Enhancing ammonia combustion with minimum hydrogen blended in presence of self-excited intermittent pulsating oscillations

The greenhouse effect induced by the combustion of fossil fuel characterized with hydrocarbon components is an urgent environmental concern. Ammonia, $NH 3$⁠, as a renewable energy with a high proportion of hydrogen content, may be utilized to achieve net-zero coalition by reducing $CO 2$ emission dramatically or completely. As one of alternative energy sources of the conventional hydrocarbon fuel, ammonia is not only a renewable resource with a high volume and a large energy density but also easy to be produced and processed. The key process for ammonia synthesis is known as the Haber–Bosch process.^1,2 It is one of the most promising carbon-free options to supply thermal power for fuel cells, internal combustion engines, ships, next-generation aircrafts, and many other power generation systems.¹ However, due to its relatively narrow flammability range, a high ignition energy, a low flame temperature, and a low flame propagation speed,² it is still quite challenging to be directly utilized as carbon-free fuel in practical combustion applications^3,4 on the conventional engines, which are designed to accommodate the classical hydrocarbon fuels. Although the combustion of ammonia does not produce $CO 2$⁠, the emission of NO_x is the main contributor to photochemical pollution. How to reduce NO_x production and emission while improving the energy conversion efficiency is another critical problem to be solved.^5,6

In order to broaden the flammability range of ammonia fuel^7–9 and to improve its flame/combustion speed, many methods/means have been attempted.^10–12 Two of them have obvious effects and been widely investigated. One way is to ignite ammonia⁸ by changing the horizontal flow to the swirling flow^11–13 at the combustor inlet. As the vortex decomposition generated, downstream of the swirling combustor at the outlet can generate a recirculating flow region. The heat release (thermal energy) and active radicals can be recirculated to the bottom of the flame, which effectively increases the flame limit. Therefore, a stable $NH 3$–air flame can be obtained within a wide range of the equivalence ratio.^14,15 In order to enable gas turbines being fueled and operated with ammonia, the flame stability and $NO x$ emissions of premix $NH 3$/air combustion are experimentally studied under ambient temperature and pressure.^16,17 Their results show that the flammability limits of such ammonia combustion are close to those of lean and rich combustion limits at different equivalence ratios and inlet velocities.¹⁷ Furthermore, the blowout limits of the flame are shown to be related to the swirling number and the geometry shape of the combustor.¹⁸ It has been found from the previous analysis of the emission composition that the emissions of $NO$ and $NH 3$ are in the same quantities under a specific equivalence ratio, when the oxygen is deficient. Furthermore, experimental studies were conducted on the structure and emission of $NH 3$/air¹⁹ swirling flame in single-stage and two-stage combustors. It is found that the combustor wall heat loss inhibited the NO emission. However, it did promote the emission of $NH 3$ and $N 2 O$⁠. Furthermore, PLIF (planar laser-induced fluorescence) imaging and FTIR (Fourier transform infrared spectroscopy) spectral analyses showed that the wall heat transfer had a greater impact on the flame than the operating pressure. Although swirling combustion can increase the flammability limit of $NH 3$⁠,¹³ it may be challenging to be applied in micro-²⁰ and meso-scale combustors or large-scale practical propulsion systems.^21–23 

The other means to significantly improve the flammability range and to reduce the ignition delay speed is mixing ammonia with fuels of high calorific value such as hydrogen,^13,23 dimethyl ether (DME),¹⁶ methane (⁠ $CH 4$⁠), or propane (⁠ $C 3 H 8$⁠). The burning performance of ammonia is found to be improved by co-firing hydrogen with ammonia¹³ via enhancing the burning velocity and reducing $NO x$ emissions.¹⁷ It is also found that the laminar burning velocity (unstretched) is increased nonlinearly with the increased hydrogen fraction. Experimental investigations on the combustion characteristics of $NH 3$/ $H 2$/air fuels with different mixing ratios in a high-pressure gas turbine combustor were conducted.^14,23 It was found that free radicals are related to the combustion speed. Furthermore, $OH$ is shown to play the most significant role on ammonia decomposition.¹⁴ In addition, the heat release rate of $NH 3$ flame is positively correlated with the concentration of $OH$ and $N$ free radicals.¹⁵ The previous studies^14,15,17 have shown that if the molar ratio of $NH 3$ to $H 2$ is approximately 7:3, then it can be applied as a stable energy source for gas turbine engines. Additionally, experimental studies¹⁴ are conducted on the flame propagation limit of $NH 3$/ $CH 4$/air in a fan-stirred fixed-volume burner under turbulent conditions. It is found that the flame propagation limit is increased due to the addition of ammonia (gas). In addition, the ammonia flame can still propagate with a high turbulent intensity, even when the equivalence ratio is reduced to 0.9. Finally, the experimental studies on spark ignition engines²¹ powered by $NH 3$/ $H 2$/air have confirmed that ammonia flame stability and combustion heat cycle can be significantly improved, if the molar fraction (volume) of hydrogen being blended is exceeding 20%.

Combustion instability^24–27 is an undesirable self-excited thermo-acoustics coupling phenomenon. It is quite often observed to occur in low-emission premixed combustion systems for power generation and propulsion applications.^26,27 It is characterized by self-sustained large-amplitude pulsating pressure/velocity oscillations.^28–30 For the low-emission premixed combustion systems, self-excited pressure/velocity oscillations may occur, when the unsteady heat release is coupled with one or more acoustic resonant modes³¹ or periodic flow/mass fluctuations^32–34 resulting from flame-holders or the geometric shapes of the combustor.³⁵ Its main characteristics include (1) periodic flame motions and fluctuating thermodynamic properties, and (2) large-amplitude flow and flame reversal and overheating.^36–38 These pulsating oscillations can promote heat and mass transfer and so combustion to a certain extent. It may also improve the efficiency of chemical energy conversion. However, at the same time, it will significantly reduce the engines' lifespan and the safe operation range.^39–42 To prevent the occurrence of such instability, passive control methods,⁴¹ such as perforated liners and an electric heater, may be applied to dampen such pulsating oscillations by changing the acoustic damping or varying the temperature fields of the combustion systems.^38,43,44 It has been shown that promising results were achieved, as an electric heater is applied as an “acoustic damper” in an open-ended thermoacoustic combustor.^45–47 

To the best knowledge of the present authors, there are few investigations, which focus on enhancing the combustion performance of $NH 3$ with minimum hydrogen blended in the presence of self-excited pulsating oscillations. In this work, an open–open longitudinal combustor with double ring-shaped inlets is proposed and numerically examined. Emphasis is placed on addressing the key question of how to reduce the blended hydrogen fraction to a minimal value while sustaining a stable ammonia combustion. For this, three  key thermodynamic parameters are identified. Their effects on triggering pulsating combustion oscillations and combustion emissions are evaluated one at a time. The structure of this paper is as follows. In Sec. II, the model and numerical method are described. In additional, the model validation is conducted. In Sec. III, the effect of the total inlet fuel flow rate $m ̇ f = m ̇ NH 3 + m ̇ H 2$ is examined. In Sec. IV, the effect of the blended hydrogen mass fraction $ω ̇ H 2$ in the mixture of both ammonia and hydrogen is evaluated to reveal the amplitude and frequency of the pulsating oscillations varied with hydrogen content. In Sec. V, the effect of the downstream heat exchanger surface temperature T_H on producing pulsating combustion oscillations is investigated. In Sec. VI, the minimal hydrogen being blended is determined in the presence of such pulsating oscillations and a sustainable combustion. In Sec. VII, the emissions of combustion products such as $NO$ and $NO 2$ and the reactants are predicted in the presence of such pulsating oscillations, as the minimum hydrogen $ω ̇ H 2 min$ is provided. Finally, the key findings are summarized in Sec. VIII.

An acoustically open–open combustor with a double ring-shaped fuel injector and heat exchangers confined is considered in this work. It is schematically shown in Fig. 1. The length (L) and diameter (D) of the combustor are 1000 and 50 mm, respectively. The geometry and dimensions are chosen by following our previous experimental setup.⁴⁸ The gases of $NH 3 / H 2$/air are premixed in a certain proportion and passes into the double-ring inlets. The air (consisting of $O 2$ and $N 2$ only) is continuously squeezed into the combustor at the bottom due to the pressure difference. The air inlet width (L₁) is 8.75 mm, and the fuel mixture inlet width (L₂) is 5 mm. Three heat exchangers with a constant surface temperature (powered by electricity in practice) are fixed 125 mm away from the combustor outlet (L_h) to amplify or attenuate the pulsating oscillations.

The 2D (two-dimensional) structure grid is generated by Hypermesh 14.0. In addition, more refined grids are applied near the entrance and the heat exchangers in order to improve the simulation accuracy. In this work, Reynolds-averaged Navier–Stokes (RANS) method and k–ϵ turbulence model are used to solve all coupled governing equations. The third-order MUSCL scheme except for pressure and turbulence dissipation (second-order upwind) is used to solve the pressure–velocity coupling equations. In addition, the eddy dissipation concept (EDC) including detail chemical mechanisms of 19 species and 63-step reactions is selected for the present model. In addition, all cases use the stable solver for calculation first. After obtaining the stable flame, it is changed to the transient solver. The time step is set as $Δ t = 1 × 10 − 4$ s. The numerical simulations are demonstrated by ANSYS Fluent R19.3. The mass fraction of oxygen in the mixture is fixed at 11.6% to ensure $NH 3$ burning at a high concentration.

The flow properties in the combustor involve with a mean (time-average) and a fluctuating part. For this, we study the effects of fluctuations on the mean flow properties by using Reynolds decomposition. The thermodynamic variables consist of a mean and fluctuating components as $u = U + u ′$ and $p = P + p ′ ( t )$⁠. Thus, the governing equations for turbulent compressible flow include thermodynamic equations and the unsteady Reynolds-averaged Navier–Stokes ones, which include (1) mass conservation, (2) Reynolds-averaged momentum equations, (3) energy conservation, and (4) species conservation.

The Reynolds stress includes $− ρ u ′ 2 ¯ , − ρ v ′ 2 ¯$⁠, $− ρ w ′ 2 ¯ , − ρ u ′ v ′ ¯$⁠, etc. Such turbulent stresses are shown to increase with the mean rate of deformation. Boussinesq proposed the equation to describe the deformation relationship. The standard $κ − ϵ$ model uses the transport equations for κ and ϵ. More details could be found in Ref. 38.

In order to guarantee that the number of selected grids can lead to sufficiently accurate results, we choose 1.5 $× 10 4$⁠, 3 $× 10 4$⁠, and 6 $× 10 4$ grids for the mesh independence study. The results of the grid sensitivity investigations are shown in Figs. 2(a) and 2(b). It can be observed from the temperature and velocity variation along the axial direction of the combustor that the deviation of the numerical results obtained from the different meshes is shown near the inlet and outlet of the combustor. The largest deviation is observed, when the 1.5 $× 10 4$ grids are used. However, as the other two numbers of numerical grids are applied, the results are well agreed and consistent.

Furthermore, comparison is conducted by comparing the numerical predicted frequency of the dominant mode with the experimentally measured ones⁴⁹ from the open-ended combustor with a single ring-shaped inlet, as the combustor total length is varied. This is summarized in Table I. It can be seen that the difference is less than 10%. More detailed comparison and validations on various turbulence models and combustion models could be found in our previous work.³⁸ It has already been shown³⁸ that the difference is less than 10% in terms of the frequency and amplitude of the dominant mode predicted from the present 2D model with the 3D ones. In general, it is confirmed that the model is applicable to predict the self-excited pulsating combustion oscillations in the open-ended combustors in the presence of the single ring-shaped inlet or two annulus ring-shaped inlets.

Figure 3 shows the time evolution of the acoustic pressure fluctuations, as the inlet fuel mass flow rate $m ̇ f$ is set to three different values. It can be seen from the phase diagrams that initial negligible pressure disturbances grow into large-amplitude periodic limit cycles, as indicated by the circle shape. As the mass flow rate $m ̇ f$ is varied, the small-amplitude pressure perturbations take different times to grow up. This indicates that the growth rates are different and related to $m ̇ f$⁠. More details will be examined in Secs. III and IV.

Figures 4(a) and 4(b) depict the time evolution of the mode-shapes of pressure fluctuations and velocity fluctuations, respectively. It can be seen that longitudinal mode-shapes are present in the combustor, as revealed by both pressure and velocity fluctuations in the normalized axial location x/L. However, the velocity mode-shapes involve with more local and small-amplitude wavy peaks in comparison with that of the pressure mode-shaped. This reveals that nonlinearity does occur to the acoustic velocity fluctuations.

For comparison, the conventional single ring-shaped inlet is chosen as the benchmark case. Figures 5(a)–5(d) illustrates the comparison of the temperature contours of the conventional single ring-shaped and double ring-shaped inlet combustors, as the total inlet fuel mass flow rate $m ̇ f$ is set to the same value. Note that the inlet mass flow ratio for the double ring-shaped inlets is set to 1:1 for simplicity. It can be seen that, under the same $m ̇ f$⁠, the flame of the double ring-shaped inlets is shorter but “fatter” than that of the single ring-shaped one. However, the downstream temperature is significantly higher. This indicates that the double ring-shaped inlet structure is more conducive to the full combustion of the non-carbon fuel, thus releasing more thermal energy. Same conclusions can be obtained from Figs. 5(c) and 5(d), as $m ̇ f$ is increased to $1.0 × 10 − 5$ kg/s from $0.5 × 10 − 5$ kg/s [see Figs. 5(a) and 5(b)]. The increase in the fuel mass flow rate leads to a longer and larger flame, and so a larger high-temperature region. In addition, a closer observation shows that the flame downstream of the double ring-shaped inlet combustor is detached from the fuel inlet at some distance downstream of the flame-holder.

Figures 5(e)–5(h) shows the corresponding mole fraction distribution contours of OH radical. It can be seen that the mole fraction of $OH$ radical in the double ring-shaped inlet structure is larger, when $m ̇ f$ is set to be the same. This phenomenon becomes more apparent with increased $m ̇ f$ [Figs. 5(e) and 5(g) in comparison with (f) and (h)]. As more $OH$ radicals are formed, the heat of reaction is also increased. This explains why the average temperature in the combustor with the double ring-shaped inlets is always higher than that in the combustor with the single inlet.

The mass fraction of ammonia and hydrogen may greatly affect the combustion heat release, thus changing the frequency and amplitude of self-excited oscillations. Figure 6 shows the pressure fluctuation at the center point of the central axis with different hydrogen mass fraction $w ̇ H 2$ and the corresponding recurrence plots (RP) [see Figs. 6(b), 6(d), and 6(f)]. It can be seen that the intermittent oscillations became more obvious, as $w ̇ H 2$ is increased from 15% to 88.4%. In addition, the oscillation period is increased. The minimum amplitude is reduced to 10 Pa. As observed from the recurrence plot [see Figs. 6(b), 6(d), and 6(f)], the combustion oscillations are quickly increased and grow into the limit cycle, even when the hydrogen mass fraction is quite small. With the increase in the hydrogen fraction $w ̇ H 2$⁠, intermittent pulsating oscillations occur. The minimum amplitude of local peaks is decreased dramatically, as observed from the dark regions variation in the recurrence plots of Figs. 6(b), 6(d), and 6(f), which are corresponding to the limit cycles as shown in Figs. 6(a), 6(c), and 6(e), respectively.

In the absence of limit cycles, the recurrence plots are expected to be involved with nodes distributed randomly. As the periodic oscillations are present, there are a number of tiny “gray” square blocks as observed from Fig. 6(b) along the diagonal (principal) in the RP. It is related to the dominant high-frequency periodic conversion between unsteady heat and sound waves. There are a number of connected horizontal and vertical lines. As multiple frequency tones are generated (i.e., intermittent oscillations), especially with the extreme low-frequency tone, as shown in Figs. 6(d) and 6(f), there are a few large black square blocks along the diagonal direction. The square edges create a network with the nodes entangled with each other, and they intersect each other. The square length is proportional to the period of the extreme low-frequency tone. It is worth noting that this kind of intermittent pulsating oscillations with such large-amplitude periodic variation should be avoided in practical applications. When it occurs, the thermodynamic properties such as density and velocity and pressure are all violently fluctuating, as shown in Fig. 7. These large-amplitude fluctuations are easy to lead to mechanical fatigue problems by inducing deformation or fracture/crack of engine casing material.

Figure 9 compares the frequency spectrum of the heat of reaction released by the premixed chemical combustion and the heat flux of the heat exchangers, before and after changing the temperature T_H at t = 4.0 s. It can be seen that their changes are closely related to each other. Moreover, with increased T_H, the amplitudes of the peaks of both the heat of reaction and the heat flux are decreased. Furthermore, the variation ranges of the dominant peak frequencies are basically the same.

There is a strong interest in determining the minimum hydrogen blended with ammonia to achieve a stable combustion. For this, we have reduced the hydrogen mass flow rate $ω ̇ H 2$ with respect to the ammonia mass flow rate to 0.1%, as self-excited pulsating oscillations are present. Here, the total flow rate $m ̇ f$ of both ammonia and hydrogen is set to $1.0 × 10 − 5$ kg/s. The mass flow of the ammonia and hydrogen fuels is distributed among the double ring-shaped burner as (1) supplying 100% $NH 3$ through the inner ring-shaped burner, i.e., $m ̇ NH 3 = 9.99 × 10 − 6$ kg/s and (2) 100% hydrogen (i.e., $m ̇ H 2 = 1.0 × 10 − 8$ kg/s) via the outer ring-shaped burner. Figure 10 illustrates the time evolution of the fluctuations of the acoustic properties (acoustic pressure and velocity) and thermodynamic properties such as temperature $T ′ ( t )$ and heat of reaction $Q ′ ( t )$⁠. The mean heat of reaction $Q ¯$ is approximately 260 W. It can be seen that self-sustained intermittent pulsating oscillations are successfully produced. Furthermore, there are two dominant modes. One is at approximately 280 Hz, and the other mode is at 2.0–4.0 Hz. The higher frequency corresponds to the longitudinal acoustic mode-shape of the combustor.^50–52 However, such extremely low-frequency pulsations at 2.0–4.0 Hz are most likely due to the pulsating fuel flow resulting from the force convection and shear layer separation through the double ring-shaped burner. It may also result from the thermal-diffusive instability.⁵³ It excites the flame sheet to move toward and away from the double ring-shaped burner periodically.

It is worth noting that further reduction of the mass flow rate of the blended hydrogen is shown to lead to an unsuccessful generation of such pulsating oscillations⁵⁴ or unsuccessful ignition. Therefore, we confirm that the minimum hydrogen blended to enhance ammonia combustion in the presence of self-excited pulsating oscillations^55–58 is 0.1% in terms of the total mass flow rate $m ̇ f$⁠.

Figures 11 and 12 below compare the profiles of the reactants and combustion product species of $NO , NO 2$⁠, and $H 2 O$ in both axial (see Fig. 11) and radial (see Fig. 12) directions, as the total fuel flow rate $m ̇ f$ is set to $1.0 × 10 − 5$ kg/s, and 0.1% hydrogen is blended with ammonia. Figures 11(a)–11(c) show the variation of oxygen, hydrogen, and ammonia distribution at three different timings, i.e., $t = 1 , t = 3$⁠, and $t = 5 s$⁠. Along the axial direction, the hydrogen and ammonia are consumed along the axial direction. There is a sudden change near the heat exchangers, which could lead to the effect of “blocking.” Complete depletion of the hydrogen and ammonia is achieved after the heat exchanger zone. As for the oxygen is concerned, there is excessive oxygen flowing out of the combustor. It reveals that the present combustion system is operated at lean combustion condition. Figures 11(d) and 11(e) depicts the combustion product variations along the axial direction. It can be seen that there is an increase in $NO 2$ emission and a decrease in $NO$ at the heat exchangers location. This means that the combustion is more complete. Finally, at different combustion times, i.e., t = 1, 3, and 5 s, the reactants and combustion products are different in term of the number of moles. This reveals that the periodic thermodynamic oscillations⁶¹ contribute to such emission difference. This finding is consistent with the radial observation as shown in Figs. 12(d)–12(f).

Figures 12(a)–12(c) show the variation of the reactants in the radial direction, as t is set to three different values. It can be seen that there are non-uniform profiles of the reactant distribution in the radial direction. The reactants are depleted more near the axis of the combustor than the regions near the combustor wall. Same non-uniform profiles of the combustion products are observed from Figs. 12(d)–12(f). This is most likely due to the periodic pressure and flow oscillations. Such pulsating fluctuations^62–64 propagate along the combustor and the double ring-shaped fuel tubes. They in turn affect the local molar fractions of the mixture species such as $H 2 , H 2 O , NH 3$⁠, $NO$⁠, and $NO 2$⁠. In general, burning ammonia and/or hydrogen does not produce any $CO X$ but $NO X$⁠. The combustion product of $NO X$ is also undesirable. However, it is widely applied to use selective catalytic reduction (SCR) process to reduce $NO X$ emission from burning ammonia.⁶⁵ Unlike the conventional hydrocarbon fuels,^66,67 less-flammable ammonia with a high ignition temperature is an alternative but promising carbon-free fuel. It may contribute to the significant reduction of the greenhouse gas of $CO 2$ emission from thermoacoustic combustors.^68,69 In order to neutralize $CO 2$ emission, next-generation gas turbines^70–72 are expected to burn $NH 3$ completely or the mixture of blending $NH 3$ with a small amount of $H 2$ or conventional hydrocarbon fuels.^73,74 In practice, it is more interesting to know the minimum hydrogen being blended with the ammonia^13,75–77 and the $NO X$ emission. This motivated the present work.

In this work, 2D numerical unsteady RANS (Reynolds-averaged Navier–Stokes) simulations are conducted on an acoustically open–open combustor with double ring-shaped fuel injectors implemented. Here, premixed ammonia–hydrogen-burnt flames are confined near the combustor inlet. The turbulence model of k–ϵ and combustion model of eddy dissipation concept (EDC) are applied. The model is fist validated by using the theoretical and experimental data available in the literature. It is then used to study the effects of (1) the mass flow rate $m ̇ f$ of the mixture consisting of $NH 3$ and $H 2$⁠; (2) the mass fraction $w ̇ H 2$ of $H 2$ blended with $NH 3$ with respect to the total fuel mixture of $NH 3$ and $H 2$⁠. It is found that nonlinear self-excited pulsating combustion oscillations could be generated, depending on the mass flow rate $m ̇ f$ of the fuel mixture. Furthermore, the amplitude and frequency of the dominant mode is found to strongly depend on the mass fraction $w ̇ H 2$ of the hydrogen. In addition, as $w ̇ H 2$ is reduced from 88% to 25%, intermittent combustion oscillations are observed. A pulsating mode at extremely low frequency of approximately $2.0 – 4.0$ Hz is found to occur. Such periodic mode is shown to related to the thermo-diffusive instability of the $NH 3$⁠. When the total mass flow rate $m ̇ f$ of $NH 3$ and $H 2$ is small, for example, $1.0 × 10 − 6$ kg/s, no apparent limit cycle oscillations are observed. This is most likely due to fact that the heat-to-sound energy conversion is not as intensified as the acoustic losses. In addition, the minimum hydrogen being blended with ammonia is determined by varying the mass fraction of the hydrogen with respect to the ammonia while maintaining the total fuel flow rate $m ̇ f$ to be constant. It is shown to be 0.1%, i.e., $w ̇ H 2 min = 0.1 %$⁠. Note that the minimum hydrogen is determined, as the pulsating oscillations are successfully generated.

Combustion products/emissions from the premixed ammonia–hydrogen flames are examined in the presence of such large-amplitude pulsating oscillations. It is observed that $NO$ emission is reduced, and the product of $H 2 O$ is increased along the axial direction. However, $NO 2$ emission is almost unchanged. Along the radial direction, the reactants such as $NH 3$ and $H 2$ are consumed/depleted more and faster near the centerline of the combustor in comparison with the regions near the combustor inner wall. The combustion products are not uniformly distributed along the radial direction. The presence of the pulsating oscillations leads to the combustion products to be varied “periodically” along both the axial and radial directions.

Finally, with the generation mechanism of self-excited pulsating combustion oscillations better understood, temperature-variable heat exchangers as an “acoustic absorber” are applied and numerically examined for controlling and enhancing the combustion stability behaviors. Such control approach is proven to be “slowly responding” and somehow dampen the intermittent pulsating combustion oscillations (at both $2.0 – 4.0$ and 250 Hz), as its surface temperature is set to T_H = 1300 K. However, it is found to be insufficient to completely attenuate such pulsating oscillations. Furthermore, increasing the surface temperature by another 200–300 K and varying its axial location may be applicable. This may lead to a further attenuation of the pulsating oscillations. However, this may lead to excessive additional heat input (thermal energy input) to the combustion system to increase its average temperature. This may prevent its application in practical engines.

This work is supported by University of Canterbury with a Grant No. 452DISDZ. This financial support is gratefully acknowledged.

The authors have no conflicts to disclose.

Yiheng Guan: Investigation (equal); Software (equal); Validation (equal); Writing – original draft (equal); Writing – review & editing (equal). Dan Zhao: Conceptualization (equal); Formal analysis (equal); Funding acquisition (equal); Investigation (equal); Methodology (equal); Project administration (equal); Resources (equal); Software (equal); Supervision (equal); Validation (equal); Writing – original draft (equal); Writing – review & editing (equal).

The data that support the findings of this study are available from the corresponding author upon reasonable request.