JP2021081988A - Pressure propagation analyzer and pressure propagation analysis method for in-duct compressible fluid - Google Patents

Abstract

PROBLEM TO BE SOLVED: To easily verify whether the analysis of pressure and flow rate in a duct is performed correctly, and to easily confirm the validity of the analysis result. SOLUTION: The pressure wave generated by the change of the boundary condition at the end of the duct filled with the compressible fluid is propagated in the duct, and the change in the pressure and the flow rate of the compressible fluid in the duct is calculated. The pressure propagation analyzer 10 for the compressible fluid in the duct to be analyzed by the above means the duct specification recording spreadsheet 11 for recording the duct specification information of each part of the duct, and the pressure propagation parameter information (sound velocity value, flow rate) in each part of the duct. Pressure propagation parameters using the pressure propagation parameter recording spreadsheet 13 (sound velocity value spreadsheet 16, flow rate value spreadsheet 17) for recording the time history of the value), the value of the duct specification information, and the current time value of the pressure propagation parameter information. It is configured to include a calculation means 14 for calculating the next time value of information and a display means 15 capable of displaying a calculation formula of the calculation means for different times. [Selection diagram] Fig. 1

Description

An embodiment of the present invention relates to a pressure propagation analyzer for a compressible fluid in a duct for analyzing a phenomenon in which a pressure wave propagates in a duct filled with a compressible fluid, and a pressure propagation analysis method for the compressible fluid in the duct.

When a fluid flows in or out from one end of a duct system filled with a compressible fluid (gas) typified by air, or when pressure fluctuation is applied to one end, a pressure wave propagates from one end to the other. Propagation of pressure waves in a duct is usually solved by a one-dimensional propagation equation in the duct axis direction. For example, if the flow velocity is 0.3 or less in Mach number, only the speed of sound as in water hammer analysis. It can be approximated by the treatment of incompressible fluid in consideration of.

However, when the flow velocity is 0.3 or more in terms of Mach number, the speed of sound differs greatly between the positive pressure part and the negative pressure part of the generated pressure wave, and the pressure waveform is distorted during propagation and deformed into a sawtooth shape. Sometimes. In such cases, it is necessary to handle compressible fluids with varying densities. In the case of three-dimensional propagation, it is necessary to solve a complicated nonlinear partial differential equation by a numerical solution method, but in one-dimensional propagation, a method of ordinary differentiation of the partial differential equation by the characteristic curve method and solving it simply has been proposed. There is.

On the other hand, in the propagation of the duct system, it is necessary to handle cases such as when ducts branch and gather, or when ducts of different diameters are connected. Dedicated analysis software for performing such analysis is also commercially available, but in many cases, the specific method of analysis is not disclosed to the user. From the viewpoint of quality assurance of analysis, so-called V & V, which verifies whether the analysis was performed correctly by disclosing the specific analysis procedure (verification) and confirms the validity of the analysis result (validation), You will need it.

Japanese Unexamined Patent Publication No. 2007-41819 Japanese Unexamined Patent Publication No. 2001-91400

However, in the above-mentioned conventional technique, V & V is not easy only by the user who created the model data when the specific analysis procedure, for example, the programmed code, etc. is not disclosed. Further, even if the programmed code is disclosed, it is necessary to be familiar with the programming language used, and there is a problem that the labor required for V & V is not small.

The embodiment of the present invention has been made in consideration of the above circumstances, and it is possible to easily verify whether or not the changes in pressure and flow rate in the duct filled with the compressible fluid have been correctly analyzed, and at the same time, it can be verified. It is an object of the present invention to provide a pressure propagation analyzer and a pressure propagation analysis method for a compressible fluid in a duct, which can easily confirm the validity of the analysis result.

The pressure propagation analyzer for the compressible fluid in the duct according to the embodiment of the present invention propagates the pressure wave generated by the change of the boundary condition at the end of the duct filled with the compressible fluid in the duct. A duct specification information record that records duct specification information of each part of the duct, which is a pressure propagation analyzer for the compressible fluid in the duct that analyzes by calculating changes in the pressure and flow rate of the compressible fluid in the duct. The pressure propagation is performed by using the means, the pressure propagation parameter information recording means for recording the time history of the pressure propagation parameter information in each part of the duct, the value of the duct specification information, and the current time value of the pressure propagation parameter information. It is characterized by having a calculation means for calculating the next time value of parameter information by a calculation formula, and a display means capable of displaying the calculation formula of the calculation means for different times.

In the method for analyzing pressure propagation of a compressible fluid in a duct according to an embodiment of the present invention, the pressure wave generated due to a change in boundary conditions at the end of a duct filled with the compressible fluid propagates in the duct. A method for analyzing pressure propagation of a compressible fluid in a duct by calculating changes in the pressure and flow rate of the compressible fluid in the duct, and recording duct specification information for recording duct specification information of each part of the duct. A means and a pressure propagation parameter information recording means for recording the time history of the pressure propagation parameter information in each part of the duct are prepared, and the value of the duct specification information and the pressure propagation parameter are prepared in the pressure propagation parameter information recording means. It is characterized in that the next time value of the pressure propagation parameter information is calculated by a calculation formula using the current time value of the information, and this calculation formula is displayed.

According to the embodiment of the present invention, it is possible to easily verify whether the analysis of the change in pressure and flow rate in the duct filled with the compressible fluid is performed correctly, and it is possible to easily confirm the validity of the analysis result.

The block diagram which shows the structure of the pressure propagation analysis apparatus of the compressible fluid in a duct which concerns on 1st Embodiment. FIG. 3 is a model diagram showing a duct to be analyzed by the pressure propagation analyzer of FIG. The chart which shows the structure of the duct specification recording spreadsheet of FIG. The chart which shows the structure of the sound velocity value spread sheet of FIG. The chart which shows the structure of the flow rate value spreadsheet of FIG. Partial details of the duct specification recording spreadsheet of FIG. 3 are shown, where (A) is an inlet boundary condition and (B) is an exit boundary condition. The graph which shows the analysis result by the pressure propagation analyzer of FIG. FIG. 5 is a model diagram showing a tunnel as a duct to be analyzed by the pressure propagation analyzer for the compressible fluid in the duct according to the second embodiment together with a high-speed moving body. (A) is a chart showing a part of the flow rate spreadsheet (inlet boundary condition) in the pressure propagation analyzer of FIG. 8, and (B) is a part of the sound velocity spreadsheet in the pressure propagation analyzer of FIG. 8 (B). A chart showing exit boundary conditions). The graph which shows the analysis result by the pressure propagation analysis apparatus of 2nd Embodiment. The block diagram which shows the structure of the pressure propagation analysis apparatus of the compressible fluid in a duct which concerns on 3rd Embodiment. FIG. 5 is a model diagram showing a duct provided with a cross-sectional area change portion, which is the object of analysis by the pressure propagation analyzer of FIG. The chart which shows the structure of the duct specification recording spreadsheet of FIG. The chart which shows the structure of the sound velocity value spreadsheet of FIG. The chart which shows the structure of the flow rate value spreadsheet of FIG. The graph which shows the analysis result by the pressure propagation analysis apparatus of FIG. The block diagram which shows the structure of the pressure propagation analysis apparatus of the compressible fluid in a duct which concerns on 4th Embodiment. FIG. 6 is a model diagram showing a duct provided with a branching / gathering portion, which is the object of analysis by the pressure propagation analyzer of FIG. A chart showing the configurations of the duct specification recording spreadsheet (FIG. 19 (A)), the sound velocity value spreadsheet (FIG. 19 (B)), and the flow rate value spreadsheet (FIG. 19 (C)) of FIG. The graph which shows the analysis result by the pressure propagation analysis apparatus of FIG.

Hereinafter, embodiments for carrying out the present invention will be described with reference to the drawings.
[A] First Embodiment (FIGS. 1 to 7)
FIG. 1 is a block diagram showing a configuration of a pressure propagation analysis device for a compressible fluid in a duct according to the first embodiment. As shown in FIG. 2, the pressure propagation analyzer 10 for the in-duct compressive fluid shown in FIG. 1 serves as an end portion (a start end 2 as an inlet or an outlet) in the duct 1 filled with a compressible fluid such as air. The propagation of the pressure wave α generated by the change in the boundary condition of the end 3 (for example, the start 2) in the duct 1 is analyzed by calculating the change in the pressure and the flow rate of the compressible fluid in the duct 1. , Duct specification recording spreadsheet 11 as duct specification information recording means, physical property value database 12, pressure propagation parameter recording spreadsheet 13 as pressure propagation parameter information recording means, calculation means 14, and display means 15. Consists of having.

As shown in FIG. 2, the duct 1 to be analyzed by the pressure propagation analyzer 10 is a single duct having a uniform cross-sectional area and no branching / gathering portion. In this duct 1, the duct length is 10 m, the end 3 is a closed end, and the pressure wave α enters the duct 1 from the open end 2 which is the open end. The inside of the duct 1 is filled with air under normal temperature and atmospheric pressure, and the sound velocity at equilibrium (sound velocity at equilibrium) at which the pressure wave α does not act is 340 m / s, and the pressure at equilibrium (pressure at equilibrium) is 100 kPa. ..

As shown in FIG. 3, the duct specification recording spreadsheet 11 records duct specification information of each part of the duct 1, and is a spreadsheet software spread having a plurality of cells set by a plurality of rows and columns. It is a sheet. That is, in the duct specification recording spreadsheet 11, each part of the duct in which the duct 1 is virtually divided in the axial direction is set in the column direction, the duct specification information is set in the row direction, and the duct specification information of each part of the duct is set in each cell. The value is recorded.

The duct specification information includes axial coordinate values (axial coordinates) from the start end 2 of the duct 1, virtual division length when the duct 1 is virtually divided in the axial direction (axial length increments), and duct cross-sectional area. is there. Specifically, the duct specification recording spreadsheet 11 is a title in the first column, and each part of the duct (node) in which the duct length of 10 m is virtually divided into 100 with a shaft length step value of 0.1 m from the second column to the 102nd column. ) Is shown, the axial coordinate value (axial coordinate value) from the start end of the duct is set in the third line, the axial length step value is set in the fourth line, and the duct cross-sectional area is set in the fifth line.

Further, in the duct specification recording spreadsheet 11, the duct specification information of each part of the duct is continuously recorded in the column direction for each part of the duct 1 having the same cross-sectional area. Further, the axial length step value recorded in the duct specification recording spreadsheet 11 is larger than the product of the time step value of the analysis and the sound velocity at equilibrium in the compressible fluid in order to ensure the computational stability of the analysis. It is set large. The condition of the shaft length step value is the same not only in the first embodiment but also in the second to fourth embodiments.

The physical property value database 12 shown in FIG. 1 records physical property value information such as the specific heat ratio of the compressible fluid, the speed of sound at equilibrium in the compressible fluid, and the pressure at equilibrium. These values are taken into the calculation means 14.

The pressure propagation parameter recording spreadsheet 13 shown in FIG. 1 records the time history of the pressure propagation parameter information of each part of the duct 1. Specifically, the pressure propagation parameter recording spreadsheet 13 includes a sound velocity value spreadsheet 16 that records the time history of the sound velocity value of each part of the duct 1 as the time history of the pressure propagation parameter information, and the flow rate of each part of the duct 1. It is configured with a flow value spreadsheet 17 that records the time history of values as the time history of pressure propagation parameter information. The time history of the sound velocity value of the sound velocity value spreadsheet 16 is converted into the time history of the pressure value by the conversion formula (mathematical expression 2) described later.

The sonic value spreadsheet 16 and the flow rate value spreadsheet 17 are spreadsheets of spreadsheet software having a plurality of cells set by a plurality of rows and columns, as shown in FIGS. 4 and 5. Further, in the sound velocity value spreadsheet 16 and the flow rate value spreadsheet 17, each part of the duct in which the duct 1 is virtually divided in the axial direction is set in the column direction, and in the row direction, the sound velocity in the case of the sound velocity value spreadsheet 16. In the case of the value and the flow rate value spreadsheet 17, each time (time axis) of the flow rate value is set. Then, the time history of the sound velocity value of each part of the duct 1 is recorded in each cell of the sound velocity value spreadsheet 16, and the time history of the flow rate value of each part of the duct 1 is recorded in each cell of the flow rate value spreadsheet 17. In the sound velocity value spreadsheet 16 and the flow rate value spreadsheet 17, the information (sound velocity value, flow rate value) of each part of the duct 1 is continuously recorded in the column direction for each part of the duct having the same cross-sectional area. ..

Specifically, the sound velocity value spreadsheet 16 shows the analysis time (time axis) after the 4th row of the 1st column, the 4th row of which is the initial time (time 0), and the 5th and subsequent rows. The analysis time increases every time step value (for example, 0.00022 seconds). From the 2nd column to the 102nd column, similar to the duct specification recording spreadsheet 11, each part (node) of the duct in which the duct length of 10 m is virtually divided into 100 with the axial length step value of 0.1 m is shown, and the cells for each row are shown. It is configured to record the sound velocity value of each part of the duct at each analysis time.

Further, the flow value spreadsheet 17 has the same configuration as the sound velocity value spreadsheet 16, and the analysis time (time axis) is shown in the fourth and subsequent rows of the first column, and the fourth row of these shows the initial time (time). In 0), the analysis time increases for each time step value from the 5th line onward. From the 2nd column to the 102nd column, each part (node) of the duct that is virtually divided into 100 with a shaft length step value of 0.1 m is shown, and the flow rate value of each part of the duct at each analysis time is recorded in the cell for each row. It is configured to be.

The calculation means 14 shown in FIG. 1 includes duct specification information recorded in the duct specification recording spreadsheet 11, physical property value information recorded in the physical property value database 12, and pressure propagation parameter recording spreadsheet 13 (sound velocity value spreadsheet 16, Using the current time value of the pressure propagation parameter information (sound velocity value, flow rate value) in the flow rate value spreadsheet 17), the next time value (1 hour from the current time value) of the pressure propagation parameter information (sound velocity value, flow rate value). The time history of the pressure propagation parameter information (sound velocity value, flow rate value) is completed by calculating the value of the next time by the step value) by the calculation formula.

This calculation formula is input and recorded in the cell for recording the next time value of the sound velocity value in the sound velocity value spreadsheet 16, and the next time value of the sound velocity value is calculated in this cell. It is input and recorded in the cell for recording the next time value of the flow value, and the next time value of the flow value is calculated in this cell. This calculation formula is the formula 3 and the formula 4 described later in the sound velocity value spreadsheet 16 of the first embodiment, and the formula 5 and the formula 6 described later in the flow rate value spreadsheet 17 of the first embodiment. ..

The display means 15 calculates the calculation formula of the calculation means 14 for different times, that is, the calculation formula input to each cell of the sound velocity value spreadsheet 16 and the flow rate value spreadsheet 17 from the fifth row onward. It can be displayed together with the time history of the sound velocity value and flow rate value recorded in each line.
Next, the sound velocity value spreadsheet 16 shown in FIG. 4 and the flow rate value spreadsheet 17 shown in FIG. 5 will be described in more detail.
The second to 102nd columns in the fourth row of the sound velocity value spreadsheet 16 and the flow rate value spreadsheet 17 are the initial states. In this example, since the pressure wave α is in the state before entering the duct 1, the sound velocity value is set to the sound velocity value in the equilibrium state (equilibrium sound velocity 340 m / s), and the flow rate value is set to zero.

で表される。なお、平衡時圧力は常温大気圧下では、約１００ｋＰａである。 Further, the second column (starting end) of the sound velocity value spreadsheet 16 is an entrance boundary condition, which is also shown in FIG. 6 (A). In this example, the time history of the pressure value is originally set, but the pressure value is converted into the sound velocity value using Equation 1 which expresses the relationship between the pressure and the sound velocity under the isentropic condition in the compressible fluid, and this sound velocity. Set the value in the sonic value spreadsheet 16. When the specific heat ratio of the compressible fluid is γ, the sound velocity value is a, the sound velocity at equilibrium is a ₀ , the pressure value (absolute pressure) is p, and the pressure at equilibrium (absolute pressure) is p ₀ .

It is represented by. The equilibrium pressure is about 100 kPa under normal temperature and atmospheric pressure.

Further, the 102nd column (end) of the flow rate spreadsheet 17 is a closed end, and the flow rate value is set to zero. That is, as shown in FIG. 6B, this outlet boundary condition is represented by a flow rate value of zero.

Next, the mathematical formulas set in the fifth row (next time) following the fourth row representing the initial time in the sound velocity value spreadsheet 16 and the flow rate value spreadsheet 17 will be described.
In the sound velocity value spreadsheet 16, the boundary condition is set in the second column as described above, but the number of columns is added to the third and 101st columns corresponding to the portion not the end of the duct 1. If the number of lines is represented by the subscript j and i = 3 to 101 and j = 4, the sound velocity value a _{i, j + of the fifth line (next time) of the third column to the 101st column, which is not the end of the duct 1. 1} is the sound velocity value a _{i-1, j} , a _{i, j} , a _{i + 1, j} at the current time and the flow value q _{i-1, j} , q _{i, j} , q _{i + 1, j at the current time.} Is set by the following formula 3.

上述のように、ダクト１の端部でない３列目〜１０１列目の５行目の音速値は、４行目の同一列及び１つ上流列、及び1つ下流列の音速値と流量値から計算される。 Here, A is the duct cross-sectional area of the duct 1, h is the shaft length step value, and is set with reference to the duct specification recording spreadsheet 11. τ is the time step value of the analysis, and γ is the specific heat ratio of the compressible fluid, which is set with reference to the physical property value database 12. These A, h, τ, and γ are commonly used in the mathematical formulas of the respective embodiments input to the sound velocity value spreadsheet and the flow rate value spreadsheet.

As described above, the sound velocity values in the 5th row of the 3rd to 101st columns, which are not the ends of the duct 1, are the sound velocity values and the flow rate values in the same column in the 4th row, one upstream column, and one downstream column. Calculated from.

Further, as for the sound velocity value in the 5th row (next time) of the 102nd column corresponding to the end, the flow rate value in the 102nd column is set as the exit boundary condition. Set. Here, the subscript N indicates the end (102nd column), and N-1 indicates the 101st column.

That is, the next time value of the sound velocity of each part in the duct 1 having the same cross-sectional area is the specific heat of the compressible fluid in the part (third row to 101st row in the sound velocity value spreadsheet 16) that is not the end part of the duct 1. The ratio γ, the time step value τ of the analysis, the axial length step value h and the duct cross-sectional area A recorded in the same row of the duct specification recording spreadsheet 11, the same row of the sound velocity value spreadsheet 16, and one less row (upstream). The current speed of sound value in the row) and one more row (downstream row) and the current time flow value in the same row, one less row (upstream row) and one more row (downstream row) of the flow value spreadsheet 17. Therefore, it is calculated using the above-mentioned equation 3.

Further, the next time value of the sound velocity of the terminal 3 (the 102nd column in the sound velocity value spreadsheet 16) in the duct 1 having the same cross-sectional area is set by the flow rate value under the outlet boundary condition as shown in FIG. 6 (B). If so, the specific heat ratio γ of the compressible fluid, the time step value τ of the analysis, the axial length step value h and the duct cross-sectional area A recorded in the same row in the duct specification recording spreadsheet 11, and the sound velocity value spread. From the sound velocity value at the current time of the same row and one less row (upstream row) of the sheet 16 and the current flow rate value of the same row and one less row (upstream row) of the spreadsheet 17, the above equation 4 Is calculated using.

このように、ダクト１の端部でない３列目〜１０１列目の５行目の流量値は、４行目の同一列、１つ上流列及び1つ下流列の音速値と流量値から計算される。 Similarly, for the third column to the 101st column corresponding to the portion of the flow value spreadsheet 17 that is not the end of the duct 1, the number of columns is represented by the subscript i and the number of rows is represented by the subscript j, and i = 3 to 101. _{, J = 4, the flow rate values q i, j + 1 in} the 5th row (next time) of the 3rd column to the 101st column are the sound velocity values a _{i-1, j} , a _{i, j at} the current time. It is set by the following equation 5 using a _{i + 1, j} and the current time flow values q _{i-1, j} , q _{i, j} , q _{i + 1, j.}

In this way, the flow rate value in the 5th row of the 3rd column to the 101st column, which is not the end of the duct 1, is calculated from the sound velocity value and the flow rate value in the same column, 1 upstream column, and 1 downstream column in the 4th row. Will be done.

Further, since the sound velocity value in the second column is set by the entrance boundary condition for the flow rate value in the fifth row (next time) of the second column corresponding to the start end 2, the following formula 6 is used using that information. Set in.

That is, when the next time value of the flow rate of each part in the duct 1 having the same cross-sectional area is not the end part of the duct 1 (third row to 101st row in the flow rate spreadsheet 17), the compressible fluid The specific heat ratio γ, the time step value τ of the analysis, the shaft length step value h and the duct cross-sectional area A recorded in the same row of the duct specification recording spreadsheet 11, the same row of the sound velocity value spreadsheet 16, and one less row ( Current time sound velocity values in the upstream row) and one more row (downstream row), and the current flow rate in the same row, one less row (upstream row), and one more row (downstream row) in the flow rate spreadsheet 17. It is calculated from the value using the above formula 5.

Further, the next time value of the flow rate of the start end 2 (second row in the flow rate value spreadsheet 17) in the duct 1 having the same cross-sectional area is set by the sound velocity value under the exit boundary condition as shown in FIG. 6 (A). If so, the specific heat ratio γ of the compressible fluid, the time step value τ of the analysis, the shaft length step value h and the duct cross-sectional area A recorded in the same row of the duct specification recording spreadsheet 11, and the sound velocity value spread. From the sound velocity value at the current time of the same row and one more row (downstream row) of the sheet 16 and the current flow rate value of the same row and one more row (downstream row) of the flow value spreadsheet 17, the above equation 6 Calculated using.

With the above, all the values in the fifth row of the sound velocity value spreadsheet 16 and the flow rate value spreadsheet 17 are set. In the above explanation, the subscript j is used for the line direction, and the values of the 6th and subsequent lines can be calculated by setting the same formula as the 5th line for the 6th and subsequent lines. Therefore, in the sound velocity value spreadsheet 16 and the flow rate value spreadsheet 17, the calculation of the sound velocity value and the flow rate value from the 6th line onward can be performed by copying the mathematical expression for each line. The sound velocity value and the flow rate value can be easily calculated.

FIG. 7 shows the analysis result by the pressure propagation analyzer 10 of the first embodiment analyzed in this way. The inlet pressure X1, the intermediate pressure Y1 and the terminal pressure Z1 shown in FIG. 7 represent a state in which the pressure wave α that has entered the start end 2 which is the inlet propagates to the intermediate portion and the end 3 (closed end) of the duct 1. ing. Although it is shown as a pressure value in FIG. 7, this is a time history of the sound velocity value analyzed using the sound velocity value spreadsheet 16 converted into a pressure value by the mathematical formula 2. As can be seen from FIG. 7, the pressure wave α represents a situation in which the rising edge of the waveform becomes steeper as it propagates downstream.

In the pressure propagation analyzer 10 for the compressible fluid in the duct configured as described above, first, the initial conditions are input to the fourth rows of each of the sound velocity value spreadsheet 16 and the flow rate value spreadsheet 17, and the sound velocity value spreadsheet In 16, the inlet boundary condition is input to the second column corresponding to the start end 2 of the duct 1, and the exit boundary condition is input to the 102nd column corresponding to the end 3 of the duct 1 in the flow rate spreadsheet 17.

Next, in the sound velocity value spreadsheet 16 and the flow rate value spreadsheet 17, enter the formula for calculating the next time value in the cell of the fifth row corresponding to the time next to the initial time (fourth row), and enter the sound velocity value. And the next time value of the flow value is calculated, and this next time value is recorded in the cell of the fifth row.
Here, in the duct specification recording spreadsheet 11, the sound velocity value spreadsheet 16, and the flow rate value spreadsheet 17, the same part of the duct 1 is set to be in the same row, and the sound velocity value spreadsheet 16 and the flow rate value spreadsheet are set. In 17, the information at the same time is set in the same line.

Therefore, next, as described above, the formulas entered in the cells in the 5th row corresponding to the time following the initial time are collectively copied to each cell in the 6th row and thereafter corresponding to the time after the next time. Then, the sound velocity value and the flow rate value at each of these times are calculated and recorded in each cell from the sixth row onward. Then, the sound velocity value recorded in each cell of the sound velocity value spreadsheet 16 is converted into a pressure value by using Equation 2.

Since it is configured as described above, according to the first embodiment, the following effects (1) and (2) are obtained.
(1) As shown in FIGS. 4 and 5, in the cells of the sound velocity value spreadsheet 16, a calculation formula (formula 3 and formula 4) for sound velocity value analysis and a sound velocity value determined by this calculation formula are input. And, in the cell of the flow value spreadsheet 17, a calculation formula for flow value analysis (Formula 5 and Formula 6) and a flow value determined by this calculation formula are input and recorded. Therefore, since the analysis process of pressure propagation is clearly specified in the sonic value spreadsheet 16 and the flow value spreadsheet 17, they are input to the same row in each of the sonic value spreadsheet 16 and the flow value spreadsheet 17. Compare the formulas, for example, make sure that the formula entered in the cell in the 5th row corresponding to the time following the initial time (4th row) is accurate, and then this formula is next. Confirm that it is copied to the cell of each row after the 6th row corresponding to the time after. As a result, was the change in pressure and flow rate in the duct 1 correctly analyzed by converting the sound velocity value in the duct 1 into a pressure value by the conversion formula (mathematical formula 2) without using a special program language? Can be easily verified.

(2) Sound velocity value The pressure value converted into the sound velocity value recorded in each cell of the spreadsheet 16 and the flow rate value recorded in each cell of the flow rate spreadsheet 17 are appropriately graphed and displayed as a waveform. Therefore, the validity of the analysis result of the pressure propagation analyzer 10 for the compressible fluid in the duct can be easily confirmed.

[B] Second embodiment (FIGS. 8 to 10, FIG. 1)
FIG. 8 is a model diagram showing a tunnel as a duct to be analyzed by the pressure propagation analyzer for the compressible fluid in the duct according to the second embodiment together with a high-speed moving body. In this second embodiment, the same parts as those in the first embodiment are designated by the same reference numerals as those in the first embodiment to simplify or omit the description.

The pressure propagation analyzer 20 (FIG. 1) for the compressible fluid in the duct of the second embodiment is installed in the tunnel 21 when the high-speed moving body 22 rushes into the tunnel 21 equivalent to the duct 1 having the same cross-sectional area. The propagation of the generated pressure wave α is analyzed by calculating the changes in the pressure and the flow rate of the compressible fluid in the tunnel 21. The pressure propagation analyzer 20 includes a duct specification recording spreadsheet 11, a physical property value database 12, and a sound velocity value spreadsheet 23 (FIG. 9 (B)) as a sound velocity value information recording means having substantially the same configuration as the sound velocity value spreadsheet 16. )), A flow value spreadsheet 24 (FIG. 9 (A)) as a flow value information recording means having substantially the same configuration as the flow value spreadsheet 17, a calculation means 26, and a display means 15. Will be done. The sound velocity value spreadsheet 23 and the flow rate value spreadsheet 24 constitute a pressure propagation parameter recording spreadsheet 25 as a pressure propagation parameter information recording means.

In the duct specification recording spreadsheet 11, the sound velocity value spreadsheet 23, and the flow rate value spreadsheet 24, the length of the tunnel 21 is virtually divided by the axial length step value h in the column direction in the column direction as in the first embodiment. Each part is set. Further, in the sound velocity value spreadsheet 23 and the flow rate value spreadsheet 24, the time axis is set in the row direction with the time step value τ of the analysis as in the first embodiment. In the sound velocity value spreadsheet 23 and the flow rate value spreadsheet 24 of the second embodiment, as shown in FIG. 9A, the entrance boundary condition is set as the flow rate value corresponding to the speed of the high-speed moving body 22. Further, as the outlet boundary condition, since the outlet (terminal 3) of the tunnel 21 is considered to have a constant pressure (atmospheric pressure) at the open end, the value of the sound velocity at equilibrium (sound velocity) according to Equation 1 as shown in FIG. 9 (B). Is set to constant).

Further, the calculation formula of the calculation means 26 for calculating the next time value of each of the sound velocity value and the flow rate value is the sound velocity of each part of the tunnel 21 which is not the end (corresponding to the third column to the 101st column of the sound velocity value spreadsheet 23). Formula 3 is used to calculate the next time value of the value, and formula 5 is used to calculate the next time value of the flow rate of each part of the tunnel 21 that is not the end (third column to 101st column of the flow value spreadsheet 24). Used. Further, as the calculation formula of the calculation means 26, the formula 7 (described later) is used for calculating the next time value of the sound velocity value at the start end of the tunnel 21 (corresponding to the second column of the sound velocity value spreadsheet 23), and the tunnel 21 is calculated. Equation 8 (described later) is used to calculate the next time value of the flow rate at the end 3 (the 102nd column of the flow value spreadsheet 24).

Next, the above-mentioned mathematical formula 7 will be described. The next time value of the speed of sound at the start end 2 in the tunnel 21 having the same cross-sectional area is the specific heat ratio γ of the compressible fluid when the flow rate value is set by the outlet boundary condition as shown in FIG. 9 (A). , The time step value τ of the analysis, the axial length step value h and the tunnel cross-sectional area A recorded in the same row of the duct specification recording spreadsheet 11, and the same row and one more row (downstream row) of the sound velocity value spreadsheet 23. It is calculated using Equation 7 from the sound velocity value of the current time of the flow rate value and the current time value of the same row and one more row (downstream row) of the flow rate spreadsheet 24.

_{Specifically, the next time values a2 and j + 1} of the sound velocity of the start end 2 (corresponding to the second column of the sound velocity value spreadsheet 23) in the tunnel 21 are _{the sound velocity values a2 and j} and the flow rate of the start end 2 at the current time. The values q _{2, j , the sound velocity values a 3, j} and the flow values q _{3, j in the} one downstream row of the start 2 at the current time, and the flow values at the start 2 at the next time (entrance boundary of FIG. 9 (A)). Condition) It is calculated by the following equation 7 using _{q 2 and j + 1.}

Further, the above-mentioned mathematical formula 8 will be described. The next time value of the flow rate of the end 3 in the tunnel 21 having the same cross-sectional area is the specific heat ratio γ of the compressible fluid when the sound velocity value is set by the outlet boundary condition as shown in FIG. 9 (B). , The time step value τ of the analysis, the axial length step value h and the tunnel cross-sectional area A recorded in the same row of the duct specification recording spreadsheet 11, and the same row and one less row (upstream row) of the sound velocity value spreadsheet 23. It is calculated by Equation 7 using the sound velocity value at the current time of the flow rate value and the flow rate value at the current time in the same row and one less row (upstream row) of the flow rate spreadsheet 20.

_{Specifically, the next time values q N and j + 1} of the flow rate of the terminal 3 (corresponding to the 102nd column (Nth column) of the flow rate value spreadsheet 24) in the tunnel 21 are the flow rate value q of the terminal 3 at the current time. _{N, j} and the sound velocity value a _{N, j , the flow rate value q N-1, j} and the sound velocity value a _{N-1, j of the} one upstream row of the terminal 3 at the current time, and the sound velocity value of the terminal 3 at the next time. (Exit boundary condition in FIG. 9B) Calculated by the following equation 8 using _{a N and j + 1.}

The above-mentioned formulas 3 and 7 are input to the cell in the 5th row corresponding to the time next to the initial time (4th row) in the sound velocity value spreadsheet 23 to calculate the sound velocity value, and then the exit boundary condition is set. Except for this, the sound velocity value is calculated by being copied and input to each cell of the sixth and subsequent rows corresponding to the next time and thereafter, and the time history of the sound velocity value is recorded in the sound velocity value spreadsheet 23. Similarly, the above-mentioned formulas 5 and 8 are input to the cell in the fifth row corresponding to the time next to the initial time (fourth row) in the flow rate spreadsheet 24 to calculate the flow rate value, and then the entrance. Excluding the boundary condition, a plurality of cells are input to each cell in the sixth and subsequent rows corresponding to the next time and thereafter to calculate the flow rate value, and the time history of the flow rate value is recorded in the flow rate value spreadsheet 24.

The formulas 3 and 7 input and recorded in each cell of the sound velocity value spreadsheet 23, and the sound velocity values calculated by these formulas are displayed by the display means 25. Similarly, the formulas 5 and 8 input and recorded in each cell of the flow rate spreadsheet 24, and the flow rate calculated by these formulas are displayed by the display means 15. Here, the time history of the pressure value is converted from the time history of the sound velocity value by the mathematical formula 2, and the time history of the pressure value is also provided so as to be displayable by the display means 15.

The analysis result by the pressure propagation analyzer 20 configured as described above is shown in FIG. In FIG. 10, the time history of the inlet pressure X2 and the inlet flow rate UX at the inlet (starting end 2) of the tunnel 21 and the intermediate pressure Y2 and the intermediate flow rate UY at the axial middle portion of the tunnel 21 are analyzed. It is displayed as a result. According to this analysis result, the pressure increase when the high-speed moving body 22 enters the tunnel 21 is analyzed.

Based on the above configuration, according to the pressure propagation analyzer 20 for the compressible fluid in the duct of the second embodiment, the time history of the sound velocity value and the time history of the flow rate value of each part of the tunnel 21 are the same. It is recorded in each of the sound velocity value spreadsheet 23 and the flow rate value spreadsheet 24 including the calculation formula and can be displayed by the display means 15, and the time history of the pressure value is converted from the time history of the sound velocity value and displayed by the display means 15. Therefore, the second embodiment also has the same effects as the effects (1) and (2) of the first embodiment.

[C] Third Embodiment (FIGS. 11 to 16)
FIG. 11 is a block diagram showing a configuration of a pressure propagation analysis device for a compressible fluid in a duct according to a third embodiment. Further, FIG. 12 is a model diagram showing a duct provided with a cross-sectional area changing portion, which is the analysis target of the pressure propagation analyzer of FIG. In this third embodiment, the same parts as those in the first embodiment are designated by the same reference numerals as those in the first embodiment to simplify or omit the description.

As shown in FIG. 12, the pressure propagation analyzer 30 for the compressible fluid in the duct according to the third embodiment includes, for example, a cross-sectional area changing portion 4 in the intermediate portion in the axial direction, the start end 2 is the open end, and the end 3 is closed. When a pressure fluctuation β occurs at the start end (inlet) 2 of the duct 33, which is the end, the propagation of the pressure wave α generated in the duct 33 is calculated as a change in the pressure and flow rate of the compressible fluid in the duct 33. It is to analyze by. The pressure propagation analyzer 30 includes a duct specification recording spreadsheet 34 (FIG. 13) as a duct specification information recording means, a physical property value database 12, and a sound velocity value spreadsheet 35 (FIG. 14) as a sound velocity value information recording means. A flow value spreadsheet 36 (FIG. 15) as a flow value information recording means, a calculation means 37, and a display means 15 are provided. The sound velocity value spreadsheet 35 and the flow rate value spreadsheet 36 constitute a pressure propagation parameter recording spreadsheet 38 as a pressure propagation parameter information recording means.

Here, a specific example of the duct 33 is shown in FIG. In the duct 33, when the first duct 31 is from the start end 2 to the cross-sectional area changing portion 4 and the second duct 32 is from the cross-sectional area changing portion 4 to the end 3, the cross-sectional area A2 of the second duct 32 is the first duct. When the cross-sectional area A1 of 31 is reduced to, for example, 1/4 times (FIG. 12 (A)), and when the cross-sectional area A1 of the first duct 31 and the cross-sectional area A2 of the second duct 32 are substantially the same ( 12 (B)) and the case where the cross-sectional area A2 of the second duct 32 is enlarged, for example, four times as large as the cross-sectional area A1 of the first duct 31 (FIG. 12 (C)). It is assumed that the end of the first duct 31 and the start of the second duct 32 overlap.

As shown in FIGS. 13 to 15, in the duct specification recording spreadsheet 34, the sound velocity value spreadsheet 35, and the flow rate value spreadsheet 36, the end of the first duct corresponding to the cross-sectional area changing portion 4 of the duct 33 (52nd row). (Equivalent to) and the start end of the second duct (corresponding to the 54th row) are set separately, and the cross-sectional area changing portion 4 is spaced in the row direction of each spreadsheet to distinguish it from the other parts of the duct 33. Is opened and set as an empty column (53rd column of each spreadsheet). Further, in the duct specification recording spreadsheet 34, the sound velocity value spreadsheet 35, and the flow rate value spreadsheet 36, the duct length of 2.5 m of the first duct 31 is virtually divided by the axial length step value of 0.05 m, and from the second row. Each part of the first duct 31 is set by the 52nd row. Similarly, the duct length of 2.5 m of the second duct 32 is virtually divided by the shaft length step value of 0.05 m, and each part of the second duct 32 is set from the 54th row to the 104th row (not shown). ..

In the sound velocity value spreadsheet 35 and the flow rate value spreadsheet 36, a time axis is set in the row direction with the time step value τ of the analysis, and the initial state is recorded in the cell of the fourth row (initial time). Further, the time history of each of the sound velocity value and the flow rate value is recorded in the fifth and subsequent rows of each of the sound velocity value spreadsheet 35 and the flow rate value spreadsheet 36. Further, the inlet boundary condition set in the second column of the sonic value spreadsheet 35 and the exit boundary condition set in the 104th column (Nth column) of the flow rate spreadsheet 36 are not shown, but are not shown. 1 It is set in the same manner as in the embodiment (FIG. 6).

The calculation formula of the calculation means 37 for calculating the next time value of each of the sound velocity and the flow rate is that the sound velocity and the flow rate of each part of the duct 33 excluding the cross-sectional area changing portion 4 having the same cross-sectional area among the ducts 33 having different cross-sectional areas. For calculating the next time value, that is, each part of the first duct 31 and the second duct 32 excluding the end of the first duct 31 (corresponding to the 52nd row) and the start end of the second duct 32 (corresponding to the 54th row). For the calculation of the next time value of the sound velocity and the flow rate, the mathematical formulas 3, 4 and 7 of the first and second embodiments, and the mathematical formulas 5, 6 and 8 are used.

Further, as the calculation formula of the calculation means 37, the formula 9-1 (described later) is used for calculating the next time value of the sound velocity at the end of the first duct 31 (corresponding to the 52nd column), and the end of the first duct 31. Formula 10-1 (described later) is used to calculate the next time value of the flow rate (corresponding to the 52nd column). The speed of sound at the beginning of the second duct 32 (corresponding to the 54th row) is equal to the speed of sound at the end of the first duct 31 (corresponding to the 52nd row) at the same time, and the flow rate at the beginning of the second duct 32. Is equal to the flow rate at the end of the first duct 31 at the same time. When these are intentionally expressed by mathematical formulas, the formula of the formula 37 is the formula 9-2 (described later) for calculating the next time value of the sound velocity at the start end (corresponding to the 54th column) of the second duct 32. Equation 10-2 (described later) is used to calculate the next time value of the flow rate at the start end (corresponding to the 54th column) of the second duct 32.

Next, the above-mentioned formulas 9-1 and 9-2 will be described. The next time values of the speed of sound in the cross-sectional area changing portion 4 of the ducts 33 having different cross-sectional areas are the specific heat ratio γ of the compressible fluid, the time step value τ of the analysis, and the same row and the empty row of the duct specification recording spreadsheet 34 ( For example, the sound velocity at the current time of the axis length step value h and the duct cross-sectional areas A1 and A2 recorded in the columns other than the 53rd column) and the same column and the empty column (for example, the 53rd column) of the sound velocity spreadsheet 35. It is calculated by Equation 9-1 and Equation 9-2 using the value and the current time value of the column excluding the same column and the empty column (for example, the 53rd column) of the flow value spreadsheet 36.

Specifically, the first subscript is the column number (indicated by i), the second subscript is the row number indicating the time history (indicated by j), and A ₁ is the duct cross-sectional area of the first duct 31. , When the _{a 2} duct cross-sectional area of the second duct 32, the acoustic velocity values of the fifth line 52 column corresponding to the end of the first duct 31 (the next time value) as i = 52, j = 4, It is calculated by the following formula 9-1.

Further, the sound velocity value in the fifth row, which is the next time value in the 54th column corresponding to the start end of the second duct 32, is calculated by the following equation 9-2 with i = 54.

Next, the above-mentioned formulas 10-1 and 10-2 will be described. The next time value of the flow rate in the cross-sectional area changing portion 4 of the ducts 33 having different cross-sectional areas is the specific heat ratio γ of the compressible fluid, the time step value τ of the analysis, and the same row and the empty row of the duct specification recording spreadsheet 34 ( For example, the sound velocity at the current time of the axis length step value h and the duct cross-sectional areas A1 and A2 recorded in the columns other than the 53rd column) and the same column and the empty column (for example, the 53rd column) of the sound velocity value spreadsheet 35. It is calculated by Equation 10-1 and Equation 10-2 using the value and the flow rate value at the current time in the same column and the empty column (for example, the 35th column) of the flow rate spreadsheet 36.

Specifically, the first subscript is the column number (indicated by i), the second subscript is the row number indicating the time history (indicated by j), and A ₁ is the cross-sectional area of the first duct 31. Assuming _{that A 2} is the cross-sectional area of the second duct 32, the flow rate value in the fifth row, which is the next time value in the 52nd column corresponding to the start end of the first duct 31, is calculated by the following equation 10-1.

Further, the flow rate value in the fifth row, which is the next time value in the 54th column corresponding to the start end of the second duct 32, is calculated by the following equation 10-2 with i = 54.

The above-mentioned formulas 9-1 and 9-2 are input to the cell in the fifth row corresponding to the time next to the initial time (fourth row) in the sound velocity value spreadsheet 35 to calculate the sound velocity value, and then the sound velocity value is calculated. , The sound velocity value is calculated by being copied and input to each cell of the sixth row and thereafter corresponding to the time after the next time, and the time history of the sound velocity value is recorded in the sound velocity value spreadsheet 35. Similarly, Equation 10-1 and Equation 10-2 are input to the cell in the fifth row corresponding to the time following the initial time (fourth row) in the flow rate spreadsheet 36 to calculate the flow rate value, and then the flow rate value is calculated. Then, the flow rate value is calculated by being copied and input to each cell of the sixth and subsequent rows corresponding to the time after the next time, and the time history of the flow rate value is recorded in the flow rate value spreadsheet 36.

Formulas 9-1 and 9-2 entered and recorded in each cell of the sound velocity spreadsheet 35, and the sound velocity values calculated by these formulas are displayed by the display means 15. Similarly, formulas 10-1 and 10-2 entered and recorded in each cell of the flow rate spreadsheet 36, and the flow rate calculated by these formulas are displayed by the display means 15. Here, the time history of the pressure value is converted from the time history of the sound velocity value by the mathematical formula 2, and the time history of the pressure value is also provided so as to be displayable by the display means 15.

FIG. 16 shows the analysis result of the compressible fluid in the duct configured as described above by the pressure propagation analyzer 30. In FIG. 16, the end 3 (closed end) of the duct 33 in which _{the cross-sectional area A 2} of the second duct 32 is 1/4 times smaller than the cross-sectional area A ₁ of the first duct 31 with respect to the same inlet pressure X3. the end pressure Y3-1 in, terminating pressure Y3-2 of the cross-sectional area _{a 2} of the second duct 32 is terminated 3 (closed end) of the cross-sectional area _{a 1} and the duct 33 is substantially the same in the first duct 31 , The end pressure Y3-3 at the end 3 (closed end) of the duct 33 in which the cross-sectional area A ₂ of the second duct 32 is four times larger than the cross-sectional area A _{1 of the first duct 31 is described.} .. According to this analysis result, it can be seen that a large pressure is generated in the duct 33 in which _{the cross-sectional area A 2} of the second duct 32 is smaller than the cross-sectional area A _{1 of the first duct 31.}

Based on the above configuration, according to the pressure propagation analyzer 30 for the compressible fluid in the duct of the third embodiment, the duct 33 including the end of the first duct 31 and the end of the second duct 32 The time history of the sound velocity value and the time history of the flow rate value of each part are recorded in each of the sound velocity value spreadsheet 35 and the flow rate value spreadsheet 36 including the calculation formulas, and can be displayed by the display means 15, and the pressure. Since the time history of the value is converted from the time history of the sound velocity value and provided so that it can be displayed by the display means 15, the same effect as the effects (1) and (2) of the first embodiment also in the third embodiment. Play.

[D] Fourth Embodiment (FIGS. 17 to 20)
FIG. 17 is a block diagram showing a configuration of a pressure propagation analysis device for a compressible fluid in a duct according to a fourth embodiment. Further, FIG. 18 is a model diagram showing a duct provided with a branching / gathering portion, which is the analysis target of the pressure propagation analyzer of FIG. In this fourth embodiment, the same parts as those in the first embodiment are designated by the same reference numerals as those in the first embodiment to simplify or omit the description.

The pressure propagation analyzer 40 for the compressible fluid of the fourth embodiment has a pressure fluctuation shown by an inlet pressure X4 (FIG. 20) at the start end (inlet) 2 of the duct 1 in the duct system 6 provided with the branching / gathering portion 5. When δ occurs, the propagation of the pressure wave α generated in the duct system 6 is analyzed by calculating the changes in the pressure and the flow rate of the compressible fluid in the duct system 6. The pressure propagation analyzer 40 includes a duct specification recording spreadsheet 44 (FIG. 19 (A)) as a duct specification information recording means, a physical property value database 12, and a sound velocity value spreadsheet 45 (FIG. 19 (A)) as a sound velocity value information recording means. 19 (B)), a flow value spreadsheet 46 (FIG. 19 (C)) as a flow value information recording means, a calculation means 47, and a display means 15. The sound velocity value spreadsheet 45 and the flow rate value spreadsheet 46 constitute a pressure propagation parameter recording spreadsheet 48 as a pressure propagation parameter information recording means.

Here, a specific example of the duct system 6 is shown in FIG. The duct 1 has a duct length of 10 m, a duct cross-sectional area of 1 m ² , a start end 2 having an open end, and a terminal 3 having a closed end. The third duct 43 is branched and attached at a position 3 m from the starting end 2 of the duct 1, and therefore the branching / gathering portion 5 is formed at this attachment position. In the duct 1, the branch / assembly portion 5 to which the start end 2 to the third duct 43 is attached is referred to as a first duct 41, and the branch / assembly portion 5 to the end 3 is referred to as a second duct 42. The third duct 43 has a duct length of 5 m, a duct cross-sectional area of 0.25 m ² , and has an open end at the end.

As shown in FIGS. 19A, 19B and 19C, in the duct specification recording spreadsheet 44, the sound velocity value spreadsheet 45 and the flow rate value spreadsheet 46, the duct length of the first duct 41 is set in the column direction. Virtually divided by the shaft length step value (for example, 0.2 m), each part of the first duct 44 is set from the second row to the 17th row, one row is provided, and the duct length of the second duct 42 is provided. Is virtually divided by the axial length step value (for example, 0.2 m), each part of the second duct 42 is set from the 19th row to the 54th row, a 1-row empty row is provided, and the duct of the 3rd duct 43 is provided. The length is virtually divided by the shaft length step value (for example, 0.2 m), and each part of the third duct 43 is set from the 56th row to the 81st row (not shown).

In the duct specification recording spreadsheet 44, the sound velocity value spreadsheet 45, and the flow value value spreadsheet 46, the branching / gathering portions 5 provided in the duct system 6 are spaced apart in the column direction, that is, in an empty column (18th column and). It is provided as the 55th row). The end of the duct connected to the branch / assembly portion 5 is the end of the first duct 41 (corresponding to the 17th row), the start end of the second duct 42 (corresponding to the 19th row), and the third duct. It is the starting end of 43 (corresponding to the 56th row).

In the sound velocity value spreadsheet 45 and the flow rate value spreadsheet 46, the time axis is set in the row direction with the time step value τ of the analysis, and the initial state is recorded in the cell of the fourth row (initial time). Further, the time history of each of the sound velocity value and the flow rate value is recorded in the fifth and subsequent rows of each of the sound velocity value spreadsheet 45 and the flow rate value spreadsheet 46.

The calculation formula of the calculation means 47 for calculating the next time value of the sound velocity and the flow rate is the end portion connected to the branching / gathering portion 5 (the end of the first duct 41, the start end of the second duct 42, and the start end of the third duct 43). For calculating the next time values of the sound velocity and the flow rate of each part of the first duct 41, the second duct 42, and the third duct 43 having the same cross-sectional area except for, the mathematical formulas for calculating the sound velocity in the first and second embodiments. 3. Formula 4 and Formula 7, and Formula 5, Formula 6 and Formula 8 for calculating the flow rate are used.

Further, in the calculation formula of the calculation means 47, the formula 12 is used for calculating the start value RS for the start end of the duct whose start end is connected to the branch / assembly portion 5, and the end is connected to the branch / assembly portion 5. For the end, Equation 11 is used to calculate the end value RE. Further, the calculation formula of the calculation means 47 is for calculating the next time value of the sound velocity at the end of the duct connected to the branching / gathering portion (the start end of the second duct 42 and the third duct 43 and the end of the first duct 41). Equation 13 is used for. Further, in the calculation formula of the calculation means 47, the formula 15 is used for calculating the next time value of the flow rate at the start end of the second duct 42 and the third duct 43 whose start ends are connected to the branch / assembly portion 5, and the branch is formed. Formula 14 is used to calculate the next time value of the flow rate at the end of the first duct 41 whose end is connected to the gathering part 5.

Next, the mathematical formula 11 will be described. Regarding the end (corresponding to the 17th row) of the duct (first duct 41) whose end is connected to the branching / collecting portion 5, the specific heat ratio γ of the compressible fluid, the duct cross-sectional area A, and the row corresponding to the end (17). The current time value of the flow rate in the (column), the current time value of the flow rate in the column (16th column) one upstream from the end, the current time value of the sound velocity in the column (17th column) corresponding to the end, And the current time value of the end value RE is calculated by the equation 11 using the current time value of the sound velocity in the column (16th column) corresponding to one upstream from the end.

ここで、
ｑ_Ｎ：終端での現時刻の流量値
ａ_Ｎ：終端での現時刻の音速値
ｑ_Ｎ１；終端から１つ上流側の節点での現時刻の流量値
ａ_Ｎ１；終端から１つ上流側の節点での現時刻の音速値 Specifically, for the above-mentioned end (corresponding to the 17th column) of the duct (first duct 41) whose end is connected to the branch / assembly portion 5, the end value RE at the current time of this end is calculated by the following formula 11. To do.

here,
q _N : Current time flow rate _{at the end a N} : Sound velocity value at the current time at the _{end q N1} ; Current time flow value at a node _{one upstream from the end a N1} ; One upstream from the end Sound velocity value at the current time at the node

Next, Equation 12 will be described. Regarding the above-mentioned starting ends (corresponding to the 19th and 56th rows) of the ducts (second duct 42, third duct 43) whose starting ends are connected to the branching / gathering portion 5, the specific heat ratio γ of the compressible fluid and the duct cross-sectional area A , The current time value of the flow rate in the columns corresponding to the start end (19th column, 56th column), the current time value of the flow rate in the column corresponding to one downstream from the start end (20th column, 57th column), the above. Using the current time value of the sound velocity in the columns corresponding to the start end (19th and 56th columns) and the current time value of the sound velocity in the column corresponding one downstream from the start end (20th and 57th columns). , The current time value of the starting value RS is calculated by the equation 12.

ここで、
ｑ_１：始端での現時刻の流量値
ａ_１：始端での現時刻の音速値
ｑ_２；始端から１つ下流側の節点での現時刻の流量値
ａ_２；始端から１つ下流側の節点での現時刻の音速値 Specifically, with respect to the above-mentioned starting ends (corresponding to the 19th and 56th rows) of the ducts (second duct 42, third duct 43) whose starting ends are connected to the branching / gathering portion 5, the starting ends of the starting ends at the current time. The value RS is calculated by the following equation 12.

here,
q ₁ : Current time flow rate value at the start a ₁ : Sound velocity value at the current time at the start q ₂ ; Current time flow value at a node _{one downstream from the start a 2} ; One downstream from the start Sound velocity value at the current time at the node

The above-mentioned end value RE and start value RS are set by inputting their values in the rows of the corresponding times in the empty columns (18th column, 55th column) of the sound velocity value spreadsheet 45 and the flow rate value spreadsheet 46. However, in a spreadsheet in which a user-defined function such as Excel can be used, formulas 11 and 12 may be defined as user-defined functions.

Next, the mathematical formula 13 will be described. The next time value of the sound velocity of the end (corresponding to the 17th row, 19th row, 56th row) of the ducts (1st duct 41, 2nd duct 42, 3rd duct 43) connected to the branching / gathering portion 5 is , The current time start value RS and end value RE defined by whether the end connected to the branch / assembly part 5 is the start end or the end value is ducted to the sound velocity value at the current time at this end (first duct 41). , 2nd duct 42, 3rd duct 43), and the sum of the sums of the values divided by the axial length increments h is divided by twice the sum of the cross-sectional areas A of the ducts connected to the branching / gathering part 5. , It is calculated from Equation 13 by multiplying the value obtained by subtracting 1 from the specific heat ratio γ of the compressible fluid and further multiplying the value obtained by multiplying the time step value τ of the analysis.

Specifically, the number k of the duct (first duct 41) to which the end (corresponding to the 17th column) is connected to the branch / assembly portion 5 is k = 1 to m, and the end value RE corresponding to this end is RE _k. , The number k of the ducts (second duct 42, third duct 43) to which the starting end (corresponding to the 19th row and the 56th row) is connected to the branching / gathering portion 5 is k = m + 1 to n, and the starting end corresponding to this starting end. represented the value RS RS k _(where m, n is a natural number representing the number of ducts) and, notation axial length increment value for each duct connected to the branch-collecting portion 5 h _k, the duct cross-sectional area as a _k Then, next to the sound velocity at the end (corresponding to the 17th row, 19th row, 56th row) of the ducts (1st duct 41, 2nd duct 42, 3rd duct 43) connected to the branching / gathering portion 5. The time values _{ai and j + 1} are calculated from the following equation 13 when the current time value of the sound velocity is _{ai and j.}

Next, the mathematical formula 14 will be described. The next time value of the flow rate at the end (corresponding to the 17th row) of the duct (first duct 41) whose end is connected to the branching / gathering part 5 is first branched from the flow rate value at the current time at the end. Compressible fluid by multiplying the difference between the next time value of the sound velocity at the end connected to the collecting part 5 (calculated by Equation 13) and the current time value by twice the cross-sectional area of the duct (first duct 41). Subtract the value divided by the value obtained by subtracting 1 from the specific heat ratio γ of, and then multiply the end value of the current time at the end by the time step value of the analysis to the axial length step value of the duct (first duct 41). It is calculated from Equation 14 by adding the values divided by.

Specifically, the number k of the duct (first duct 41) to which the end (corresponding to the 17th column) is connected to the branch / assembly portion 5 is k = 1 to m, and the end value RE corresponding to this end is RE _k. (M is a natural number representing the number of ducts), if the axial length step value of the duct (first duct 41) connected to the branch / assembly portion 5 is expressed as h _k and the duct cross-sectional area _{is expressed as Ak} , the branch / assembly portion 5 _{The next time values qi and j + 1} of the flow rate at the end of the duct (first duct 41) to which the end (corresponding to the 17th row) is connected to are the current time values of the flow rate when the current time values of the flow rate are q _{i and j} . It is calculated from the following formula 14.

Next, the mathematical formula 15 will be described. The next time value of the flow rate at the start end (corresponding to the 19th and 56th rows) of the ducts (2nd duct 42, 3rd duct 43) whose start ends are connected to the branching / gathering portion 5 is the current value at the start end. The difference between the current time value and the next time value (calculated by Equation 13) of the sound velocity at the start end connected to the branching / gathering part 5 is the difference between the time flow value and the above ducts (second duct 42, third duct). 43) Multiply the duct cross-sectional area by 2 and add the value divided by the value obtained by subtracting 1 from the specific heat ratio γ of the compressible fluid, and then add the value obtained by subtracting 1 from the specific heat ratio γ of the compressible fluid. It is calculated by Equation 15 by multiplying the step value τ and subtracting the value divided by the axial length step value of the ducts (second duct 42, third duct 43).

Specifically, the number k of the ducts (second duct 42, third duct 43) to which the starting end (corresponding to the 19th row and the 56th row) is connected to the branching / gathering portion 5 is k = m + 1 to n, and this starting end. The starting value RS corresponding to is RS _k (where m and n are natural numbers representing the number of ducts), and the ducts connected to the branching / gathering part 5 (the shaft length increments of the second duct 42 and the third duct 43). h _k, if the duct cross-sectional area is denoted as _{a k,} beginning at the branch-collecting portion 5 in the beginning of the duct is connected (19 column, corresponding to 56 column) (second duct 42, the third duct 43) The next time values q _{i and j + 1} of the flow rate of the above are calculated by the following equation 15 when the current time values of the flow rate are q _{i and j.}

The above formula 13 is input to the cell in the fifth row corresponding to the time next to the initial time (fourth row) in the 17th, 19th, and 56th columns of the sound velocity value spreadsheet 45, and the sound velocity value is input. Then, the sound velocity value is calculated by being copied and input to each cell in the sixth and subsequent rows corresponding to the time after the next time, and the time history of the sound velocity value is the 17th column of the sound velocity value spreadsheet 45. Recorded in the 19th and 56th columns.

Similarly, Equation 14 corresponds to the 17th column of the flow rate spreadsheet 46, and Equation 15 corresponds to the time following the initial time (4th row) in the 19th and 56th columns of the flow rate spreadsheet 46. The flow rate value is calculated by being input to the cell in the 5th row, and then copied and input to each cell in the 6th and subsequent rows corresponding to the time after the next time to calculate the flow rate value. The history is recorded in the 17th, 19th and 56th columns of the flow rate spreadsheet 46.

The formula 13 input and recorded in each cell of the 17th column, the 19th column, and the 56th column of the sound velocity value spreadsheet 45 and the sound velocity value calculated by the formula 13 are displayed by the display means 15. Similarly, the formula 14 entered and recorded in each cell of the 17th column of the flow rate spreadsheet 46, the flow rate calculated from the formula 14, and each of the 19th and 56th columns of the flow rate spreadsheet 46. The formula 15 input and recorded in the cell and the flow rate value calculated by the formula 15 are displayed by the display means 15.

Here, the end connected to the branch / assembly portion 5 of the first duct 41 (corresponding to the 17th row) and the start end connected to the branch / assembly portion 5 of the second duct 42 and the third duct 43 (19th row, The time history of the pressure value in (corresponding to the 56th column) is converted by Equation 2 from the time history of the sound velocity in the 17th, 19th, and 56th columns of the sound velocity value spreadsheet 45. The time history is also provided so as to be displayable by the display means 15.

FIG. 20 shows the analysis result of the compressible fluid in the duct configured as described above by the pressure propagation analyzer 40. In FIG. 20, the inlet pressure X4 due to the pressure fluctuation δ at the start end of the first duct 41, the branch / gather part pressure Y4 at the branch / gather part 5, and the end pressure at the end 3 (closed end) of the second duct 42. Z4 and are displayed respectively. According to this analysis result, it can be seen that the terminal pressure Z4 is generated as a pressure larger than the inlet pressure X4 and the branching / gathering part pressure Y4.

Since it is configured as described above, according to the fourth embodiment, each part of the first duct 41 including the end connected to the branch / collecting part 5, and the second including the starting end connected to the branch / collecting part 5. The time history of the sound velocity value and the time history of the flow rate value of each part of the third duct 43 including the start end connected to each part of the duct 42 and the branching / gathering part 5 are the sound velocity value spreadsheet 45 including the calculation formula. It is recorded in each of the flow value spreadsheets 46 and can be displayed by the display means 15, and the time history of the pressure value is converted from the time history of the sound velocity value and can be displayed by the display means 15. The fourth embodiment also has the same effects as those of the first embodiment (1) and (2).

Although some embodiments of the present invention have been described above, these embodiments are presented as examples and are not intended to limit the scope of the invention. These embodiments can be implemented in various other forms, and various omissions, replacements, and changes can be made without departing from the gist of the invention, and their replacements and changes can be made. Is included in the scope and gist of the invention, and is also included in the invention described in the claims and the equivalent scope thereof.

For example, in each spreadsheet in the first to fourth embodiments, each part of the duct is set in the column direction and the time axis is set in the row direction, but each part of the duct is set in the row direction and the time is set in the column direction. You may set the axis and copy and enter the formula in the column direction cell where the time history of the pressure propagation parameter information is recorded. Further, the calculation formulas (mathematical expressions) of the calculation means 14, 26, 37, 47 in each embodiment can be displayed on the display means 15 even if they are not the spreadsheets 16, 17, 23, 24, 35, 36, 45, 46. Once configured, the analysis of pressure propagation can be easily verified by comparing these formulas.

1 ... duct, 2 ... start end (entrance), 4 ... cross-sectional area change part, 5 ... branch / assembly part, 10 ... pressure propagation analyzer, 11 ... duct specification recording spreadsheet (duct specification information recording means), 13 ... pressure Propagation parameter recording spreadsheet (pressure propagation parameter information recording means), 14 ... calculation means, 15 ... display means, 16 ... sound velocity value spreadsheet (sound velocity value information recording means), 17 ... flow value spreadsheet (flow value information recording means) ), 20 ... Pressure propagation analyzer, 21 ... Tunnel (duct), 22 ... High-speed moving body, 23 ... Sound velocity value spreadsheet (sound velocity value information recording means), 24 ... Flow value spreadsheet (flow value information recording means), 25 ... Pressure propagation parameter recording spreadsheet (pressure propagation parameter information recording means), 26 ... Calculation means, 30 ... Pressure propagation analyzer, 31 ... 1st duct, 32 ... 2nd duct, 33 ... Duct, 34 ... Duct specification recording Spreadsheet (duct specification information recording means), 35 ... Sound velocity value spreadsheet (sound velocity value information recording means), 36 ... Flow value spreadsheet (flow value information recording means), 37 ... Calculation means, 38 ... Pressure propagation parameter recording spread Sheet (pressure propagation parameter information recording means), 40 ... pressure propagation analyzer, 41 ... 1st duct, 42 ... 2nd duct, 43 ... 3rd duct, 44 ... duct specification recording spreadsheet (duct specification information recording means), 45 ... Sound velocity value spreadsheet (sound velocity value information recording means), 46 ... Flow value spreadsheet (flow value information recording means), 47 ... Calculation means, 48 ... Pressure propagation parameter recording spreadsheet (pressure propagation parameter information recording means)

Claims (12)

To calculate the propagation of the pressure wave generated by the change of the boundary condition at the end of the duct filled with the compressible fluid in the duct, and the change in the pressure and the flow rate of the compressible fluid in the duct. It is a pressure propagation analyzer for compressible fluid in the duct to be analyzed in
Duct specification information recording means for recording duct specification information of each part of the duct, and
A pressure propagation parameter information recording means for recording the time history of pressure propagation parameter information in each part of the duct, and
A calculation means for calculating the next time value of the pressure propagation parameter information by a calculation formula using the value of the duct specification information and the current time value of the pressure propagation parameter information.
A display means capable of displaying the calculation formula of the calculation means for different times, and a display means.
A pressure propagation analyzer for a compressible fluid in a duct, characterized in that it is configured with. The pressure propagation parameter information recording means is a sound velocity value information recording means that records the time history of the sound velocity value of each part of the duct as the time history of the pressure propagation parameter information, and the pressure propagation parameter information recording means that records the time history of the flow value of each part of the duct as the time history of the pressure propagation parameter information. Claim 1 is characterized in that it is configured to include a flow value information recording means for recording as a time history, and the time history of the sound velocity value is converted into a time history of a pressure value using a conversion formula. A pressure propagation analyzer for a compressible fluid in a duct according to. The duct specification information recording means and the pressure propagation parameter information recording means are spreadsheets of spreadsheet software having a plurality of cells set by a plurality of rows and columns.
In the spreadsheet of the duct specification information recording means, each part of the duct in which the duct is virtually divided in the axial direction is set in the column direction, duct specification information is set in the row direction, and the duct of each part of the duct is set in each cell. The value of the specification information is recorded,
In the spreadsheet of the pressure propagation parameter information recording means, each part of the duct in which the duct is virtually divided in the axial direction is set in the column direction, the time of the pressure propagation parameter information is set in the row direction, and the cell is described. The time history of the pressure propagation parameter information of each part of the duct is recorded.
The calculation formula of the calculation means is input and recorded in the cell for recording the next time value of the pressure propagation parameter information in the spreadsheet of the pressure propagation parameter information recording means, and is recorded, and the next time value of the pressure propagation parameter information is recorded. The pressure propagation analyzer for a compressible fluid in a duct according to claim 1 or 2, wherein the formula is a mathematical expression for calculating. In each of the spreadsheets of the duct specification information recording means and the pressure propagation parameter information recording means, the information of each part of the duct is continuously recorded in the column direction for each part of the duct having the same cross-sectional area, and the cross-sectional areas are different. The pressure of the compressible fluid in the duct according to claim 3, wherein the cross-sectional area changing portion of the duct or the collecting branch portion provided in the duct is configured to be recorded at intervals in the column direction. Propagation analyzer. In the duct specification information recorded in the duct specification information recording means, the virtual division length when the duct is virtually divided in the axial direction is recorded as the shaft length step value, and this shaft length step value is the time step of the analysis. The pressure propagation analyzer for a compressible fluid in a duct according to any one of claims 1 to 4, wherein the value is set to be larger than the product of the value and the sound velocity value at equilibrium of the compressible fluid. The next time value of the speed of sound of each part in the duct having the same cross-sectional area is
If it is not at the end of the duct, the specific heat ratio of the compressible fluid, the time step value, the axial length step value and the duct cross-sectional area as duct propagation information recorded in the same row in the spreadsheet of the duct specification information recording means. And the same row in the spreadsheet of the sound velocity information recording means, the same row in the spreadsheet of the flow rate information recording means, the same row in the spreadsheet of the flow rate information recording means, and the same row, one less row, and one more row. Calculated by a predetermined formula from the current velocity value of
When the flow rate value is set by the boundary condition at the start end of the duct, the specific heat ratio of the compressible fluid, the time step value, and the same row in the spreadsheet of the duct specification information recording means are recorded. The axial length step value and the duct cross-sectional area, the sound velocity value at the current time of the same row and one more row in the spreadsheet of the sound velocity value information recording means, and the same row of the spreadsheet of the flow rate value information recording means. And the flow velocity value at the current time in one more column, calculated by a predetermined formula,
When the flow rate value is set by the boundary condition at the end of the duct, the specific heat ratio of the compressible fluid, the time step value, and the same row in the spreadsheet of the duct specification information recording means are recorded. The axial length step value and the duct cross-sectional area, the sound velocity value at the current time of the same row and one less row in the spreadsheet of the sound velocity value information recording means, and the same row in the spreadsheet of the flow rate value information recording means. The pressure propagation of the compressible fluid in the duct according to any one of claims 3 to 5, characterized in that it is configured to be calculated by a predetermined mathematical expression from the flow velocity value at the current time in one less column. Analytical device. The next time value of the flow rate of each part in the duct having the same cross-sectional area is
If it is not at the end of the duct, the specific heat ratio of the compressible fluid, the time step value, the shaft length step value and the duct cross-sectional area as the duct specification information recorded in the same row in the spreadsheet of the duct specification information recording means. And the same row in the spreadsheet of the sound velocity information recording means, the same row in the spreadsheet of the flow rate information recording means, the same row in the spreadsheet of the flow rate information recording means, and the one more row. Calculated by a predetermined formula from the current velocity value of
When the sound velocity value is set by the boundary condition at the beginning of the duct, the specific heat ratio of the compressible fluid, the time step value, and the spreadsheet of the duct specification information recording means are recorded in the same row. The axial length step value and the duct cross-sectional area, the sound velocity value at the current time of the same row and one more row in the spreadsheet of the sound velocity value information recording means, and the same row and the same row in the spreadsheet of the flow rate value information recording means. It is calculated by a predetermined formula from the current velocity value of one more column at the current time.
When the sound velocity value is set by the boundary condition at the end of the duct, the specific heat ratio of the compressible fluid, the time step value, and the same row in the spreadsheet of the duct specification information recording means are recorded. The axial length step value and the duct cross-sectional area, the sound velocity value at the current time of the same row and one less row in the spreadsheet of the sound velocity value information recording means, and the same row in the spreadsheet of the flow rate value information recording means. The pressure propagation of the compressible fluid in the duct according to any one of claims 3 to 6, characterized in that it is configured to be calculated by a predetermined mathematical expression from the flow velocity value at the current time in one less column. Analytical device. The next time value of the speed of sound at the cross-sectional area change part of the duct having a different cross-sectional area is the specific heat ratio of the compressible fluid, the time step value, and the column excluding the same row and the empty row in the spreadsheet of the duct specification information recording means. Shaft length step value and duct cross-sectional area as duct specification information recorded in, the sound velocity value at the current time of the same row and the row excluding the empty row in the spreadsheet of the sound velocity value information recording means, and the flow rate value information recording means. Calculated by a predetermined formula from the flow rate value at the current time of the same column and the column excluding the empty column in the above spreadsheet.
Claims 4 to 7 are characterized in that the next time value of the sound velocity of each part of the duct having the same cross-sectional area among the ducts having different cross-sectional areas is configured to be calculated by the mathematical formula according to claim 6. The pressure propagation analyzer for the compressible fluid in the duct according to any one of the above items. The next time value of the flow rate at the cross-sectional area change part of the duct having a different cross-sectional area is the specific heat ratio of the compressible fluid, the time step value, and the column excluding the same row and the empty row in the spreadsheet of the duct specification information recording means. The shaft length step value and duct cross-sectional area as duct specification information recorded in, the sound velocity value at the current time of the same row and the row excluding the empty row in the spreadsheet of the sound velocity value information recording means, and the flow rate value information recording means. It is calculated by a predetermined formula from the current flow rate value of the same column and the column excluding the empty column in the spreadsheet.
Claims 4 to 8 are characterized in that the next time value of the flow rate of each part of the duct having the same cross-sectional area among the ducts having different cross-sectional areas is configured to be calculated by the mathematical formula according to claim 7. The pressure propagation analyzer for the compressible fluid in the duct according to any one of the above items. For the start end of the duct whose start end is connected to the branching / gathering portion, the specific heat ratio of the compressible fluid, the cross-sectional area of the duct, the current time value of the flow rate of the row corresponding to the start end, and the row corresponding to one downstream from the start end. Defines the start value RS calculated by a predetermined formula from the current time value of the flow rate, the current time value of the sound velocity in the column corresponding to the start end, and the current time value of the sound velocity in the column corresponding to one downstream from the start end. And
Regarding the end of the duct whose end is connected to the branch / assembly portion, the specific heat ratio of the compressible fluid, the cross-sectional area of the duct, the current time value of the flow rate of the row corresponding to the end, and one upstream from the end. The end value calculated by a predetermined formula from the current time value of the flow rate of the corresponding column, the current time value of the sound velocity of the column corresponding to the end, and the current time value of the sound velocity of the column corresponding one upstream from the end. Define RE,
The next time value of the speed of sound at the end of the duct connected to the branch / assembly is the sound velocity value at the current time at the end, and whether the end connected to the branch / assembly is the start or the end. The total cross-sectional area of the duct connected to the branch / assembly portion by adding the sum of the values obtained by dividing the start value RS and the end value RE at the current time defined by the end value by the axial length step value of the duct. It is calculated by dividing by 2 times the sum of the above, multiplying by the value obtained by subtracting 1 from the specific heat ratio of the compressible fluid, and then adding the value multiplied by the time step value.
The next time value of the sound velocity of each part of the duct having the same cross-sectional area other than the end part connected to the branching / gathering part is configured to be calculated by the mathematical formula according to claim 6. Item 6. The pressure propagation analyzer for a compressible fluid in a duct according to any one of Items 2 to 6. For the start end of the duct whose start end is connected to the branching / gathering portion, the specific heat ratio of the compressible fluid, the cross-sectional area of the duct, the current time value of the flow rate of the row corresponding to the start end, and the row corresponding to one downstream from the start end. Defines the start value RS calculated by a predetermined formula from the current time value of the flow rate, the current time value of the sound velocity in the column corresponding to the start end, and the current time value of the sound velocity in the column corresponding to one downstream from the start end. And
Regarding the end of the duct whose end is connected to the branch / assembly portion, the specific heat ratio of the compressible fluid, the cross-sectional area of the duct, the current time value of the flow rate of the row corresponding to the end, and one upstream from the end. The end value calculated by a predetermined formula from the current time value of the flow rate of the corresponding column, the current time value of the sound velocity of the column corresponding to the end, and the current time value of the sound velocity of the column corresponding one upstream from the end. Define RE,
Regarding the next time value of the flow rate at the end of the duct connected to the branching / gathering part
The next time value of the flow rate at the end of the duct to which the start end as the end is connected to the branch / assembly is the flow value at the current time at the end, and first to the branch / assembly. The difference between the next time value and the current time value of the speed of sound at the end to be connected is multiplied by twice the cross-sectional area of the duct and divided by the value obtained by subtracting 1 from the specific heat ratio, and then the current value is added. It is calculated by multiplying the start value RS of the time by the time step value and subtracting the value divided by the shaft length step value of the duct.
The next time value of the flow rate at the end of the duct to which the end as the end is connected to the branch / assembly is first connected to the branch / assembly from the current time flow value at the end. The difference between the next time value and the current time value of the speed of sound at the end is multiplied by twice the cross-sectional area of the duct and divided by the value obtained by subtracting 1 from the specific heat ratio, and then the value of the current time is subtracted. It is calculated by multiplying the end value RE by the time step value and adding the value divided by the shaft length step value of the duct.
The next time value of the flow rate of each part of the duct having the same cross-sectional area other than the end point connected to the branching / gathering part is configured to be calculated by the mathematical formula according to claim 7. The pressure propagation analyzer for a compressible fluid in a duct according to any one of items 2 to 5 and 7. To calculate the propagation of the pressure wave generated by the change of the boundary condition at the end of the duct filled with the compressible fluid in the duct, and the change in the pressure and the flow rate of the compressible fluid in the duct. It is a pressure propagation analysis method of the compressible fluid in the duct to be analyzed in
A duct specification information recording means for recording duct specification information of each part of the duct and a pressure propagation parameter information recording means for recording the time history of pressure propagation parameter information in each part of the duct are prepared.
In the pressure propagation parameter information recording means, the next time value of the pressure propagation parameter information is calculated by a calculation formula using the value of the duct specification information and the current time value of the pressure propagation parameter information, and this calculation formula. A method for analyzing pressure propagation of a compressible fluid in a duct, which comprises displaying.

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