Safety aspects of Organic Rankine Cycles (ORC) with combustible working fluid and sub-ambient condenser pressure

ORCs are often designed with the lower pressure limited by the ambient pressure, to avoid air leaking into the working fluid. Safely lowering this limit will be beneficial for power-production efficiency. First, cycle operations with air inleak are investigated. Exemplary cases with n-pentane and benzene are used. The investigation combines tools from thermodynamics of cycle working fluids, pump operation and analysis and combustion science. It appears that pumps customarily used in ORC will forward only liquid, and air mixing into the working fluid at the high-pressure side will not be sufficient for flammable conditions. Next, combustion properties of the air/working fluid mixture in the condenser are evaluated. Transient zero-dimensional and one-dimensional steady state laminar premixed flames are applied for the modelling. Detailed chemical mechanisms from the CRECK and TDTVT groups are used for benzene and n-pentane. It is found that some substances, like pentane, will not make flammable mixtures within the conditions of the power cycle. However, fluids that at the relevant temperatures have saturation pressure much lower than the ambient, might give flammable mixtures with air inleak. For potential sub-ambient use of these, ignition energy sources and quenching geometries have to be considered carefully.


Introduction
Increasing demand for electric energy calls for increasing efficiency of thermal power plants and better utilization of other thermal energy sources.Large amounts of thermal energy are found in the gases and liquids discharged to the environment (Tchanche et al., 2011;Papapetrou et al., 2018;Castelli et al., 2019), often called ''waste heat''.Streams at temperatures 100-200 • C are hard to utilize by conventional steam vapour power cycles.For such cases, organic Rankine cycles (ORCs) can be more applicable.Also for the increased efficiency of engines for vehicles (Wu et al., 2020), heavy-duty (Lion et al., 2017) or marine applications (Suárez de la Fuente et al., 2017), ORCs are of interest, as well as for natural heat sources like solar (Ferrara et al., 2014) and geothermal (Astolfi et al., 2014).
The thermodynamic and economic performance for a certain application is the primary or sole criterion for several studies.Among other criteria are the flammability of the fluid and the avoidance of air leakage into the cycle.These aspects are common issues for both power and refrigeration cycles.It is worth noting that while the number of installed ORC power plants counts to a few thousand units (ORC World Map, 2021;Tartière and Astolfi, 2017), organic working fluids are commonly used in the household market of refrigerators and freezers, with a very large number of installations.* Corresponding author.
A few decades ago, it seemed that only non-flammable working fluids were acceptable (Wali, 1980).However, the halocarbons recommended then were soon after banned for their ozone depletion.Eventually, flammable working fluids were found acceptable, although not preferred (Badr et al., 1985;Kajurek et al., 2019).Suárez de la Fuente et al. (2017) and Yang et al. (2021) discussed how to deal with the combustion risk.Several studies mentioned flammability as a criterion, although without further discussion (e.g., Ferrara et al., 2014;Haervig et al., 2016).The safety criteria set by the concurrent ASHRAE and ISO standards (ISO 817:2014(E), 2014) are often referred.These standards distinguished four classes of fluids from ''no flame propagation'' to ''higher flammability'', based on certain flame properties of the fluid mixed with air.Studies in literature included among other cycles using n-pentane (Invernizzi et al., 2007;Patel et al., 2017;Santiago et al., 2022), toluene (Patel et al., 2017), n-octane (Al-Sulaiman et al., 2012) and acetone (Ferrara et al., 2014), which are all highly flammable.Some of these authors (Invernizzi et al., 2007;Santiago et al., 2022) pointed out that there is a balance between a lower cost of flammable fluids and the cost of necessary safety precautions.The use of flammable fluids may require additional precautions for specific applications, such as marine (Suárez de la Fuente et al., 2017) or offshore (Nami et al., 2018)  Another aspect or criterion in working fluid selection is the saturation pressure at the temperatures relevant for the condenser.Several authors stated (e.g., Tchanche et al., 2011;Quoilin et al., 2013) that this pressure should, or is preferred to, be above the ambient (atmospheric) pressure to avoid leakage of air into the cycle, or pointed (e.g.Garg et al., 2013;Kajurek et al., 2019) at the benefits of avoiding subambient pressure in the cycle.Others (Tocci et al., 2017;Castelli et al., 2019) pointed at the extra cost of preventing leakages, without discussing this further.Some investigators simply followed the thermodynamic performance and utilized the lower condenser pressure when available (e.g., Al-Sulaiman et al., 2012;Haervig et al., 2016).Quoilin et al. (2013) discussed the changes in the working fluid properties when non-condensable gases like air are dissolved into it.Such changes can influence the pump performance.A similar discussion was made by Kruse and Rinne (1992) for property changes due to uneven out-leakage of mixtures.Others mentioned the issue without elaborating, e.g., Garg et al. (2013).
ORCs are often designed with a constraint on the lower pressure: The condenser pressure is set to a value just above the ambient pressure.This is partly to avoid the need for gas removal (Astolfi, 2017).It can also partly be due to the fear of a flammable mixture of air and the combustible working fluid.For cycles based on water/steam, or other non-combustible fluids, this is not an issue.These are constrained by the available cooling temperature and by properties of the condenser materials.
From the viewpoint of thermodynamics and power cycle efficiency, a condenser pressure as low as possible is desired.This is well known from water/steam-based cycles, where a low coolant temperature allows a low condenser pressure.The practice of setting the condenser pressure at or above the ambient pressure will inevitably limit the cycle efficiency for many cases.Moreover, since ORCs are often used to utilize lower-temperature heat, the relative impact of the condenser pressure constraint can be substantial.
The problem to be investigated in this study is the possible effects of air inleak into the combustible working fluid of the cycle.A question is whether the mixture of air and fluid can reach potentially flammable conditions, or if the changed properties of the air/fluid mixture cause the cycle to halt before the issue becomes relevant at all.It seems that such investigations have not been published previously, making this an original contribution of the study.
The methods will be thermodynamic analysis and combustion analysis by numerical models.No experiments are conducted here.The scope of the work does not include the specific optimization of cycles and their efficiency.Toxicity, pollution or other impacts on the environment are not considered.Furthermore, fires outside the cycle due to discharged working fluid are also out of the scope.However, combustion inside the cycle can lead to breaches and subsequent leakages and fires on the outside.All studies and considerations of flammability and combustion found in literature seemed to deal with leakages out of the cycle.
The paper might find readers both from the field of process/cycle analysis and that of combustion engineering, whom are not fully familiar with the theory of the other field.Therefore the theory description is slightly elaborated for both branches.In the first part of the work, cycle operation with air inleak, although no combustion, will be investigated.In the second part, the possibilities for combustion will be assessed.This paper was based on the master thesis of the first author (Dalbakken, 2021), where some further details were given.In spite of an extensive literature search, it seemed that the problems were not investigated previously.

Cycle base model
The basic Rankine cycle is sketched in Fig. 1, with pump, vapourizer, expander and condenser.The working fluid leaving the condenser  (State 1) was assumed as saturated liquid.The fluid leaving the vapourizer (State 3) was either saturated or superheated vapour.For the base cycle model, the working fluid was pure, with no air.
The cycle was assumed as a steady-state steady-flow process, with constant pressures in condenser and vapourizer, adiabatic pumping and expansion, and negligible change in liquid density over the pump.
Selected hydrocarbons were chosen as working fluids in this study.To investigate the effects of sub-ambient condenser pressure, the temperature at the condenser outlet was assumed as 30 • C. For the present study, the saturation pressure at this temperature should be less than the atmospheric pressure, excluding light hydrocarbons like propane and butane.The vapourizer outlet flow was chosen as saturated vapour at 150 • C. The corresponding pressure should be above ambient, and the range 5-15 bar was preferred.Accordingly, the heat-source temperature was above 150 • C, while the ambient (coolant) temperature was below 30 • C.These temperatures are exemplary values for this study.The high temperature at, say, 10-30 • C above 150 • C represent substantial amounts of so-called waste heat, see e.g., Papapetrou et al. (2018).The low temperature will be at 10-20 • C and represents, e.g., sea temperature in the temperate zones (cf.e.g., Nami et al. (2018)).

Cycle inleak model
In order to investigate the effects of air mixed into the working fluid, a particular air-inleak model was set up as a modification of the base cycle.
To simplify the simulation, a number of assumptions and simplifications were made: The air inleak was modelled as a stepwise steady-state steady-flow process.This was obtained by disconnecting the condenser outlet from the pump, as shown in Fig. 2. Air was mixed with pure, saturated working fluid (''WF'') at 30 • C before the pump.The new mixture (State 1) also had 30 • C and proceeded through the cycle.The outlet of the condenser (State 1 ′ ) had the same temperature as State 1, and saturated working fluid.In the subsequent steps, the amount of air was increased, while the ''WF'' inlet was maintained.
Furthermore, the assumption of equilibrium in State 1, entering the pump, was maintained from the base cycle model.The air flow entering between the expander and the pump was gradually increased as long as the pressure there was below the ambient pressure.The mixing was isothermal and formed a two-phase mixture.The liquid phase was approximated as working fluid, that is, the air dissolved into the liquid was assumed not to affect the properties in the cycle simulations.The gaseous phase consisted of air and working-fluid vapour and was assumed as an ideal-gas mixture.At State 3, exiting the vapourizer, the mixture was gas phase only.In the cycle simulations, the mixture components were assumed not to react.

Phase transition
After mixing with air, the cycle fluid consists of a liquid phase dominated by working fluid and a gaseous phase of air and working fluid vapour.The molar flow rate of the working fluid was set equal to that of the base cycle model.The two phases were assumed as equilibrium, and the properties related by the Clapeyron equation.
The main input quantity for the inleak model was the relative amount of air.The air caused some working fluid to evaporate.The amount of vapour then depended on the amount of air.This is described by the Gas Volume Fraction, which is the ratio of the gas phase volumetric flow rate to the total volumetric flow rate,

Qgas
Qgas + Qliq =  gas ṅgas  gas ṅgas +  liq ṅliq  gas ∕ liq . (1) Here, the subscripts gas and liq denote, respectively, the gaseous and liquid phases.Q is the volumetric flow rate,  is the molar mass, and  is the mass density.It was desired to relate   to the air molar flow rate, ṅair .The gaseous molar flow rate consisted of air and working fluid vapour (''WFv''), ṅgas = ṅair + ṅWFv , while the total working fluid (''WF0'') molar flow was decomposed into vapour and liquid (''WFlq'') phase flows, ṅWF0 = ṅWFv + ṅWFlq .Introducing the partial pressures,  gas =  air +  WFv , the gas volume fraction can be expressed as ) −1 . (2) This is a function of the normalized air molar flow rate ṅair ∕ ṅWF0 and the gas-phase pressure  gas .The gas and liquid phase mass densities were obtained from Refprop as functions of temperature and pressure.Eq. ( 2) relies on the assumption of phase equilibrium and, hence, only valid between condenser outlet and pump inlet.
It was supposed that the pump would stop working at a certain limiting value of the normalized air molar flow rate.The following work will try to reveal this limit.

Pump model
In this work, the pump was allowed to bring liquid to the high pressure, whereas gas was left on the low-pressure side.This model was selected from considerations in literature (Bracco et al., 2017;Aoun, 2008;Clemente, 2013;Serena, 2016).
Basically, the pump of an ORC is meant to pump just liquid.According to Astolfi (2017), multistage centrifugal pumps are usually found in large/medium scale ORCs, however not suitable for small systems (Bracco et al., 2017).Aoun (2008) investigated the suitability of equipment for small-scale cycles and pointed towards diaphragm pumps.Clemente (2013) revisited Aoun's results and argued that gear pumps are suitable for low-viscosity fluids.Both investigators concluded that positive displacement pumps have challenges with lowviscosity fluids.Serena (2016) and Serena and Bakken (2016a,b) found that gas pockets can clog centrifugal pumps.
Based on these considerations, the pump was assumed to only forward liquid phase.

Numerical inleak model
The quantities of interest were the mole fractions of air at the low and high pressure sides, and the pressure evolution at the low-pressure side.It was found in Section 2.3 that suitable independent variables were the normalized air molar flow rate ( ṅair ∕ ṅWF0 ) and the gas pressure on the low-pressure side,  gas .
The air mole fraction in the gas phase at the low-pressure side (subscript ''LP'') is  air,LP = 1 −  WFv ∕ gas . (3) The trivial constraints are  WFv <  gas <  amb , or 0 <  air <  amb −  WFv .The first (lower) limit comes from the requirement that some air must be present for working fluid to evaporate (otherwise, the issue is not relevant).The second (upper) limit simply states that inleak requires a pressure difference.Solubility of air into hydrocarbons (n-alkanes and benzene) was estimated from temperature and air partial pressure by using data fits by Battino et al. (1984) for nitrogen.These were assumed sufficiently accurate used for air, since nitrogen is the main constituent of air.The equations are valid for the ranges of temperature and pressure that were relevant in the present study.They provide the mole fraction solubility , which is the molar ratio of dissolved air to the total of the liquid (air and working fluid).
It was assumed that only liquid phase was forwarded from the pump, and the solubility  was evaluated at the pump inlet.That is, the fluid entering the vapourizer was the liquid working fluid and air dissolved in it.The mole fraction of air in the eventually evaporated, single phase flow at the high pressure side (''HP'') is which for small values approximates as  air,HP ≈ .
The normalized molar flow rate on the high-pressure side can be expressed as The relation shows that the molar flow rate increases as the gas pressure (before the pump)  gas increases, but decreases as the air inleak ( ṅair ∕ ṅWF0 ) increases.Furthermore, the solubility  increases with  gas .For a small , this is a minor effect.

Fuel-air mixtures
Combustion is an exothermic chemical reaction between a fuel and an oxidizer, usually oxygen in air.The relative amounts of fuel and oxygen in a mixture can be denoted by the equivalence ratio, where ṅF and ṅO 2 are the molar flow rates of fuel and oxygen, respectively, and the subscript st denotes stoichiometric conditions (aka.theoretical air).Assuming air as 21% oxygen and 79% nitrogen molar based gives ṅO 2 = ṅair ∕4.762.Furthermore, the gas mixture consisted of fuel and air only, hence This relates the equivalence ratio to the mole fractions of the air-inleak ORC conditions above.The low-pressure conditions give which corresponds to Eq. ( 3).For the high-pressure conditions,

Reaction kinetics
The overall conversion of fuel and oxygen consists of a large number of individual elementary reactions involving numerous intermediate species.This can be described (Turns and Haworth, 2021) as a set of reversible (forward and reverse) reactions, where   is the number of two-way individual reactions,   denotes a chemical species,   is the total number of species and  ′  and  ′′  are the stoichiometric coefficients for the th species in the th reaction.
The molar production rate per unit of volume for a species is expressed as where   is the molar concentration of species  and  f and  r are the forward and reverse rate coefficients of the th reaction.The forward rate coefficients are usually expressed from an Arrhenius model (Turns and Haworth, 2021;Warnatz et al., 2006), where  is the temperature,   is the universal gas constant and the parameters   ,   and   are specified for each elementary reaction.The reverse (backward) rate coefficients can be expressed similarly, but are more often determined from the relation  r =  , ∕ f , where  , ( ) is the equilibrium constant of the th reaction.A set of elementary reactions (Eq.( 10)) with specified parameters   ,   and   is known as a chemical mechanism.

Reactive flow model
The governing equations for a flame are the balances for momentum, continuity (mass), energy and mass of individual species.For a steady state, planar 1-dimensional premixed laminar flame, the latter three can be simplified as Here,  denotes the spatial coordinate in the 1-dimensional system,  is the mass density of the mixture,  the velocity in the  direction,  is the temperature of the mixture,   and  are the specific heat and the thermal conductivity of the mixture,   is the diffusive flux of species  in the  direction, h• f, ( ) is the molar enthalpy of species  at the reference pressure and the temperature  ,   is the mass fraction of species  in the mixture and   is the molar mass.The volumetric molar reaction rate ω was described above, Eq. ( 11).
The momentum equation corresponding to these conditions is simplified to a constant pressure, ∕ = 0.
In addition to the balances above, models for   ,  and   are required, together with the ideal gas equation of state.The mixtureaveraged transport properties were used.Then, the pressure diffusion, Soret (thermo-diffusion) and Dufour effects were neglected.Furthermore, radiation heat transfer was neglected.
The boundary conditions for this configuration are specified values of the inlet ( = 0) temperature and species mass fractions in the unreacted mixture.At the outlet, a zero gradient can be set to all solved variables.Since the momentum equation is not solved, no boundary conditions are required for it, except the value of the constant pressure.The velocity, including inlet and outlet, is calculated from the continuity.
Solving this set of equations, with appropriate parameters for the relevant substances and reactions, will give information about the flame and the mixture.Key quantities are (laminar) flame speed, flame thickness and chemical time scale.

Ignition
Ignition is the onset of combustion in a mixture.A criterion for this was formulated by Williams (1985, p. 268) (see also Turns and Haworth (2021), p.288), which related ignition to the energy required to heat a certain volume of gas to its adiabatic flame temperature.The initial heating can be a spark or a hot surface due to mechanical malfunction (friction).If the heating leads to a sustained flame, the reaction heat release has to, at least, balance the heat loss from the same volume.In the initial process, the heat loss can be neglected if the chemical reactions are faster than the heat transfer.The energy and species mass balances then reduce to transient forms of Eqs. ( 14)-( 15) without spatial gradients.
A simplified approach to ignition analysis is using flammability limits (Drysdale, 2011).In widespread engineering use, these are based on a certain apparatus developed by US Bureau of Mines (Zabetakis, 1965).Another apparatus was described for the ASHRAE and ISO standards (ISO 817:2014(E), 2014).The upper and lower flammability limits are the limiting rich and lean compositions of fuel-air mixtures that can ignite and burn at certain criteria in said apparatus.It should be noted that ignition depends on geometry, heat transfer, temperature and pressure.The apparatus is set up at atmospheric pressure.The range of flammability appears to widen with pressure, such that richer and leaner mixtures become flammable (Drysdale, 2011).Hence, the tabulated limits just give a rough indication of ignitability.

Numerical approach for combustion
The open-source code Cantera (Goodwin et al., 2021) was used for the combustion analysis.It contains a solver for the reactive flow equations, handling of thermo-chemical properties and transport properties, boundary conditions etc.It also comes with exemplary case specifications, among other for planar laminar flames and for ignition.Chemical mechanism, thermal and transport properties can be supplied or changed.
For the ignition analysis, the initial composition was defined by setting a value of the equivalence ratio, which in turn, corresponded to a gas pressure.Furthermore, the initial temperature was set to a certain value.This corresponds to heating the gas by some external influence, e.g. a spark.The simulation was allowed to run for some time to see the development.If the temperature increased notably, ignition was indicated.A lack of temperature increase indicated that ignition did not take place.
For the planar flame, the flow equations were solved from specified initial and inlet temperature and species mass fractions.The grid was determined iteratively by the code.Convergence was regulated by the grid refinement criteria (Goodwin et al., 2021) (ratio = 3, slope = 0.06, curve = 0.12).

Flammability -ignition and propagation
To cause real problems, the fuel-air mixture of the leaking power cycle has to ignite at a location, and the ignited flame has to propagate through the mixture.Since the eventual pressure increase will appear when a significant portion of the mixture has reacted, the emulated onset of combustion was made at constant pressure.In the following, when possible mixtures are identified, the 0-dimensional transient ignition simulation will be conducted.Next, the propagation in space will be analysed using the 1-dimensional premixed-flame model.If a mixture both ignites and propagate, it seems plausible that there is a real possibility of combustion to occur in the cycle.

Case descriptions and assumptions
The present investigations were made for a limited set of exemplary cases.As mentioned above, the condenser temperature (State 1 in Figs. 1 and 2) was assumed as 30 • C, while the turbine inlet temperature (State 3) was set to 150 • C.
The cycles were simulated with pump and expander isentropic efficiencies of 0.80.Pressure losses in vapourizer and condenser (without inleak) was neglected.The heat transfer area and heat-source and coolant temperatures were assumed sufficient for the purpose.
The choice of working fluids for the exemplary computations were made on the following criteria: (1) A detailed chemical mechanism should be available, for the combustion analysis.(2) The saturation pressure at the chosen condenser temperature (30 • C) should be below the ambient pressure of 1 atm (1.013 bar).(3) The saturation pressure at the chosen vapourizer exit temperature (150 • C) should be reasonable, say, in the range 5-15 bar.
The working fluids chosen were n-pentane and benzene.In addition to the criteria mentioned, these two substances had notably different saturation pressures at the relevant temperatures.
The lower and upper flammability limits for n-pentane and benzene in air mixtures are shown in Table 1 as mole fractions (in %) (Drysdale, 2011) and equivalence ratios (Eq.( 7)).It is worth noting that other apparatuses and other conditions (temperature, pressure) specified, will give other values for the flammability limits.
Properties of the simulated base cycles are shown in Table 2.These are without air inleak.

Inleak cycle analysis
Using the own numerical model described in Section 2.5, the saturation pressures at 30 • C were found at 0.8199 bar and 0.1592 bar, respectively, for pure n-pentane and benzene.These values were based on Refprop data (see Section 2.3).
At increasing air inleak, the gas-phase pressure will increase from the saturation pressure.Using the gas-phase pressure as the input parameter, the mole fractions of air on the low-pressure and high-pressure sides were evaluated from the model.It was seen that the mole fractions increased rapidly when inleak was allowed.At the low pressure side (condenser, before the pump), notable values were reached.Indeed, at the high-pressure side (turbine inlet), the mole fractions became rather small.The results are shown in Fig. 3 expressed as the equivalence ratios, which are inversely related to the air mole fractions, Eq. ( 7).
The high-pressure side normalized molar flow rates, ṅHP ∕ ṅWF0 , were evaluated from Eq. ( 5) with the gas phase pressure  gas and the normalized air molar flow rate ṅair ∕ ṅWF0 as input.The results are shown in Fig. 4 as isocontours of ṅHP ∕ ṅWF0 with values denoted by the colour in the scale to the right.It was noted that increasing gas-phase pressure led to an increasing ṅHP ∕ ṅWF0 for fixed values of ṅair ∕ ṅWF0 .The reason was to a minor degree the increased solubility, , however, mainly the increase of the quantity in the right-hand side bracket of Eq. ( 5).
The gas volume fraction,   , evaluated from Eq. ( 2) is shown in Fig. 5.It was seen that this fraction increased with increasing values of ṅair ∕ ṅWF0 .At fixed values of the latter quantity, the gas volume fraction decreased with an increased  gas ∕ WFv .In the discussion of centrifugal pumps, Serena (2016) found limits about 30% or lower, where the pump flow rate came to a halt.If this limit is imposed, while allowing the gas-phase pressure to take any value, the parameter ṅair ∕ ṅWF0 must be limited by a value dependent on the gas-phase pressure.In Fig. 5,   = 0.3 is the second iso-contour from below.When this was regarded as the limit, ṅair ∕ ṅWF0 was restricted to less than 7 ⋅ 10 −4 for n-pentane and to less than 2 ⋅ 10 −3 for benzene.

Mixtures
The equivalence ratios  of Eqs. ( 8)-( 9) are directly related to the air mole fractions of Eqs. ( 3) and (4), cf.Eq. ( 7).The resulting values for the low and high pressure sides for the two working fluids were shown in Fig. 3.Not unexpected, the equivalence ratio was far higher at the high-pressure side, since the air then had to be dissolved in the liquid working fluid before pumping.It was also seen that, at the low pressure side for benzene, the equivalence ratio became less than 10 when the gas pressure approached the ambient pressure.For n-pentane, the value was still above 10 2 at this limit.
Considering the flammability limits (Table 1), it was apparent that the high-pressure side equivalence ratios were far higher.For the lowpressure side mixtures, n-pentane was well above the upper limit.Also for benzene, the mixture equivalence ratio was above the upper limit, however, not very far above.

Ignition
Ignition was simulated by setting the initial temperature to 500 • C and to 1000 • C. The results for 1000 • C are shown in Figs. 6 and 7 for npentane and benzene.For n-pentane, the temperature simply faded off, and no ignition occurred.For benzene, at the lower equivalence ratios, the temperature was seen to increase for a second or two, before fading off.The increase can be explained by oxidation of fuel, which ends as the oxygen is consumed.The temperature decline can be attributed to endo-thermal reactions like decomposition of the hydrocarbons to simpler species.This continues also after the early depletion of oxygen.For an initial temperature of 500 • C, n-pentane gave a lesser decline of temperature, meaning that less fuel decomposed.Benzene gave a tiny increase in temperature (0.001 K), undetectable in practice.2)), iso-contours with values and colours from the scale on the right-hand side, as functions of the gas phase pressure  gas and the normalized air molar flow rate ṅair ∕ ṅWF0 (note logarithmic axis).

Flame structure results
The planar flame was simulated from the model of Section 3.3.The inflow temperature and the pressure were set to the values found in the non-reacting analysis, Table 2. Simulations were conducted for ten values of the equivalence ratio in logarithmically equal steps from 0.10 to 10 4 .The grid and computational domain, and hence the width of the flame, were computed by the code, Cantera.
The temperature profiles through the flame for the different equivalence ratios are shown in Fig. 8.The width of the reaction zone, or flame thickness, is indicated by the axial distance where the increase from the low (unburned) temperature to the high (burned) temperature takes place (cf.Turns and Haworth (2021), pp. 259-60).The flame simulations of n-pentane gave substantial temperature increase for equivalence ratios in the order of magnitude of 0.1 to 10.For richer mixtures (higher equivalence ratios), the temperature increase was low, and the spatial extent of the reaction zone was very wide.On the other hand, the air-inleak model gave pentane-air mixtures (Fig. 3) with equivalence ratios above 10 2 , that is, not flammable conditions.For benzene, on the contrary, high temperatures and short reactionzone widths were seen for mixtures within the results if the inleak model simulations.Fig. 9 shows the temperature and mole fraction profiles for selected species of the benzene flame with equivalence ratio 6.66.This was the lower value found from the inleak model, cf.Fig. 3.The temperature rise to 1200 K was seen to coincide with the virtually complete consumption of oxygen.Benzene was partially converted to CO, hydrogen (mole fraction approximately 0.05, not shown in Fig. 9), acetylene (mole fraction 0.02, not shown) and other light hydrocarbons.
The CRECK mechanism was also tried for n-pentane.The numerical results deviated from those of the TDTVT mechanism.However, the qualitative results were the same: large flame thicknesses and low temperature increases for very rich mixtures.
Results were also obtained for the high-pressure side.For the large values of equivalence ratio (order of 10 3 -10 4 ), modest temperature increases were found (10-30 K for n-pentane, 200 K for benzene) and wide reaction zones (10 2 m).These results are not shown here.

Sub-ambient pressure
Mixing of inleak air into combustible working fluids for ORCs with sub-ambient condenser pressures is investigated.The issue is the possibility for combustion inside the cycle.This problem seems not to have been studied previously.The present work is a first step, with exemplary cases, rather than a comprehensive investigation of the ranges of fluids and temperatures that can be relevant.
The customary practice of restricting the condenser pressure to just above ambient temperature can have a significant impact on the efficiency of ORCs, see e.g.Nami et al. (2018).With a potentially large number of installations, the accumulated defect can be considerable.The practice is argued (e.g.Astolfi (2017, p. 74) and Astolfi et al. (2017, p. 183)) by the difficulties of removing air from the working fluid, including the greenhouse gas potential of the working fluid if released in a deareator.This appears as a plausible argument.On the other hand, the argument apparently does not prohibit widespread use of e.g.iso-butane (R600a) as a working fluid for domestic refrigerators and freezers.With a freezer temperature of −20 • C to −30 • C, these have sub-ambient pressure in the refrigeration-cycle evaporators.The experience acquired for refrigeration cycles might be transferable to power cycles.
Air inleak will change the properties of the working fluid, and the first issue is how much air that can leak in, before the cycle cease working.Halt of the cycle will not bring more air to the high-pressure side, while the leakage into the condenser may continue until the ambient pressure is reached.However, in the latter case, mixing can depend on the geometry of the condenser.

Pump model
Above, it was assumed that the pump only transferred liquid, and hence, only air dissolved in the liquid to the evaporator.This lead to very rich (low-air) mixtures in the evaporator and turbine inlet.At those conditions, the mixtures were clearly not flammable.The assumption was based on notions of the more commonly used pumps in ORCs.This outcome might become different, if any pump used in ORCs appears to be capable of two-phase flow pumping.Here it is worth keeping in mind that two-phase pumping is more complex, more demanding and more expensive, and not needed or desired in an ORC.Indeed, the issue has to be considered when designing ORC with sub-ambient condenser pressure.

Flammability and ignition
For the condenser, cases investigated here showed that some relevant working fluids at certain temperatures can lead to mixtures when air is leaking in.A potential reaction requires ignition energy.Possible sources can be a mechanical malfunction (friction), e.g. of the pump, or unintended external heating.Whether the relevant ranges of pressure and temperature can be reached have to be evaluated for each device.Then, also the geometry of the condenser has to be evaluated with respect to quenching distances, etc.Furthermore, a lower condenser (saturation) pressure due to a lower heat-sink temperature, will allow more air to enter in case of a leakage and make the mixture more prone to combustion.
On the other hand, some fluids can hardly or not at all, lead to flammable mixtures inside the cycle.With a careful evaluation of the cycle and working fluid properties, the possibility of inside combustion can be ruled out.Hence, in such cases, the ambient pressure need not be a limit for the efficiency of the ORC.
It is worth noting that the substance with the potentially flammable air/working fluid mixture, here benzene, had a lower ratio of saturation pressure to ambient pressure, cf.Table 2.This indicated that the potential benefit for operation below ambient pressure is larger than for pentane.Also worth noting is that a flammable mixture is not the only requirement for an accidental fire.Ignition energy is required, and absence of a quenching geometry.
Finally, for sake of order, it is mentioned that the risk of fire due to leakage of a combustible working fluid out of the cycle was not in the scope of this study.This is a possibility for any cycle utilizing such fluids -and for any vehicle or installation intentionally using fuel for combustion.

Concluding remarks
Based on exemplary calculations of ORCs with n-pentane and benzene, the following conclusions are made: The commonly used pumps in ORCs only forward liquid phase.With such a pump, the air mixed into the working fluid at the high-pressure side of a cycle does not reach flammable conditions.
In the condenser, i.e. low pressure side of the cycle, the mixture can reach flammable conditions for substances with a saturation pressure notably lower than the ambient pressure, like benzene.For such a substance, the necessary ignition energy, and the potential sources of this energy, should be carefully considered together with preventive measures such as quenching distances in the specific geometry.
Working fluids with a relatively higher saturation pressure, such as pentane, appear not to reach flammable conditions when air leaks into a condenser with sub-ambient pressure.

Fig. 3 .
Fig. 3. Equivalence ratio  as a function of gas-phase pressure, air-inleak model.Note the logarithmic vertical axis.

Fig. 4 .
Fig. 4. Normalized molar flow rate at the high-pressure side ṅHP ∕ ṅWF0 (Eq.(5)), iso-contours with values and colours from the scale on the right-hand side, as a function of gas-phase pressure (horizontal axis) and for different values of the normalized air flow rate (note the logarithmic vertical axis).

Fig. 5 .
Fig. 5. Gas volume fraction,   (Eq.(2)), iso-contours with values and colours from the scale on the right-hand side, as functions of the gas phase pressure  gas and the normalized air molar flow rate ṅair ∕ ṅWF0 (note logarithmic axis).

Fig. 6 .
Fig. 6.Ignition simulations on the side: Temperature developments for different values of gas pressure and equivalence ratios.Initial temperature set to 1000 • C (1273 K).

Fig. 7 .
Fig. 7. Ignition simulations on the low-pressure side for two benzene cases: Composition developments for different values of gas pressure and equivalence ratios.Initial temperature 1000 • C (1273 K).

Fig. 8 .
Fig. 8. Planar flame simulations for the low-pressure side: Temperature developments for different values of equivalence ratio.

Fig. 9 .
Fig.9.Structure of a flame on the low-pressure side of a benzene-cycle with  = 6.66.

Table 2
Properties of ORC base cycles, simulated with Hysys.