Turbulent Flow Simulation.
Abstract
Understanding the physiochemical processes used in predictive modelling of engine combustions is key in improving the performance of engines and reducing emissions caused by the burning of fluids. Through the use of Navier stokes equation, the importance of convection and diffusion mechanisms in fluid dynamics are appreciated. Although the computation of turbulent flow and combustion is a complicated exercise, it has been made easier by the coming of computerised methods of simulation. Some of the most complex issues in turbulence include modelling, the chemistry of turbulence and chemical kinetics in fluid flow—the processing of information about fluid dynamics. In the computation, there are three very important steps which include processing, solve and post-processing. The first stage involves defining the equations and their properties, including a volumetric element that monitor the movement of the fluid. The second stage involves the actual computation of the equations is done through selection of discretisation schemes. In the third stage, the results of the second stage are analysed and interpreted using the flow, pressure and temperature. In this paper, the focus will be on the various methods used in the simulation of turbulent flow and combustion numerical simulation. This includes the direct numerical simulation method, low dissipation simulation method, habitat method and habitat rating method, Monte Carlo, large eddy simulation method, scenario simulation and representative method of simulation. They are using a detailed approach to show how this method helps in the computation of fluid dynamics. The paper also makes use of engine injector flames of real gases and the models that they use. This paper will also discuss the various similarities in simulation methods, differences and the advantages and disadvantages that come with multiple ways. The different formulas used in the computation, different approaches and which approach is best for certain situations will also be discussed in minor details.
Contents
Low-dissipation simulation method. 5
Direct numerical simulation (DNS). 5
Habitat simulation methods or habitat rating methods. 7
Monte Carlo Simulation Method, variance reduction techniques and historical simulation. 8
Historical and Monte Carlo simulation Similarities and differences. 9
Large-eddy simulation method. 9
Reynolds Averaged Navier-Stokes (RANS) turbulence. 12
Representative simulation methods. 13
Boussinesq equation simulation model 15
Presumed probability distribution function model 17
Conditional moment closure(CMC). 18
The chemical equilibrium model 18
The flame surface density model 19
Introduction
Turbulence is the unsteady movement of fluid or fluid motion. It has confused moulders and theoreticians for several years. Turbulence notably intensifies the rate of mixing and various other transport process involving more friction and loss of energy. It is relied on by reactor technologies to inflate rates of motion. Turbulence is, therefore, significant in the development of turbulence models that can make quantitative predictions. Through turbulence flow, many various approaches have been developed, such as direct numerical simulations (DNS), Reynolds-averaged Navier-Stokes equations (RANS) and large eddy simulations (LES) (Kuerten, 2016). It noted that the K-e model expresses the primary characteristics of several turbulent flows via time scale and length scale. Advanced RANS models, for example, Reynolds stress models (RSM) requires a keen assessment from the cost-to-profit in every case. Therefore, the RANS model is recommended as the baseline model. However, RANS models have versatile constants that require experimental data for determination. Despite the scantiness of turbulence models best modern computational models and numerical methods accept most of the flows to be calculated to higher accuracy. In turbulent flow simulation method, the exact turbulence is computed using a complex method. Calculating the turbulent flow is a little challenging due to the unsteady aperiodic motion, spatial variations and the wide range of scale involved. This makes its application three-dimensional, time-sensitive and extremely fine grids. While simulation is a technology-based model that is used in the analysis of process behaviour, risks and complicated systems with their uncertainties, it offers insights into the designs of development processes and projects before time and cost are invested (Soligo, Roccon, & Soldati, 2019). Simulation is used in various areas such as safety engineering, training, education, testing and video games. Turbulent burning of gaseous fuels is broadly used in power generation stationary to convert energy, for example, land transportation, aviation, piston engines and gas turbines. However, primary understanding about turbulent combustion is scant because it highly non-linear and multiscale process that includes various phenomena, for instance, gasoline-air mixtures of chemical reactions between species, including those that control emissions from flames. Therefore, advanced numerical models and methods are required to control physical mechanisms of flame-turbulence interactivity, and it helps inefficient response to environmental challenges through the development of new effective internal combustion engines (Sweet, Richter, & Thain, 2018).
The results of the numerical study and joint experiment of knock-in spark-ignition engines that cause autoignition of fuel-air mixture.And indicate that ignition delay times soliciting decreased chemical mechanisms for different gasoline surrogates are compared with the lineup of knock onset dignified for pressure and higher temperatures. After the study of surrogate properties and chemical mechanisms, results indicate that they can be used in the calculation of gasoline autoignition in a spark in spark-ignition engine, as computed ignition hold up time leads to responsiveness when choosing a mechanism (Long et al. 2018).
Low-dissipation simulation method.
The simulation of turbulent flow through the calculation of fluid dynamics is not easy. For instance, direct numerical simulation DNS is quite expensive. This makes engineers run away from it to obtain cheaper models like (LES) large-eddy simulation. For methods to be fit for use in the computation of turbulence, they should not dissipate the structure of the flow. In this section the paper will focus on the direct numerical simulation, large-eddy simulation method and the Reynolds—average Navier stokes model (Lehmkuhl, et al 2019)
Direct numerical simulation (DNS)
In fluid dynamics computation, there ae three faces; preparation, solving and processing. The statistical formula of calculating turbulent flow is an infinitely changing assembly of vortexes. For this reason, simulation methods are paramount. The first simulation method is a direct simulation. This method aims at solving the time-dependent numerical simulation (NS) equations. It also resolves all the scale for just enough time interval to bring the fluid to an equilibrium. DNS makes use of all the spatial scales of the turbulence in the computational mesh (Zhang, Xiao, & Jordan, 2017). This includes the Kolmogorov microscales and the large integral levels (L), which is associated with the motions containing most of the energy in motion. In the Kolmogorov’s scale the kinetic energy is dissipated to heat and viscosity dominates the flow. In DNS the cascade of kinetic energy is captured up to the smallest Kolmogorov scale. In this method, increasing the Reynolds number by a factor 10 leads to an increase in the complexity of the by 1000 factors. It is therefore feasible for flows that have a moderate number of Reynolds. The (time and space) details given by DNS are NOT essential for purposes of design (Elghobashi, 2019).
One of the techniques commonly used under DNS is the Sandia`s parallel DNS code, S3D which was developed in collaboration with the Basic Energy Sciences. The code is critical because it solves the entire comprehensible reacting Navier-Stokes, total energy, species as well as mass continuity equations. Advancement in time is achieved through six stage and fourth order explicit Runge-Kutta method.
DNS of 3D turbulent non-premixed CO/H2/N2-air jet flames with detailed chemistry have been conducted. In this method, an inner turbulent fuel core flows within quiescent air and they are separated using mean shear to react different layers. This results in turbulent structures which are similar but not identical to those observed in spatially evolving planar jet and it has a window of observation that moves with the mean jet velocity. The mean jet velocity is better than the spatially evolving jet because it allows more flame turbulence interaction within a given computational domain with wider separations in mixing scales as compared to other methods and hence creating a wrinkled flame surface through intense turbulent mixing. The initialisation process is carried out using a smoothly varying profile with a specified mean convective velocity difference, the jet height and shear layer thickness. Velocity varies from -U/2 at the boundaries in the transverse direction to U/2 at the center of the jet. There is a small force between the two fields known as solenoidal isotropic velocity field and it has a turbulence intensity and integral scale. The force is confined partially to the jet region and it is centered to the core of the het or in the shear layer depending on varying cases. An initial profile of mixture fraction in the domain similar to velocity profile is used to initialise scalar fields. The initial condition results to the flow and the boundary conditions are periodic in the streamwise and spanwise direction and non-reflecting. The little initial turbulent force triggers instability in the shear layer of the jet and eventually develops into a shear driven full turbulence flow. The mixing and the reaction as a result of the turbulence interact strongly during the middle of the simulation process. At the later stages of the process, the jet breaks down and hence resulting to a decrease in shear rates, mixing rates and the local thermochemical state begins to move towards equilibrium. There are two runs which are performed on DNS, Reynolds number is indicated as Re-UH/v and it is based on the jet velocity and height where the oxidiser viscosity is represented by symbol v. The domain dimensions in the streamwise, transverse and spanwise directions, transverse and spanwise directions are represented as Lx, Ly and Ls respectively. Mach number us defined as U/2C where c is the speed of sound. The Mach number is so small to the extent that compressible effects can be abandoned but at the same time, not so small that the computational cost become excess due to acoustic CFL criteria. DNS is similar to LES where by the simulation time dependent. However, they differ in grid whereby, in DNS grid can be more rough if the grid size falls inside Kolmogorov inertial length scale unlike LES.
Outcome
is filtering Kernel
is the resolvable scale and is the sub grid-scale part. Although, most practical implementations of LES use the grid itself as the filter and perform no explicit filtering.
Habitat simulation methods or habitat rating methods
These methods are associated with quality requirement and flow of physical habitats settled in various living species. These methods consider a number of environmental elements such as water quality and sediment transport (Yi, et al 2017) Habitat simulation methods are more developed compared to hydrological rating and hydrological methods. Moreover, assessment shows that simulation methods provide more accurate outcome compared with hydrological and hydraulic rating methods. Also, these methods can be applied to high-risk projects. Instream flow incremental methodology is the most common. Advanced computer programs can be used to effectively draw accurate curves and areas in habitat simulation methods. However, these methods are time consuming as they take 2-5 years to obtain data and examine it. They are also expensive because they require advanced technology (Belletti et al 2017).
Scenario Simulation method
Scenario Simulation method is divided into time series method that is used to sample the stochastic variables in accordance to the probability distribution. The first type measures the sensitive portfolio value to some specific market variables. Second type is wide because it calculates the probability distribution of the portfolio value at a specific horizon.it helps to control common risk via summarising of portfolio risk for example the value of risk (VR) (Yang et al 2019). This method is computationally efficient alternative to conventional Monte Carlo for multicurrency fixed-income portfolios. Apart from VaR it helps in computation of other risk measures such as coherent measures of risk. Scenario simulation method is also applicable in joint market to approximate a portfolio’s overall risk and credit risk (Zhang, et al 2017)
Monte Carlo Simulation Method, variance reduction techniques and historical simulation
Monte Carlo Simulation Method (MCSM) use repeated trails to simulate different load and resistance conditions.it can calculate the probability of failure despite the lack of mathematically defined probability density functions of variations of load and resistance. However, the number of simulations required in order to provide reliable statistical results is large. The variance reduction techniques are efficient although they are limited to larger probability values therefore, disproportional computational support for analysis of realistic problems is required despite its efficiency (Louvin, 2017).
Historical simulation
It involves use of historical record of random variables to simulate the possible results. The method use the past performance to approximate the future performance by use of the figures that have ever been used before (Low, 2016).
Historical and Monte Carlo simulation Similarities and differences
The both methods can be applied to determine the risk in financial project although they use varying assumptions and techniques in order to produce probability distribution of most likely results. Monte Carlo simulation incorporate many varieties of scenario than historical data which has scarce information. Historical simulation applies actual distribution oft risk factors but the past performance is not considered in future performance (McCrickerd, & Pakkanen, 2018).
Large eddy simulation method
Large eddy simulations are carried out by allowing complex combustion chemistry at different pressures. Results indicates that as turbulent flame speed at conditions close to flashback reduces with raising pressure as flashback propensity is increased by pressure. According to the study, turbulent flame speed is a poor indicator for the onset of boundary layer flashback due to the complexity of the flashback. The flashback is high -flown the speed and thickness of the flame, and also the distance and size of local separation zone. Additionally, computed results indicate that the assumptions of boundary layer are not content for example, applying of one-dimensional pressure approximately leads to overestimation of pressure increase ahead of flame (Jacob, Malaspinas, & Sagaut, 2018).
In performance of large eddy simulations of turbulent burning of ethanol sprays, development of a modelling strategy that allows for complex combustion chemistry via combination of flamelet Generated Manifolds (FGM) and 0also due to evaporative cooling effects, Artificially Thickened Flame (ATF) approach may be considered to control enthalpy variations. Through application of evaporation model that allow inter-phase non-equilibrium and use of Euler-Lagrangian approach, ethanol droplets are tracked. Numerical outcome is authenticated by use of experimental data collected from flame EtF5 of the Sydney diluted spray flame burner. Additionally, a parametric numerical study is carried out to evaluate magnitudes of impacts as a result of evaporation cooling and wrinkling of flame surface by turbulent eddies focusing on better results (Fernandez, Nguyen, & Peraire, 2017).
Application of large eddy simulation can assist in study of other challenges such as flame-wall interaction which facilitate pollution and result to raise of heat losses, thus reducing the efficiency of an internal combustion engine. Flame-turbulence interaction and complex combustion chemistry are to be taken into consideration when adopting FGM and AFT approach respectively. Therefore, numerical model is verified by use of experimental data extinguishing of turbulent flames (Lombard et al 2016). The verification study indicates that the adapted numerical approach can handle sidewall quenching of turbulent flames. There are three different layout that include upstream, downstream and jump-like upstream movement of flame. According to research, the demand for energy will be increasing gradually and the largest percentage will be provided by combustion and since the resources are scarce and combustion may lead to pollution, it is crucial to understand the requirements.one of the vital fields that require research is flame-wall interaction (FWI).As a result of technical advancement, for example, internal combustion engines it relevance increases.in this case the reaction zone of the flame come near the cold walls and quenches. Thus, decreasing the affiance and increasing pollution formation. The FWI is divided into two configurations including Head on quenching (HOQ) and Sidewall quenching (SWQ). the flames move uprightly along the wall but only the tip of the flame is high-flown.in case of HOQ the flame movement is parallel towards the wall and then the whole flame quenches (Breton, et al 2017) The quantities that do not have dimensions differ in cases of heat flux and quenching distance and the importance of flame-wall interaction and Head on quenching configuration are considered has been thoroughly researched in all ways including numerically, experimentally and theoretically. Fuels such as hydrogen and gaseous hydrocarbons, for instance propane, ethylene, methane were used. However, it was a challenge to experimentally handle some fuels with hydrogen being the most difficult to handle. The reaction limit closer to the wall, depend on the equivalence ratio of the fuels (Di Mascio et al 2017).
According to a study carried out in china, hydrogen combustion was carried out in three-dimensional direct numerical simulation (DNS), where by the data showed that near-wall coherent turbulent structures are fundamental for the wall heat flux while the exothermic radical recombination reactions vigorously control the rate at which the is heat released. Moreover, there is distinctive behave between hydrogen and hydrocarbon based fuels.it because hydrocarbon has higher consumption rate (Vasaturo, et al 2018). Investigations carried out on the effect on quenching layer thickness of various hydrocarbons with difference in equivalence ratio and various wall conditions. Different fuels and equivalence ratios were used during the investigations although inconstant volume chamber. The unsteady heat transfer was measured during the SWQ and thermal formulation for single-wall quenching without empirical coefficients was developed. The formulation uses experimental data and it applied for lean and stoichiometric air mixtures in a pressure range. Direct numerical simulation research together with single step mechanism that imitate lean methane flame with an inlet temperature. The experimental based design on SWQ burner configuration was carried out, where the premixed V-shaped flame interacts with cooled wall under laminar and turbulent conditions. The first results showed that with highly-resolved Large eddy simulation with Direct numerical simulation are spatially resolved while comparison and analysation of turbulent, laminar case and the experiment was done. in this case, turbulent structures of the flow cannot be compared with the channel. However, the method used gave accurate results for the velocities, temperature field, global structure of the flame and the flame position (Flad, & Gassner, 2017). Additionaly, a transient analysation of Flame-wall-turbulence interaction is carried out to influence heat fluxes, quenching distances and positions beyond experimental outcome. It will be indicated that there is dependency in direction of movement of the flame tip for the characteristics of the properties while heat fluxes take place due to turbulent sidewall quenching flame that behave locally just like Head on quenching flame. Some of the methods used includes: Numerical description and numerical domain (Bazdidi et al 2017)
Reynolds Averaged Navier-Stokes (RANS) turbulence
This model is interested with modeling the Reynolds stress tensor.in cases where the primary modeled quantities are the scalar and vector potentials of the turbulent body force-the divergence of the Reynolds stress tensor, RANS turbulence modeling is proposed. This mode has the capability to model non-equilibrium turbulence situations accurately at a cost and proportional to the two-equation models that are commonly used for example k-ε. The similarity between Reynolds stress transport equation models and the proposed models is that they do not require a hypothesised constitutive relation between the turbulence and the mean flow variables (Xiao et al 2016). Adtionally, the proposed model of partial differential equations is simpler to model and compute compared to Reynolds stress transport equation model. Majority of the existing RANS models requires a constitutive algebraic relation between mean flow gradients and Reynolds stress tensor. the widely used relation is the eddy viscosity model (Ling, Kurzawski, & Templeton, 2016).
Difference and similarities between Reynolds-averaged Navier-Stokes (RANS) and Large eddy simulation (LES)
LES is based on local filtering and the equation is unsteady while RANS is based on statistical averaging that results to steady equation. RANS is less costly compared to LES.RANS simulate all the turbulence spectrum and provide time average mean value for the velocity field while LES does not give averaging but it based on filtering and it calculates only high frequency while computing the small ones which are required to be independent to the configuration of the flow. Both methods use grid. Where by calculations prior to grid generation has to be performed so that turbulence integral length scale of fluid flow can be approximated. Also, laminar flamelet approximation is used by both Reynolds-averaged Navier-Stokes (RANS) and Large eddy simulation (LES) (Liu, Kokjohn, Wang, & Yao, 2019).
Representative simulation methods
These methods are used for accurate model gas turbine engines and the model need alignment to actual engine test data so as to produce perfect representative model. The method that align predictive models to test data is referred to as Analysis-Synthesis. This program calculate performance of each engine components for example pressure drops, isentropic efficiency and effectiveness from many measurements at various stations in the engine fuel flow shaft speeds, total pressures, temperatures and air 9mass flow. Synthesis program work in opposite direction and use assumptions of the component performance turbine traits, airmass flows and pressure drops among others, to integrate the value of thermodynamic parameters such as pressure in every engine station, shaft speeds and temperatures (Fredette, & Ozguner, 2017).
The synthesis and analysis models both use numerical methods to simulate steady-state gas turbine performance. The program relies on guesses from the beginning whereby, it start with guessing the working points for the compressor, power turbine nozzle area, heat exchanger air-side exit conditions, intake mass flow and power output.by use of flow equality and continuity of powers and speeds the recuperate exit conditions, turbine capacities, compressor inlet flows and engine inlet pressure are calculated. They are later compared with the values needed to identify errors, then iterative procedure is used to rectify the guessed values to minimise the errors (Bao, Chen, & Cao 2018).
The flux code
Combustion modelling is very critical in modern design and optimisation of low-emission and high performance combustion engines and it plays a critical role in reducing environmental pollution. The Flux Code works through combination of conservation element and solution element (CE/SE) to solve conservation challenges. It has triangles which are contiguous as well as tetrahedrons in 3dimension. This combustion simulation technique produces algebraic equations which are non-linear and are used for temporary advancement of conservative variables and coming up with solution nodes ( Stegmeir, et al 2016). It uses space-time conservation technique to evaluate the values of integrals. A comparison of Flux code and Corsair-CCD method indicates that flux code is less dispersive numerically and predominantly less dissipative. Flux code can also calculate compressible flows over a variety of Mach numbers unlike Corsair-CCD code. The flux Code simulation method can also be used to calculate low Mach number compressible flows without pre-conditioning of low Mach numbers and it can sense strong shockwaves as compared to Corsair-CCD. The other advantage of this simulation technique is that it helps in high-speed repulsion and unsteady processes (Grandgirard et al 2016).
Boussinesq equation simulation model
Boussinesq equations are a set of partial differentiation equations which are non-linear. This is because the model takes into account vertical structure of the horizontal and vertical flow velocity. The main idea behind the model is to eliminate the vertical coordinate from the equations of flow while retaining influences of vertical structure of the flow of the waves. This is very important because propagation of waves occurs at a horizontal angle and their behavior is not of waves when they move in a vertical direction. One of the common characteristic of this simulation method is that it consists of frequency dispersion while shallow water equations are not frequency dispersive. The method is widely used in flow simulation in shallow and moderately long sea waves (Benosman et al 2017). To solve the equations, a person needs to assume a linear vertical distribution of the flow field with non-hydrostatic effects. the equations consist of the effects of diffraction, refraction, reflection and wave-current interactions. The first step in boussinesq equation is making a tailor expansion made of horizontal and vertical flow velocity. The next step is truncating the Taylor expansion to a finite number of terms and then the conservation of mass for an incomprehensible flow and zero curl for irrigational flow (Innes, 2018).
Stokes wave
Stokes wave is a non-linear and periodic surface wave on a fluid layer which is inviscid and of mean depth. It was developed by Sir George Stokes using an approach known as perturbation series method and it is currently called stokes expansion method. It was aimed at coming up with a solution to non-linear wave motion. It is used to simulate the behavior of intermediate and deep-water waves and it is used in coastal and offshore structures with the intention of determining kinematics of waves. One of the examples of stokes waves is third-order stokes wave on deep water (Dyachenko, Lushnikov, & Korotkevich, 2016). According to this approach, the free surface elevation and the velocity as well as phase speed are of progressive surface gravity wave in deep waters. The layer of fluid is of infinite depth and the speed of phases increase with increase in non-linearity of a waves. The height of the wave iOS the difference between the elevation of the surface and the trough. Third order waves consist of circular motion at every point but the lagrangian paths of fluid parcels are not in closed circles. This is as a result of the reduction of velocity amplitude at increasing depths below the surface of the water and hence causing a shift known as stokes drift. One of the challenges initially faced with this simulation approach is finding a solution for surface gravity waves because of boundary conditions (Lyons, 2016). The boundary conditions need to be applied at the free surface position but they are not known prior to simulation. Stokes found a solution tot his problems in the 1840s by expanding potential flow quantities using Taylor series around the surface elevation. This therefore ensures that boundary condition can be measured in terms of quantities at the mean or surface elevation. Phase speed of waves which are not linear also depends on the height of the waves (Lushnikov, 2016). This therefore results to spurious secular variation of the solution and hence contradicting the periodic behavior of waves. The similarities between boussinesq equation simulation model and the stokes waves model of simulation is that they are both used to carry out simulation of waves. One of the differences is that the boussinesq model is used to study shallow waves while the stokes waves model is used to study deep sea waves Dyachenko, & Hur, 2019).
laminar flamelet model
it estimates the turbulent flame as sequence of laminar flamelet region concentrated close to the stoichiometric surfaces of the reacting mixture. It utilises experimental data to determine relationship between the variables viewed as mass fraction, temperature and many others. The experimental data collected during laminar diffusion flame experiment is still used to predict the type and nature of dependence of the variables and also laminar flamelet relationship is gathered using the same experimental data (Pant, Han, & Wang, 2019).. The relationships are then used in solving the transport equations for mixture composition and species mass fraction. This model can be implemented where concentration of minor species in combustion is to be computed for instance quantifying the generation of pollutants. Laminar flamelet approximation is used by Reynolds-averaged Navier-Stokes (RANS) and Large eddy simulation (LES). An example of laminar flamelet estimation is used to produce a table of species compositions and reaction rates with well chose reaction progress variable and assumed probability density function. The requirement here is an estimate for mean properties.
ρR is the density of unburned reactants, SL0 is the laminar flame speed, and the flame surface density (Ladeinde, & Lou, 2018).
Spalart Allmaras model
This is a one equation model with no wall functions. this model is also stable with good convergence. It is also convenient for aerodynamics flows and transonic slows over airfoils. The limitation of this model is that it is difficult to solve shear flows, separated flow and decaying turbulence (Tamaki, Harada, & Imamura, 2017).
Presumed probability distribution function model
This model considers the statistical approach used in calculating various variables such as species, mass fractions, temperatures and density while at the same time mixture composition is calculated at the grids. The variables are then calculated as functions of the mixture fraction using probability distribution function. The model produces good results for turbulent reactive flows where convection effects as a result of the mean and changing components of velocity are dominant. This model can also be applied for adiabatic and non-diabetic situations and hence making it more convenient and reliable (Assam et al 2018).
Conditional moment closure(CMC)
Conditional moment closure method was published by Klimenko and Bilger. The development of the method was motivated by the need to achieve accurate closure for average non-linear turbulent reactive source term. It was originally developed as a mixture fraction based approach for turbulent combustion which is non-mixed. This method is very similar to the laminar flameless method because it uses experimental data to determine relationship between variables (Lee, Wilson, & Vahdati, 2018). The main focus of CMC method is to take advantages of the strong relationship between reactive scalar species and the mixture fraction and hence making it possible to associate fluctuations in reactive scalar space with fluctuations in mixture fraction space. Reactive species conditioning therefore leads to small fluctuations around the conditional mean a first order closure for the chemical source can be established. Transport equations for the reactive species mass fractions conditioned on mixture fraction have been derived and terms such as conditional velocity and average scalr dissipation should be modelled (Spalart, & Garbaruk, 2020). There have been various developments to the theory and one of the development has been on flame regime models where local correlations between reactive scalrs and mixture fraction are weakened. Fluctuations around conditional mean is critical but CMC is not rendered invalid if conditioned quantities are into correlated. CMC method is also applied to complex glow geometry and flame conditions such as engine and gas turbine environments (Blomberg et al 2016).
The chemical equilibrium model
Scientists have developed a lot of interest in hypersonic gas dynamics and supersonic turbulent reacting flows. Most of these flows involve chemical activity of fuel and oxidiser mixtures and it has received a lot of attention globally. The real process of expanding in a rocket or ramjet nozzle is between the extremes of frozen and equilibrium flow where equilibrium flow produces higher performance due to recovery of some of the chemical energy produced during decomposition of complex molecules (Brachi, et al 2018) Simulations performed using the chemical equilibrium model have the ability to come up with results which are just a fraction of the computational cost related to finite rate calculations. Chemical equilibrium models require a flow solver which solves the four basic flow equations in two dimensions instead of N+3 which are critical for finite rate solver with N representing the number of chemical species in the flow. The advantage of chemical equilibrium model as compared to other flow simulation models because the composition of the gas mixture is known from classical thermodynamics and the thermodynamic data for gas species is still known (Garneau et al 2017).
The flame surface density model
Flame surface density (FSD) intensity is one of the most widely used models of turbulent combustion. The FSD assumptions are derived from first principles but they require closure assumptions. The assumptions may be deduced from analysis, direct numerical simulation as well as experiments are applied where there is need turbulent premixed propane air V flame and hence making it critical to perform detailed measurements. Velocity profiles are obtained using laser doppler velocimetry and the front of the flames is visualised using high speed laser sheets imaging (Allauddin, Klein, Pfitzner, & Chakraborty, 2017).. The results of the above processes are then processed to obtain flame front characteristics which includes the density, flame front normal vector and the curvature. The analysis is of front flame dynamics is done using turbulent transport showing the occurrence of counter-gradient turbulent diffusion. Thermal expansion is used to control the strain rate acting on the surface of the flame. The Reynolds shear stresses is used to control the factors of flame orientation. The curvature and propagation terms act as a source of fresh gas side and sink terms of the steam which has been burned. The similarity between the FSD method and other combustion simulation method is the use of Reynolds shear stress. The difference between the FSD simulation technique and other simulation models is that the FSD model is very simple and it produces very accurate results (Sellmann, et al 2017)
Conclusion
Turbulence is important in development of turbulence models that are capable of making quantitative assumptions. Several approaches have been developed through turbulences flow. The approaches include Direct numerical simulations (DNS) that involves three faces which include preparation, solving and processing. This approach aims at solving time dependent numerical simulation equations. There is also Large eddy simulation approach (LES) where turbulent flame speed is a poor indicator for the onset of boundary layer flashback as a result of complexity of the flashback. Reynolds Averaged Navier-Strokes (RANS) turbulence is involved modelling the Reynolds stress tensor. This model has the ability to model non-equilibrium turbulence situations accurately at a cost. Other approaches are flux code, Boussineq equation simulation model and many others. Simulation is used in various places including in education, safety engineering and video games among other areas. While turbulent burning of gaseous fuels is widely used in power generation stationary to convert energy such as gas turbines.
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