The present paper deals with the numerical study of high pressure LOx/H2 or LOx/hydrocarbon combustion for propulsion systems. The present research effort is driven by the continued interest in achieving low cost, reliable access to space and more recently, by the renewed interest in hypersonic transportation systems capable of reducing time-to-destination. Moreover, combustion at high pressure has been assumed as a key issue to achieve better propulsive performance and lower environmental impact, as long as the replacement of hydrogen with a hydrocarbon, to reduce the costs related to ground operations and increase flexibility. The current work provides a model for the numerical simulation of high- pressure turbulent combustion employing detailed chemistry description, embedded in a RANS equations solver with a Low Reynolds number k-omega turbulence model. The model used to study such a combustion phenomenon is an extension of the standard flamelet-progress-variable (FPV) turbulent combustion model combined with a Reynolds Averaged Navier-Stokes equation Solver (RANS). In the FPV model, all of the thermo-chemical quantities are evaluated by evolving the mixture fraction Z and a progress variable C. When using a turbulence model in conjunction with FPV model, a probability density function (PDF) is required to evaluate statistical averages of chemical quantities. The choice of such PDF must be a compromise between computational costs and accuracy level. State- of-the-art FPV models are built presuming the functional shape of the joint PDF of Z and C in order to evaluate Favre-averages of thermodynamic quantities. The model here proposed evaluates the most probable joint distribution of Z and C without any assumption on their behavior.
The flamelet approach offers a viable framework for combustion modeling of homogeneous charge compression ignition (HCCI) engines under stratified mixture conditions. Scalar dissipation rate acts as a key parameter in flamelet-based combustion models which connects the physical mixing space to the reactive space. The aim of this paper is to gain fundamental insights into turbulent mixing in low temperature combustion (LTC) engines and investigate the modeling of scalar dissipation rate. Three direct numerical simulation (DNS) test cases of two-dimensional turbulent auto-ignition of a hydrogen-…
The combustion instability is investigated computationally for a multi-injector rocket engine using the flamelet progress variable (FPV) model. A C++ code is developed based on OpenFOAM 4.0 to apply the combustion model. Flamelet tables are generated for methane/oxygen combustion at the background pressure of $200$ bar using a 12-species chemical mechanism. A power law is determined for rescaling the reaction rate for the progress variable to address the pressure effect. The combustion is also simulated by the one-step-kinetics (OSK) method for comparison with the FPV approach. A study of comb…
Axisymmetric simulations of a liquid rocket engine are performed using a delayed detached-eddy-simulation (DDES) turbulence model with the Compressible Flamelet Progress Variable (CFPV) combustion model. Three different pressure instability domains are simulated: completely unstable, semi-stable, and fully stable. The different instability domains are found by varying the combustion chamber and oxidizer post length. Laminar flamelet solutions with a detailed chemical mechanism are examined. The $β$ Probability Density Function (PDF) for the mixture fraction and Dirac $δ$ PDF for both the press…
This paper provides an extension of the standard flamelet progress variable (FPV) approach for turbulent combustion, applying the statistically most likely distribution (SMLD) framework to the joint PDF of the mixture fraction, Z, and the progress variable, C. In this way one does not need to make any assumption about the statistical correlation between Z and C and about the behaviour of the mixture fraction, as required in previous FPV models. In fact, for state-of-the-art models, with the assumption of very-fast-chemistry,Z is widely accepted to behave as a passive scalar characterized by a …
This paper provides an improved flamelet/progress variable (FPV) model for the simulation of turbulent combustion, employing the statistically most likely distribution (SMLD) approach for the joint probability density function (PDF) of the mixture fraction, Z, and of the progress parameter, Λ . Steady-state FPV models are built presuming the func- tional shape of the joint PDF of Z and Λ in order to evaluate Favre-averages of thermody- namic quantities. The mixture fraction is widely assumed to behave as a passive scalar with a mono-modal behaviour modelled by a \b{eta} -distribution. Moreover…
Assessment of turbulent fire dynamics and combustion instabilities using a flamelet model
University of Science and Technology of China（中国科学技术大学）；State Key Laboratory of Fire Science（火灾科学国家重点实验室）；University of Wuppertal（乌珀塔尔大学）；Technical University of Darmstadt（达姆施塔特工业大学）
The present work reports on the numerical investigation of NOx in three turbulent piloted diffusion flames of different levels of extinction. The study involves two-dimensional axisymmetric modeling of combustion in these flames with fairly detailed chemistry, i.e. GRI 3.0 mechanism. The main focus of the study is to analyze the effects of the two different combustion model approaches, such as infinitely fast chemistry based unsteady flamelet and finite rate chemistry based EDC, in predicting the NOx formation in three piloted methane jet flames (Sandia D, E, and F). The EDC approach is able t…
This paper describes the numerical simulation of the NASA Langley Research Center supersonic H2 -Air combustion chamber performed using two approaches to model the presumed probability density function (PDF) in the flamelet progress variable (FPV) framework. The first one is a standard FPV model, built presuming the functional shape of the PDFs of the mixture fraction, Z, and of the progress parameter, Λ. In order to enhance the prediction capabilities of such a model in high-speed reacting flows, a second approach is proposed employing the statistically most likely distribution (SMLD) techcni…
In the application of the combustion models based on low-dimensional manifolds (for instance flamelet models) to large-eddy simulation (LES) of reactive turbulent flows, the modeling simplifications of the combustion process is a critical source of uncertainty in addition to those due to the turbulent closure model and numerical discretization. The ability to quantitatively assess this uncertainty in absence of the reference result is vital to the reliable and predictive simulations of practical combustion devices.In the present study, the Pareto-efficient combustion (PEC) framework is extende…
Combustion stabilization and enhancement of the flammability limits are mandatory objectives to improve nowadays combustion chambers. At this purpose, the use of an electric field in the flame region provides a solution which is, at the same time, easy to implement and effective to modify the flame structure. The present work describes an efficient flamelet progress-variable approach developed to model the fluid dynamics of flames immersed in an electric field. The main feature of this model is that it can use complex ionization mechanisms without increasing the computational cost of the simul…
Neural networks (NN) are implemented as sub-grid flame models in a large-eddy simulation of a single-injector liquid-propellant rocket engine with the aim to replace a look-up table approach. The NN training process presents an extraordinary challenge. The multi-dimensional combustion instability problem involves multi-scale lengths and characteristic times in an unsteady flow problem with nonlinear acoustics, addressing both transient and dynamic-equilibrium behaviors, superimposed on a turbulent reacting flow with very narrow, moving flame regions. Accurate interpolation between the points o…
Large eddy simulation of propane/air jet flame in the wrinkled flamelets regime of the Borghi diagram is used to assess the performance of a recently developed consumption speed correction model in premixed combustion. The combustion is modelled using flamelet tabulation with a presumed probability density function. The investigated flame does not lie in the shear layer and is subjected to self-driven oscillations, which is ideal to test the model performance. The flame behaviour is first discussed using an accurate simulation performed on a refined mesh requiring no correction. The same model…
An extension to the classical FPV model is developed for transcritical real-fluid combustion simulations in the context of finite volume, fully compressible, explicit solvers. A double-flux model is developed for transcritical flows to eliminate the spurious pressure oscillations. A hybrid scheme with entropy-stable flux correction is formulated to robustly represent large density ratios. The thermodynamics for ideal-gas values is modeled by a linearized specific heat ratio model. Parameters needed for the cubic EoS are pre-tabulated for the evaluation of departure functions and a quadratic ex…
A computational model is developed to assist the design of the first hybrid rocket engine of the McGill Rocket Team, using liquid nitrous oxide as an oxidizer and solid paraffin wax as a fuel. The model is developed in three phases: In the first phase, a steady-state model which neglects transient performance decrease of the hybrid engine is considered. The steady-state model considers: a constant oxidizer mass flow rate; a combustion chamber in chemical equilibrium; a one-dimensional isentropic nozzle; and a one-dimensional constant-thrust rocket ascent. The steady-state model is used to cond…
The simulation of turbulent combustion phenomena is still an open problem in modern fluid dynamics. Considering the economical importance of hydrocarbon combustion in energy production processes, it is evident the need of an accurate tool with a relatively low computational cost for the prediction of this kind of reacting flows. In the present work, a comparative study is carried out among large eddy simulations, performed with various grid resolutions, a Reynolds averaged Navier-Stokes simulation, and experimental data concerning the well-known Sandia D flame test case. In all the simulations…
In order to reduce CO2 emissions, hydrogen combustion has become increasingly relevant for technical applications. In this context, lean H2-air flames show promising features but, among other characteristics, they tend to exhibit thermo-diffusive instabilities. The formation of cellular structures associated with these instabilities leads to an increased flame surface area which further promotes the flame propagation speed, an important reference quantity for design, control, and safe operation of technical combustors. While many studies have addressed the physical phenomena of intrinsic flame…
Combustion instabilities are a major concern in the design of Liquid Rocket Engines (LREs) and gas turbines. During this PhD work, several directions were explored to understand and mitigate their effects. First, more efficient and robust numerical methods for their prediction in complex combustors were designed. In this matter, a novel type of modal expansion, named a frame expansion and comparable to the classical Galerkin expansion, was introduced to build more accurate acoustic Low-Order Models (LOMs), able to account for the full geometrical complexity of industrial combustors. In particu…
In this paper, neural network (NN)-based models are generated to replace flamelet tables for sub-grid modeling in large-eddy simulations of a single-injector liquid-propellant rocket engine. In the most accurate case, separate NNs for each of the flame variables are designed and tested by comparing the NN output values with the corresponding values in the table. The gas constant, internal flame energy, and flame heat capacity ratio are estimated with 0.0506%, 0.0852%, and 0.0778% error, respectively. Flame temperature, thermal conductivity, and the coefficient of heat capacity ratio are estima…
This article aims to numerically investigate the combustion phenomenon of coaxial gaseous CH4 LOx at supercritical pressures. The choice of turbulence model, real gas model, and chemical kinetics model are the critical parameters in numerical simulations of cryogenic combustion at high pressure. At this supercritical operating pressure, the ideal gas law does not remain valid for such cases. Therefore, we have systematically carried out a comparative study to analyze the importance of real gas models, turbulence parameters, and chemical kinetics at such conditions. The comparison of real gas m…
Distributed combustion, often associated with the low-oxygen condition, offers ultra-low NOX emission. However, it was recently achieved without combustion air dilution or internal flue gas recirculation, using a distinct approach called Mixture Temperature-Controlled combustion. Here, the fuel-air stream is cooled at the inlet to delay ignition and hence foster homogeneous mixture formation. The aim of this numerical study aims to understand the operation of this combustion concept better and present a robust framework for distributed combustion modeling in a parameter range where such operat…
To effectively simulate the combustion of hydrocarbon-fueled supersonic engines, such as rocket-based combined cycle (RBCC) engines, a detailed mechanism for chemistry is usually required but computationally prohibitive. In order to accelerate chemistry calculation, an artificial neural network (ANN) based methodology was introduced in this study. This methodology consists of two different layers: self-organizing map (SOM) and back-propagation neural network (BPNN). The SOM is for clustering the dataset into subsets to reduce the nonlinearity, while the BPNN is for regression for each subset. …
LES/PDF approaches can be used for simulating challenging turbulent combustion configurations with strong turbulence chemistry interactions. Transported PDF methods are computationally expensive compared to flamelet-like turbulent combustion models. The pre-partitioned adaptive chemistry (PPAC) methodology was developed to address this cost differential. PPAC entails an offline preprocessing stage, where a set of reduced models are generated starting from an initial database of representative compositions. At runtime, this set of reduced models are dynamically utilized during the reaction frac…
Flamelet Progress Variable (FPV) combustion models allow the evaluation of all thermo chemical quantities in a reacting flow by computing only the mixture fraction Z and a progress variable C. When using such a method to predict a turbulent combustion in conjunction with a turbulence model, a probability density function (PDF) is required to evaluate statistical averages (e.g., Favre average) of chemical quantities. The choice of the PDF is a compromise between computational costs and accuracy level. The aim of this paper is to investigate the influence of the PDF choice and its modeling aspec…
A purely data-driven approach using deep convolutional neural networks is discussed in the context of Large Eddy Simulation (LES) of turbulent premixed flames. The assessment of the method is conducted a priori using direct numerical simulation data. The network has been trained to perform deconvolution on the filtered density and the filtered density- progress variable product, and by doing so obtain estimates of the un-filtered progress variable field. Any non-linear function of the progress variable can then be approximated on the LES coarse mesh and explicitly filtered to advance the LES s…
Under rocket-relevant conditions, real-gas effects and thermodynamic non-idealities are prominent features of the flow field. Experimental investigations indicate that phase separation can occur depending on the operating conditions and on the involved species in the multicomponent flow. During the past decades, several research groups in the rocket combustion community have addressed this topic. In this contribution we employ a high-fidelity thermodynamic framework comprising real-gas and multicomponent phase separation effects to investigate liquid oxygen-methane and liquid oxygen-hydrogen f…
The accurate and robust simulation of transcritical real-fluid effects is crucial for many engineering applications, such as fuel injection in internal combustion engines, rocket engines and gas turbines. For example, in diesel engines, the liquid fuel is injected into the ambient gas at a pressure that exceeds its critical value, and the fuel jet will be heated to a supercritical temperature before combustion takes place. This process is often referred to as transcritical injection. The largest thermodynamic gradient in the transcritical regime occurs as the fluid undergoes a liquid-like to a…
Combustion in automotive and aerospace applications employing diesel, gas turbine and liquid rocket engines is preceded by injection and mixing of fuel and oxidizer at high pressures, often exceeding mixture critical values. Experimental observations indicate that the jets injected at supercritical pressures exhibit significantly different dynamics than the jets at subcritical conditions, owing to the lack of distinct liquid and gas phases in supercritical state. As a result, the averaged flow quantities such as the potential core length, jet spatial growth rate and velocity decay profiles dif…
Accurate simulations of high-pressure transcritical fuel sprays are essential for the design and optimization of next-generation gas turbines, internal combustion engines, and liquid propellant rocket engines. Most important and challenging is the accurate modelling of complex real-gas effects in high-pressure environments, especially the hybrid subcritical-to-supercritical mode of evaporation during the mixing of fuel and oxidizer. In this paper, we present a novel modeling framework for high-fidelity simulations of reacting and non-reacting transcritical fuel sprays. In this method, the high…
