JPH0462446A - Pressure pulsation analyzing device - Google Patents

Abstract

PURPOSE:To improve the accuracy by finding pressure pulsation from an excitation flow rate Qn based upon the impedance Zn of piping. CONSTITUTION:The (n)th-order complex amplitude Xn of the volume of fluid which flows in and out of a cylinder is found from the pressure pulsation P in the piping in a frequency range based upon the impedance Zn of the piping and the pressure variation Pc in the cylinder in the frequency range of a pressure source. Then the excitation flow rate Qn of the fluid in the piping is found by using Xn in consideration of the successive generation of the fluid. Then Qn is used to find the pressure pulsation P in the piping in consideration of the successive generation of fluid in the frequency range.

Description

[Detailed Description of the Invention] [Industrial Application Field] The present invention relates to a pressure pulsation analysis device that analyzes pressure pulsations in piping based on pressure fluctuations caused by pressure sources such as reciprocating compressors and pumps. .

[Prior art]

Fluid intermittently sucked in and discharged from a pressurizing source such as a reciprocating compressor or a pump as described above becomes a source of pulsation, causing the fluid in the piping to vibrate. If this vibration of the fluid resonates with the excitation cycle of the pressure source and becomes large, it may cause piping to vibrate and be damaged, or the performance of the pressure source such as a compressor pump may deteriorate. Therefore, in consideration of the interaction between the fluid in the cylinder of the pressure source such as a compressor or pump and the fluid in the piping, the dimensions of the piping must be determined so that the excitation by the pressure source and pressure fluctuations in the piping do not resonate. In order to determine the design, it is necessary to analyze the pressure pulsations within the piping taking into account the fluid interaction described above.

The pressure pulsation analysis method that does not take fluid interaction into account as described above is
Already (Pressure pulsation analysis of reciprocating compressor piping system Kobe Steel Technical Report V
It has a long history and track record, and is well known in literature such as o1.37 No. 1).

[Problem to be solved by the invention]

However, in the conventional pressure pulsation analysis method as described above, fluid interaction is not taken into consideration, and the accuracy of the three-pulsation analysis is not sufficient.

In addition, pressure pulsation analysis methods are broadly divided into those performed in the frequency domain and those performed using one time history, as disclosed in the above literature, but the methods performed using the above time history are more difficult than calculation methods in the frequency domain. It took a huge amount of calculation time, and there were problems in terms of calculation costs.

Accordingly, one object of the present invention is to provide a pressure pulsation analysis device that can efficiently perform highly accurate pressure pulsation analysis in the frequency domain, taking fluid interaction into consideration.

[Means for Solving the Problems] In order to couple the above objects, the first invention provides pressure pulsation ΔP in the pipe at a frequency of 5Ulx based on the impedance Z7 of the pipe and a cylinder in the frequency domain of the Caro pressure source. means for determining the n blowing component complex amplitude χ7 of the volume of fluid flowing in and out of the cylinder from the pressure fluctuation ΔPc in the cylinder;
A means for determining the excitation flow rate Q of the fluid in the pipe considering the fluid coupling using n, and a means for calculating the pressure pulsation ΔP in the pipe considering the fluid coupling in the frequency domain using the above Qn. The pressure pulsation analysis device is configured as a pressure pulsation analysis device comprising a means for determining the pressure pulsation.

Further, the second invention provides that the impedance Z of the assumed piping
Based on the pressure pulsation ΔP in the pipe in the frequency domain based on n and the pressure fluctuation ΔPc in the cylinder in the frequency range of the pressurization source, the n fire component complex amplitude of the volume of fluid flowing in and out of the cylinder is calculated. A means for determining X, a means for determining the excitation flow rate Q of the fluid in the piping considering the fluid coupling using the above X, and a means for determining the excitation flow rate Q of the fluid in the pipe considering the fluid coupling using the above Q. The means for determining the pressure pulsation ΔP in the piping and the corrected impedance Z1' of the piping are determined from the corrected pressure pulsation ΔP, and the impedance Z1' is compared with the impedance z6 before modification, and the difference is determined to be within a predetermined range. The pressure pulsation analysis apparatus is configured as a pressure pulsation analysis apparatus comprising means for repeating the execution of each of the above-mentioned means until the pressure pulsation ΔP in the pipe is within a predetermined range.

(Example) Next, an example embodying the present invention will be described with reference to a flowchart showing a calculation procedure shown in FIG.

Note that a detailed explanation of the pressure pulsation analysis method in the frequency domain that does not take fluid coupling into account is well known from the above-mentioned literature and others, and will not be described here.

The pressure pulsation analysis method in the examples described below is summarized as follows. That is, the interaction of the fluid is the specific gravity of the fluid,
It is related to the viscosity 1 volume, etc., and this is the impedance Z of the piping
, is coupled by considering . Impedance Z of such piping.

is known, the volume of fluid flowing in and out of the cylinder can be calculated from the pressure pulsation P in the piping in the frequency domain based on Z7 and the pressure fluctuation ΔPc in the cylinder in the frequency domain of the pressurization source. First, the n-blown component complex amplitudes Xn are determined.

Next, the excitation flow rate Qn of the fluid in the pipe is determined using the above Xn. Since this excitation flow rate Qn is based on the impedance Z of the piping, fluid coupling is naturally taken into account.

Next, using the excitation flow rate Q1, the pressure pulse ΔP in the pipe is determined in consideration of the fluid coupling in the frequency domain.

In this way, in a relatively simple system such as a single pressurization source, the impedance Z of the piping.

It is a relatively simple calculation method because it can be estimated with high accuracy.

However, in cases such as 2. where there are multiple pressurizing sources or 1. where the impedance Z1 is a function of the excitation flow rate Q1, the impedance Z is not known, so this is first given as an assumed value. It is necessary to repeat the correction. That is, in this case, pressure pulsation ΔP in the piping in the frequency domain based on the appropriately assumed impedance Zn of the piping, and pressure fluctuation ΔP in the cylinder in the frequency domain of the pressurizing source, n component complex amplitudes of the volume of fluid flowing in and out. seek. Next, using the above Xn, the excitation flow rate Qn of the fluid in the piping is determined, taking into account the fluid coupling as described above.

Next, the above excitation flow rate Q. The pressure pulsation ΔP in the piping is corrected by considering the fluid coupling in the frequency domain using
seek. Furthermore, the corrected piping impedance z, / is determined from the above corrected pressure pulsation ΔP, and this Zn'
and the impedance Z1 before correction, and repeat the above calculation procedure until the difference is within a predetermined range.
The pressure pulsation ΔP in the pipe at the time when the impedance difference falls within a predetermined range is adopted as the corrected pressure pulsation.

The above procedure will be explained in detail as follows.

First, in step S1 in FIG. 1, constants necessary for calculation are input. Factors required for calculation are (1) Factors related to fluid properties, such as sound velocity, density, average pressure, viscosity coefficient, bulk modulus, index of state change, etc. (2) Factors related to piping characteristics, such as pipe length, pipe diameter, etc. (3) Compressor After inputting the factors related to the characteristics of the constant pressure source, such as the movement of the piston, the diameter of the piston, and the constant number of revolutions, calculate the complex amplitude Xn of the nth order of the volume of the fluid flowing in and out of the cylinder of the pressure source (S2).
The above complex amplitude Xn is calculated based on the following calculation method.

Pressure fluctuation ΔP in the cylinder of a pressurizing source such as a compressor or pump
e is.

-y ΔP, = γP, ... (1) ■ It is expressed as

Here, T... An index representing a change in the state of the fluid P0...
Average pressure of fluid in the piping V: Volume inside the cylinder chamber X: Volume y of fluid flowing in and out of the cylinder chamber: Volume displacement of the piston.

On the other hand, the formula for the Fourier expansion of P to pressure pulsations in the pipe is ΔP=ΣJ n ωZn
−(2).

Here, 1 j...Imaginary number n...Order of Fourier expansion ω...Rotational speed of pressurizing source such as compressor zll...Piping impedance Xn...N of the volume of fluid flowing into the cylinder Blowing component complex amplitude t... is time.

Here, when the piping and the pressurization source are in communication as described above, 8P, = ΔP, and when X is expressed in Fourier expansion, X = Σ The following equation (3) is obtained.

■ y −Σ (I J n ω
Z*) χfi e -1γP0...(3) Above (+1. The piping impedance Z used in each equation (2) and (3) is not a simple system or Zn is not a function of Q. In such cases, it can be treated as known, but in cases where there are multiple pressure sources, Z,
is a function of Ql, it cannot be determined at once.

Therefore, in this embodiment, the impedance Z used in equations (2) 2 and (3) above is a value appropriately assumed at the beginning. Note that the other values y, v, and ω are determined according to the specifications of the pressurizing machine, and γ and Pa are uniquely determined once the piping fluid and operating conditions are determined.

When the above equation (3) is obtained, the complex amplitude X of the n blowing components of the volume of the fluid flowing in and out of the cylinder.

is found. This procedure is the step S2.

Next, the excitation flow rate Qn of the fluid in the pipe is a differential value of the above-mentioned X.

X = ΣjnωX1leJIl#t, and Qn = J n (11X n ... (4
), the excitation flow rate Qn is determined (S3).

The amount of excitation 2ii obtained in this way Qn is based on fluid interaction. A pressure pulsation value ΔP within is calculated (S4).

Here, if the assumed Z7 is an appropriate value, the corrected impedance Z is obtained by substituting the pressure pulsation value ΔP etc. obtained in the above S4 into equation (2).

(S5) and the impedance Z7 before being modified should be equal to or close to each other.

Therefore, in cases where the piping system is simple or where Zn is not a function of Qn, the pressure pulsation value ΔP obtained in S4 above may be output as the first result.

However, if the above Zn is not known, the initially assumed Zo is not an appropriate value, so the impedance Zn' obtained in step S5 above and the Z before correction are
n and S6), and if the difference between the two is larger than a predetermined range, the corrected Z. The steps 32 to S6 are repeated with ' being the newly assumed piping impedance. The impedance Z of the piping thus assumed. is gradually modified, and when it becomes suitable for the system, the two before and after modification
1 matches. The pressure pulsation value ΔP at this time is output as the final result.

As a result of this calculation, if the pressure pulsation value ΔP is larger than a predetermined standard, for example, the piping layout (inner diameter of the piping, piping length, etc.) may be changed or a damping function (accumulator, orifice, etc.) may be added. By doing so, pulsation is attenuated.

[Effects of the Invention] Since the present invention is configured as described above, it is possible to perform efficient and highly accurate analysis in consideration of coupling in two frequency regions.

[Brief explanation of drawings]

FIG. 1 is a flowchart showing the processing procedure of a pressure pulsation analysis device according to an embodiment of the present invention. (Explanation of symbols) Z, l... Piping impedance ΔP... Pressure pulsation in the pipe ΔPc... Pressure fluctuation in the cylinder Xn... N fire component complex amplitude Q of the volume of fluid sucked into the cylinderゎ・・・Excitation flow rate of fluid in piping

Claims (2)

[Claims] (1) Based on the pressure pulsation ΔP in the piping in the frequency domain based on the impedance Z_n of the piping and the pressure fluctuation ΔP_c in the cylinder in the frequency domain of the pressurization source, the volume n of the fluid flowing in and out of the cylinder is means for determining the next component complex amplitude Xn; means for determining the excitation flow rate Q_n of the fluid in the piping in consideration of fluid coupling using the X_n; and the Q_n
1. A pressure pulsation analysis device comprising: means for determining pressure pulsation ΔP in a pipe in consideration of fluid coupling in the frequency domain using . (2) Based on the pressure pulsation ΔP in the piping in the frequency domain based on the assumed impedance Z_n of the piping and the pressure fluctuation ΔP_c in the cylinder in the frequency domain of the pressurization source, the flow of fluid flowing in and out of the cylinder is determined by means for determining the n-dimensional component complex amplitude X_n of the volume; means for determining the excitation flow rate Q_n of the fluid in the piping in consideration of fluid coupling using the X_n; and means for determining the fluid coupling in the frequency domain using the Q_n A means for determining the pressure pulsation ΔP in the piping considering A pressure pulsation analysis device comprising: repeating the execution of each of the above means until the pressure falls within a predetermined range, and determining the corrected pressure pulsation ΔP in the piping at the time when the pressure falls within the predetermined range.