝑠𝑜𝑢𝑡) = ṁ𝑤𝑓(ℎ3 − ℎ2) =

= 𝑄𝑒𝑣 (3)

ṁ𝑠𝑐𝑝𝑠(𝑇𝑠𝑖𝑛 − 𝑇𝑠𝑟) = ṁ𝑤𝑓(ℎ3 − ℎ𝐹) (4)

EXPANDER:

𝜂𝑒𝑥𝑝 =ℎ3−ℎ4

ℎ3−ℎ4𝑖𝑠 (5)

𝑃𝑒𝑥𝑝 = ṁ𝑤𝑓(ℎ3 − ℎ4) (6)

CONDENSER:

ṁ𝑝𝑐𝑝𝑝(𝑇𝑝𝒐𝒖𝒕 − 𝑇𝑝𝒊𝒏) = ṁ𝑤𝑓(ℎ𝟒 − ℎ1) =

= 𝑄𝑐𝑜𝑛𝑑 (7)

ṁ𝑝𝑐𝑝𝑝(𝑇𝑝𝑟 − 𝑇𝑝𝒊𝒏) = ṁ𝑤𝑓(ℎ𝐺 − ℎ1) (8)

The pump and expander efficiencies were set equal to 0.8.

The net power output of the cycle is hence:

𝑃𝑛𝑒𝑡 = 𝑃𝑡𝑢𝑟𝑏 − 𝑃𝑝𝑢𝑚𝑝 (9)

As regards the cycle efficiency, two performance

indexes were calculated.

The first one is the thermal efficiency, defined as the ratio of the net power gained over the thermal power

absorbed during the evaporation process:

𝜂𝑡ℎ =𝑃𝑛𝑒𝑡

𝑄𝑒𝑣 (10)

This index does not take into account the heat-exchange efficiency, which is considered in the

system efficiency, defined as the product of the

thermal efficiency by the heat exchange efficiency:

𝜂𝑠𝑦𝑠𝑡 = 𝜂𝑡ℎ 𝜒 =𝑃𝑛𝑒𝑡

𝑄𝑒𝑣∙

𝑄𝑒𝑣

𝑄ℎ𝑠=

𝑃𝑛𝑒𝑡

𝑄ℎ𝑠 (11)

where Qhs is determined as follows:

𝑄ℎ𝑠 = ṁ𝑠𝑐𝑝𝑠(𝑇𝑠𝑖𝑛 − 𝑇𝟎)

3 The ASD-PSO algorithm The standard Particle Swarm Optimizer (PSO) is a

relatively recent heuristic population-based search

method based on the social behaviour of a swarm of

insects or a flock of birds where a continuous exchange of information allows each component to

move towards promising regions of the search space

by exploiting both its own knowledge and the knowledge of the swarm as a whole.

In the context of a multivariable optimization, the

swarm is characterized by a specified number of

particles (where “particle” denotes a bird or an insect), each one characterized by a position and a

velocity. The particles, initially located at random

locations, wander around in the search space with a

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target (for example the identification of the food

source). When a particle locates a good position, it

instantaneously communicates this information to the

swarm that does not directly converge to that position. Each particle maintains its independent

thinking and adjusts its position and velocity on the

basis of the swarm information on good positions, but also of its own best position, gradually going to the

target after some iterations.

As regards the PSO algorithms, the mathematical problem is to find the n-dimensional vector

X={x1,...xn} that minimizes the objective function

f(X), i.e. the target of the “swarm random search”

(where n is the number of variable to be optimized). The search space is defined by the lower X(l) and

upper X(u) bounds on X:

X(l) ≤ X ≤ X(u) The procedure of the PSO can be summarized

through the following steps:

1. Definition of the swarm size: the number of particles np of the swarm should be assumed: X1,

…Xnp. If n is the number of variables to optimize,

Fan et al. suggests, as a criterion, assuming a number

of particles equal to 2n [22]. 2. Initialization of the swarm: a random location for

each particle Xi(0) (i=1,…np) is generated in the

search space. All the particles may be assumed

initially to be at rest (iteration 1).

3. Velocity update: each particle wanders around in

the search space updating at each iteration t its own

position Xi(t) and velocity Vi(t) on the basis of its own past flight experience (the historical own best

position of Xi(t): Pbest,i) and on that of the swarm (the

historical best position encountered by any of the particles: Gbest).

The particle velocity is updated as follows:

𝑉𝑖(𝑡) = 𝜔 ∙ 𝑉𝑖(𝑡 − 1)+

+𝐶1𝑟1 ∙ [𝑃𝑏𝑒𝑠𝑡,𝑖 − 𝑋𝑖(𝑡 − 1)]+

+𝐶2𝑟2 ∙ [𝐺𝑏𝑒𝑠𝑡 − 𝑋𝑖(𝑡 − 1)] (𝑖 = 1,2, ⋯ , 𝑛𝑝)

where C1 and C2 are positive constants representing

the individual and group learning rates respectively,

is an inertia weight, and r1 and r2 are two

independent sequences of random numbers generated in the range 0 and 1, used to avoid entrapment on

local minima and to allow the divergence of a small

percentage of particles for a wider exploration of the search space. As observed, the particle updates its

velocity on the basis of three components: the

previous velocity moderated by the inertia weight,

the tendency of the particle to move toward the previously discovered best position, and the tendency

to move towards the best position discovered by the

swarm.

Figure 2 - Distribution of the acceleration coefficients and of the inertia weight for the i-th particle as a

function of the particle distance dj,i from the global best solution: (a) C1; (b) C2; (c) . 𝑑𝑚𝑎𝑥𝑗

is the maximum

distance reached by the swarm in the j-th dimension

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4. Position update: the particle position at the

iteration t is updated as follows:

𝑋𝑖(𝑡) = 𝑋𝑖(𝑡 − 1) + 𝑉𝑖(𝑡) ∙ ∆𝑡 (𝑖 = 1,2, ⋯ , 𝑛𝑝)

5. Convergence check: the convergence is achieved

when the positions of all particles converge to the same set of values.

In the standard PSO algorithm, the weight of the

cognitive experience (C1) of a particle is the same as that of the social experience (C2) acquired by the

swarm to balance the attraction toward the global best

solution (gbest) with the wandering aptitude of each particle in the search space. Kennedy and Eberhart

[23] suggested C1 = C2 = 2, whereas the inertia weight

is often reduced linearly from 0.9 to 0.4 during a run [24]. Such a compromise has generally proved to

be useful in avoiding premature convergence in a local optimum, even though it is very hard to prevent

early convergence when solving multimodal

problems.

In the adaptive PSO strategy [25], adopted in this

analysis, a different concept of cooperation among the particles of the swarm has been developed. The

particles are diversified depending on their relative

position compared to the Gbest, which roughly represents the center of the swarm. During the swarm

random search, the particles on the external periphery

of the swarm are mainly involved in enhancing the

exploration ability of the swarm, while the particles closer to the global best solution discovered so far are

mainly involved in local search refinement of the

current best solution, that is in the exploitation of the current promising search space. To do this, both the

inertia weight and the acceleration coefficient C1 and C2 properly vary as a function of the distance di,j

of the particle i (i=1, 2,…, np) in each spatial

dimension j (j=1, 2,…, n - number of variables to optimize) from the global best solution (Fig. 2).

A simplified scheme of the ASD-PSO procedure is

reported in Fig. 3. More details about the ASD-PSO

Figure 3 - A simplified flow chart of the ASD-PSO procedure

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algorithm can be found in [25].

In the optimization procedure, the ASD-PSO was set

as follows: np=20; C1max=3, C2max=3, C2min=0.5,

min=0.4 and max=0.9. In the optimization model, the following parameters have been chosen as independent variables:

The evaporating pressure (pev)

The temperature difference at the pinch point

in both the heat exchangers:

(ΔT𝑝𝑝)𝑐𝑜𝑛𝑑

= 𝑇𝐺 − 𝑇𝑝𝑟 (12)

(ΔT𝑝𝑝)𝑒𝑣𝑎𝑝

= T𝑠𝑟 − T𝐹 (13)

The approach point temperature difference in

both the heat exchangers:

(ΔT𝑎𝑝)𝑒𝑣𝑎𝑝

= 𝑇𝑠𝑖𝑛 − 𝑇3 (14)

(ΔT𝑎𝑝)𝑐𝑜𝑛𝑑

= 𝑇1 − 𝑇𝑝𝑖𝑛 (15)

As regards the search bounds, the temperature

differences at the pinch points (ΔTpp) were fixed to vary between 5° and 25°C, whereas those at the

approach point between 10°C and 25°C.

The input parameters were optimized in order to achieve the maximum net power output Pnet for each

considered working fluid. Since the aim of the ASD-

PSO algorithm is to search for a minimum, the

following objective function was built:

𝑎 =𝑃𝑟𝑒𝑓−𝑃𝑛𝑒𝑡

𝑃𝑟𝑒𝑓 (16)

where Pref is the net power output obtained by an

ideal Carnot cycle operating between the same heat and sink temperatures (Tsin=80÷150 °C; Tpin=10°):

𝑃𝑟𝑒𝑓 = 𝑄𝐶𝜂𝐶 =

= ṁ𝑠𝑐𝑝𝑠(𝑇𝑠𝑖𝑛 − 𝑇𝑝𝑖𝑛) (1 −𝑇𝑝𝑖𝑛

𝑇𝑠𝑖𝑛) (17)

4 Results Figs. 4 and 5 report net power output and system

efficiency obtained for different working fluids depending on the temperature of the heat source.

As it can be seen, the influence of the working fluid

on the resulting ORC performance in terms of net power output and system efficiency becomes smaller

as the temperature of the heat source reduces. The

percentage difference in terms of net power output

between the most performing working fluid and the less performing one reduces from 24.88% to 8% for

a heat source temperature of 100°C and to 4.32% for

a temperature of 80°C. It is also interesting to notice that the ranking of the

working fluids is not significantly modified by the

temperature decrease. R1234yf and R227ea are able to maintain good

performance in the whole considered range of

temperature.

R134a and R236fa slightly reduces their performance

as the temperature decrease, whereas R245ca,

Butane, Pentane and Isopentane remain near the

bottom apart from the temperature. These results are mainly affected by the different

values of heat recovery efficiency characterizing the considered fluids (fig. 6).

For ultra low heat source temperatures (T≤100°C),

despite of thermal efficiency values th almost

equivalent (fig. 7), the heat recovery efficiency (fig. 6) presents more remarkable differences between the working fluids, significantly affecting their final

ranking.

For example, for a heat source temperature of 100°C,

the thermal efficiencies are included between 7.98% and 8.34%, whereas the heat recovery efficiency

varies of about 4% between the less and the most

performing fluid.

Fluid Pnet [kW] th syst

R1234yf 84.27 8.34% 60.37% 5.03%

R227ea 83.10 8.18% 60.65% 4.96%

R134a 81.12 8.18% 59.22% 4.84%

R236fa 81.12 8.18% 59.22% 4.84%

RC318 80.89 7.98% 60.55% 4.83%

R236ea 80.00 8.18% 58.45% 4.78%

Isobutane 79.79 8.23% 57.87% 4.77%

R245fa 79.74 8.27% 57.56% 4.76%

Butane 79.13 8.20% 57.60% 4.73%

R245ca 79.10 8.27% 57.12% 4.72%

Isopentane 78.07 8.23% 56.68% 4.66%

Pentane 78.05 8.25% 56.49% 4.66%

Table 1 - Performance in terms of net power output and efficiencies of the difference working fluids at

100 °C

For heat source temperatures greater than 100°C, this

behaviour is generally confirmed (Table 2). Near the top position, it is possible to find working fluids

characterized by the greatest values of heat recovery

efficiency with two exceptions represented by R134a

and R236fa due to the widest range of thermal efficiency values.

R134fa is able to achieve a very good value of heat

recovery efficiency combined (76.19%) with good value of thermal efficiency (11.90%), gaining the top

of the list, whereas R236fa makes up for the small

value of heat recovery efficiency (65.27%) with the greatest value of thermal efficiency (13.32%).

The reason of these different “strategies” adopted by

the optimization algorithm to optimize the ORC

parameters, are related to the different thermo-fluid-dynamic characteristics of the considered working

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fluids and can be understood analyzing the influence

of the evaporation pressure on the resulting ORC

cycle (figures 8-10).

Figure 4 – Net power output achieved by the different working fluids as a function of the heat source

temperature

Figure 5 – ORC system efficiency sist (eq. 11) achieved by the different working fluids as a function of the heat source temperature

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Figure 6 – Heat exchange recovery achieved by the different working fluids as a function of the heat

source temperature

Figure 7– Thermal efficiency th achieved by the different working fluids as a function of the heat

source temperature

Fluid Pnet

[kW] th syst

R134a 246.7 11.90% 76.19% 9.07%

R1234yf 244.4 10.98% 81.81% 8.98%

R227ea 242.7 10.93% 81.58% 8.92%

R236fa 236.6 13.32% 65.27% 8.69%

RC318 234.2 11.37% 75.73% 8.61%

Isobutane 219.8 12.60% 64.15% 8.08%

R236ea 218.8 12.25% 65.61% 8.04%

R245fa 217.3 12.39% 64.47% 7.99%

Butane 214.8 12.40% 63.53% 7.88%

R245ca 213.3 12.28% 63.83% 7.84%

Pentane 207 12.11% 62.82% 7.61%

Isopentane 206.7 12.05% 63.04% 7.60%

Table 2 - Performance in terms of net power output

and efficiencies of the difference working fluids at 150 °C

Figure 8 – Influence of the evaporation pressure on

the enthalpy drop at the expander for a heat source

temperature of 100°C for R1234yf, R245fa, RC318

Figure 9 – Influence of the evaporation pressure on

the vapour mass flow rate for a heat source

temperature of 100°C for R1234yf, R245fa, RC318

An increase of the evaporation pressure causes two

different events, having conflicting effects on the net power output.

Greater evaporation pressure values determine an

increase of the enthalpy drop at the expander (figure 8) with a consequent increase of the net power output.

However, the heat absorbed during the evaporation

process decreases with increasing evaporation

pressure, resulting in a smaller vapour mass flow rate produced in the evaporator (fig. 9) and hence in a

reduction of the net power output of the

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thermodynamic cycle (fig. 10).

Figure 10 – Influence of the evaporation pressure on the net power output for a heat source temperature of

100°C for R1234yf, R245fa, RC318

As a consequence, the net power output of the cycle

increases as long as the increase in enthalpy drop

prevails against the decrease of vapour mass flow rate. It reaches a maximum value when the two

conflicting events are balanced and then starts to

decrease due to the greater influence of the vapour

mass flow rate reduction. Depending on the thermo-fluid-dynamic properties

of the working fluid, the optimal condition is located

on a greater or smaller value of evaporation pressure, hence favouring the thermal efficiency of the ORC

cycle or the heat recovery efficiency respectively.

For example, the greater values of latent heat characterizing the hydrocarbons reduces the

influence of the vapour mass flow rate on the net

power output, determining an optimal condition with

greater values of thermal efficiency (greater entropy drops) and smaller values of heat recovery efficiency

(smaller vapour mass flow rates) than the refrigerants

(Table 3). These thermo-fluid-dynamic characteristics penalize

the hydrocarbons in comparison with the refrigerants

for low heat source temperatures (100 °C <T<150

°C). However, for ultra low heat source temperatures (T<100 °C), also the heat recovery efficiency of the

refrigerants decreases and this reduces the difference

between the most and the less performing fluids in terms of net power output (4.32%) and system

efficiency (0.15%).

Fluid ṁ𝐰𝐟

[kg/s]

h3-h4

[kJ/kg]

R134a 8.034 33.2

R1234yf 9.532 28.0

R227ea 11.65 22.6

R236fa 8.183 30.9

RC318 11.41 22.0

Isobutane 3.492 66.3

R236ea 7.356 30.8

R245fa 6.188 36.0

Butane 3.19 69.6

R245ca 5.806 37.3

Pentane 3.072 68.2

Isopentane 3.214 65.2

Table 3 – Vapour mass flow rate and enthalpy drop

of the difference working fluids at 150 °C

5 Conclusions A thermodynamic optimization of Organic Rankine

Cycles (ORCs) for power generation from low and ultra low grade waste heat recovery was carried out.

The analysis was aimed at providing a preference

selection order of working fluids for applications

characterized by low and ultra low heat source temperatures (from 80°C to 150 °C).

Among the commonly available working fluids, a

selection based on environmental and technical criteria was carried out resulting in a list of 12

working fluids: R245fa, R245ca, R1234yf, R134a,

R227, R236fa, RC318, Isobutane, Butane, Isopentane, Pentane.

A model of a simple ORC cycle was developed and

optimized by means of a recent evolution of the

Particle Swarm Optimization (PSO) algorithm. The evaporation pressure and the approach and pinch

point temperature differences were chosen as

decisional variables. The influence of the working fluid on the resulting

ORC performance in terms of net power output and

system efficiency became smaller as the temperature

of the heat source reduced. The ranking of the working fluids resulted not to be

significantly modified by the temperature decrease.

R1234yf, R227ea were able to maintain good performance in the whole considered range of

temperature. R134a and R236fa slightly reduced

their performance as the temperature decrease, whereas R245ca, Butane, Pentane and Isopentane

remained near the bottom apart from the temperature.

These results were mainly affected by the different

values of heat recovery efficiency characterizing the considered fluids. In particular it was demonstrated that hydrocarbons,

due to their great values of latent heat, did not reach

significant values of heat exchange efficiency and

were not able to made up for it by significantly

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increasing the thermal efficiency. However, for heat

source temperatures lower than 100 °C, also the heat

recovery efficiency of the refrigerants decreased and

this reduced the difference between the most and the less performing fluids in terms of net power output

(4.32%) and system efficiency (0.15%).

Therefore, even though some refrigerants and in particular R1234yf showed better performance than

the other in low grade waste heat recovery

applications, the maximum net power output could not be an exhaustive selection criterium for ultra low

heat source temperatures but further considerations

on the environmental impact and on the cost of the

ORC components should be added.

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Nomenclature

a Objective function (-)

A Area (m2)

cp Heat Capacity at constant pressure (kJ/kg °C)

h Enthalpy (kJ/kg) ṁ Mass flow rate (kg/s)

p Pressure (kPa)

P Power (kW) Q Heat Power (kW)

T Temperature (°C)

Greek letters Δ Difference

χ Heat recovery efficiency (%)

η Efficiency (%)

Superscripts and subscripts a Approach Point

av Available

C Carnot cycle

cond Condenser ev Evaporator

hs Heat Source

in Inlet is Isentropic

out Outlet

p Cooling fluid pp Pinch Point

pump Pump

ref Reference

s Heat source fluid

syst System th Thermal

tot Total

turb Turbine/expander device v Vaporization

wf Working fluid

0 Environment Condition

Mechanics, Energy, Environment

ISBN: 978-1-61804-346-7 41