Analytical and Numerical Feasibility Analysis of a Contra-Rotary Ramjet Engine

energies

Article Analytical and Numerical Feasibility Analysis of a Contra-Rotary Ramjet Engine

Tomasz Laube and Janusz Piechna * Institute of Aeronautics and Applied Mechanics, Warsaw University of Technology, 00-665 Warsaw, Poland; [email protected] * Correspondence: [email protected]

Received: 11 November 2019; Accepted: 23 December 2019; Published: 30 December 2019

Abstract: A new idea for a contra-rotary ramjet engine is presented. To define the theoretical limits of the non-typical, contra-rotary ramjet engine configuration, its analytical model was developed. The results obtained from that model and the analytical results were compared with those received from numerical simulations. The main weakness of existing rotary ramjet engine projects is the very high rotational speed of the rotor required for achieving supersonic inlet flow. In this paper, a new idea for a contra-rotary ramjet engine (CORRE) is presented and analyzed. This paper presents the results of analytical analysis and numerical simulations of a jet engine system with two rotors rotating in opposite directions. Contra-rotating rotors generate a supersonic air velocity at the inlet to the compressor at two times slower rotor’s speed. To determine the flow characteristics, combustion process, and engine efficiency of the double-rotor engine, a numerical solution of the average Navier-Stokes equations was used with the k-eps turbulence model and the non-premixed combustion model. The results of numerical simulations of flow and the combustion process inside the contra-rotary jet engine achieving a shockwave compression are shown and compared with similar data for a single-rotor engine design and analytical data. This paper presents only the calculation results of the flow processes and the combustion process, indicating the advantages of the proposed double-rotor design. The results of the numerical analysis were presented on the contours and diagrams of the pressure and flow velocity, temperature distribution, and mass fraction of the fuel.

Keywords: shockwave compression; non-premixed combustion; rotary ramjet engine; contra-rotary ramjet engine; hybrid car range extender

1. Introduction The concept of a rotating jet engine is an old idea. The first helicopter designs equipped with ramjet engines, placed at the main rotor’s blade tips and transferring the generated torque directly to the rotor itself, were created in the 1950s [1]. Based on the concept of a jet engine with shockwave compression [2], the idea of a rotational supersonic engine generating torque [3] was created. Due to the benefits that are possible with jet engines using shockwave compression and torque generation, many proposals for such designs have been made around the world. A very high rotational speed is necessary to obtain the supersonic flow of the working medium at the inlet to these devices, which is their characteristic feature. These speed levels result in high centrifugal forces acting on the rotor, thus creating a great challenge from the point of view of the structure’s strength [4]. Despite these complications, many concepts of rotational supersonic engines have been created. Some of them are merely theoretical considerations [4], while there are also cases of technical designs [5–10]. A comprehensive description of a rotary ramjet design is presented in Picard et al. [11]. A very general description without details can be found in Madasamy et al. [12]. New ideas for combustion in rotary ramjet engines are considered in Brouillette et al. [13].

Energies 2020, 13, 163; doi:10.3390/en13010163 www.mdpi.com/journal/energies Energies 2020, 13, 163 2 of 29

In 1998, Ramgen Power Systems proposed the first rotary ramjet for on-ground power generation [2]. The pre-prototype engine was fully assembled in July 1998. In 1999, tests validated the ignition phase, flame holding at idle rotor speeds, mechanical integrity of the rotor at supersonic tip speeds, and overall system integrity. The engine was designed to operate at 500 m/s (Mach number 1.5), with thermal (cycle) efficiencies comparable to gas turbines. The Ramgen company continued development of the shockwave compression idea with the technical realization of the CO2 compressor based on this principle [5] and considered building a flow engine. In 2004, Ramgen developed a rotary engine design that utilizes the compression generated by the supersonic engine air inflow. Development continues and in considered solutions compression ratios reach values of 30 [6]. The structural design and experimental validation of a proof-of-concept prototype of a rotary ramjet engine is presented in Rancourt et al. [14]. The engine can sustain a 500 m/s tip speed at 200 krpm and transient combustion, which is initiated by an integrated ignition system. Part II [14] presents a discretized, one-dimensional (1-D) aerothermodynamic model that estimates the engine performance. A simple buoyancy-driven combustion model makes it possible to estimate the combustor length and shows good agreement with numerical simulations, which demonstrates that the combustion efficiency is higher than 85%, which includes some reactants bypassing the flame holder [15]. A thermodynamic analysis of a rotary ramjet engine with internally open ram channels has also been considered in Dahm et al. [16]. The theory of a moving shockwave compression and non-heated flow field in the ram-compressor rotor disk cavity was analyzed in Wang et al. [17]. There are also results of numerically solved steady 3-D Reynolds Average Navier-Stokes (RANS) equations. In conventional, high rotational speed designs, the rotor requires a special type of bearing [18]. The authors analyzed one of the possible solutions of such an engine in a previous study [19]. Starting from the classic design of a jet engine used in aviation [2], a geometric model of a rotational jet engine was prepared and subjected to an optimization process. Analyzing the results of subsequent calculations, the shape of all channels was modified to obtain the best possible performance of such a construction. In addition, a relatively wide range of typical engine operating parameters was considered, which in this case involved different rotational speeds and the consumption of fuel injected into the combustion chamber [19]. An analysis of the numerical calculation results made it possible to consider other construction solutions for the engine in the form of a rotary ram jet engine. Despite satisfactory performance (efficiency at 20%), the engine has been subjected to further modifications. The main purpose of these activities was to further increase the efficiency and to reduce the relatively high speed at which the motor shaft should rotate (speeds up to 30,000 revolutions per minute). A presentation of these modifications, as well as an analysis of their impact on engine operation, is the subject of this paper. One of the main challenges associated with the design of such engines are flow calculations. This study used the current possibilities of numerical analysis for 2-D flow calculations with combustion. The presented contra-rotary ramjet engine (CORRE) idea is based on the results of an analysis of the features of an earlier investigation of a single-rotor rotary ramjet engine [19]. Therefore, some basic information about this solution is presented. Laube et al. [19] presents an extensive description of the process of searching for the correct shape of the single-rotor rotary shockwave compression engine channels. Various shapes of the engine flow channels were considered and their impact on the compression processes, as well as the combustion process, were analyzed. As a result, the geometry of the engine channels was optimized, ensuring that the operating parameters of the entire engine were at a level close to simple turbine engines. In contrast to existing publications, which concentrate on some specific aspects of rotary ramjet engine construction, the presented study not only presents the novelty of the idea, but also presents a complex model containing the details of the compressible flow, accompanied by the combustion model, which were both solved by the CFD technique and compared with the analytical model. Energies 2020, 13, 163 3 of 29

Energies 2020, 13, x FOR PEER REVIEW 3 of 29 2. Analytical Analysis of a Contra-Rotary Ramjet Engine Because a contra-rotary ramjet engine does not exist physically, it was necessary to find a Because a contra-rotary ramjet engine does not exist physically, it was necessary to ﬁnd a reference example. reference example. Therefore, a simplified analytical model of the physical processes existing in the considered Therefore, a simpliﬁed analytical model of the physical processes existing in the considered engine engine construction was built and used for the prediction of the basic engine operational parameters. construction was built and used for the prediction of the basic engine operational parameters.

2.1. Ramjet Idea The ramjet is a simple engine concept that is a combination of a special inlet channel achieving compression in a shockwave system; a didiffuserﬀuser achievingachieving subsonic air compression; a burner (or combustion chamber) achieving heat addition; and a nozzle expanding exhaust gases that generates thrust, and ﬁnally,finally, torque.torque. The The engine engine scheme scheme an andd an example pressure distribution is shown in Figure1 1..

(a)

(b)

Figure 1. (a) Scheme of the ramjet engine geometry; and (b) an example pressure distribution with a Figuresingle normal1. (a) Scheme shockwave of the structure ramjet engine [19]. geometry; and (b) an example pressure distribution with a single normal shockwave structure [19]. The design has no moving parts, compression is realized due to the supersonic motion of the engineThe in design relation has to theno moving stationary parts, air. compression is realized due to the supersonic motion of the engineDuring in relation this process, to the stationary the air flow air. velocity decreases from supersonic to subsonic speeds by means of twoDuring typical this oblique process, shockwave the air flow systems velocity accompanied decreases from by asupersonic normal shockwave to subsonic inside speeds the by di meansffuser, ofincreasing two typical the airoblique pressure shockwave in the combustion systems accompan chamber.ied In by the a fixednormal combustor shockwave area inside (consisting the diffuser, of fuel increasinginjectors and the flame air pressure holders) in atthe high combustion air pressure, chambe massr. In is addedthe fixed through combustor fuel injection.area (consisting Then, heatof fuel is injectorsgenerated and by flame burning holders) the fuel at mixedhigh air with pressure, the incoming mass is airadded flow. through Finally, fuel the injection. Laval nozzle Then, expands heat is generatedthe outgoing by combustionburning the flow,fuel mixed converting with potentialthe incoming energy air toflow. kinetic Finally, energy the to Laval produce nozzle thrust. expands This thesolution outgoing is known combustion and tested flow, in converting many supersonic potentia engines.l energy to kinetic energy to produce thrust. This solution is known and tested in many supersonic engines.

2.2. Rotary Ramjet Engine The rotary ramjet engine involves the idea of locating a series of channels of ramjet engines on the tip part of a fast-rotating disk to achieve supersonic air velocity in the vicinity of the engine inlets.

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2.2.Energies Rotary 2020 Ramjet, 13, x FOR Engine PEER REVIEW 4 of 29 The rotary ramjet engine involves the idea of locating a series of channels of ramjet engines on The disk drives the engine channels to supersonic speeds before the engine starts, and transmits the tip part of a fast-rotating disk to achieve supersonic air velocity in the vicinity of the engine inlets. torque generated during the engine’s operation. The disk drives the engine channels to supersonic speeds before the engine starts, and transmits torque A typical shockwave compression set comprises two oblique shockwaves and a normal generated during the engine’s operation. shockwave, and depending on the heat release, (at a high release ratio) can be reduced to a single A typical shockwave compression set comprises two oblique shockwaves and a normal shockwave, normal shockwave. and depending on the heat release, (at a high release ratio) can be reduced to a single normal shockwave. Figure 2 shows a comparison of a typical ramjet engine geometry that is axisymmetric and a Figure2 shows a comparison of a typical ramjet engine geometry that is axisymmetric and a rotary ramjet engine geometry that is essentially planar. rotary ramjet engine geometry that is essentially planar.

Figure 2. Comparison of axisymmetric geometry of a typical ram jet engine and the planar geometry Figure 2. Comparison of axisymmetric geometry of a typical ram jet engine and the planar geometry of the rotary ram jet engine. Markers: 0—deﬁne the external conditions, 1—inlet cross-section, of the rotary ram jet engine. Markers: 0—define the external conditions, 1—inlet cross-section, 2— 2—combustion chamber inlet, 3—nozzle inlet, 4—nozzle outlet. combustion chamber inlet, 3—nozzle inlet, 4—nozzle outlet 2.3. Contra-Rotary Ramjet Engine 2.3. Contra-Rotary Ramjet Engine A contra-rotary ramjet engine uses an additional axial compressor rotating in the opposite direction to theA rotation contra-rotary of the mainramjet rotor engine to increase uses an the addition air velocityal axial in frontcompressor of the main rotating rotor in ramjet the opposite engine inlets.direction It is to driven the rotation by the of additional the main axialrotor turbineto increase located the air outside velocity the in main front rotor of the exhaust main rotor gas outlets. ramjet Anengine additional inlets. compressorIt is driven andby the additional additional turbine axial are turbine located located on the outside auxiliary the rotor main and rotor rotate exhaust with thegas sameoutlets. rotational An additional speed. compressor and additional turbine are located on the auxiliary rotor and rotate withIn the front same of rotational the main rotorspeed. inlets, the tip velocities of the compressor rotor and the main rotor are summed,In front and of behind the main the rotor main inlets, rotor, thethe inlettip velocities velocity onof the the compressor turbine blades rotor is equaland the to main the di rotorﬀerence are betweensummed, the and main behind rotor the tip main speed rotor, and the turbine inlet tipvelocity speed, on as the shown turbine in Figure blades3 .is equal to the difference between the main rotor tip speed and turbine tip speed, as shown in Figure 3.

Energies 2020, 13, 163 5 of 29 Energies 2020, 13, x FOR PEER REVIEW 5 of 29

FigureFigure 3. 3. Contra-rotaryContra-rotary ramjet ramjet engine engine idea idea and and features. features.

TheThe flow flow structure isis didifferentfferent on on the the turbine turbine side side because because the the relative relative velocity velocity of the ofexhaust the exhaust gases gasesreaching reaching the turbine the turbine blades blades is reduced is reduced by the by sumthe sum of the of absolutethe absolute values values of the of the main main rotor rotor and and the theauxiliary auxiliary rotor rotor speeds. speeds. Therefore, Therefore, the devicethe device is operational is operational if the if speed the speed of the exhaustof the exhaust gases leaving gases leavingthe main the rotor main is rotor significantly is significantly larger thanlarger the than sum the of sum the absolute of the absolute values ofva thelues main of the rotor main and rotor the andauxiliary the auxiliary rotor speeds. rotor speeds. TheThe main main advantage advantage of of the the contra-rotary contra-rotary ramjet ramjet en enginegine is is that that the the main main rotor rotor and and the the combined combined additionaladditional compressor compressor and and turbine turbine driving driving it it can can rota rotatete with with speeds speeds that that are are half half that that required required for for a a singlesingle main main rotor rotor to to obtain obtain the the expected expected inlet inlet Mach Mach number. number. This This feature feature dramatically dramatically reduces reduces the the technicaltechnical problems problems of of engine engine design. design. TheThe analyzed analyzed engine engine contains contains two two rotors rotors rotating rotating in in opposite opposite directions. directions. The The main main rotor rotor contains contains classicclassic rotary rotary ramjet ramjet engine engine components. components. These These ar aree the the inlet inlet compression compression system system in in the the shockwave shockwave system,system, the the diffuser, diffuser, the the combustion combustion chamber, chamber, an andd the the supersonic outlet nozzle. The The secondary secondary (auxiliary)(auxiliary) rotor rotor includes subsonicsubsonic compressorcompressor blades blades and and action action turbine turbine blades blades located located in frontin front of and of andbehind behind the mainthe main rotor, rotor, respectively. respectively. The subsonic The subs compressoronic compressor is designed is designed to increase to theincrease peripheral the peripheralspeed of the speed air enteringof the air it entering to a speed it to close a sp toeed the close speed to ofthe sound speed at of its sound outlet. at its outlet. TheThe action-type action-type turbine turbine that that drives drives the the subson subsonicic compressor compressor spins spins at the at thesame same speed speed as the as compressor.the compressor. TheThe main main rotor rotor compression compression system system is is shaped shaped like like a a side side surface surface and and the the inlet inlet channel channel is is shaped shaped suchsuch that that it it generates generates two two oblique oblique waves. waves. The The first first is is the the shockwave shockwave arising arising on on the the ramp ramp of of the the side side surfacesurface of of the the main main rotor rotor with with an an angle angle of of 12° 12◦ relarelativetive to to the the direction direction of of the the air air inflow. inflow. The The second second wavewave is is formed formed in in the the area area behind behind the the first first shockwav shockwave,e, at at the the inlet inlet blade blade to to the the engine engine channel, channel, at at an an angleangle of of 10° 10◦ toto the direction ofof airair flowflow behind behind the the first first shockwave. shockwave. The The second second shockwave shockwave changes changes the thedirection direction of airof air flow flow parallel parallel to theto the inlet inlet channel channel walls walls and and does does not not create create a reflected a reflected wave. wave. TheThe arrangement arrangement of of these these oblique oblique waves waves is is term terminatedinated by by a a normal normal shockwave shockwave located located in in the the engineengine diffuser diffuser in in front front of of the the combustion combustion chamber chamber (see (see Figure Figure 44).).

Energies 2020, 13, 163 6 of 29 Energies 2020, 13, x FOR PEER REVIEW 6 of 29

FigureFigure 4. 4.Characteristic Characteristic areas areas and and cross-sections cross-sections of of the the main main rotor rotor of of a a rotary rotary ram ram jet jet engine. engine. Markers: Markers: 0—define0—define the the external external conditions, conditions 1—area, 1—area behind behind primary primary oblique oblique wave, wave, 2—area 2—area behind behind secondary secondary obliqueoblique wave, wave, 3—area 3—area behind behind the the normal normal shock shock wave, wave, 4—combustion 4—combustion chamber chamber inlet, inlet, 5—nozzle 5—nozzle inlet, inlet, 6—nozzle6—nozzle outlet. outlet. Figure3 explains the basic relationship between the velocities existing inside and between di fferent Figure 3 explains the basic relationship between the velocities existing inside and between moving elements of the engine. different moving elements of the engine. 2.4. Analytical Contra-Rotary Ramjet Engine Model 2.4. Analytical Contra-Rotary Ramjet Engine Model The proposed model can be divided into two parts. The first part covers the flows inside the main The proposed model can be divided into two parts. The first part covers the flows inside the rotor and the second part concentrates on the flows inside the auxiliary rotor. main rotor and the second part concentrates on the flows inside the auxiliary rotor. 2.4.1. Compression 2.4.1. Compression Given the inlet geometry shown in Figure4 and the Mach number in front of the inlet makes a shockwaveGiven configuration the inlet geometry possible shown with in two Figure oblique 4 and shockwaves the Mach and number a single in front normal of shockwave,the inlet makes it is a possibleshockwave to analytically configuration calculate possible the compressionwith two oblique ratio shockwaves and static temperature and a single increase normal of shockwave, air reaching it theis combustionpossible to chamber.analytically Figure calculate4 presents the numberedcompression areas ratio separated and static by the temperature shockwaves increase in the initial of air supersonicreaching the part combustion of the flow chamber. and numbered Figure characteristic 4 presents numbered flow cross-sections areas separated in the subsonic by the shockwaves and outlet supersonicin the initial areas. supersonic part of the flow and numbered characteristic flow cross-sections in the subsonicThe area and represented outlet supersonic by the areas. number 0 is an inlet supersonic area. Area number 1 represents the supersonicThe area flow represented downstream by of the the number first oblique 0 is an shock inlet withsupersonic a changed area. flow Area direction. number Area1 represents number the 2 representssupersonic the flow supersonic downstream flow in of the the supersonic first oblique diff shockuser downstream with a changed of the flow second direction. oblique Area shockwave, number which2 represents achieves the a flowsupersonic direction flow parallel in the to superson the diffuseric diffuser walls and downstream does not generate of the second a reflection oblique of theshockwave, oblique shockwave. which achieves Area a number flow direction 2 is separated parallel by to thethe normaldiffuser shockwave walls and does from not the generate subsonic a areareflection downstream. of the oblique Cross-section shockwav numbere. Area 3 represents number 2 theis separated air parameters by the after normal the normalshockwave shockwave. from the Betweensubsonic cross-sections area downstream. 3 and 4, Cross-section there exists a number subsonic 3 di representsffuser that producesthe air parame an increaseters after of the the channel normal cross-section.shockwave. Between The combustion cross-sections chamber 3 and starts 4, atthere cross-section exists a subsonic 4. Cross-section diffuser that number produces 5 represents an increase the inletof the to thechannel supersonic cross-section. expansion The nozzle, combustion while chambe numberr 6starts indicates at cross-section the outlet of 4. theCross-section expansion nozzle.number 5 representsBetween cross-sectionsthe inlet to the 4 andsupersonic 5, a combustion expansion process nozzle, with while constant number pressure 6 indicates is produced the outlet according of the toexpansion the ideal Braytonnozzle. cycle. Furthermore, between cross-sections 5 and 6, an ideal expansion process Between cross-sections 4 and 5, a combustion process with constant pressure is produced through the Laval nozzle (p6 = p0) is assumed. The working fluid inside the engine to the combustion chamberaccording is air,to the which ideal is Brayton assumed cycle. to behave Furthermore, as a perfect between gas withcross-sections a constant 5 specificand 6, an heat. ideal Inside expansion the combustionprocess through chamber, the airLaval is mixed nozzle with (p6 = the p0) fuel is assumed. and burned. The Exhaustworking gases fluid leavinginside the the engine combustion to the chambercombustion have chamber a different is air, ratio which of specific is assumed heat at to constant behave as pressure a perfect and gas constant with a constant volume ( kspecifice). heat. InsideEquations the combustion describing chamber, the gas dynamicsair is mixed of supersonicwith the fuel and and subsonic burned. flows Exhaust can be gases found leaving in many the elementarycombustion books, chamber such have as References a different [ 20ratio–23 ].of specific heat at constant pressure and constant volume (ke).The oblique shockwave is generated by the rapid change of the flow direction by a ramp inclined Equations describing the gas dynamics of supersonic and subsonic flows can be found in many to the flow by angle θ1 which causes the oblique shockwave inclination γ1. elementary books, such as References [20–23]. The oblique shockwave is generated by the rapid change of the flow direction by a ramp inclined θ γ to the flow by angle 1 which causes the oblique shockwave inclination 1 .

Energies 2020, 13, 163 7 of 29

Unfortunately, the relation between the upstream Mach number M, ramp inclination angle θ, and oblique shockwave angle γ is in an implicit form. For the ﬁrst oblique shockwave, such a relation is presented by Equation (1): 2 2 tg(γ1 θ1) (k 1)M sin γ1 + 2 − = − 0 . (1) 2 tgγ1 ( + ) 2 k 1 M0 sin γ1

After ﬁnding the numerical solution of Equation (1), the oblique shockwave angle γ1 can be found by knowing the Mach number M0 and the ramp angle θ1. The Mach number downstream of the oblique shockwave M1 is expressed by Equation (2): v tu 2 (k 1)(M0 sin γ1) + 2 M1 = − . (2) sin2(γ θ ) 2k(M sin γ )2 (k 1) 1 − 1 0 1 − − The compression ratio is described by Equation (3):

p1 2k 2 k 1 = (M0 sin γ1) − . (3) p0 k + 1 − k + 1

The loss of mechanical energy is represented by the stagnation pressure ratio:

k 2 k 1 (k+1)(M0 sin γ1) − 2 p01 2+(k 1)(M0 sin γ1) = − 1 . (4) p 2 00 2k(M sin γ ) (k 1) k 1 0 1 − − − (k+1)

The static temperature ratio is described by Equation (5):

h 2 ih 2 i T 2k(M0 sin γ1) (k 1) (k 1))(M0 sin γ1) + 2 1 = − − − . (5) T 2 2 0 (k + 1) (M0 sin γ1)

Using Equations (1)–(5) and the inlet channel geometry (angles θ1 and θ2), it is possible to define, in a similar way, the flow parameters after two oblique shockwaves. The supersonic diffuser is designed to transfer these flow parameters to the initial cross-section of the subsonic diffuser where the normal shockwave is located. The Mach number downstream of the normal shockwave is defined by Equation (6):

M2 + 2 2 2 k 1 M = − . (6) 3 2k 2 k 1 M2 1 − − The static pressure ratio is given by Equation (7):

p3 2k 2 (k 1) = M2 − . (7) p2 (k + 1) − (k + 1)

The compression eﬃciency is described by the stagnation pressures ratio:

k k+1 2 ! k 1 2 M2 − k 1 2 p 1+ − M 03 = 2 2 1 . (8) p02 2k (k 1) k 1 M2 − − (k+1) 2 − (k+1) Energies 2020, 13, 163 8 of 29

The temperature rise is described by Equation (9): 1 + k 1 M2 2k M2 1 T3 −2 2 k 1 2 = − − 2 . (9) T2 (k+1) 2 2(k 1) M2 − The flow in the subsonic diffuser is assumed to be isentropic. The critical area of cross-section A corresponding to the value of the cross-section A3 downstream ∗ of the normal shockwave and flow parameters downstream of the shockwave is the same along the subsonic diffuser and can be defined as:

!! k+1 − 2(k 1) A 2 k 1 2 − A = A3 ∗ = A3M3 1 + − M3 , (10) ∗ A3 k + 1 2 which makes it possible to obtain the Mach number M4 at the end of the subsonic diffuser, just at the inlet to the combustion chamber. Knowing A3 and A4, it is possible to find the Mach number M4 from Equation (11): k+1 " !# 2(k 1) A4 1 2 k 1 2 − = 1 + − M4 . (11) A M4 k + 1 2 ∗ The subsonic combustion ramjet combustor flow velocities correspond to an M4 that is typically between 0.3 and 0.35. In a recent paper, the use of a more detailed model of heat addition, as suggested in References [24,25], takes into account the variation of the Mach number in a combustion chamber and the drop of static p4 > p5 (12) and stagnation pressure (p05) caused by the heat delivery, and is based on equations relating the local stagnation temperature to the critical stagnation temperature [23]: 2(1 + k)M2 1 + k 1 M2 T05 5 −2 5 = , (13) T0 + 2 ∗ 1 kM5 and the relationship between stagnation pressure and the critical stagnation pressure:

k  k 1 2 k 1 + − p05 1 + k 2 1 −2 M5  =   . (14) 2   p0 1 + kM  k + 1  ∗ 5

The Mach number M5 for the combustion chamber outlet can be found because the inlet and outlet combustion chamber stagnation temperature are known; therefore, the stagnation pressure on the combustion chamber outlet also can be found. Notice the relation

p04 > p05 (15)

The combustion process can be modeled as an increase of the stagnation temperature from T04 = T00 to T05 due to the heat release during the burning process. Therefore, the stagnation temperature in the inlet T04 = T00 and at outlet from combustion chamber T05 are important. With the assumed geometry of the inlet channel, the described shockwave structure can exist when the initial Mach number is higher than 1.86, such that the calculation starts from a Mach number equal to 1.9 and ends with a Mach number of 2.6 due to high energy losses in the shockwaves. Energies 2020, 13, x FOR PEER REVIEW 9 of 29

k  k −1  k−1 21+ M2 + 5 p05 1 k 2 = . (14) + 2 + pk0 1 kM5 1 *  

EnergiesWith2020 ,the13, 163assumed geometry of the inlet channel, the described shockwave structure can9 exist of 29 when the initial Mach number is higher than 1.86, such that the calculation starts from a Mach number equal to 1.9 and ends with a Mach number of 2.6 due to high energy losses in the shockwaves. FigureFigure5 5shows shows the the variation variation of of local local values values of of the the Mach Mach number number after after the the primary primary oblique oblique shockwaveshockwave ((MM11),), afterafter thethe secondarysecondary obliqueoblique shockwaveshockwave ((MM22),), afterafter thethe normalnormal shockwaveshockwave ((MM33),), andand onon thethe combustioncombustion chamberchamber inletinlet cross-sectioncross-section ((MM44).).

FigureFigure 5.5. LocalLocal valuesvalues ofof thethe MachMach numbernumber inin thethe followingfollowing cross-sections:cross-sections: afterafter thethe primaryprimary obliqueoblique

shockwaveshockwave ((MM11),), afterafter thethe secondarysecondary obliqueoblique shockwaveshockwave ((MM22),), afterafter thethe normalnormal shockwaveshockwave ((MM33),), andand onon thethe combustioncombustion chamberchamber inletinlet cross-sectioncross-section ((MM44).).

InIn FigureFigure6 ,6, local local values values of of the the static static pressure pressure compression compression ratio ratio after after the the primary primary oblique oblique shockwaveshockwave ((pp11//pp00), after the secondarysecondary obliqueoblique shockwaveshockwave ((pp22//pp11), after thethe normalnormal shockwaveshockwave ((pp33//pp22), andEnergiesand forfor 2020 thethe, 13combustioncombustion, x FOR PEER chamber chamberREVIEW inletinlet cross-sectioncross-section ((pp44//pp33) are depicted. 10 of 29

Figure 6. Local values of compression ratios in the follo followingwing cross-sections: after the primary oblique

shockwave (p11/p0),), after after the the secondary oblique shockwave ((pp22/p1),), after after the normal shockwave ((pp33/p2),), and for the combustion chamber inlet cross-section ((pp44/p3).).

In Figure Figure 77,, the the compression compression ratio ratio of of the the static static pressure pressure in the in combustion the combustion chamber chamber inlet cross- inlet cross-sectionsection to the tostatic the staticinlet pressure, inlet pressure, ratio ratioof the of st theagnation stagnation pressure pressure after after the shockwave the shockwave system system to the to theinlet inlet static static pressure, pressure, and and the theratio ratio of the of thestagnation stagnation pressure pressure after after the the ideal ideal isentropic isentropic compression compression to tothe the static static inlet inlet pressure pressure versus versus the the inlet inlet Mach Mach is presented. is presented.

Figure 7. Local values of stagnation pressure to static inlet pressure after isentropic compression

(p00/p0), after the shockwave system (p03/p0), and the ratio of the static pressure at the combustion

chamber inlet to inlet pressure (p5/p0).

The compression efficiency in the set of two oblique shockwaves and one normal shockwave is given by the ratio of the stagnation pressure on the combustion chamber inlet cross-section to the pressure achieved in an ideal isentropic compression, as presented in Figure 8.

Energies 2020, 13, x FOR PEER REVIEW 10 of 29

Figure 6. Local values of compression ratios in the following cross-sections: after the primary oblique

shockwave (p1/p0), after the secondary oblique shockwave (p2/p1), after the normal shockwave (p3/p2),

and for the combustion chamber inlet cross-section (p4/p3).

In Figure 7, the compression ratio of the static pressure in the combustion chamber inlet cross- section to the static inlet pressure, ratio of the stagnation pressure after the shockwave system to the Energiesinlet static2020 ,pressure,13, 163 and the ratio of the stagnation pressure after the ideal isentropic compression10 of to 29 the static inlet pressure versus the inlet Mach is presented.

Figure 7. LocalLocal values values of of stagnation pressure to static inlet pressure after isentropic compression

(p00//pp00),), after after the the shockwave shockwave system system ( (pp0303/p/p0),0), and and the the ratio ratio of of the the static static pressure pressure at the combustioncombustion chamber inlet to inlet pressure ((p55/p0).).

The compression efficiency eﬃciency in in the the set set of of two two ob obliquelique shockwaves shockwaves and and on onee normal normal shockwave shockwave is isgiven given by by the the ratio ratio of of the the stagnation stagnation pressure pressure on on the the combustion combustion chamber chamber inlet inlet cross-section cross-section to the pressureEnergies 2020 achieved, 13, x FOR inin PEER anan idealidealREVIEW isentropicisentropic compression,compression, asas presentedpresented inin FigureFigure8 .8. 11 of 29

Figure 8. Compression efficiency eﬃciency in the set of two obliqueoblique shockwaves and sing singlele normal shockwave

represented byby thethe stagnationstagnation pressurepressure ratioratio ((pp0303/p00).).

The air compression in a set of oblique and normal shockwaves was accompanied by an increase in static air temperature,temperature, as shown in FigureFigure9 9.. TheThe initialinitial staticstatic airair temperaturetemperature roserose toto moremore thanthan twice its initial valuevalue inin thethe analyzedanalyzed rangerange ofof MachMach numbersnumbers atat thethe inletinlet toto thethe engine.engine. The air temperature at the inlet toto thethe combustioncombustion chamberchamber rangedranged fromfrom 500500 KK atat MM == 1.9 to 680 K at M = 2.6.2.6. Such a high air temperature at the inlet to the combustioncombustion chamber is one of the disadvantages of shockwave compression.

Figure 9. Local values of the static temperature ratio after isentropic compression (T00), after the

shockwave system (T03/T00), and the static temperature at the combustion chamber inlet (T5/T1).

At the same ramp angles in the main rotor inlet channel, for different inlet Mach numbers, the oblique shockwave inclination varied, as shown in Figure 10, which required modification of the engine inlet geometry or operation with a non-optimal configuration with side effects.

Energies 2020, 13, x FOR PEER REVIEW 11 of 29

Figure 8. Compression efficiency in the set of two oblique shockwaves and single normal shockwave

represented by the stagnation pressure ratio (p03/p00).

The air compression in a set of oblique and normal shockwaves was accompanied by an increase in static air temperature, as shown in Figure 9. The initial static air temperature rose to more than twice its initial value in the analyzed range of Mach numbers at the inlet to the engine. The air temperature at the inlet to the combustion chamber ranged from 500 K at M = 1.9 to 680 K at M = 2.6. EnergiesSuch a2020 high, 13 air, 163 temperature at the inlet to the combustion chamber is one of the disadvantages11 of of 29 shockwave compression.

Figure 9.9. Local values of the static temperaturetemperature ratioratio afterafter isentropicisentropic compressioncompression ((TT0000), after thethe shockwave system ((T 03//TT0000),), and and the the static static temperature temperature at at the the combustion combustion chamber chamber inlet inlet ( (TT55/T/T1).1).

At the same same ramp ramp angles angles in in the the main main rotor rotor inle inlett channel, channel, for fordifferent different inlet inlet Mach Mach numbers, numbers, the theoblique oblique shockwave shockwave inclination inclination varied, varied, as asshown shown in inFigure Figure 10, 10 ,which which required required modification modification of of the engineEnergies 2020 inlet, 13 geometry, x FOR PEER oror REVIEW operationoperation withwith aa non-optimalnon-optimal configurationconfiguration withwith sideside eeffects.ffects. 12 of 29

Figure 10.10. AnglesAngles of of primary primary and and secondary secondary oblique oblique shockwaves shockwaves generated generated by the inletby the ﬂow inlet at diflowﬀerent at Machdifferent numbers. Mach numbers.

2.4.2. Combustion One of the most important parameters for deﬁningdefining a ramjet engine operation is the temperature of thethe compressedcompressed airair atat thethe inlet inlet to to the the combustion combustion chamber. chamber. In In Figure Figure9, the9, the local local temperature temperature rise rise in thein the shockwave shockwave system system is is shown, shown, giving giving the the variation variation of of the the combustion combustion chamberchamber inletinlet temperaturetemperature ratio withwith thethe engineengine inletinlet staticstatic temperature.temperature. The combustioncombustion processprocess was was simulated simulated by by introducing introducing fuel fuel in in various various quantities quantities and and assuming assuming set values of the excess air coeﬃcient. By assuming the stoichiometric air-fuel ratio Ssci and the excess air set values of the excess air. coefficient. By assuming the stoichiometric. air-fuel ratio Ssci and the ratio nair, the fuel output m f and the air-exhaust gas mixture output mout at the combustion chamber outlet can be calculated: excess air ratio nair, the fuel output m f and the. air-exhaust gas mixture output mout at the . min m f = , (16) combustion chamber outlet can be calculated: Sscinair . . . m = m + m . (17) =out m inin f m f , (16) Sscinair = + mout min m f . (17)

Assuming a LHV (lower heating value) for the aviation fuel used, the heat supplied in the combustion chamber to the air and exhaust mixture is: = Ecomb m f LHV. (18)

The stagnation temperature rise in the combustion chamber is:

Δ = Ecomb T0 . (19) m outcp

The temperature at the outlet of the combustion chamber is: = +Δ T05 T00 T0 . (20)

Subsonic combustion ramjet combustor flow velocities correspond to an M2 typically between 0.3 and 0.35.

2.4.3. The Expansion Process in the Nozzle The expansion process takes place from the combustion chamber (cross-section 5) to the outlet (cross-section 6). It was assumed that the expansion process is isentropic and the pressure losses inside the nozzle can be omitted.

Energies 2020, 13, 163 12 of 29

Assuming a LHV (lower heating value) for the aviation fuel used, the heat supplied in the combustion chamber to the air and exhaust mixture is:

. Ecomb = m f LHV. (18)

The stagnation temperature rise in the combustion chamber is:

Ecomb ∆T0 = . . (19) moutcp

The temperature at the outlet of the combustion chamber is:

T05 = T00 + ∆T0. (20)

Subsonic combustion ramjet combustor ﬂow velocities correspond to an M2 typically between 0.3 and 0.35.

T06 = T05. (22) The Mach number at the convergent and divergent nozzle outlet depends only on the ratio of the stagnation pressure in the combustion chamber and the outlet static pressure: v u  ke 1  t ! −  ke  2  p06  Mout = M6 =  1 (23) k 1 p −  − 6

Please note that the exponent of the isentropic exhaust gases’ expansion ke is diﬀerent to the one used for the air. The outlet velocity depends on the outlet Mach number and the stagnation temperature: s 1 k RT u = u = M a = M a = M e 06 . (24) out 6 6 6 6 06 q 6 k 1 k 1 + 2 + 2 1 −2 M6 1 −2 M6

2.4.4. Momentum Equation

The key point of the contra-rotary ramjet engine is the main rotor outlet velocity uout because the exhaust gas velocity relative to the auxiliary rotor turbine blades urel_turb_in is reduced by the sum of the main rotor velocity umain and the auxiliary rotor velocity uauxil. Therefore, the successful operation of a contra-rotary ramjet engine requires the high compression and high temperature of exhaust gases for the generation of high velocity exhaust gases (uout). In the analyzed proposition, the subsonic compressor increases only the rotational velocity of the air, which is sent at a supersonic relative speed (being the sum of abs (uauxil) and abs (umain)) to the main rotor inlet. The torque generated by the main rotor, assuming an almost tangential inflow and outflow, is defined by Equation (25):

. . T = F R = moutuoutβ m u + (peAe p A ) R. (25) main main − in in − in in Energies 2020, 13, 163 13 of 29

The power generated by the main rotor is:

. . N = ω F R = ω moutuoutβ m u + (peAe p A ) R. (26) main main main main − in in − in in The torque generated by the auxiliary rotor is:

. . Naux = ω F R = ω (2mout( uout β ( u + u )) m u )R. (28) auxil auxil auxil | | − | main| | auxil| − in auxil Using Equations (1)–(28), the theoretical ideal operating parameters of the engine were predicted and used for the validation of the numerical model of the same geometry. The engine efficiency was calculated by comparing the mechanical engine power generated by the rotors with the heat stream added inside the combustion chamber: Energies 2020, 13, x FOR PEER REVIEW 14 of 29 Nmain ηmain = , (29) Ecomb Nmain η = . (30) mainNmain + Naux ηtotal = Ecomb . (30) Ecomb TheThe variationvariation of of engine engine power, power, efficiency, efficiency, and combustion and combustion chamber chamber outlet temperature outlet temperature is presented is aspresented a function as a offunction the equivalence of the equivalence ratio representing ratio representing the inversion the inversion of the of excess the excess air coeair coefficientfficient in Figuresin Figures 11– 11–1313 for for the the inlet inlet Mach Mach number number 2.5. 2.5.

FigureFigure 11.11. Estimated power of the main and auxiliary rotors and the totaltotal engineengine powerpower atat anan inletinlet MachMach numbernumber 2.52.5 inin relationrelation toto thethe equivalenceequivalence ratio.ratio.

Figure 12. Efficiency of the main rotor and double-rotor engines for the range of inlet Mach numbers as a function of the equivalence ratio.

Energies 2020, 13, x FOR PEER REVIEW 14 of 29

N η = main main . (30) Ecomb

The variation of engine power, efficiency, and combustion chamber outlet temperature is presented as a function of the equivalence ratio representing the inversion of the excess air coefficient in Figures 11–13 for the inlet Mach number 2.5.

EnergiesFigure2020, 1311., 163 Estimated power of the main and auxiliary rotors and the total engine power at an inlet14 of 29 Mach number 2.5 in relation to the equivalence ratio.

FigureFigure 12.12. EEfficiencyﬃciency of thethe mainmain rotorrotor andand double-rotordouble-rotor enginesengines forfor thethe rangerange ofof inletinlet MachMach numbersnumbers Energies 2020, 13, x FOR PEER REVIEW 15 of 29 asas aa functionfunction ofof thethe equivalenceequivalence ratio.ratio.

Figure 13. Combustion chamber outlet temperature versus the equivalence ratio (inversion of excess air coecoefficient)fficient) at thethe inletinlet MachMach numbernumber 2.5.2.5. 2.4.5. Reference Conditions 2.4.5. Reference Conditions To present the obtained results in a universal way, three reference quantities were defined. These To present the obtained results in a universal way, three reference quantities were defined. These are the reference air flow rate, reference fuel mass flow rate, and reference power. As the reference are the reference air flow rate, reference fuel mass flow rate, and reference power. As the reference flow of air flowing through the engine flow channel, the flow in a minimum cross-section of the inlet flow of air flowing through the engine flow channel, the flow in a minimum cross-section of the inlet diffuser under specific ambient pressure and temperature was assumed. To determine this value, diffuser under specific ambient pressure and temperature was assumed. To determine this value, the the following relationship was used: following relationship was used:

1 k r ! − − . Are f Pt_re f k k 1 2(k 11)k 2 −()− ma_re f = A P k Mre f 1 + k −−1M 2 k 1, (31) = pref t _ ref R  + 2 re2 f  m a _ ref Tt_re f M ref 1 M ref  , (31) Tt _ ref R  2  where: where:. m is the determined value of the reference air mass ﬂow rate (kg/s), • a_re f • Am = 0.000179 is the determined m2 is the minimalvalue of cross-sectionthe reference ofair the mass inlet flow channel rate (kg/s), diﬀuser with a height of 1 cm, • rea f_ref • = 2 Aref 0.000179 m is the minimal cross-section of the inlet channel diffuser with a height of 1 cm, • Pt _ref = 101,300 Pa is the assumed absolute flow reference pressure, • Tt _ref = 288 K is the assumed reference flow temperature, • k = 1.4 is the adiabatic exponent of the air, • Mref = 1 is the assumed reference value of the flow Mach number in the inlet diffuser, and • R = 287 J/(kg K) is the air gas constant. Using the above formula and the assumed values, the reference air mass flow rate of the engine equipped with four stream channels with a height of 1 cm was 0.2725 kg/s. On this basis, the fuel mass flow rate at an equivalence ratio equal to 1 was calculated to be 0.01859 kg/s, while the reference power was defined as the fuel mass flow rate times the fuel LHV value (45,000 kJ/(kg K)), giving a value of 836.6 kW. Some results of the investigation using the analytical model are presented in Figures 11–13. In Figure 11, an almost linear growth of the main rotor power, auxiliary rotor power, and engine total power can be observed with an increase of fuel in the combustion mixture (increasing equivalence ratio). A low value of the equivalence ratio means a lean mixture (excess air coefficient equals to 4.5) and a high value means a rich stoichiometric mixture. A rich mixture on the one hand gives higher power, but on the other hand, the combustion chamber outlet temperature is very high, as can be seen in Figure 13.

Energies 2020, 13, 163 15 of 29

P = 101,300 Pa is the assumed absolute flow reference pressure, • t_re f T = 288 K is the assumed reference flow temperature, • t_re f k = 1.4 is the adiabatic exponent of the air, • M = 1 is the assumed reference value of the flow Mach number in the inlet diffuser, and • re f R = 287 J/(kg K) is the air gas constant. • Using the above formula and the assumed values, the reference air mass flow rate of the engine equipped with four stream channels with a height of 1 cm was 0.2725 kg/s. On this basis, the fuel mass flow rate at an equivalence ratio equal to 1 was calculated to be 0.01859 kg/s, while the reference power was defined as the fuel mass flow rate times the fuel LHV value (45,000 kJ/(kg K)), giving a value of 836.6 kW. Some results of the investigation using the analytical model are presented in Figures 11–13. In Figure 11, an almost linear growth of the main rotor power, auxiliary rotor power, and engine total power can be observed with an increase of fuel in the combustion mixture (increasing equivalence ratio). A low value of the equivalence ratio means a lean mixture (excess air coefficient equals to 4.5) and a high value means a rich stoichiometric mixture. A rich mixture on the one hand gives higher power, but on the other hand, the combustion chamber outlet temperature is very high, as can be seen in Figure 13. The amount of fuel used, as represented by the equivalence ratio, has an influence on the position of the normal shockwave in the insulator, whose effect is not taken into account in the simplified analytical model. An almost linear increase of the generated power (see Figure 11) and combustion chamber outlet temperature (see Figure 13) can be observed in contrast to the decreasing efficiency of the main rotor operation and a strongly nonlinear variation of the double-rotor engine efficiency versus the equivalence ratio, as seen in Figure 12. An addition of an auxiliary rotor dramatically increased the total engine power and total engine efficiency. In Figure 12, a reduction of the main rotor efficiency with an increasing value of the equivalence ratio can be observed. The theoretical contra-rotary ramjet engine configuration shows (see Figure 12) a much higher total efficiency over the main rotor efficiency, which can be treated as a single-rotor engine configuration. Also, the total power generated by the contra-rotary configuration (see Figure 11) is almost two times higher than in the single-rotor design. The results of the analytical model have been used for the validation of the more sophisticated and more exact numerical model of the engine. It was used to establish the theoretical limits of the engine parameters.

3. Technical Realization

3.1. Rotary Ramjet Engine Idea A technical solution for a single-rotor rotary ramjet engine is presented in Figure 14. It shows the channel outline of one of the four flow systems forming a rotary engine with shockwave compression and an example pressure distribution in the channels of this engine segment. In Figure 14, one can observe the existence of the oblique shockwave system due to the normal shockwave compressing the air in the inlet channel, followed by subsonic compression in the diffuser and an almost constant pressure zone corresponding to the combustion chamber area with fuel injectors and flame stabilizers, finished by the decompression process in the supersonic nozzle. The engine operation was considered for inlet Mach numbers between 2.0 and 2.5. Energies 2020, 13, x FOR PEER REVIEW 16 of 29

The amount of fuel used, as represented by the equivalence ratio, has an influence on the position of the normal shockwave in the insulator, whose effect is not taken into account in the simplified analytical model. An almost linear increase of the generated power (see Figure 11) and combustion chamber outlet temperature (see Figure 13) can be observed in contrast to the decreasing efficiency of the main rotor operation and a strongly nonlinear variation of the double-rotor engine efficiency versus the equivalence ratio, as seen in Figure 12. An addition of an auxiliary rotor dramatically increased the total engine power and total engine efficiency. In Figure 12, a reduction of the main rotor efficiency with an increasing value of the equivalence ratio can be observed. The theoretical contra-rotary ramjet engine configuration shows (see Figure 12) a much higher total efficiency over the main rotor efficiency, which can be treated as a single-rotor engine configuration. Also, the total power generated by the contra-rotary configuration (see Figure 11) is almost two times higher than in the single-rotor design. The results of the analytical model have been used for the validation of the more sophisticated and more exact numerical model of the engine. It was used to establish the theoretical limits of the engine parameters.

3. Technical Realization

3.1. Rotary Ramjet Engine Idea A technical solution for a single-rotor rotary ramjet engine is presented in Figure 14. It shows the channel outline of one of the four flow systems forming a rotary engine with shockwave compression and an example pressure distribution in the channels of this engine segment. In Figure 14, one can observe the existence of the oblique shockwave system due to the normal shockwave compressing the air in the inlet channel, followed by subsonic compression in the diffuser and an almost constant pressure zone corresponding to the combustion chamber area with fuel injectors and flameEnergies 2020stabilizers,, 13, 163 finished by the decompression process in the supersonic nozzle. The engine16 of 29 operation was considered for inlet Mach numbers between 2.0 and 2.5.

Figure 14. GeometryGeometry of of the the channels of of one of the fo fourur engine segments and an example pressure distribution in the engineengine channels (Pa).

EnergiesConsidering 2020, 13, x FOR that PEER the REVIEW engine consisted of four channels, the power of the entire engine was17 close of 29 Considering that the engine consisted of four channels, the power of the entire engine was close to 300 kW, with an efficiency of 16–18% [19]. to 300 kW, with an efficiency of 16–18% [19]. TheThe eefficiencyfficiency ofof thethe engineengine waswas notnot high,high, butbut itit waswas comparablecomparable toto thethe eefficiencyfficiency ofof aa smallsmall turbineturbine engine.engine. TheThe performed performed calculations, calculations, using using a three-dimensional a three-dimensional model ofmodel the analyzed of the engine analyzed construction, engine indicatedconstruction, the existenceindicated ofthe three-dimensional existence of three-dimensio effects in thenal vicinity effects ofin the sidevicinity walls of ofthe the side main walls flow of channelthe main of flow theengine, channel while of the maintaining engine, while a flow maintaining structure ata flow half thestructure height at of half the channelthe height that of was the identicalchannel that to the was two-dimensional identical to the solution,two-dimensional as shown solution, in Figure as 15 shownb. in Figure 15b.

(a) (b)

FigureFigure 15.15.( (aa)) TheThe discretizingdiscretizing gridgrid inin aa three-dimensionalthree-dimensional modelmodel andand ((bb)) thethe pressurepressure distribution distribution in in thethe middle middle plane plane of of the the 3-D 3-D engine engine channels channels [ 19[19]] (at (at a a radius radius of of 0.3 0.3 m). m).

TheThe pressurepressure distributiondistribution shownshown inin FigureFigure 15 15bb inin thethe circumferentialcircumferentialplane, plane,placed placed atat halfhalf ofof thethe engineengine channelchannel height,height, coincidedcoincided veryvery wellwell withwith thethe resultsresults ofof thethe two-dimensionaltwo-dimensional solutionssolutions [[19].19]. ConsideringConsidering the the conclusions conclusions of of the the previous previous study study [19 [19],], all all analyses analyses in in recent recent studies studies were were limited limited to to a two-dimensionala two-dimensional geometry. geometry.

3.2. Contra-Rotary Ramjet Engine Idea Analyzing the obtained velocity distributions of the exhaust gases leaving the exit nozzles of the single-rotor rotary engine, the existence of their large peripheral component (Figure 16) and the associated large losses of kinetic energy were noticed. Therefore, the possibility of using an additional rotor driven by the exhaust gases from the main rotor was considered and was the basis for a new solution.

Figure 16. Distribution of the flow velocity (m/s) relative to the single-rotor engine (M = 2.5).

Energies 2020, 13, x FOR PEER REVIEW 17 of 29

The efficiency of the engine was not high, but it was comparable to the efficiency of a small turbine engine. The performed calculations, using a three-dimensional model of the analyzed engine construction, indicated the existence of three-dimensional effects in the vicinity of the side walls of the main flow channel of the engine, while maintaining a flow structure at half the height of the channel that was identical to the two-dimensional solution, as shown in Figure 15b.

(a) (b)

Figure 15. (a) The discretizing grid in a three-dimensional model and (b) the pressure distribution in the middle plane of the 3-D engine channels [19] (at a radius of 0.3 m).

The pressure distribution shown in Figure 15b in the circumferential plane, placed at half of the engine channel height, coincided very well with the results of the two-dimensional solutions [19].

EnergiesConsidering2020, 13 ,the 163 conclusions of the previous study [19], all analyses in recent studies were limited17 of 29to a two-dimensional geometry.

3.2.3.2. Contra-RotaryContra-Rotary RamjetRamjet EngineEngine IdeaIdea AnalyzingAnalyzing the obtained velocity velocity distributions distributions of of the the exhaust exhaust gases gases leaving leaving the the exit exit nozzles nozzles of the of thesingle-rotor single-rotor rotary rotary engine, engine, the theexistence existence of thei of theirr large large peripheral peripheral component component (Figure (Figure 16) 16and) and the theassociated associated large large losses losses of kinetic of kinetic energy energy were noticed. were noticed. Therefore, Therefore, the possibility the possibility of using an of additional using an additionalrotor driven rotor by driventhe exhaust by the gases exhaust from gases the frommain the rotor main was rotor considered was considered and was and the was basis the for basis a new for asolution. new solution.

Energies 2020, 13, x FOR PEER REVIEW 18 of 29 FigureFigure 16.16. DistributionDistribution ofof thethe ﬂowflow velocityvelocity (m(m/s)/s) relativerelativeto tothe the single-rotor single-rotor engine engine ( M(M= = 2.5).2.5). The disadvantages of the basic design solution of a single-rotor engine is the high linear velocity The disadvantages of the basic design solution of a single-rotor engine is the high linear velocity of the edges of the inlet engine channels located on the rotor perimeter, which are necessary to obtain of the edges of the inlet engine channels located on the rotor perimeter, which are necessary to obtain supersonic speeds at the inlet. The high linear speed of the engine channels is associated with high supersonic speeds at the inlet. The high linear speed of the engine channels is associated with high loads from centrifugal forces and high rotor speeds, limiting the possibility of using ball or roller loads from centrifugal forces and high rotor speeds, limiting the possibility of using ball or roller bearings. As the speed of air relative to the moving inlet is decisive, the possibility of using an bearings. As the speed of air relative to the moving inlet is decisive, the possibility of using an additional rotor upstream of the inlet of the compressor, rotating in the opposite direction, causing additional rotor upstream of the inlet of the compressor, rotating in the opposite direction, causing the the relative velocity at the inlet to the supersonic compressor to be the summed value of the speeds relative velocity at the inlet to the supersonic compressor to be the summed value of the speeds of of both rotors, is proposed. It was assumed that the additional rotor will be driven by a turbine both rotors, is proposed. It was assumed that the additional rotor will be driven by a turbine located located downstream of the engine’s main rotor utilizing the exhaust gases. The discussed double- downstream of the engine’s main rotor utilizing the exhaust gases. The discussed double-rotor engine rotor engine scheme is shown in Figure 17. scheme is shown in Figure 17.

Figure 17. Comparison of the one-shaft and two-shaft engine. Figure 17. Comparison of the one-shaft and two-shaft engine.

The 3-D diagram in Figure 18 illustrates the potential construction solution of the discussed engine.

Figure 18. Visualization of a construction scheme for a double-rotor engine structure.

Energies 2020, 13, x FOR PEER REVIEW 18 of 29

The disadvantages of the basic design solution of a single-rotor engine is the high linear velocity of the edges of the inlet engine channels located on the rotor perimeter, which are necessary to obtain supersonic speeds at the inlet. The high linear speed of the engine channels is associated with high loads from centrifugal forces and high rotor speeds, limiting the possibility of using ball or roller bearings. As the speed of air relative to the moving inlet is decisive, the possibility of using an additional rotor upstream of the inlet of the compressor, rotating in the opposite direction, causing the relative velocity at the inlet to the supersonic compressor to be the summed value of the speeds of both rotors, is proposed. It was assumed that the additional rotor will be driven by a turbine located downstream of the engine’s main rotor utilizing the exhaust gases. The discussed double- rotor engine scheme is shown in Figure 17.

Figure 17. Comparison of the one-shaft and two-shaft engine. Energies 2020, 13, 163 18 of 29 The 3-D diagram in Figure 18 illustrates the potential construction solution of the discussed engine. The 3-D diagram in Figure 18 illustrates the potential construction solution of the discussed engine.

Figure 18. Visualization of a construction scheme for a double-rotor engine structure. Figure 18. Visualization of a construction scheme for a double-rotor engine structure. The auxiliary impeller with the pre-compressor was mechanically fastened with an external turbine that drove it outside the main rotor. The use of two drive shafts rotating in opposite directions distinguished the proposed concept from existing ones. On the first shaft, an auxiliary system consisting of a subsonic compressor and an axial turbine were placed together, while on the second shaft, there was the main arrangement of the rotary jet engine channels. The main rotor of this engine was located between the axial blades of the compressor and the axial turbine of the auxiliary system. The rotors shown rotated in opposite directions to each other. This solution was intended to reduce the rotational speed of the rotors while maintaining a high relative speed of the air inflow at the inlet to the channels of the jet engine. Of course, from the turbine side, such a system reduced the relative speed of the exhaust gas flow to the auxiliary turbine blades. However, the calculations showed that the exhaust flow velocities from the main rotor nozzles were high enough to drive the auxiliary rotor that moved in the opposite direction. The lowering of the rotational speed of the engine shafts made possible the use of the rotors’ ball bearings. They do not require service, and the reduced revolution rate increases their service life. When using higher rotational speeds, compressing the air to a higher pressure using a subsonic axial compressor should positively affect the efficiency of the engine, assuming that mechanical energy is extracted from both shafts. It was assumed that the drive torques received from both shafts are transferred to two electric generators, whose rotations are controlled by electronic systems, and the generated electrical energy is stored in accumulators or supercapacitors. The air entering the engine first flowed through a steering stage located in the housing, aimed at correcting the flow direction, such that the air flowing into the blades of the axial compressor moved in a direction parallel to the axis of the drive shafts. Then, the air flow was picked up by the subsonic compressor rotor vanes, which accelerated the working medium, thus transmitting mechanical energy to it, increasing the kinetic energy of the air. This system made it possible to achieve relative flow velocities of M = 2 and more at much lower rotational speeds of both rotors.

4. Numerical Model Figure 19a shows the geometry of the subsonic compressor vanes, main rotor channels (supersonic compressor, insulator, combustion chamber, expansion nozzle), and turbine blades driving the subsonic compressor, with an example pressure distribution in the ﬂow ﬁeld areas depicted in Figure 19b. Energies 2020, 13, x FOR PEER REVIEW 19 of 29

The auxiliary impeller with the pre-compressor was mechanically fastened with an external turbine that drove it outside the main rotor. The use of two drive shafts rotating in opposite directions distinguished the proposed concept from existing ones. On the first shaft, an auxiliary system consisting of a subsonic compressor and an axial turbine were placed together, while on the second shaft, there was the main arrangement of the rotary jet engine channels. The main rotor of this engine was located between the axial blades of the compressor and the axial turbine of the auxiliary system. The rotors shown rotated in opposite directions to each other. This solution was intended to reduce the rotational speed of the rotors while maintaining a high relative speed of the air inflow at the inlet to the channels of the jet engine. Of course, from the turbine side, such a system reduced the relative speed of the exhaust gas flow to the auxiliary turbine blades. However, the calculations showed that the exhaust flow velocities from the main rotor nozzles were high enough to drive the auxiliary rotor that moved in the opposite direction. The lowering of the rotational speed of the engine shafts made possible the use of the rotors’ ball bearings. They do not require service, and the reduced revolution rate increases their service life. When using higher rotational speeds, compressing the air to a higher pressure using a subsonic axial compressor should positively affect the efficiency of the engine, assuming that mechanical energy is extracted from both shafts. It was assumed that the drive torques received from both shafts are transferred to two electric generators, whose rotations are controlled by electronic systems, and the generated electrical energy is stored in accumulators or supercapacitors. The air entering the engine first flowed through a steering stage located in the housing, aimed at correcting the flow direction, such that the air flowing into the blades of the axial compressor moved in a direction parallel to the axis of the drive shafts. Then, the air flow was picked up by the subsonic compressor rotor vanes, which accelerated the working medium, thus transmitting mechanical energy to it, increasing the kinetic energy of the air. This system made it possible to achieve relative flow velocities of M = 2 and more at much lower rotational speeds of both rotors.

4. Numerical Model Figure 19a shows the geometry of the subsonic compressor vanes, main rotor channels (supersonic compressor, insulator, combustion chamber, expansion nozzle), and turbine blades drivingEnergies 2020the , 13subsonic, 163 compressor, with an example pressure distribution in the flow field areas19 of 29 depicted in Figure 19b.

(a) (b)

FigureFigure 19. 19. (a()a Engine) Engine components’ components’ geometry geometry showing showing th thee subsonic subsonic compressor compressor vanes, vanes, main main rotor rotor channelschannels (supersonic (supersonic compressor, compressor, insulator, insulator, combustion combustion chamber, chamber, expansion expansion nozzle), nozzle), and and turbine turbine bladesblades driving driving subsonic subsonic compressor; compressor; and and (b (b) )an an example example pressure pressure distribution. distribution.

4.1. Fluid Flow and Combustion Models The flow inside the engine, as well as outside of it, is assumed to be steady, turbulent, and compressible. In the case of ramjet engines, the compression process is performed around the inlet of the engine through an advanced system of shockwaves. In general, a sequence of oblique shockwaves has a relatively higher compression efficiency compared to a single normal shockwave due to the smaller growth of entropy in oblique shockwaves. The flow was described using averaged Navier-Stokes equations, supplemented by the k-ε turbulence model. Due to such a turbulence model being used, a wall function on the engine walls was used. This turbulence model was applied due to the requirements of the combustion model needing to be used simultaneously. After compression in the shockwave system, air at subsonic speed was transferred to the combustion chamber. Then, fuel was added to the compressed air. In the used combustion chamber embodiment, the injectors were a part of the flame stabilizers. The combustion mechanism was assumed to be of a diffusion type, and the combustion process was controlled by the turbulent diffusion of fuel and oxygen in the combustion zone. Under such assumptions, the non-premixed combustion model was used for the simulation of the combustion process in the engine combustion chamber. The applied model was based on several simplifying assumptions. These were: high speed combustion chemistry, equilibrium of the process, and control of the combustion process solely by turbulent diffusion of the fuel and oxidizer. This means that the level of turbulent diffusion had to be many times greater than the molecular diffusion of the individual components of the reactants. This reduced the large set of individual transport equations to a single transport equation of a mixture fraction. This is valid only in high turbulence areas. Such conditions exist in the considered combustion chamber. The influence of the turbulence on the combustion process was taken into account by the additional transport of the mixture fraction variation. This equation contains terms that depend on the local turbulence parameters, such as the turbulent kinetic energy (k) and the energy dissipation rate (ε). In the full complex solution of the averaged Navier-Stokes equations, two transport equations for k and ε, along with two additional transport equations of two quantities, namely the mixture fraction and the variance of the mixture fraction, were solved. The additional set of transport equations of the Energies 2020, 13, 163 20 of 29 two variables, mixture fraction and mixture fraction variation, consisted of the mixture fraction ( f ) and the mixture fraction variation ( f 0):

∂(ρ f ) µt + (ρ→u f ) = f + sm, (32) ∂t ∇ · ∇ · σt ∇

2 ∂(ρ f ) µt ε 0 → 2 2 2 2 + (ρu f 0 ) = f 0 + Cgµt f Cdρ f 0 , (33) ∂t ∇ · ∇ · σt ∇ ∇ − k

f 0 = f f , (34) − with model constants: σt = 0.85 Cg = 2.86 . Cd = 2.0 Due to the assumption of fast chemical reactions occurring during combustion, the process itself could be calculated (solved) independently of the flow process, forming a set of tables containing solutions (temperature, density, and fraction of individual components of the fuel) that were dependent on only two parameters: mixture fraction and mixture fraction variation. EnergiesBefore 2020, finding13, x FOR thePEER solution REVIEW of the flow field with combustion, data sets describing all possible21 of 29 cases of combustion defined by mixture fraction and turbulence influence represented by the possible mixturemixture fraction variation variation were were defined defined in in discrete discrete form form and and later later interpolated interpolated when when finding finding the flow- the flow-fieldfield solution. solution. DuringDuring simulationsimulation ofof thethe flow,flow, thethe combustioncombustion processprocess results,results, basedbased onon thethe locallocal valuesvalues ofof thethe mixturemixture fractionfraction andand itsits variance,variance, were were retrieved retrieved from from the the prepared prepared tables tables (see (see Figure Figure 20 20).).

Figure 20. An example of the distribution of a two-parameter function of carbon dioxide formation in Figure 20. An example of the distribution of a two-parameter function of carbon dioxide formation in a fuel combustion process. a fuel combustion process. 4.2. Boundary Conditions 4.2. Boundary Conditions It was assumed that the engine operated under atmospheric conditions (pressure and temperature), suckingIt airwas from assumed the environment that the andengine expelling operated exhaust under gases atmospheric to the atmosphere. conditions (pressure and temperature),Therefore, sucking at the inlet air from to the the computational environment domain,and expelling the pressure exhaust inlet gases conditions to the atmosphere. were applied with anTherefore, assumed at turbulence the inlet to level the ofcomputational 3% and a length domain, scale the value pressure of 0.04 inlet m. conditions were applied withAt an the assumed outlet, turbulence the pressure level outlet of 3% conditions and a length were applied.scale value of 0.04 m. AllAt simulatedthe outlet, enginethe pressure walls outlet were treated conditions as adiabatic were applied. with non-slip conditions. All simulated engine walls were treated as adiabatic with non-slip conditions.

4.3. Grid Sensitivity For numerical calculations, a two-dimensional calculation grid was used, which was a reflection of the engine’s circumference section. The current calculation area of the engine, along with the calculation grid, is shown in Figure 21a. Two mesh nets were used to test the effect of the mesh density, one with 130,000 elements and the other with 365,000 elements. The differences in the generated torques did not exceed 8%, and most calculations were made using a finer grid. The computational domain was divided into seven subdomains: four steady and three moving linearly. The moving frame technique was used for the simulation of the moving subdomains. In this technique, the grid in a subdomain was not moving and fluid motion was realized by the addition of motion velocity in all subdomain elements. As shown in Figure 21a, the inlet and outlet subdomains were steady. The subdomain containing blades of the subsonic compressor and subdomain containing the action turbine blades had the same velocity direction and value because the subsonic compressor and turbine were mechanically connected. The domain containing the jet engine components (inlet channel, combustion chamber, and nozzle) had the opposite direction of motion. To fulfill the requirements of the periodicity of the analyzed flow area, the periodic conditions were applied to the rest of the boundaries surrounding the computational domain. The small part of combustion chamber presented in Figure 21b illustrates the system of flame stabilizers with fuel injectors, defined as boundary conditions of the mass flow inlet type.

Energies 2020, 13, 163 21 of 29

4.3. Grid Sensitivity EnergiesFor 2020 numerical, 13, x FOR PEER calculations, REVIEW a two-dimensional calculation grid was used, which was a reflection22 of 29 of the engine’s circumference section. The current calculation area of the engine, along with the The geometry of the turbine and compressor blades were not optimized in any way. The calculation grid, is shown in Figure 21a. Two mesh nets were used to test the effect of the mesh density, presented results were the first attempt to investigate the two contra-rotary rotor configuration of the one with 130,000 elements and the other with 365,000 elements. The differences in the generated ramjet engine. The aim of the investigation was to test the potential features of the new configuration. torques did not exceed 8%, and most calculations were made using a finer grid.

(a) (b)

FigureFigure 21. 21. (a)( aGrid) Grid used used inside inside the thecomputational computational domain domain and andthe applied the applied boundary boundary conditions. conditions. (b) Mesh(b) Mesh used used in the in vicinity the vicinity of the of theinjectors injectors and and flam ﬂamee stabilizers, stabilizers, and and boundary boundary conditions conditions representing representing fuelfuel injectors. injectors.

TheThe stoichiometric computational reference domain mass was divided flow rate into of seventhe fuel subdomains: was calculated four to steady be 0.01859 and threekg/s. moving linearly.To enable The moving the transfer frame or techniquecomparison was of usedthe obtain for theed simulation results with of the the results moving obtained subdomains. for the In fuel this ratestechnique, of other the geometries, grid in a subdomain the variation was of notthe movingengine operating and fluid parameters motion was were realized presented by the in addition relation of tomotion the equivalence velocity in ratio, all subdomain which was elements. defined as the stoichiometric air-fuel ratio to the current air–fuel ratio. As shown in Figure 21a, the inlet and outlet subdomains were steady. The subdomain containing blades of the subsonic compressor and subdomain containing the action turbine blades had the same 5.velocity Calculation direction Results and value because the subsonic compressor and turbine were mechanically connected. TheThe domain main containing purpose of the using jet engine a double-shaft components structur (inlete channel,is to reduce combustion the relatively chamber, high androtational nozzle) speedshad the that opposite the engine direction rotors of would motion. operate at. To this end, several numerical analyses were carried out forTo the fulfill case the in which requirements both shafts of the rotated periodicity at the ofsame the speed analyzed but flowin opposite area, the directions. periodic To conditions obtain properwere applied supersonic to the flow rest conditions of the boundaries in the channel surrounding of the jet the engine, computational both rotors domain. were rotated at 15,915 rpm. UsingThe small this assumption, part of combustion a series of chamber calculations presented for various in Figure values 21b of illustrates fuel mass theflow system rates injected of flame intostabilizers the combustion with fuel chamber injectors, on defined the main as boundary rotor were conditions made. The of graphs the mass below flow present inlet type. the potential performanceThe geometry for the ofassumptions the turbine andunder compressor consideration. blades were not optimized in any way. The presented resultsPractically, were the at first constant attempt rotor to investigaterotational speeds, the two th contra-rotarye air mass flow rotor rate configuration is limited by of the the engine ramjet inletengine. geometry The aim such of that the investigationthe addition of was fuel to not test only the potentialincreases featuresthe heat ofrelease the new and configuration. generated power, but alsoThe decreases stoichiometric the air-fuel reference ratio. mass flow rate of the fuel was calculated to be 0.01859 kg/s. TheTo enableabove thedistribution transfer orof comparisonthe ratio of ofmass the obtainedair and fuel results consumption with the results (related obtained to the forreference the fuel conditions)rates of other presents geometries, the theanalyzed variation range of the of engine the operatingengine working parameters points were presentedunder study. in relation While to maintainingthe equivalence constant ratio, speeds which of was both defined shafts, as the the air stoichiometric mass flow rate air-fuel was kept ratio constant; to the current the only air–fuel variable ratio. was the mass flow of fuel (in the range shown in the chart). The analyzed cases were characterized 5. Calculation Results by the value of the mass ratio of air and fuel consumption in the range from 1.5 (for the highest analyzedThe fuel main dose) purpose up to of4.85 using (for the a double-shaft lowest analyzed structure fuel dose) is to reduceof the stoichiometric the relatively multiple high rotational of the mixture.speeds thatThese the values engine show rotors that would the operateanalyzed at. work To this points end, were several characterized numerical analyses by a high were excess carried of air, out whosefor the purpose case in whichwas to both cool shaftsthe channel rotated walls. at the same speed but in opposite directions. To obtain proper supersonic flow conditions in the channel of the jet engine, both rotors were rotated at 15,915 rpm. 5.1. Comparison of the Overall Engine Characteristics To show the advantages of the proposed contra-rotary ramjet engine (CORRE) idea, results obtained for a single-rotor and a double-rotor construction of the engine are presented in non- dimensional form using the reference parameters defined earlier.

Energies 2020, 13, 163 22 of 29

Using this assumption, a series of calculations for various values of fuel mass flow rates injected into the combustion chamber on the main rotor were made. The graphs below present the potential performance for the assumptions under consideration. Practically, at constant rotor rotational speeds, the air mass flow rate is limited by the engine inlet geometry such that the addition of fuel not only increases the heat release and generated power, but also decreases the air-fuel ratio. The above distribution of the ratio of mass air and fuel consumption (related to the reference conditions) presents the analyzed range of the engine working points under study. While maintaining constant speeds of both shafts, the air mass flow rate was kept constant; the only variable was the mass flow of fuel (in the range shown in the chart). The analyzed cases were characterized by the value of the mass ratio of air and fuel consumption in the range from 1.5 (for the highest analyzed fuel dose) up to 4.85 (for the lowest analyzed fuel dose) of the stoichiometric multiple of the mixture. These values show that the analyzed work points were characterized by a high excess of air, whose purpose was to cool the channel walls.

5.1. Comparison of the Overall Engine Characteristics To show the advantages of the proposed contra-rotary ramjet engine (CORRE) idea, results obtained forEnergies a single-rotor 2020, 13, x FOR and PEER a double-rotor REVIEW construction of the engine are presented in non-dimensional23 formof 29 using the reference parameters deﬁned earlier. The single-rotorsingle-rotor engine engine (rotating (rotating at at 27,000 27,000 rpm) rpm) performance performance was was compared compared with with the double-rotorthe double- enginerotor engine (rotating (rotating at 16,000 at 16,000 rpm) performance.rpm) performance. As a reference, datadata valuesvalues presentedpresented inin SectionSection 2.42.4 werewere applied.applied. InIn FigureFigure 2222,, thethe airair compressioncompression ratioratio realizedrealized byby competingcompeting solutions at the samesame fuelfuel consumptions is is shown. shown. It Itis isclear clear that that a similar a similar or higher or higher compression compression ratio ratiocan be can obtained be obtained using usingthe double the double rotor at rotor only at half only the half ro thetational rotational speeds speeds of the ofsingle the single rotor. rotor.

Figure 22. The air compression ratio in terms of the amount of fuel supplied in one- and Figure 22. The air compression ratio in terms of the amount of fuel supplied in one- and two-shaft two-shaft engines. engines. The graph presented in Figure 23 shows the power generated by both rotors as a function of the ratioThe ofgraph the currentpresented mass in Figure ﬂow of 23 fuel shows to the the reference power generated value. With by both the increaserotors as in a function the amount of the of injectedratio of the fuel, current the power mass values flow of increased fuel to the almost referenc linearly.e value. The With power the curve increase generated in the amount by the single-rotor of injected solutionfuel, the waspower added values for increased comparison. almost One linearly. can notice The apower 100% increasecurve generated of power by generated the single-rotor by the solution was added for comparison. One can notice a 100% increase of power generated by the double-rotor engine version in the same range of fuel consumption due to the power generated by the auxiliary rotor.

Energies 2020, 13, x FOR PEER REVIEW 23 of 29

The single-rotor engine (rotating at 27,000 rpm) performance was compared with the double- rotor engine (rotating at 16,000 rpm) performance. As a reference, data values presented in Section 2.4 were applied. In Figure 22, the air compression ratio realized by competing solutions at the same fuel consumptions is shown. It is clear that a similar or higher compression ratio can be obtained using the double rotor at only half the rotational speeds of the single rotor.

Figure 22. The air compression ratio in terms of the amount of fuel supplied in one- and two-shaft engines.

The graph presented in Figure 23 shows the power generated by both rotors as a function of the ratio of the current mass flow of fuel to the reference value. With the increase in the amount of injected Energies 2020, 13, 163 23 of 29 fuel, the power values increased almost linearly. The power curve generated by the single-rotor solution was added for comparison. One can notice a 100% increase of power generated by the double-rotordouble-rotor engineengine versionversion in in the the same same range range of of fuel fuel consumption consumption due due to theto the power power generated generated by theby auxiliarythe auxiliary rotor. rotor.

Energies 2020, 13, x FOR PEER REVIEW 24 of 29

Figure 23. Variability of the generated power by a single-rotor and double-rotor engine and the power Figure 23. Variability of the generated power by a single-rotor and double-rotor engine and the power generatedgenerated byby itsits rotors.rotors.

TheThe graphgraph inin Figure Figure 24 24 shows shows the the effi efficiencyciency of individualof individual rotors rotors as a as function a function of the of fuel the massfuel mass flow rateflow in rate relation in relation to its reference to its reference value. The value. aggregate The (total)aggregate efficiency (total) and efficiency the main and shaft the effi mainciency shaft was definedefficiency as was the ratiodefined of the as powerthe ratio generated of the power by both gene shaftsrated (or bythe both main shafts shaft (or itself) the main to the shaft value itself) of the to powerthe value that of should the power be generated that should due tobe the generated total combustion due to the of total a given combustion amount of of fuel a given used (Equationsamount of (29)fuel andused (30)). (Equations (29) and (30)).

FigureFigure 24.24. Theoretical overall engine eefficiencyfficiency andand eeffifficiencyciency ofof engineengine componentscomponents comparedcompared withwith thethe eefficiencyfficiency obtainedobtained viavia numericalnumerical simulations.simulations.

The numerical model was limited to an inlet Mach number equal to 2.5 and a lean fuel–air mixture corresponding to combustion outlet temperatures lower than 2000 K and an excess air coefficient higher than 1.5, giving a chance to locally cool the engine channel walls and obtain the highest efficiency. In Figure 24, the theoretical engine efficiency calculated by the analytical model is compared with the efficiency obtained by numerical simulations. One can notice that the single-rotor configuration was just below the theoretical limit and prospects of the development of such a construction is rather limited. The contra-rotary configuration reached 80–85% of its theoretical limit and has the potential for further development. In the area of the simulated low fuel mass flows, one can observe a characteristic efficiency jump resulting from the appropriate location of the normal shockwave inside the inlet of the channel on the main rotor. With the increase in the amount of fuel used, and thus the amount of heat supplied to the air flowing through the combustion chamber, the normal shockwave moved from the vicinity of the combustion chamber toward the initial inlet sections of the jet channel. Both rotors had interesting relationships. The main rotor achieved maximum efficiency values for relatively low fuel mass flow rates and began to lose it (almost linearly) with further increases of the amount of fuel used. The auxiliary rotor, in turn, achieved a maximum efficiency for larger quantities of fuel injected, although the optimal point of engine operation appeared at an excess air coefficient of 3.33 (equivalence ratio 0.3), where the total efficiency of the engine was then the highest and reached up to 31.4%.

Energies 2020, 13, 163 24 of 29

The numerical model was limited to an inlet Mach number equal to 2.5 and a lean fuel–air mixture corresponding to combustion outlet temperatures lower than 2000 K and an excess air coefficient higher than 1.5, giving a chance to locally cool the engine channel walls and obtain the highest efficiency. In Figure 24, the theoretical engine efficiency calculated by the analytical model is compared with the efficiency obtained by numerical simulations. One can notice that the single-rotor configuration was just below the theoretical limit and prospects of the development of such a construction is rather limited. The contra-rotary configuration reached 80–85% of its theoretical limit and has the potential for further development. In the area of the simulated low fuel mass flows, one can observe a characteristic efficiency jump resulting from the appropriate location of the normal shockwave inside the inlet of the channel on the main rotor. With the increase in the amount of fuel used, and thus the amount of heat supplied to the air flowing through the combustion chamber, the normal shockwave moved from the vicinity of the combustion chamber toward the initial inlet sections of the jet channel. Both rotors had interesting relationships. The main rotor achieved maximum efficiency values for relatively low fuel mass flow rates and began to lose it (almost linearly) with further increases of the amount of fuel used. The auxiliary rotor, in turn, achieved a maximum efficiency for larger quantities of fuel injected, although the optimal point of engine operation appeared at an excess air coefficient of 3.33 (equivalence ratio 0.3), where the total efficiency of the engine was then the highest and reached up to 31.4%. The auxiliary rotor achieved only compression and expansion processes, even without any optimization of the compressor and turbine blades, and was characterized by a relatively high efficiency.

5.2. Details of the Flow Structure at the Operational Point To understand the details of engine operation, some detailed information about the flow structure and flow parameters distribution are presented. Knowing the optimal operating parameters and engine performance for equal rotor speeds, the flow conditions inside the engine were analyzed for this configuration. The drawings presented in Figure 25 illustrate the contours of the static pressure inside the engine channels. The air entering the structure was pre-compressed by an axial compressor (minor change compared to the supersonic main rotor channels). It then flowed into the supersonic inlet channels where an oblique shockwave was generated, which was reflected several times inside the channel and ended with a perpendicular (normal) shockwave with the subsonic flow moving downstream to the combustion chamber. The flowing air was slowed down in the diffuser channel, with a simultaneous increase in the static pressure. Inside the combustion chamber, the exhaust gas pressure decreased slightly, and then, flowing through the convergent-divergent nozzle, the combustion products were rapidly accelerated to high speeds, while the static pressure dropped. In the last part of the engine, the moving fumes flowed through the area of the axial turbine of the auxiliary rotor. In this sector, the exhaust gas transferred its energy to the turbine, accelerating it to a sufficiently high rotational speed. The exhaust gas pressure leaving the engine was comparable to the ambient pressure, which minimized the flow losses resulting from the difference in pressure between the environment and the exhaust gases. Energies 2020, 13, x FOR PEER REVIEW 25 of 29

The auxiliary rotor achieved only compression and expansion processes, even without any optimization of the compressor and turbine blades, and was characterized by a relatively high efficiency.

5.2. Details of the Flow Structure at the Operational Point To understand the details of engine operation, some detailed information about the flow structure and flow parameters distribution are presented. Knowing the optimal operating parameters and engine performance for equal rotor speeds, the flow conditions inside the engine were analyzed for this configuration. The drawings presented in Figure 25 illustrate the contours of the static pressure inside the engine channels. The air entering the structure was pre-compressed by an axial compressor (minor change compared to the supersonic main rotor channels). It then flowed into the supersonic inlet channels where an oblique shockwave was generated, which was reflected several times inside the channel and ended with a perpendicular (normal) shockwave with the subsonic flow moving downstream to the combustion chamber. The flowing air was slowed down in the diffuser channel, with a simultaneous increase in the static pressure. Inside the combustion chamber, the exhaust gas pressure decreased slightly, and then, flowing through the convergent-divergent nozzle, the combustion products were rapidly accelerated to high speeds, while the static pressure dropped. In the last part of the engine, the moving fumes flowed through the area of the axial turbine of the auxiliary rotor. In this sector, the exhaust gas transferred its energy to the turbine, accelerating it to a sufficiently high rotational speed. The exhaust gas pressure leaving the engine was comparable to

Energiesthe ambient2020, 13, 163 pressure, which minimized the flow losses resulting from the difference in pressure25 of 29 between the environment and the exhaust gases.

FigureFigure 25. 25.Contours Contours of of the the pressure pressure distribution distribution inside inside the the engine engine channels. channels. The graph presented in Figure 26 shows the distribution of the static pressure ratio at the engine’s The graph presented in Figure 26 shows the distribution of the static pressure ratio at the main rotor channel walls. The shape of the analyzed engine elements is presented just above the graph engine’s main rotor channel walls. The shape of the analyzed engine elements is presented just above in Figure 26. The color of each line corresponds to the color of the data in the graph. Only the data set the graph in Figure 26. The color of each line corresponds to the color of the data in the graph. Only in light blue did not have its equivalent on the sketch of the channel; it is the pressure value at the the data set in light blue did not have its equivalent on the sketch of the channel; it is the pressure inlet to the calculated area (mean value of the atmospheric pressure, treated as a reference). Based value at the inlet to the calculated area (mean value of the atmospheric pressure, treated as a on the above specification, it was easy to determine the total compression of the engine, as well as Energiesreference). 2020, 13Based, x FOR on PEER the REVIEW above specification, it was easy to determine the total compression26 of of the 29 the compression of individual elements. The air flowing into the stream passages already had an engine, as well as the compression of individual elements. The air flowing into the stream passages elevatedthe reference pressure value); relative this was to the a direct inlet pressureeffect of the (it axial was aboutcompressor three timesplaced higher in front than of the the ramjet reference rotor. already had an elevated pressure relative to the inlet pressure (it was about three times higher than value);Then, thisdue was to the a direct interaction effect ofof the the axial shockwave compressor system placed and inthe front diffuser, of the the ramjet flow rotor. pressure Then, increased due to thedramatically interaction ofto thea value shockwave about system12 times and higher the di thanffuser, the the atmospheric flow pressure pressure. increased Therefore, dramatically it can to abe valuestated about that 12 the times total higher compression than the ratio atmospheric of the en pressure.gine could Therefore, reach values it can beof stated12 under that thethe totalgiven compressionconditions. ratio of the engine could reach values of 12 under the given conditions.

Figure 26. Pressure distribution on the walls of the engine channels. Figure 26. Pressure distribution on the walls of the engine channels. The temperature distributions shown in Figures 27 and 28 confirm the areas in which the flow The temperature distributions shown in Figures 27 and 28 confirm the areas in which the flow pressure increased (axial compressor and the area of the diffuser generating the shockwave system). pressure increased (axial compressor and the area of the diffuser generating the shockwave system). The area of maximum temperature was inside the combustion chamber and the temperature of the exhaust gases successively decreased, moving within the convergent-divergent nozzle, and in the area of the axial turbine.

Figure 27. Contours of static temperature inside the engine channels.

Energies 2020, 13, x FOR PEER REVIEW 26 of 29 the reference value); this was a direct effect of the axial compressor placed in front of the ramjet rotor. Then, due to the interaction of the shockwave system and the diffuser, the flow pressure increased dramatically to a value about 12 times higher than the atmospheric pressure. Therefore, it can be stated that the total compression ratio of the engine could reach values of 12 under the given conditions.

Figure 26. Pressure distribution on the walls of the engine channels.

EnergiesThe2020 temperature, 13, 163 distributions shown in Figures 27 and 28 confirm the areas in which the26 flow of 29 pressure increased (axial compressor and the area of the diffuser generating the shockwave system). The area of maximum temperature was inside the combustion chamber and the temperature of the The area of maximum temperature was inside the combustion chamber and the temperature of the exhaust gases successively decreased, moving within the convergent-divergent nozzle, and in the exhaust gases successively decreased, moving within the convergent-divergent nozzle, and in the area area of the axial turbine. of the axial turbine.

Energies 2020, 13, x FOR PEER REVIEW 27 of 29 FigureFigure 27.27. ContoursContours ofof staticstatic temperaturetemperature insideinside thethe engineengine channels.channels.

FigureFigure 28. 28.Static Static temperature temperature distribution distribution on on the the walls walls of of the the engine engine channels. channels. In order to accurately analyze the operation of the flow channels placed on the main shaft, In order to accurately analyze the operation of the flow channels placed on the main shaft, the the above temperature diagram was made for the characteristic internal and external walls of one of above temperature diagram was made for the characteristic internal and external walls of one of the the stream channels, with an additional sketch of the geometry of the analyzed surfaces, aimed at stream channels, with an additional sketch of the geometry of the analyzed surfaces, aimed at facilitating the monitoring of individual changes. In the case of the external walls, their temperature did facilitating the monitoring of individual changes. In the case of the external walls, their temperature not change significantly; however, minor fluctuations in the temperature of these surfaces were found. did not change significantly; however, minor fluctuations in the temperature of these surfaces were The temperature distributions of the internal walls were much more interesting. To a large extent, they found. The temperature distributions of the internal walls were much more interesting. To a large reflected the static pressure distributions. In the inlet area and the inlet diffuser, temperature jumps extent, they reflected the static pressure distributions. In the inlet area and the inlet diffuser, were noticeable due to the shockwaves present in this section (resulting in sudden pressure surges). temperature jumps were noticeable due to the shockwaves present in this section (resulting in sudden The combustion chamber section was characterized by the largest increase in the temperature of the pressure surges). The combustion chamber section was characterized by the largest increase in the walls due to the combustion process. In the convergent-divergent nozzle, as a result of the rapid flue temperature of the walls due to the combustion process. In the convergent-divergent nozzle, as a gas expansion process, a drop in the temperature of the walls was noticeable. result of the rapid flue gas expansion process, a drop in the temperature of the walls was noticeable. The numerical analyses carried out made it possible to determine the optimal parameters of the The numerical analyses carried out made it possible to determine the optimal parameters of the engine’s operation, enabling a high level of efficiency. Table1 presents the optimal working parameters engine’s operation, enabling a high level of efficiency. Table 1 presents the optimal working and the performance of the current version of the engine, which was equipped with 1 cm high channels. parameters and the performance of the current version of the engine, which was equipped with 1 cm high channels.

Table 1. Estimated engine parameters.

Performance Parameter Ramjet Rotor Auxiliary Rotor Summarized Performance Rotational speed (rpm) 15,915 15,915 - Excess air coefficient 1.37 0 1.37 Torque (Nm) 108.7 108.3 217.0 Power (kW) 181.2 180.5 361.7 Efficiency (%) 15.73 - 31.4

6. Conclusions Based on the presented results, it can be concluded that the concept of a two-shaft rotary shockwave compression engine (contra-rotary ramjet engine) was technically feasible, yielding relatively high levels of efficiency. The main findings of the analyzed study were: • The presented numerical model indicated a good match with the analytical model. • The geometry of the flow channels, as well as the use of a second rotary shaft with an axial compressor and turbine, had an important effect on the operational parameters of the engine. • The implementation of a double-rotor design made it possible to reduce the engine shaft speeds from 28,000 rpm (tip speed 840 m/s) to 16,000 rpm (tip speed 540 m/s), keeping the flow characteristics inside the ramjet channels intact. • The modifications considered in this study (using a second rotary shaft with an axial compressor and turbine, as well as minor modifications of the jet channels) made it possible to achieve a

Energies 2020, 13, 163 27 of 29

Table 1. Estimated engine parameters.

Performance Parameter Ramjet Rotor Auxiliary Rotor Summarized Performance Rotational speed (rpm) 15,915 15,915 - Excess air coeﬃcient 1.37 0 1.37 Torque (Nm) 108.7 108.3 217.0 Power (kW) 181.2 180.5 361.7 Eﬃciency (%) 15.73 - 31.4

The presented numerical model indicated a good match with the analytical model. • The geometry of the flow channels, as well as the use of a second rotary shaft with an axial • compressor and turbine, had an important effect on the operational parameters of the engine. The implementation of a double-rotor design made it possible to reduce the engine shaft speeds • from 28,000 rpm (tip speed 840 m/s) to 16,000 rpm (tip speed 540 m/s), keeping the flow characteristics inside the ramjet channels intact. The modifications considered in this study (using a second rotary shaft with an axial compressor • and turbine, as well as minor modifications of the jet channels) made it possible to achieve a significant improvement in engine performance. Assuming that power would be received from both shafts, the channels generated the total power at an efficiency of 31.4%.

The final version of the presented structure was the result of a simple optimization process of flow channels of the main rotor, based on the analysis of characteristic flow parameter visualizations. The geometry of the turbine and compressor blades was not optimized in any way. The presented results were the first attempt to investigate the two contra-rotary rotor configuration of the ramjet engine. The aim of the investigation was to test the potential features of the new configuration. To summarize, further development and improvement of engine performance is possible. Despite using approximated assumptions (adiabatic walls), the results of this analysis are very promising, while at the same time, not precluding further development, which may result in further improvements of the working parameters of the rotational supersonic engine. The analytical model provided information on the theoretical limits of the considered solution. The single-rotor design almost reached the theoretical, not very high performance limit, which means there are no great prospects for further improvement. The design of the contra-rotary ramjet engine has, on the one hand, a relatively high theoretical performance limit, and on the other hand, the efficiency of the existing technical solution simulated using CFD was relatively high but was still far from the theoretical limit. Therefore, there are good prospects for further improvement. However, the numerical calculations in this study concerned a hydrocarbon fuel. Hydrogen could also be used as a fuel in the engine under analysis. The most likely application of the proposed CORRE engine seems to be a hybrid car range extender.

7. Patents A patent claim for the presented idea of the contra-rotary ramjet engine has been submitted. Patent application nr p. 424280. 16 January 2018, “Usprawnienie konstrukcji rotacyjnego silnika cieplnego wykorzystuj ˛acegospr˛e˙zaniefalami uderzeniowymi” (“Improving the design of a rotary heat engine using shock wave compression”), authors: Janusz Piechna, Tomasz Laube. Energies 2020, 13, 163 28 of 29

Author Contributions: Conceptualization, J.P.; methodology, T.L. and J.P.; software, T.L.; validation, J.P. and T.L.; formal analysis, J.P.; investigation, T.L. and J.P.; writing—original draft preparation, J.P. and T.L.; writing—review and editing, J.P. and T.L.; visualization, J.P. and T.L.; supervision, J.P. All authors have read and agreed to the published version of the manuscript. Funding: This research received no external funding. Conﬂicts of Interest: The authors declare no conﬂict of interest.

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