Numerical investigation of supercritical combustion of H2-O2

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Numerical investigation of supercritical combustion of H2-O2 Amir Mardani, and Ehsan Barani Energy Fuels, Just Accepted Manuscript • DOI: 10.1021/acs.energyfuels.7b03025 • Publication Date (Web): 04 Jan 2018 Downloaded from http://pubs.acs.org on January 4, 2018

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Fig. 1. Mascotte cryogenic combustion test facility [59]

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Fig. 2. Sketch of the computational domain and detail injector used for the CFD simulations.

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Fig. 4. Compare axial temperature distribution of the numerical study (case No.9 in Table 4) with experimental data [52].


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Fig. 5. Comparisons of contour of OH mass fractions: Abel transformed OH* emission image (bottom) [21], Current numerical study, (case No. 9 in Table 4), (top)

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Fig. 7. The comparison of temperature, density, species mass fraction, specific heat in constant pressure and compressibility factor between ideal and non-ideal EOS in axial direction (case No.1 and No.2 in Table 4)


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Fig. 8. Distribution of static and dynamic pressure, axial velocity, density, specific heat in constant pressure, and molar volume at the axial direction (No.9 in Table 4)

Fig. 9. Streamlines of combustion flows (The color based on static pressure) (Case No.9 in Table 4)


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Fig. 10. The zero axial velocity (dotted line) and zero radial zones (dashed-double dot line), Stagnation point and Anchor point (Case No.9 in Table 4).

Fig. 11. the temperature of Near Injector region of a LOX-GH2 shear-coaxial injector at supercritical pressure (The injection temperatures are 100 and 300 K for oxygen and hydrogen streams, respectively, and the chamber pressure is 4.5 MPa) [12]


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Fig. 12. The measured contour of OH* emissions normalized based on the oxygen injector diameter [21] and the defining parameters on that.

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Fig. 13. The numerical OH mass fraction counter of each turbulence model (top) in comparison with the experimental OH* emission contour (bottom)

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Fig. 14. comparison between the position of the maximum intensity of the Abel-transformed images for cryogenic flames at A-60 operating conditions [21] and position of the predicted OH mass fraction maximum in the examinations (Cases No. 6, 7, 8, 9 in Table 4)


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Fig. 15. Axial profiles of the temperature, density, OH mass fraction, specific heat in constant pressure, axial velocity, and compressibility factor for different turbulence models and axial temperature measurements [52], (Cases No. 6, 7, 8, 9 in Table 4).


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Fig. 16. Contours of OH mass fraction and the flow streamlines for various turbulence models (Cases No. 6, 7, 8, 9 in Table 4).

Fig. 17. The effect of ARK and PR equations of state on the flame shape and comparisons it with SRK equation of state for temperature and OH mass fraction contours (Cases No. 9, 10, 11 in Table 4).


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Fig. 18. The comparison between the position of the maximum intensity of the Abel-transformed images for cryogenic flames at A-60 operating conditions [21] and position of the maximum OH mass fraction for SRK, ARK, and PR (Cases No. 9, 10, 11 in Table 4).

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Fig. 19. Axial profiles of temperature, density, OH and O2 mass fraction, specific heat in constant pressure, axial velocity, and compressibility factor for ARK, SRK, and PR EOS (No. 9, 10, 11 in Table 4).


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Fig. 20. (a) The contour of temperature, (b) contour of OH mass fraction and streamlines of the flow field for two chemical mechanisms of Burke and Konnov, (Cases No. 9 and 12 in Table 4).

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Fig. 23. Axial profiles of temperature, density, the mass fraction of OH species, and specific heat at constant pressure for three pressures of 100, 80, and 60 bar (No. 9, 13, and 14 in Table 4).


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Fig. 24. The pathway of the H+O2 reaction at different conditions [64]

Fig. 25. The flow residence time contour and the isolines of HO2 production (dashed line) and consumption (solid line) (Cases No. 9 in Table 4).


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Fig. 26. Comparison of mass fraction contours of H2O, O2, H2O2, and H species between Pch=100 bar (top) and Pch=60 bar (bottom) (Cases No. 9 and 14 in Table 4).

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Fig. 27. comparison of radial profiles of OH mass fraction for three chamber pressures of 100,80, and 60 bar at X/D of 5 and 10(Cases No. 9, 13 and 14 in Table 4).


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Numerical investigation of supercritical combustion of H2-O2 A. Mardani*1, E. Barani*2 *

Sharif university of technology, Tehran, Iran, Zip Code: 1458889694 1

[email protected]; [email protected]

Abstract This study investigates GH2/LOX coaxial jet flame at transcritical and supercritical conditions using the Reynolds Averaged Navier-Stokes approach. Four two-equation-turbulence models, three real equation of states, two chemical mechanisms, and three different chamber pressures are examined. Predictions show a good agreement with measurements qualitatively and quantitatively. Based on the results, the predictions of SRK EOS are closer to the experiment, while the ARK EOS has more deviation than the others. Moreover, the 𝑘 − 𝜔 𝑆𝑆𝑇 model has a better performance than the other turbulence models. It is also found that the flow field is controlled by two vortices which resulted from extreme expansion of oxygen dense core and high velocity of inlet gaseous hydrogen into the chamber. Chamber pressure increment delays transcritical condition and also increases flame length and length of secondary vortex and decreases expansion zone. Furthermore, two detailed chemical mechanisms of Burke and Konnov, had a similar result. Keywords: Real equation of state; High pressure; Combustion; GH2/LO2; Supercritical 1. Introduction: High-pressure combustion devices such as gas turbines [1], diesel engines [2-4], and liquid rocket engines demonstrate more complicated combustion phenomena rather than the conventional combustion devices due to pressure effects. Approximately, the range of critical pressure for most of the hydrocarbon fuels is around 15 to 30 bar [5], while, the operating pressure of air turbine engines is about 30 bar [6] and over time, it has being increased nearly by linear rate [6]. Moreover, the


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operating pressure of typical diesel engines are as high as 60 bar [7] and it is much higher for rocket engine chambers [8]. Using high-pressure injection devices with pressures higher than propellant critical pressure causes more complicated phenomena which ha to be considered. These devices always operate over supercritical pressures but the injection temperature could be either sub or supercritical. A cryogenic propellant demonstrates even a more complicated condition in which liquid oxidizer with subcritical temperature is injected into a chamber with much higher pressure and temperature than the critical point of the fluid, so the injected liquid undergoes a transcritical state that is a fast transition to the supercritical state. In these chambers, there are high-density ratios of species, the drastic decrement of surface tension and evaporation enthalpy, and variations in transport properties [9, 10]. Behavior of the injected fluid in supercritical or transcritical condition could not be accounted as liquid or gas; actually, its behavior is liquid like in term of density and gas like in term of transport properties [11, 12]. Subcritical injection phenomenon is exposed to standard processes associated with droplet and atomization [13]. On the other hand, this phenomenon disappears at near-critical and supercritical conditions [14]. At subcritical condition, the flame structure would be controlled by droplet evaporation and break up resulted from high momentum flux ratios, while at supercritical condition turbulent mixing, due to supercritical fluid gradients at the shear layer, local strain rates, and contact surface area conduct the flame structure [15]. Until now several numerical and experimental investigations have been carried out to identify the phenomenological aspects of combustion under transcritical or supercritical combustion but it seems that they are insufficient. H2/O2 combustion was studied experimentally by AFRL (Air Force Research Laboratory) in France, DLR (Deutsches Zentrum für Luftund Raumfahrt) in Germany [11, 16-18], Mascotte test facility operated at ONERA [13, 19-21] in France, University of Florida [22, 23], Cryogenic Combustion Laboratory (CCL) at Pennsylvania State University [24, 25], and FFSC (French Family Science Center) laboratory in Duke University [26]. Moreover, CH4/O2 supercritical combustion is also


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investigated in less rather than H2/O2 by some researchers [27-29]. To reach a more depth understanding of supercritical or transcritical injections, injections of CO2 and N2 into a high-pressure environment including N2 and CO2 mixture are experimentally investigated by Newman and Brzustowski [14]. They showed that the jet structure under supercritical condition is different from subcritical one and Jet acts like a single phase fluid but with a high-density gradient, suppression of surface tension and spray formation. Chehroudi et al. [18, 30-33] performed experiments on liquid N2 injection, with subcritical temperature, into an N2 containing environment at 300 K and different pressures. They also reported a drastic variation in jet surface structure and disappearing the ligaments and droplets formations under supercritical in agreement with the Newman results. Mayer et al. [10, 12, 34] also investigated the liquid nitrogen injection into a mixture of nitrogen/helium under a range of pressures from subcritical to supercritical conditions. They showed that for injected liquid N2, conversion to gas like phase is due to the shear layer instability and also disappearing the surface tension inside of it. Oswald et al. [16] reported the axial profiles of temperature and density for injection of cryogenic jet under supercritical pressures. They reported high gradients inside the jet during transition from sub to supercritical condition due to variation of thermophysical properties during this transition. Some more quantitative, rather than qualitative, experimental study on injection in supercritical condition, were also done to provide the basis for numerical studies. Pal et al. [35] measured droplet size and velocity of LOX/GH2 and compared the results with a water/air injection. The results indicated that measured droplets for reacting cases were larger than that of coldflow cases. Mayer & Tamura [12] studied the injection, ignition, and steady-state combustion at chamber pressures between 1.5-10.0 MPa. In the cold-flow, the results showed a spray atomization behavior at subcritical pressures whereas a gas-gas type of mixing behavior resulted in supercritical pressure. For the reacting cases, flames always attached immediately to the LOX post. The recirculation zone behind the LOX post controlled the LOX/GH2 mixing process. Juniper et al. [21] experimentally studied the combustion of LOX and GH2 at both sub- and supercritical chamber pressures (5 to 70 bar). They also reported the attached flame to the LOX post tip at supercritical


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pressures and dominant role of the large-scale turbulent mixing. Ivancic & Mayer [36] measured the length and time scales of the turbulent reacting flow of a coaxial injector experimentally and numerically. Clauss et al. [37] gave an overview of research at DLR and ONERA labs on LOX/GH2 spray and combustion and focused on Coherent Antistoke Raman Scattering (CARS) diagnostics for temperature and species measurements. overview of work performed at ONERA’s Mascotte test bench on cryogenic propellant (LOX/GH2) combustion was done by Habiballah et al. [19] and showed the consistency between the results of different works. Candel et al. [38] studied cryogenic combustion at high pressures on the Mascotte facility experimentally. They indicated that the combustion at supercritical condition is mixing-limited and reported the attachment of the flame to the oxygen injector over the whole operation range. The reported measurements on the aforementioned experiments are limited to OH contours and temperature profiles. The velocity field was not measured which is not often the case for an experimental database intended to be a validation benchmark for the numerical predictions. In parallel with measurements, some numerical studies were also done to complement our understanding of supercritical spray and combustion. Bellan et al. [39, 40] investigated the effect of the equations of state and turbulence on flow filed using a Direct Numerical Simulation (DNS) approah. They showed the DNS ability in the modeling of the supercritical condition, especially in mixing layer. Foster and Miller [41, 42] investigated the reacting mixing layer between O2 and H2 flows using LES and DNS methodologies and presented an analytical method for the sub-grid scale modeling.

Although their predictions for the direction of the mass diffusion vectors were accurate, somewhere, there were some disagreements in terms of the magnitude. Oefelein and Yang [43] studied the stabilization point of O2-H2 flame at cryogenic conditions using the Eulerian method. They observed the flame is stabled near the tip of the injector at transcritical and supercritical mixing condition. Juniper [44] investigated the extinction strain rate for LOX/GH2 and found that it increases with pressure. Masquelet [45] investigated flame dynamics inside LREs (Liquid Rocket Engines) using LES method and studied the effect of multiple-injector on combustor and wall heat flux. Their modeling


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using a simplified chemical mechanism showed some deficiency in the heat flux prediction. Cutrone et al. [46] studied the H2-O2 flame structure using Reynolds Averaged Navier–Stokes equations (i.e. RANS) method using low-Reynolds number 𝑘 − 𝜔 turbulence model, Flamelet/Progress Variable (FPV) combustion model, Peng–Robinson equation of states (EOS), and four chemical mechanisms of Li [47], Warnatz [48], Jachimowski [49], Marinov [50]. They showed that the Eulerian single phase approach is suitable for such conditions and the Li mechanism leads to a more accurate prediction of fame structure compared to the other chemical mechanisms. Poschner and Pfitzner [51-53] presented an implementation of real gas models into a CFX commercial CFD tool in the RANS context to study combustion under transcritical and supercritical conditions. They applied the standard 𝑘 − 𝜀 turbulence model, CFX-RIF combustion model, Redlich–Kwong, Peng–Robinson, and ideal gas EOS on the test study. In their work, the predicted flame length is longer than the measured length. Park et al. [54] examined various PISO algorithms at a RANS approach for a GH2-LOX flame at supercritical pressure using the Soave–Redlich–Kwong (SRK) and ideal gas EOS, flamelet model, and the standard 𝑘 − 𝜀 turbulence model. They did a comparison between different solution methods and recommended a solution procedure with updating the mole fractions in the pressure correction loop to increase modeling stability; however, the flame length was overestimated. Banuti [55] presented a new model for real gas thermodynamics. This model was applied to RANS simulation of the supercritical reactive LOX/GH2 injection and improved the predictions. Their computation of 0D phase change with heat addition shows good cost performance even near the critical point. It should be considered that most studies mainly employed Peng–Robinson [56] or Soave–Redlich– Kwong [57] equations of state and the standard 𝑘 − 𝜀 turbulence model. The performance of other EOS models such as ARK and other two-equations turbulence models could also be investigated for the supercritical combustion regime. Indeed, most of the studies in relation with transcritical and supercritical combustion are in progress while they are costly and time consuming rather than the conventional combustion condition. In this way, finding a modeling setup with reasonable time and


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cost might be worthy and is still a challenge in process of parametric studies. In this way, the main objective of present work is to model the supercritical combustion with a comprehensive investigation of the effect of different turbulence models, equations of state, and chemical kinetic mechanisms for various operating pressures on flame structure. In this work, the geometry and operating conditions are first explained. Then, numerical methods are explained completely. In section 4, flame structure is considered through the effects of equation of state, turbulence, chemical kinetics, and pressure. 2. Geometry and operating conditions The geometry of Mascotte cryogenic combustion test facility is shown in Fig. 1 [58]. In this cryogenic combustion test facility of the ONERA in France [19], hydrogen-oxygen and methane-oxygen flames are tested at different pressures and flow rates. The A-60 test case is similar to the RCM03 case which is defined at the 2nd International Workshop on Rocket Combustion Modeling [59]. Data measurement of the combustion test facility was done by optical diagnoses including planar Laser-Induced Fluorescence (PLIF) [21, 38, 60, 61], backlighting, and Coherent Anti-Stokes Raman Spectroscopy (CARS) [19, 62]. Quantitative temperature measurement was measured using CARS and flow visualization was achieved through OH PLIF. The combustion chamber is a quadrangular duct in which the inner and total length are 50 mm and 458 mm respectively. The chamber has a nozzle with a 9 mm throat diameter and a 20mm convergent length. The combustor has one single coaxial injection element as shown in Fig. 2. The oxygen injector diameters are 3.6mm in the inlet and 5 mm in the outlet which are connected by a slop of an 8◦ angle. Hydrogen is injected through a coaxial injector within oxygen. This injector has 5.6 mm and 10mm inner and outer diameters respectively. The combustion of GH2-LOX has been studied in a wide range of pressure from 0.1 MPa to 7 MPa. In terms of momentum-flux ratio, the combustion of GH2-LOX is classified into two low and high


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momentum-flux ratios which are respectively entitled to (C) and (A). The operating conditions of Mascotte test facility were determined for pressures about 1.0 MPa (A10, C10), 3.0 MPa (A30, C30) and 6.0 MPa (A60, C60) [19]. In this study, the experimental test case is A-60 which its operating conditions are given in Table 1. The Chamber pressure is at 60 bar which is higher than the critical pressure of oxygen (i.e. 50.4 bar) while oxygen temperature is lower than the critical one (i.e. 85 K). However, hydrogen is injected into the chamber at a supercritical pressure and temperature. 3. Numerical method As mentioned above, the A-60 test case is used here. Flow field inside the chamber is threedimensional. By applying some simplifying assumptions, the geometry was modeled using a 2Daxisymmetric computational domain. According to the method used by Poschner and Pfitzner [51], the Mascotte square duct is equivalent to a cylinder with the radius of 28.81 mm. Figure 2 shows quasi-two-dimensional model which is used as a computational domain. Reynolds-Averaged Navierstokes equations are solved using a pressure-based approach by the Simple-C pressure correction algorithm under steady state condition. Two-equation turbulent models including 𝑘 − 𝜀 standard, 𝑘 − 𝜀 RNG, 𝑘 − 𝜀 Realizable, 𝑘 − 𝜔 SST have been examined in this study. Turbulence-chemistry interaction was embedded by the (Eddy-Dissipation Concept EDC model. In this model, Arrhenius finite rate is applied for every fine scale control volume characterized by the flow field turbulence properties. The H2/O2 reaction mechanism of Burke et al.[63] is used to represent the chemical kinetics as shown in Table 2. A hybrid grid with approximately 35,000 cells which distributed among multi-block structures has been used for the computational domain. More than 94 percent of cells are structured. Mass flow inlet is used for hydrogen and oxygen boundary conditions. The no-slip adiabatic condition is assumed on all walls. The computational domain, the coaxial injector, and the boundary conditions are shown in Fig. 2.


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3.1. Equation of state, thermodynamic and transport properties At high-pressure condition, when pressure is above the critical point, mean-free-path decreases and intermolecular interaction can no longer be ignored. Also, the molecules volumes that occupy space are not negligible. So, the Ideal gas equation of state at supercritical conditions is not able to predict the properties correctly, such as density. In 1873, van der Waals used two assumptions and suggested a new equation of state that established the base of cubic equations of state. Researchers have proposed different real state equations, but the most applicable ones are Soave–Redlich–Kwong (SRK) [57], Peng–Robinson (PR) [56], and Aungier–Redlich–Kwong (ARK) [64]. So, these real EOSs are examined in this work. The equations of state can be summarized in the following general formula and coefficients given in Table 3.

𝑃=

𝑅𝑇 𝑎0 𝛼(𝑇, 𝜔) − 2 𝜐̃ − 𝑏 + 𝜉 𝜐̃ + 𝛩𝑏𝜐̃ + 𝛯𝑏 2

(1)

Where 𝑅 is the universal gas constant and 𝜐̃ is the molar volume. The parameters 𝑎 = 𝑎0 𝛼(𝑇, 𝜔) and 𝑏 account for the effects of attractive and repulsive forces between molecules. 𝛼(𝑇, 𝜔) is an nondimensional factor which becomes unity by 𝑎(𝑇𝑐 ) = 𝑎0 . Acentric factor, 𝜔, is used for quantifying the deviation from the spherical symmetry in a molecule. The subscripts 𝑐 and 𝑟 refers to critical and reduced condition, respectively. 𝜉, 𝛩, and 𝛯 are Coefficients of the general equation. In a mixture of several gases, equations of state should be used with non-linear mixing rules [5]. Therefore, to calculate the parameters 𝑎𝛼 (i.e. 𝑎0 𝛼(𝑇, 𝜔)) and 𝑏, the following relations can be applied. 𝑁

𝑁

𝑎𝛼 = ∑ ∑ 𝑋𝑖 𝑋𝑗 √𝑎𝑖 𝑎𝑗 𝛼𝑖 𝛼𝑗 (1 − 𝜅𝑖𝑗 )

(2)

𝑖=1 𝑖=1

𝑁

𝑏 = ∑ 𝑋𝑖 𝑏𝑖

(3)

𝑖=1


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Where 𝑋𝑘 is the mole fraction of species 𝑘 (among N species) and 𝜅𝑖𝑗 is the binary interaction coefficient. At high-pressure condition, to estimate the thermodynamic properties such as enthalpy, entropy, internal energy, and specific heat, their dependency on pressure as well as temperature could be considered. Therefore, to calculate the thermodynamic properties, constant pressure and temperature paths are used [5]. Due to the fact that the properties in reference state can be easily calculated, constant pressure is usually selected as the reference pressure, so the subscript 0 refers to it. The use of constant temperature path leads to pressure correction term. By implementing the departure functions and Maxwell relations, they can be represented in a practical form [5, 65]. Finally, the thermodynamic properties can be expressed as follows [66, 67]: 𝜌

𝑒(𝑇, 𝜌) = 𝑒0 (𝑇) + ∫ [ 𝜌0 𝑃

𝑃 𝑇 𝜕𝑃 − 2 ( )𝜌 ] 𝑑𝜌 2 𝜌 𝜌 𝜕𝑇 𝑇 1

ℎ(𝑇, 𝑃) = ℎ0 (𝑇) + ∫ [ − 𝑃0

𝜌

𝑇 𝜕𝜌 ( ) ] 𝜌2 𝜕𝑇 𝑃 𝑇

𝑑𝑃

(4)

(5)

𝜌

1 𝜕𝑃 𝑠(𝑇, 𝜌) = 𝑠0 (𝑇, 𝜌0 ) − ∫ [ 2 ( )𝜌 ] 𝑑𝜌 𝜌 𝜕𝑇 𝑇

(6)

𝜌0

𝜌

𝐶𝑝 (𝑇, 𝜌) = 𝐶𝑉0 (𝑇) − ∫ [ 𝜌0

𝑇 𝜕2𝑃 𝑇 𝜕2𝑃 𝜕𝑃 ] ( ) 𝑑𝜌 + ( 2 )𝜌 /( ) 𝑇 𝜌 2 2 2 𝜌 𝜕𝑇 𝜌 𝜕𝑇 𝜕𝜌 𝑇

(7)

Where 𝑒, ℎ, 𝑇, 𝑃, 𝑠, 𝜌, 𝐶𝑝 , and 𝐶𝑉 represents the internal energy, enthalpy, Temperature, Pressure, entropy, density, constant pressure specific heat, and constant volume specific heat, respectively. The viscosity and thermal conductivity of transcritical or supercritical fluid conditions are generally based on the model derived by Chung et al. [68]. In this model, the viscosity and thermal conductivity of low-pressure dilute gases formulated based on the kinetic gas theory- that extends the Chapman– Enskog theory (CET) [69]- are corrected by empirical correlated functions of density and temperature to confirm dense fluid effects at high pressures.


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3.2. Grid study For the current study, 14 test cases have been studied and described in Table 4 to conduct the study toward the investigation of effects of turbulence models, the equation of state, chamber pressure, and chemical mechanisms. At first, to achieve optimal computational domain cells, several grids were examined. Grid independence study is done for three grids of 35000, 53000, and 70000. The grid with lower cost is chosen as shown in Fig. 3. It is worthy to say that the grid study has been performed using adaptation technique base on OH gradient. In Fig. 3, the temperature and mass fraction of species OH, O2, H2O have been compared which show acceptable agreement with each other therefore a grid with 35000 is chosen in continuation. To ensure the accuracy of the modeling, the numerical results are validated with the available experimental data [51]. Fig. 4 illustrates the axial temperature distribution in the chamber. Fig. 5 represents the contour of OH and the Comparisons with experimental data [21] (Abel transform of the time-averaged natural OH* emission images). As can be seen, the numerical results are in good agreement with the experimental data. Therefore, it can be concluded that the assumptions applied in the modeling have been had reasonable performances. 4. Result and Discussion In this study, to investigate GH2-LOX supercritical combustion, the following steps are considered. First, the effect of ideal and real gas equations of state are examined. Second, the structure of predicted flame in the best result is considered and the flame structure is described. Third, different turbulence models are checked for supercritical condition. Fourth, the behavior of three of the real gas EOSs (PR, SRK, ARK) is compared. Fifth, the effect of two different chemical mechanisms on prediction is studied. Finally, the effect of pressure increase on the flame structure is investigated. 4.1. The effect of real gas equation of state


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When the pressure is too high, the assumptions about the ideal gas is no longer true, because the intermolecular interaction cannot be ignored. As the mean-free-path is decreased, the volume occupied by the molecules should not be ignored. Therefore, modern equations of state are needed to be more accurate. Fig. 6 shows the predicted flame shape of A-60 test facility using the ideal and the non-ideal equation of state. All conditions are same in both modeling and just only the equation of state is different. It is seen that the flame shape and its length is too different for two predictions. Evidently, the real gas EOS is much closer to the experimental data (i.e. Abel transform of the timeaveraged natural OH* emission images). Fig. 7 shows axial profiles of density, pressure constant specific heat, compressibility factor, and temperature resulted from two mentioned equation of states. For the ideal gas EOS, the density of oxygen core (i.e. Fig. 7-a) is one-fourth of value predicted by the non-ideal gas EOS. So the velocity and consequently the length of the flame has increased for ideal gas EOS. Although maximums of temperature axial profiles for both models are equal, their locations are so different (i.e. Fig. 7-b). The difference between the flame shapes is due to the wrong estimations about the density of oxygen core, inappropriate estimations on the gradient of the density of oxygen core passing through the transcritical state, and inability to approximate the pseudo boiling process of dense oxygen core when passing the transcritical state. When the chamber pressure is higher than critical pressure of propellants and 𝑇⁄𝑇𝑐 < 1, as the chamber is at a high temperature, the temperature of the dense core will increase and should pass the transcritical state. When passing the critical temperature, severe gradients appear in thermo-physical properties. For example, the density decreases three orders of magnitude in a distance of 5 cm. Specific heat at constant pressure (𝑐𝑝 ) has drastic changes and increases five times compared to the ideal condition (i.e. Fig. 7-c). High specific heat enables the fluid to absorb heat while its temperature changes is very little. Fig. 7-d show that the compressibility factor at the entrance of the chamber is estimated to be 0.2 and its deviation from the ideal state is very high.


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Finally, it can be said that the assumptions of the ideal EOS is not suitable for this situation and this results confirm the previous studies of Pohl et al [70], Cutrone et al [46, 71], T.Kim et al [72-74], Poschner et al [51], Smith et al [75], Petit et al [76], S.Kim [77], and Ruiz [78]. 4.2. The structure of flame Due to the combustion complexities at critical condition, the different experimental investigations have been done on the flame structure. Juniper et al [21] provided experimental data on jet flames of liquid oxygen and gaseous hydrogen via spectroscopy and backlighting for OH* emission to investigate the flame structure. Habiballah et al [19] studied experimentally on LOX/H2 flame structure, using imaging techniques such as shadowgraphy and CARS diagnostics. They emphasized on differences of flame structure in the sub and supercritical regimes. In this way, it has been tried to get a more comprehensive explanation of the trans and supercritical flame structure by current numerical data. From hereafter the analysis of flame structure is based on the most accurate modeling (i.e. case No.9). The results of the test case 9 has the most compatibility with the experimental data in which the turbulence model 𝑘 − 𝜔 𝑆𝑆𝑇 and SRK EOS are used. In the current simulation, according to the operating conditions of chamber pressure(i.e. 60 bar), the Burke et al. [63] mechanism is used which includes 13 species and 27 elementary reactions. This mechanism is presented for oxygen-hydrogen combustion in high pressure. Fig. 8 describe the static and dynamic pressure, axial velocity, density, specific heat in constant pressure, and molar volume at the axis. As seen in Fig. 8, the density has a severe gradient and decreases rapidly along the axis. The specific heat, 𝑐𝑝 , has drastic changes and goes upward first, then it comes down. Raise in 𝑐𝑝 increases the capacity of heat and then pseudo boiling happens. Dynamic pressure reaches a maximum and suddenly decreases rapidly. Static pressure decreases severely, reaches a minimum, then rises up and goes constant. Due to trifle changes in axial velocity in the range of 2 ≤ X/dLOX ≤ 13 and severe decrease in density of LOX, static pressure increases. Regarding the


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pressure behavior, it can be said that the reduction of intermolecular attraction leads to drop in density that means for a constant mass, the volume must expand. Therefore, the mean-free-path increases which leads to an increase in the pressure. According to the Fig. 8, axial velocity between 2 < X/dLOX < 13 is approximately constant while density decreases drastically. The extreme density gradient causes an expansion of LOX and diverts the hydrogen stream upwards. On the other hand, the zone in which the hydrogen flows, has a low pressure. The inlet velocity of hydrogen is about 300m/s and in spite of low density, it causes a high dynamic pressure and consequently a low static pressure. The deviation of the hydrogen stream leads to a collision with the chamber wall. Part of the stream continues its pathway and part of it returns and makes recirculation zone. As the recirculation, by itself, has a high velocity, it creates a lowpressure zone and influences the hydrogen jet mutually. The streamlines in Fig. 9 show that from X/dLOX>6, the expanded oxygen core in radial axis, selects the low-pressure zone; Therefore, it makes a backflow stream. The pressure difference begins with 5 KPa and grows more along the axial direction. The backflow stream of expansion strikes the high velocity injected hydrogen and inevitably goes in the same way with it. Now if the zone 11 < X/dLOX < 16 and 2 < R/dLOX < 4 is considered, axial velocity changes will be seen along the radial direction. In this zone, there is a location in which axial velocity direction variation of 180 degrees is observed causing an inner recirculation zone (IRZ). It was observed that in X/dLOX > 16 the expanded volume of oxygen was affected by the hydrogen stream near the wall and was directed to the same direction and had no longer backflow stream. In addition, from X/dLOX = 16 onwards, the compressibility factor was 1.0, the effects of real gas were gone and its behavior was close to ideal gas. Also in agreement with aforementioned descriptions, the transcritical mixing and reacting flow are studied numerically by Kim et al. [72] and is founded that weak flow recirculation is induced by the sudden expansion of cold core cryogenic oxygen associated with the pseudo-boiling process. This weak recirculation zone is effective on flame length and spreading angle. Ruiz [79] examined flame structure with LES and DNS method


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and emphasized on the mentioned flame zone near the injector. Also, he showed that a corner and a central recirculation zone are present in this flame structure although did not explain widely about that. Fig. 10 shows the zero axial velocity and zero radial zones which are respectively displayed by dotted and dashed-double dot lines . These lines meet each other in four points which are illustrated in the figure. Point A is the location which happens right after the tip. By drawing the streamlines, a vortex was seen in it. It is called the anchor which causes the oxygen and hydrogen to premix well with each other right after the tip in shear layer. This location is fuel rich and is ignited immediately, so combustion happens. Fig. 11 shows the measurements temperature of Near Injector region of a LOXGH2 shear-coaxial injector at supercritical pressure [12]. The bright spot in Fig. 11 shows the recirculation zone right after the tip. In agreement with the measurements, the region near the shear injector and the recirculation zone was also illustrated in Fig. 10. It is worthy to say that the near injector tip recirculation also has reported in Candel et al [38], Oefelein [80], and Oefelein et al [81]. Point B indicates the center of outer recirculation zone which is generated by the impingement of the outer hydrogen jet on the chamber walls. Point C illustrates the center of inner recirculation zone. Point D shows the end of the IRZ which the expanded oxygen no longer returns. In other words, Point D is a stagnation point. The distance between C and D is taken as a criterion of IRZ length and is shown by 𝐿𝐼𝑅𝑍 and will be used in subsequent sections. As the results, the flow field in the trans and supercritical combustion is different. The structure of two recirculation zones and the backflow streamlines are observed. As another point, the extreme density gradient causes an expansion of LOX and great effect on flow field and diverting the hydrogen stream upwards. 4.3. The effect of turbulence models The experimental data of A-60 test case is not enough for validation. So, by defining parameters on experimental contours (i.e. Abel transform of the time-averaged natural OH* emission image), a


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better comparison can be done. It is worthy to say that although OH and OH* could not be collocated due to OH* dependency on heat-release rate and temperature, the trends of both of them may be considered similar, as typically used in some reports [82], especially regarding the compared parameters in this study. Fig. 12 indicates the contour of OH* emissions in which the locations are normalized based on the oxygen injector diameter. There is a region in which the OH* spreading rate is constant. It is shown by 𝐿1 that is in a range of 0-8 for X/dLOX . In 𝐿1 , the spreading angle is shown by 𝛽 which is the location of maximum OH* intensity in this region. The measured amount of 𝛽 is 4.4o degrees. The axial location of maximum intensity of OH* is shown by 𝐿2 which is in 22 × X/dLOX . The location in which the OH* intensity is half of its maximum was selected for a criterion of maximum spreading. Point G show the location of maximum spreading, and two lengths 𝐿𝑥 and 𝐿𝑦 are defined by this point. The measured amounts of Lx and Ly are respectively 12.4 × X/dLOX and 2.7 × Y/dLOX . Now, according to the extracted data from the existence experimental contour, an appropriate quantitative comparison can be done. The most popular of turbulence model that has been used for trans and supercritical condition is the standard 𝑘 − 𝜀 model [51-54, 59, 70, 74, 83-85]. However, another turbulence model such as 𝑘 − 𝜔 model [46, 71, 86, 87] and Spalart-Allmaras [55, 82] was studied for this condition. The results of all studies were compared to the experimental contour qualitatively. While, the results are similar to the experimental contour, but the flame length and the location of expanded area are different in comparison to experiment. So in the following, four different two-equation-turbulence-models are studied to show their performances, both qualitatively and quantitatively. In order to study the turbulence models, SRK EOS is assumed. The studied two-equation turbulence models are 𝑘 − 𝜀 Standard, 𝑘 − 𝜀 RNG, 𝑘 − 𝜀 Realizable, and 𝑘 − 𝜔 SST. By implementing the mentioned parameters to the predictions, the quantitative comparison with experimental data is done and shown in Table 5. The error of each parameter is measured and total error is calculated based on L2 error norm of them, as shown in Table 6. The results in Table 6 indicate that all turbulence models have errors. Based on the defined parameters, 𝑘 − 𝜀 Standard and 𝑘 − 𝜔 SST have the least error.


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The OH mass fraction contour of each model is compared with the experimental OH* emission contour, shown in Fig. 13. In addition, Fig. 14 shows the comparison between the position of the maximum intensity of the Abel-transformed images for cryogenic flames at A-60 operating conditions [21] and position of the predicted maximum OH mass fraction for each modeling. These two figures illustrate the similarities and differences between the predicted flame shapes and the OH* contour of current experimental data and points out that the 𝑘 − 𝜔 SST turbulence model has better compatibility. These behavior is discussed in more detail in continuation. So far, the 𝑘 − 𝜔 SST is seemed has a better prediction between the two-equation-turbulence models and it has the least error based on the defined parameters and the highest similarity with the experimental data. At following, another aspect of the comparison is tried to study. Fig. 15 studies the distribution of the temperature, density, OH mass fraction, specific heat in constant pressure, axial velocity, compressibility factor in the axial direction for different turbulence models and experimental data available for the temperature distribution at the axial direction. The maximum temperature in experimental data happens at X/dLOX = 20 and its value is 3565K. For all turbulence models, the quantity and the location of the maximum temperature are measured and is shown in Table 7. The Fig. 15 and the results in Table 7 illustrate that 𝑘 − 𝜔 SST has again a better performance among other models and its results are closer to the measured temperature. In Fig. 15, it is observed that density distribution for different turbulence models at axis direction, performs very differently. It has little change for 𝑘 − 𝜀 Standard and 𝑘 − 𝜀 RNG up to X/dLOX = 20 , and then has extreme gradients. On the other hand, for 𝑘 − 𝜀 Realizable and 𝑘 − 𝜔 SST, the oxygen, a little after entering the chamber, has extreme gradients. Constant pressure specific heat and compressibility factor are also very sensitive to turbulence model and oppose sharp gradients as seen in the figure.


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It was worthy to say that the maximum temperature which affected by the interaction between turbulence and chemical kinetics in the EDC model, is the same for all turbulence models, although its location is predicted differently. The temperature flow field could be used to understand the changes in density, constant pressure specific heat, and compressibility factor. By remembering that Critical temperature of oxygen is 154 K, figure 15 shows that Extreme density gradient is made when the temperature of dense core reaches the critical value. For 𝑘 − 𝜀 Realizable model, the dense core reaches the critical temperature very fast (i.e. closer to the nozzle tip) and after that the transcritical state could be seen. Such an observation is slower for 𝑘 − 𝜔 SST model and much slower for 𝑘 − 𝜀 RNG and 𝑘 − 𝜀 Standard models. That means the extreme density gradient postpone to the downstream of flow for 𝑘 − 𝜀 RNG. The reason of such behavior may be related to the turbulent conductivity coefficient. On the other hand, it may be related to the turbulent viscosity coefficient and therefore different mixing level resulted from different turbulence models. The effects of turbulence models on flame shape can be observed in Fig. 16. It is seen that for the 𝑘 − 𝜀 Standard and 𝑘 − 𝜀 RNG models, the recirculation at near the wall happens at more downstream rather than the others. Moreover Fig. 16 shows IRZ appears differently in different turbulence models. The 𝑘 − 𝜀 Standard model cannot predict the IRZ, maybe due to its poor performance for flows with adverse pressure gradients or predicting axisymmetric jet expansion. A correction in 𝑘 − 𝜀 Standard model by increment in 𝐶𝜀1 coefficient was done (not shown here) but it was not led to improve the prediction accuracy. This finding is in compatible with results of [51]. Therefore, the 𝑘 − 𝜀 Standard model improvement via its constants was not considered here. In comparison with the 𝑘 − 𝜀 Standard model, other models predict flow field’s aspects differently. The vortexes, which are resulted from the hydrogen jet deviation and its strike with the wall, depend on the location in which the extreme density gradient in oxygen core occurs. The faster the extreme gradient, the closer the center of ORZ to the injector and vice versa. The Table 8 indicates the location of points A, B, C, and length of IRZ (𝐿𝐼𝑅𝑍 ) based on X/dLOX . 𝐿𝐼𝑅𝑍 for 𝑘 − 𝜀 Realizable model is estimated to be the longest. The longer 𝐿𝐼𝑅𝑍 , the higher the vortex strength. As a result, the flame is elongated more after the flame expanded


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area (𝐿2 − 𝐿𝑥 ). This phenomenon is probably due to the effect of turbulence field on reaction intensity and the thickness of the reaction zone at (Lx, Ly) which it may be consequently led to a strong flow expansion in this region. As a whole due to few available experimental data, the results of other studies were compared to the experimental contour qualitatively. At this section, it has been tried to get a comparison between numerical and experimental data more accurately and quantitatively. The aforementioned process leads to the selection of the k-w SST turbulence model as the best turbulence model among the twoequation-turbulence models for current study. The high sensitivity of predictions to turbulence model arise from its effect on the turbulent conductivity and viscosity coefficients, and therefore different super to subcritical occurrence location and mixing levels. 4.4. Effect of real equations of state Sove-Redlich-Kwong (SRK EOS) and Peng-Robinson (PR EOS) are the most popular real equation of states that used between the others. Some of the reports used the PR EOS [39, 46, 67, 88-90] and the others used SRK EOS [54, 66, 72, 73, 91-94]. Some researchers considered a comparison between the performance of SRK and PR equation of states [74, 76, 79, 95] in their studies, However, they are not too many. In the present study, three equations of states were chosen and their performances were compared including; PR equation of state, SRK equation of state, and Aungier-Redlich-Kwong (ARK). A modified form of the Redlich-Kwong (RK) two-parameters equation of state is called ARK which employs the acentric and critical point compressibility factors as additional parameters to improve its accuracy and extend its application range to include the critical point and has a better prediction in some thermodynamic properties [64]. Thus, the effect of the three equations of state for supercritical combustion conditions is discussed and compared with each other. Fig. 17 shows the effect of ARK and PR equations of state on the flame shape and compares it with SRK equation of state for temperature and OH mass fraction contours. Fig. 18 shows the comparison between the position of the measured maximum intensity of the Abel-transformed images for


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cryogenic flames at A-60 operating conditions [21] and position of the OH mass fraction maximum in SRK, ARK, and PR. By applying ARK, the flame length is estimated to be 7% less than SRK EOS. Consequently, it has the highest deviation from the experimental contour. The flame length by PR EOS is predicted to be 2% less than SRK EOS. Fig. 19 compares temperature, density, OH and O2 mass fractions, specific heat in constant pressure, axial velocity, and compressibility factor in the axial direction for ARK, SRK and PR EOS. For different equations of state, the density of core oxygen changes. ARK, SRK, and PR EOS show the oxygen density of 1201 𝑘𝑔/𝑚3 , 1321 𝑘𝑔/𝑚3 , and 1180 𝑘𝑔/𝑚3 , respectively. Moreover, the rate of decrease in the density using ARK is higher in comparison to the other two equations of state. The reason goes back to the CP changes in less LC. Therefore, pseudo boiling region in ARK EOS is estimated to be less. Fig. 19 also shows the temperature distribution near the injector, maximum temperature, and its location. Maximum temperature by ARK, PR, and SRK is predicted to be 3510, 3537, and 3550K, respectively. Furthermore, trends of O2 and OH mass fraction variations are in consistency with the density and temperature distribution, respectively. On the other hand, at X/dLOX > 15, the behavior of the three real equations are similar to that of ideal gas. To explain the aforementioned observations, it would be worthy to notice that Van der wales who is the founder of real EOS, assumed that by an increase in pressure, the molecules get close together, so the intermolecular attraction force cannot be ignored which results in pressure reduction. As was mentioned, to calculate the thermodynamics properties at high pressure, the dense fluid correction term is implemented using departure functions. Departure functions use real EOS to calculate its own relations; therefore, it is called self-consistent. The differences in real EOS can be attributed to different attitudes towards pressure attraction coefficient functions. The difference in attitudes appears in specific heat changes in constant pressure and leads to little differences in flame structure. To sum up, the results of SRK and PR are very similar to each other but ARK equation of state shows a little different prediction rather than the other ones. Although this three equation of states have not


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diversity in comparison to each other, the SRK equation of state has the least difference in comparison to the experimental contour. 4.5. Effect of chemical mechanism In this section the effect of chemical mechanism on predictions are investigated through three chemical mechanisms; one overall one-step mechanism, and two detail chemical mechanisms. First, a one-step mechanism was studied in cases 1-5 of Table 4. The result showed a maximum temperature 4400K on the axis which was about 750K away from the experimental data. It also estimates the location of maximum temperature inaccurately at downstream. At high-pressure condition, some of the elementary reactions get noticeable and should be considered in modeling. Burke mechanism [63] was presented for high-pressure condition in 2012. It is a 27-step mechanism with 13 species and is applicable for oxygen-hydrogen combustion with inert gases. It is an improved version of Li mechanism[47] which is a mechanism for hydrogen-oxygen combustion at high-pressure conditions in range of pressure 0.3 to 87 atm, temperature from 298 to 3000K, and equivalence ratio from 0.25 to 5. Li mechanism is based on Mueller [96] mechanism and introduced in 2004 which in comparison to Mueller, it is validated in a wider range for shock tube, flow reactors, and laminar premixed flames and showed a good performance. Hence, Burke mechanism has been used in the current numerical simulation, to study the effect of mechanism on the flame structure, another different mechanism has been selected which is developed by Konnov [97] in 2008. H2/O2 Konnov mechanism has 31 steps with 10 species and is used for high-pressure condition which is tested experimentally for temperature in the range of 950 to 2700K and pressure in the range of 0.3 to 87 atm. Fig. 20 shows the contours of temperature and OH mass fraction and superimposed streamlines for Burke and Konnov chemical mechanisms cases. Comparisons of results show that the flame shape and the streamlines have no difference. Moreover, profiles of OH, O2, H2 , and H2O mass fractions at axial and some radial directions are relatively same for both chemical mechanisms. Furthermore, the maximum temperature at axis for both mechanisms were 3550K. Therefore, it can be concluded that


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the performance of these two mechanisms at supercritical combustion for the A-60 operating condition, is the same. Simultaneous effect of the non-ideal gas EOS, the chemical mechanism, and turbulence model can be seen in Fig. 21. Initially, as it was expected, ideal-gas EOS cannot estimate the correct location of the flame maximum temperature on the axis. Therefore, according to the reasons mentioned in the previous, by the alternation of the ideal gas EOS into non-ideal gas EOS, the predicted location of the maximum temperature improved. By implementing detailed chemical mechanism instead of the overall one step, the location and amount of the maximum temperature at axis improved in more. The effect of turbulence models could be seen in the figure which is the 𝑘 − 𝜔 SST model has gotten the best agreement with the experimental data. It seems that both of Burke and the Konnov chemical mechanisms has the same performance for the current supercritical test case. 4.6. Effect of pressure on flame structure One of the most important parameters for the transcritical and supercritical combustion is pressure to figure out what happened to the flame structure. In this section, the flame shape at higher pressures is studied. To study the effect of pressure, two other high-pressure chambers of 80 bar and 100 bar were modeled. Fig. 22, shows contours of temperature and OH mass fraction, and streamlines in the flow field for chamber pressures of 60,80, and 100 bar. As it can be seen maximum temperature, as well as flame length, is increased for higher pressures. To get a more precise description of the pressure effect on the flame structure the defined parameters in Fig. 12 are focused here. In this way, the parameters defined on OH* experimental contour, are presented in Table 9 based on three pressure levels. It is observed that L1, in comparison to P= 60 bar, had 3% increase for P=80 bar and 25% for P= 100 bar. Thus, by pressure increase, L1 enlarges. L2, defining the flame length, increased 2% at P=80 bar and 10% at P=100 bar. In comparison to P=60 bar,


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Lx and Ly had 1% and -0.5% changes at the P=80 bar, respectively, and at P=100 bar, 14.5% and -8.7%. So, by pressure increase, Lx increases and Ly decreases. At pressures of 80 bar and 100 bar, spreading angle changes are 1% and 25% which means it decreases with increasing pressure . In Fig. 23, maximum temperatures at pressures 60, 80, and 100 bar, are respectively 3550, 3582 and 3613 K. Thus, by pressure increase, not only does the location of maximum temperature changes, but also the maximum temperature increases. Most probably, by pressure increase, recombination reactions are augmented, so the temperature increases. Such as observation is also reported by Kim et al. [70] for CH4/O2. Although the flame structure of CH4/O2 in comparison to H2/O2 is different, they attributed the effect of pressure to the weakening of pseudo-boiling characteristics by elevating temperature and pressure. By studying streamlines and vortexes, it is observed that the center of the vortex near the wall at P=80 bar does not change very much, but, at P=100 bar, is produced away from the injector. Based on what was mentioned, the reason could go back to the changes in specific heat in constant pressure. It is also seen that increasing pressure makes the size of ORZ greater. When the pressure increases, molecular diffusion increases too. Consequently, it raises the reaction rate and affects the recombination reactions, so it elevates the temperature. This uplifts the velocity and affects the LIRZ. Table 10 presents the locations of points B, C, D, and also LIRZ, based on X/dLOX. To complete the discussion on the pressure effects on the flame structure, Fig. 23 is considered to show axial profiles of temperature, density, mass fraction of OH, and specific heat at constant pressure for three pressures. By pressure increase, CP profile changes in the axial direction. For 60 bar and 80 bar, CP increment begins at X/dLOX =1 and reaches its lowest amount at X/dLOX = 15.2. But at pressure 100 bar, CP changes in range X/dLOX =1 and X/dLOX =16.8. To study the behavior, these range of changes will be shown by LC. By observing the behavior of CP through the LC, temperature changes can be studied. CP changes at pressure 100 bar happen at a greater LC. Thus, the zone of little changes in temperature happens in a greater range and the rapid rise in temperature, in comparison to pressure


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60 and 80, happens at farther X/dLOX . In other words, jet dense core preserves its nature to further areas from the entrance and transition delays. With the same attitude, density profiles differences at different pressures along the radial direction are definable. For example, in X/dLOX =15, oxygen density at pressures 60, 80, and 100 bar is respectively 396, 387 and 168 K; The lower the temperature, the higher the density. According to the report of Li [47] and Burke [63] (Fig. 24), In hydrogen-oxygen combustion, H+O2 reaction which is one of the chain branching reactions is very important. When the pressure of the chamber is low and the temperature is high, oxygen turns into two oxygen atom radicals and one of them reacts with a hydrogen atom and becomes OH radical. But when the pressure is high and the temperature is low, only one of the oxygen molecular bonds will break and combines with a hydrogen atom and becomes stable HO2 species. So, the HO2 chemical reaction is highly regarded. To go into the detail, Figure Fig. 25 shows the flow residence time contour, in which HO2 production and consumption zones are imposed on it. As it can be seen, HO2 is produced and consumed inside or near the regions with considerable flow residence time. Indeed, there are two regions with the largest flow residence time resulted from the backflow; one in the inner region of the reaction zone and another one in the outer region. Interestingly, in the inner region, HO2 is consumed very intensely and the region with the highest residence time is bounded the HO2 reaction. That means any change in residence time resulted from flow field prediction could directly affect heat release rate and vis versa. Because the flow field inside the chamber completely depends on oxygen jet expansion and the recirculation and their impact on residence time, so this combustion chamber shows a high sensitivity to the predicted ratio of flow residence time to the chemical time-scale. To follow the aforementioned description of Fig.24 here Fig. 26 are shown for the comparison of contours of mass fraction of species between Pch=100 bar (top) and Pch=60 bar (bottom). By increasing pressure, it is observed that the H radical decreases. It is also found that HO2 radical has increased in the regions where the pressure is high and the temperature is lower than flame. Increased H2O2 and


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O2 can also be seen there. So, at this condition, HO2+HO2 reaction, in Fig. 24, is augmented and the reaction becomes more important by increasing pressure. It means that the ignition is fortified by an increase in pressure. On the other hand, as a result of higher penetration of oxygen core (according to density contour) and delay in transition, flame length enlarges by pressure increase which is confirmed by the distribution of H2O, O2, H2O2 and H species. In addition, the flame thickness at radial direction is measured and the results are showed that the thickness of flame decreases by elevating pressure, it is clear in Fig. 27. In agreement with the mentioned discussions, also Ribert et al [66] investigated a laminar counterflow diffusion flame of H2/O2 for the effect of the pressure on heat release and flame structure. They showed that the H radical depleted and the role of H+O2



HO2

pathway was highlighted. On the other hand, by increasing pressure, thinner flame with a higher flame temperature was seen. Lacaze et al [67] studied non-premixed H2/O2 flame at supercritical combustion and the heat release sensitivity to pressure was inquired. By elevating pressure, they also explored that the maximum flame temperature increased and the flame thickness changed. Moreover, Kim et al. [73] examined the flamelet equation in the mixture fraction space for the transcritical and supercritical H2/O2 combustion. They discussed the effect of real fluid and the pressure on the flame structure. The examinations showed a high sensitivity of H and HO2 to the pressure and found that the OH zone is briefly reduced by increasing pressure. All in all, chamber pressure increment affected the flame shape in terms of length, spreading angle, the size and the position of IRZ and ORZ through an increase in molecular diffusion, the reaction rate, and so temperature. On the plus side, in H2/O2 combustion, a great deal of importance is placed on the H+O2 reaction which is related to the chain branching reactions. This reaction produce the HO2 stable species at the high pressure and the low temperature. So, by increasing pressure, the concentrations of HO2 and H2O2 species augment in the hydrogen jet zone and the importance of the HO2+HO2 reaction is highlighted. 5. Conclusion


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The present study has investigated numerically combustion of gaseous hydrogen/ liquid oxygen at the transcritical and supercritical condition. The A-60 Mascotte test facility has been chosen for the investigation. This framework was modeled using a 2D axisymmetric RANS method in the steady state condition. For turbulence-chemistry interaction, the EDC method was selected. Also, the detail chemical mechanism of Burke which is an updated form of Li mechanism was chosen. It is a 27-step mechanism with 13 species and presented for high-pressure condition. The following main conclusions can be drawn from results. It is clear that the ideal gas cannot satisfy the PVT behavior of supercritical condition, so, the real EOS must be used. When the oxygen dense core is faced to the transcritical state, the extreme expansion occurs which this diversity affects the flow dynamics. In addition, two recirculation zones have been seen. The ORZ is created by the impingement of the H2 jet to the wall, while the extreme expansion of oxygen dense core is caused the IRZ. Effect of turbulence models: Some two-equation-turbulence models (i.e. 𝑘 − 𝜀 Standard, 𝑘 − 𝜀 RNG, 𝑘 − 𝜀 Realizable, 𝑘 − 𝜔 SST) were examined and the results showed that the 𝑘 − 𝜔 SST turbulence model has the nearest answer in comparison to the experiment (i.e. temperature distribution at axial direction, the OH* contour, and the defined parameters) rather than the other models. The effects of the turbulence model on flame shape showed that the predicted aspects of the size and the location of recirculation zones were different using various turbulence models. The 𝑘 − 𝜀 Standard model couldn’t predict the IRZ. The predicted flame lengths after expansion area were different and probably due to the effect of turbulence field on reaction intensity and the thickness of the reaction zone in L x and Ly which it may be consequently led to a strong flow expansion in this zone. On the other hands, the transition from the critical point is affected by turbulence models. The reason of such a behavior may be related to the turbulent conductivity and viscosity coefficients, therefore different mixing level resulted from different turbulence models.


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Effect of real EOS: three real equation of states were done on the supercritical combustion and the structure of flame was investigated. The results of SRK and PR are very similar to each other but ARK equation of state shows a little different prediction rather than the other ones. Although this three equation of states have not diversity in comparison to each other, the SRK equation of state has the least difference in comparison to the measured contour. Probably, the difference between the predictions of the real EOSs are related to the different attitudes in defining the EOS. Effect of chemical mechanism: Two H2/O2 chemical mechanisms that are developed for high-pressure conditions were examined on the flame structure. It seems that the performances of Burke and Konnov mechanisms are the same on all aspects of the flame at supercritical condition. Effect of pressure: By increasing pressure, the amount and the location of the maximum temperature changed. Also, the flame was elongated and the spreading angle was decreased. Theses diversities could attribute to the change of Cp (i.e. Lc) in a wide range of axial direction. On the other hands, other effects of increasing pressure were variation in the size and the position of IRZ due to the enhancement of molecular diffusion, the reaction rates and so temperature. Also, the position of ORZ was changed by pressure variation. On the plus side, by increasing pressure, the concentrations of HO2 and H2O2 species are augmented in the hydrogen jet zone and the importance of the HO2+HO2 reaction is highlighted. For future studies simulation using Large Eddy Simulation (LES) approach to get a more precise description of the flame structure and combustion-turbulence interaction could be valuable. Furthermore, assessment of Reynolds-Stress Model (RSM) for modeling the A60 test case is worthy to investigate in future works. 6. Acknowledgments Authors would like to thanks, Dr. Mohammad Farshchi and Mr. Hamed zenivand for their help regarding the current research.


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Tables Table 1. Operating conditions of A60 Operating conditions Pressure [MPa] Mass flow rate [g/s] Temperature [K] Density at injector inlet [kg/m3] Velocity inlet [m/s]

H2 6 70 287 5.51 236

O2 6 100 85 1177.8 4.35

Table 2. Detailed H2 /O2 reaction mechanism of Burke et al. [63]. Reaction A H2 /O2 chain reactions 1. H + O2 = O + OH 1.04E+14 2. O + H2 = H + OH 3.82E+12 O + H2 = H + OH 8.792E+14 3. H2 + OH = H2O + H 2.16E+08 4. OH + OH = O + H2O 3.34E+04 H2 /O2 dissociation/recombination reactions 5. H2 + M = H + H + M 4.58E+19 6. H2 + Ar = H + H + Ar 5.84E+18 7. H2 + He = H + H + He 5.84E+18 8. O + O + M = O2 + M 6.16E+15 9. O + O + Ar = O2 + Ar 1.89E+13 10. O + O + He = O2 + He 1.89E+13 11. O + H + M = OH + M 4.71E+18 12. H2O + M = H + OH + M 6.06E+27 13. H2O + H2O = H + OH + H2O 1.01E+26 Formation and consumption of HO2 14. H + O2 (+M) = HO2 4.65E+12 15. HO2 + H = H2 + O2 2.75E+06 16. HO2 + H = OH + OH 7.08E+13 17. HO2 + O = O2 + OH 2.85E+10 18. HO2 + OH = H2O + O2 2.89E+13 Formation and Consumption of H2O2 19. HO2 + HO2 = H2O2 + O2 4.20E+14 HO2 + HO2 = H2O2 + O2 1.300E+11 20. H2O2(+M) = OH + OH(+M) 2.00E+12 21. H2O2 + H = H2O + OH 2.41E+13 22. H2O2 + H = HO2 + H2 4.82E+13 23. H2O2 + O = OH + HO2 9.55E+06 24. H2O2 + OH = HO2 + H2O 1.74E+12 7.590E+13 H2O2 + OH = HO2 + H2O

n

E

0 0 0 1.51 2.42

1.53E+04 7.95E+03 1.917E+04 3.43E+03 -1.93E+03

-1.4 -1.1 -1.1 -0.5 0 0 -1 -3.32 -2.44

1.04E+05 1.04E+05 1.04E+05 0.00E+00 -1.79E+03 -1.79E+03 0.00E+00 1.21E+05 1.20E+05

0.44 2.9 0 1 0

0.00E+00 -1.45E+03 2.95E+02 -7.24E+02 -4.97E+02

0 0 0.9 0 0 2 0 0

1.20E+04 -1.6293E+03 4.88E+04 3.97E+03 7.95E+03 3.97E+03 3.18E+02 7.270E+03

Units are cm3, mol, s, kcal, and K, where k = ATn exp(−E/RT).


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Table 3. Coefficients of the equations of state formula based on equation (1). Equation

𝛩

𝛯

𝜉

𝑏

𝑎0

𝛼(𝑇, 𝜔)

VDW

0

0

0

𝑅𝑇𝑐 8𝑃𝑐

27 𝑅 2 𝑇𝑐2 64 𝑃𝑐

1

RK

1

0

0

0.08664𝑅𝑇𝑐 𝑃𝑐

0.4275𝑅 2 𝑇𝑐2.5 𝑃𝑐

1 𝑇 0.5

SRK

1

0

0

0.08664𝑅𝑇𝑐 𝑃𝑐

0.42747𝑅 2 𝑇𝑐2 𝑃𝑐

[1 + (𝑓𝜔 )(1 − 𝑇𝑟0.5 )]2 𝑓𝜔 = 0.48 + 1.57𝜔 − 0.176𝜔2

PR

2

-1

0

0.07780𝑅𝑇𝑐 𝑃𝑐

0.42747𝑅 2 𝑇𝑐2 𝑃𝑐

[1 + (𝑓𝜔 )(1 − 𝑇𝑟0.5 )]2 𝑓𝜔 = 0.37464 + 1.54226𝜔 − 0.26992𝜔2

ARK

1

0

𝑅𝑇𝑐 𝑎0 𝑃𝑐 + + 𝑏 − 𝑉𝑐 𝑉𝑐 (𝑉 + 𝑏)

0.08664𝑅𝑇𝑐 𝑃𝑐

0.42747𝑅 2 𝑇𝑐2 𝑃𝑐

1 2 𝑇 −[0.4986+1.173𝜔+0.475𝜔 ]

Table 4. Test cases

1 2 3 4 5 6 7 8 9 10 11 12 13 14

*

* * * * * * * *

* * * * * *

* * * * * * * * * * * *


konnov

Burke

Chemical mechanism

global

100 bar

80 bar

60 bar

𝑘 − 𝜔 SST

𝑘 − 𝜀 Realizable

𝑘 − 𝜀 RNG

Chamber Pressure

* *

* * * * * * * *

* * *

𝑘 − 𝜀 Standard

Turbulence Model

ARK

PR

No.

SRK

Equation of States Ideal Gas

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Energy & Fuels

* * * * * * * * * * * * * *

* *

Energy & Fuels 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Page 52 of 55

Table 5. Effect of turbulence model on defined parameters in comparison with (cases No. 6, 7, 8, 9) experimental data Turbulence Model Experimental 𝑘 − 𝜀 Standard 𝑘 − 𝜀 RNG 𝑘 − 𝜀 Realizable 𝑘 − 𝜔 SST

𝑳𝟏 8 10.8 12 6.2 6.3

𝑳𝟐 22 27 31.7 31.4 21

𝑳𝒙 12.4 15.5 16.7 9.4 10.3

𝑳𝒚 2.70 2.76 2.45 2.68 3.35

𝜷 4.40 2.52 1.51 8.13 6.3

Table 6. The absolute deviation between prediction and measurement (Cases No. 6, 7, 8, 9) |%𝑳𝟏 | 10.8 12 6.2 6.3

Turbulence Model 𝑘 − 𝜀 Standard 𝑘 − 𝜀 RNG 𝑘 − 𝜀 Realizable 𝑘 − 𝜔 SST

|%𝑳𝟐 | 27 31.7 31.4 21

|%𝑳𝒙 | 15.5 16.7 9.4 10.3

|%𝑳𝒚 | 2.76 2.45 2.68 3.35

|%𝜷| 2.52 1.51 8.13 6.3

|%Error| 13.0 20.0 20.1 11.3

Table 7. The effect of turbulence models on value and location of the axial maximum temperature (Cases No. 6, 7, 8, 9) Turbulence Model Experimental 𝑘 − 𝜀 Standard 𝑘 − 𝜀 RNG 𝑘 − 𝜀 Realizable 𝑘 − 𝜔 SST

TMax [K]

Axial Location of TMax (based on X/dLOX )

3565 3568 3473 3592 3550

20 27.5 32.2 32.2 21

Table 8. Location of points D, B, C and 𝐿𝐼𝑅𝑍 based on X/dLOX for different turbulence models (Cases No. 6, 7, 8, 9 ). Turbulence Model 𝑘 − 𝜀 Standard 𝑘 − 𝜀 RNG 𝑘 − 𝜀 Realizable 𝑘 − 𝜔 SST

Point B 11.05 13.22 6.02 6.25

Point C 18.76 13.04 12.70

Point D 21.56 18.91 13.92

LIRZ 2.80 5.87 1.22

Table 9. Effect of pressure on the defined parameters in OH* experimental contour (Cases No. 9, 13, and 14). Pressure 60 bar 80 bar 100 bar

𝐿1 6.3 6.4 7.9

𝐿2 20.7 20.8 22.5

𝐿𝑥 10.3 10.4 11.8

𝐿𝑦 3.35 3.25 3.00

𝛽 6.3 6.1 4.7

Table 10. Location of points B, C, D and𝐿𝐼𝑅𝑍 based on X/dLOX for different pressures (Cases No. 9, 13, and 14 ). Pressure 100 bar 80 bar 60 bar

Point B 8.9 6.41 6.25

Point C 13.6 12.5 12.70

Point D 16 14.7 13.92


LIRZ 2.4 2.2 1.22

Page 53 of 55 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Energy & Fuels

Subscripts of Tables Table 1. Operating conditions of A60

Table 2. Detailed H2 /O2 reaction mechanism of Burke et al. [63].

Table 3. Coefficients of the equations of state formula based on equation (1).

Table 4. Test cases

Table 5. Effect of turbulence models on defined parameters in comparison with (cases No. 6, 7, 8, 9) experimental data

Table 6. The absolute deviation between prediction and measurement (Cases No. 6, 7, 8, 9)

Table 7. The effect of turbulence models on value and location of the axial maximum temperature (Cases No. 6, 7, 8, 9)

Table 8. Location of points D, B, C and 𝐿𝐼𝑅𝑍 based on X/dLOX for different turbulence models (Cases No. 6, 7, 8, 9 ). Table 9. Effect of pressure on the defined parameters in OH* experimental contour (Cases No. 9, 13, and 14).

Table 10. Location of points B, C, D and𝐿𝐼𝑅𝑍 based on X/dLOX for different pressures (Cases No. 9, 13, and 14 ).


Energy & Fuels 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Subscripts of Figures

Fig. 1. Mascotte cryogenic combustion test facility [58]

Fig. 2. Sketch of the computational domain and injector.

Fig. 3. Grid independence study of Mascotte A-60 test facility (case No.9)

Fig. 4. Comparision of the predicted axial profile of temperature (case No.9 in Table 4) with experimental data [51].

Fig. 5. Comparisons of contours of OH: Abel transformed OH* emission image [21], and prediction (case No. 9).

Fig. 6. The predicted temperature of A-60 using ideal (case No.1) and non-ideal equations of state (case No.2)

Fig. 7. The effect of EOS on axial profiles of temperature, density, Cp and compressibility factor (cases No.1 and No.2)

Fig. 8. Axial profiles of static and dynamic pressure, velocity, density, Cp, and molar volume (case No.9)

Fig. 9. Streamlines of reacting flow (colored by static pressure) (Case No.9 in Table 4)

Fig. 10. The locations of zero axial (dotted line) and zero radial velocities (dashed-double dot line), and Stagnation points (Case No.9). Fig. 11. The temperature contour of LOX-GH2 shear-coaxial injector at supercritical condition[12] Fig. 12. Measured OH* emissions normalized based on the oxygen injector diameter [21] and the defining parameters. Fig. 13. The predicted OH mass fraction using different turbulence models in comparison with the measurements Fig. 14. comparison between measured [21] and predicted position of maximum OH mass fraction (Cases No. 6, 7, 8, 9)

Fig. 15. Effect of different turbulence models on predictions and a comparison with measurements [51](Cases No. 6, 7, 8, 9).

Fig. 16. OH mass fraction and the flow streamlines for various turbulence models (Cases No. 6, 7, 8, 9). Fig. 17. The effect of EOS of ARK and PR on the flame shape in comparison with SRK (Cases No. 9, 10, 11).


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Energy & Fuels

Fig. 18. The comparison between measured [21] and predicted position of the maximum OH mass fraction for SRK, ARK, and PR (Cases No. 9, 10, 11).

Fig. 19. Comparisons between predictions of ARK, SRK, and PR EOS (No. 9, 10, 11). Fig. 20. Effects of chemical mechanism on predictions of temperature, OH, and streamlines (Cases No. 9 and 12).

Fig. 21. summery on the effect of EOS, chemical mechanism, and turbulence model on axial temperature profile (Cases No. 1, 2, 6, and 9)

Fig. 22. Effect of pressure on flame structure (Cases No. 9, 13, and 14).

Fig. 23. Effect of pressure on Axial profiles of flame parameters (No. 9, 13, and 14).

Fig. 24. The pathway of the H+O2 reaction at different conditions [63]

Fig. 255. The flow residence time contour and the isolines of HO2 production (dashed line) and consumption (solid line) (Cases No. 9 in Table 4). Fig. 26. Effect of pressure on contours of some species (Cases No. 9 and 14). Fig. 27. Effect of pressure on radial profiles of OH at X/dLOX of 5 and 10(Cases No. 9, 13 and 14).


Numerical investigation of supercritical combustion of H2-O2

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