Three-dimensional Numerical Model of Kerosene Evaporation in Gas Turbine Combustors

The Authors 2023. This paper is published


Introduction
1) Numerical modeling is the most appropriate tool to study liquid fuel evaporation.In gas turbine design, it is often necessary to develop devices for the atomization, evaporation, and mixing of liquid fuel within a given fuel droplet size range and uniformity of droplet distribution in the gas stream.At the same time, as a rule, a detailed experimental study of atomization and evaporation using real nozzles is difficult due to the wide range of particle sizes and the density of filling the gas stream with fuel particles.Therefore, the results of the evaporation and kerosene mixing detailed study under conditions similar to aircraft engines and stationary gas turbines demonstrated in [7] are of particular interest.
2) The experimental data is for validation of numerical modeling.One of the reasons for the experimental data given in [7] significance is their potential for validation (debugging, calibration, calculation methods development) of programs for fuel evaporation process numerical modeling.Numerical modeling is the most appropriate way (tools) to understand (comprehend) the flow structure and identify the factors that affect the fuel atomization and evaporation efficiency, and, therefore, the gas turbine energy conversion efficiency.For the evaluation of the mixing quality in the combustion chambers of aircraft and rocket engines, numerical modeling of the droplet jet formation is currently used to determine the fineness of atomization by the calculation of Sauter mean diameter, taking into account primary and secondary decay, fusion and collision of droplets, which makes it possible to evaluate liquids atomization in a wide range of devices and modes.In turn, the correct evaluation of the fuel atomization is the fundament for a correct (detailed) description of its evaporation.This knowledge is very much in demand for device design.Therefore, at the stages of design, modernization, and optimization of these installations' operating modes, it is impossible to do without mathematical modeling of the processes occurring in these installations.The reliability of the results obtained in this case can only be guaranteed by the validation of the numerical model and its software implementation carried out on reliable experimental data.Validation of an analytical technique is experimental proof that the technique is suitable for solving the intended problems.
3) FlowVision CFD is validated on experimental data.In [7], a model of a pre-evaporator channel with full optical access operating at a pressure of up to 15 bar and a temperature of up to 850 K was created to conduct experiments on kerosene evaporation.During the experiment, the pressure, temperature, and airflow velocity, as well as the initial jet temperature and fuel consumption, were changed.It means there are unique data for the calibration of complex three-dimensional numerical models of kerosene atomization, evaporation, and mixing under conditions similar to aircraft engines and gas turbines.In this study, the FlowVision software package (FlowVision PC) is validated [3,4] based on the unique experimental data from [7] in terms of the reliability of the results obtained on its basis for solving phase transition problems.
4) Effective technique for numerical simulation fuel evaporation is of interest.Even though a large number of works have been carried out on experimental and numerical studies of the processes of liquid evaporation in gas and the dependencies of the quality of gas, fuel and its evaporation products on the main parameters of fuel input have been compiled, interest in a more thorough study of the vaporization process is constantly increasing.New models are being developed, validated, and verified for both primary and secondary decay and droplet fusion, as well as evaporation and fuel combustion.The works considered below are the closest in terms of the studied processes and research methods.In [8], an effective technique for numerical simulation of a liquid jet decay in a compressed gas stream based on the Reynolds equations and the volume of fluid (VOF) method was developed.The technique describes the formation of primary droplets, and their transition to the Eulerian dispersed phase, where they undergo the secondary break-up and evaporation.In [11], Eulerian multicomponent model of liquid atomization and evaporation based on the WAVE decay model is presented.Special attention is paid to the modeling of thermal processes occurring inside moving droplets.A successful simulation of the dense liquid jets complex dynamic behavior has been carried out.In [9,10], the large eggy simulation (LES) was used to describe the spray.In [9] a special attention is paid to the setting of turbulent boundary conditions.The comparison of the results obtained experimentally and numerically by the proposed model showed its good accuracy.A similar study was carried out in [10], which also investigated the effect of the mesh resolution on the spray global characteristics such as the penetration depth.In [12], direct numerical simulation (DNS) was applied to describe the sputtering of the flame of n-heptane in a vortex combustion chamber.Using the model, the contribution of the combustion of the preliminary mixture and the diffusion flame to the total heat release is estimated.Studies [13,14] are devoted to the research of the fuel spray evolution in the engines combustion chambers.The CFD analysis carried out in [13] turned out to be the only chance to get a complete view on the fuel spray process, which made it possible to design the optimal geometry of the chamber.In [14], calculations were carried out for chambers of various working volumes; it is noted that the simulation results show a good agreement with experimental data.Works by S. Tonini et al. [21,22] are also devoted to modeling the spraying of dense diesel fuel compressed to high pressure -in [21] a description of the model, the approaches used, validation of the model is presented, and in [22] the influence of the number of fuel injections and the time between injections on the development of a cloud of droplets in the working chamber is studied.Several papers [18,19] are devoted to the study of the flow parameters inside the nozzle influence on the fuel atomization in the working chamber.In [18], the effect of primary droplet decay on the characteristics of atomization and fuel combustion in diesel engines was studied.In particular, the KH-ACT model is considered, taking into account the contributions of cavitation and turbulence inside the nozzle to the droplets primary breakup.The results show improved agreement with the experiments in comparison with modeling using the KH model.In [19], the Eulerian model based on the VOF method and implemented in the CONVERGE CFD code was investigated.For the model, the influence of the nozzle outlet geometry on both the flow inside the nozzle and the further spray in the chamber is studied.The influence of the hole geometry on the droplets primary break-up of was established, which, in turn, affects further processes and characteristics, such as the fuel penetration depth into the working area, fuel evaporation, its mixing with air, and the spray fineness.A hybrid procedure for numerical simulation of two-phase flows in the combustion chamber is proposed in [17].It is a two-stage combination of Eulerian and Lagrangian approaches.The Euler method gives a preliminary two-phase flow field.The Lagrangian method tracks the particle movement with a detailed description of the droplets secondary break-up.A 30% calculation of the spraying acceleration has been achieved compared to modeling based only on the Lagrangian method.
5) The work is aimed at the fuel evaporation calculation and validation.It should be noted that the works given in our brief review, as well as the works [3,4], describe methods for calculating both atomization and evaporation of the dispersed phase.The FlowVision PC has a model of particle atomization during the secondary droplet decay and, in general, the secondary decay can be calculated in the package.However, the present work is aimed at the results of the fuel evaporation calculation validation.Therefore, the characteristics (parameters) of the fuel spray are taken from [7] for the calculation of the experimental setup [7].At the same time, the possibility of varying the kerosene droplet diameter spectrum set at the chamber inlet is presented in the formulation of the problem.Analyzing the solution sensitivity to the spectrum, the range of changes in the diameters of kerosene droplets supplied to the chamber is selected, which ensures the evaporation rate and Sauter mean diameter of fuel droplets as much as possible coinciding with their values obtained experimentally.The proof of the FlowVision PC suitability for solving the vaporization of the dispersed phase problem is relevant for numerical studies presented in [3,4] since the correctness of the carbon black production reactor operation evaluation obtained in these works significantly depends on this.
6) The article is organized as follows.Section 1 is described a problem statement as experimental setup and assumptions that we used for mathematical model.Section 2 contains description of mathematical model into FlowVision CFD.That model contains continues and dispersed phased that are described by different set of equations.In section 3 we showing results of numerical modeling in comparison of physical experiment.Several hypotheses were tested in additional to the comparison of mathematical model and experiment.Conclusion summarizes the study and results from section 3.

Problem Statement 1.Experimental Setup
The experimental setup from [7] is shown in Fig. 1.The experimental setup working section is a rectangular duct with a cross-section of 25 mm × 40 mm and an observable streamwise pathlength of about 180 mm.To prevent overheating of the pressure housing, the quartz glass dust was surrounded by a cooling airflow.At a given temperature of the main air, the pressure inside the duct was regulated by changing the air flux and using throttles of different diameters at the duct outlet.The setup allows to install a liquid fuel atomizer inside the channel in two axial positions.The atomizer shape is shown in Fig. 2.There was used an atomizer with a flat film section.The film was atomized by a high-speed incoming airflow.The atomizer width is 8 mm, the slit height is 0.1 mm.The atomizer material is stainless steel.The atomizer film section coincides with the horizontal symmetry plane of the duct XY.The origin of the coordinate system is located in the middle of the atomizer edge.To measure the fuel temperature, a thermocouple was installed on the atomizer film section surface.To protect against the atomizer housing thermal conductivity, the thermocouple was insulated with a ceramic bond.More than 70% of the sensor volume was located in the insulator so that the film flow on the atomizer surface was not disturbed by the sensor.Jet A1 kerosene, whose physical properties are of kerosene itself and its vapors, presented in [15], was used as a liquid fuel during the experiment.The parameters of the experimental mode, defined as the basic ones for numerical simulation, are given in Tab. 1.The control sections of the computational domain at which the flow characteristics are analyzed are located at distances from the sprayer x = 30 mm, 60 mm, 100 mm, 150 mm.The computational domain is sectioned and flow characteristics are analyzed at distances of x = 30 mm, 60 mm, 100 mm, 150 mm from the sprayer.The fuel evaporation rate V evap /V 0 (the ratio of the difference in the fuel droplets volume flows in the input section x 0 and control sections x k to the flow in x 0 ) and droplets Sauter mean diameter are taken as control flow characteristics (hereinafter referred to as "control parameters").

Numerical Model Assumptions
As noted in the introduction, atomization of the film is not considered in the computational model.A discrete distribution of droplet diameters by size -a droplet size spectrum -is set at the chamber inlet (the atomizer exit).The fuel inlet is established as the zero x-coordinate (atomizer edge), though according to experimental materials it is noted that the film primary atomization is completed at the distance of 10 mm from the atomizer.The velocity of the dispersed phase (droplets) V d at the fuel inlet is assumed to be 10 m/s based on the calculation data in [7].The fuel phase volume fraction at the inlet is determined by taking into account the selected speed and the experimental mass flow rate (Tab.1).The distribution function dQ dD of the volume occupied by droplets with diameter D and normalized to its maximum value dQ dD is taken from the results of the "cold" experiment in [7].This distribution function is shown in Fig. 3 as a solid line, and its values are shown on the right.
According to the given curve, a discrete distribution of the droplet volume fraction φ is calculated.To do this, N d (the number of droplets with a diameter d i in the diameter spectrum) is determined, for which the value dQ dD (d i ) is calculated.After that, the volume fraction φ i of droplets with a diameter d i in the dispersed phase is calculated . (1) Here V (d i ) is the drop of diameter d i volume.It is assumed in this model that all drops are balls of diameter d i .The equations given in paragraphs 2.1-2.2 are solved separately for each particles family i.It should be noted that in the case of solving this problem based on the Eulerian-Lagrangian approach, the number of fuel droplets N i passed through the atomizer exit per unit of time in each family (set) corresponding to the current diameter d i of a given fuel droplet size spectrum may be calculated from (2) as The inlet gas velocity is selected based on preliminary calculations of the carrier phase without taking into account the dispersed phase results at a distance of 10 mm from the atomizer near its film section level.Due to the lack of experimental data on the effect on the problem solution changes of: Three-dimensional Numerical Model of Kerosene Evaporation in Gas Turbine Combustors

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Supercomputing Frontiers and Innovations • fuel velocity in the flow after the film is torn off the edge of the atomizer; • droplet size distribution (diameter) after the film atomization; • degree of turbulence in the incoming airflow; the accepted assumptions are verified in this study by investigation of the sensitivity of the problem solution to change: • droplet velocity at the fuel inlet; • droplet size range at the fuel inlet; • turbulence parameters at the air inlet.

Mathematical Model
The study of the liquid fuel evaporation is carried out in the FlowVision software package [1][2][3][4].The evaporation of fuel droplets in the air stream is modeled using the Eulerian approach to describe the interaction between the continuous (carrier) and dispersed phase [20].The following physical processes are modeled in the continuous phase: motion, turbulence, heat transfer, mass transfer; in the dispersed phase -motion, mass transfer, heat transfer.A detailed description of the mathematical model is given in [3], this paper only provides the short form of the main equations used in obtaining the problem solution.

Continuous Phase
The equations for continuity and momentum conservation in a continuous medium are Here φ c , ρ c , V c , p are the volume fraction, the density, the velocity, and the pressure of the continuous phase, Q mass d is the source term, n d and M d are the dispersed phase particle concentration and mass, τ eff is the effective viscous stress tensor, which depends on the continuous phase dynamic coefficient of molecular and turbulent viscosities.Turbulence is described using the KEFV model [3,5,[20][21][22][23].The dispersed phase influences the carrier phase through the terms on the right-hand side of the Navier-Stokes equations describing the motion of the carrier phase (coolant gas).The equation for the energy balance of a continuous phase, written with respect to the total enthalpy H c , has the form Here J q is the effective enthalpy diffusion flux, Q vis,G and Q enth d are source terms.The mass fraction of the evaporated raw material is determined from where Y i and J i,eff are the continuous phase mass fraction and the effective diffusion flux of the i-th substance, Q mass d,i is the continuous phase i-th substance mass source due to dispersed phase mass change (if the dispersed phase consists of one substance, then and Sc t = µt ρcDt are the molecular and turbulent Schmidt numbers and D i is the continuous phase diffusion coefficient of the i-th substance.The evaporated raw materials are added to the heat carrier gas, forming the carrier phase.

Approaches to modeling evaporation/condensation of particles (droplets)
Evaporation/condensation processes of particles on a surface are described by the particle mass transfer equation for variable M d n d : The values of particle concentration n n d , n n+1 d on two adjacent layers in time are assumed to be known during the equation integration.The source member Q mass d is figured out as Here ṁd is the specific rate of the particle phase mass change, ṁd,i is the specific rate of i-th substance of the particle phase mass change, N d is the number of the dispersed phase substances, d is the particle diameter.

Particle mass, momentum, and energy conservation equations
The particles transport is described by the inhomogeneous convective-diffusion equation for the particles concentration: , where V d is the dispersed phase (particles) velocity, ν t,d and ν t,c are the dispersed and continuous phase kinematic coefficients of the turbulent viscosity and Sc t,d -turbulent Schmidt number.The velocity of the dispersed phase (particles) in the main flow V d is determined by the particle momentum transfer equation, which is a non-uniform convective-diffusion equation for the conservative variable The force F D should be understood as the total force acting on the particle.It is obtained from the addition of repulsive, lift and drag forces.The values of the particle concentration n n d , n n+1 d and their masses M n d , M n+1 d on two adjacent layers in time are assumed to be known during the equation integration.The dispersed phase energy transfer is described by an inhomogeneous convective-diffusion equation for the conservative variable h d M d n d : where h d is the thermodynamic enthalpy of the particle phase.
Three-dimensional Numerical Model of Kerosene Evaporation in Gas Turbine Combustors

Computational grid
Grid convergence studies were performed for a 2D formulation of the problem.In this case, the central cross-section of the rectangular chamber was selected as the computational domain.The shape of the atomizer cross-section was modeled as illustrated in Fig. 4. The initial mesh was generated with a uniform characteristic cell size of about 1.25 mm.Next, mesh adaptation of the computational domain volume was applied near the atomizer inlet and channel walls.In the FlowVision software, one level of adaptation involves dividing a Cartesian cell into 8 equal ones.As the computational domain was refined, the pressure drop change in the channel was monitored.As a result of the grid convergence studies, the third level of adaptation was chosen to be used near atomizer and channel walls.Selecting the fourth level of adaptation gives about a 3% change in the control parameter.The average Y + value was about 50.The single-phase flow of air alone is firstly considered under the conditions specified in Table 1 on the grid constructed as mentioned below.The turbulence intensity at the channel entrance was set to 3%, and the turbulence scale was 2.5 mm.In the simulation of single-phase flow, the air velocity obtained at a distance of 10 mm from the atomizer, near its film section, was 106 m/s.This value was set as the gas boundary condition in the fuel inlet section for the grid design refinement taking into account the dispersed phase.At the same kerosene inlet, the volume fraction of the dispersed phase was set equal to 0.1844, which provides the required fuel consumption when its velocity equals 10 m/s.In two-phase calculations of the gas-plus-kerosene system, additional adaptation of the computational mesh was applied behind the atomizer.The level of additional adaptation was based on a condition of dispersed phase volume fractiononly regions where the dispersed phase volume fraction had values in the range 10 −10 to 1 were adapted.Figure 5 shows the profiles of the liquid-fuel volume fraction and the mass fraction of its vapors, obtained at different adaptation levels in the control section furthest from the atomizer, at x = 150 mm.
The third level of the adaptation with the dispersed phase volume condition was selected for use in further calculations.The cell count was 150.4 thousand.The resulting grid, which was used in calculations, is shown in Fig. 6.

Assessment of the influence of atomizer shape
Due to the lack of precise dimensions parameters of the atomizer used in the experiments, taking into account the accepted method of the fuel supply (droplets form from the atomizer edge), the transition to a simplified atomizer model with a rectangular cross-section, which sizes are equal to the atomizer length and the kerosene supply gap size (Fig. 8), is considered.The negligible change in the control parameters as a result of calculations with a simplified geometry indicates a weak influence of its shape on the solution in the given formulation.Subsequent calculations model the atomizer with a rectangular cross-section (simplified geometry).

Assessment of the influence of the spectrum of inlet fuel droplets
As observed in the calculation results presented above, the deviation of the droplet Sauter mean diameter from experimental values increases in control sections located further away from the atomizer.To identify the source of the deviation of this control parameters calculated values from experimentally obtained ones, the computational model solution sensitivity analysis to the spectrum of kerosene droplet diameters, which are set as inlet parameter, was carried out.The basic spectrum of fuel droplet diameters was obtained from the results of the cold experiments [7].The considered spectrum variations, which were obtained by changing the values of the largest particle group volume fractions in the dispersed phase at the fuel inlet, are shown in Tab. 3. The basic spectrum corresponds to the set of droplets denoted D1.A comparison of the control parameters calculated for the spectra of Tab. 3 is shown in Fig. 10.The spectrum of fuel droplet sizes at the input has the greatest influence on the solution out of all the considered modeled input parameters , ambiguously determined from [7].The closest match of SMD control cross-sections to experimental data was obtained with the D5 spectrum.Subsequent studies were carried out using the inlet kerosene droplet diameter spectrum denoted D5 in Tab. 3.

Assessment of jet spray width
According to the experimental data in [7], the control sections are given a value Z0.9, defined as the half-width of the profile which contains 90% of the measured volumetric fuel flow rate (liquid and vapor).The factors affecting the spray width of the jet are the following: • gas turbulence [7,16]; • fuel droplets, which are tearing off atomizer edge, fluctuations [7,16]; • main stream velocity fluctuations [6].
Three-dimensional Numerical Model of Kerosene Evaporation in Gas Turbine Combustors To study the effect on the jet spray width in the computational model, it was opted to alter the parameter of inlet air turbulence.Figure 11 shows the magnitude of Z0.9 values obtained from calculations using different values of pulsations and turbulence scales in the air flow at the channel entrance.Increasing the incoming flow pulsations from 3% to 10% achieves an up to 2× increase in profile width, which contains 90% of the measured volumetric fuel consumption, thus matching the experimentally measured values.At the same time, the change in the control characteristics of evaporation rate and droplet Sauter mean diameter is negligible.Figure 12 shows changes in the kerosene vapors mass fraction distribution as a result of an increase in the airflow turbulence intensity at the inlet.

Influence of airflow temperature regime and pressure
In the basic experimental scenario, the air temperature is equal to 750 K and pressure is 9 bar in the duct setup.[7] presents results with these parameters changed to the following values: • air temperature 650 K, 850K; • air pressure 6 bar, 12 bar.Numerical simulations with these conditions were performed using the computational model constructed in the FlowVision CFD package.Simulations were performed with a simple change in air temperature and pressure, but also with an adjustment of fuel parameters to account for the change in its properties under the new conditions.Airflow under different temperature regime interactions leads to a change in fuel temperature on the atomizer surface.Values measured with a thermocouple under different experimental conditions are given in [6].The corresponding correction of the liquid kerosene thermophysical properties (in particular, its surface tension) determines the change in its dispersed composition after the film spraying.In order to confirm the droplet diameter size distribution, which was accepted as an input parameter from the cold experiment (paragraph 2.1) based on the [7], the droplet size diameter adjustment is defined as , where D n ew is the new diameter value, D i ni is the original diameter value, σ f uel is the liquid fuel surface tension, and ρ air is the air density.The results of control parameters (the evaporation rate and droplet Sauter mean diameter) calculations under another set of experimental conditions are shown in Fig. 13.The calculation results approach the experimental data by adjusting the input data for fuel droplets, taking into account changes in air pressure and temperature.However, the chosen method of the correction probably does not accurately describe real conditions (in particular, the droplet size spectrum), which is the reason for the observed deviations in the control parameter values.

Influence of the dimensionality in the problem statement
The study of kerosene evaporation in the premix duct for a gas turbines combustion chamber at high pressure is also considered as a three-dimensional formulation within the scope of this work.The parameters of the derived two-dimensional model were transferred to a threedimensional formulation for the rectangular duct.The atomizer shape was modeled as the simplified one obtained as a result of studies carried out in paragraph 3.1.2. Figure 14 shows the isometry of the spatial computational domain and boundary conditions.
FlowVision provides the following options for boundary conditions of dispersed phase particles near solid walls.Particles can: • bounce elastically off the wall; • bounce inelastically; • stick to it.The choice of boundary condition is determined by the tangent and normal components (k x and k y , respectively) of the particle momentum recovery coefficient after collision with the wall.For example, in the case of a perfectly elastic rebound conserving velocity tangential component, k x = 1, k y = 1; for a perfectly inelastic rebound conserving velocity tangential component, k x = 1, k y = 0; in case of sticking, k x = 0, k y = 0.In this study, particle interaction with the wall is defined as "perfectly inelastic rebound conserving velocity tangential component".The adaptive grid, built for the three-dimensional problem statement, contained 3.96 million cells.Figure 15 shows the distributions of the kerosene volume fraction (top) and the droplet diameter (bottom).Figure 16 shows the distributions of the kerosene vapor mass fraction (top) and the air temperature (bottom).

Conclusion
A study of kerosene evaporation in a premix duct for gas turbine combustion chambers at high pressure was carried out in the FlowVision software package based on the experimental data available in literature.Fuel droplet motion and evaporation in the airflow are modeled using the Eulerian approach to continuous-and dispersed-phase interaction.There was a study of the influence on the solution of model parameters such as the computational grid, the atomizer shape, the fuel inlet boundary conditions in terms of the velocity and droplet size, and the inlet air turbulence.In particular, it is found that • in the modeled scenario of fuel supply in the form of droplets , the atomizer shape has negligible effect on the calculated control values; • change in the droplet velocity at the inlet from 2 m/s to 10 m/s (in accordance with available data from other published computational studies) affects the results only in the control section closest to the atomizer, where, according to experimental data, an overestimated evaporation rate is observed; • simulation results significantly depend on the size of fuel droplets at the inlet.It is possible to obtain a correct distribution of control parameters only for a specific droplet size spectrum, which allows to refine results by taking into account the change in droplet acceleration due to flow, the rate of their heating and evaporation depending on droplet diameter and the initial spectrum (as selected based on the cold experiment data); • inlet air turbulence parameters affect the jet spray width.An increase in the incoming flow pulsations from 3% to 10% achieves an up to 2x increase in the profile width, which contains 90% of the measured volumetric fuel consumption, matching experimentally achieved values.
The evaporation rate and droplet Sauter mean diameter obtained in the selected observed duct sections as a result of the simulation deviate from their corresponding experimentally obtained values by 9% and 12%, respectively, for the basic calculation mode , taking into account the existing uncertainties of the initial data and the assumptions made.Based on a series of calculations for different experimental conditions, it is shown that for the constructed computational model the correct change in fuel evaporation rate with variations in temperature and air pressure is obtained.

Figure 4 .
Figure 4.The computational domain with a schematized atomizer in the two-dimensional problem formulation (a) liquid fuel volume fraction (b) fuel vapor mass fraction

Figure 5 .
Figure 5. Dependence on the grid adaptation levels of the fuel (a) and vapor (b) distributions in the cross-section x = 150 mm along the duct length from the center line

Figure 6 .
Figure 6.A grid for a two-dimensional formulation based on the results of the numerical solution convergence study

Figure 7 .
Figure 7. Fuel droplets evaporation rate and Sauter mean diameter in basic calculation mode

Figure 8 .
Figure 8. Assessment of the influence of atomizer shape 3.1.3.Assessment of the influence of droplet inlet velocity Two types of fuel inlet boundary conditions were considered: • inlet droplets velocity 10 m/s, dispersed phase volume fraction 0.1844, air velocity 106 m/s (droplet velocity values based on calculations in [7]); • inlet droplets velocity 1.844 m/s, dispersed phase volume fraction 1, air velocity 0 m/s (droplet velocity values based on the experimental fuel flow rate).The respective calculation results are shown in Fig. 9.These results indicate that determining kerosene inlet velocity from its flow rate is both acceptable and justifiable.

Figure 9 .
Figure 9. Assessment of the influence of droplet inlet velocity

Figure 10 .
Figure 10.Droplets inlet size spectrum change estimation

Figure 11 .
Figure 11.The half-width of the profile, which contains 90% of the measured volumetric fuel consumption (liquid and vapor)

Figure 12 .
Figure 12.Kerosene vapors mass fraction distribution for different airflow turbulence parameters Three-dimensional Numerical Model of Kerosene Evaporation in Gas Turbine Combustors40Supercomputing Frontiers and Innovations

Figure 13 .
Figure 13.Calculation results for another set of experimental conditions

Figure 14 .
Figure 14.The computational domain and boundary conditions in the 3D problem formulation

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. The resources of the Moscow State University (MSU) supercomputer complex allowed for the optimization of the time required to run the required series of test calculations and to speed up the calculation model debugging process and program validation.

Figure 17 .
Figure 17.Calculation results on the 3D problem statement

Table 1 .
Experimental mode parameters defined as the basic for the numerical simulation

Table 3 .
Variations of the particle diameter spectrum at the inlet