A Review of Shock Wave Compression Rotary Engine Projects, Investigations and Prospects

Abstract

Compression by shock waves is a specific way of compressing gases. It has been practically applied for many years in supersonic flying objects. The idea of using this method in rotary engines is extremely appealing because one disk can replace several or a dozen disks of an axial compressor, significantly reducing the weight and production costs of the engine and lowering the fuel consumption due to possible increased compression ratio. This paper presents a review of existing technical solutions and the results of published research devoted to the construction of shock wave compression rotary engines: patents, scientific publications describing various research methods, numerical calculations, and the experimental results of unusual technical solutions. The characteristic solutions and problems that arose during the implementation of these methods are presented and described. Judging from the presented overview, these have wide application possibilities, and an enormous intellectual and financial effort has been put into the construction of such engines. Conversely, there is a rather hermetic group of scientists involved in this activity.

1. Introduction

Shock wave compression flying heat engines (ramjet) have been known about and developed for many years [1,2]. While they possess the primary advantage of having no moving parts, they also have one significant disadvantage: they require acceleration to supersonic speeds to operate. A shock wave compression rotary engine is basically a simple ramjet engine located on the disk’s circumference at some distance from its axis of rotation. The thrust of the ramjet unit on this arm is converted into torque. The intensity of the shock wave or set of shock waves, and therefore the compression ratio, increases exponentially with the Mach number. In air at Mach 1.6, a compression ratio of 3.5:1 is achieved, while at Mach 2.4 the compression reaches about 15:1. The efficiency of compression depends on the structure of the shock wave array. More oblique shock waves mean higher efficiency. A higher Mach number is obtained by spinning the disc faster.

The idea of a rotary ramjet engine is simple, but it generates many technical problems. Figure 1 shows the general idea and the transition to its more realistic form.

By convention, a ramjet is an engine that contains no moving parts and generates thrust. However, three important functions have to be realized to qualify as such. They compress air with shock waves, generate heat in the combustion chamber and expand hot gases in the exhaust nozzle, providing thrust. When additional moving parts, in the form of compressor disks and turbines, appear in the engine design, it is difficult to call the engine a ramjet. I do not feel competent in changing the usual names, but it seems that it would be appropriate to promote with the systematization of the terminology of shock wave compression rotary engines. A review of existing works will show that compression can take place in both moving and stationary shock wave systems. In light of this, I suggest as a proposal the name—Shock Wave Compression Rotary Engine—for when additional moving elements appear in the design of these systems. In the text I will use both names, depending on the engine design discussed.

Figure 1. (a) The idea of ramjet motors on shaft arms; (b) A realistic channel geometry on the disk of a rotary ramjet engine. The arrows indicate the direction of rotation.

Figure 1. (a) The idea of ramjet motors on shaft arms; (b) A realistic channel geometry on the disk of a rotary ramjet engine. The arrows indicate the direction of rotation.

Figure 2 shows a comparison of the shape of the channels in a ramjet engine and a rotary ramjet engine. The similarities and significant differences are readily apparent.

The shape and arrangement of the rotary engine channels can vary. A critical component of a rotary shock wave compression engine is the compressor. The current pinnacle of such a compressor is a two-stage CO₂ compressor, achieving a 100:1 compression ratio [3]. It uses disks, with an arrangement of channels around the perimeter, with a geometry similar to that shown in Figure 3.

The idea of compressing air with shock waves is simple in concept but difficult in technical implementation. The development of this idea into shock wave compression in rotating machines is another challenge. The main problem is achieving supersonic velocity at the inlet of the rotating channel. This requires very high rotor speeds, which results in very high centrifugal forces.

Located at radius $r$ from the axis of rotation, and rotating at $\omega$ speed, the inlet edge of the shock wave compression channel must have a supersonic velocity $u$ relative to the axially moving air. This velocity is $u=\omega r$ and the Mach number $Ma=\frac{u}{a}$, with the speed of sound defined as $a=\sqrt{kRT}$.

Where

$k$—isentropic exponent (ratio of specific heat at constant pressure to specific heat at constant volume)

$R$—the gas constant of air

$T$—temperature of the air

Thus, with a known radius $r$, the Mach number directly depends on the rotational speed $\omega$

$$Ma=\frac{u}{a}=\frac{\omega r}{\sqrt{kRT}}$$

The tensile stress $\sigma$ in a thin ring, made of material with density, $\rho$ spinning with velocity $u$ is described by the equation

$$\sigma =\rho u^2$$

Additionally, in a thin ring made of a carbon composite with a density $\rho$ of 1760 kg/m³, spinning at a peripheral velocity $u$ of 1000 m/s, the tensile stress $\sigma$ reaches values of 1.76 GPa at the claimed strength of this material of 1.8 GPa.

For classic materials (steel) and other disk shapes, the maximum speed may be different.

Material properties are therefore the limiting factor, and in practice a peripheral speed of 1000 m/s is taken as the maximum.

The development of the idea of a rotary shock wave compression engine, and the huge intellectual potential focused on this topic, was due to the undeniable advantages of this solution. The work carried out on the idea of the rotary shock wave compression engine was conducted mainly in academic centers and small and large companies.

Several prototypes built in academic centers showed the potential capabilities of this technology, but they also revealed a number of problems.

Industrial companies have exploited the idea of shock wave compression in the specific niche of compressing of carbon dioxide at very high pressures.

The publications available on this are from Université de Sherbrooke, University of Michigan, Arizona State University and Warsaw University of Technology, as well as the firms RAMgen and Dresser-Rand.

The intellectual effort related to this topic, presented in the form of scientific publications, is also evident in the resulting series of patents.

2. Projects Known Only from Patents

The unpublished activities of groups of individuals or companies are manifested in the form of patents. A review of these usually gives a picture of the extent of interest in the subject and specific design solutions. By paying attention to construction details, one can read the physical phenomena hidden behind them.

Figure 4, Figure 5, Figure 6, Figure 7, Figure 8, Figure 9, Figure 10, Figure 11, Figure 12, Figure 13, Figure 14, Figure 15, Figure 16 and Figure 17 indicate characteristic or interesting elements of patented design solutions for shock wave compression rotary engines. It seems that the first patent presenting the idea of shock wave compression rotary engine holistically is the patent [4] (Improvements in gas generators) from 1971. The main idea of the patent is shown in Figure 4.

The classic jet engine arrangement here uses two rotors, the inner rotor bearing on the shaft of the outer rotor. The outer rotor, bearing in the housing, contains two disks. One is a disk with vanes that imparts the rotation to the flowing air and which is driven by an action turbine through a shaft connecting them. The inner rotor, which rotates in the direction opposite to that of the outer rotor, contains a system of parallel compression channels extended through a combustion chamber and supersonic nozzle.

There is also an inner rotor version with a hollow space between the ends of the compression channels and the beginnings of the supersonic nozzles. The hollow space is a common combustion chamber fed with fuel through the outer casing.

The next patents [5] (Ramjet Engine for Power Generation) and [6] (Method and apparatus for power generation using rotating ramjet which compresses inlet air and expands exhaust gas against stationary peripheral wall) arrived in 1998.

Publication [7] describes the idea of this last patent, with some analytical estimations given.

As can be seen in Figure 5 simple rotary ramjet engine idea, from the beginning generated very complicated technical solutions.

Figure 5. General view (a) and cross section (b) of patented engine from patent [6]. Circles indicate interesting details of the object.

Figure 5. General view (a) and cross section (b) of patented engine from patent [6]. Circles indicate interesting details of the object.

The next patents under review [8,9] (Ramjet Engine for Power Generation) were published in 2001. General view of the air compressing rotor is depicted in Figure 6. Spiral channels of variable height, containing compression segments, a combustion chamber and expansion nozzles were located on the periphery of rotor. Around a single rotor, a complex supporting system was arranged. The presented solution was the basis for many other constructions.

Figure 6. Air compressing rotor with ramps generating shock waves from patent [8]. Circles indicate interesting details of the object.

Figure 6. Air compressing rotor with ramps generating shock waves from patent [8]. Circles indicate interesting details of the object.

In 2002, a patent was published [10] (Method and apparatus for power generation using rotating ramjets) referring to the primitive idea of locating ramjet engines on the arm at a certain distance from the axis of the arm rotation. Two thrusters were placed at the ends of a beam, the axis at its midpoint, with a complex system of recovery, heat and mechanical energy by an additional action turbine bearing at a very large radius (see Figure 7).

Figure 7. (a) Patent of a solution with a ramjet engine at the ends of a single beam spinning around its center; (b) general engine arrangement from patent [10]. Circles indicate interesting details of the object.

Figure 7. (a) Patent of a solution with a ramjet engine at the ends of a single beam spinning around its center; (b) general engine arrangement from patent [10]. Circles indicate interesting details of the object.

In 2004, another patent [11] (Compact rotary Ramjet engine generator set) was published.

As can be seen in Figure 8, there is a single rotor. This contains helical channels of varying heights that form compression channels, combustion chambers and exhaust nozzles. Due to the presence of the turbine, such an engine configuration should be called a shock wave compression rotary engine.

Figure 8. An engine in the form of a single disk with engine channels around its perimeter, from patent [11]. Circles indicate interesting details of the object.

Figure 8. An engine in the form of a single disk with engine channels around its perimeter, from patent [11]. Circles indicate interesting details of the object.

In 2006, an interesting solution was patented [12] (Gas turbine power plant with supersonic gas compressor).

As can be noticed in Figure 9, the engine in the proprietary version contains 70–80% of the components of a classic turbine engine with a shock wave compressor disk. Additionally, in this case due to the presence of radial pre-compressor and turbines, such an engine configuration should be called a shock wave compression rotary engine.

Figure 9. General view of the engine utilizing shock wave compression rotor (from [12]). Circles indicate interesting details of the object.

Figure 9. General view of the engine utilizing shock wave compression rotor (from [12]). Circles indicate interesting details of the object.

From 1996 to 2012, the firm Ragmen filed a number of patents relating to general and specific solutions for the shock wave compression rotary engines, and are as follows: [13] (Method and apparatus for starting supersonic compressors), [14] (Supersonic compressor), [15] (Gas turbine with supersonic compressor), [16] (Supersonic Compressor), [17] (Gas turbine engine), [18] (Supersonic compressor), [19] (Vortex generators), [20] (Stator for supersonic compressor), [21] (Vortex combustor for low NOX emissions when burning lean premixed high hydrogen content), and [22] (Vortex combustor for low NOX emissions when burning lean premixed high hydrogen content).

Special attention should be paid here to the patent [15] containing a revolutionary solution in the form of a fixed compression channel with shock waves, a vortex trap-type combustion chamber and a supersonic expansion nozzle. A fixed compression ramp geometry with a wall layer removal system exists in the compression region.

Figure 10 and Figure 11 show two versions of this particular solution.

Figure 10. Engine with pre-swirl rotor and multistage turbine rotor and a set of fixed shock wave compression channels and a classic combustion chamber from patent [15]. Circles indicate interesting details of the object.

Figure 10. Engine with pre-swirl rotor and multistage turbine rotor and a set of fixed shock wave compression channels and a classic combustion chamber from patent [15]. Circles indicate interesting details of the object.

Figure 11. Engine with pre-swirl rotor and set of fixed shock wave compression channels and trap vortex-type combustion chamber. From patent [15]. Circles indicate interesting details of the object.

Figure 11. Engine with pre-swirl rotor and set of fixed shock wave compression channels and trap vortex-type combustion chamber. From patent [15]. Circles indicate interesting details of the object.

The patent details a completely new approach to shock wave compression. A moving rotor with an array of blades imparts supersonic velocity to the air and directs it to a stationary array of compression channels in a pattern of oblique shock waves and a final normal shock wave. The duct system contains obstacles that form an area of vortex separation and capture in which combustion occurs, and which is characterized by very low NOX emissions. The solution is interesting but requires high rotational speeds of the turbine rotor and compressor, coupled with a single shaft bearing in the housing.

The patents cover two pre-swirl rotor blade geometries. The solution, with a system of stationary spiral compression ducts forming the combustion chamber and expansion nozzle, is very interesting, has great potential, and seems to be undescribed in the literature.

One of the interesting solutions in the last patent is a movable compression ramp that can raise for operation at high compression ratios and lower during startup to form a suitable and stable arrangement of oblique shock waves over the full operating range. The moving elements of the ramp have a slot arrangement for draining the wall layer during the startup process. The details of that solution are presented in Figure 12.

Figure 12. Movable compression ramp with a slot arrangement for draining the wall layer during startup from patent [15]. Circles indicate interesting details of the object.

Figure 12. Movable compression ramp with a slot arrangement for draining the wall layer during startup from patent [15]. Circles indicate interesting details of the object.

Patent [23] (Rotary Ramjet Engine) from 2008 presents a solution that uses a ring with an internal channel arrangement.

A complicated system for assembling components is characteristic of this solution (see Figure 13). Generally, a single rotor with completely closed channels is formed. This is an arrangement of parallel compression channels, with a combustion chamber and supersonic nozzle, but is located on the internal surface of a ceramic disk. The system ultimately constitutes a classic arrangement of spiral channels arranged on a rotating disk.

Figure 13. An engine solution with channels on internal side of rotating ring: (a) Cross section; (b) Expanded view from patent [23]. Circles indicate interesting details of the object.

Figure 13. An engine solution with channels on internal side of rotating ring: (a) Cross section; (b) Expanded view from patent [23]. Circles indicate interesting details of the object.

Similar solution was patented [24] (Rotary ramjet turbo-generator) in 2010. The idea of this patent is described in the work [25] and presented in Figure 14.

Figure 14. (a) Cross section; (b) Channel arrangement on the hub from patent [24]. Circles indicate interesting details of the object.

Figure 14. (a) Cross section; (b) Channel arrangement on the hub from patent [24]. Circles indicate interesting details of the object.

A group of scientists from Sherbrook University has filed a patent application [26] (Rotor assembly having a concentric arrangement of a turbine portion, a cooling channel and reinforcement wall) for a shock wave compression rotary engine, with reverse flow through a single rotor. The cross section of the patented engine is presented in Figure 15.

Figure 15. Cross section of the engine with reversed flow from patent [26]. Circles indicate interesting details of the object.

Figure 15. Cross section of the engine with reversed flow from patent [26]. Circles indicate interesting details of the object.

Details of the design, fabrication and testing are included in the paper [27] and discussed in the following section.

In 2015 patent [28] (Gas turbine engine), presenting a stationary compression channel with a boundary layer extraction system, was published. In this solution, the compression channels are stationary

In 2017, another group at Sherbrook University patented [29] (Combustion Systems and Combustion System Components for Rotary Ramjet Engines) an engine design solution called R4E, the principles, design and test results of which will be discussed later. It is an example of a typical ramjet rotary engine.

The solution is very compact, with compression channels, a central combustion chamber and expansion nozzles being located on the single ring. Fuel injection is realized in the stator in front of the intake.

A certain disadvantage of this solution, presented in Figure 16, is the introduction of fuel into the incoming air before it is compressed. When hydrogen is used as a fuel, this lowers the Mach number at the inlet to that of the compression channels. In the proposed solution, centrifugal forces are transmitted through a lightweight composite ring on the outer surface of the disk.

Figure 16. General view and cross section of engine from patent [29]. Circles indicate interesting details of the object.

Figure 16. General view and cross section of engine from patent [29]. Circles indicate interesting details of the object.

Of interest is the use of an angled labyrinth seal on the sides of the rotating disk.

Radial and axial flame stabilizers, with a central common combustion chamber, can be noticed in Figure 17.

Figure 17. General view and cross section of engine from patents [29,30]. Circles indicate interesting details of the object.

Figure 17. General view and cross section of engine from patents [29,30]. Circles indicate interesting details of the object.

The next patent discussed [30] (High G-field Combustion) has been issued to cover details of the solution for a combustion chamber operating under very high centrifugal force loads.

3. Scientific Publications

3.1. Analytical Work

The first theoretical scientific paper presenting an analytical model of the elements of a shock wave compression rotary engine is a paper [25] from 2006.

This work presents the idea of locating a system of shaped channels of a ramjet engine on the inner surface of a rotor ring, which is loaded with tensile forces and supported by ceramic elements loaded in this system only by the compressive forces from centrifugal forces. According to the authors, the combustor exit temperature can reach 1850 K without any cooling, and with moderate cooling can correspond to the current limit of 1920 K for conventional gas turbines. This is attained in a rotary ramjet engine with flow on the inner side of the ring with internal flow channels and with SiNi ceramic ramjet channels via a method called inside-out by the authors.

In Figure 18, schematic views of the ceramic rotor are presented, showing inside-out helical ramjet channels and ramjet flowpath in helical channels (top) and cross-sectional views (bottom).

The theoretical thermodynamic calculations of such a flow system are included in this paper.

3.2. Numerical Works

The first paper containing complete numerical model of a rotating shock wave compression engine is the 2014 paper [31].

This paper, published in the niche journal Archivum Combustionis, presents the process of building a computational model of an axisymmetric RAM engine, using a two-dimensional modified version of it for use in a rotary engine. The authors’ idea was to build a two-dimensional numerical model of an engine with axisymmetric geometry, including modeling of compressible flow with a shock wave system in the compression part, fuel combustion in the combustion chamber and exhaust gas expansion in a supersonic nozzle, and optimizing of the geometry of the engine channels for maximum thrust. The geometry of the internal channels of the flying ramjet engine, thus selected, was to be adapted to a rotary engine.

The main stage of the work was to build the geometry of the channels on the periphery of the rotary engine disk and simulate its operation. In Figure 19, an example is given of the geometry of the engine channels, distributed around the perimeter of the rotating disk, and the pressure distributions in the peripheral section at half the height of the channel.

During the ongoing work covering the entire flow in the engine channels, it was possible to learn about the coupling between its components and the amount of heat generated in the combustion process. Changes in the temperature of the exhaust gas upstream of the exhaust nozzle changed the mass output of the exhaust gas and affected the structure of shock waves in the compressing part of the ducts. An example of such changes is shown in Figure 20.

The presented results of numerical simulations appear to be the first results of numerical calculations obtained for such a complex flow model, involving the simulation of compressible flow with combustion and heat transfer in the solid parts of the engine.

Based on the presented results, it can be concluded that the concept of a rotary ramjet engine in the analyzed geometry can be technically realized, achieving acceptable efficiency. As shown by performing calculations for a number of variants of engine channels, the details of their geometry have a significant impact on the performance of the engine.

A 0.3 m radius engine disk rotates at 28,000 rpm and is equipped with four 1 cm high channels, allowing the generation of a maximum power of 270 kW with an efficiency of 18%, and a maximum power of 370 kW with a slight (2%) decrease in efficiency.

To check the influence of three-dimensional effects, the flow in the moving channels of the 3D model was simulated. The analysis showed that the three-dimensional flow effects modify the flow structure in the channels, and so their geometry needs further modification.

Figure 21 shows the 3D model mesh and pressure distributions at the mid-height of the engine flow channels

Optimistically, there is a wide range of possible fuel flow rates corresponding to high values of engine efficiency. This means that the engine could be very flexible in operation, and the power generated could be easily controlled.

In 2014, a paper [32] appeared that numerically analyzed only one of the components of a shock wave compression rotary engine, its compression system.

The authors developed a 2D model of the compression channel based on data from the literature and validated their model by comparing the pressure distributions obtained with data from the existing publications They analyzed the behavior of the compression system under the influence of perturbations of the rotational speed of the channel. The results indicated that rotor spinning has a significant effect on the flow excitation characteristics and performance of the Rampressor inlet.

By increasing the rotor spinning frequency and spinning amplitude, the complexity of compressor inlet excitation increases, and the stability of the Rampressor inlet deteriorates.

3.3. Analytical and Numerical Work

An extension of an earlier paper [31] from 2014 is the work [33] from 2019. In this paper, attention was drawn to the very high discharge velocities of the engine nozzles described in [31].

This allowed the thesis that this energy could be used in a counter-rotating turbine driving a counter-rotating compression disk. The geometry of the flow channels located at the periphery of the main disk, along with an indication of its characteristic cross sections and fragments, is shown in Figure 22.

This paper presents an analytical model of engine operation with an assumed compression model in a system of two oblique waves, one normal shock wave and flow in a subsonic diffuser, adding the heat of the combustion of fuel in the combustion chamber and expansion in a convergent–divergent nozzle.

The engine scheme under consideration is shown in Figure 22. Figure 23 shows the reciprocal relationship of rotor speeds and the flowing medium. Such a design, with two-counter rotating rotors, is a typical example of a shock wave compression rotary engine.

The results obtained with the analytical model were compared with the results of numerical calculations. The comparisons are presented in a graphical form. The dependence of compression, power ratio (actual to reference) and overall engine efficiency on the equivalence ratios for a single-shaft engine and a twin-shaft engine, calculated analytically and obtained from numerical simulations, is shown.

Figure 24 shows the design diagrams of the single-shaft and double-shaft engines.

Figure 25 shows a comparison of the efficiency of the one-shaft and two-shaft engines, calculated analytically and obtained from numerical simulations as a function of the equivalence ratio. Based on the presented results, it can be concluded that the concept of a contra-rotary ramjet engine is technically feasible, giving a relatively high level of efficiency.

The main conclusions of the analyzed study were as follows. The numerical model indicated good agreement with the analytical model. The geometry of the flow channels, as well as the use of a second counter rotating shaft with an axial compressor and turbine, had a significant impact on the engine’s performance. The use of a twin-rotor design allowed the engine shaft speed to be reduced, from 28,000 rpm (tip speed of 840 m/s) to 16,000 rpm (tip speed of 540 m/s), while maintaining the flow characteristics within the ramjet channels.

The modifications considered in this study (the use of a second counter rotating shaft with an axial compressor and turbine, as well as minor modifications to 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 total power at an efficiency of 31.4%.

The analytical model provided information about the theoretical limitations of the considered solution. The single-rotor design has almost reached the theoretical, not very high performance limit, which means that there is little prospect of further improvement.

The contra-rotary ramjet engine design, on the one hand, has a relatively high theoretical performance limit. On the other hand, the efficiency of the existing technical solution simulated with CFD was relatively high, but still far from the theoretical limit. Therefore, there are good prospects for further improvement.

However, the numerical calculations in this study were for hydrocarbon fuel. Additionally, hydrogen could be used as a fuel in the analyzed engine.

3.4. Design, Analytical Calculations, Prototype Numerical Calculations, Experimental Tests

The paper [27] presents the design assumptions, calculation results and test results of a prototype engine developed at Sherbrook University, based on an inactive patent [34]. This work describes an engine with reverse flow through a single rotor. A version of the engine was developed that compresses air in a shock wave system, with a stationary combustion chamber, a supersonic expansion nozzle and an action turbine using reverse flow in a single supersonic rotor. A design was developed, and a prototype engine named supersonic rim–rotor gas turbine (SRGT) was fabricated, which is a gas turbine with a supersonic axial compressor and a transonic axial turbine concentrically located in a single rotating disk. The paper presents a preliminary design of a 5 kW SRGT prototype, with an outer diameter of 72.5 mm and a rotational speed of 125,000 rpm.

This new flow system, called the supersonic rim–rotor gas turbine (SRGT), uses a single rotating assembly containing a central hub, supersonic turbine rotor, supersonic compressor rotor and outer support ring. The compressor and turbine were located on a single reverse-flow rotor.

Overall view and the cross section of the SRGT engine are presented in Figure 26.

The critical part of the engine is a supersonic compressor, divided into rotating and steady parts, as is depicted in Figure 27. In used 1D flow models, oblique shock waves are expected in rotating and steady parts of compressor. So, air compression is realized in a rotating shock wave system, as well as in a stationary shock wave system.

Taking into account the flow diagram shown in Figure 27, for the rotor and stator values, it can be assumed that the rotor of the compressor acted as a supersonic pre-swirl element and that the main compression process was carried out in the stator part. This is an interesting solution.

The details of the disassembled rotor—external compressor and internal turbine with expected velocity triangles—are shown in Figure 28.

This paper presents the details of a set of several separate analytical and numerical models used during the structural design of the various engine components.

The engine flow model was divided into independent segments.

One of the most important of these was a 1D model of the compression process made using shock waves. The compressor rotor is supersonic, with an oblique shock wave on either side of each rotor blade. The flow analysis stopped at using the 1D model for the inlet duct, the compressor rotor and stator downstream. The one-dimensional model, while it expanded to include heat transfer and friction, does not take into account the effects of multidimensional flow, wall layer interaction and transient flow effects.

Figure 28. Disassembled rotor—external compressor (left) and internal turbine (right) with expected velocity triangles, (from [35]). Arrows indicate flow direction and rotor rotation direction.

Figure 28. Disassembled rotor—external compressor (left) and internal turbine (right) with expected velocity triangles, (from [35]). Arrows indicate flow direction and rotor rotation direction.

The curvilinear geometry of the compressor blades was selected by the characteristics method, ensuring that the reflection of oblique shock waves is avoided for a given supersonic Mach number at the inlet. The flow remains supersonic at a relatively constant Mach number throughout the rotor. The compressor rotor provides a supersonic pre-swirl stage for the stator. The compressor stator inlet is similar to the compressor rotor inlet, with an oblique shock wave on each side of each blade, with no reflection. Just after the oblique shock wave there is a normal shock wave, and the flow then remains subsonic all the way to the combustion chamber. The stator provides axial flow at the combustion chamber inlet. The compressor diffuser is completely subsonic and reduces the flow velocity to a Mach number of 0.1 at the combustion chamber inlet.

Another independently designed and optimized engine component was the combustion chamber. The authors used a zero-equation model and a three-dimensional numerical model with simulation of the combustion process in the design process.

Initially, the 0-equation model was used with a 4-zone division, and then the numerical simulation capabilities were used. The 3D numerical calculations were for a 36-degree annular segment of the combustion chamber. Details of the design process can be found in the paper [36]. Simulations were performed using the solver Fluent with a non-premixed combustion model. Modifications to the distribution of the covers and their openings were optimized. During the simulation, a study of the sensitivity of the solution to the density of the grid, discretizing the computational area, was carried out. Two turbulence models were compared: realizable k-ε and transport k-ω with shear stress. For each model, the effect of turbulence intensity at the combustion chamber inlet was analyzed: at low turbulence level (1%), medium turbulence level (10%) and high turbulence level (20%). The non-premixed combustion model used in the study responds strongly to the level of turbulence at the combustion chamber inlet. The study showed that both turbulence models produce similar results, except for the maximum temperature at the combustion chamber outlet. The results of the coupled heat transfer analysis show similar behavior with a lower maximum outlet temperature. From the results of this sensitivity study, it was concluded that the CFD models show sufficient robustness and accuracy to be used at the design stage.

Based on the results of the design analysis, a prototype engine was fabricated, and preliminary tests were conducted. The engine accelerated to 117,000 rpm after a fuel injection and ignition at 102,000 rpm. During testing, it proved necessary to modify the hydrogen supply due to flow being blocked by excessively high exhaust gas temperatures at the turbine inlet. After ignition, oscillations were noticed coming from adjusting the fuel flow rate aimed at maintaining an exhaust temperature of 1000 K. After ignition, hot gases in the combustion chamber caused an increase in backpressure, causing a decrease in compressor mass airflow, necessitating fuel flow adjustments. Similar effects of flue gas overheating in the form of a change in flow structure were also observed in calculations in the paper [31]. The average outlet temperature observed during steady state was 975 K.

During tests of the operation of the compression system without combustion, it was noted that the achieved air mass flow rate was significantly lower than expected. The expected compression was estimated at 2.75, and the maximum obtained was 1.8. Given current knowledge, it can be assumed that the main reason for this could be the lack of pre-swirl vanes in the duct before the compressor rotor. Without the guide vanes, the vortex formed in the inlet duct reduced the relative inflow velocity to the compressor rotor blades.

Nevertheless, the engine worked and could be the basis for the further development of this interesting and novel design.

In parallel, an engine design with a slightly different concept of its construction was developed at Sherbrook University. The engine in question, named R4E, had a very compact design and a sophisticated flow system. A comprehensive description of a rotary ramjet design is presented in in publication [37]. The idea of the engine boils down to an annular flow design with a short system of parallel shaped compression ducts, a central annular combustion chamber and a short system of parallel arranged expansion nozzles. The engine has a very compact design and, with its small diameter, develops very high speeds (more than 100,000 rpm). It is important to emphasize here the intersecting design of the rotor whose outer ring transmits all centrifugal forces. The rotor disk itself can be thin because it carries only small circumferential forces. The results of calculations and experimental tests of the mechanical part of the structure are presented in the paper [38].

Figure 29 shows a view of the complex shape of the rotor and cross sections of the patented version of the motor.

The paper [36] presents the development of a quasi-one-dimensional aerothermodynamic model for predicting the performance of a novel rotary ramjet engine (R4E). This geometry-dependent model accounts for all major physical effects: periodic intake and exhaust, friction, high g field combustion, heat transfer, shock waves and leakage losses. A simple analytical combustion model that takes into account buoyancy force to estimate the appropriate burner length is needed to achieve complete combustion. The model shows that such a combustion concept is scalable. This is because length and diameter scale together for a given tangential velocity or, in the case of a ramjet rotary engine, compression ratio. Based on the first estimation of the burner length, a three-dimensional version of it was designed, and both ignition and stationary combustion were studied using three-dimensional numerical simulations.

The results of calculations of the three-dimensional combustion process in the engine compartment are presented in papers [39,40].

The ignition simulations show that the flame stabilizers correctly capture the flame coming from the inlets, and that the flame propagates rapidly toward the external flame stabilizers, which ensure complete combustion. The feasibility of the chamber’s concept of operation is shown, with a predicted combustion efficiency of more than 85% for all tested speeds.

Papers [39,40] present the test results of a prototype made of easy-to-manufacture materials and designed for short-term operation, shown in Figure 29. They showed successful ignition at tangential velocities ranging from 250 to 380 m/s. Combustion efficiency was estimated at 60–75%, based on exhaust gas temperature for centrifugal accelerations up to 700,000× g.

Due to the successful design of the combustion chamber, the recorded positive power at the engine shaft manifested itself at tangential velocities of 277 to 328 m/s, a first for this type of engine. During testing, the engine went from generating 240 W at a peripheral speed of 277 m/s to producing 320 W at a speed of 326 m/s.

The R4E could also be used as a turbojet to directly produce thrust.

The paper [41] contains the results of supersonic tunnel testing of a cascade of rotary ramjet engine compression vanes and their application to the R4E engine.

4. Ramgen’s Large Engine Project

Ramgen Power Systems has been working on the use of shock wave compression in rotating machinery for a number of years. The work has involved rotary ramjet engines, as well as their applications, in the compression system itself for compressing process gases. Analysis of these works is hampered by a number of parallel activities often merging at experimental test sites. Emerging publications often contain a number of common elements.

Papers [42,43] present the working principles and test results of a pre-prototype ramjet engine and the results of CFD calculations of a three-dimensional combustion chamber model with a flame stabilizer. The engine is built in a classical system of oblique circumferential channels so that its variable heights form the shock wave compression ramp system, combustion chamber and expansion nozzle. The paper presents the results of 3D CFD calculations of the combustion chamber and of the corresponding tests on a pre-prototype engine. The scheme of the flow system in the engine’s channels is presented in Figure 30.

The pre-prototype engine was fully assembled in Tacoma, WA, in July 1998. Tests conducted in 1999 confirmed ignition and flame maintenance at slow rotor speeds and flame maintenance at idle rotor speeds, the mechanical strength of the rotor at supersonic speeds, and the overall integrity of the entire system. The development work carried out from late 1999 to September 2000 focused on improving combustion stability, methods for delivering a variety of, sometimes unusual, fuel, and surface cooling systems using an air film. These efforts resulted in significant progress toward operating the engine at full rotor speeds (4300 rpm, Mach 1.1 inflow conditions).

Parallel work was carried out by another group of researchers with ties to the military industry. The paper [44] presents basic information on the design of rotary engines from the point of view of their usefulness in the military. The paper includes a description of the assumptions of the design of an engine with an electric generator for vehicle propulsion. The Defense Advanced Research Projects Agency (DARPA) has awarded a contract to Ramgen Power Systems to complete the design definition and layout of the proposed ASCE (Advance Supersonic Component Engine) concept.

The goal of the project was to provide a new engine that will meet the requirements for long life, high efficiency and long time periods between periodic overhauls in vehicle propulsion applications.

The 1000 hp engine, proposed for DARPA, is a two-stage counter-rotating engine with a 30:1 pressure ratio and ~40% simple-cycle efficiency. The efficient multi-fuel engine directly drives a permanent magnet (PM) generator/electric motor, and is designed for the electric propulsion of hybrid vehicles.

The ASCE system delivers fuel consumption equal to or less than reciprocating diesel engines in this range of generated power, but with a 10:1 reduction in weight and a 4:1 improvement in service interval time. This is a 2:1 increase in fuel efficiency at full power compared to existing gas turbines in this size range. Pressure increase ratios of 40:1 with ~45 + % cycle efficiency are considered to be achievable targets for its further development.

There was also a report in 2006 [45] that laid out the premise of a shock wave compression rotary engine for military applications. The report gave the basic equations of compression by shock waves in the intake channel. A scheme was given for forming a supersonic expansion nozzle based on the method of characteristics.

Additionally, discussed were the basic assumptions of the advanced supersonic component engine (ASCE)—a multi-fuel, shock wave compression rotary engine driving an electric generator.

Another report [46] about the possible military applications of ramjet rotary engines was published in 2007. This report contains a number of interesting details about the construction of such an engine. Among other things, the rotary engine uses supersonic expansion nozzles that generate torque on the engine shaft.

Figure 31 shows a nozzle with a wall outline, obtained using the characteristics method, as well as the results of numerical simulations, confirming the correctness of this shape.

The paper also presents the assumptions and results of the numerical simulations of the operation of a modern low-NOx emission vortex trap combustion chamber (see Figure 32).

Figure 33 shows the pre-swirl nozzles palisade, which is essential for compressor operation but has not been appreciated until now, increasing relative inlet velocity at rotor channels inlets.

Ramgen has successfully demonstrated the correct operation of its Rampressor supersonic compressor as part of a 12-month test program conducted at the Boeing Company’s Nozzle Test Facility (NTF) in Seattle, WA, USA. The main objective of this test was to demonstrate the successful adaptation of supersonic air intake design and operating methods in the rotating ducts of the supersonic compressor. A Rampressor rotor, with a pressure ratio of 2.5:1, was thoroughly instrumented to measure the performance and operating characteristics of the test rotor. It was shown how, after running the rotor to 80% speed and tuning the control parameters, there was an increase in discharge and, after throttling adjustment, also an increase in compression.

After completing the RP-1 test, Ramgen started the Rampressor-2 (RP-2) test program to demonstrate the supersonic compression of the rotor at higher compressions. These tests were again supervised by Boeing at the world-class Nozzle Test Facility in Seattle, WA, USA.

Figure 34 shows the much larger palisade of pre-swirl nozzles necessary for the new Rampressor-2 compressor to operate at higher Mach numbers at the inlet and compressions up to 13:1 magnitude.

The target rotor speed is 41,439 rpm, with a disk radius of 5.45 inches—13.85 cm.

In selecting the new channel geometry, methods of three-dimensional numerical simulations were used to check its correctness.

Figure 35 shows the results from the CFD analysis of the shape of the compression channel, designed to operate with an inflow Mach number of 2.4. The figure shows the Mach number contours in three planes routed in the engine compression channel. This image shows the structure of oblique shock waves created by the compression ramp, oblique shock waves reflected from the stationary casing and a normal shock wave generated in the throat region of the channel in front of the subsonic diffuser. The shape of the compression ramp shown in Figure 35 was designed for an average inlet Mach number of 2.4, and the simulation shown indicates the achievement of a supersonic rotor pressure ratio of 13:1, with an adiabatic efficiency of 89.4 percent.

Figure 36 shows only slight changes in the Mach distribution due to the development of the boundary layer.

As an illustration of the target ASCA engine design, the geometry presented in Figure 36 is often shown.

Figure 36. Proposed ASCE configuration (from [46]).

Figure 36. Proposed ASCE configuration (from [46]).

The details of the design solutions changed in subsequent years as the research and design work progressed. The last fairly detailed description of the design was included in the paper [47] (see Figure 37).

The paper includes a very interesting illustration, shown in Figure 38. It contains the schematic arrangement and directions of rotation of the individual rotors and the steady vanes separating them. This drawing allows for an easier understanding of the bearing arrangement of the rotors of this engine.

There are still works focused on individual components of the ASCE engine.

The paper [48] provides the results of three-dimensional CFD calculations of the compressor of this engine. The design methodology and predicted performance of a high-pressure ratio supersonic compression stage were both presented. Two methods of forming a focused and defocused shock wave system, shown in Figure 39, were compared. The comparison demonstrated the potential benefits of the defocused shock system for off-design performance.

The numerical scheme and turbulence model used was shown to capture the physics of boundary layers, shock wave/boundary layer interaction and flow separation. It was concluded that the CFD predictions of the Rampressor performance would be adequately reliable.

The results of the experimental and numerical testing of the Rampressor-2 were presented in the paper [49] from 2008.

Tests are described of a supersonic rotor of a single-stage axial compressor with a pressure ratio of 8:1, referred to as Rampressor-2. The design of this shock wave compression system is based on the principles used in supersonic inlets, consisting of an oblique wave compression system and near-wall layer treatment. The rotor consists of three channels, in which the shock system is provided by a ramp, throat and diffuser, which are profiled on the hub.

The technology was previously demonstrated in an experimental test compressor with a pressure ratio of 2.3:1 (Rampressor-1). The measurements were compared with numerical predictions. Further development to improve the performance of the Rampressor was discussed.

The paper [49] presented the geometry schemes of a shock wave compression rotor, with an arrangement of three channels around the perimeter of the rotor and with a palisade of pre-swirl vanes to increase the relative velocity of air inflow into the inlets of the rotor channels. Consequently, an increase in the Mach numbers was achieved.

In this work, more details of the inflow system were provided for the first time.

An annular channel, bounded by a bell throat and a center body, fed the inlet guide vanes (IGV), as shown in Figure 40. The IGV outlet angle was set at 61°, and IGV Mach numbers from 0.7 to 0.9 generated a triangle of inflow velocities into the rotor channels for relative Mach numbers of 2.4 to 2.7. The rotor exhaust was discharged into the ring, and then radially into the collection chamber. Comparisons of the results, obtained experimentally with the results of CFD calculations, are presented. By modifying the shape of the channel at the beginning of the diffuser, the flow detachment, occurring at this location with its initial shape, was eliminated.

Here, the preliminary test results of a pre-prototype engine are presented.

The engine was designed to convert thrust from the ramjet modules placed on the rim of the disk into shaft torque, which in turn can be used to generate electricity or mechanical drives. The initial combustion tests revealed the importance of flame volume and surface area in increasing combustion efficiency, regardless of the fuel injection scheme. During the study, it was shown in a sample test geometry, in which the gradual increase of natural gas and hydrogen flow were tested separately, that the modeling of chemical kinetics accurately depicts the important flow characteristics. The results confirm via visual observations that, due to the nature of the engine generating and the use of a complex shock wave structure, drastic changes in the flow field occur during both startup and during changes in the amount of pilot fuel fed.

5. Recent Developments in Rotary Shock Wave Compression Systems

There is an early publication [50] presenting the history of the development of the rotary ramjet engine.

Due to the greater interest of the chemical industry in such solutions, practical industrial applications have found CO₂ compressors of this type. There is a number of works, showing the development and achievements of this technology, which are not presented in this review.

One of the most recent is the work [3], entitled Report of 2018 year, containing the current performance of rotary shock wave compressors summary.

• Testing of high pressure (HP) and low pressure (LP) compressors has been completed, yielding a pressure ratio of 11.5:1 in HP and 12.0:1 in LP;
• The discharge temperature is approximately ~550 °F = 560 K.

Currently, Dresser-Rand continues to develop and commercialize supersonic compression technology to reduce costs and improve compression efficiency in carbon capture and sequestration (CCS) applications, requiring “100:1” total CO₂ compression ratios.

This information is relevant to shock wave compression rotary heat engine designs.

6. Summary of Design Solutions

The most important structural solutions could be encapsulated in several diagrams shown in Figure 41.

Figure 41 shows the most characteristic features of the proposed solutions.

Figure 41a shows the first significant proposal for a rotor design rotating in opposite directions, whereby the relative velocity of the air entering the shock wave compression section is the sum of the peripheral velocities of the two sets of channels in the rotors and exceeds the local speed of sound at the subsonic peripheral velocities of each rotor. This idea is repeated in many subsequent solutions.

Figure 41b shows the most common rotary engine channel geometry when the height of the outer rotor surface varies locally in the radial direction. The outer casing is a stationary wall, enclosing a channel open from the outside.

Figure 41c shows a less common channel geometry when the height of the inner rotor surface changes and the inner casing is a stationary wall enclosing the open channel. This design allows the use of ceramic materials supported by a metal outer ring.

Figure 41d shows a sensational configuration found only in patents, in which the shock wave compression channels are stationary, the shock wave has steady position, the combustion chamber and expansion nozzles are stationary, and only the supersonic rotor and turbine are rotating elements.

Figure 41e shows the practical partial use of configuration (d), as the compression of the shock waves takes place initially in the rotating channels of the turbine-driven compressor and partially in the fixed channels in front of the combustion chamber. By this, I mean that steady shock waves can also be realized in rotary engines.

Figure 41f shows the most elaborate configuration, in which two counter-rotating shock wave compression rotors, separated by a vane system, can have different rotational speeds. The outer rotor must achieve supersonic speeds relative to the incoming axial air, while the second rotor can have lower speeds as it receives counter-rotating air from the first rotor.

Figure 41g recalls an arrangement of stationary blades, generating a peripheral component of air velocity opposite to the motion of the compression channels in the rotating disk. This was proven in some design solutions but was underestimated in others.

Figure 41h shows the only case of closed flow channels.

From the analysis of the presented results of the work, it can be concluded that the basic elements of almost all solutions are more or less based on the scheme contained in the solution shown in Figure 41a, and that more attention should be paid to fixed pre-swirl vanes Figure 41g.

7. Forward-Looking Solutions

Applications for patents were filed in 2019, and subsequently two—[51] (Rotary supersonic heat engine with rotating detonation wave combustion chamber) and [52] (Rotational supersonic heat engine with rotating detonation wave combustion chamber with improved efficiency)—were published in 2021. They aimed to assist in increasing the pressures and temperatures of the Humphrey cycle by recommending the use of another compression stage in a shock wave compression rotary engine in the form of a spinning detonation wave in a combustion chamber rotating with the main rotor.

In Figure 42, the cross section of a contra-rotating shock wave compression engine with spinning detonation wave in combustion chamber is depicted. The rotary combustion chamber with spinning detonation waves is marked as number 37.

Shock wave compression, performed using contra-rotary rotors, already gives high compressions at moderate rotors speeds, and this solution proposes to use a moving combustion chamber in which the spinning detonation wave is realized.

Thus, the engine operates according to the Humphrey cycle rather than the Brayton cycle, a fact which reduces entropy generation and improves engine efficiency (see Figure 43).

Work on the use of a moving combustion chamber with a rotating detonation wave has already passed the stage of practical implementation. The rotary engine, equipped with a spinning detonation wave, was realized in Japan [53].

An engine has been built that takes the form of a rotating disc-shaped combustion chamber with a spinning detonation combustion chamber inside it, as was shown in Figure 44.

Recorded detonation wave propagation speed was 600–1300 m/s. This is about 25–45% of Chapman–Jouget detonation velocity. A 6.5% increase in rotor velocity was observed during the short 0.2 s duration of the combustion process.

However, the first step has been taken.

8. Summary

Based on the available materials, it can be concluded that the idea of rotary and steady shock wave compression has been practically proven and used in the chemical industry to realize CO₂ compression to a compression ratio of 10:1–12:1 in a single disk, reaching a compression ratio of 100:1 in a two-stage system.

A characteristic feature of shock wave compression is a much higher temperature of the compressed medium than that found in classical multistage compression, which translates into better opportunities to use the heat of compression. In the case of engines with an RAM compressor, this means less fuel consumption is needed to reach the required exhaust gas temperature.

The interest in this topic is evidenced by the development of a number of patent applications for various solutions to engine design with shock wave compression.

It is interesting that one of the patents presenting a sensational solution with fixed compression ducts, featuring a boundary layer control system, with a fixed combustion chamber and a fixed expansion nozzle but with a movable pre-swirl system, was left without any information about the scientific research into this solution.

Some aspects of this solution can be traced back to the SRGT engine and the ASCE engine design.

The well-prepared design of the ASCE ramjet engine for vehicles developed by Ramgen has only lived to see tests of its components, such as shock wave compression in a supersonic tunnel, tests of the shock wave compression rotor and the effectiveness of the vanes placed in front of the inlet to the rotor ducts, tests of the combustion chamber with an unusual vortex trap combustion chamber type, and the design, manufacture and testing of the expansion nozzles on a modified ISCE B1 turbine engine.

There are several designs of the engine designated as ASCE, modified after analyzing the results of experimental tests of its various components.

Practically, only two prototypes of shock wave compression micro-engines have been made. Both were made at Sherbrook University in Canada.

The first R4E engine was a single rotating module with a shock wave compression system, a central combustion chamber and exhaust nozzles. Powered by hydrogen ignited by a spark system, accelerated to operating speed by an air turbine, after being supplied with hydrogen and ignition in the combustion chamber, the engine manifested an increase in speed from 102,000 to 117,000 rpm, showing net power generation.

The second supersonic rim–rotor micro gas turbine (SRGT) engine, with a completely different reverse-flow design, showed net power generation. Its operation was practically tested, obtaining some information about its performance characteristics.

It should be noted here that the designs of both of these engines underestimated the effectiveness of pre-swirl guides located in other design solutions before the inlet to the compression channels showing even a 50% increase in relative Mach number.

Numerical calculations of the operation of a single-disk shock wave compression engine were carried out. The two-dimensional model took into account the flow of compressible fluid in the compression channel of the shock wave compression engine, the combustion of fuel in the combustion chamber and the supersonic expansion of the exhaust gas in the exhaust nozzle. A theoretical engine efficiency of 18% was obtained.

Analytical and numerical calculations of the operation of an engine with two contra-rotary ramjet disks (CORRE) were performed. The main purpose of using contra-rotating disks was to reduce their rotational speeds to the operating range of ball bearings and to use the exhaust energy generated by the main rotor. The limits of engine operation were determined analytically and compared with the results of numerical calculations. A theoretical engine efficiency of 32% was obtained.

The theoretical possibility of improving the efficiency of a shock wave compression engine by using a rotating detonation wave combustion chamber was shown.

9. Conclusions

A review of information on work on rotary shock wave compression engines indicates a huge variety of possible design solutions for such an engine. Shock wave compression can be implemented with a single disc rotating at high speed or two counter-rotating discs rotating at two times lower speed. Otherwise, a single disc and compression in fixed compression channels can be used. It is possible to use compact solutions in which all the necessary components of the engine—the air compression system, combustion chamber and expansion nozzle that produces thrust—are placed on a single disk. At the same time, according to the review, the analyzed or realized projects of rotary shock wave compression engines have shown their great potential to simplify their design by reducing the number of engine components, simplifying their geometry, using new technologies (carbon composites), and leading to a reduction in their weight and lower production costs. It is possible to increase their efficiency by increasing the compression ratio compared to turbine engines. A completely new direction in the development of rotary shock wave compressor engines is the use of rotary detonation wave combustion chambers to obtain even higher total air compression ratio in the engine. This solution is particularly interesting from the point of view of the possibility and necessity of using hydrogen as a fuel. It seems possible, by selecting and combining the salient features of various existing solutions, to develop a structurally simple, compact, shock wave and detonation wave compression rotary engine with high thermodynamic efficiency, powered by hydrogen and used as a range extender in electric cars. In the era of development and intensive evolution of electric cars, the development and application of such an engine would have a very broad, far-reaching and highly significant impact on their design, reducing vehicle weight by limiting size of heavy batteries and using environmentally friendly fuel.