In order to get the pipeline simulation model, it is necessary to discretize the pipeline. Divide the pipe into several pipe segments. For each pipe segment with a shorter length, ignore the distribution effect of flow and pressure along the pipe, and only consider the frequency-related characteristics of the pipe. The approximate processing of the differentials in each pipe reflects the spatial distribution effect of the pipe model. In this way, the distribution parameter effect and the frequency-related effect of the pipeline are organically combined to obtain a frequency-dependent friction model of the pipeline distribution parameter that is easy to simulate.
Consider three adjacent pipe segments k-1, k, k+1, and the differential is used to approximate the pipeline discretization model dQ/dx=(Qk-Qk-1)/$x, dp/dx=(pk+1-pk ) /$x therefore has: pk=c$xZc(Qk-1-Qk)s(3)ZcQk=cN(s)$xpk-pk+1s(4) according to (3), (4) Show block diagram model, where: N(s)=11-2J1(jrs/M)jrs/MJ0(jrs/M) where: J0 and J1 are zero-order and first-order Bessel functions respectively; r is the tube radius.
The simulation block diagram model N(s) can be roughly approximated as: N(s)=1+A/s(5) where A is the viscosity factor and A=8M/r2 (M is the fluid kinematic viscosity). For N(s), Trikha derives an expression <6>: N(s)=1+As+0.15151+0.3030s/A+0.16201+0.04s/A+0.0201+0.001s/A(6) The degree of approximation is good in the frequency range of s = X < 300A.
N(s) can be calculated by formulas (5) and (6), and the double logarithmic amplitude-frequency curve and logarithmic phase-frequency curve can be drawn. The solid and dashed lines are (6) and (5) respectively. Corresponding curve. It can be seen from the figure that the two modes have a common asymptote in the high frequency band and the low frequency band respectively, and the asymptote in the high frequency band is limA/s→0N(s)=lims/A→∞N(s)= 1, corresponding to the ideal fluid model with negligible flow resistance at high frequencies; the asymptote of the low frequency band is limA/s→∞N(s)=lims/A→0N(s)=A/s, corresponding to low frequency The liquid sensation can be ignored by considering only the average friction model of viscous flow resistance.
(a) Double logarithmic amplitude frequency characteristic (b) Logarithmic phase frequency characteristic N(s) logarithmic phase curve According to equation (6), the middle dashed line portion can be expanded to the illustrated refinement model. The removal of the dashed box portion is a refinement model corresponding to the equation (5). The most important feature of the model shown is that it is easy to couple the pipe segments. Combined with the boundary conditions, the pipe system can be combined into a multi-link simulation block diagram model.
The boundary condition of the channel boundary is disturbed. The terminal is the load inlet pressure disturbance p1(s)=R(s), and the terminal is the impedance Z(s)=pn(s)/Qn(s), G(s)=1/ Z(s) is the terminal admittance, and the coupling model is as shown. For the case where the terminal is closed, Z(s)=∞, then Qn(s)=0, and only the middle dashed box is removed. The termination impedance can be a nonlinear expression in the time domain. For the case where the terminal G(s) is a differential link (such as the terminal is a concentrated cavity) or with a differential factor, due to the existence of the differential factor, the existing simulation software such as the Simulink tool in Matlab is difficult to process, and the simulation cannot be performed. The differential factor can be removed by equivalent transformation using the integral factor of cs$x in the forward channel, that is, the midpoint line portion is changed into a form, and F(s) does not contain a differential factor.
The ingress traffic is disturbed. The terminal is the load ingress traffic disturbance Q1(s)=R(s), and the terminal is the impedance Z(s)=pn(s)/Qn(s). The coupling model is shown in (a). For the case where the terminal is open, pn(s)=0, and it needs to be processed in the way of (b); the case where the terminal G(s) is differentiated can be imitated.
The inlet pressure is constant, the outlet flow disturbance inlet pressure is constant, the outlet flow disturbance coupling model inlet pressure is constant p1(s)=0, and the outlet flow disturbance Qn(s)=R(s) is also one of the common operating conditions, such as the downstream valve. Sudden opening or closing of the mouth often causes vibration of the pipeline. The coupling model is as shown.
In addition, for the pipe network system, the boundary conditions of the pipeline and the concentrating components, the pipe bifurcation and the pipe convergence must also be considered. Due to the space, the author will study it separately. According to the above boundary conditions, a complete simulation model of the pipeline system can be established, and the simulation can be performed by using relevant software tools.
In the simulation results of 2N(s), the simulation results are compared with the literature and the calculation results. The waveforms are similar, and the peaks of the impact peaks and the peaks coincide with each other, which can fully meet the engineering needs, thus proving the correctness of the model. The more the number of pipe segments, the higher the accuracy. When n=16, both the peak value of the vibration and the attenuation process are very close to the literature.
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