JP7358211B2 - Pressure propagation analysis device for compressible fluid in ducts - Google Patents

Description

Embodiments of the present invention relate to an apparatus for analyzing pressure propagation of compressible fluid in a duct, which analyzes a phenomenon in which pressure waves propagate within a duct filled with compressible fluid.

When fluid flows in and out from one end of a duct system filled with compressible fluid (gas), such as air, or when pressure fluctuations are applied to one end, pressure waves propagate from one end to the other. The propagation of pressure waves in a duct is usually solved using a one-dimensional propagation equation in the axial direction of the duct.For example, if the flow velocity is less than 0.3 in Mach number, only the sound velocity is used in water hammer analysis. It can be approximated by treating an incompressible fluid with consideration of

However, when the flow velocity is Mach number 0.3 or higher, the sound speed 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 deforms 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 complex nonlinear partial differential equations using numerical methods, but for one-dimensional propagation, a method has been proposed in which the partial differential equations are ordinary differentiated and solved simply using the characteristic curve method. There is.

On the other hand, in the propagation of duct systems, it is necessary to handle cases such as when ducts branch or converge, and when ducts of different diameters are connected. Although specialized analysis software for performing such analysis is commercially available, the specific manner in which the analysis is performed is often not disclosed to the user. From the perspective of quality assurance of analysis, so-called V&V, which involves disclosing specific analysis procedures to verify whether the analysis was performed correctly (verification) and confirming the validity of the analysis results (validation), is important. It becomes necessary.

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

However, in the above-mentioned conventional technology, if a specific analysis procedure, such as a programmed code, is not disclosed, V&V is not easy to perform only by the user who created the model data. 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 effort required for V&V is not small.

The embodiments of the present invention have been made in consideration of the above-mentioned circumstances, and can easily verify whether the analysis of changes in pressure and flow rate in a duct filled with compressible fluid has been performed correctly. It is an object of the present invention to provide a pressure propagation analysis device for compressible fluid in a duct that allows easy confirmation of the validity of analysis results.

A pressure propagation analysis device for compressible fluid in a duct according to an embodiment of the present invention analyzes the propagation of a pressure wave within the duct that occurs due to a change in boundary conditions at the end of a duct filled with compressible fluid. A pressure propagation analysis device for a compressible fluid in a duct that performs analysis by calculating changes in the pressure and flow rate of the compressible fluid in the duct, and a duct specification information record that records duct specification information for each part of the duct. pressure propagation parameter information recording means for recording a time history of pressure propagation parameter information in each part of the duct; The present invention is characterized in that it includes a calculation means for calculating the next time value of the parameter information using a calculation formula, and a display means capable of displaying the calculation formula of the calculation means regarding a different time.

According to the embodiments of the present invention, it is possible to easily verify whether the analysis of changes in pressure and flow rate in a duct filled with compressible fluid has been performed correctly, and to easily confirm the validity of the analysis results.

FIG. 1 is a block diagram showing the configuration of a pressure propagation analysis device for compressible fluid in a duct according to a first embodiment. FIG. 2 is a model diagram showing a duct to be analyzed by the pressure propagation analysis device of FIG. 1. FIG. A diagram showing the structure of the duct specification record spreadsheet in FIG. 1. A chart showing the structure of the sound speed value spreadsheet in FIG. 1. FIG. 2 is a diagram showing the configuration of the flow rate value spreadsheet in FIG. 1. FIG. Part of the details of the duct specification record spreadsheet shown in FIG. 3 is shown, with (A) showing the inlet boundary conditions and (B) showing the outlet boundary conditions. 2 is a graph showing analysis results by the pressure propagation analysis device of FIG. 1. FIG. 7 is a model diagram showing a tunnel as a duct to be analyzed by the pressure propagation analysis device for compressible fluid in a duct according to the second embodiment, together with a high-speed moving body. (A) is a diagram showing a part of the flow rate value spreadsheet (inlet boundary conditions) in the pressure propagation analysis device of FIG. 8, and (B) is a diagram showing part of the sound velocity value spreadsheet ( Diagram showing exit boundary conditions). 7 is a graph showing analysis results by the pressure propagation analysis device of the second embodiment. FIG. 7 is a block diagram showing the configuration of a pressure propagation analysis device for compressible fluid in a duct according to a third embodiment. FIG. 12 is a model diagram showing a duct including a cross-sectional area changing portion, which is an analysis target of the pressure propagation analysis device of FIG. 11; FIG. 12 is a diagram showing the configuration of the duct specification record spreadsheet in FIG. 11. A chart showing the structure of the sound speed value spreadsheet in FIG. 11. 12 is a chart showing the configuration of the flow rate value spreadsheet of FIG. 11. 12 is a graph showing analysis results by the pressure propagation analysis device of FIG. 11. FIG. 7 is a block diagram showing the configuration of a pressure propagation analysis device for compressible fluid in a duct according to a fourth embodiment. FIG. 18 is a model diagram showing a duct with branching and gathering parts, which is an analysis target of the pressure propagation analysis device of FIG. 17; A chart showing the respective configurations of a duct specification record spreadsheet (FIG. 19(A)), a sound velocity value spreadsheet (FIG. 19(B)), and a flow rate value spreadsheet (FIG. 19(C)) in FIG. 17. 18 is a graph showing analysis results by the pressure propagation analysis device of FIG. 17.

EMBODIMENT OF THE INVENTION Hereinafter, the form for implementing this invention is demonstrated based on drawing.
[A] First embodiment (FIGS. 1 to 7)
FIG. 1 is a block diagram showing the configuration of a pressure propagation analysis device for compressible fluid in a duct according to a first embodiment. As shown in FIG. 2, the pressure propagation analysis device 10 for compressible fluid in a duct shown in FIG. The propagation of the pressure wave α generated by a change in the boundary condition at the end 3 (for example, the start end 2) within the duct 1 is analyzed by calculating the changes in the pressure and flow rate of the compressible fluid within the duct 1. , a duct specification recording spreadsheet 11 as a duct specification information recording means, a physical property value database 12, a pressure propagation parameter recording spreadsheet 13 as a pressure propagation parameter information recording means, a calculation means 14, and a display means 15. It is composed of:

As shown in FIG. 2, the duct 1 to be analyzed by the pressure propagation analysis device 10 is a single duct with a uniform cross-sectional area and no branching or gathering parts. This duct 1 has a duct length of 10 m, a terminal end 3 is a closed end, and a pressure wave α enters the duct 1 from a starting end 2 which is an open end. The inside of duct 1 is filled with air at room temperature and atmospheric pressure, and the sound velocity at equilibrium (equilibrium sound velocity) when no pressure wave α acts is 340 m/s, and the equilibrium pressure (equilibrium pressure) is 100 kPa. .

The duct specification record spreadsheet 11 records duct specification information for each part of the duct 1, as shown in FIG. It is a sheet. In other words, in the duct specification record spreadsheet 11, each part of the duct that is a virtual division of the duct 1 in the axial direction is set in the column direction, duct specification information is set in the row direction, and duct specification information of each part of the duct is set in each cell. The value is recorded.

The above duct specification information includes the axial coordinate value (axis coordinate) from the starting end 2 of the duct 1, the virtual division length (axial length step value) when the duct 1 is virtually divided in the axial direction, and the duct cross-sectional area. be. Specifically, the duct specification record spreadsheet 11 has the title in the first column, and each part (node ), the third line sets the axial coordinate value (axis coordinate value) from the starting end of the duct, the fourth line sets the axial length step value, and the fifth line sets the duct cross-sectional area.

Further, in the duct specification recording spreadsheet 11, the duct specification information for each part of the duct is recorded continuously in the column direction for each part of the duct 1 having the same cross-sectional area. In addition, the axial length step value recorded in the duct specification record spreadsheet 11 should be greater than the product of the time step value of the analysis and the equilibrium sound velocity in a compressible fluid to ensure the computational stability of the analysis. It is set large. The conditions for this axis length increment value are not limited to the first embodiment, but are the same 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 equilibrium sound velocity in the compressible fluid, and the equilibrium pressure. These values are taken into calculation means 14.

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

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

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

Further, the flow rate value spreadsheet 17 has a similar configuration to the sound speed value spreadsheet 16, and the analysis time (time axis) is shown from the 4th line of the first column, and the 4th line of these indicates the initial time (time axis). 0), the analysis time increases for each time step value from the 5th line onward. From the 2nd column to the 102nd column, the duct length 10m is virtually divided into 100 parts (nodes) with an axial length increment of 0.1m, and the flow rate values of each part of the duct at each analysis time are recorded in the cells of each row. configured to be used.

The calculation means 14 shown in FIG. Using the current time value of the pressure propagation parameter information (sonic velocity value, flow rate value) in the flow rate value spreadsheet 17), calculate the next time value (one hour from the current time value) of the pressure propagation parameter information (sonic 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 next time value by the increment value using a calculation formula.

In the sound velocity value spreadsheet 16, this calculation formula is input and recorded in the cell that records the next time value of the sound velocity value, and the next time value of the sound velocity value is calculated in this cell, and in the flow rate value spreadsheet 17, It is input and recorded in a cell that records the next time value of the flow rate value, and the next time value of the flow rate value is calculated within this cell. These calculation formulas are Equations 3 and 4 (described later) in the sound speed value spreadsheet 16 of the first embodiment, and Equations 5 and 6 (described later) in the flow rate value spreadsheet 17 of the first embodiment. .

The display means 15 displays the calculation formulas of the calculation means 14 regarding different times, that is, the calculation formulas input into each cell from the 5th line onward of the sound speed value spreadsheet 16 and the flow rate value spreadsheet 17. It is possible to display the time history of the sound velocity value and flow rate value recorded in each row.
Next, the sound speed value spreadsheet 16 shown in FIG. 4 and the flow rate value spreadsheet 17 shown in FIG. 5 will be explained in more detail.
The 2nd column to the 102nd column in the 4th row of the sound velocity value spreadsheet 16 and the flow rate value spreadsheet 17 are in the initial state. In this example, since the state is before the pressure wave α enters the duct 1, the sound speed value is set to the sound speed value in the equilibrium state (sound speed at equilibrium is 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 speed value spreadsheet 16 is the entrance boundary condition, which is also shown in FIG. 6(A). In this example, the time history of pressure values is originally set, but the pressure values are converted to sound speed values using Equation 1, which expresses the relationship between pressure and sound speed under isentropic conditions in a compressible fluid. The values are set in the sound velocity 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 expressed as Note that the equilibrium pressure is approximately 100 kPa at room temperature and atmospheric pressure.

Furthermore, the 102nd column (terminus) of the flow rate value spreadsheet 17 is the closed end, and the flow rate value is set to zero. In other words, this outlet boundary condition is expressed by a flow rate value of zero, as also shown in FIG. 6(B).

Next, the formula set in the fifth line (next time) after the fourth line representing the initial time in the sound speed value spreadsheet 16 and the flow rate value spreadsheet 17 will be explained.
In the sound speed value spreadsheet 16, the boundary conditions are set in the second column as described above, but for the third to 101st columns, which correspond to the parts that are not the ends of the duct 1, the column numbers are indicated by the subscript i, The number of rows is represented by the subscript j, and if i=3 to 101 and j=4, then the sound speed value a _i,j+ of the 5th row (next time) of the 3rd column to the 101st column that is not at the end of duct 1 ₁ is the current time sound speed values a _i-1,j , a _i,j , a _i+1,j and the current time flow values q _i-1,j , q _i,j , q _i+1,j is set using the following equation 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 axial length step value, and is set with reference to the duct specification record spreadsheet 11. τ is the time step value of 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 formulas of each embodiment input into the sound speed value spreadsheet and the flow rate value spreadsheet.

As mentioned above, the sound velocity value in the 5th row of the 3rd column to the 101st column that is not at the end of duct 1 is the sound velocity value and flow rate value of the same column in the 4th row, one upstream column, and one downstream column. Calculated from.

Furthermore, since the flow rate value in the 102nd column is set as the exit boundary condition, the sound velocity value in the 5th row (next time) of the 102nd column, which corresponds to the terminal end, is calculated using the following equation 4 using that information. Set. Here, the subscript N indicates the end (102nd column), and N-1 indicates the 101st column.

In other words, the next time value of the sound velocity at each part in the duct 1 with the same cross-sectional area is the specific heat of the compressible fluid in the part other than the end of the duct 1 (columns 3 to 101 in the sound velocity value spreadsheet 16). The ratio γ, the analysis time step value τ, the axial length step value h and the duct cross-sectional area A recorded in the same column of the duct specification record spreadsheet 11, and the same column and one less column (upstream) of the sound velocity value spreadsheet 16. sound velocity values at the current time in the column) and one more column (downstream column), and flow rate values at the current time in the same column, one less column (upstream column), and one more column (downstream column) of flow rate value spreadsheet 17 It is calculated using Equation 3 above.

In addition, the next time value of the sound speed at the terminal end 3 (column 102 in the sound speed value spreadsheet 16) in the duct 1, which has the same cross-sectional area, is determined by the flow rate value set using the exit boundary condition as shown in FIG. 6(B). In the case of From the current time sound speed values in the same row and one less column (upstream row) of the sheet 16 and the current time flow values in the same row and one less column (upstream row) of the flow rate value spreadsheet 17, the above formula 4 is calculated. 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 3rd to 101st columns corresponding to the parts other than the ends of the duct 1 in the flow rate value spreadsheet 17, the column number is represented by the subscript i, and the row number is represented by the subscript j, where i=3 to 101. , j=4, the flow rate value q _i,j+1 in the 5th row (next time) of the 3rd column to the 101st column is the sound speed value a _i-1,j , a _i,j , It is set using 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 that is not at the end of duct 1 is calculated from the sound speed value and flow rate value in the same column of the 4th row, one upstream column, and one downstream column. be done.

In addition, the flow rate value in the 5th row (next time) of the 2nd column, which corresponds to starting point 2, is calculated using the following formula 6, since the sound velocity value in the 2nd column is set in the inlet boundary condition. is set.

In other words, the next time value of the flow rate of each part in the duct 1 with the same cross-sectional area will be the value of the compressible fluid if it is not at the end of the duct 1 (columns 3 to 101 in the flow rate value spreadsheet 17). The specific heat ratio γ, the analysis time step value τ, the axial length step value h and the duct cross-sectional area A recorded in the same column of the duct specification record spreadsheet 11, and the same column and one less column of the sound speed value spreadsheet 16 ( The sound speed values at the current time in the upstream column) and one more column (downstream column), and the flow rate at the current time in the same column, one less column (upstream column), and one more column (downstream column) of the flow rate value spreadsheet 17 The value is calculated using Equation 5 above.

In addition, the next time value of the flow rate at the starting end 2 (second column in the flow rate value spreadsheet 17) in the duct 1, which has the same cross-sectional area, is set so that the sound velocity value is set according to the exit boundary condition, as shown in FIG. 6(A). In the case of From the sound velocity values at the current time in the same row and one more column (downstream row) of the sheet 16 and the flow rate values at the current time in the same row and one more column (downstream column) of the flow rate value spreadsheet 17, the above formula 6 is calculated. Calculated using

As described above, all the values in the fifth row of the sound velocity value spreadsheet 16 and the flow rate value spreadsheet 17 have been set. In the above explanation, the subscript j is used for the row direction, and by setting the same formula for the 5th line for the 6th and subsequent lines, the values for the 6th and subsequent lines can be calculated. 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 onwards can be done by copying the formula for each line. The speed of sound value and the flow rate value can be easily calculated.

FIG. 7 shows the analysis results obtained by the pressure propagation analysis apparatus 10 of the first embodiment analyzed in this way. The inlet pressure X1, the intermediate pressure Y1, and the end pressure Z1 shown in FIG. ing. Although pressure values are shown in FIG. 7, the time history of the sound speed values analyzed using the sound speed value spreadsheet 16 is converted into pressure values using Equation 2. As can be seen from FIG. 7, the rise of the waveform of the pressure wave α becomes steeper as it propagates downstream.

In the pressure propagation analysis device 10 for compressible fluid in a duct configured as described above, first, initial conditions are input in the fourth row of each of the sound speed value spreadsheet 16 and the flow rate value spreadsheet 17, and the sound speed value spreadsheet 16, the inlet boundary condition is entered in the second column corresponding to the starting end 2 of the duct 1, and the outlet boundary condition is entered in the 102nd column corresponding to the ending end 3 of the duct 1 in the flow rate value spreadsheet 17.

Next, in the sound speed value spreadsheet 16 and the flow rate value spreadsheet 17, input the formula for calculating the next time value into the cell in the 5th row, which corresponds to the time after the initial time (4th row), and The next time value of the flow rate value is calculated, and this next time value is recorded in the cell in the fifth row.
Here, in the duct specification record spreadsheet 11, the sound velocity value spreadsheet 16, and the flow rate value spreadsheet 17, the same parts of the duct 1 are set to be in the same column, and the sound velocity value spreadsheet 16 and the flow rate value spreadsheet 17, information of the same time is set in the same line.

Therefore, next, the formulas entered in the cells in the 5th row corresponding to the time following the initial time as described above are copied all at once to each cell in the 6th row and subsequent rows corresponding to the time after that. The sound velocity value and the flow rate value at each of these times are calculated and recorded in each cell from the 6th row onward. Thereafter, the sound speed values recorded in each cell of the sound speed value spreadsheet 16 are converted into pressure values using Equation 2.

As configured as above, the first embodiment provides the following effects (1) and (2).
(1) As shown in FIGS. 4 and 5, the calculation formulas for sound speed value analysis (Formula 3, Formula 4) and the sound speed values determined by these calculation formulas are input into the cells of the sound speed value spreadsheet 16. Further, in the cells of the flow rate value spreadsheet 17, calculation formulas for flow rate value analysis (Formula 5, Formula 6) and the flow rate values determined by these calculation formulas are input and recorded. For this reason, since all the pressure propagation analysis processes are clearly shown in the sound velocity value spreadsheet 16 and the flow rate value spreadsheet 17, the information is entered in the same row in each of the sound velocity value spreadsheet 16 and the flow rate value spreadsheet 17. Verify that the formula entered in the cell in the 5th row, which corresponds to the next time after the initial time (4th row), is accurate, and then compare the formulas entered in the next cell after the initial time (4th row). Confirm that the data has been copied to the cells in each row from the 6th row onward, which corresponds to the time after. As a result, by converting the sound velocity value in duct 1 into a pressure value using the conversion formula (Equation 2) without using a special programming language, it was confirmed that the changes in pressure and flow rate in duct 1 were correctly analyzed. can be easily verified.

(2) The pressure value converted from the sound velocity value recorded in each cell of the sound velocity value spreadsheet 16 and the flow rate value recorded in each cell of the flow rate value spreadsheet 17 are appropriately graphed and displayed in a waveform. Thus, the validity of the analysis results of the pressure propagation analysis device 10 for 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 analysis device for compressible fluid in a duct according to the second embodiment, together with a high-speed moving body. In this second embodiment, the same parts as in the first embodiment are given the same reference numerals as those in the first embodiment to simplify or omit the explanation.

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

In the duct specification record spreadsheet 11, the sound velocity value spreadsheet 23, and the flow rate value spreadsheet 24, the length of the tunnel 21 is virtually divided in the column direction by the axial length step value h, as in the first embodiment. Each part is set. Further, in the sound speed value spreadsheet 23 and the flow rate value spreadsheet 24, the time axes are set in the row direction using the analysis time step value τ, as in the first embodiment. In the sound speed value spreadsheet 23 and flow rate value spreadsheet 24 of the second embodiment, the inlet boundary condition is set as a flow rate value corresponding to the speed of the high-speed moving object 22, as shown in FIG. 9(A). In addition, the exit boundary condition is that the exit (terminal end 3) of the tunnel 21 is an open end and the pressure is constant (atmospheric pressure), so as shown in FIG. constant).

In addition, the calculation formula of the calculation means 26 for calculating the next time values of the sound speed value and the flow rate value is the sound speed of each part of the tunnel 21 other than the end (corresponding to the 3rd column to the 101st column of the sound speed value spreadsheet 23). Equation 3 is used to calculate the next time value of the flow rate, and Equation 5 is used to calculate the next time value of the flow rate at each part of the tunnel 21 that is not the end (columns 3 to 101 of the flow rate value spreadsheet 24). used. Further, as the calculation formula of the calculation means 26, Formula 7 (described later) is used to calculate the next time value of the sound speed value at the starting point of the tunnel 21 (corresponding to the second column of the sound speed value spreadsheet 23). Equation 8 (described later) is used to calculate the next time value of the flow rate at the terminal end 3 (column 102 of the flow rate value spreadsheet 24).

Next, Equation 7 above will be described. When the flow rate value is set using the exit boundary condition as shown in FIG. 9(A), the next time value of the sound velocity at the starting end 2 in the tunnel 21 with the same cross-sectional area is determined by the specific heat ratio γ of the compressible fluid. , the analysis time step value τ, the axial length step value h and tunnel cross-sectional area A recorded in the same column of the duct specification record spreadsheet 11, and the same column and one more column (downstream column) of the sound velocity value spreadsheet 23. is calculated from the sound speed value at the current time and the current time value in the same column and one more column (downstream column) of the flow rate value spreadsheet 24 using Equation 7.

Specifically, the next time value _a2,j+1 of the sound speed at the starting end 2 in the tunnel 21 (corresponding to the second column of the sound speed value spreadsheet 23) is the sound speed value a2 _{,j at the starting end 2} at the current time and the flow rate. The value q _2,j , the sound velocity value a _3,j and the flow rate value q _3, j of one row downstream of the starting point 2 at the current time, and the flow rate value of the starting point 2 at the next time (the inlet boundary in Fig. 9 (A) Condition) It is calculated by the following formula 7 using q2 _{and j+1} .

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

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

The above formulas 3 and 7 are input into the cell in the 5th row corresponding to the time after the initial time (4th row) in the sound speed value spreadsheet 23 to calculate the sound speed value, and then the exit boundary condition is calculated. The sound speed values are calculated by copying and inputting them into each cell from the 6th row onward corresponding to the next time onwards, and the time history of the sound speed values is recorded in the sound speed value spreadsheet 23. Similarly, Equations 5 and 8 above are input into the cell in the 5th row corresponding to the time following the initial time (4th row) in the flow rate value spreadsheet 24 to calculate the flow value, and then the inlet Except for the boundary conditions, a plurality of values are input into each cell from the 6th row onward corresponding to the next time onward to calculate the flow rate value, and the time history of the flow rate value is recorded in the flow rate value spreadsheet 24.

Equations 3 and 7 entered and recorded in each cell of the sound speed value spreadsheet 23 and the sound speed values calculated using these equations are displayed by the display means 25. Similarly, Equations 5 and 8 input and recorded in each cell of the flow rate value spreadsheet 24 and the flow rate values calculated by these equations are displayed on the display means 15. Here, the time history of the pressure value is converted from the time history of the sound velocity value using Equation 2, and the time history of the pressure value is also provided so as to be displayed by the display means 15.

FIG. 10 shows the analysis results obtained by the pressure propagation analysis device 20 configured as described above. In FIG. 10, the respective time histories of the inlet pressure X2 and inlet flow rate UX at the entrance (starting end 2) of the tunnel 21, and the intermediate part pressure Y2 and intermediate part flow rate UY at the axially intermediate part of the tunnel 21 are analyzed. 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.

As configured as described above, according to the pressure propagation analysis device 20 for compressible fluid in a duct according to the second embodiment, the time history of the sound velocity value and the time history of the flow rate value at each part of the tunnel 21 are as follows. The calculation formulas are recorded in the sound speed value spreadsheet 23 and the flow rate value spreadsheet 24, respectively, 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 speed value and displayed on the display means 15. Therefore, the second embodiment also provides effects similar to effects (1) and (2) of the first embodiment.

[C] Third embodiment (FIGS. 11 to 16)
FIG. 11 is a block diagram showing the configuration of a pressure propagation analysis device for compressible fluid in a duct according to a third embodiment. Moreover, FIG. 12 is a model diagram showing a duct provided with a cross-sectional area changing portion, which is an analysis target of the pressure propagation analysis device of FIG. 11. In the third embodiment, the same parts as in the first embodiment are given the same reference numerals as in the first embodiment, so that the explanation will be simplified or omitted.

As shown in FIG. 12, the pressure propagation analysis device 30 for compressible fluid in a duct according to the third embodiment includes, for example, a cross-sectional area changing portion 4 in the axially intermediate portion, with a starting end 2 being an open end and a terminal end 3 being a closed end. When a pressure fluctuation β occurs at the starting end (inlet) 2 of the duct 33, which is the end, the propagation of the pressure wave α generated within the duct 33 is calculated by calculating the change in pressure and flow rate of the compressible fluid within the duct 33. This is what we analyze. This pressure propagation analysis device 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 rate value spreadsheet 36 (FIG. 15) as a flow rate value information recording means, a calculation means 37, and a display means 15. The sound velocity value spreadsheet 35 and the flow rate value spreadsheet 36 constitute a pressure propagation parameter recording spreadsheet 38 as 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 starting end 2 to the cross-sectional area changing part 4, and the second duct 32 is from the cross-sectional area changing part 4 to the terminal end 3, the cross-sectional area A2 of the second duct 32 is the first duct. When the cross-sectional area A1 of the first duct 31 and the cross-sectional area A2 of the second duct 32 are approximately the same (FIG. 12A), for example, 12(B)) and a case where the cross-sectional area A2 of the second duct 32 is, for example, four times larger than the cross-sectional area A1 of the first duct 31 (FIG. 12(C)). Note that the terminal end of the first duct 31 and the starting end of the second duct 32 are assumed to overlap.

As shown in FIGS. 13 to 15, in the duct specification record 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 part 4 of the duct 33 (52nd column ) and the starting end of the second duct (corresponding to the 54th column) are set separately, and the cross-sectional area changing part 4 is set at intervals in the column direction of each spreadsheet to distinguish it from other parts of the duct 33. is set as an empty column (column 53 of each spreadsheet). Furthermore, in the duct specification record spreadsheet 34, the sound speed value spreadsheet 35, and the flow rate value spreadsheet 36, the duct length of the first duct 31, 2.5 m, is virtually divided in axial length increments of 0.05 m, and from the second row Each part of the first duct 31 is set up to the 52nd column. Similarly, the duct length of 2.5 m of the second duct 32 is virtually divided into axial length increments of 0.05 m, and each part of the second duct 32 is set from the 54th column to the 104th column (not shown). .

In the sound speed value spreadsheet 35 and the flow rate value spreadsheet 36, time axes are set in the row direction by the time step value τ for analysis, and the initial state is recorded in the cell in the fourth row (initial time). In addition, from the fifth line onwards in each of the sound speed value spreadsheet 35 and the flow rate value spreadsheet 36, time histories of the sound speed values and the flow rate values are recorded. Furthermore, although not shown, the inlet boundary condition set in the second column of the sound velocity value spreadsheet 35 and the outlet boundary condition set in the 104th column (N column) of the flow rate value spreadsheet 36 are The settings are the same as in the first embodiment (FIG. 6).

The calculation formula of the calculation means 37 for calculating the next time values of the sound velocity and flow rate is based on the sound velocity and flow rate of each part of the duct 33 having the same cross-sectional area, excluding the cross-sectional area changing part 4, among the ducts 33 having different cross-sectional areas. For calculating the next time value of each of Equations 3, 4, and 7, as well as Equations 5, 6, and 8 of the first and second embodiments are used to calculate the next time values of the sound velocity and flow rate.

Further, as the calculation formula of the calculation means 37, Formula 9-1 (described later) is used to calculate the next time value of the sound velocity at the end of the first duct 31 (corresponding to the 52nd column); Equation 10-1 (described later) is used to calculate the next time value of the flow rate (corresponding to the 52nd column). Note that the sound velocity at the starting end of the second duct 32 (corresponding to the 54th row) is equal to the sound velocity at the terminal end of the first duct 31 (corresponding to the 52nd row) at the same time, and the flow rate at the starting end of the second duct 32 is equal to the flow rate at the end of the first duct 31 at the same time. If these are expressed numerically, the calculation formula 37 is the formula 9-2 (described later) used to calculate the next time value of the sound speed at the starting end of the second duct 32 (corresponding to the 54th column). Equation 10-2 (described later) is used to calculate the next time value of the flow rate at the starting end of the second duct 32 (corresponding to the 54th column).

Next, the above equations 9-1 and 9-2 will be described. The next time value of the sound velocity in the cross-sectional area changing unit 4 of the duct 33 having a different cross-sectional area is determined by the specific heat ratio γ of the compressible fluid, the time step value τ of the analysis, and the same column and empty column ( For example, the axial length step value h and duct cross-sectional area A1, A2 recorded in the column excluding the 53rd column) and the sound speed at the current time in the same column of the spreadsheet 35 and the column excluding the empty column (for example, the 53rd column) 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 rate 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 _A1 is the duct cross-sectional area of the first duct 31. , _A2 is the duct cross-sectional area of the second duct 32, then the sound speed value at the 52nd column and 5th row (next time value) corresponding to the end of the first duct 31 is as follows, assuming i=52 and j=4. It is calculated using the following formula 9-1.

In addition, the sound speed value in the fifth row, which is the next time value in the 54th column corresponding to the starting end of the second duct 32, is calculated using the following equation 9-2 with i=54.

Next, the aforementioned equations 10-1 and 10-2 will be described. The next time value of the flow rate in the cross-sectional area changing unit 4 of the duct 33 having a different cross-sectional area is determined based on the specific heat ratio γ of the compressible fluid, the time step value τ of the analysis, and the same column and empty column of the duct specification record spreadsheet 34 ( For example, the axial length step value h and duct cross-sectional area A1, A2 recorded in the column excluding the 53rd column) and the sound speed at the current time in the same column of the spreadsheet 35 and the column excluding the empty column (for example, the 53rd column) It is calculated by Equation 10-1 and Equation 10-2 using the flow rate value and the flow rate value at the current time in the columns of the flow rate value spreadsheet 36 excluding the same column and the empty column (for example, the 35th column).

Specifically, the first subscript is the column number (denoted by i), the second subscript is the row number indicating the time history (denoted by j), _A1 is the cross-sectional area of the first duct 31, When 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 starting end of the first duct 31, is calculated using the following equation 10-1.

Further, the flow rate value in the 5th row, which is the next time value in the 54th column corresponding to the starting end of the second duct 32, is calculated using the following equation 10-2 with i=54.

The above-mentioned formulas 9-1 and 9-2 are input into the cell in the 5th row corresponding to the time following the initial time (4th row) in the sound speed value spreadsheet 35 to calculate the sound speed value, and then , is copied and input into each cell from the 6th row onward corresponding to the next time onwards, and the sound velocity value is calculated, and the time history of the sound velocity value is recorded in the sound velocity value spreadsheet 35. Similarly, formulas 10-1 and 10-2 are input into the cell in the fifth row corresponding to the time after the initial time (fourth row) in the flow rate value spreadsheet 36 to calculate the flow rate value, and then Then, it is copied and input into each cell from the 6th row onward corresponding to the next time onwards, and the flow rate value is calculated, and the time history of the flow rate value is recorded in the flow rate value spreadsheet 36.

Equations 9-1 and 9-2 input and recorded in each cell of the sound speed value spreadsheet 35 and the sound speed values calculated using these equations are displayed on the display means 15. Similarly, the numerical formulas 10-1 and 10-2 input and recorded in each cell of the flow rate value spreadsheet 36 and the flow rate values calculated by these formulas are displayed on the display means 15. Here, the time history of the pressure value is converted from the time history of the sound velocity value using Equation 2, and the time history of the pressure value is also provided so as to be displayed by the display means 15.

FIG. 16 shows an analysis result by the pressure propagation analysis device 30 for compressible fluid in a duct configured as described above. In FIG. 16, the terminal end 3 (closed end) of the duct 33 has a cross-sectional area _A2 of the second duct 32 that is 1/4 times smaller than the cross-sectional area _A1 of the first duct 31 for the same inlet pressure X3. and the terminal pressure Y3-2 at the terminal end 3 (closed end) of the duct 33 where the cross-sectional area _A2 of the second duct 32 is approximately the same as the cross-sectional area _A1 of the first duct 31. , and the terminal pressure Y3-3 at the terminal end 3 (closed end) of the duct 33, where the cross-sectional area _A2 of the second duct 32 is four times larger than the cross-sectional area _A1 of the first duct 31 are shown. . According to this analysis result, it can be seen that a large pressure is generated in the duct 33 where the cross-sectional area _A2 of the second duct 32 is smaller than the cross-sectional area _A1 of the first duct 31.

As configured as above, according to the pressure propagation analysis device 30 for compressible fluid in a duct according to the third embodiment, the duct 33 including the terminal end of the first duct 31 and the terminal end of the second duct 32 can be The time history of the sound velocity value and the time history of the flow rate value of each part, including the calculation formula, are recorded in the sound velocity value spreadsheet 35 and the flow rate value spreadsheet 36, respectively, and can be displayed by the display means 15. Since the time history of the value is converted from the time history of the sound velocity value and is provided to be displayed by the display means 15, the third embodiment also has the same effects as effects (1) and (2) of the first embodiment. play.

[D] Fourth embodiment (FIGS. 17 to 20)
FIG. 17 is a block diagram showing the configuration of a pressure propagation analysis device for compressible fluid in a duct according to a fourth embodiment. Moreover, FIG. 18 is a model diagram showing a duct provided with branching and converging parts, which is an analysis target of the pressure propagation analysis device of FIG. 17. In the fourth embodiment, the same parts as in the first embodiment are given the same reference numerals as in the first embodiment to simplify or omit the explanation.

The compressible fluid pressure propagation analysis device 40 of the fourth embodiment has a pressure fluctuation indicated by an inlet pressure When δ occurs, the propagation of the pressure wave α generated within the duct system 6 is analyzed by calculating changes in the pressure and flow rate of the compressible fluid within the duct system 6. This pressure propagation analysis device 40 includes a duct specification recording spreadsheet 44 (FIG. 19A) 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 rate value spreadsheet 46 (FIG. 19(C)) as a flow rate 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 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 , and has a starting end 2 as an open end and a terminal end 3 as a closed end. A third duct 43 is branched and attached at a position 3 m from the starting end 2 of this duct 1, and therefore a branch/gathering part 5 is formed at this attachment position. In the duct 1, the part from the starting end 2 to the branching/collecting part 5 to which the third duct 43 is attached is called a first duct 41, and the part from the branching/collecting part 5 to the terminal end 3 is called 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 an open end.

As shown in FIGS. 19A, 19B, and 19C, the duct specification record spreadsheet 44, sound velocity value spreadsheet 45, and flow rate value spreadsheet 46 show the duct length of the first duct 41 in the column direction. Each part of the first duct 44 is set in the 2nd to 17th rows by virtual division by axial length increments (for example, 0.2 m), and one empty row is provided to determine the duct length of the second duct 42. is virtually divided into axial length increments (for example, 0.2 m), each part of the second duct 42 is set from the 19th row to the 54th row, and one empty row is provided, and the duct of the third duct 43 is set. The length is virtually divided by axial length increments (for example, 0.2 m), and each part of the third duct 43 is set from the 56th column to the 81st column (not shown).

In the duct specification record spreadsheet 44, the sound velocity value spreadsheet 45, and the flow rate value spreadsheet 46, the branching/converging parts 5 provided in the duct system 6 are spaced apart in the row direction, that is, the empty rows (the 18th row and 55th column). The ends of the ducts connected to this branching/gathering part 5 are the terminal end of the first duct 41 (corresponding to the 17th row), the starting end of the second duct 42 (corresponding to the 19th row), and the end of the third duct 41 43 (corresponding to the 56th column).

In the sound speed value spreadsheet 45 and the flow rate value spreadsheet 46, time axes are set in the row direction by the time step value τ for analysis, and the initial state is recorded in the cell in the fourth row (initial time). Further, from the fifth line onwards in each of the sound speed value spreadsheet 45 and the flow rate value spreadsheet 46, time histories of the sound speed values and the flow rate values are recorded.

The calculation formula of the calculation means 47 for calculating the next time values of the sound velocity and flow rate is based on the ends connected to the branching/converging section 5 (the terminal end of the first duct 41, the starting end of the second duct 42, and the starting end of the third duct 43). For calculating the next time values of the sound speed and flow rate of each part of the first duct 41, second duct 42, and third duct 43 having the same cross-sectional area except for 3, Equations 4 and 7, and Equations 5, 6, and 8 for flow rate calculation are used.

Further, as the calculation formula of the calculation means 47, Equation 12 is used to calculate the starting end value RS for the starting end of the duct whose starting end is connected to the branching/collecting part 5, and the above formula of the duct whose terminal end is connected to the branching/collecting part 5. For the termination, Equation 11 is used to calculate the termination value RE. Furthermore, 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/converging part (starting end of the second duct 42 and third duct 43, and terminal end of the first duct 41). Equation 13 is used for . Further, as the calculation formula of the calculation means 47, Formula 15 is used to calculate the next time value of the flow rate at the starting ends of the second duct 42 and the third duct 43 whose starting ends are connected to the branching/converging part 5, and Equation 14 is used to calculate the next time value of the flow rate at the terminal end of the first duct 41 whose terminal end is connected to the collecting section 5.

Next, Equation 11 will be described. Regarding the terminal end (corresponding to the 17th row) of the duct (first duct 41) whose terminal end is connected to the branching/collecting part 5, the specific heat ratio γ of the compressible fluid, the duct cross-sectional area A, the row (17th column) corresponding to the terminal end the current time value of the flow rate in the column (column 16) corresponding to one upstream from the termination point, the current time value of the speed of sound in the column (column 17) corresponding to the termination point, Using the current time value of the sound speed in the column (16th column) corresponding to one upstream from the termination point, the current time value of the termination value RE is calculated according to Equation 11.

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 terminal end (corresponding to the 17th column) of the duct (first duct 41) whose terminal end is connected to the branch/collection section 5, the terminal value RE at the current time of this terminal terminal is calculated using the following formula 11. do.

here,
q _N : Flow rate value at the current time at the terminal a _N : Sound velocity value at the current time at the terminal q _N1 ; Flow rate value at the current time at the node one upstream from the terminal a _N1 ; Sound speed value at the node at the current time

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

here,
q ₁ : Flow rate value at the current time at the starting point a ₁ : Sound velocity value at the current time at the starting point q ₂ ; Flow rate value at the current time at the node one position downstream from the starting point a ₂ ; Sound speed value at the node at the current time

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

Next, Equation 13 will be described. The next time value of the sound velocity at the ends (corresponding to the 17th, 19th, and 56th columns) of the ducts (first duct 41, second duct 42, and third duct 43) connected to the branch/converge section 5 is , the starting end value RS and the ending end value RE at the current time, which are defined depending on whether the end connected to the branching/converging part 5 is the starting end or the ending end, are added to the sound speed value at the current time at this end (the first duct 41 , the second duct 42, and the third duct 43) divided by the axial length increment value h, and then divide the sum by twice the sum of the cross-sectional areas A of the ducts connected to the branching/converging part 5. , is calculated from Equation 13 by multiplying by a value obtained by subtracting 1 from the specific heat ratio γ of the compressible fluid, and then adding a value obtained by further multiplying by the analysis time step value τ.

Specifically, the number k of the duct (first duct 41) whose terminal end (corresponding to the 17th column) connects to the branching/gathering part 5 is k=1 to m, and the terminal value RE corresponding to this terminal end is RE _k , the number k of the duct (second duct 42, third duct 43) whose starting end (corresponding to the 19th column, 56th column) connects to the branching/gathering part 5 is k=m+1~n, the starting end corresponding to this starting end The value RS is expressed as RS _k (here, m and n are natural numbers representing the number of ducts), the axial length step value of each duct connected to the branching/converging part 5 is expressed as h _k , and the duct cross-sectional area is expressed as A _k Then, the speed of sound at the ends (corresponding to the 17th, 19th, and 56th columns) of the ducts (first duct 41, second duct 42, and third duct 43) connected to the branching/converging part 5 is The time value a _i,j+1 is calculated from the following equation 13, where the current time value of the speed of sound is a _i,j .

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

Specifically, the number k of the duct (first duct 41) whose terminal end (corresponding to the 17th column) connects to the branching/gathering part 5 is k=1 to m, and the terminal value RE corresponding to this terminal end is RE _k (m is a natural number representing the number of ducts), the axial length step value of the duct (first duct 41) connected to the branching/converging section 5 is expressed as h _k , and the duct cross-sectional area is expressed as A _k , then the branching/converging section 5 The next time value q _{i, j+1} of the flow rate at the above terminal end of the duct (first duct 41) whose terminal end (corresponding to the 17th column) is connected to is, when the current time value of the flow rate is q _{i, j} . It is calculated using the following formula 14.

Next, Equation 15 will be described. The next time value of the flow rate at the starting ends (corresponding to the 19th and 56th columns) of the ducts (second duct 42, third duct 43) whose starting ends are connected to the branch/collection section 5 is the current value at the starting end. First, the difference between the current time value and the next time value of the sound velocity at the starting end connected to the branch/converge part 5 (calculated using formula 13) is calculated based on the flow rate value at the time. 43) is multiplied by twice the duct cross-sectional area and divided by the specific heat ratio γ of the compressible fluid minus 1, and then the analysis time is added to the starting point value RS at the current time at the starting point. It is calculated by Equation 15 by multiplying by the step value τ and subtracting the value obtained by dividing by the axial length step value of the duct (second duct 42, third duct 43).

Specifically, the number k of the duct (second duct 42, third duct 43) whose starting end (corresponding to the 19th column and 56th column) connects to the branching/gathering part 5 is k=m+1 to n, and this starting end The start end value _RS corresponding to h _k and the duct cross-sectional area is expressed as A _k , then at the above starting ends of the ducts (second duct 42, third duct 43) whose starting ends (corresponding to the 19th and 56th columns) connect to the branching/converging part 5 The next time value q _i,j+1 of the flow rate is calculated from the following equation 15, where the current time value of the flow rate is q _i,j .

The above formula 13 is inputted into the cell in the 5th row corresponding to the time after the initial time (4th row) in the 17th, 19th, and 56th columns of the sound speed value spreadsheet 45 to obtain the sound speed value. is calculated, and then copied and input into each cell from the 6th row corresponding to the next time onwards to calculate the sound speed value, and the time history of the sound speed value is shown in the 17th column of the sound speed value spreadsheet 45. It is recorded in the 19th column and the 56th column.

Similarly, Equation 14 corresponds to the 17th column of the flow rate value spreadsheet 46, and Equation 15 corresponds to the time next to the initial time (4th row) in the 19th and 56th columns of the flow rate value spreadsheet 46. It is input into the cell on the 5th line to calculate the flow rate value, and then it is copied and input to each cell from the 6th line onward corresponding to the next time onwards to calculate the flow rate value, and the time of the flow rate value is calculated. The history is recorded in columns 17, 19, and 56 of flow value spreadsheet 46.

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

Here, the terminal end (corresponding to the 17th column) connected to the branching/converging part 5 of the first duct 41 and the starting end (corresponding to the 19th column) connected to the branching/converging part 5 of the second duct 42 and the third duct 43 The time history of the pressure value in the 56th column (corresponding to the 56th column) is converted from the time history of the sound velocity in the 17th, 19th, and 56th columns of the sound velocity value spreadsheet 45 using Formula 2. The time history is also provided to be displayable by the display means 15.

FIG. 20 shows an analysis result by the pressure propagation analysis device 40 for compressible fluid in a duct configured as described above. FIG. 20 shows the inlet pressure X4 due to pressure fluctuation δ at the starting end of the first duct 41, the branching/merging part pressure Y4 at the branching/merging part 5, and the terminal pressure at the terminal end 3 (closed end) of the second duct 42. Z4 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 branch/collection part pressure Y4.

As configured above, according to the fourth embodiment, each part of the first duct 41 including the terminal end connected to the branching/collecting part 5, and the second part including the starting end connecting to the branching/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 duct 42 and each part of the third duct 43 including the starting end connected to the branching/collecting part 5, including the calculation formula, are stored in the sound velocity value spreadsheet 45, The flow rate values are recorded in each of the spreadsheets 46 and can be displayed by the display means 15, and the time history of the pressure values is converted from the time history of the sound velocity values and can be displayed by the display means 15. The fourth embodiment also provides effects similar to effects (1) and (2) of the first embodiment.

Although several 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, substitutions, and changes can be made without departing from the gist of the invention, and those substitutions and changes can be made. are included within the scope and gist of the invention, and are included within the scope of the invention described in the claims and its equivalents.

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 axis is set in the column direction. The axis may be set, and the formulas may be copied and input into cells in the column direction where the time history of pressure propagation parameter information is recorded. Further, the calculation formulas (formulas) of the calculation means 14, 26, 37, and 47 in each embodiment can be displayed on the display means 15 even if they are not spreadsheets 16, 17, 23, 24, 35, 36, 45, and 46. With this configuration, pressure propagation analysis can be easily verified by comparing these formulas.

DESCRIPTION OF SYMBOLS 1...Duct, 2...Starting end (inlet), 4...Cross-sectional area changing part, 5...Branching/merging part, 10...Pressure propagation analysis device, 11...Duct specification record 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 rate value spreadsheet (flow rate value information recording means) ), 20... Pressure propagation analysis device, 21... Tunnel (duct), 22... High-speed moving body, 23... Sound velocity value spreadsheet (sound velocity value information recording means), 24... Flow rate value spreadsheet (flow rate value information recording means), 25...Pressure propagation parameter recording spreadsheet (pressure propagation parameter information recording means), 26...Calculation means, 30...Pressure propagation analysis device, 31...First duct, 32...Second duct, 33...Duct, 34...Duct specification record Spreadsheet (duct specification information recording means), 35...Sonic velocity value spreadsheet (sound velocity value information recording means), 36...Flow rate value spreadsheet (flow rate value information recording means), 37...Calculation means, 38...Pressure propagation parameter recording spread sheet (pressure propagation parameter information recording means), 40... pressure propagation analysis device, 41... first duct, 42... second duct, 43... third duct, 44... duct specification recording spreadsheet (duct specification information recording means), 45...Sonic velocity value spreadsheet (sound velocity value information recording means), 46...Flow rate value spreadsheet (flow rate value information recording means), 47...Calculation means, 48...Pressure propagation parameter recording spreadsheet (pressure propagation parameter information recording means)

Claims (11)

calculating the propagation of a pressure wave within the duct that occurs with a change in boundary conditions at an end of a duct filled with compressible fluid, and changes in the pressure and flow rate of the compressible fluid within the duct; A pressure propagation analysis device for compressible fluid in a duct,
duct specification information recording means for recording duct specification information of each part of the duct;
Pressure propagation parameter information recording means for recording a time history of pressure propagation parameter information in each part of the duct;
Calculating means for calculating the next time value of the pressure propagation parameter information using a calculation formula using the value of the duct specification information and the current time value of the pressure propagation parameter information;
Display means capable of displaying the calculation formula of the calculation means regarding different times;
A pressure propagation analysis device for a compressible fluid in a duct, characterized in that it is configured to have the following features: The pressure propagation parameter information recording means includes a sound velocity value information recording means for recording a time history of sound velocity values at each part of the duct as a time history of pressure propagation parameter information, and a sound velocity value information recording means for recording a time history of sound velocity values at each part of the duct as a time history of the flow rate value at each part of the duct as pressure propagation parameter information. 2. The flow rate value information recording means for recording as a time history, the time history of the sound velocity values being converted into the time history of pressure values using a conversion formula. A pressure propagation analysis device for compressible fluid in a duct described in . 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 which is a virtual division of the duct 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 that is virtually divided in the axial direction of the duct is set in the column direction, the time of the pressure propagation parameter information is set in the row direction, and the time of the pressure propagation parameter information is set in each cell. A time history of the pressure propagation parameter information of each part of the duct is recorded,
The calculation formula of the calculation means is inputted 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 the next time value of the pressure propagation parameter information is The pressure propagation analysis device for compressible fluid in a duct according to claim 1 or 2, wherein the pressure propagation analysis device for compressible fluid in a duct is a mathematical formula for calculating. In the respective spreadsheets of the duct specification information recording means and the pressure propagation parameter information recording means, information on each part of the duct is recorded continuously in the column direction for each part of the duct with the same cross-sectional area, and information on each part of the duct with the same cross-sectional area is recorded continuously in the column direction, and the information on each part of the duct is recorded continuously in the column direction. 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 gathering branch portion provided in the duct is recorded at intervals in the column direction. Propagation analysis device. 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 an axial length increment value, and this axial length increment value is used as the time increment for analysis. The pressure propagation analysis device for compressible fluid in a duct according to any one of claims 1 to 4, wherein the pressure propagation analysis device for compressible fluid in a duct is set to be larger than the product of the sound velocity value and the sound velocity value at equilibrium of the compressible fluid. The next time value of the sound speed at each part in the duct with 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 line in the spreadsheet of the duct specification information recording means. and the sound speed values at the current time in the same column, one less column, and one more column in the spreadsheet of the sound velocity value information recording means, and the same column, one less column, and one more column in the spreadsheet of the flow rate value information recording means. Calculated using a predetermined formula from the current flow velocity value of
When the flow rate value is set based on boundary conditions at the starting end of the duct, the specific heat ratio of the compressible fluid, the time step value, and the duct specification information recording means are recorded in the same line in the spreadsheet. The axial length step value and the duct cross-sectional area, the current time sound velocity value in the same column and one more column in the spreadsheet of the sound velocity value information recording means, and the same column in the spreadsheet of the flow rate value information recording means. and the flow velocity value at the current time in one more column, using a predetermined formula,
When the flow rate value is set based on boundary conditions at the end of the duct, the specific heat ratio of the compressible fluid, the time step value, and the duct specification information recording means are recorded in the same line in the spreadsheet. the axial length increment values and the duct cross-sectional area; the current time sound velocity values in the same column and one column less in the spreadsheet of the sound velocity value information recording means; and the same column in the spreadsheet of the flow rate value information recording means. and the flow velocity value at the current time in one less column.The pressure propagation of the compressible fluid in the duct according to any one of claims 3 to 5, is configured to be calculated by a predetermined formula from the current time flow velocity value of one less column. Analysis device. The next time value of the flow rate at each part in the duct with the same cross-sectional area is:
If 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 specification information recorded in the same column in the spreadsheet of the duct specification information recording means. and the sound speed values at the current time in the same column, one less column, and one more column in the spreadsheet of the sound velocity value information recording means, and the same column, one less column, and one more column in the spreadsheet of the flow rate value information recording means. Calculated using a predetermined formula from the current flow velocity value of
When the sound velocity value is set as a boundary condition at the starting end of the duct, the specific heat ratio of the compressible fluid, the time step value, and the duct specification information recording means are recorded in the same line in the spreadsheet. The axial length increment value and the duct cross-sectional area, the current time sound velocity values in the same column and one more column in the spreadsheet of the sound velocity value information recording means, and the same column and one more column in the spreadsheet of the flow rate value information recording means. Calculated using a predetermined formula from the current time flow velocity value of one more column,
When the sound velocity value is set as a boundary condition at the end of the duct, the specific heat ratio of the compressible fluid, the time step value, and the duct specification information recording means are recorded in the same line in the spreadsheet. The axial length increment value and the duct cross-sectional area, the current time sound velocity value in the same column and one column less in the spreadsheet of the sound velocity value information recording means, and the same column in the spreadsheet of the flow rate value information recording means. and the flow velocity value at the current time in one column less than the current time value. Analysis device. The next time value of the sound velocity at the cross-sectional area changing section 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 column and empty column in the spreadsheet of the duct specification information recording means. The axial length step value and the duct cross-sectional area as the duct specification information recorded in the sound velocity value information recording means, the sound velocity value at the current time in the columns excluding the same row and empty rows in the spreadsheet of the sound velocity value information recording means, and the flow rate value information recording means Calculated using a predetermined formula from the flow rate value at the current time of the columns excluding the same column and empty columns in the spreadsheet,
Claims 4 to 7 are characterized in that the next time value of the sound speed of each part of the duct having the same cross-sectional area among the ducts having different cross-sectional areas is calculated using the formula set forth in claim 6. The pressure propagation analysis device for compressible fluid in a duct according to any one of the above. The next time value of the flow rate at the cross-sectional area changing 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 column and empty column in the spreadsheet of the duct specification information recording means. The axial length step value and duct cross-sectional area as duct specification information recorded in Calculated using a predetermined formula from the flow rate value at the current time in columns excluding the same column and empty columns 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 calculated using the formula set forth in claim 7. The pressure propagation analysis device for compressible fluid in a duct according to any one of the above. Regarding the starting end of the duct whose starting end connects to the branching/collecting part, the specific heat ratio of the compressible fluid, the duct cross-sectional area, the current time value of the flow rate of the row corresponding to the starting end, and the row corresponding to one downstream from the starting end. Define a starting point value RS that is calculated using a predetermined formula from the current time value of the flow rate of , the current time value of the sound speed in the row corresponding to the starting point, and the current time value of the sound speed in the row corresponding to one downstream from the starting point. death,
Regarding the terminal end of the duct whose terminal end is connected to the branch/converge part, the specific heat ratio of the compressible fluid, the duct cross-sectional area, the current time value of the flow rate of the column corresponding to the terminal end, and the current time value of the flow rate of the column corresponding to the terminal end, one position upstream from the terminal end. A terminal value calculated using a predetermined formula from the current time value of the flow rate of the corresponding column, the current time value of the sound speed of the column corresponding to the terminal, and the current time value of the sound velocity of the column corresponding to one position upstream from the terminal. Define RE,
The next time value of the sound speed at the end of the duct that connects to the branch/converge section will be the current speed of sound value at the end, and whether the end that connects to the branch/converge section is the starting point or the The cross-sectional area of the duct connected to the branch/converge part is calculated by adding the sum of the values obtained by dividing the start end value RS and the end value RE at the current time defined by the end end value, respectively, by the axial length step value of the duct. It is calculated by dividing by twice the sum of
The next time value of the sound velocity of each part of the duct having the same cross-sectional area other than the end connected to the branching/converging part is calculated using the formula according to claim 6. 7. The pressure propagation analysis device for compressible fluid in a duct according to any one of items 2 to 6. Regarding the starting end of the duct whose starting end connects to the branching/collecting part, the specific heat ratio of the compressible fluid, the duct cross-sectional area, the current time value of the flow rate of the row corresponding to the starting end, and the row corresponding to one downstream from the starting end. Define a starting point value RS that is calculated using a predetermined formula from the current time value of the flow rate of , the current time value of the sound speed in the row corresponding to the starting point, and the current time value of the sound speed in the row corresponding to one downstream from the starting point. death,
Regarding the terminal end of the duct whose terminal end is connected to the branch/converge part, the specific heat ratio of the compressible fluid, the duct cross-sectional area, the current time value of the flow rate of the column corresponding to the terminal end, and the current time value of the flow rate of the column corresponding to the terminal end, one position upstream from the terminal end. A terminal value calculated using a predetermined formula from the current time value of the flow rate of the corresponding column, the current time value of the sound speed of the column corresponding to the terminal, and the current time value of the sound velocity of the column corresponding to one position upstream from the terminal. Define RE,
Regarding the next time value of the flow rate at the end of the duct connected to the branch/collection part,
The next time value of the flow rate at the end of the duct where the starting end as the end connects to the branching/merging part is the current flow rate value at the end, and first the flow rate at the branching/merging part at the current time. Multiply the difference between the next time value and the current time value of the sound speed at the end to be connected by twice the cross-sectional area of the duct, then add the value obtained by subtracting 1 from the specific heat ratio, and then add the value obtained by subtracting 1 from the specific heat ratio. Calculated by subtracting the value obtained by multiplying the starting point value RS of the time by a time step value and dividing by the axial length step value of the duct,
The next time value of the flow rate at the end of the duct whose terminal end is connected to the branch/converge section is determined from the flow rate value at the current time at the end, which is first connected to the branch/converge section. The difference between the next time value and the current time value of the sound speed at the end is multiplied by twice the cross-sectional area of the duct, divided by the specific heat ratio minus 1, and then subtracted. Calculated by multiplying the terminal value RE by a time step value and dividing the value by the axial 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 connected to the branching/converging part is calculated using the formula according to claim 7. The pressure propagation analysis device for compressible fluid in a duct according to any one of Items 2 to 5 and 7.

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