Improvement of Combustion Process of Spark-Ignited Aviation Wankel Engine

energies

Article Improvement of Combustion Process of Spark-Ignited Aviation Wankel Engine

Lev Finkelberg, Alexander Kostuchenkov, Andrei Zelentsov * and Vladimir Minin Central Institute of Aviation Motors n.a. P.I. Baranov, Aviamotornaya St., 2, Moscow 111116, Russia; piston@ciam.ru (L.F.); [email protected] (A.K.); [email protected] (V.M.) * Correspondence: [email protected]

Received: 15 May 2019; Accepted: 13 June 2019; Published: 15 June 2019

Abstract: This paper deals with the creation of modern high-performance aircraft power units based on the Wankel rotary piston engine. One of the main problems of Wankel engines is high specific fuel consumption. This paper solves the problem of improving the efficiency of this type of engine. The mathematical model of non-stationary processes of transfer of momentum, energy, mass, and the concentration of reacting substances in the estimated volume provides for the determination of local gas parameters in the entire computational region, which are presented as a sum of averaged and pulsation components. The k-ζ-f model is used as the turbulence model; the combustion is described by the coherent flame model (CFM) based on the concept of laminar flame propagation. As a result of the calculation, we obtained the values of temperature, pressure, and velocity of the working fluid in the working chamber cross-sections of a rotary–piston engine. Various options of the rotor recess shape are considered. Based on the data obtained, the rotor design was improved. The offered shape of the rotor recess has reduced emissions of both nitrogen oxides and carbon dioxide.

Keywords: Wankel engine; gasoline engine; workﬂow simulation; combustion

1. Introduction Wankel engines (WEs), in comparison with traditional engines with a crank mechanism, have a smaller weight and dimensions. In this regard, they are well suited for use on aircrafts. WE high performance should be provided by improving the efficiency of the processes of intake, exhaust, and the combustion of the fuel–air mixture. These engines are also characterized by a fewer number of parts in comparison with traditional piston engines [1,2]. In addition, due to the rotational motion of the rotor, WEs have an advantage in terms of low vibration [2]. On the other hand, these engines have a high fuel consumption and relatively low engine life. Due to these reasons, it is necessary to increase the WE operation efficiency and improve the engine’s life. This study is aimed at solving the first problem; we only mention that a possible solution of the second problem is the use of perspective materials for the manufacture of seals and the hardening of the stator surface. The simulation of gas and thermodynamic processes in the WE working chamber is hampered by its geometrical features. The work of the Wankel engine with external air–fuel mixing (fuel injection at the inlet) and ignition from an electric spark are considered. The change in working volumes is provided by the rotation of trochoidal triangular rotor in almost elliptical (epitrochoidal) stator housing (Figure1)[ 3]. The geometry of these parts forming the combustion chamber in the WE is described by a known relationship [4,5]. The combustion chamber geometry strongly affects the characteristics of the working fluid flow, and, as a result, the efficiency of the fuel combustion process [6]. In this work, we conducted numerical studies of the processes of air–fuel mixing and combustion in the WE working chamber with various combustion chambers (CC) in the rotor. The shapes of the rotor recesses were chosen in such a

Energies 2019, 12, 2292; doi:10.3390/en12122292 www.mdpi.com/journal/energies EnergiesEnergies 20192019, 12, 12, x, 2292 2 of2 of11 11 with various combustion chambers (CC) in the rotor. The shapes of the rotor recesses were chosen in suchway a asway to accelerateas to accelerate the propagation the propagation of the of flame the flame front throughfront through the working the working chamber. chamber. Based Based on the onresearch the research findings, findings, a conclusion a conclu onsion the on degree the degree of influence of influence of the shapeof the ofshape the combustion of the combustion chamber chamberon the performance on the performance of the rotary of the piston rotary engine piston is given. engine In is addition, given. In the addition, rotor design the modificationrotor design is modificationcarried out. is carried out. TheThe object object of the of thestudy study was wasa single-section a single-section Wankel Wankel engine engine with an with intake an port intake injection port (Figure injection 1a,b).(Figure 1a,b). TheThe engine engine is is equippedequipped withwith a a fail-operative fail-operative ignition ignition system, system, which which is caused is caused both byboth the specificsby the specificsof the fuel of combustionthe fuel combustion process and process by increasing and by increasing the reliability the ofreliability its operation. of its Theoperation. target indicators The target for the developed WE are as follows: Effective power, N = 70–100 hp; minimum specific fuel consumption indicators for the developed WE are as follows: Effectivee power, Ne = 70–100 hp; minimum specific ge, up to 210 g/(hp h); engine specific weight, 0.42–0.45. The studies were conducted at the nominal fuel consumption ge,· up to 210 g/(hp·h); engine specific weight, 0.42–0.45. The studies were conducted atmode the nominal of operation, mode withof operation, the rotational with the speed rotati ofonal the eccentric speed of shaftthe eccentric n = 6500 shaft rpm. n = 6500 rpm.

(a) (b)

FigureFigure 1. 1.3D3D model model of ofdeveloped developed Wankel Wankel engine: engine: (a) ( aReady-assembled;) Ready-assembled; (b ()b rotor-stator) rotor-stator assembly. assembly.

2.2. Mathematical Mathematical Model Model It Itis is worth worth noting noting that that the the one-dimensional one-dimensional appr approach,oach, which which is isoften often used used to to estimate estimate effective effective indicatorsindicators of of the the WE WE and and which which implies implies a achange change in in the the operating operating parameters parameters of of the the engine engine in in one one or or severalseveral zones zones of of the the working working chamber, chamber, does notnot allowallow forfor aa properproper consideration consideration of of the the geometry geometry of of the theWE WE working working chamber. chamber. There There is is also also no no opportunity opportunity to to optimize optimize the the position position and and ignition ignition points points for forspark spark plugs plugs and and to to evaluate evaluate the the effi efficiencyciency of of filling. filling. These These features features are are correctly correctly described described using using the thethree-dimensional three-dimensional approach approach [7 ,[7,8].8]. TheThe mathematical mathematical model ofof thethe working working process proce ofss traditionalof traditional piston piston engines engines and Wankel and Wankel engines enginesis based is on based the fundamental on the fundamental equations equations of three-dimensional of three-dimensional nonstationary nonstationary transport with transport allowance with for allowancethe combustion for the chemistry: combustion The chemistry: equations ofThe momentum equations (Navier–Stokes), of momentum energy(Navier–Stokes), (Fourier–Kirchho energyff ), (Fourier–Kirchhoff),diffusion (Fick), and diffusion the conservation (Fick), and of the mass conservation (continuity), of which mass take(continuity), the form which of Reynolds take the after form the ofaveraging Reynolds procedureafter the averaging by the Favre proc methodedure by [7 ,the9,10 Favre]: method [7,9,10]: " ! # 𝐷𝑊 𝜕𝑝̅ 𝜕 𝜕𝑊 𝜕𝑊∂W 2 𝜕𝑊 ρ DW=𝐺i − ∂p+ ∂ μ ∂Wi + j − 2 δ ∂Wk −ρ𝑊𝑊, ρ Dτ = Gi + µ + 3 δij ρW0iW 0 j , | 𝐷𝜏 −𝜕𝑥∂xi 𝜕𝑥∂xj 𝜕𝑥∂xj 𝜕𝑥∂xi − 3 ∂𝜕𝑥xk − ∂qR ρ DH = + ∂p + ∂ τ + ∂ λ ∂T ρ + + 𝜕𝑞j 𝐷𝐻Dτ GjWj 𝜕𝑝 τ 𝜕 ijWj 𝜕 𝜕𝑇 cp T0W0 wrQr , ρ =𝐺𝑊 + ∂+ ∂xτi 𝑊 + ∂xjλ ∂xj −−𝑐 ρ𝑇𝑊j +𝑤 𝑄 +∂xj , (1)(1) . 𝐷τ 𝜕τ 𝜕𝑥DC ∂ ∂C𝜕𝑥 𝜕𝑥 𝜕𝑥 = D ρC0W0 j + m, Dτ ∂xj ∂xj − 𝐷𝐶̅ ∂𝜕ρ ∂𝜕𝐶 ̅ + ρW j =0, = ∂τ 𝐷∂xj −ρ𝐶′𝑊′+𝑚 , 𝐷τ 𝜕𝑥 𝜕𝑥

Energies 2019, 12, 2292 3 of 11

2 where W is the velocity; m/s; p is the pressure, N/m ; Gi is the projection of the density vector of 3 the volume forces (N/m ) onto the Oxi axis of a rectangular Cartesian coordinate system; C is the 3 concentration, kg/m ; H is the total specific energy, J/kg; µ is the dynamic viscosity, kg/(m s); cp is the heat capacity at constant pressure, J/(kg K); wr is the rate of a chemical reaction per unit volume, kg/(s 3 · m ); Qr is the amount of heat released per unit mass, J/kg; λ is the thermal conductivity, W/(m K); δij is . the Kronecker symbol; D is the diffusion coefficient, m2/s; m is the intensity of the mass source (the 3 D rate of change in the mass of the chemical component per unit volume, kg/cm ); Dτ is the substantial ∂qR derivative; and j is the radiation heat flux from the radiation source. When gasoline fuel is used in ∂xj engines with an external mixture formation, the combustion process is homogeneous, there is almost no formation of soot particles, and the combustion generators are carbon dioxide and water vapor with negligible selective radiation [11,12]. In Equation (1), the Einstein summation rule is used for the twice repeated i, j, and k indices. The system of transport equations in the Reynolds form (1) is closed by the k-ζ-f model of turbulence specially developed and verified for the processes of flow, combustion, and heat transfer in piston engines [13–15]. It consists of three equations: For the k kinetic energy of turbulence, for the ε dissipation rate of this energy known from the k-ε model of turbulence, and the equations for 2 the normalized velocity scale ζ = W /k. The k-ζ-f turbulence model proposed by Hanjaliˇcet al. [14] contains the Durbin elliptical function of f, which takes into account the near-wall anisotropy of turbulence. The sensitivity to the cell type and degree of mesh grinding, which are characteristics of the Durbin turbulence model, decreases in the k-ζ-f model, and the stability of the numerical solution improves, which is especially important for the calculation of the turbulent transport in the combustion chamber of a piston engine. Unlike standard functions, the new hybrid interpretation of the wall flow developed by Popovaˇcand Hanjaliˇc[16] connects the viscous and logarithmic layers with a universal dimensionless relationship and allows for integration up to the wall surface with the well-known wall functions. The k-ζ-f model is currently used in the 3D-CFD-code AVL FIRE as the main model in the modeling of turbulent flow and turbulent heat transfer in the boundary layers of piston engines. The model is particularly reliable in the calculation of processes with moving parts (piston, inlet, and exhaust valves) and the flow of highly compressed gas that occurs in reciprocating engines. The k-ζ-f model, in conjunction with this hybrid interpretation of the near-wall flow, provides the optimal (from the point of view of reliability, accuracy, and counting time) solution for the entire coordinate grid [9]. To describe the process of combustion of the air–fuel mixture, the coherent flame model (CFM) is used [7]. This model is based on the concept of laminar flame propagation, according to which the velocity wl is averaged over the entire flame front, and the front thickness δl depends only on the pressure, temperature, and composition of the fresh charge. It is believed that, in this case, the reaction begins in relatively thin layers that separate the fresh unburned gas from the combustion products. An additional differential equation of the flame front density transfer is introduced in the model, written with respect to Σ—the flame front area per volume unit. This equation has the form [17,18]: ! ∂Σ ∂ ∂ νt ∂Σ + W jΣ = + SΣ, (2) ∂τ ∂xj ∂xj PrtD ∂xj where νt is eddy viscosity, PrtD is the turbulent diffusion Prandtl number (Schmidt number), and SΣ is the source term equal to the difference in the generation (Sg) of the surface area of the flame front as a result of deformation due to the turbulent combustion and annihilation (Sa) of the flame front surface as a result of the consumption of reagents.

Sg = α Kt Σ, (3) · · ρ w T p l 2 Sa = β · Σ , (4) · ρT · Energies 2019, 12, x 4 of 11

𝜌т ∙𝑤 Energies 2019, 12, 2292 𝑆 =𝛽∙ ∙𝛴 , 4 of(4) 11 𝜌т

where α, β are the calibration constants, Kt is the mean stretch rate of the flame, 𝜌т is the fuel partial where α, β are the calibration constants, Kt is the mean stretch rate of the flame, ρT p is the fuel partial density, and wl is the laminar flame speed, depending on the local pressure p, temperature T of inlet density, and wl is the laminar flame speed, depending on the local pressure p, temperature T of inlet gas, and the local excess air factor λair. gas, and the local excess air factor λair. ε K = 𝜀C̅ , (5) t𝐾 = t∙𝐶, (5) k ·𝑘 u lt where Ct = f 0 , is a function which accounts for the size of turbulence scales, viscous effects, and wl δl where 𝐶 =𝑓 , is a function which accounts for the size of turbulence scales, viscous effects, transient effects [19 ]. and Thetransient initial effects flame kernel[19]. radius is equal to 3 mm (which corresponds to the interelectrode distance for theThe spark initial plug flame used), kernel and theradius value is equal of calibration to 3 mm constant(which correspondsα = 0.75. An to increase the interelectrode of the stretch distance factor leadsfor the to spark an intensification plug used), ofand the the production value of ofcalibration the flame constant surface densityα = 0.75. and, An hence, increase in aof shorter the stretch and fasterfactor combustion leads to an intensification phase. Consumption of the production factor β = of1. the The flame initial surface flame surfacedensity densityand, hence, is equal in a shorter to 500 1and/m for faster the decreasingcombustion of phase. the ignition Consumption delay. factor β = 1. The initial flame surface density is equal to 500 1/mThe for values the decreasing of the model of constantsthe ignition were delay. specified based on the correspondence of the indicator diagramsThe fromvalues the of 3Dthe calculation model constants to the previouslywere specified obtained based pressures on the correspondence from the 1D calculation. of the indicator Then, thediagrams average from reaction the 3D rate calculation of fuel combustion to the previously is defined obtained as pressures from the 1D calculation. Then, the average reaction rate of fuel combustion is defined as wr = ρTpwlΣ, (6) 𝑤 =−𝜌− 𝑤𝛴, (6) TheThe samplingsampling ofof thethe computationalcomputational domaindomain (mesh(mesh construction)construction) inin thethe casecase ofof aa rotaryrotary pistonpiston engineengine is is didifficultfficult due due to to the the needneed toto conductconduct calculationscalculations in in anan isolatedisolated segment,segment, thethe volumevolume of of whichwhich variesvaries accordingaccording toto aa complexcomplex lawlaw determineddetermined byby thethe shapeshape ofof thethe rotorrotor andand thethe innerinner surfacesurface ofof thethe stator.stator. InIn thethe coursecourse ofof thethe calculation,calculation, thethe movablemovable meshmesh segmentsegment performsperforms aa complexcomplex rotationalrotational motion;motion; atat thethe samesame time,time, atat thethe momentsmoments ofof thethe freshfresh chargecharge intakeintake andand thethe releaserelease ofof exhaustexhaust gases,gases, interactioninteraction occurs occurs with with the the fixed fixed segments segments (intake (intake and and exhaust exhaust ports; ports; Figure Figure2 ).2).

(a) (b)

FigureFigure 2.2. CombustionCombustion chamberchamber ofof thethe WankelWankel engineengine (a(a)) and and control control volume volume mesh mesh ( b(b).).

TheThe meshmesh construction feature feature is is the the invariance invariance of ofthe the total total number number of cells of cells in the in process the process of rotor of rotormovement movement (77,000 (77,000 control control volumes volumes for forpreliminary preliminary calculations calculations and and 410,000 410,000 for for specified speciﬁed ones);ones); herewith,herewith, the the mesh mesh is is rebuiltrebuilt (its (its deformationdeformation for for the theinternal internal volume volume of of thethe workingworking chamber)chamber) at at eacheach consideredconsidered angleangle ofof rotationrotation ofof thethe eccentric eccentric shaft.shaft. TheThe volumesvolumes ofof thethe intakeintake andand exhaustexhaust ports,ports, asas wellwell as as the the recess recess in in the the rotor, rotor, are are not not repartitioned. repartitioned.

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3. Results and Discussion 3. Results and Discussion The dependence of pressure and temperature—as well as heat generation rates and the amount The dependence of pressure and temperature—as well as heat generation rates and the amount of heat given to parts of the WE combustion chamber—on the angle of rotation of the eccentric shaft of heat given to parts of the WE combustion chamber—on the angle of rotation of the eccentric shaft (obtained as a result of a three-dimensional calculation of the WE workflow) allowed us to estimate (obtained as a result of a three-dimensional calculation of the WE workﬂow) allowed us to estimate its its effective performance and predict the level of thermal load on the main parts of the engine. eﬀective performance and predict the level of thermal load on the main parts of the engine.

3.1.3.1. Validation ForFor aa preliminarypreliminary assessmentassessment ofof thethe correctnesscorrectness ofof thethe three-dimensionalthree-dimensional calculationcalculation results,results, aa 1D-model—the1D-model—the schemescheme ofof whichwhich isis givengiven inin FigureFigure3 —was3—was used. used. DuringDuring verification,verification, a comparisoncomparison of indicatorindicator diagramsdiagrams waswas conductedconducted (Figure4 4),), andand thisthis showedshowed aa satisfactorysatisfactory reconciliationreconciliation of thethe calculatedcalculated data (in thisthis case,case, thethe errorerror inin thethe maximummaximum pressure pz did not exceed 0.5%, and the angle of its achievement was less than 1%). pressure pz did not exceed 0.5%, and the angle of its achievement was less than 1%). TheThe discrepancydiscrepancy betweenbetween thethe indicatorindicator diagramsdiagrams at the momentmoment ofof thethe startstart ofof heatheat generationgeneration whenwhen thethe spark spark plugs plugs are are triggered triggered is explained is explained by the dibyff erencethe difference in the configuration in the configuration of the combustion of the chambercombustion of thechamber Wankel of the engine Wankel from engine the traditional from the traditional piston-type piston-type one with sparkone with ignition: spark Theignition: WE combustionThe WE combustion chamber ischamber characterized is characterized by relatively by relatively large longitudinal large longitudinal dimensions dimensions with small with transverse small dimensions,transverse dimensions, which slows which the spread slows of the the spread flame of front. the flame In addition, front. itIn is addition, necessary it tois takenecessary into account to take theinto presence account ofthe two presence spark plugs,of two whichspark plugs, is diffi cultwhich in ais1D-model. difficult in a 1D-model. InIn thethe future,future, itit isis alsoalso plannedplanned toto useuse experimentalexperimental datadata asas aa criterioncriterion forfor thethe adequacyadequacy ofof thethe three-dimensionalthree-dimensional model.model. BasedBased onon aa comparisoncomparison ofof thethe availableavailable resultsresults ofof 1D1D andand 3D3D calculations,calculations, itit cancan bebe concludedconcluded thatthat thethe 3D CFD model of the workflow workflow process process of the the perspective perspective aviation aviation Wankel Wankel engine adequately describesdescribes thethe real real thermophysical thermophysical processes processes in thein th estimatede estimated volume volume and canand be ca usedn be for used further for further engine research.engine research. As a strand As ofa research,strand of the research, determination the de oftermination the influence of ofthe the influence WE design of parameters the WE design (such asparameters the shape (such of the as combustion the shape of chamber the combustion (recess) in chamber the rotor (recess) and the in arrangement the rotor and of the spark arrangement plugs) on theof spark engine plugs) performance on the engine can be performance chosen. It is alsocan possiblebe chosen. to useIt is the also developed possible to model use the to analyze developed the influencemodel to analyze of various the moments influence of of spark various plugs mome operationnts of spark on the plugs workflow. operation on the workflow.

Figure 3. Design model for the single-section Wankel engine (WE): 1: Unit that sets operating parameters Figure 3. Design model for the single-section Wankel engine (WE): 1: Unit that sets operating of the engine; 2: Block simulating the WE section; 3 and 4: Boundary conditions deﬁnition; 5 and 6: parameters of the engine; 2: Block simulating the WE section; 3 and 4: Boundary conditions definition; Restrictions; 7 and 8: Measuring points; 9: Injector; 10: Throttle; 11: Intake pipes; 12: Exhaust pipes. 5 and 6: Restrictions; 7 and 8: Measuring points; 9: Injector; 10: Throttle; 11: Intake pipes; 12: Exhaust pipes.

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FigureFigure 4. 4. ModelModel verification—comparison verification—comparison ofof thethe indicatorindicator diagrams diagrams of of the the Wankel Wankel engine engine in in case case of 1Dof Figure 4. Model verification—comparison of the indicator diagrams of the Wankel engine in case of 1Dand and 3D 3D calculations. calculations. 1D and 3D calculations. 3.2.3.2. Results Results of of Numerical Numerical Experiments Experiments 3.2. Results of Numerical Experiments AsAs the the boundary conditions forfor three-dimensionalthree-dimensional calculation, calculation, the the pressures pressures and and temperatures temperatures of ofgas gas atAs at the the the engine boundary engine inlet inlet andconditions and outlet, outlet, previouslyfor previouslythree-dimensional calculated calculated according calculation, according to thethe to 1Dpressuresthe model 1D model (Figureand (Figuretemperatures5a,b), 5a,b), were wereofassigned. gas assigned. at the Wall engine Wall temperatures temperaturesinlet and for outlet, the for inlet previouslythe and inlet outlet and calculated outlet ports, ports, as wellaccording as as well the to rotor,as the stator,rotor,1D model sidestator, covers(Figure side (heads)covers 5a,b), (heads)were assigned. set were as follows: set Wall as follows: temperaturesTwrotor =Tw553rotor K,= for 553Tw the statorK, inlet Tw(dependingstator and (depending outlet on ports, the on angleas the well angle of as eccentric the of eccentricrotor, shaft stator, shaft rotation) side rotation) covers from from(heads)393 K 393 (inlet) were K to(inlet)set 530 as follows: Kto (combustion 530 KTw (comrotor = zone bustion553 K, and Tw zone exhaust),stator (dependingand andexhaust),Tw onheads theand= angle393 Tw Kheads of (inlet)–470 eccentric= 393 K Kshaft(inlet)–470 (combustion rotation) K (combustionfromzone and393 exhaust).K zone(inlet) and to exhaust).530 K (com bustion zone and exhaust), and Twheads = 393 K (inlet)–470 K (combustionInIn the the WE WE zone section, section, and exhaust). the the inlet inlet and and exhaust ports initial conditions (pressure p 0,, temperature temperature T T00)) werewere Inalso also the set set WE according according section, to tothe the the inlet results and of exhaust 1D calculation. ports initial The The conditions initial initial value value (pressure of of turbulent turbulent p0, temperature kinetic kinetic energy energy T0) 2 2 2 2 kwerek00 == 5 5malso m/s/ sset, and, andaccording turbulence turbulence to thelength length results scale scale of TLS 1DTLS 0calculation. =0 0.001= 0.001 m m The initial value of turbulent kinetic energy k0 = 5AsAs m 2a a/s result result2, and ofturbulence of the the calculation, calculation, length thescale the values values TLS0 of= of 0.001 te temperature,mperature, m pressure, pressure, and and velocities velocities of of the the working working fluidfluid As in theathe result cross-sectionscross-sections of the calculation, of of the the WE WEthe working valuesworking chamberof techmperature,amber were were obtained pressure, obtained both and forboth velocities the for processes the of processesthe of working exhaust, of exhaust,fluidscavenging, in thescavenging, cross-sections filling of filling theworking ofof thethe WEworking chamber working chambe (Figure chamberr6 (Figurea–c), were and 6a–c), combustionobtained and combustion both of thefor fuel-airthe of processes the mixturefuel-air of mixtureexhaust,(Figure7 (Figure a–d).scavenging, 7a–d). filling of the working chamber (Figure 6a–c), and combustion of the fuel-air mixture (Figure 7a–d).

(a) (b) (a) (b) FigureFigure 5. 5. BoundaryBoundary conditions conditions for for the the subsequent subsequent 3D 3D calculation calculation of of the the working working process: process: (a (a) )Pressure; Pressure; (Figure(bb)) gas gas temperatures5. temperatures Boundary conditions in in measuring measuring for thepoints points. subsequent. 3D calculation of the working process: (a) Pressure; (b) gas temperatures in measuring points.

EnergiesEnergiesEnergies 20192019 2019,, 12,12 12,, x, 2292 x 7 77of of 11 1111

(a(a) ) (b(b) ) (c(c) )

FigureFigureFigure 6. 6.6. Calculation CalculationCalculation results resultsresults for forfor exhaust exhaustexhaust ( (a(aa),),), scavenging scavengingscavenging of ofof the thethe combustion combustioncombustion chamber chamberchamber ( (b(bb),),), and andand intake intakeintake ((c(c)c) )processes processesprocesses in in in Wankel Wankel Wankel engine engine. engine. .

ItItIt isisis worth worthworth noting notingnoting that thatthat in traditional inin traditionaltraditional piston pistonpiston engines, engines,engines, an increase anan increaseincrease in the effi inciencyin thethe ofefficiencyefficiency the combustion ofof thethe combustionofcombustion the air–fuel of of the mixture, the air–fuel air–fuel as wellmixture, mixture, as a reductionas as well well as as ina a reduction emissionsreduction in in of emissions emissions harmfulsubstances, of of harmful harmful cansubstances, substances, be achieved can can be bybe achievedprofilingachieved by the by profiling intakeprofiling ports the the intake and intake the ports ports combustion and and the the chambercomb combustionustion [20 –chamber 22chamber]. In a [20–22]. Wankel[20–22]. engine,In In a a Wankel Wankel the e ffengine, engine,ect of flowthe the effectswirleffect atof of theflow flow inlet swirl swirl is less at at the noticeablethe inlet inlet is is dueless less to noticeable noticeable the characteristic due due to to the shapethe characteristic characteristic of the combustion shape shape chamber,of of the the combustion combustion which, by chamber,thechamber, time thewhich, which, rotor by by reaches the the time time the the TDCthe rotor rotor (top reaches reaches dead center, th thee TDC TDC the (top point(top dead dead of the center, center, minimum the the point point combustion of of the the minimum minimum chamber combustionvolume),combustion is stronglychamber chamber deformed volume), volume), inis is thestrongly strongly radial deformed direction.deformed Asin in the athe result, radial radial at direction. thisdirection. time, Asthe As a shapea result, result, of at theat this this recess time, time, in thethethe shape rotorshape hasof of the the a major recess recess impact in in the the rotor onrotor the has has rotational a a major major impact flowsimpact in on on the the the CC rotational rotational instead offlows flows the inshape in the the CC ofCC theinstead instead intake of of andthe the shapeexhaustshape of of ports.the the intake intake and and exhaust exhaust ports. ports. ItItIt is isis noticeable noticeablenoticeable that thatthat when whenwhen the thethe spark sparkspark plugs plugsplugs are areare simultaneously simultaneouslysimultaneously actuated actuatedactuated (the (the(the spark sparkspark angle angleangle is isis 1046° 10461046°◦ ESA,ESA,ESA, i.e., i.e.,i.e., 34° 3434°◦ ESA ESA to to TDC), TDC), TDC), there there there is is isa a asignificant significant significant i rregularityirregularity irregularity of of offlame flame flame propagation propagation propagation in in the in the the direction direction direction of of rotorofrotor rotor movementmovement movement (in(in (in FigureFigure Figure 6,6,6 the,the the rotorrotor moves moves coun counterclockwise).counterclockwise).terclockwise). This This fact factfact indicates indicatesindicates the thethe needneed to toto introduceintroduceintroduce different di differentfferent spark spark angles angles for for the the two two two plugs,plugs, plugs, withwith with aa a later laterlater ignition ignitionignition of ofof the thethe trailing trailingtrailing one oneone (the (the(the interval intervalinterval betweenbetweenbetween spark sparkspark plug plugplug actuation actuationactuation is isis 15° 1515°◦ ESA). ESA).ESA). AnAnAn alternativealternative way wayway of ofof influencing influencinginfluencing the the naturethe naturenature of the ofof flame thethe flame frontflame propagation frontfront propagationpropagation over the overover WE workingthethe WEWE workingchamberworking chamber chamber is to modify is is to to modify themodify shape the the ofsh shape theape of chamberof the the chamber chamber (recess) (recess) (recess) in the in in rotor.the the rotor. rotor. According According According to theto to the the results results results of ofnumericalof numerical numerical simulation, simulation, simulation, a modification a a modifica modificationtion of theof of the rotorthe rotor rotor design design design was was owasffered, offe offe withred,red, with awith recess a a recess recess of variable of of variable variable depth depthexpandingdepth expanding expanding in the in directionin the the direction direction of the of rotor of the the movementrotor rotor movement movement (Figure (Figure 8(Figureb). 8b). 8b).

(a(a) ) (b(b) )

(c(c) ) (d(d) )

FigureFigureFigure 7 7.7. .Temperature—( Temperature—(Temperature—(aaa)) )and andand ( (b(bb)—and)—and)—and velocity velocityvelocity values—( values—(values—(cc)c) )and andand ( (d(dd)—in)—in)—in cross-section cross-sectioncross-section of ofof the thethe base basebase

WEWEWE combustion combustioncombustion chamber. chamber.chamber. ( (a(aa)) )and andand ( (c(c):c):): Rotor RotorRotor position positionposition in inin top toptop dead deaddead center centercenter ( (φ(ϕφ == = 1080° 10801080°◦ ESA); ESA); ( b (b) ))and andand ( (d(dd):):): MaximumMaximumMaximum pressure pressurepressure angle angleangle position positionposition of of rotor rotor ( φϕ(φ == = 1105° 11051105°◦ ESA) ESA).ESA). .

Energies 2019, 12, x 8 of 11

EnergiesUnlike2019, 12the, 2292 basic shape of the recess (Figure 8a), the offered modification provides for better8 of 11 access of the combustion products to the peripheral regions of the CC, which allows for a more uniformEnergies distribution 2019, 12, x of local temperature fields in the volume of the combustion chamber8 of 11 of the Unlike the basic shape of the recess (Figure8a), the o ffered modification provides for better access Wankel engine, increasing its efficiency while reducing maximum temperature values (Figure 9). As of the combustionUnlike the basic products shape toof thethe peripheralrecess (Figure regions 8a), the of offered the CC, modification which allows provides for afor more better uniform a result, there is an increase in the maximum pressure values in the WE working chamber (Figure distributionaccess of ofthe local combustion temperature products fields to inthe the peripheral volume ofregions the combustion of the CC, chamberwhich allows of the for Wankel a more engine, 10), and its power indices increase. It is noticeable that the modified combustion chamber provides a increasinguniform itsdistribution efficiency of while local reducingtemperature maximum fields in temperaturethe volume of values the combustion (Figure9). chamber As a result, of the there is smoother increase in the heat release rate at the initial stage (until the TDC = 1080° ESA) at a slightly an increaseWankel engine, in the increasing maximum its pressure efficiency values while re inducing the WE maximum working temperature chamber (Figurevalues (Figure 10), and 9). itsAs power highera result, maximum there isvalue an increase at a subsequent in the maximum stage (99 pressure J/deg valuesfor the in modified the WE workingchamber chamber and 86 J/deg(Figure for the indices increase. It is noticeable that the modified combustion chamber provides a smoother increase in base10), form; and Figure its power 11). indices increase. It is noticeable that the modified combustion chamber provides a the heat release rate at the initial stage (until the TDC = 1080◦ ESA) at a slightly higher maximum value smootherLower maximum increase in gas the temperaturesheat release rate (T atmax the = 2821initial K stage for modified (until the TDCCC and = 1080° 2967 ESA) K for at abase slightly CC) lead at a subsequent stage (99 J/deg for the modified chamber and 86 J/deg for the base form; Figure 11). to a 42%higher improvement maximum value in theat a engine’ssubsequent envi stageronmental (99 J/deg indexesfor the modified of nitrogen chamber oxide and (NO 86 J/degx) emissions for the and Lower maximum gas temperatures (Tmax = 2821 K for modified CC and 2967 K for base CC) an increasebase form; in Figureits efficiency 11). in regard to the reduction of carbon dioxide (CO2) emissions (by 5%) lead to aLower 42% improvementmaximum gas temperatures in the engine’s (Tmax environmental = 2821 K for modified indexes CC of and nitrogen 2967 K oxidefor base (NO CC)x) lead emissions (Figure 12 a,b). It should be noted that today there are no restrictions on NOx and CO2 emissions for andto an a 42% increase improvement in its effi inciency the engine’s in regard envi toronmental the reduction indexes of of carbon nitrogen dioxide oxide (NO (COx) emissions) emissions and (by 5%) aircraft piston engines, which is primarily due to the relatively small number of2 aircraft equipped (Figurean increase 12a,b). in It its should efficiency be noted in regard that to today the reduction there are of no carbon restrictions dioxide on (CO NO2) emissionsand CO (byemissions 5%) for with such power units [23,24]. However, since the tendency to strengthenx environmental2 aircraft(Figure piston 12 a,b). engines, It should which be noted is primarily that today due there to the are relatively no restrictions small on number NOx and of CO aircraft2 emissions equipped for with requirements leads to the possibility of such restrictions in the future, they should be taken into suchaircraft power piston units engines, [23,24]. which However, is primarily since the due tendency to the relatively to strengthen small environmentalnumber of aircraft requirements equipped leads accountwith when such designingpower units new [23,24]. engine However,units. From sinc theis thepoint tendency of view, to the strengthen offered combustion environmental chamber to the possibility of such restrictions in the future, they should be taken into account when designing looksrequirements promising, leadssince toit allowsthe possibility for the ofreduction such restrictions of both NOin thex and future, CO 2they emissions. should be taken into newaccount engine when units. designing From this new point engine of units. view, From the o thfferedis point combustion of view, the chamber offered combustion looks promising, chamber since it allowslooks for promising, the reduction since it of allows both NOfor thex and reduction CO2 emissions. of both NOx and CO2 emissions.

(a()a ) (b) (b)

FigureFigureFigure 8. 8. WE WEWE rotorrotor rotor variants: variants: ( a()a (Base;)a )Base; Base; (b )( bmodified (b) )modified modiﬁed.. .

(a) (b) (a) (b)

Figure 9. Temperature—(a) and (b)—and velocity values—(c) and (d)—in a cross-section of a modiﬁed

WE combustion chamber. (a) and (c): Rotor position in top dead center (ϕ = 1080 ◦ESA); (b) and (d): ϕ Maximum pressure angle position of rotor ( = 1105 ◦ESA). Energies 2019, 12, x 9 of 11 EnergiesEnergies 2019 2019, 12, 12, x, x 9 9of of 11 11

Figure 9. Temperature—(a) and (b)—and velocity values—(c) and (d)—in a cross-section of a FigureFigure 9. 9. Temperature—( Temperature—(a)a )and and ( b()—andb)—and velocity velocity values—( values—(c)c )and and ( d()—ind)—in a across-section cross-section of of a a modified WE combustion chamber. (a) and (c): Rotor position in top dead center (φ = 1080 °ESA); (b) Energiesmodifiedmodified2019, 12 WE, 2292WE combustion combustion chamber. chamber. (a ()a and) and (c ():c ):Rotor Rotor position position in in top top dead dead center center (φ (φ = =1080 1080 °ESA); °ESA); (b ()b 9) of 11 and (d): Maximum pressure angle position of rotor (φ = 1105 °ESA). andand (d ():d ):Maximum Maximum pressure pressure angle angle position position of of rotor rotor (φ (φ = =1105 1105 °ESA) °ESA). .

(a) (b) (a()a ) (b()b ) Figure 10. Indicator diagram of a WE with a base (a) and modified (b) combustion chamber. FigureFigureFigure 10. 10.10. Indicator IndicatorIndicator diagram diagramdiagram of ofof a aaWE WEWE with withwith a aabase basebase (a ((a)a )and) andand modified modiﬁedmodified (b ((b)b )combustion) combustioncombustion chamber chamber.chamber. .

Figure 11. Rate of heat release in base and modiﬁed combustion chambers of a WE. Figure 11. Rate of heat release in base and modified combustion chambers of a WE. FigureFigure 11. 11. Rate Rate of of heat heat release release in in base base and and mo modifieddified combustion combustion chambers chambers of of a aWE. WE.

(a) (b) (a()a ) (b()b )

Figure 12. NOx (a) and CO2 (b) mass fractions in base and modified WE combustion chambers. FigureFigureFigure 12 12. 12. NO.NO NOx x(xa (()aa )and) andand CO COCO2 2(2b ()b mass) mass fractions fractionsfractions in inin base basebase and andand modified modifiedmodified WE WEWE combustion combustioncombustion chambers chambers.chambers. . For a further improvement of the rotor chamber design, it is also planned to reduce the angle of ForForFor a a afurther furtherfurther improvement improvement of of the the rotor rotor rotor chamber chamber chamber desi desi design,gn,gn, it itis it is also is also also planned planned planned to to reduce to reduce reduce the the theangle angle angle of of the inclination of the recess walls relative to the working surface of the rotor in order to minimize theofthe theinclination inclination inclination of of the of thethe recess recess recess walls walls walls relative relative relative to to tothe the the working working working surface surface surface of of ofthe the rotor rotor in in order orderorder to toto minimize minimizeminimize separated flows. separatedseparatedseparated flows. flows.flows. 4. Conclusions 4.4.4. Conclusions ConclusionsConclusions 1. A mathematical model of the Wankel engine has been developed, one which allows three- 1.1.1. AA mathematical mathematical mathematical model model model of of ofthe the theWankel Wankel Wankel engine engine engine has has been hasbeen beendeveloped, developed, developed, one one which which one whichallows allows three- allows three- dimensional determining of the parameters of the working fluid in the entire calculated volume, dimensionalthree-dimensionaldimensional determining determining determining of of the the parameters parameters of the parameters of of the the working working of the workingfluid fluid in in the fluidthe entire entire in the calculated calculated entire calculated volume, volume, taking into account inlet and exhaust processes. This model also takes into account the geometric takingvolume,taking into into taking account account into inlet inlet account and and exhaust inletexhaust and processes. processes. exhaust processes.This This model model This also also modeltakes takes into alsointo account takesaccount into the the accountgeometric geometric the geometric features of the WE combustion chamber and allows for the determination of the best

design in terms of improving the engine eﬃciency. Energies 2019, 12, 2292 10 of 11

2. A later ignition of the trailing spark plug was proposed (the interval between spark plug actuation is 15 ◦ESA), which reduced the irregularity of flame propagation in the direction of the rotor movement. 3. According to the results of modeling the processes of turbulent combustion and transfer in the WE working chamber, a significant influence of the shape of the recess in the rotor on the engine performance has been determined. An alternative design of the chamber shape in the rotor, which allows increasing the efficiency of the WE operation, has been offered.

4. It has been shown that lower values of maximum gas temperature (Tmax = 2821 K for modiﬁed CC and 2967 K for base CC) lead to 42% improvement in the engine environmental performance of nitrogen oxide (NOx) emissions and an increase in its eﬃciency in regard to the reduction of carbon dioxide (CO2) emissions (by 5%).

Author Contributions: Conceptualization, L.F. and A.K.; Methodology, A.K. and A.Z.; Validation, A.Z. and V.M.; Formal Analysis, A.K. and A.Z.; Investigation, A.Z.; Resources, L.F.; Writing—Original Draft Preparation, A.Z.; Writing – Review & Editing, A.K.; Visualization, A.Z.; Supervision, L.F.; Project Administration, L.F. Funding: This research received no external funding. Acknowledgments: The authors would like to express sincere gratitude to the Researcher Links program of the British Council for the financial support of this publication. Conflicts of Interest: The authors declare no conflict of interest.

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