Two-phase Reactive Flow Research Articles

Modelling and simulation on compressible multi-component gas-liquid flows with chemical reaction and phase transition effects

In this paper, mathematical models and numerical algorithm are conducted for simulating compressible two-phase multi-component reactive flows, coupling with the finite-rate-based chemistry and the instantaneous-equilibrium phase transition model. Distinctive from previous multi-component two-phase governing equations, all volume fraction transport equations, with non-conservative characteristics, of gaseous components are substituted with a thermal equilibrium assumption inside the gaseous mixture for closure. Moreover, based on the temperature polynomial (NASA-7) fitted gas properties and the stiffened gas equation of state (SG-EOS) described liquid properties, the instantaneous-equilibrium phase transition model is re-derived, and the solving strategy of the transient phase transition model is detailly provided using an algebraical approach rather than the iterative process. Having included these elements, the proposed model is validated on three canonical tests, first for pure reactive flows, second for pure two-phase flows, and third for complex compressible multi-component two-phase reactive flows with phase transition effects: hydrogen-oxygen detonation interacting with a water droplet. The cases have well demonstrated the proposed model capability and the expected fluid physics in both the multiphase and reactive flows are reproduced.

Influence of embedded structure on two-phase reactive flow characteristics for a small combustion chamber with a moving boundary

In special launch scenarios such as armament and aerospace, the scale of the launch system is severely restricted, which causes unstable combustion of propellant. An embedded structure for the small propulsion system driven by solid propellant is proposed to overcome this problem. This study aims to demonstrate the two-phase flow behaviors and launch safety of the combustion chamber with an embedded structure. A two-dimensional two-phase flow model based on the modified two-fluid theory is developed to describe the detailed two-phase flow behaviors in the combustion chamber during launching. Different from most of the existing studies, the constitutive equations determined from actual physical conditions are used to close the system of continuity equations. The numerical results are compared with that of the experiment to verify the accuracy of the numerical model. On this basis, the launch performance of the embedded structure is investigated. The numerical results indicate that the embedded structure facilitates the ignition process and reduces the risk of excessive pressure, but decreases the muzzle velocity at the same time. In addition, the effect of design parameters on launch safety is further investigated. Design parameters directly affect the launch safety, and the selection of reasonable parameters is a useful method for enhancing the launch performance.

A benchmark study on reactive two-phase flow in porous media: Part II - results and discussion

A benchmark study on reactive two-phase flow in porous media: Part II - results and discussion

A benchmark study on reactive two-phase flow in porous media: Part I - model description

A benchmark study on reactive two-phase flow in porous media: Part I - model description

A novel structure for improving the service life of a propulsion system by controlling two-phase reactive flow

Methods to control two-phase reactive flow induced by the combustion of propellant particles are important for improving the service life of mechanical systems. A novel groove structure was proposed to control the two-phase reactive flow. A two-phase flow model was utilized to predict propellant combustion in fluid fields and coupled with the transient heat transfer process. The numerical model was validated by comparing numerical and experimental results. Numerical results indicate that the groove structure effectively decreases the scouring velocity of two phases and the accumulation of particles near the barrel surface. The groove also reduces the peak temperature of the barrel surface, which contributes to less thermal erosion. Furthermore, shooting tests prove that the groove structure greatly extends the service life of the barrel. The findings of the study will be applied to improve the service life of propulsion systems.

A porous-media model for reactive fluid–rock interaction in a dehydrating rock

We study the General Equations of Non-Equilibrium Reversible–Irreversible Coupling (GENERIC) structure of models for reactive two-phase flows and their connection to a porous-media model for a reactive fluid–rock interaction used in geosciences. For this, we discuss the equilibration of fast dissipative processes in the GENERIC framework. Mathematical properties of the porous-media model and first results on its mathematical analysis are provided. The mathematical assumptions imposed for the analysis are critically validated with the thermodynamical rock datasets.

Study on Shock Initiation Randomness of Energetic Materials on a Macroscopic Scale

The shock initiation randomness problem of energetic materials (SIREM) is an important problem in the research field of energetic material safety. With the purposes of solving SIREM on a macroscopic scale and obtaining the statistics, such as the initiation probabilities of energetic materials and the statistical characteristics of the detonation pressure, this paper considers the effect of the randomness of the parameters of the Lee–Tarver equation of reaction rate and the JWL equation of state of energetic materials and the randomness of load intensity parameters—such as fragment shock velocity—on the randomness of the shock initiations of energetic materials. It then decomposes SIREM into an initiation probability problem (IP) and a detonation pressure randomness problem (DPR). Further, with the Back Propagation Neural Networks optimized by the Genetic Algorithm (GABPNN) as the surrogate models of the numerical models of two-phase reactive flow, this paper proposes the approach of solving IP and DPR in turn, adopting Monte Carlo Simulations, which use the calculations of GABPNNs as repeated sampling tests (GABP-MCSs). Finally, by taking the shock initiation randomness problem of Composition B as an applied example, this paper adopts GABP-MCS under the randomness conditions that the means of fragment shock velocities are 1050 m/s and 1000 m/s and that the coefficients of variation (CVs) of BRVs are 0.005, 0.01, 0.015, and 0.02 in order to obtain the initiation probabilities of Composition B and the statistical characteristics, such as the means and CVs of the detonation pressure. It further observes the variation tendencies that these statistics show under various randomness conditions, so as to prove the effectiveness of GABP-MCS in solving SIREM. Therefore, this paper investigates SIREM on a macroscopic scale and proposes a universal technique for solving SIREM by GABP-MCS, in the hope of shedding some light on the SIREM study.

Chemically reactive two-phase flow of viscous-Casson fluids in a rotating channel

An analysis is carried out to examine the effects of chemical reactions on the flow of two-phase non-miscible liquids streaming through rotating parallel plates. The plates are isothermal and insulated electrically. The Couette flow is considered for the electrically conducting two phase viscous-Casson fluids under the impacts of inclined magnetic flux and applied electric field. The problem is also discussed under the influence of different orders of chemical reactions. The modelled equations elaborating the present situation under the implemented suppositions are transformed to ordinary differential equations. The numerical solution for the obtained equations is obtained with suitable matching conditions at the interface region using the shooting technique. The results are also validated by comparing them with the results of a well-known finite difference based numerical scheme known as the Keller-Box method. The numerical results for sundry parameters involved in the flow problem are presented through graphs and discussed in detail.

The Particle Element Method to Obtain Parameter Distributions of Two-phase Reactive Flow in a Propulsion Combustion System

ABSTRACT Large-particle porous propellant has good surface-enhancing combustion performance and may improve the muzzle velocity of combustion propulsion system effectively. The proposed particle element method is further refined to investigate particle motion characteristics and flow field distribution in a large-particle charge combustion system with moving boundary. The particle element parameter aggregation is established to describe particle parameter distribution in the system, and the motion is controlled by particle motion equations during combustion and propulsion, so that the particle element is stretched and coupled with the gas phase. The particle element method accurately describes the distribution of the particle movement process and the evolution of the flow field in the chamber, and the numerical simulation results are in good agreement with the AGARD code. In particular, the overall efficiency of the entire calculating procedure is improved by 21.7%. The research results will effectively solve the flow field problem in the large-particle charge combustion system.

Reaction front development from ignition spots in n-heptane/air mixtures: Low-temperature chemistry effects induced by ultrafine water droplet evaporation

Effects of low-temperature chemistry induced by ultrafine water droplet evaporation on reaction front development from an ignition spot with temperature gradient are studied in this work. The Eulerian–Eulerian method is used to simulate the gas–liquid two-phase reactive flows, and the physical model is one-dimensional spherical reactor with stoichiometric gaseous n-heptane/air mixture and ultrafine monodisperse water droplets (initial diameter 5 μm). Homogeneous ignitions of two-phase mixtures are first simulated. The water droplets can completely evaporate in the reactor prior to ignition, and hence pronouncedly reduce gas temperature, which may induce the low-chemistry reactions. It is found that the turnover temperature for negative temperature coefficient range increases with droplet volume fraction. Three-stage ignitions are present when the volume fraction is beyond a critical value, that is, low-temperature, intermediate-temperature, and high-temperature ignitions. The chemical explosive mode analysis also confirms the low-chemistry reactions induced by the evaporation of ultrafine water droplets. Then, reaction front development from an ignition spot with temperature gradient in two-phase mixtures is analyzed based on one-dimensional simulations. Different modes for reaction front origin in the spot are identified, based on the initial gas temperature and lower turnover temperature. Specifically, the reaction front can be initiated at the left and right ends of the ignition spot, and inside it. Detailed reaction front developments corresponding to the above three modes are discussed. In addition, the pressure wave from high-temperature ignition is important, compared to those from low and intermediate chemistries. The reaction front propagation speed and thermal states of fluid particles corresponding to different reaction front initiation modes are analyzed. Moreover, autoignition modes are summarized in the diagrams of normalized temperature gradient vs normal acoustic time and droplet volume fraction. The detonation limits of two-phase mixtures highly depend on the droplet volume fraction and are not regularly peninsular-shaped, like those for purely gaseous mixtures.

Combustion for aircraft propulsion: Progress in advanced laser-based diagnostics on high-pressure kerosene/air flames produced with low-NOx fuel injection systems

The challenges in designing high-performance aeronautical combustion systems have not changed significantly over the years, but the increase of stringent regulations and the need to tackle rising fuel prices require new sophisticated analysis processes. To address this concern, the theme of this study was cast in terms of the ability of improving the performances of advanced non-intrusive instrumentation in high-pressure turbulent reactive two-phase flows to enhance the combustion efficiency and reduction of pollutants of new innovative low-NOx injection systems fed with liquid kerosene. In the first part, a Lean Premixed injection system designed for helicopter engines was first studied using the Particle Image Velocimetry (PIV), Phase Doppler Anemometry (PDA) and Planar laser-induced fluorescence (PLIF) of OH, kerosene vapor and NO. These diagnostics were applied individually or in combination for custom-made solutions for accessing to detailed information on the spatial distributions of velocity, droplets size, OH, kerosene and NO molar fractions in pressure conditions ranging from 0.4 to 1.8 MPa. Complementary large-Eddy simulations of these flames were performed using the PCM-FPI tabulated chemistry approach in conjunction with a polydisperse Euler–Lagrangian approach. Comparison of simulations with experiments highlighted the importance of the size distribution of the droplets injected into the flow on the mutual predictions of the aerodynamic field, the structure of the flame and its anchorage point as well as the spatial distribution of the fuel and OH species. The second part of this work was aimed to study the advantages and limitations of the chirped probe pulse femtosecond coherent anti-Stokes Raman scattering (CPP fs-CARS) diagnostic for performing time-series of single-shot temperature measurements on an aircraft multi-point injection system developing two-phase flames under realistic pressure conditions.

Computational Modeling of Bubbles Growth Using the Coupled Level Set-Volume of Fluid Method.

Understanding the generation, growth, and dynamics of bubbles as they absorb or release dissolved gas in reactive flows is crucial for optimizing the efficiency of electrochemically gas-evolving systems like alkaline water electrolysis or hydrogen production. To better model these bubbly flow systems, we use a coupled level set and volume of fluid approach integrated with a one-fluid transport of species model to study the dynamics of stationary and rising bubbles in reactive two-phase flows. To accomplish this, source terms are incorporated into the continuity and phase conservation equations to allow the bubble to grow or shrink as the species moves through the interface. Verification of the hydrodynamics of the solver for non-reactive systems demonstrates the requisite high fidelity interface capturing and mass conservation necessary to incorporate transport of species. In reactive systems where the species impacts the bubble volume, the model reproduces the theoretically predicted and experimentally measured diffusion-controlled growth rate (i.e., R(t) ∝ t0.5). The model is then applied to rising bubbles to demonstrate the impact of transport of species on both the bubble velocity and shape as well as the concentration field in its wake. This improved model enables the incorporation of electric fields and chemical reactions that are essential for studying the physicochemical hydrodynamics in multiphysics systems.

Numerical simulation of reactive gas-particle flow in a solar jet spouted bed reactor for continuous biomass gasification

Solar steam gasification of beech wood biomass in a novel solar conical jet spouted bed reactor was studied. A 3D numerical model of the reactive two-phase gas-particle flow was developed and the model was experimentally validated. The cavity-type solar reactor was operated in both direct and indirect heating configurations at a constant wall temperature of 1200 °C with a biomass feeding rate that varied from 1.2 g/min to 2 g/min. Experiments showed that directly heating the particles increases the H2 yield and the carbon conversion efficiency. The Computational Fluid Dynamics (CFD) model was developed to thoroughly investigate the biomass conversion process inside the conical jet spouted bed subjected to direct or indirect solar irradiations. The desired vigorous cyclic flow pattern of the biomass particles was accurately predicted by the model with peak particles velocity of 2 m/s in the spout region. The maximum temperature reached by the indirectly-irradiated particles is about 1200 °C while it is above 1500 °C when considering directly-irradiated particles. Direct heating thus increases both particles gasification rates and carbon conversion efficiency. Furthermore, simulations reveal that the reaction zone temperature is 100 °C higher for the direct heating configuration. This promotes the H2 formation at the expense of CH4. The steam oxidant concentration, gas products distribution and particles trajectories inside the cavity were also investigated to identify improvement strategies for enhancing the phase mixing and the gas/solid residence time.

Computational Investigation of Weakly Turbulent Flame Kernel Growths in Iso-Octane Droplet Clouds in CVC Conditions

Numerical simulations of turbulent flame kernel growths in monodisperse clouds of iso-octane liquid droplets are conducted in conditions relevant to constant volume combustors. The simulations make use of a low-Mach number Navier-Stokes solver and a thermodynamic pressure evolution model has been implemented to reproduce the pressure variation that may be issued from either experiments or from a standard (i.e., analytical) compression law. Chemistry is described with a representative skeletal mechanism featuring 29 species and 48 elementary reaction steps. The computational results clearly confirm the enhancement of flame propagation in constant volume combustion conditions. The impact of the droplet diameter on the turbulent flame development is scrutinized for two distinct values of the Stokes number St equal to 0.1 and 1.0. Significant influence on the flame dynamics is put into evidence. This is a direct outcome of the equivalence ratio and temperature heterogeneities, which are themselves very sensitive to the choice of the Stokes number value. Then, small-scale turbulence-scalar interactions (TSI) are studied by analyzing the fields of the scalar gradients and strain-rate. Their dynamics is investigated for both non-reactive and reactive two-phase flows conditions. The TSI analysis is performed on the basis of time evolution equations written for quantities that characterize the couplings between the velocity gradient tensor and scalar gradients vectors. Special emphasis is placed on the possible influence of mass exchange terms between the liquid and gaseous phases.

Numerical investigation of two-phase reactive flow with two moving boundaries in a two-stage combustion system

The quest to achieve higher muzzle velocity is one of the key goals for researchers in the fields of propulsion and ballistic. Based on the conventional chemical propulsion, the two-stage combustion system as a new launch principle can provide higher muzzle velocity without exceeding the maximum pressure in the chamber. In this paper, the modified two-fluid model with two moving boundaries is proposed to simulate the detailed multi-dimensional flow and energy conversion behaviors of the combustion gas and propellant grains in the two-stage chamber. The dynamic self-adapting mesh update method is developed to expand and merge the computational domain for both projectile and piston motions. The application to a standard virtual gun as a standard benchmark for interior ballistic codes is used to validate the accuracy and reliability. The calculation results are in good agreement with those of codes in different countries. After that, a two-stage chamber system is set up based on the standard virtual gun. The numerical results present deep understanding of the two-phase flow behaviors in the two-stage chamber. Then the effects of design parameters on the performances in the additional chamber are numerically investigated. Finally, a suggested scheme of the additional chamber is proposed. The findings of the study put a further prediction tool for the understanding and design of the two-stage combustion system with moving boundaries.

Magma ascent in planetesimals: Control by grain size

Rocky planetesimals in the early solar system melted internally and evolved chemically due to radiogenic heating from 26Al. Here we quantify the parametric controls on magma genesis and transport using a coupled petrological and fluid mechanical model of reactive two-phase flow. We find the mean grain size of silicate minerals to be a key control on magma ascent. For grain sizes ≳1 mm, melt segregation produces distinct radial structure and chemical stratification. This stratification is most pronounced for bodies formed at around 1 Myr after formation of Ca,Al-rich inclusions. These findings suggest a link between the time and orbital location of planetesimal formation and their subsequent structural and chemical evolution. According to our models, the evolution of partially molten planetesimal interiors falls into two categories. In the magma ocean scenario, the whole interior of a planetesimal experiences nearly complete melting, which would result in turbulent convection and core–mantle differentiation by the rainfall mechanism. In the magma sill scenario, segregating melts gradually deplete the deep interior of the radiogenic heat source. In this case, magma may form melt-rich layers beneath a cool and stable lid, while core formation would proceed by percolation. Our findings suggest that grain sizes prevalent during the internal heating stage governed magma ascent in planetesimals. Regardless of whether evolution progresses toward a magma ocean or magma sill structure, our models predict that temperature inversions due to rapid 26Al redistribution are limited to bodies formed earlier than ≈1 Myr after CAIs. We find that if grain size was ≲1 mm during peak internal melting, only elevated solid–melt density contrasts (such as found for the reducing conditions in enstatite chondrite compositions) would allow substantial melt segregation to occur.

An in-depth study on the implementation aspect of unified time integrators in reactive two-phase flows with consistent time level

PurposeA consistent implementation of the general computational framework of unified second-order time accurate integrators via the well-known GSSSS framework in conjunction with the traditional Finite Difference Method is presented to improve the numerical simulations of reactive two-phase flows.Design/methodology/approachIn the present paper, the phase interaction evaluation in the present implementation of the reactive two-phase flows has been derived and implemented to preserve the consistency of the correct time level evaluation during the time integration process for solving the two phase flow dynamics with reactions.FindingsNumerical examples, including the classical Sod shock tube problem and a reactive two-phase flow problem, are exploited to validate the proposed time integration framework and families of algorithms consistently to second order in time accuracy; this is in contrast to the traditional practices which only seem to obtain first-order time accuracy because of the inconsistent time level implementation with respect to the interaction of two phases. The comparisons with the traditional implementation and the advantages of the proposed implementation are given in terms of the improved numerical accuracy in time. The proposed approaches provide a correct numerical simulation implementation to the reactive two-phase flows and can obtain better numerical stability and computational features.Originality/valueThe new algorithmic framework and the consistent time level evaluation extended with the GS4 family encompasses a multitude of past and new schemes and offers a general purpose and unified implementation for fluid dynamics.

A computational framework for predicting the combustion of energetic materials in an expanding chamber

PurposeVarious simplifications are introduced into the establishment of numerical models for problems with strong nonlinear interactions. The combustion of energetic materials in a chamber with moving boundaries is a typical example. This paper aims to establish a coupled numerical model for predicting the internal combustion in a launch process.Design/methodology/approachA two-fluid model is used to predict the fluid field induced by the propellant combustion. The moving boundary is located by using a finite element method. Based on a user subroutine interface in the commercial software ABAQUS, the development of the fluid field and the mechanical interactions is coupled with each other.FindingsThe paper is devoted to provide a coupled computational framework for predicting the propellant combustion in an expanding chamber. The coupling strategy is validated through predicting a pressure-driven piston system. Based on the validated computational framework, the two-phase reactive flows in a launch process is studied. The predicted parameters agree well with experimental measurements.Originality/valueThis paper provide a method to address the difficulties in realizing the dynamic interactions between multi-phase reactive flows and mechanical behaviors. The computational framework can be used as a research tool for investigating fluid field in a combustion chamber with moving boundaries.

Large Eddy Simulation of Light-Round in an Annular Combustor With Liquid Spray Injection and Comparison With Experiments

The light-round is defined as the process by which the flame initiated by an ignition spark propagates from burner to burner in an annular combustor, eventually leading to a stable combustion. Combining experiments and numerical simulation, it was recently demonstrated that under perfectly premixed conditions, this process could be suitably described by large eddy simulation (LES) using massively parallel computations. The present investigation aims at developing light-round simulations in a configuration that is closer to that found in aero-engines by considering liquid n-heptane injection. The LES of the ignition sequence of a laboratory scale annular combustion chamber comprising sixteen swirled spray injectors is carried out with a monodisperse Eulerian approach for the description of the liquid phase. The objective is to assess this modeling approach of the two-phase reactive flow during the ignition process. The simulation results are compared in terms of flame structure and light-round duration to the corresponding experimental images of the flame front recorded by a high-speed intensified charge-coupled device camera and to the corresponding experimental delays. The dynamics of the flow is also analyzed to identify and characterize mechanisms controlling flame propagation during the light-round process.

Simulation of reactive polydisperse sprays strongly coupled to unsteady flows in solid rocket motors: Efficient strategy using Eulerian Multi-Fluid methods

In this paper, we tackle the issue of the accurate simulation of evaporating and reactive polydisperse sprays strongly coupled to unsteady gaseous flows. In solid propulsion, aluminum particles are included in the propellant to improve the global performances but the distributed combustion of these droplets in the chamber is suspected to be a driving mechanism of hydrodynamic and acoustic instabilities. The faithful prediction of two-phase interactions is a determining step for future solid rocket motor optimization. When looking at saving computational ressources as required for industrial applications, performing reliable simulations of two-phase flow instabilities appears as a challenge for both modeling and scientific computing. The size polydispersity, which conditions the droplet dynamics, is a key parameter that has to be accounted for. For moderately dense sprays, a kinetic approach based on a statistical point of view is particularly appropriate. The spray is described by a number density function and its evolution follows a Williams–Boltzmann transport equation. To solve it, we use Eulerian Multi-Fluid methods, based on a continuous discretization of the size phase space into sections, which offer an accurate treatment of the polydispersion. The objective of this paper is threefold: first to derive a new Two Size Moment Multi-Fluid model that is able to tackle evaporating polydisperse sprays at low cost while accurately describing the main driving mechanisms, second to develop a dedicated evaporation scheme to treat simultaneously mass, moment and energy exchanges with the gas and between the sections. Finally, to design a time splitting operator strategy respecting both reactive two-phase flow physics and cost/accuracy ratio required for industrial computations. Using a research code, we provide 0D validations of the new scheme before assessing the splitting technique's ability on a reference two-phase flow acoustic case. Implemented in the industrial-oriented CEDRE code, all developments allow to simulate realistic solid rocket motor configurations featuring the first polydisperse reactive computations with a fully Eulerian method.