A method for predicting in-cylinder fuel liquid-phase spray penetration

Abstract

The application provides a cylinder fuel liquid-phase spray penetration distance prediction method, which can make the prediction result closer to the actual situation and more accurately predict the liquid-phase spray penetration distance. By setting the open coefficient and the LPL prediction model, the acceleration of the fuel droplet is calculated according to the Sauter mean diameter and the mass of the fuel droplet, and finally, the expression of LPL with respect to time is calculated according to the LPL prediction model and the acceleration of the fuel droplet. The LPL prediction of this mode considers the interaction between the spray and the wall surface, and therefore has higher prediction accuracy.

Description

Technical Field

[0001] This invention relates to a method for predicting the penetration distance of in-cylinder fuel liquid phase spray, belonging to the field of engine design technology. Background Technology

[0002] Liquid spray penetration distance (LPL) is a crucial parameter for evaluating the combustion dynamics of direct injection engines, closely related to ignition delay time, premixed / diffusion combustion efficiency, and engine performance. The distance from the tip of the liquid spray to the nozzle orifice is typically referred to as LPL. The length of LPL depends on the atomization, evaporation, and air-fuel mixing processes under high temperature and pressure conditions during the liquid jet. During spray development, heat transfer between the surrounding high-temperature gas and fuel droplets causes the droplet temperature to rise. When the fuel evaporation rate equals the injection rate, the tip of the liquid spray stops penetrating, and the penetration length fluctuates slightly in a quasi-steady state. An excessively long LPL during spray development can cause liquid fuel droplets to impact the combustion chamber wall, leading to wet-wall phenomena, severely affecting mixture formation, significantly reducing combustion efficiency during the low-temperature combustion stage, and drastically worsening pollutant emissions. LPL is a key parameter characterizing spray development, therefore, the prediction of fuel liquid spray penetration distance has been a focus of research both domestically and internationally.

[0003] Existing LPL prediction formulas are all based on experimental data from free jets, without considering the influence of the interaction between the fuel spray and the combustion chamber wall. They typically use the liquid phase penetration length obtained from the free jet as the design basis for combustion chamber configuration to avoid fuel impact. However, the finite volume of the combustion chamber makes the interaction between the spray and the wall unavoidable. Under certain conditions, this interaction leads to a significant difference in LPL compared to free jets. The interaction between the spray and the wall reconstructs the spray field; changes in turbulence scale and air entrainment result in atomization and evaporation characteristics that differ from free jet sprays, directly affecting the spray penetration process and mixture formation. The behavior of fuel droplets after impacting the wall, the heat transfer process between fuel droplets and the wall, the reconstruction of the spray structure due to wall obstruction, and the changes in the internal and external flow fields of the spray are macroscopically reflected in the morphology of the gas and liquid phase sprays. This invention, based on spray visualization experiments and stagnation flow theory, constructs a liquid phase penetration distance prediction model considering near-wall effects. This model is more closely aligned with actual engineering applications and can more accurately predict the in-cylinder liquid phase spray penetration process.

[0004] In summary, current methods for predicting the penetration distance of in-cylinder fuel liquid spray do not consider the interaction between the near-wall spray and the wall, and therefore cannot accurately predict the penetration distance of the near-wall liquid spray. There is an urgent need for a new method for predicting the penetration distance of in-cylinder fuel liquid spray. Summary of the Invention

[0005] In view of this, the present invention proposes an in-cylinder fuel liquid spray penetration distance prediction method, which takes into account the interaction between the liquid spray and the wall surface during the calculation process, so that the prediction results are closer to the actual situation and the liquid spray penetration distance is predicted more accurately.

[0006] The technical solution for implementing the present invention is as follows:

[0007] A method for predicting the penetration distance of in-cylinder fuel liquid phase spray includes the following steps:

[0008] The first step is to set a constant coefficient α and define the LPL prediction model LPL1.

[0009] The second step is to calculate the Sauter mean diameter and mass of the fuel droplet, and then calculate the acceleration of the fuel droplet based on the Sauter mean diameter and mass.

[0010] The third step is to calculate the LPL expression with respect to time, specifically:

[0011] Step 3.1: Calculate the penetration velocity of the liquid spray tip based on the LPL prediction model LPL1(t) and the acceleration of the fuel droplets.

[0012]

[0013] Among them, v f It is the penetration velocity of the liquid spray tip, t represents time, and a drop Let τ be the acceleration of the fuel droplets, and τ be the time during which the liquid phase spray deceleration phenomenon occurs.

[0014] Step 3.2, based on the penetration velocity of the liquid spray tip, calculate the expression for LPL with respect to time:

[0015]

[0016] Furthermore, the LPL prediction model LPL1 is defined as follows:

[0017]

[0018] Among them, C v ρ is the flow coefficient, Δp is the pressure difference between the injection pressure and the ambient pressure, and ρ is the flow coefficient. f Where is the fuel density, α is a constant coefficient, and D is the fuel density. n ρ is the nozzle diameter. a For environmental density, t b t represents the initial breakup time of the liquid fuel. r Ta represents the time it takes for the liquid phase spray to reach a stable state, and Ta represents the ambient temperature.

[0019] Furthermore, the initial breakup time of the liquid fuel is calculated as follows:

[0020]

[0021] Among them, t b This refers to the initial breakup time of the liquid fuel.

[0022] Furthermore, the calculation of the Sauter mean diameter and mass of the fuel droplets includes the following:

[0023]

[0024]

[0025] Where SMD is the Sauter mean diameter of the fuel droplet, in meters. droplet This represents the mass of the fuel droplet.

[0026] Furthermore, based on the Sauter mean diameter and mass of the fuel droplet, the acceleration of the fuel droplet is calculated, including the following:

[0027]

[0028] Among them, a drop Let be the acceleration of the fuel droplet. This represents the drag force experienced by the droplet along the spray axis, where SMD is the Sauter mean diameter of the fuel droplet, in meters (m). droplet This represents the mass of the fuel droplet.

[0029] Beneficial effects:

[0030] First, this method introduces the time τ of liquid spray deceleration phenomenon in the calculation of the penetration velocity of the near end of the liquid spray. This is because in actual operation, the development of the LPL of the fuel spray depends on the density and pressure of the environment. In particular, at the spray tip, the fuel droplet velocity is relatively low and the penetration ability is relatively low. When the high-pressure zone caused by the interaction between the spray and the wall obstructs the flow, the fuel droplet velocity drops sharply. Therefore, the time τ of liquid spray deceleration phenomenon is introduced to divide the time into segments. This means that this method considers the interaction with the wall during the processing. This method avoids the problem that most current methods cannot consider the avoidance effect, thus improving the accuracy and realism of the prediction.

[0031] Secondly, in the preferred implementation of this method, when establishing the LPL prediction model LPL1(t), it is divided into three time periods for analysis, which is closer to the actual situation. Moreover, after the time for liquid phase spray to penetrate to a stable state, the parameters are modified compared with the existing commonly used formula, and the power exponent of ambient temperature is modified, so that the prediction results obtained by this method can more realistically and accurately reflect the actual situation of fuel in the cylinder.

[0032] Third, this method is simple to implement. It calculates the acceleration of the fuel droplet based on the Sauter mean diameter and mass of the fuel droplet, and then completes the corresponding calculation based on the acceleration and the prediction model LPL1. It is easy to implement and easy to replicate. Attached Figure Description

[0033] To more clearly illustrate the technical solutions of the embodiments of the present invention, the drawings used in the embodiments will be briefly introduced below. Obviously, the drawings described below are only some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0034] Figure 1 This is a simplified schematic diagram of the stationary flow model according to an embodiment of the present invention.

[0035] Figure 2 This invention provides corrections to the LPL prediction model under different environments in its embodiments.

[0036] Figure 3 The penetration velocity of the liquid spray tip in an embodiment of the present invention.

[0037] Figure 4 The results of wall-impact jet spray LPL test and model calculation are presented in this embodiment of the invention. Detailed Implementation

[0038] The embodiments of the present invention will now be described in detail with reference to the accompanying drawings.

[0039] This invention provides a method for predicting the penetration distance of in-cylinder fuel liquid phase spray. To facilitate the explanation of the underlying technical principles, this embodiment includes the corresponding derivation process, including the following:

[0040] Step 1: During the process of fuel spray impacting the wall, the area near the stagnation point is a typical flat plate stagnation flow. The complex interaction between the spray and the wall is simplified into a three-dimensional axisymmetric flat plate stagnation flow model, as shown in the attached figure. Figure 1The diagram shows a cross-sectional view of a stagnation flow on an axisymmetric flat plate. The X-direction is parallel to the wall, and the Y-direction is the spray axis, perpendicular to the wall, with the direction away from the wall being positive. u and ν represent the velocity components in the X and Y directions, respectively, and can be described as follows:

[0041] u=xf′(y) (1)

[0042] v=-f(y) (2)

[0043] Here, x and y are variables representing the positions in the x and y directions of the coordinate system, and f(y) is a function of y.

[0044] Step 2: Himenz provides the exact solution for stagnation flow:

[0045]

[0046] In the formula, p0 is the pressure at the stagnation point (x=0, y=0); p is the pressure at any point in the flow field; ρ is the density; and a is a constant used to characterize the intensity of the flow at the stagnation point, F(y)=y 2 .

[0047] Step 3: In Newtonian fluid flow (solving equations 1-3 simultaneously and substituting them into equations 4 and 5), the Navier-Stokes equations (NS equations) can determine the two functions f and F. The constant NS equations are:

[0048]

[0049]

[0050] In the formula, μ is the kinematic viscosity of the fluid. Substituting equations (1)-(3) into equations (4) and (5) yields:

[0051] f′ 2 -ff″=a 2 +μf″′ (6)

[0052] ff′=0.5a 2 F′-uf″ (7)

[0053] Step 4: Set the boundary conditions as follows:

[0054] (1) When y = 0, u = 0; v = 0;

[0055] (2) When y = ∞, u = U = ax; U is the velocity of the potential flow. In a plane potential flow, U = ax.

[0056] (3) Stationary location (x=0,y=0), p=p0;

[0057] Combining the above boundary conditions, we can obtain:

[0058]

[0059] Step 5: Obtain f from equation (6) and the corresponding boundary conditions, and set the similarity transformation relationship as follows:

[0060]

[0061] The formula can be simplified to:

[0062] α 2 A 2 =a 2 =uAα 3 (10)

[0063]

[0064]

[0065] Formula (6) is simplified to:

[0066]

[0067]

[0068] Step Six: Himenz and Froessling presented numerical solutions for planar and axisymmetric stagnant flow, respectively. They showed that planar stagnant flow forms a boundary layer near the wall, within which the flow velocity decreases significantly, and kinetic energy is converted into pressure potential energy. Simultaneously, a pressure gradient with gradually decreasing pressure is formed along and away from the wall. Furthermore, they gave the boundary layer thickness for axisymmetric planar stagnant flow as... The pressure gradient is:

[0069]

[0070]

[0071] In the formula, μ is the dynamic viscosity of the fluid.

[0072]

[0073] In the formula, Ta is the ambient temperature, u0 is the gas viscosity at an ambient temperature of 288.15 K, and u0 = 1.7894e -5 B is a constant relating to the properties of a gas, typically B = 110.4 K.

[0074] Steps one through six introduce the stagnation flow model, the purpose of which is to gradually derive the expression for the pressure gradient (15) that stagnation flow causes a significant reduction in the flow velocity within the boundary layer and converts kinetic energy into pressure potential energy, while forming a pressure gradient with gradually decreasing pressure along the wall and away from the wall.

[0075] Based on the above derivation, the predicted value of LPL is calculated through the following steps.

[0076] Step 1: During the fuel spray penetration process, LPL can be divided into three stages. Stage 1 (0 <t≤t b The first stage (t) is the initial breakup stage of liquid fuel; the second stage (t) is the initial breakup stage of liquid fuel. b <t≤t r () is the square root of LPL versus time after the initial breakup of the liquid fuel. Proportional; Third stage (t) r ≤t) represents the point where the liquid spray reaches a quasi-steady state, where the LPL no longer increases significantly but fluctuates slightly. Based on the above conclusions, an LPL prediction model for the liquid spray reaching the steady state is established:

[0077]

[0078]

[0079] In the formula, C v The flow coefficient is Δp = P. inj -P a Injection pressure (P) inj ) and environmental pressure (P) a The pressure difference between () and (D); n ρ is the nozzle diameter; a α is the ambient density; α is a constant coefficient; Ta is the ambient temperature; t b This refers to the initial breakup time of the liquid fuel.

[0080] According to formula (19), the LPL development of fuel spray depends on the density and pressure of the environment, especially at the spray tip, where the fuel droplet velocity is lower and the penetration ability is weaker. When there is obstruction from the high-pressure zone caused by the interaction between the spray and the wall, the fuel droplet velocity drops sharply, thus shortening the LPL.

[0081] The LPL prediction model was modified by comparing the experimental data of this invention, and the results are shown in the appendix. Figure 2 As shown. The prediction model for the stable phase of free-spraying LPL is as follows.

[0082]

[0083] By combining formulas (19) and (20), the LPL prediction model for the free jet spray development process can be obtained:

[0084]

[0085] In the formula, ρ f For fuel density, the constant coefficient α is taken as α = 13.3 according to the recommendation for high-pressure common rail fuel systems.

[0086] According to formula (21), the penetration velocity of the liquid phase spray tip during the development of free jet spray can be obtained:

[0087]

[0088] According to the stagnation flow theory, when LPL approaches the wall-hitting distance:

[0089]

[0090] y=D w -LPL(τ) (24)

[0091] In the formula, τ is the moment when the liquid spray tip begins to be affected by stagnation flow, and D w The distance to the wall is τ. When the ambient temperature is 760K, τ = 2.11ms, and LPL is 23.32mm. This means that the liquid spray begins to decelerate significantly at a distance of 3.88mm from the wall due to the high-pressure zone generated by the stagnant flow.

[0092] The second step is to calculate the Sauter mean diameter and mass of the fuel droplet, and then calculate the acceleration of the fuel droplet based on the Sauter mean diameter and mass.

[0093] Under the influence of the pressure gradient near the stagnation point, the velocity of fuel droplets in the spray decreases rapidly, exhibiting an additional deceleration compared to free-jet spray. To quantify the deceleration process of fuel droplets in the spray, we assume that all fuel droplets are spherical with a Sauter Mean Diameter (SMD). Lefebvre and Elkotb proposed that the SMD of liquid fuel droplets in diesel engines is related to fuel properties such as viscosity, density, and surface tension. In high-temperature environments, changes in ambient temperature also have a significant impact on the SMD of fuel droplets in the spray, as described below:

[0094]

[0095]

[0096]

[0097] The third step is to calculate the LPL expression with respect to time, specifically:

[0098] Step 3.1: Calculate the penetration velocity of the liquid spray tip based on the LPL prediction model LPL1(t) and the acceleration of the fuel droplets.

[0099]

[0100] Among them, v f It is the penetration velocity of the liquid spray tip, t represents time, and a drop Let τ be the acceleration of the fuel droplets, and τ be the time during which the liquid phase spray deceleration phenomenon occurs.

[0101] Step 3.2, based on the penetration velocity of the liquid spray tip, calculate the expression for LPL with respect to time:

[0102]

[0103] The LPL expression for time, derived from the above formula, can be used to calculate the LPL at each time point.

[0104] The above description is merely a specific embodiment of the present invention, but the scope of protection of the present invention is not limited thereto. Any variations or substitutions that can be easily conceived by those skilled in the art within the technical scope disclosed in the present invention should be included within the scope of protection of the present invention. Therefore, the scope of protection of the present invention should be determined by the scope of the claims.

Claims

1. A method for predicting the penetration distance of in-cylinder fuel liquid phase spray, characterized in that, Includes the following steps: The first step is to set constant coefficients. and Set the LPL prediction model to LPL1; The second step is to calculate the Sauter mean diameter and mass of the fuel droplet, and then calculate the acceleration of the fuel droplet based on the Sauter mean diameter and mass. The third step is to calculate the LPL expression with respect to time, specifically: Step 3.1: Calculate the penetration velocity of the liquid spray tip based on the LPL prediction model LPL1 and the acceleration of the fuel droplets. in, It is the penetration velocity of the liquid spray tip. t Indicates time, Let be the acceleration of the fuel droplet. The time when the liquid spray deceleration phenomenon occurs; Step 3.2, based on the penetration velocity of the liquid spray tip, calculate the expression for LPL with respect to time: The expression for the LPL prediction model LPL1 is as follows: in, For flow coefficient, The pressure difference between the fuel injection pressure and the ambient pressure. For fuel density, and These are constant coefficients. The nozzle diameter is... For environmental density, The initial breakup time of the liquid fuel oil. The time from liquid phase spray penetration to a stable state, where Ta is the ambient temperature; The calculation of the Sauter mean diameter and mass of fuel droplets includes the following: Wherein, SMD is the Sauter mean diameter of the fuel droplet. Mass of fuel droplets; Calculate the acceleration of the fuel droplet based on its Sauter mean diameter and mass, including the following: in, Let be the acceleration of the fuel droplet. This represents the drag experienced by the droplet along the spray axis, and SMD is the Sauter mean diameter of the fuel droplet. This represents the mass of the fuel droplet.

2. The method as described in claim 1, characterized in that, The initial breakup time of the liquid fuel oil is calculated as follows: in, This refers to the initial breakup time of the liquid fuel.

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