KR101764666B1 - Calculation method of the diameters of branch pipes for uniform flow distribution - Google Patents

Abstract

The present invention relates to a pipe diameter calculation method of a branch pipe or a branch hole for uniform distribution of a flow rate. More specifically, supply pressure of fluid and a diameter of a supply pipe (a header pipe) are set to calculate a diameter for each branch pipe or each branch hole to equalize a flow rate distributed in each branch pipe or each branch hole.

Description

BACKGROUND OF THE INVENTION 1. Field of the Invention The present invention relates to a branch pipe for uniform flow distribution,

More particularly, the present invention relates to a method for calculating the diameter of a branch pipe for uniform flow distribution, and more particularly, to a method for calculating the diameter of a branch pipe from a supply pipe (header pipe) of a pipe to a plurality of branch pipes or branch pipes, The present invention relates to a method for calculating a diameter of each branch pipe or branch pipe for making a branch pipe.

A plurality of branch pipes are connected to a supply pipe (header pipe) for supplying a heated or heat-exchanged fluid from a boiler or a heat exchanger to a required place, and branching to a place requiring a heated or heat-exchanged fluid. It is desirable to distribute the necessary branching amount for each branch pipe branching from the supply pipe (header pipe).

Fig. 1 is a conceptual diagram showing a case where fluid is distributed from a typical horizontal supply pipe (header pipe) to a plurality of branch pipes. In the figure, the pressure of the horizontal feed pipe (header pipe) increases as it goes to the outlet, and therefore the flow rate distributed to the branch pipe also increases. In other words, there is a peculiar phenomenon in which the flow rate increases as the branch pipe is distant from the inlet. For reference, Figure 3 shows the simulation result of the flow from a horizontal supply pipe (header pipe) to the branch pipe. From the figure, it can be seen that as the distance from the inlet of the horizontal supply pipe (header pipe) increases, the flow rate discharged to the branch pipe increases.

In general, the temperature and the vapor pressure in a state in which the two states of liquid and gas can not be distinguished are called critical points. When the critical state is exceeded, that is, in the critical state, it becomes a gas and not liquid state. (Supercritical Fluid).

This supercritical fluid has inherent properties different from ordinary gases and liquids.

The supercritical fluid has a physical property such as a medium property between a gas and a liquid, which can change abruptly depending on a slight change in pressure and temperature, has good spreading power, and has a high mass transfer rate.

Supercritical CO ₂ (supercritical CO ₂ ) has similar diffusivity and viscosity to gas, but it has recently been applied to various industrial processes because it has density close to that of liquid.

For example, in a supercritical carbon dioxide dyeing machine, supercritical carbon dioxide is appropriately used, and a new dyeing method in which a dye is mixed with supercritical carbon dioxide to permeate the fiber is used. This method is different from a water dyeing machine using water It is a dyeing method.

FIG. 2A is an exemplary diagram showing the case where the pressure of a fluid to be supplied as a dyeing beam of a supercritical carbon dioxide dyeing machine is high and the injection flow rate increases toward the outlet when the supplied flow rate is large. FIG. And the flow rate decreases toward the outlet when the supplied flow rate is small.

In order to solve the flow rate biasing phenomenon occurring as the flow rate is increased or decreased as shown in Figs. 1 to 2A and 2B, the following Patent Document 1 discloses a yarn dyeing spindle structure for leveling.

A guide piece of an orifice type or a cone type is provided in the spindle inlet portion of Patent Document 1 such that a passage narrower than the cross sectional area of the hollow spindle tube body is formed at the spindle inlet portion by the guide piece, A simple device for increasing the static pressure by allowing the salt solution to flow allows rapid diffusion of the saline solution into the lower inlet portion of the spindle installed in the dyeing tank to achieve even salt.

However, as shown in Patent Document 1, it is troublesome to install the guide piece in the passage, and since the shape of the guide piece varies depending on the supply pressure and the diameter, there is a great difficulty in achieving substantially equalization.

As shown in Fig. 2a, it is not possible to discharge uniform flow rate through the multiple branches of the supercritical carbon dioxide staining beam. The supply pressure of supercritical carbon dioxide supplied to the staining beam, the diameter of the staining beam, Separation distance, and diameter of the spray gun.

Therefore, in order to solve the problem of uneven discharge flow rate, it is necessary to provide a calculation method for calculating the branch pipe or the branch pipe diameter by the separation distance of the branch pipe or the branch pipe so as to distribute a uniform flow rate.

Korean Patent Publication No. 10-2009-0087297 (published on Aug. 17, 2009)

SUMMARY OF THE INVENTION An object of the present invention is to solve the problem of uneven discharge flow rate in a plurality of branch tubes or branch tubes of a supply tube (header tube) according to the prior art, to set the supply pressure of the fluid and the diameter of the supply tube (header tube) The present invention is to provide a calculation method for calculating the diameter of each branch tube or branch pipe so as to make the flow rate distributed in each branch tube or branch pipe uniform by setting a separation distance between the branch tube or the branch pipe.

In order to achieve the above object, a method for calculating a pipe diameter of a branch pipe for flow rate equalization according to the present invention includes: (S1) setting an initial pressure p _i at an inlet of a fluid supply pipe 110; Setting a diameter of the fluid supply pipe 110 (S2); Setting (S3) the initial flow velocity (u _i ) of the supply pipe (110); Calculating (S4) the flow velocity (u _{i + 1} ) of the supply pipe (110); Calculating (S5) the pressure ( _{pi + 1} ) of the supply pipe (110); (S6) calculating all the branch pipe flow velocities (u _n ) sequentially from the set initial pressure, the initial flow velocity, and the calculated flow velocity (u _{i + 1} ) and pressure (p _{i + 1} ) of the branch pipe; And calculating (S7) the diameter (d _i ) of each branch pipe from the calculated flow velocity (u) for each branch pipe.

The method for calculating the diameter of the branch tube for flow rate equalization according to the present invention may further include calculating a flow rate of the branch tube i of the supply tube 110 by calculating the flow rate S of the branch tube n of the supply tube 110, Until the flow rate (u _{n + 1} ) at the time after the start of the operation is "0".

The method for calculating the pipe diameter of the branch pipe for the flow rate equalization according to the present invention may further include the step S4 of calculating the flow velocity u _{i + 1} of the supply pipe 110, .

(5)

(5)

(Where, p _1: the initial pressure, u _1: The initial velocity u _1, m = d ₁ / D: supply line (header pipe) and the flow path cross-sectional area ratio, ρ of the branch tube 1 is the height of the branch tube: fluid density, h p _a is the pressure at the location where the fluid is discharged from the branch tube, and R is the pressure loss factor.

The method for calculating the pipe diameter of the branch pipe for the flow rate equalization according to the present invention may further include calculating (S5) the pressure p _{i + 1} of the supply pipe 110 by using the following equation (1) .

(1)

(One)

(Where n is the pressure recovery coefficient and _pi is the initial pressure).

Pipe diameter calculation method of branch tubes for flow even distribution according to the present invention, the step (S7) for calculating the branch pipe by a diameter (d _i): is characterized in that which is calculated by the equation (7) below.

(7)

(7)

(Q _i : Equivalent flow rate, A _si : Cross sectional area of branch tube i)

A method for calculating the diameter of a branch pipe for equalizing the flow rate according to the present invention is characterized in that the supply pipe includes a hot water supply pipe for the boiler, a heat exchanged fluid supply pipe for the heat exchanger, a refrigerant supply pipe for the air conditioner, a cold water supply pipe for the refrigerator, And is one of the dyeing beams of the critical carbon dioxide dyeing machine.

According to the method for calculating the pipe diameter of the branch pipe or the branch pipe for the flow rate equalization according to the present invention, the hot water supply pipe of the boiler, the supply pipe of the heat exchanged fluid of the heat exchanger, the refrigerant supply pipe of the air conditioner, the cold water supply pipe of the refrigerator, , It is possible to equalize the flow rate to be distributed by branch tubes branched from the dyeing beam of the supercritical carbon dioxide dyeing machine, or to individually control the flow rates to be distributed by the branch tubes.

According to the method for calculating the pipe diameter of the branch pipe or the branch pipe for equalizing the flow rate according to the present invention, it is very effective to calculate the pipe diameter per branch pipe in an in-pipe device such as a dyeing machine in which the flow rate distributed from the supply pipe must be uniform.

In particular, the amount of the dye injected into the fabric in the dyeing beam of the fabric dyeing machine can be made uniform, and the fabric can be uniformly dyed, thereby greatly improving the dyeing quality.

According to the present invention, supercritical carbon dioxide uniformly passing through the fabric is discharged from the entire length of the dyeing chamber of the supercritical carbon dioxide dyeing machine, So that evenness can be achieved and dyeing quality can be improved.

According to the pipe diameter calculating method for the flow rate equalization according to the present invention, by calculating the diameter for equalizing the flow rate discharged for each branch pipe according to the flow rate and pressure at the inlet of the supply pipe, the supply pressure of the supplied fluid is changed , The branch pipe diameter can be easily calculated for each of a plurality of branch pipes even if the diameter of the supply pipe is changed.

BRIEF DESCRIPTION OF THE DRAWINGS FIG. 1 is a diagram showing an uneven distribution of branch tubes having a plurality of branch tubes of a supply pipe (header tube) for supplying cooling / heating refrigerant according to the prior art,
FIG. 2A is an illustration showing a nonuniform distribution of branching points when the inlet flow rate of the supply pipe according to the prior art is small; FIG.
FIG. 3 is a graph showing a simulation result showing a uniform flow distribution in the case of FIG. 2A,
FIG. 4 is a conceptual diagram of a balance of momentum in a plurality of branch tubes or branching holes of a supply pipe (header tube)
FIG. 5 is a flowchart of a method for calculating the diameter of a branch pipe for flow rate equalization according to the present invention,
6 is a simulation graph showing the variation of the center velocity of the supply pipe in the longitudinal direction of the supply pipe according to the result of calculation of the branch pipe diameter for the flow equalization of the present invention.
7 is a simulation graph showing the variation of the branch pipe flow rate in the longitudinal direction of the supply pipe according to the result of calculation of the branch pipe diameter for the flow equalization of the present invention.
8 is a view showing a uniform flow distribution by applying different pipe diameters according to the result of the branch pipe diameter calculation for the flow equalization of the present invention.

Hereinafter, a method of calculating a bifurcation diameter for the flow rate equalization according to the present invention will be described in detail with reference to the accompanying drawings.

In the following, the terms "upward", "downward", "forward" and "rearward" and other directional terms are defined with reference to the states shown in the drawings.

The present invention relates to a device for distributing a fluid introduced into a branch pipe of a supply pipe (header pipe) in the fields of a boiler and a heat exchanger, air conditioning and refrigeration, a dyeing beam of an aqueous dyeing device and a dyeing beam of a supercritical carbon dioxide dyeing device to a plurality of branching devices The present invention relates to a calculation method for calculating a diameter of a branch pipe or a branch pipe in a pipe.

In the case of a supply pipe having a plurality of branch pipes or branch holes while being supplied with fluid from one side of the fluid supply pipe illustrated in FIGS. 1, 2A, and 2B and having an inlet side opened and a closed end, The fluid has a flow rate, but the flow rate at the end of the last injection hole becomes "0".

In the present invention, when the branch pipe or the branch pipe formed from the inlet to the end of the fluid supply pipe 110 is 1 to N, the flow rate in the branch pipe 1 or the branch pipe 1 is calculated, Calculate the flow rate and calculate the flow rate in branch tube 3 or branch 3. After calculating the flow rate of the last branch tube or branched branch tube N or the branch tube N, the branch tube N + 1 or the branch tube N + 1 , The flow velocity from the branch pipe 1 or the branch pipe 1 to the branch pipe N or the branch pipe N is the flow rate value in the branch pipe or branch pipe.

Therefore, if the flow rate value in the branch pipe or branch pipe is divided by the number of branch pipe or branch pipe from the total supplied flow rate, it becomes equal flow rate (Q _i ) per branch pipe or branch pipe, Since the cross-sectional area of the branch pipe or branch pipe can be known by dividing the flow rate in the branch pipe or branch pipe from the flow rate (Q _i ), the diameter of the branch pipe or branch pipe can be calculated from this cross-sectional area.

First, prior to calculating the pipe diameter of the supply branch pipe or the branch pipe for the flow rate equalization according to the present invention, the initial pressure p _i of the fluid supplied to the supply pipe (header pipe), the initial velocity u _i of the fluid, The height h of the branch tube, and the flow cross sectional area ratio m = di / D of the supply pipe (header pipe) and the branch pipe are set.

FIG. 4 is a conceptual diagram of a momentum balance in a branch pipe or a branch pipe or a branch pipe, and FIG. 5 is a flowchart of a method of calculating a pipe diameter of a supply branch pipe or a branch pipe for the flow rate distribution according to the present invention.

4 is a supply line (header pipe) from the i-th position branch tube and the pressure in the supply line (header pipe) occurring in sangharyu respectively to p _i and p _{i + 1,} which, at this time, branch tubes, or at a rate of from jigong of inlet Are defined as u _i and u _{i + 1} , respectively. In this case, the pressure difference between upstream and downstream of the branch tube is given by Eq. (1).

(1)

(One)

(Where n is the pressure recovery coefficient).

4, when the mass m _s of the fluid flowing in the direction perpendicular to the flow direction of the supply pipe (header pipe) is taken into consideration, considering the momentum balance of the unit cross-sectional area in the flow direction in the supply pipe (header pipe)

(2)

(2)

이다.(2), m _s u, the third term of the right side of the equation (2), represents the momentum in the flow direction of the supply pipe (header pipe) held by the fluid toward the branch pipe,

to be.

를 포함하는 항은

에 비하여 매우 작으므로

≒ 0 이므로, 식(2)는 아래 식 (3)과 같다.In the above formula (2)

≪ / RTI >

Is very small compared to

(2) is given by the following equation (3).

(3)

(3)

When the above equation (3) is integrated with respect to the branch tubes or the branch holes immediately upstream and downstream of the branch tube,

(4) is obtained.

(4)

(4)

라고 하면 압력회복계수는 n=1로 된다.(1), assuming that n = 1, and the momentum of the flow toward the branch tube or branch is

, The pressure recovery coefficient is n = 1.

Generally, a vortex is generated when the fluid in the supply pipe (header pipe) flows into the branch pipe. In this case, the fluid momentum in the flow direction of the supply pipe may flow into the branch pipe, so that the pressure recovery coefficient becomes n = 1. Here, when only the component perpendicular to the supply pipe is considered, the momentum in the flow direction toward the branch pipe becomes "0 ".

Therefore, by removing the third term in Eq. (2), the pressure recovery coefficient becomes n = 2, and the pressure difference between the inlet and outlet of the branch tube is given by the following equation (5).

(5)

(5)

In the above equation (5), p _a is a pressure that can be measured at a constant pressure at a position discharged from the branch pipe.

In the above equation (5), the first term on the right side is the pressure drop, the second term is the hydrostatic head, and R is the pressure loss coefficient.

(6)

(6)

In Equation (6), ξ is the loss coefficient of the pipe inlet, f is the friction loss coefficient, D is the diameter of the branch pipe, and h is the height of the branch pipe.

In Eq. (6), ξ and f are empirical constants of the pressure loss caused by the branch tube, which is a function of the flow rate generated just upstream of the branch tube and the Reynolds number of the flow based on the tube tube diameter.

On the other hand, as described below, if the pressure loss coefficient generated in the branch pipe is very large, it becomes a uniform distribution, so acceleration loss due to the reduced flow path from the supply pipe to the branch pipe can be ignored.

The above equations (1) and (5) are the basic formulas for determining the distribution characteristics of the flow generated in the feed pipe. The important parameters for determining the flow distribution in the equations (1) and (5) The area ratio m, the pressure recovery factor n, and the pressure loss factor R of the branch pipe.

Figure 5 shows the procedure for calculating the distribution characteristics of the flow when assuming the flow velocity at the inlet of the supply pipe. Assuming the pressure at the inlet of the supply pipe at the beginning of the calculation and using the equations (1) and The pressure and flow rate of the upstream and downstream branches are calculated. Repeat this procedure and repeat the calculation by modifying the pressure at the inlet of the line until the flow rate downstream of the last branch is "0".

Generally, the larger the area ratio m and the branch pipe resistance R, the more uniform flow distribution is obtained. If a uniform flow distribution can not be obtained, increase the diameter of the supply pipe or increase the resistance by inserting an orifice into the branch pipe How to apply it becomes a woman.

The method for calculating the pipe diameter of the branch pipe for the flow rate equalization according to the present invention,

The formula (5)

(5)

(5)

To obtain the flow velocity u ₂ (u _{i + 1} ) of the second branch tube (2 = i + 1). In this case, the initial pressure p _{1, the} initial velocity u ₁ , the flow cross-sectional area ratio m = d ₁ / D between the supply pipe (header pipe) and branch pipe 1, the fluid density ρ and the height h of the branch pipe are set, Measure the pressure p _a at the position where the fluid is discharged.

The fluid velocity u ₂ in the branch pipe 2, which is the second branch, is calculated from the set initial pressure, initial velocity, cross-sectional area ratio, density, height of the branch pipe, and pressure measured at the discharge position.

Substituting u ₂ calculated in the above into equation (1)

It is possible to calculate the pressure p ₂ at the branch pipe 2 which is the second branch pipe.

Substituting the pressure p ₂ at the branch pipe 2 to the re-calculated in the equation (5),

And the fluid velocity u ₃ at the branch pipe 3, which is the third branch, is calculated.

When the fluid velocity u ₃ in the branch pipe 3 calculated above is substituted into equation (1)

It is possible to calculate the pressure p ₃ at the branch pipe 3 which is the third branch pipe.

With this calculation method, the fluid velocity at the next branch tube and the pressure at the next branch tube are continuously calculated.

When the fluid velocity and pressure are calculated in this order, it is possible to calculate the fluid velocity below the last branch tube, and when the calculated fluid velocity becomes "0", the fluid velocity at each branch tube calculated above This is the fluid velocity of the branch pipe.

If the fluid velocity at the bottom of the last branch tube does not become "0 &

Change the initial pressure or change the diameter of the supply pipe (header pipe) and continue until the fluid velocity below the last branch pipe becomes "0 ".

When the velocity of the fluid in each branch tube is known from the method of calculating the diameter of the branch tube for the flow equalization of the present invention according to the present invention shown in FIG. 5, the flow rate discharged from the branch tube is expressed by Equal Flow Rate (Q _i ) (7), the cross-sectional area of each branch tube can be calculated by dividing the flow rate of each branch tube.

(7)

(7)

In the above equation (7), Q and u are the flow rate and velocity in branch pipe i, respectively, and A is the cross-sectional area of branch pipe i.

The diameter of each branch pipe can be calculated by using the uniform flow rate (Qi) and the fluid velocity in each branch pipe. Therefore, in order to distribute the uniform flow rate from the supply pipe (header pipe) to a plurality of branch pipes or branch pipes, a branch pipe, a branch pipe or a branch pipe having different sectional areas obtained by this method may be applied.

6 is a simulation result showing the flow velocity at the center of the supply pipe according to the method of calculating the pipe diameter of the branch pipe for the flow rate equalization of the present invention. This results in a decrease in the flow rate at the center of the supply line and finally a flow rate at the end of the supply line at the end becomes "0 ".

FIG. 7 is a simulation result showing the flow velocity of each branch pipe according to the direction of the supply pipe according to the method of calculating the pipe diameter of the branch pipe for the flow equalization of the present invention. Simulation results show that the flow rate in the branch pipe increases as the length of the supply pipe increases. This indicates that the flow rate in the branch pipe or branch pipe increases in the longitudinal direction of the supply pipe in the prior art Figs. 1 and 2A This is the same result as the flow rate fluctuation of the branch tube. When the pipe diameter of each branch pipe is calculated by calculating the pipe diameter of each branch pipe through the flow rate of each branch pipe calculated in FIG. 7, the flow rate distributed from all the branch pipes becomes equal.

8 is an exemplary view showing that the flow rate can be uniformly distributed over the entire length of the supply pipe having the diameter of each branch pipe calculated according to the method for calculating the pipe diameter of the branch pipe for the flow equalization of the present invention of the present invention.

Although the present invention has been described in detail with reference to the above embodiments, it is needless to say that the present invention is not limited to the above-described embodiments, and various modifications may be made without departing from the spirit of the present invention.

110: Supply pipe (header pipe)
D: Diameter of the supply pipe (header pipe)
d: Diameter of branch tube or branch

Claims (6)

Setting an initial pressure p _i of the inlet of the fluid supply pipe 110;
Setting a diameter of the fluid supply pipe 110 (S2);
Setting (S3) the initial flow velocity (u _i ) of the supply pipe (110);
Calculating (S4) the flow velocity (u _{i + 1} ) of the supply pipe (110);
Calculating (S5) the pressure ( _{pi + 1} ) of the supply pipe (110);
(S6) calculating all the branch pipe flow velocities (u _n ) sequentially from the set initial pressure, the initial flow velocity, and the calculated flow velocity (u _{i + 1} ) and pressure (p _{i + 1} ) of the branch pipe;
(S7) of calculating the diameter (d _i ) of each branch pipe from the calculated flow velocity (u) of each branch pipe,
(S4) of calculating the flow rate (u _{i + 1} ) of the supply pipe 110
Is calculated by the following equation (5)
The step (S6) of calculating the flow velocity of the branch pipe (i) of the supply pipe (110)
Until the flow rate (u _{n + 1} ) of the downstream branch pipe (n) of the supply pipe (110) becomes zero.

(5)
However, p _1: the initial pressure, u _1: The initial velocity _{u 1, m = d 1 /} D: supply line (header pipe) and the branch tube 1 of the flow path cross-sectional area ratio, ρ: fluid density, h: height of the branch tube, p _a : Pressure at the position where the fluid is discharged from the branch pipe, and R: Pressure loss factor. delete delete Setting an initial pressure p _i of the inlet of the fluid supply pipe 110;
Setting a diameter of the fluid supply pipe 110 (S2);
Setting (S3) the initial flow velocity (u _i ) of the supply pipe (110);
Calculating (S4) the flow velocity (u _{i + 1} ) of the supply pipe (110);
Calculating (S5) the pressure ( _{pi + 1} ) of the supply pipe (110);
(S6) calculating all the branch pipe flow velocities (u _n ) sequentially from the set initial pressure, the initial flow velocity, and the calculated flow velocity (u _{i + 1} ) and pressure (p _{i + 1} ) of the branch pipe;
(S7) of calculating the diameter (d _i ) of each branch pipe from the calculated flow velocity (u) of each branch pipe,
Calculating (S5) the pressure p _{i + 1} of the supply pipe 110;
Is calculated by the following equation (1)
The step (S6) of calculating the flow velocity of the branch pipe (i) of the supply pipe (110)
Until the flow rate (u _{n + 1} ) of the downstream branch pipe (n) of the supply pipe (110) becomes zero.

(One)
Where n is the pressure recovery coefficient and _pi is the initial pressure. Setting an initial pressure p _i of the inlet of the fluid supply pipe 110;
Setting a diameter of the fluid supply pipe 110 (S2);
Setting (S3) the initial flow velocity (u _i ) of the supply pipe (110);
Calculating (S4) the flow velocity (u _{i + 1} ) of the supply pipe (110);
Calculating (S5) the pressure ( _{pi + 1} ) of the supply pipe (110);
(S6) calculating all the branch pipe flow velocities (u _n ) sequentially from the set initial pressure, the initial flow velocity, and the calculated flow velocity (u _{i + 1} ) and pressure (p _{i + 1} ) of the branch pipe;
(S7) of calculating the diameter (d _i ) of each branch pipe from the calculated flow velocity (u) of each branch pipe,
The step (S6) of calculating the flow velocity of the branch pipe (i) of the supply pipe (110)
Until the flow rate (u _{n + 1} ) of the downstream branch pipe (n) of the supply pipe 110 becomes "0"
The step (S7) of calculating the diameter (d _i ) per branch tube is calculated by the following equation (7).

(7)
Q _i : Equivalent flow rate, A _si : Cross sectional area of branch tube i. The method according to any one of claims 1, 4, and 5,
Wherein the supply pipe is one of a hot water supply pipe of a boiler, a supply pipe of a heat exchanged fluid of a heat exchanger, a refrigerant supply pipe of an air conditioner, a cold water supply pipe of a refrigerator, a dyeing beam of a water dyeing machine, and a dyeing beam of a supercritical carbon dioxide dyeing machine. A method for calculating the diameter of a branch pipe for a pipe.

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