JPH09268544A - Simulation device for water conduit system - Google Patents

Abstract

PROBLEM TO BE SOLVED: To alter the fluid model formula change of a piping whole part by employing a fluid model formula derived from a stationary inspection volume in a water conduit system simulation device used in the fluid analyzation of a water conduit system such as a pumped storage hydroelectric plant. SOLUTION: The water conduit system 1 is comprised of an upper cistern 2, a piping 3, valves 4 arranged in a plurality of places, and a discharge channel. The water conduit system information analyzing means 21 of a water conduit system simulation device 20 operates to obtain each information of hydraulic pressure, a flow rate and the like by deriving a fluid model formula from the volume change of a stationary inspection volume caused by impact waves, digitizing it through a node junction, and applying a skyline method on the solution of derived simultaneous equations. Adding a hydraulic turbine formula to the fluid model formula can simulate the pumped storage hydroelectric plant. Thus, in the case of adding a branched pipe 3 to the way of the constructed piping 3, the fluid model formula change is made readily, and the simulation time can be shortened by making calculation efficient.

Description

Detailed Description of the Invention

[0001]

BACKGROUND OF THE INVENTION 1. Field of the Invention The present invention relates to a waterway system simulating device capable of easily constructing and changing a flow model equation used for flow analysis of a waterway system of a pumped storage power plant, for example.

[0002]

2. Description of the Related Art FIG. 10 is a block diagram showing a conventional waterway system simulating device. In the figure, 1 is a waterway system, 2 is an upper reservoir, 3 is a pipe, 4 is a valve which is arranged at a plurality of positions in a pipe 3. ,
6 is a water discharge channel, 10 is a conventional water channel system simulation device, 11 is an initial value input means for inputting initial values such as the flow rate of the pipe 3 and water pressure, 12 is a valve opening degree input means for inputting the opening / closing degree of the valve 4. ,
Reference numeral 13 is an in-valve flow rate calculating means for calculating a flow rate flowing in the valve 4 from the opening / closing degree of the valve 4, and 14 is various information input from the initial value input means 11 and the in-valve flow rate calculating means 13 based on a flow model formula. It is a waterway system information analysis means that analyzes and obtains various information such as the flow velocity, water pressure and flow rate in the pipe 3.

In each field, there are many problems in which the influence of water destruction caused by a rapid change in the flow velocity of the fluid in the pipeline of the piping system on the surroundings of the power plant must be taken into consideration. It was necessary to derive the flow model equation considering the influence of the water hammer wave in which the pressure in the pipe changes due to the expansion and contraction of water and the compression and expansion of water.

FIG. 11 is an explanatory diagram showing the inspection volume of a pipeline for deriving a flow model formula used in the conventional channel information analysis means of a pumped storage power plant.
Is a conduit, 8 is a minute portion in the conduit 7, and 9 is a minute portion after a minute time. Assuming that the minute portion 8 in the conduit 7 moves to the position of the minute portion 9 in a minute time and the end faces A and B thereof move to the positions C and D, respectively, the inspection volume in the minute time is AC-BD. A change in length occurs. The flow model equation is derived by regarding the change in length as equal to the change in length caused by the expansion and contraction of the pipe wall of the pipe 7 and the compression and expansion of water caused by the water hammer wave.

[0005]

Since the conventional waterway system simulating device is constructed as described above, that is, since the flow model formula is obtained based on the moving inspection volume,
The flow model formula for the entire pipe 3 must be obtained. Therefore, if a pipe that branches in the middle of the already constructed pipe 3 is newly added, the flow model formula for the entire pipe 3 must be obtained from the beginning. However, there is a problem that the flow model formula for the entire pipe 3 cannot be easily changed.

The present invention has been made in order to solve the above problems. Even when a branch pipe is newly added in the middle of an already constructed waterway system, a flow model formula for the entire waterway system is obtained. The purpose is to obtain a waterway system simulator that can be easily changed.

[0007]

According to a first aspect of the present invention, there is provided a waterway system information analyzing means for expanding and contracting a pipe wall by a water hammer wave and compressing and expanding water flowing in the pipeway. The change in the fixed test volume that occurs is regarded as a change in length, and the product of the cross-sectional area and the density is used as the flow model formula derived as the difference between the inflow and outflow in the test volume. is there.

In the waterway system simulating apparatus according to the second aspect of the invention, when the flow model equation is discretized, the waterway system is divided into a plurality of volume elements as nodes, and the nodes are virtual as junctions. The nodes are connected in a space, and the node-junction method is applied to calculate by applying the mass conservation law to the nodes and the momentum conservation law to the junctions.

In the waterway system simulating device according to the third aspect of the present invention, the skyline method is applied to the solution of simultaneous equations derived by discretization.

According to a fourth aspect of the present invention, there is provided a waterway system simulating device in which a water turbine model formula is added to a flow model formula so that a power plant can be simulated.

[0011]

DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS One embodiment of the present invention will be described below. Embodiment 1. FIG. 1 is a configuration diagram showing a waterway system simulating device according to a first embodiment of the present invention. In the figure, 1 is a waterway system, 2 is an upper reservoir, 3 is a pipe, and 4 is arranged at a plurality of positions of a pipe 3. A valve, 20 is a waterway system simulator, 11 is an initial value input means for inputting initial values such as the flow rate and water pressure of the pipe 3 of the waterway system 1, 12 is a valve opening degree input means for inputting the opening / closing degree of each valve 4, Reference numeral 13 is a valve flow rate calculating means for calculating the flow rate flowing in the valve 4 from the opening / closing degree of each valve 4, 21 is a water hammer wave in consideration of various information input from the initial value input means 11 and the valve flow rate calculating means 13. Analysis based on the flow model formula
It is a waterway system information analysis means for obtaining various information such as water pressure and flow rate in the pipe 3.

Next, the procedure for deriving the basic equation of the flow model equation in consideration of the water hammer wave used in the waterway system information analyzing means 21 will be explained based on the elastic water column theory. First, FIG. 2 is an explanatory view showing the inspection volume of a pipeline for deriving a flow model formula used in the waterway system information analysis means of the waterway system simulator according to Embodiment 1 of the present invention. Reference numeral 31 is a conduit, 32 is a minute portion in the conduit 31, and 33 is a minute portion after a minute time. The minute portion 32 in the pipe 31 is fixed, and the pipe wall expands and contracts due to a water hammer wave in a short time and the pipe 31
The volume change of the inspection volume when the minute portion 33 is formed by the compression and expansion of the water flowing inside is regarded as the change of the length, and the product of this and the cross-sectional area and the density is the difference between the inflow and outflow in the inspection volume. From the above, the equation (1) of the mass conservation law of the flow model equation is derived.

[0013]

[Equation 1]

A: Propagation velocity of pressure wave P: Pressure w: Flow rate V: Volume of minute portion

In this elastic water column theory, the compressibility of water in the pipe 3 is taken into consideration, the pipe wall expands and contracts due to the pressure in the pipe, the pipe 3 is always filled with water, and the minimum pressure in the pipe is Above the vapor pressure of water, hydraulic loss and velocity head can be omitted compared to pressure change, velocity of water in pipe axial direction is uniform in cross section of pipe, and water pressure is uniform in cross section of pipe. Yes, and its value is assumed to be equal to the water pressure on the tube centerline.

First, considering the change in the length of the minute portion of the conduit due to the expansion and contraction of the pipe wall, FIG. 3 shows the dimensions of each portion of the minute portion (length dx ₁ ) in the conduit 31 and the longitudinal length of the pipe wall. Direction and circumferential stress, and the change in the radius of the pipe wall due to the stress change in the longitudinal and circumferential directions of the pipe wall in this minute part is

[0017]

[Equation 2]

The change in the axial length is δ _X1 = dx ₁ / E (Δσ ₁ −μΔσ ₂ ) ... (3) R: Inner radius of pipe e: Thickness of pipe wall E: Modulus of longitudinal elasticity of pipe wall material μ: Poisson's ratio of pipe wall material Δσ ₁ : Change in longitudinal stress caused by pressure change Δσ ₂ : Pressure Change in the circumferential direction caused by the change

## EQU1 ## The volume of the minute portion under this stress is π (R + ΔR) ² (δ _X1 + dx ₁ ) (4)

The change in the length of the minute portion corresponding to this change in volume is obtained by dividing the equation (4) by the cross-sectional area πR ² .

[0021]

(Equation 3)

The amount of change in this length is determined by how the pipe can move in the vertical direction. Here, ρ for three typical cases where the movement of the pipe is restricted.
The amount of change in the length of the minute portion caused by the pressure change of dH is calculated as follows.

First, in the case where the upper end of the pipe is fixed and is freely movable in the longitudinal direction over its entire length and no expansion joint is provided, δ _X1 + (2ΔR / R) dx ₁ = dx ₁ / E [(ρDdH / 4e)-(μρDdH / 2e)] + 2dx ₁ / E [(ρDdH / 2e)-(μρDdH / 4e)] = (ρDdH / Ee) (5 / 4-μ) dx ₁ ·・ ・ (6)

Next, when the tube is fixed so that it cannot move in the longitudinal direction over the entire length, δ _X1 + (2ΔR / R) d ₁ = dx ₁ / E [(μρDdH / 2e )-(ΜρDdH / 2e)] + 2dx ₁ / E [(ρDdH / 2e)-(μ ² ρDdH / 2e)] = (ρDdH / Ee) (1-μ ² ) dx ₁ (7)

Further, when an expansion joint is provided between the fixed bases over the entire length of the pipe, δ _X1 + (2ΔR / R) dx ₁ = dx ₁ / E [0- (μρDdH / 2e)] + 2dx ₁ / E [(ρDdH / 2e) -0] = (ρDdH / Ee) (1-μ / 2) dx ₁ (8)

As described above, 3 in the equations (6), (7) and (8)
In each case, C ₁ = 5 / 4−μ (9) C ₁ = 1−μ ² (10) C ₁ = 1−μ / 2 (11)

Therefore, the amount of change in the length of the minute portion due to the pressure change of ρdH is δ _X1 + (2ΔR / R) dx ₁ = [ρDdHdx ₁ / Ee] c ₁ (12) D: Inner diameter of conduit ρ: Density of water H: Pressure head, and as shown in equation (12), the amount of change in the length of the minute portion of the conduit due to expansion and contraction of the pipe wall was obtained.

Next, the length dx ₁ due to the effect of compressibility of water.
Considering the change in the length of the minute portion of water, when the minute portion of the water of length dx ₁ is subjected to a pressure change of ρdH, the amount of change in volume due to the elasticity of water is (ρπR ² / k) dHdx ₁ ... (13)

Therefore, the amount of change in length corresponding to this is obtained by dividing the equation (13) by the cross-sectional area πR ² . [(ΡπR ² / k) / πR ² ] dHdx ₁ = (ρ / k) dHdx ₁ (14) As described above, the amount of change in the length of the minute portion due to the compressibility of water as shown in Expression (14). Was asked.

From equations (12) and (14), the total change in the length of the minute portion of water caused by the compressibility of water and the expansion and contraction of the pipe wall due to the pressure change of ρdH is ρ [( 1 / k) + (D _C1 / Ee)] dHdx ₁ (15)

A product obtained by multiplying this by a cross-sectional area and density of a fixed pipeline can be grasped as a difference between an amount entering a minute inspection volume and an amount leaving it. Therefore, the formula for the law of conservation of mass is

[0032]

(Equation 4)

## EQU1 ## Here, the head H is a function of x ₁ and t, and since ax ₁ / d _t = u,

[0034]

(Equation 5)

And again

(Equation 6)

V = dx ₁ A (19)

When expressed as, the equation (20) is as follows.

(Equation 7)

A: Propagation velocity of pressure wave P: Pressure A: Cross-sectional area of minute portion w: Flow rate

The law of conservation of momentum is as follows. (L / A) (∂w / ∂t) = {- (1 / A) [▽ (w 2 / ∂A)]} - ▽ P-ρg △ h- (h 1 + h V) ··· (21 ) As described above, the equations (20) and (21) are the basic equations of the water hammer wave model.

Next, the operation will be described. FIG. 4 is a flowchart showing an operation procedure of the waterway system simulating device according to the first embodiment of the present invention. First, in the initial value input means 11 of the waterway system simulating device 20, initial values such as the flow velocity, the flow rate and the water pressure of the pipe 3 of the waterway system 1 of the pumped storage power plant are input (step ST1), and the valve opening degree input means 12 is entered.
In, input the opening / closing degree of each valve 4 (step ST
2). Next, the in-valve flow rate calculating means 13 calculates the flow rate flowing in the valve 4 from the opening / closing degree of each valve 4 (step ST
3) In the waterway system information analysis means 21, various kinds of information input from the initial value input means 11 and the valve flow rate calculation means 13 are calculated based on the basic formula of the water hammer wave model considering the water hammer wave, Various information such as water pressure and flow rate in 3 are analyzed (step ST4). Then, it is judged whether or not it is the analysis end time (step ST5), and if it is not the analysis end time, the process returns to step ST2 for each analysis time interval and is repeatedly executed.

Applying the basic equations of the water hammer wave model of the above equations (20) and (21), the flow velocity in the pipe 3,
As a result of analyzing various information such as the water pressure and the flow rate, the water hammer wave when the valve 4 started to be closed propagated to the upstream side, and the pressure gradually increased from the downstream side according to the propagation speed of the water hammer wave. I was able to analyze the starting state. Also, after the valve 4 is fully closed, the oscillation of the upstream pressure due to the propagation of the water hammer wave continues, and this period is four times the distance from the valve 4 to the upper reservoir 2 divided by the propagation speed of the water hammer wave. I confirmed that they match. Therefore, the basic equations of the water hammer wave model of the above equations (20) and (21) are to be understood as basic equations that qualitatively and quantitatively consider the influence of the water hammer wave.

As described above, according to the first embodiment, the basic equation of the water hammer wave model considering the water hammer wave used for the analysis in the waterway system information analyzing means 21 is the water hammer wave in a short time. Since the volume change amount of the inspection volume caused by the expansion and contraction of the pipe wall due to the wave and the compression and expansion of the water flowing in the pipe line 31 is obtained as the difference between the amount of water flowing into the inspection volume and the amount of water flowing out, Even when a pipe 3 that branches off is already added in the middle of the already constructed pipe 3, the flow model formula for the entire pipe 3 can be easily changed.

Embodiment 2 In the first embodiment, the pipe 3
Although it has been shown that the flow model formula for the whole can be easily changed, in the second embodiment, as shown in FIG.
The flow model formula may be constructed by combining Further, as shown in FIG. 6, when the new pipe 3 is branched and connected to the main pipe 3, data defining the connection relationship between the node 41 and the junction 42 is added,
It is possible to easily add or change the flow model formula only by changing it.

This node 41 and junction 42
Can be derived by discretizing the flow model equations represented by the above equations (20) and (21) spatially by the staggered mesh method and temporally by the semi-implicit method. In the staggered mesh method, as shown in FIG. 5, the flow path is divided into spaces called nodes 41, the mass conservation law is applied to each node 41, and the junction 4
The momentum conservation law is applied to the virtual space between the nodes 41 called 2.

As shown in FIG. 5, the flow model equation for the configuration of the node 41 and the junction 42 is as follows.

[0046]

(Equation 8)

[0047]

[Equation 9]

Here, the first advection term on the right side of the equation (23) represents the upstream difference approximation and is as follows. (1) (w _K ) ⁿ ≧ 0

[0049]

(Equation 10)

(2) (w _K ) ⁿ <0

[0051]

[Equation 11]

In equations (22) and (23), (W
_K ) ^{n + 1} and (P _i ) ^{n + 1} are unknowns. By solving the equation (23) for W ^{n + 1} , the equation (26) is obtained. (W _K ) ^{n + 1} = R _K {(P _i ) ^{n + 1} − (P _j ) ^{n + 1} } + S _K (26) R _K = D _K δt (A _K / l _K ) ...・ (27) D _K = f {(W _K ) ⁿ , θ} (28)

[0053]

(Equation 12)

Is as follows. The variable represented by S _K includes the advection term, the pressure loss of the pipe, and the pressure loss of the valve, and is non-linear with respect to the flow rate w. However, this term is known because it uses the value one step before in the time difference, resulting in a linear simultaneous equation. By substituting equation (26) into equation (22), a simultaneous equation whose pressure is unknown and whose number is equal to the number of nodes 41 can be obtained, and this simultaneous equation can be solved by matrix calculation.

As described above, according to the second embodiment, the flow model equation is set to the node 41 and the junction 4.
Since it is constructed by combining the two, it is possible to obtain an effect that the flow model formula can be easily added or changed.

Embodiment 3 In the second embodiment, by substituting equation (26) into equation (22), a simultaneous equation whose pressure is unknown and whose number is equal to the number of nodes 41 is obtained, and this simultaneous equation is solved by matrix calculation. Although the case has been described, since the coefficient matrix of the simultaneous equations has many zero elements, the simultaneous equations may be solved by applying the skyline method. In the skyline method, when the coefficient matrix of unknowns of the multi-dimensional simultaneous linear equations has a skyline structure 51 as shown in FIG. 7, the internal components, to be exact, the non-zero element portion 52 due to symmetry. By storing only the components, the capacity required for storage is saved. Therefore, it is possible to eliminate the waste of the operation spent due to the zero existing outside the skyline structure 51, reduce the calculation time required for the decomposition, forward and backward substitution (about 1/3), and improve the efficiency of the calculation. Therefore, in the third embodiment, in addition to the effects of the first and second embodiments, the simulation time of the flow model equation can be shortened.

Embodiment 4 FIG. In the above-described first to third embodiments, only the water channel system 1 is simulated, but as shown in FIG. 8, a water turbine generator 5 may be provided to enable simulation of a power plant. it can. FIG. 8 is a configuration diagram showing a pumped storage power generation plant according to Embodiment 4 of the present invention. In the figure, the same reference numerals as those in Embodiments 1 to 3 indicate the same or corresponding portions, and therefore the description thereof will be omitted. To do. Reference numeral 5 is a generator directly connected via a water wheel shaft, and when the guide vane opening degree is changed to some extent, the flow velocity of water sharply decreases and a water hammer wave is generated. 61 is a surge tank and 62 is a water turbine.

Next, the procedure for deriving the water wheel model formula will be described. Given the guide vane opening, rotation speed, and effective head, calculate the flow rate and generated torque. From the given effective head h _WW and the rotational speed ω, the peripheral velocity coefficient K _v1 is given by the formula (3
0).

[0059]

(Equation 13)

From the circumferential velocity coefficient K _v1 and the given guide vane opening β, the flow coefficient Q ₁₁ and torque coefficient M ₁₁ are obtained from the data called the complete characteristic curve, and the equation (31) is obtained.
Then, the flow rate w and the generated torque M _T are obtained by the equation (32).

[0061]

[Equation 14]

M _T = M ₁₁ D ³ H _WW (32) D: Runner diameter

Next, the operation will be described. FIG. 9 is a flow chart showing the operation of the waterway system simulating device according to the fourth embodiment of the present invention. First, the initial values of the flow rate and pressure of the pipe 3, the rotational speed of the water turbine 62, the initial values of the torque, and the initial value of the generator 5 are read (steps ST11 to ST1).
3). Next, the characteristics of the generator 5 are calculated (step ST1
4) Read the guide vane opening (step ST1
5) The characteristics of the water turbine 62 are calculated based on the above water wheel model formula (step ST16). In consideration of the characteristics of the water turbine 62, the pressure, the flow rate, etc. of the pipe 3 are calculated for each analysis time interval, and the process ends when the analysis ends (step ST.
17).

As a result of analysis according to the above procedure, the water turbine 6
It can be analyzed that the pressure wave generated by the water hammer wave when the guide vanes of No. 2 start to be closed is propagating to the upstream side, and the pressure is gradually increasing from the downstream side according to the propagation speed of the pressure wave. It was Further, after the guide vanes of the water turbine 62 are fully closed, the oscillation of the upstream pressure due to the propagation of the pressure wave continues, and this period is four times the distance from the water turbine 62 to the upper reservoir 2 divided by the propagation speed of the pressure wave. Since it matched
The power plant to which this turbine model formula is added can be analyzed qualitatively and quantitatively.

As described above, according to the fourth embodiment, since the flow channel system information analyzing means 21 uses the flow model equation in consideration of the turbine model equation, the power plant having the turbine 62 and the generator 5 is used. It is possible to obtain the effect that the analysis can be performed.

[0066]

As described above, according to the first aspect of the present invention, the waterway system information analyzing means includes the inspection volume generated by the expansion and contraction of the pipe wall by the water hammer wave and the compression and expansion of the water flowing in the pipe. Since it is configured to use the flow model equation that the volume change of is regarded as the change of length and the product of the cross-sectional area and the density is derived as the difference of the inflow and outflow in the inspection volume, it is already constructed. Even if a pipe that branches in the middle of the waterway system is newly added, the flow model formula for the entire waterway system can be easily changed.

According to the invention described in claim 2, when the flow model equation is discretized, the water channel system is divided into volume elements as a plurality of nodes, and the nodes are connected by a virtual space as a junction. , It is configured to use the node-junction method in which the conservation of mass rule is applied to the above nodes and the conservation of momentum is applied to the above junctions.Therefore, a new branch pipe is added in the middle of the already constructed waterway system. Even in this case, there is an effect that the flow model formula for the entire waterway system can be easily changed.

According to the third aspect of the invention, the skyline method is applied to the solution of the simultaneous equations derived by the discretization, so that the analysis time can be shortened.

According to the fourth aspect of the invention, since the water wheel model equation is added to the flow model equation, there is an effect that the power plant can be analyzed.

[Brief description of drawings]

FIG. 1 is a configuration diagram showing a waterway system simulating device according to a first embodiment of the present invention.

FIG. 2 is an explanatory diagram showing an inspection volume of a pipeline for deriving a flow model formula used in a channel information analysis means of a pumped storage power plant according to Embodiment 1 of the present invention.

FIG. 3 is an explanatory diagram showing dimensions of respective portions of a minute portion in a pipe line and longitudinal and circumferential stresses applied to a pipe wall.

FIG. 4 is a flowchart showing an operation procedure of the waterway system simulating device according to the first embodiment of the present invention.

FIG. 5 is a configuration diagram showing configurations of a node and a junction according to a second embodiment of the present invention.

FIG. 6 is a configuration diagram showing a waterway system model in which a new waterway system is branched and connected to a main waterway system.

FIG. 7 is an explanatory diagram showing a skyline structure according to a third embodiment of the present invention.

FIG. 8 is a configuration diagram showing a power plant according to a fourth embodiment of the present invention.

FIG. 9 is a flowchart showing an operation of the waterway system simulating device according to the fourth embodiment of the present invention.

FIG. 10 is a configuration diagram showing a conventional waterway system simulating device.

FIG. 11 is an explanatory diagram showing an inspection volume of a pipeline for deriving a flow model formula used in a conventional waterway system information analyzing means of a power plant.

[Explanation of symbols]

1 channel system, 4 valves, 11 initial value input means, 12 valve opening input means, 13 valve internal flow rate calculation means, 20 channel system simulation device, 21 channel information analysis means, 41 node, 42
Junction.

Claims (4)

[Claims] 1. Initial value input means for inputting initial values such as flow rate and water pressure of a water channel system of a pumped storage power generation plant, and valve opening degree input means for inputting an opening / closing degree of each valve provided in the water channel system. , Considering the water hammer wave, the various information input from the valve flow rate calculation means for calculating the flow rate flowing in the valve from the opening / closing degree of each valve, the initial value input means and the valve flow rate calculation means. In a waterway system simulating device including a waterway system information analyzing means for obtaining various information such as water pressure and flow rate in the waterway system by analyzing based on the flow model equation, the waterway system information analyzing means is based on the water hammer wave. The volume change of the inspection volume, which is a minute portion caused by the expansion and contraction of the pipe wall and the compression and expansion of the water flowing in the pipe, is regarded as the change in length, and the product of the cross-sectional area and the density is inflowed into the inspection volume. Output A waterway system simulator characterized by using a flow model formula derived as the difference between 2. When discretizing a flow model equation, the water channel system is divided into volume elements as a plurality of nodes, and the nodes are connected by a virtual space as a junction, and the nodes are connected with a mass conservation function. The waterway system simulating device according to claim 1, wherein a node-junction method for applying a momentum conservation law is applied to the conservation law and the junction. 3. The waterway system simulating device according to claim 2, wherein the skyline method is applied to a solution of simultaneous equations derived by discretization. 4. A water turbine model formula is added to the flow model formula,
The waterway system simulating device according to claim 2, wherein the power generation plant can be simulated.