METHOD FOR CALCULATING ONE-DIMENSIONAL SPATIAL FLUCTUATION IN UNBRANCHED HIGH-PRESSURE FUEL PIPE OF COMMON RAIL SYSTEM

Abstract

An objective of the disclosure is to provide a method for calculating a one-dimensional (1D) spatial fluctuation in an unbranched high-pressure fuel pipe of a common rail system. The method includes the following steps: dividing a flow in the unbranched high-pressure fuel pipe according to a spatial length into sections for solving, to obtain forward and reverse pressure fluctuation forms; iteratively calculating forward and reverse pressure fluctuations propagating in a fuel pipe model to obtain fluctuations of various sections of the fuel pipe from an inlet to an outlet within one step, and calculating a flow velocity at a corresponding position in the pipe; and extracting a corresponding flow rate of the system, and substituting into an iterative calculation of the overall system to obtain an output pressure.

Claims

1. A method for calculating a one-dimensional (1D) spatial fluctuation in an unbranched high-pressure fuel pipe of a common rail system, comprising the following steps: (1) establishing a system model, comprising setting initial parameters, such as a control step N.sub.t of the system, a total time N.sub.T (0<N.sub.t≤N.sub.T) of a calculation process, and structure parameters and pressures of the high-pressure fuel pipe; (2) dividing a flow in the unbranched high-pressure fuel pipe according to a spatial length into sections for solving, to obtain forward and reverse pressure fluctuation forms, namely forward pressure fluctuation F.sub.L and reverse pressure fluctuation R.sub.L: $F_x=F_{x=0}\left(N_t-\frac{\Delta .Math.L}{\alpha }\right).Math.e^{-\frac{K.Math.\Delta .Math.L}{\alpha }},R_x=R_{x=L}\left[N_t-\frac{\left(L-\Delta .Math.L\right)}{\alpha }\right].Math.e^{-\frac{K\left(L-\Delta .Math..Math.L\right)}{a}},$ wherein, α is a speed of sound; calculating real-time forward and reverse pressure fluctuations of each section in one control step N.sub.t according to current data; and (3) saving the current forward and reverse pressure fluctuations forms F and R into two arrays, calculating forward and reverse pressure fluctuations Fnd and Rnd propagating to a next step, and performing an iterative calculation on a fuel pipe model in N.sub.T/N.sub.t steps, to obtain a series of status values.

2. The method for calculating a 1D spatial fluctuation in an unbranched high-pressure fuel pipe of a common rail system according to claim 1, wherein in step (1), the initial parameters that need to be set comprise: a control step N.sub.t of the system, a total time N.sub.T (0<N.sub.t≤N.sub.T) of a calculation process, a length L and diameter d.sub.hp of the high-pressure fuel pipe, fuel pressures P.sub.enter and P.sub.exit at an inlet and an outlet of the high-pressure fuel pipe and an initial pressure P.sub.0 in the pipe; initial forward and reverse pressure fluctuations in the pipe are set as follows: $F=\left[\begin{array}{c}0\\ \mathrm{.Math.}\\ 0\end{array}\right];R=\left[\begin{array}{c}0\\ \mathrm{.Math.}\\ 0\end{array}\right].$

3. The method for calculating a 1D spatial fluctuation in an unbranched high-pressure fuel pipe of a common rail system according to claim 1, wherein in step (2), according to a spatial length, a flow in the unbranched high-pressure fuel pipe is divided into sections for solving, to obtain forms of forward and reverse fluctuations caused by hydraulic shocks; a current pressure wave propagation distance is set as 0, and pressure fluctuation parameters in one control step N.sub.t are calculated as follows: a forward pressure fluctuation in the length of L from a length of ΔL: $F=\left[\begin{array}{c}F\left(0\right)\\ F(\Delta .Math.L)\\ F(\Delta .Math.L+\Delta .Math.L)\\ \mathrm{.Math.}\\ F\left(L\right)\end{array}\right];$ a reverse pressure fluctuation from the current length of ΔL: $R=\left[\begin{array}{c}R\left(L\right)\\ R(L-\Delta .Math.L)\\ \mathrm{.Math.}\\ R(\Delta .Math.L)\\ R\left(0\right)\end{array}\right];$ forward and reverse pressure fluctuations in N.sub.T/N.sub.t steps from N.sub.t:
Fnd(L*+ΔL)=F(L*).Math.e.sup.−KN′, and Rnd(L*+ΔL)=R(L*).Math.e.sup.−KN′; where, 0<L*<L−ΔL, K is a dissipation factor; when L*=0, the forward and reverse pressure fluctuations at a boundary are expressed as follows:
Fnd(ΔL)=P.sub.enter−P.sub.0+Rnd(ΔL); when L*=L−ΔL, the forward and reverse pressure fluctuations at the boundary are expressed as follows:
Rnd(L)=P.sub.0−P.sub.exit+Fnd(L);

4. The method for calculating a 1D spatial fluctuation in an unbranched high-pressure fuel pipe of a common rail system according to claim 1, wherein in step (3), a flow velocity v(L*) at any spatial position in the high-pressure fuel pipe is used to extract a corresponding flow rate, and the flow rate is substituted into an iterative calculation of the system, to output the system's pressure at any time.

Description

BRIEF DESCRIPTION OF THE DRAWINGS

[0021] FIG. 1 is a flowchart of the disclosure.

[0022] FIG. 2 is a schematic diagram of division of a spatial length of a high-pressure fuel pipe.

[0023] FIG. 3 shows a comparison of simulation and experimental results of an injection pressure of a fuel system.

DETAILED DESCRIPTION

[0024] The disclosure is described in detail below with reference to the accompanying drawings and examples.

[0025] As shown in FIGS. 1 to 3, the disclosure provides a method for calculating a one-dimensional (1D) spatial fluctuation in an unbranched high-pressure fuel pipe of a common rail system. According to the overall flowchart as shown in FIG. 1, the method specifically includes the following steps:

[0026] Step 1: establish a system model, including setting initial status parameters, such as a control step N.sub.t of the system, a total time N.sub.T (0<N.sub.t≤N.sub.T) of a calculation process, and structure parameters and pressures of the high-pressure fuel pipe.

[0027] The initial parameters that need to be set include:

[0028] a control step N.sub.t of the system, a total time N.sub.T (0<N.sub.t≤N.sub.T) of a calculation process, a length L and diameter d.sub.hp of the high-pressure fuel pipe, fuel pressures P.sub.enter enter and P.sub.exit at an inlet and an outlet of the high-pressure fuel pipe and an initial pressure P.sub.0 in the pipe; initial forward and reverse pressure fluctuations in the pipe are set as follows:

[00005]$\begin{array}{cc}F=\left[\begin{array}{c}0\\ \mathrm{.Math.}\\ 0\end{array}\right]& \left(1\right)\\ R=\left[\begin{array}{c}0\\ \mathrm{.Math.}\\ 0\end{array}\right].& \left(2\right)\end{array}$

[0029] Step 2: divide a flow in the unbranched high-pressure fuel pipe according to a spatial length into sections (as shown in FIG. 2) for solving, to obtain forms of forward and reverse fluctuations caused by hydraulic shocks, namely forward pressure fluctuation F.sub.L and reverse pressure fluctuation R.sub.L:

[00006]$\begin{array}{cc}{F}_x=F_{x=0}\left(N_t-\frac{\Delta .Math.L}{\alpha }\right).Math.e^{-\frac{K.Math.\Delta .Math.L}{\alpha }}& \left(3\right)\\ R_x=R_{x=L}\left[N_t-\frac{\left(L-\Delta .Math.L\right)}{\alpha }\right].Math.e^{-\frac{K\left(L-\Delta .Math..Math.L\right)}{\alpha }}& \left(4\right)\end{array}$

[0030] where, α is a speed of sound; K is a dissipation factor, which is calculated by a resistance coefficient of the high-pressure fuel pipe:

[0031] first calculate the dissipation factor K, and then calculate real-time forward and reverse pressure fluctuations of each section in one control step N.sub.t according to the current relevant data;

[0032] assume that the flow in the pipe is a turbulent flow, and calculate a Reynolds number based on a current average flow velocity in the pipe according to the following formula:

[00007]$\begin{array}{cc}\mathrm{Re}=\frac{\stackrel{\_}{V}.Math.d_{h.Math.p}}{\nu }& \left(5\right)\end{array}$

[0033] where, V is the average flow velocity in the pipe, and v is a kinematic viscosity;

[0034] calculate the resistance coefficient λ of the fuel pipe according to a semi-empirical formula of the target fuel pipe, after obtaining the current Reynolds number;

[0035] dissipation factor:

[00008]$\begin{array}{cc}K=\lambda .Math.\frac{\stackrel{\_}{V}}{2.Math.d_{\mathrm{hp}}}& \left(6\right)\end{array}$

[0036] assume that a current pressure wave propagation distance is 0, and calculate pressure fluctuation parameters in one control step N.sub.t as follows:

[0037] a forward pressure fluctuation in the length of L from a length of ΔL:

[00009]$\begin{array}{cc}F=\left[\begin{array}{c}F\left(0\right)\\ F(\Delta .Math.L)\\ F(\Delta .Math.L+\Delta .Math.L)\\ \mathrm{.Math.}\\ F\left(L\right)\end{array}\right]& \left(7\right)\end{array}$

[0038] a reverse pressure fluctuation from the current length of ΔL:

[00010]$\begin{array}{cc}R=\left[\begin{array}{c}R\left(L\right)\\ R(L-\Delta .Math.L)\\ \mathrm{.Math.}\\ R(\Delta .Math.L)\\ R\left(0\right)\end{array}\right]& \left(8\right)\end{array}$

[0039] forward and reverse pressure fluctuations in N.sub.T/N.sub.t steps from N.sub.t:

Fnd(L*+ΔL)=F(L*).Math.e.sup.−KN′  (9)

Rnd(L*+ΔL)=R(L*).Math.e.sup.−KN′  (10)

[0040] where, 0<L*<L−ΔL, K is a dissipation factor;

[0041] when L*=0, the forward and reverse pressure fluctuations at a boundary are expressed as follows:

Fnd(ΔL)=P.sub.enter−P.sub.0+Rnd(ΔL)  (11)

[0042] when L*=L−ΔL, the forward and reverse pressure fluctuations at the boundary are expressed as follows:

Rnd(L)=P.sub.0−P.sub.exit+Fnd(L)  (12)

[0043] a flow velocity at any spatial position in the high-pressure fuel pipe is:

v(L*)=└F(L*)+R(L*)┘/(αρ)  (13).

[0044] Step (3): save the current forward and reverse pressure fluctuations F and R into two arrays, calculate forward and reverse pressure fluctuations Fnd and Rnd propagating to a next step, use the flow velocity v(L*) at any spatial position in the high-pressure fuel pipe obtained in step (2) to extract a corresponding flow rate, and substitute the flow rate into an iterative calculation of the system, to output the system's pressure at any time.

[0045] Assuming j is a number of iterations, then the pressure output is:

P.sub.f(j+1)=P.sub.f(j)+ΔP.sub.f  (14)

[0046] where,

[00011]$\Delta .Math..Math.P_f=\frac{E}{V}.Math.\left(Q_{I.Math.N}-Q_{\mathrm{OUT}}\right),$

Q.sub.IN=S.Math.v(L) is an outlet flow rate of the high-pressure fuel pipe.

[0047] FIG. 3 shows a comparison of simulation and experimental results of the injection pressure of the fuel system, which indicates that the pressure fluctuations have good consistency.