Motivation and background

Decarbonisation of hard-to-abate high-temperature endothermic chemical reaction processes, such as steam cracking of hydrocarbons, ethylene dichloride cracking, plastic recycling, hydrogen production through steam methane reformation (SMR), and ammonia decomposition, is a significant challenge of this decade (Thiel and Stark, 2021). These processes are essential components of large-scale global industries. For example, the hydrocarbon cracking market was recently valued at $240 billion, with a global annual capacity of 400 million tons per annum (Mtpa) (Bender, 2014). This is expected to grow to $350 billion, with a capacity of 600 Mtpa, by 2030. Furthermore, with the rapidly growing support for low-carbon hydrogen and ammonia for transport, industry, energy storage, and power generation, it is expected that their demand will increase exponentially, potentially reaching to 200 Mtpa by 2030, with a market value of $320 billion (IEA, 2022).

The primary challenge is that large-scale energy-intensive sectors (e.g., chemical/petrochemicals steel, and cement) account for almost 20% of global CO2 emissions (IEA, 2021), mainly due to heat generated by fossil fuel combustion. To address this challenge, a new class of turbomachines has been developed to replace gas-fired surface heat exchangers (specifically the firebox/furnace unit) used in these industrial processes, as shown in Figure 1.

Figure 1.

A schematic analysis of the energy transfer mechanism in a surface heat exchanger against that in the turbo-reactor.

Heavy industry can be transformed radically by exploiting the complex flow physics and controllable energy conversion processes possible within a turbomachine. This novel turbomachine, known as the RotoDynamic Reactor (RDR) or turbo-reactor, works on the principle of directly imparting mechanical energy to the working fluid supplied by a renewably powered electric motor as the mechanical driver (Rubini et al., 2021; Coolbrook Oy, 2022). As a result, Figure 1 demonstrates that the turbo-reactor can significantly increase power density by up to two orders of magnitude compared to a surface heat exchanger, leading to a reduced plant footprint, as well as lower capital, operating, and maintenance costs. This is achieved by converting almost all of the imparted mechanical energy into internal energy, rather than compressing the gas as is done in a compressor (which is another example of an energy-imparting machine). Therefore, high working fluid temperatures of up to 1700∘C can be achieved within short axial distances of less than one metre, depending on the working fluid properties. This can result in a significant improvement in the efficiency and yield of the reaction (Rubini et al., 2022b). Previous work by the authors presents a detailed introduction and analysis of stage design, energy transformation train, and fundamental flow physics (Rubini et al., 2021, 2022a,b; Karefyllidis et al., 2023).

Figures 2 and 3 highlight the significant role of the RDR in decarbonising a diverse set of high-temperature endothermic reaction processes for the production of high-value commodity chemicals in the chemical industry, such as steam cracking, thermochemical plastic waste recycling, SMR for hydrogen production, and ammonia decomposition for hydrogen recovery. Alternative strategies to decarbonise these sectors include hydrogen-fired (Weydahl et al., 2013) or electric furnaces (Delikonstantis et al., 2019), but these suffer from large thermal resistances that hinder energy transfer (Venkataraman et al., 2003), low power density, and non-uniform temperature profiles within the tubes, all of which can degrade the efficiency of the process. Furthermore, there are additional challenges related to scalability at high temperatures for electric furnaces and low energy conversion efficiency ≤60% (Lu et al., 2022) and nitrous oxide emissions for hydrogen-fired furnaces.

Figure 2.

A schematic of the elemental stage and multistage environment for the RotoDynamic Reactor, illustrating a typical temperature profile for some example endothermic chemical processes that could be driven by the RDR.

Figure 3.

Schematic illustration of potential opportunities for turbomachines to decarbonise high-temperature endothermic reaction processes in the chemical and petrochemical industry.

Objectives of this study

This first-of-its-kind paper demonstrates the applicability of the RDR for decarbonising a wide range of endothermic reactions within the chemical industry (see Figure 3). This study confirms the robustness and controllability of the system subjected to different feedstocks, variable reaction states, and a range of operating points. A broad spectrum of operating states is generated by harnessing variations in thermophysical/thermochemical fluid properties corresponding to different feedstocks (e.g., n-hexane, methane, etc.) and reaction progress states. The RDR is shown to be resilient and flexible, and energy can be effectively imparted and dissipated despite using a fixed stage design and boundary conditions.

Controllable elemental stage design for ultra-high power density energy input

The turbo-reactor concept and detailed design have been developed over many years of collaboration with Coolbrook Oy (2022) and are based on the original patent of Bushuev (2016). This new machine unlocks a radically new design space for high-power-density energy-imparting machines, as shown in Figures 2 and 4. Figure 4 compares the single-stage constant speed ϕ−ψ and ϕ−CψTS characteristics between the turbo-reactor and an axial compressor. As the primary objective of an axial compressor is the increase of pressure, the work coefficient ψ is limited by isentropic efficiency constraints throughout the operating range (see Figure 4b), and system instability considerations at low flow coefficients ϕ (see Figure 4c). For the RDR, by eliminating the requirement for an increase in static pressure, these constraints are bypassed within the relevant operating range (that is, pexit/p0,in≤1). This results in the following key design differences from a compressor:

Figure 4.

A comparison between an axial compressor and turbo-reactor (both energy imparting machines), showing (a) the primary objectives, (b) the single-stage flow coefficient ϕ against stage loading ψ characteristic speedline, and (c) the single-stage flow coefficient ϕ against total-to-static pressure rise coefficient CψTS characteristic.

In a multistage environment, the flow must be reconditioned before the next rotor row. A stator vane is used to rapidly accelerate the flow to help it recover before entering the downstream row and to provide the necessary high Mach number with a large negative swirl angle (to the rotor). The favourable pressure gradient attenuates residual flow non-uniformities from the upstream mixing process, ensuring high performance across the multistage architecture (Karefyllidis et al., 2023).

Addressing the limitations of surface heat exchange

Compared to radiant furnaces, the RDR provides a fundamental advantage: mechanical energy is directly transferred into the fluid, making it the hottest part of the system. This is in contrast to furnaces, where the walls are the hottest part of the system due to the heat transfer process. This inherent feature of volumetric energy addition bypasses two key challenges encountered in radiant coils. First, the heat transfer area requirement is avoided, allowing a significantly shorter gas path (see Figure 1). Reaction selectivity is a function of residence time; therefore, the primary product yield can be increased.

Second, as indicated in Figure 1, the thermal and velocity boundary layers within the tubes are thick and mismatched. As a result, the majority of the fluid’s mass is concentrated at the centre, but the highest temperature is at the surface. This results in coke deposition on the walls due to high metal temperatures (for hydrocarbon feeds) and overcracking due to nonhomogeneous reaction progress. By avoiding these limitations, the RDR enables a more homogeneous and efficient reaction for all chemical processes, as well as lower coking rates for hydrocarbon-based feeds.

Fine-tuned control of the endothermic reaction dynamics

For high-temperature endothermic chemical reactions, where the enthalpy of reaction ΔrxnH2980 is positive, a turbomachine can be used to replace conventional radiant furnaces. The turbo-reactor preheats the gas mixture to a temperature where the reaction proceeds efficiently, followed by further customised stages to maintain the average optimum reaction temperature during the subsequent enthalpy-draining reaction, as shown in Figure 2. This paper will show the versatility of the RDR using four example applications (see Figure 3) summarised below.

The objective of the non-reacting, ultra-fast preheating section (150∘C≤T≤620∘C) for all chemical processes is to maximise the flow of energy into the fluid within a minimum distance and time scale. In some configurations of the preheating zone, the vaneless space can be eliminated by integrating the diffuser and the stator. As a result, the flow can enter successive stages with a higher and higher flow coefficient, enabling a potential increase in stage loading across the multistage architecture (until an equilibrium is reached).

Once preheating is complete and the gas mixture is at the reaction activation temperature, the vapour enters the reaction zone where the turbo-reactor provides a tailored temperature profile based on the application-specific reaction dynamics (see Figure 2). This is achieved using a non-uniform axial distribution for the interstage vaneless space length (see Figure 2). For each stage, the axial dimension depends on the local heat of reaction, which is a function of the thermochemical state.

A decoupled framework for evaluating the effects of chemistry on aerothermal performance

A low-order approach is taken to decouple computational fluid dynamic (CFD) simulations and chemical kinetics. This is summarised in Figure 5 and can be explained as follows. Offline, 1-D detailed kinetic simulations are conducted for steam cracking (of an n-hexane and ethane feed), SMR, and ammonia decomposition reactions across a broad temperature range (150∘C≤T≤1,000∘C) covering both the preheating and reaction zones. All of the reactions are taken near completion to capture a broad range of reaction states.

Figure 5.

(Left) The methodology for constructing performance maps of the RDR for a broad range of chemical processes and reaction states and (Right) temperature-dependent variations in thermophysical properties, speed of sound, and non-dimensional choking mass flow rate w.r.t. reaction progress in the range 150–1,000°C.

The impact of the chemical reaction is effectively lumped into changes in the fluid properties, with four variables forming the parameter space: static temperature T, heat capacity ratio γ, isobaric specific heat capacity cp and dynamic viscosity μ. By sampling from this fluid property space (see Figure 5) and performing a non-reacting CFD calculation for each sample, the performance can be evaluated under different reaction conditions without performing costly reacting flow simulations. The aerothermal performance of the turbomachine is characterised in the same way as conventional turbomachines using the non-dimensional groups shown in Equation 1 and defined in Dixon and Hall (2013):

(1)

where p0 is the total pressure, R is the gas constant, m˙ is the mass flow rate, D is the mean diameter and Ω is the rotational speed. The terms highlighted in red are composition-dependent, indicating that turbomachinery performance is a direct function of the state of progress through each reaction. It is noted that there are two key implicit assumptions in this analysis. First, it is assumed that the aerodynamics and chemistry can be decoupled, and therefore are not assumed to be strongly interacting. Second, the fluid properties are assumed to be constant across a stage. In general, these are crude assumptions; however, these approximations allow us to gain rapid insight into how different reaction states change aerothermal performance.

Influence of Reynolds number on aerodynamic performance

The Reynolds number Re=ρVb/μ (based on the stator exit conditions and true blade chord) varies with feed composition and reaction progress due to changes in fluid density and dynamic viscosity. Figure 6a suggests that stage loading is weakly dependent on Reynolds number over a wide range (1×104≤Re≤2.5×106), dropping by only 9% over the investigated range. As expected, more energy can be imparted into the fluid at high Reynolds numbers. Figure 6b indicates that this is because, in the low Reynolds number regime, there is a higher level of flow separation as the boundary layer is more sensitive and cannot negotiate local adverse pressure gradients. Higher flow separation leads to higher blockage and lower throughflow capacity, as well as increased flow deviation. Since stage loading scales with flow coefficient and flow turning, the specific energy input falls at low Reynolds numbers. However, the change is relatively minor (see Figure 6a).

Figure 6.

(a) Variation of stage loading coefficient with Reynolds number and (b) the isentropic Mach number distribution for two extreme Reynolds number states, corresponding to different reactions powered by the RDR.

Aerothermal performance maps covering a wide operating range

This section demonstrates the applicability of using a turbomachine for four different chemical processes using a uniform stage design, fixed annulus flow area, and fixed boundary conditions. These conditions include a fixed imposed pressure ratio pexit/p0,in≈0.98 and blade tip speed. As highlighted at the bottom right of Figure 7, by varying the fluid properties (see Figure 5) while fixing pexit/p0,in, the system naturally experiences variations in the operating point, set by the flow coefficient ϕ=Vx/U. This variation is exploited to probe the response of the dynamical system (i.e., the RDR) subject to input perturbations (i.e., fluid properties). As a result, the robustness and controllability of the machine can be demonstrated over a wide range of fluid properties and hence operating regimes. Of course, during normal operation, the delivery pressure, stage design, and annulus flow area can be customised for each stage and for each chemical reaction to maintain and match the optimum velocity triangles.

Figure 7.

Aerothermal performance maps showcasing the reaction-progress trajectories with thick solid lines for four applications of the turbo-reactor (for a fixed Re = 100,000 and pressure ratio pexit/p0,in=0.98).

Each thick solid line indicated in Figure 7 represents the trajectory through non-dimensional parameter space using decoupled detailed 1-D kinetic calculations. This detailed chemical analysis is performed independently, and the results are superimposed on the performance maps. These lines effectively illustrate how aerothermal performance varies along the streamwise direction across a multistage machine for each chemical process. For all reactions, the imposed pressure ratio is fixed; therefore, the Mach number decays across the multistage machine. Since density decreases and the flow area is fixed, this is accompanied by an increase in the flow coefficient toward the rear of the machine. Therefore, the stage loading is higher near reaction completion. At the beginning of the reaction, the feeds are initially separated in the non-dimensional parameter space (see Figure 7). However, as the reactions progress, they all converge toward the higher loading region.

More generally, two insights can be gained from the response of the performance metrics shown in Figure 7. First, the ratio of specific heats has a relatively small impact on the stage loading. Secondly, the dominant parameters driving changes in flow physics are the non-dimensional blade speed and flow coefficient. The non-dimensional blade speed is inversely proportional to the speed of sound (see Figure 5 and Equation 1) and varies by almost a factor of 4.5, whilst the flow coefficient, which sets the velocity triangles, varies by almost a factor of 2 (due to the density variation). The stage loading coefficient does not respond significantly, with a maximum deviation of 15%, illustrating the robustness of the turbo-reactor despite the use of a fixed elemental stage. This margin can be further reduced by adjusting the delivery pressure and modifying the flow area to match the flow coefficient and the restore the velocity triangles. Since there is no onset condition for violent system instability (see Figure 4c), the machine can provide a high enthalpy input over a broad range of reaction and operating states.

Parameter space boundaries: extremes of the Mach number regime

Two extreme Mach number regimes, covering a wide range of feed molecular weights (2.0–86.0 g mol⁻¹) and hence the speeds of sound (280–1,150 ms⁻¹), are selected from the parameter space shown in Figure 7 and are compared in more detail in Figure 8. The low Mach number regime corresponds to an ammonia feed toward reaction completion, and the high Mach number regime corresponds to an n-hexane feed before the reaction starts. The first case represents a front stage of the machine, which is capacity-limiting due to the low speed of sound (see Figure 5 (Right)), and the second case represents a rear stage. The high Mach number case (see Figure 8 (Right)) is presented to illustrate the robustness of the flow at off-design regimes. However, in practice, the mismatched velocity triangles can be partially corrected by adjusting the delivery pressure to accommodate a higher mass flow rate, increasing the annulus flow area, and/or increasing the throat area to raise the swallowing capacity near the choke point.

Figure 8.

Comparison of the midspan relative Mach number distribution at two “extreme” corners of the parameter space where the fluid properties and local gas composition lead to two polar speed of sound regimes.

Figure 8 provides three key insights into the flow physics of the system. First, within the rotor, the low Mach number case is mainly affected by PS separation and blockage, whereas for the high Mach number case, an increased positive incidence angle results in a higher level of SS separation contaminating the flowfield. This is because (I) the flow coefficient drops by almost a factor of 2 for the high Mach number case (II) the Mach number is supersonic, making the flow sensitive to small changes in incidence (≤1.5∘), and (III) a shockwave at the rotor inlet contributes to further SS boundary layer separation through shockwave boundary layer interaction (SWBLI).

Second, the gas mixture in the low Mach number regime (Figure 8 (Left)) consists of 70% hydrogen on a mole basis. As hydrogen has a low molecular weight and hence a high speed of sound, it can accommodate a higher flow coefficient at a given pressure ratio and a fixed annulus area. This allows for a greater change in tangential velocity whilst avoiding the SWBLI in the rotor, resulting in higher stage loading (see Figure 8). As the flow is far below the choking limit, an even higher flow coefficient can be achieved by increasing the delivery pressure (see Figure 4b). Therefore, it is evident that the local fluid properties (set by the local composition state) have a significant influence on the operating range, compressibility, and loading capability for a fixed geometry. With the current datum design, the operating range of the high molecular weight n-hexane feed (Figure 8 (Right)) is more restricted, and the ϕ−ψ characteristic is almost vertical (see the low speed of sound boundary in Figures 4b and 4c). However, for a given fluid, the design can be altered to balance the operating range and the specific energy input rate per stage.

Finally, the results presented demonstrate that the RDR can still achieve a reasonably high level of specific energy input (Δh0≈220kJkg−1) despite large-scale flow separation due to incidence and SWBLI, as indicated in Figure 8 (Right). This flexibility of the machine is a direct consequence of the fact that isentropic efficiency does not impact the performance of the machine. Without a requirement to resist an adverse pressure gradient, entropy can be generated without dramatic repercussions for the specific energy that can be imparted into the fluid. Despite an elevated level of flow separation within the passage, the flow within the rotor is turned through an angle close to the blade metal angles. Therefore, the specific energy imparted into the fluid remains high, albeit at the expense of a reduced flow coefficient due to blockage. In the high Mach number regime, a higher total pressure ratio across the rotor (see Figure 7) results in an increased local choking mass flow rate. This ensures that a reasonable level of mass can still be swallowed, despite a reduction in the effective throat area due to blockage in the diffuser. As the total pressure is rapidly dissipated downstream, there is no global adverse pressure gradient, as discussed in the next section.

A breakdown of the energy conversion mechanisms

Once the kinetic energy (KE) has been absorbed by the flow through the rotor, it must eventually dissipate into internal energy u within the diffuser and vaneless space. In some configurations of the machine, such as the ultra-fast gas preheating zone before the reaction starts, the vaneless space can be removed, and the majority of the energy dissipation occurs every 2–4 stages. In contrast, for a gas mixture undergoing reactions, it is more optimal to dissipate the mechanical energy at every stage to repeatedly balance and compensate for the drop in temperature caused by the reaction.

A well-designed energy transformation system aims to convert kinetic energy into internal energy over the minimum possible time scale, typically less than 0.5ms. This is achieved controllably through both an isentropic pressure rise and through entropic dissipation mechanisms equivalent to aerodynamic losses. By increasing the entropic rise ds, the increase in static temperature dT can be maximised within a minimum time scale while removing any minor unwanted gains in static pressure dp. This principle can be expressed by the Gibbs equation cpdT=(1/ρ)dp+Tds. Exploiting aerodynamic losses in this way is in stark contrast to conventional energy-imparting machines.

Figure 9 illustrates an approximate breakdown of the energy conversion mechanisms at the two flow regimes shown earlier in Figure 8 above. The energy conversion breakdown is determined by integrating the viscous dissipation rate S˙vsic (Denton, 1993) zonally for five regions in the diffuser-vaneless-space system listed in Figure 9 (Left). A more detailed description of the “loss audit” methodology can be found in Moore and Moore (1983) and Pullan et al. (2004). The sixth energy conversion mechanism accounted for is the isentropic pressure rise ζisentropic (see Equation 2), which is calculated using isentropic relations between two known states. Other conversion sources, such as tip leakage, are neglected.

Figure 9.

A breakdown of kinetic energy (KE) to internal energy (Δu=cvΔT) conversion mechanisms including both entropic dissipation and isentropic pressure rise contributions. The breakdown for a single stage is compared for two extreme Mach regimes corresponding to thermophysical properties encountered for two different reactions.

Equation 3 is used to calculate the entropic portion ζentropic of the total energy conversion coefficient ζ=ζisentropic+ζentropic. It is noted that the subscript (rotor) refers to the rotor exit station.

Figure 9 illustrates the differences in the energy conversion mechanisms for two feeds at different reaction states. In the subsonic case (i.e., high-temperature decomposed ammonia), isentropic energy conversion dominates since the flow in the blade passage is more attached. For the supersonic case, there is still a contribution from isentropic pressure rise, but the contribution is smaller, and the mechanism is dominated by pressure rise due to the isentropic component of the shockwave action rather than diffusion induced by changes in the effective flow area.

In both cases, the energy conversion due to trailing edge (TE) mixing is large since the TE is thick (42% of the blade pitch), blunt and square. In the supersonic case, this energy conversion source is well over 50% of the total energy conversion. This is significantly higher than the subsonic case as TE mixing loss scales with Mach number Denton and Xu (1990). In the supersonic case, the entropy generated through the shock is relatively small, meaning that the direct impact of the shock is minor. However, there is a substantial indirect impact from the shockwave due to shock-induced boundary layer separation. This significantly enhances boundary layer dissipation as well as downstream mixing.

This analysis shows that, despite variations in the incoming dynamic head over a wide range of operating points and feeds, almost 60% of the rotor exit kinetic energy can be dissipated into internal energy over a short distance (<50 mm). In different regimes, the flow self-adjusts the contributions from each conversion mechanism to match the downstream boundary condition. Future work will investigate the energy conversion mechanisms in more detail.

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