CN115994453A - High-precision simulation method for aero-engine combustion chamber - Google Patents

High-precision simulation method for aero-engine combustion chamber Download PDF

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CN115994453A
CN115994453A CN202310088180.2A CN202310088180A CN115994453A CN 115994453 A CN115994453 A CN 115994453A CN 202310088180 A CN202310088180 A CN 202310088180A CN 115994453 A CN115994453 A CN 115994453A
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combustion chamber
interface
combustion
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邵长孝
柴敏
罗坤
樊建人
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Zhejiang University ZJU
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Abstract

The invention provides a high-precision simulation method of an aero-engine combustion chamber, which comprises the following steps of: step 1: inputting fuel oil and air flow at the inlet of a combustion chamber of the aero-engine; step 2: simulation of atomization process in combustion chamber, simulation of evaporation process and simulation of combustion process; step 3: judging whether the iteration of the residual error of the outlet of the combustion chamber is finished, if so, entering the next step, otherwise, returning to the step 2; step 4: outputting parameters at the outlet of the combustion chamber of the aero-engine. The beneficial effects of the invention are as follows: the invention can greatly improve the overall accuracy of the atomized combustion, has high-accuracy characteristics, does not need the step of parameter adjustment according to specific atomized combustion working conditions, has strong generality, and can meet the high-accuracy requirement in the iterative optimization of the combustion chamber of the aero-engine.

Description

High-precision simulation method for aero-engine combustion chamber
Technical Field
The invention relates to the technical field of aeroengines or gas turbines, in particular to a high-precision simulation method of an aeroengine combustion chamber.
Background
The atomization combustion process inside the combustion chamber of the engine comprises complex processes of atomization, evaporation, steam and air mixing, combustion and the like of liquid fuel. Today, the overall simulation of atomized combustion has simplified the atomization process, for example, described by the lagrangian method. Instead of being injected in the form of a liquid column, the liquid fuel is reduced to a large number of droplets [1] which are completely atomized, each droplet being characterized by a Lagrangian point, we call this type of model a first type of atomization model. Still further, researchers have developed typical atomization models to describe the atomization process, such as the Taylor Analogy Breakup (TAB) disruption model [2] proposed by O' Rourke and Amsden in the eighties, the WAVE model [3] proposed by Reitz, the Kelvin-Helmholtz Rayleigh-Taylor (KH-RT) model [4] proposed by Beale et al, and the stochastic breakup model [5] proposed by Apte, among others. The TAB model is based on Taylor's theory of similarity, which analogizes the oscillation and deformation of the droplets with the elastic particle system. The WAVE model assumes KH instability as the dominant mechanism for atomization, and the KH-RT model additionally accounts for RT instability due to interfacial acceleration. Random break up models assume that the size and number density of the droplets obey a probability density function distribution. We call these models, which are controlled by a large number of artificial parameters and presuppose the mechanism of atomization, the second type of atomization model.
In fact, the evolution mechanism of atomization does not have a unified theory, and the adoption of the atomization model with the two strong assumptions can seriously affect the overall simulation accuracy of atomization combustion. For example, som and Aggarwal [6] found that the predicted difference in atomization penetration distance for different atomization models (KH and KH-ACT models) reached 33% and even 50% for flame elevation by studying the effect of the different atomization models on combustion characteristics. Greenberg [7] found that the use of different droplet size distribution hypotheses caused flame oscillations. Esclapez et al [8] perform large vortex simulation on the atomizing combustion process of a real aero-engine combustion chamber, and find that the downstream liquid drop velocity obtained by adopting a random atomizing model is nearly 100% different from the experimental value. The two types of atomization models developed in the eighth nineties are used until now, the limitation of the two types of atomization models has severely restricted the accuracy of atomization combustion simulation, and the improvement of the accuracy of atomization simulation becomes a problem to be solved urgently for the overall simulation accuracy of atomization combustion.
At present, the simulation precision of the aero-engine combustion chamber is limited, wherein the atomization combustion overall simulation inside the combustion chamber is simplified in the atomization process. Although the simulation of the atomization combustion can generally meet a part of demands in engineering at present, a great deal of researches show that the simulation precision of the atomization process is low for the unsteady state phenomena such as liquid mist spontaneous combustion, ignition and flameout, so that the whole prediction precision of the atomization combustion is limited, and the engineering demands cannot be met.
Disclosure of Invention
The invention provides a high-precision simulation method of an aero-engine combustion chamber, which comprises the following steps of:
step 1: fuel and air flow are input at the inlet of the combustion chamber of the aircraft engine.
Step 2: simulation of atomization process in combustion chamber, simulation of vaporization process and simulation of combustion process.
Step 3: and judging whether the iteration of the residual error of the outlet of the combustion chamber is finished, if so, entering the next step, otherwise, returning to the step 2.
Step 4: outputting parameters at the outlet of the combustion chamber of the aero-engine.
As a further improvement of the present invention, in the step 2, the simulation of the atomization process in the combustion chamber adopts a Level Set method to track the gas-liquid interface.
As a further development of the invention, in the Level Set method, the gas-liquid interface is represented as a zero-isosurface of a smooth function phi (x, t), which is typically taken as a signed distance function:
|G(x,t)|＝|x-x Γ |，
wherein t is time, x Γ Is the point on the interface where the distance x is shortest;
the motion of the phase interface is determined by the following transport equation:
Figure BDA0004073773160000021
where u is the fluid velocity; adopting sub-grid interface characterization, namely refining the grid only at the phase interface;
the semi-Lagrangian transport format is employed and is based on the fact that:
the scalar G should remain unchanged along the trajectory of the substance point under the effect of the transport speed u, at a time t n+1 Through position x n+1 The trajectory of (2) may be traced back to time t n ＝t n+1 - Δt, thereby obtaining the position point x of the last moment n Thus in position x n+1 LS function value G of (2) n+1 Obtained by the following form:
G n+1 (x n+1 )＝G n (x n )。
in x, using Lagrange's transport format n To x n+1 Solving a normal differential equation.
As a further improvement of the invention, the smoothing function in the liquid phase takes a positive value, the smoothing function in the gas phase takes a negative value, and the smoothing function takes a value of 0 at the interface.
As a further improvement of the invention, a reinitialization is required for the Level Set method.
As a further improvement of the invention, the re-initialization only needs to interpolate the speed u and LS (level set) scalar G between the right intersections using tri-linear interpolation with 8 nearest grid points.
As a further development of the invention, the reinitialization is carried out every 100 time steps.
As a further improvement of the present invention, in the step 2, the simulation of the evaporation process in the combustion chamber includes:
during and after the atomization of aviation liquid fuel in a combustion chamber, along with the evaporation process of the liquid fuel, solving a Navier-Stokes equation with variable density and low Mach:
Figure BDA0004073773160000031
Figure BDA0004073773160000032
wherein ρ is,
Figure BDA0004073773160000033
p and μ represent density, velocity, pressure and dynamic viscosity, respectively;
the evaporation of the droplets is controlled by the temperature at the interface and the concentration of the components, and thus the temperature of the whole field and the mass fraction of each component are solved using a conservation equation as follows:
Figure BDA0004073773160000034
Figure BDA0004073773160000035
t, Y, C in p Lambda and D m Respectively representing temperature, mass fraction, constant pressure specific heat capacity, thermal conductivity and mass diffusion coefficient;
the step condition at the interface is referred to as a Rankine-Hugoniot step, which can be considered as conservation of energy and mass on both sides of the interface, as shown in the following formula,
Figure BDA0004073773160000036
Figure BDA0004073773160000037
h in lg Representing the latent heat of evaporation, the solution of the evaporation rate can be simplified by considering the gradient of mass fraction in the liquid phase as zero:
Figure BDA0004073773160000038
in the middle of
Figure BDA0004073773160000039
Represents the vapor concentration at the gas phase side interface, +.>
Figure BDA00040737731600000310
Can be obtained by the Clausius-Clapeyron relation:
Figure BDA0004073773160000041
Figure BDA0004073773160000042
in the middle of
Figure BDA0004073773160000043
Is the vapor pressure at the interface, p atm Is the ambient pressure, m vap Is the molar mass of the steam, R is the ideal gas constant, T Γ Is the interface temperature, T B Is the boiling temperature of the liquid at ambient pressure, m g Is the molar mass of the gas phase;
the step condition is processed by adopting a virtual fluid method, the calculation domain adopts uniform staggered grids, namely scalar quantity is defined in the center of the grids, and velocity components are stored on grid surfaces, and virtual velocity values on the virtual grids, namely expansion of gas/liquid phase velocity in a liquid/gas phase calculation domain, are required to be determined in consideration of discontinuity of a velocity field at an interface, and can be expressed as follows:
Figure BDA0004073773160000044
Figure BDA0004073773160000045
as a further improvement of the present invention, in said step 2, the simulation of the combustion process of the combustion chamber comprises:
gas phase combustion is described by the Navier-Stokes equation of variable density, low Mach number, where the influence of liquid mist is the mass source term in the continuity equation
Figure BDA0004073773160000046
In the momentum equation is the momentum source term +.>
Figure BDA0004073773160000047
The equation is expressed as
Figure BDA0004073773160000048
Figure BDA0004073773160000049
Furthermore, scalar transport equations for fuel (F), oxidant (O) and product (P) mass fractions need to be solved according to a single step chemical reaction mechanism, including the chemical reaction source term
Figure BDA00040737731600000410
And the source term of liquid fuel in the continuity equation
Figure BDA00040737731600000411
Figure BDA00040737731600000412
/>
Figure BDA00040737731600000413
Figure BDA0004073773160000051
And finally, solving a transport equation of gas phase temperature:
Figure BDA0004073773160000052
wherein is
Figure BDA0004073773160000053
The energy exchange rate with the droplet is +.>
Figure BDA0004073773160000054
Heat release rate of combustion, heat capacity c P And viscosity μ, the Lewis number for each component being 1.
As a further development of the invention, in said step 4, temperature and pollutant parameters at the aircraft engine combustion chamber outlet are output.
The beneficial effects of the invention are as follows: the invention can greatly improve the overall accuracy of the atomized combustion, has high-accuracy characteristics, does not need the step of parameter adjustment according to specific atomized combustion working conditions, has strong generality, and can meet the high-accuracy requirement in the iterative optimization of the combustion chamber of the aero-engine.
Drawings
FIG. 1 is a flow chart of a high-precision simulation method of the present invention.
Detailed Description
The invention discloses a high-precision simulation method of an aero-engine combustion chamber, which uses a high-precision interface tracking algorithm to realize the accurate simulation of an atomization process, couples the evaporation and combustion processes, and realizes the overall high-precision simulation of the atomization combustion process.
The invention discloses a high-precision simulation method of an aero-engine combustion chamber, which comprises the following steps of:
step 1: fuel and air flow are input at the inlet of the combustion chamber of the aircraft engine.
Step 2: simulation of atomization process in combustion chamber, simulation of vaporization process and simulation of combustion process.
Step 3: and judging whether the iteration of the residual error of the outlet of the combustion chamber is finished, if so, entering the next step, otherwise, returning to the step 2.
Step 4: outputting parameters at the outlet of the combustion chamber of the aero-engine.
In the step 2, the method specifically further includes:
1. simulation of the atomization process in the combustion chamber. The atomization process in the combustion chamber is the result of the comprehensive action of aviation liquid fuel and air in the combustion chamber, and the key of high-precision simulation of the process is the tracking of a gas-liquid interface. In the Level Set method, the gas-liquid interface is represented as a zero-isosurface of a smooth function phi (x, t), which is typically taken as a signed distance function:
|G(x,t)|＝|x-x Γ |，
wherein t is time, x Γ Is the point on the interface where the distance x is shortest. The function takes a positive value in the liquid phase, takes a negative value in the gas phase, and takes a value of 0 at the interface. The motion of the phase interface is determined by the transport equation,
Figure BDA0004073773160000061
where u is the fluid velocity. The most typical LS transport format is the WENO format, which can guarantee the accuracy and numerical stability of the transport, however, WENO is prone to excessive dissipation for small scale scalar structures of transport, which can create serious problems for the gas-liquid two-phase flow under investigation. The invention adopts the subgrid interface characterization, namely, the grid is refined only at the phase interface, thereby greatly reducing the calculated amount.
The semi-Lagrangian type transport format is an efficient and accurate scalar transport format that avoids severe CFL limitations due to rapidly decreasing distances between orthogonal points. Without the need for discrete transport equations, the semi-Lagrangian format is based on the fact that: the scalar G should remain unchanged along the trajectory of the substance point under the effect of the transport speed u. At time t n+1 Through position x n+1 The trajectory of (2) may be traced back to time t n ＝t n+1 - Δt, thereby obtaining the position point x of the last moment n . Thus in position x n+1 LS function value G of (2) n+1 Can be obtained by the following forms: g n+1 (x n+1 )＝G n (x n ). Because of the Lagrangian type transport format, larger time steps can be used, and at the same time, x is needed n To x n+1 Solving a normal differential equation (ODE). The phase interface transport equation adopts a four-order-precision Longer-Kutta (Runge-Kutta) mode for dispersion.
For the Level Set method, a re-initialization process is required, and only 8 nearest grid points are required for re-initialization, and a tri-linear interpolation is adopted to interpolate a speed u and an LS (Level Set) scalar G between the right-angle points. Through inspection, the reinitialization process is not needed to be carried out in each step, and the reinitialization is carried out once every 100 time steps.
2. Simulation of the vaporization process in the combustion chamber. In the atomization process and the subsequent stage of aviation liquid fuel in a combustion chamber, along with the evaporation process of the liquid fuel, the invention solves the Navier-Stokes equation with variable density and low Mach:
Figure BDA0004073773160000062
Figure BDA0004073773160000071
wherein ρ is,
Figure BDA0004073773160000072
p and μ represent density, velocity, pressure and dynamic viscosity, respectively.
The evaporation of the droplets is controlled by the temperature at the interface and the concentration of the components, and thus the temperature of the whole field and the mass fraction of each component are solved using a conservation equation as follows:
Figure BDA0004073773160000073
Figure BDA0004073773160000074
t, Y, C in p Lambda and D m Respectively represent temperature, mass fraction, constant pressure specific heat capacity, thermal conductivity and mass diffusion coefficient.
In addition, the transmission equation of the Level Set method capture interface used in the invention needs to consider the evaporation effect:
Figure BDA0004073773160000075
in the middle of
Figure BDA0004073773160000076
And ρ l The hyperbolic tangent function, evaporation rate and liquid phase density are shown, respectively.
The important step condition at the interface is a Rankine-Hugoniot step, which can be considered as conservation of energy and mass at both sides of the interface, as shown in the following formula,
Figure BDA0004073773160000077
/>
Figure BDA0004073773160000078
h in lg Indicating the latent heat of evaporation. Considering that the gradient of mass fraction in the liquid phase is zero, the solution of evaporation rate can be simplified as:
Figure BDA0004073773160000079
in the middle of
Figure BDA00040737731600000710
Representing the vapor concentration at the gas phase side interface. />
Figure BDA00040737731600000711
Can be obtained by the Clausius-Clapeyron relation:
Figure BDA00040737731600000712
Figure BDA00040737731600000713
in the middle of
Figure BDA0004073773160000081
Is the vapor pressure at the interface, p atm Is the ambient pressure, m vap Is the molar mass of the steam, R is the ideal gas constant, T Γ Is the interface temperature, T B Is the boiling temperature of the liquid at ambient pressure, m g Is the molar mass of the gas phase. It is to be understood that vapor and liquid phase vapors are different.
The accurate discretization of the boundary conditions at the interface is of great importance in the method. The present invention employs a virtual fluid approach to handle these step conditions. The computational domain all employs a uniformly staggered grid, i.e., scalar definitions are at the center of the grid and velocity components are stored on the grid face. Considering that the velocity field is discontinuous at the interface, we need to determine virtual velocity values on the virtual grid, i.e. the expansion of the gas/liquid phase velocity within the liquid/gas phase computation domain. The method can be concretely expressed as follows:
Figure BDA0004073773160000082
Figure BDA0004073773160000083
3. simulation of combustion process in combustion chamber. Gas phase combustion is described by the Navier-Stokes equation of variable density, low Mach number, where the influence of liquid mist is the mass source term in the continuity equation
Figure BDA0004073773160000084
In the momentum equation is the momentum source term +.>
Figure BDA0004073773160000085
The equation is expressed as
Figure BDA0004073773160000086
Figure BDA0004073773160000087
Furthermore, scalar transport equations for fuel (F), oxidant (O) and product (P) mass fractions need to be solved according to a single step chemical reaction mechanism, including the chemical reaction source term
Figure BDA0004073773160000088
And the source term of liquid fuel in the continuity equation
Figure BDA0004073773160000089
Figure BDA00040737731600000810
/>
Figure BDA00040737731600000811
Figure BDA00040737731600000812
And finally, solving a transport equation of gas phase temperature:
Figure BDA0004073773160000091
wherein is
Figure BDA0004073773160000092
The energy exchange rate with the droplet is +.>
Figure BDA0004073773160000093
Heat release rate of combustion. Heat capacity c P And viscosity μ, the Lewis number for each component being 1.
The beneficial effects of the invention are as follows: the invention can greatly improve the overall accuracy of the atomized combustion, has high-accuracy characteristics, does not need the step of parameter adjustment according to specific atomized combustion working conditions, has strong generality, and can meet the high-accuracy requirement in the iterative optimization of the combustion chamber of the aero-engine.
The foregoing is a further detailed description of the invention in connection with the preferred embodiments, and it is not intended that the invention be limited to the specific embodiments described. It will be apparent to those skilled in the art that several simple deductions or substitutions may be made without departing from the spirit of the invention, and these should be considered to be within the scope of the invention.

Claims (10)

1. The high-precision simulation method for the aero-engine combustion chamber is characterized by comprising the following steps of:
step 1: inputting fuel oil and air flow at the inlet of a combustion chamber of the aero-engine;
step 2: simulation of atomization process in combustion chamber, simulation of evaporation process and simulation of combustion process;
step 3: judging whether the iteration of the residual error of the outlet of the combustion chamber is finished, if so, entering the next step, otherwise, returning to the step 2;
step 4: outputting parameters at the outlet of the combustion chamber of the aero-engine.
2. The high-precision simulation method according to claim 1, wherein in the step 2, the simulation of the atomization process in the combustion chamber adopts a Level Set method to track the gas-liquid interface.
3. A high-precision simulation method according to claim 2, characterized in that in the leveset method, the gas-liquid interface is represented as a zero-valued surface of a smooth function Φ (x, t), which is usually taken as a signed distance function:
|G(x,t)|＝|x-x Γ |，
wherein t is time, x Γ Is the point on the interface where the distance x is shortest;
the motion of the phase interface is determined by the following transport equation:
Figure FDA0004073773150000011
where u is the fluid velocity; adopting sub-grid interface characterization, namely refining the grid only at the phase interface;
the semi-Lagrangian transport format is employed and is based on the fact that:
the scalar G should remain unchanged along the trajectory of the substance point under the effect of the transport speed u, at a time t n+1 Through position x n +1 The trajectory of (2) may be traced back to time t n ＝t n+1 - Δt, thereby obtaining the position point x of the last moment n Because ofThis is at position x n +1 LS function value G of (2) n+1 Obtained by the following form:
G n+1 (x n+1 )＝G n (x n )。
in x, using Lagrange's transport format n To x n+1 Solving a normal differential equation.
4. A high-precision simulation method according to claim 3, wherein the smooth function in the liquid phase takes a positive value, the smooth function in the gas phase takes a negative value, and the smooth function takes a value of 0 at the interface.
5. A high-precision simulation method according to claim 3, characterized in that a reinitialization is required for the Level Set method.
6. The high-precision simulation method according to claim 5, wherein the re-initialization only needs to interpolate the speeds u and LS scalar G between the right intersection points using tri-linear interpolation using 8 nearest grid points.
7. The high-precision simulation method according to claim 5, wherein the reinitialization is performed every 100 time steps.
8. The high-precision simulation method according to claim 1, wherein in the step 2, the simulation of the combustion chamber evaporation process includes:
during and after the atomization of aviation liquid fuel in a combustion chamber, along with the evaporation process of the liquid fuel, solving a Navier-Stokes equation with variable density and low Mach:
Figure FDA0004073773150000021
Figure FDA0004073773150000022
wherein ρ is,
Figure FDA0004073773150000023
p and μ represent density, velocity, pressure and dynamic viscosity, respectively;
the evaporation of the droplets is controlled by the temperature at the interface and the concentration of the components, and thus the temperature of the whole field and the mass fraction of each component are solved using a conservation equation as follows:
Figure FDA0004073773150000024
Figure FDA0004073773150000025
t, Y, C in p Lambda and D m Respectively representing temperature, mass fraction, constant pressure specific heat capacity, thermal conductivity and mass diffusion coefficient;
the step condition at the interface is referred to as a Rankine-Hugoniot step, which can be considered as conservation of energy and mass on both sides of the interface, as shown in the following formula,
Figure FDA0004073773150000026
Figure FDA0004073773150000027
h in lg Representing the latent heat of evaporation, the solution of the evaporation rate can be simplified by considering the gradient of mass fraction in the liquid phase as zero:
Figure FDA0004073773150000031
in the middle of
Figure FDA0004073773150000032
Represents the vapor concentration at the gas phase side interface, +.>
Figure FDA0004073773150000033
Can be obtained by the Clausius-Clapeyron relation:
Figure FDA0004073773150000034
Figure FDA0004073773150000035
in the middle of
Figure FDA0004073773150000036
Is the vapor pressure at the interface, p atm Is the ambient pressure, m vap Is the molar mass of the steam, R is the ideal gas constant, T Γ Is the interface temperature, T B Is the boiling temperature of the liquid at ambient pressure, m g Is the molar mass of the gas phase;
the step condition is processed by adopting a virtual fluid method, the calculation domain adopts uniform staggered grids, namely scalar quantity is defined in the center of the grids, and velocity components are stored on grid surfaces, and virtual velocity values on the virtual grids, namely expansion of gas/liquid phase velocity in a liquid/gas phase calculation domain, are required to be determined in consideration of discontinuity of a velocity field at an interface, and can be expressed as follows:
Figure FDA0004073773150000037
Figure FDA0004073773150000038
9. the high-precision simulation method according to claim 1, wherein in the step 2, the simulation of the combustion process of the combustion chamber includes:
gas phase combustion is described by the Navier-Stokes equation of variable density, low Mach number, where the influence of liquid mist is the mass source term in the continuity equation
Figure FDA0004073773150000039
In the momentum equation is the momentum source term +.>
Figure FDA00040737731500000310
The equation is expressed as
Figure FDA00040737731500000311
Figure FDA00040737731500000312
/>
Furthermore, scalar transport equations for fuel (F), oxidant (O) and product (P) mass fractions need to be solved according to a single step chemical reaction mechanism, including the chemical reaction source term
Figure FDA00040737731500000313
And the source term of liquid fuel in the continuity equation +.>
Figure FDA00040737731500000314
Figure FDA0004073773150000041
Figure FDA0004073773150000042
Figure FDA0004073773150000043
And finally, solving a transport equation of gas phase temperature:
Figure FDA0004073773150000044
wherein is
Figure FDA0004073773150000045
The energy exchange rate with the droplet is +.>
Figure FDA0004073773150000046
Heat release rate of combustion, heat capacity c P And viscosity μ, the Lewis number for each component being 1.
10. The high-precision simulation method according to claim 1, wherein in said step 4, temperature and pollutant parameters at the combustion chamber outlet of the aeroengine are output.
CN202310088180.2A 2022-10-25 2023-01-12 High-precision simulation method for aero-engine combustion chamber Pending CN115994453A (en)

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Cited By (1)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN117252128A (en) * 2023-11-17 2023-12-19 中国空气动力研究与发展中心计算空气动力研究所 Swirl nozzle atomization process simulation method, device, equipment and storage medium

Cited By (2)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN117252128A (en) * 2023-11-17 2023-12-19 中国空气动力研究与发展中心计算空气动力研究所 Swirl nozzle atomization process simulation method, device, equipment and storage medium
CN117252128B (en) * 2023-11-17 2024-01-26 中国空气动力研究与发展中心计算空气动力研究所 Swirl nozzle atomization process simulation method, device, equipment and storage medium

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