CN111046569B - Cavitation water jet nozzle structure design method - Google Patents
Cavitation water jet nozzle structure design method Download PDFInfo
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Abstract
The invention relates to a cavitation water jet nozzle structure design method, which sequentially comprises the following steps: (1) calculating the proportional relationship between the pressure at a certain point in the fluid and the diameter of the cross section of the fluid at the certain point according to the Bernoulli principle; (2) calculating the proportional relation between the fluid pressure drop in the cavitation water jet nozzle and the necking length according to the proportional relation in the step (1); (3) and (3) calculating the functional relation between the inner diameter of the cross section of the nozzle and the length of the necking when the fluid pressure in the nozzle is changed with the movement distance in a continuous function according to the proportional relation in the step (2). The invention starts from the Bernoulli principle of water flow, and based on theoretical deduction calculation, the relation between the diameter and the length of the section of the inlet and outlet of the nozzle is designed based on quantitative control of the water pressure change of the inlet and outlet of the nozzle, so that design methods and ideas can be provided for nozzle designers, and theoretical basis and basis of selection are provided. To further optimize the nozzle structure, the foundation is tamped to improve cavitation efficiency.
Description
Technical Field
The invention belongs to the field of metal surface strengthening and surface cleaning, and particularly relates to a cavitation water jet nozzle structure design method.
Background
The cavitation water jet technology is to utilize a large amount of tiny cavitation groups generated by high-speed water jet flow, and the cavitation groups generate impact pressure and microjet of thousands MPa when collapsing near a solid boundary, so that the cavitation water jet technology can be used for cleaning, surface strengthening and the like and has the characteristics of environmental protection, energy saving, high efficiency, easy operation and the like. The nozzle designer usually selects circular, elliptic, square, conical and the like as the cross section of the traditional cavitation nozzle, and adopts a trial-and-error method to perform the selection design, and although a lot of results are obtained in the aspects of numerical simulation and experimental research, the theoretical basis of the structural design is insufficient, and the nozzle structure is still not optimized.
Disclosure of Invention
The invention aims to overcome the defects of the prior art and provide a cavitation water jet nozzle structure design method.
In order to achieve the above purpose, the technical scheme adopted by the invention is as follows:
the design method of the cavitation water jet nozzle structure sequentially comprises the following steps:
(1) calculating the proportional relationship between the pressure at a certain point in the fluid and the diameter of the cross section of the fluid at the certain point according to the Bernoulli principle;
(2) calculating the proportional relation between the fluid pressure drop in the cavitation water jet nozzle and the necking length according to the proportional relation in the step (1);
(3) and (3) calculating the functional relation between the inner diameter of the cross section of the nozzle and the length of the necking when the fluid pressure in the nozzle is changed with the movement distance in a continuous function according to the proportional relation in the step (2).
Preferably, the pressure at a point in the fluid in step (1) is inversely proportional to the fourth power of the cross-sectional diameter of the fluid at that point.
Preferably, the pressure drop of the fluid in the nozzle in step (2) is proportional to the inverse 4 th power of the neck length.
Preferably, the variation of the fluid pressure in the nozzle in step (3) as a continuous function of the length of the constriction comprises: 1. the fluid pressure changes in equal proportion with the length of the necking; 2. the fluid pressure varies linearly with the length of the constriction.
Preferably, the proportional relation calculation method in the step (1) is as follows: according to the calculation formula of the Knudli principle, p+0.5ρv 2 +ρgh＝C
Wherein p is the pressure of a certain point in the fluid, v is the flow rate of the fluid at the point, ρ is the fluid density, g is the gravitational acceleration, h is the height of the point, C is a constant, after deformation,
p＝C-0.5ρv 2 -ρgh
substituting the flow velocity v=q/S (q is the flow rate, S is the cross-sectional area) into the above formula,
for a circular cross-section nozzle, s=pi d 2 And/4, d is the cross-sectional diameter, substituting the diameter into the above formula,
the pressure p at a point in the fluid is calculated in inverse relation to the fourth power of the nozzle cross-sectional diameter d.
Preferably, the proportional relation calculation method in the step (2) is as follows: the flow velocity, the pressure and the water head of the fluid at the outlet end of the nozzle inlet end box are v respectively 1 、p 1 、h 1 And v 2 、p 2 、h 2 The pressure drop is then the same as the pressure drop,
when the nozzle is vertically arranged, h 1 -h 2 =l, i.e
When the nozzle is horizontally arranged, then
Preferably, the functional relationship p=f (L) between the nozzle cross-sectional inner diameter d and the neck length L in step (3) is based on
It is possible to obtain a solution,
preferably, the nozzle cross-sectional inner diameter d as a function of neck length L, with the fluid pressure p varying in equal proportion to neck length L: according toWherein k is 1 Is a constant of proportionality and is used for the control of the temperature,
the deformation can be achieved by a combination of the two,
preferably, in the case of a linear variation of the fluid pressure p with the neck length L, the nozzle cross-sectional internal diameter d is a function of the neck length L: l=k 2 -k 3 p 2 Or (b)Wherein k is 2 ，k 3 Is a constant value, and is used for the treatment of the skin,
then
It is possible to obtain a solution,
due to the implementation of the technical scheme, compared with the prior art, the invention has the following advantages:
the invention starts from the Bernoulli principle of water flow, based on theoretical deduction calculation, and based on quantitative control of the water pressure change of the inlet and outlet of the nozzle, designs the relationship between the section diameter and the length of the inlet and outlet of the nozzle, can obtain the nozzle structure with water pressure equal ratio change, continuous change and step change, and can provide design methods and ideas for nozzle designers and theoretical basis and basis of selection. To further optimize the nozzle structure, the foundation is tamped to improve cavitation efficiency.
Drawings
FIG. 1 is a schematic diagram of a micro-cell structure at a necking position formed by cavitation bubbles;
FIG. 2 is a plot of nozzle inner diameter versus neck length as pressure decreases linearly with neck length;
FIG. 3 is a graph of nozzle inner diameter versus neck length for a slow-to-fast parabolic decrease in pressure with neck length;
FIG. 4 is a schematic view of a necking configuration in which the inside diameter of the nozzle varies in series with the length in steps.
Detailed Description
The invention will now be described in further detail with reference to the drawings and to specific examples.
As shown in fig. 1 to 4, according to the bernoulli principle, for a constant flow (the properties of a fluid at any point in a flow system do not change with time), an incompressible flow (the density is constant), no friction flow (the friction effect is negligible, the viscous effect is ignored), a fluid flowing along a streamline, the following relationship is satisfied at any position:
p+0.5ρb 2 +ρgh＝C
where p is the pressure at a point in the fluid, v is the flow rate at that point in the fluid, ρ is the fluid density, g is the gravitational acceleration, h is the height at which that point is located, and C is a constant. The deformation is carried out to obtain:
p＝C-0.5ρv 2 -ρgh
substituting the flow velocity v=q/S (q is the flow rate, S is the cross-sectional area) into the above equation:
for a circular cross-section nozzle, s=pi d 2 And (4) the cross-sectional diameter is obtained by substituting the formula:
it can be seen that the pressure p at a point in the fluid is inversely proportional to the fourth power of the nozzle cross-sectional diameter d.
As shown in FIG. 1, the key factors of cavitation are in the necking (nozzle cross section change) of the nozzle structure, the nozzle is assumed to be I before necking, II after necking, liquid flows in from the I section and flows out from the II section, and the flow velocity, pressure and water head of the liquid flows in the I section and the II section are assumed to be v respectively 1 、p 1 、h 1 And v 2 、p 2 、h 2 The pressure drop is then:
when vertically placed, h 1 -h 2 =l, i.e
When horizontally placed, then
Since the inlet end water pressure is often tens of MPa during the experiment, the outlet end pressure is very low, approaching atmospheric pressure, and thus the pressure drop (p 1 -p 2 ) Is very large. The nozzle height h is generally about 10-20mm, and the value of ρgL is about 0.0001-0.0002MPa, which is small and negligible. According to conservation of mass, inThe flow rates at the two points are equal, and assuming that the density of the water is unchanged, or that the influence of the density change is negligible, the pressure drop for a cavitation water jet nozzle can be considered to be related only to the inside diameter of the nozzle, i.e. proportional to the inverse to the 4 th power of the neck length.
During cavitation water jet cavitation, the water pressure at the constriction needs to be reduced to a certain extent. The pressure drop rate is different for different cross-sectional shapes, resulting in different cavitation effects of the effluent. By adopting the method for controlling the rate of pressure decreasing along with the length of the necking, a new idea can be provided for a designer, and the method is specifically as follows:
the relation between the inner diameter d of the nozzle section and the necking length L is designed by adopting the fact that the pressure changes with the necking length as a continuous function, and the pressure rising and falling value changes according to a specific rule. Namely:
it is possible to obtain a solution,
1. the fluid pressure varies in equal proportion to the length of the constriction (see figure 2); i.e.
k 1 As a proportionality constant, the deformation is as follows:
therefore, the inside diameter d of the nozzle cross section is in a reciprocal fourth relationship with the length L of the neck, namely:
or d= (a 2 *L+B 2 ) -1/4
Wherein the method comprises the steps of
Example one: the loading water pressure p of the high-pressure pump for test is 30MPa, and the water density rho is 1000kg/m 3 Flow q is 2m 3 And/h, the diameter of the nozzle inlet is 10 mm=0.01m, the nozzle inlet is horizontally placed, the height h is 0, the necking length L of the nozzle inlet section is 20mm, the inner diameter is 2mm, and then:
when l=0, p 0 ＝30MPa，
The constant C is:
when l=20 mm, d=2 mm has
Obtaining k 1 ＝781 250 000
Then
The curve equation becomes: d= (3 119 639 062 500*L+99 828 450) -1/4
2. The fluid pressure varies linearly with the length of the constriction (see fig. 3), i.e. l=k 2 -k 3 p 2 Or (b)k 2 ，k 3 Is constant, then
It is possible to obtain a solution,
example two:
when l=0, p=30 MPa, i.e
When l=20 mm, d=2 mm, as above, there is p= 14 375 000, i.e
Solving for k 2 ＝0.02596，k 3 ＝2.884*10 -17
In addition, the invention is also suitable for designing the relation between the inner diameter of the nozzle section and the length of the necking by adopting a discontinuous function to form a step series structure, as shown in fig. 4.
In summary, the invention starts from the Bernoulli principle of water flow, based on theoretical deduction calculation, and based on quantitative control of the water pressure change of the inlet and outlet of the nozzle, designs the relationship between the section diameter and the length of the inlet and outlet of the nozzle, and can obtain the nozzle structure with water pressure equal ratio change, continuous change and step change, thereby providing design methods and ideas for the nozzle designer and providing theoretical basis and basis for selection. To further optimize the nozzle structure, the foundation is tamped to improve cavitation efficiency.
The above embodiments are only for illustrating the technical concept and features of the present invention, and are intended to enable those skilled in the art to understand the present invention and to implement the same, but are not intended to limit the scope of the present invention, and all equivalent changes or modifications made according to the spirit of the present invention should be included in the scope of the present invention.
Claims (5)
1. A cavitation water jet nozzle structure design method is characterized in that: the design method sequentially comprises the following steps:
(1) calculating the proportional relationship between the pressure at a certain point in the fluid and the diameter of the cross section of the fluid at the certain point according to the Bernoulli principle;
(2) calculating the proportional relation between the fluid pressure drop in the cavitation water jet nozzle and the necking length according to the proportional relation in the step (1);
(3) calculating the functional relation between the inner diameter of the cross section of the nozzle and the length of the necking when the fluid pressure in the nozzle changes continuously along with the movement distance according to the proportional relation in the step (2);
the variation of the fluid pressure in the nozzle in step (3) as a continuous function of the length of the neck comprises: 1. the fluid pressure changes in equal proportion with the length of the necking; 2. the fluid pressure varies linearly with the length of the constriction;
the proportional relation calculation method in the step (1) is as follows: according to Bernoulli principle calculation formula, p+0.5ρv 2 +ρgh＝C
Wherein p is the pressure of a certain point in the fluid, v is the flow rate of the fluid at the point, ρ is the fluid density, g is the gravitational acceleration, h is the height of the point, C is a constant, after deformation,
p＝C-0.5ρv 2 -ρgh
substituting the flow velocity v=q/S into the above equation, where q is the flow rate, S is the cross-sectional area,
for a circular cross-section nozzle, s=pi d 2 And/4, d is the cross-sectional diameter, substituting the diameter into the above formula,
calculating that the pressure p at a certain point in the fluid is inversely proportional to the fourth power of the cross section diameter d of the nozzle;
the proportional relation calculation method in the step (2) is as follows: the flow velocity, the pressure and the water head of the fluid at the inlet end and the outlet end of the nozzle are respectively v 1 、p 1 、h 1 And v 2 、p 2 、h 2 The pressure drop is
When the nozzle is vertically arranged, h 1 -h 2 Length of neck L, i.e
When the nozzle is horizontally arranged, then
The functional relation between the inner diameter of the cross section of the nozzle and the length of the necking is calculated in the step (3) as follows:
substituting the functional relation p=f (L) between the pressure p and the neck length L into the formulaA functional relationship between nozzle cross-sectional inner diameter d and neck length L is obtained:
2. the cavitation water jet nozzle structural design method according to claim 1, wherein: the pressure at a point in the fluid in step (1) is inversely related to the fourth power of the cross-sectional diameter of the fluid at that point.
3. The cavitation water jet nozzle structural design method according to claim 1, wherein: the pressure drop of the fluid in the nozzle in step (2) is in direct proportion to the inverse 4 th power of the length of the neck.
4. The cavitation water jet nozzle structural design method according to claim 1, wherein: in the case of a constant proportional variation of the fluid pressure p with the neck length L, the inner diameter d of the nozzle cross section is a function of the neck length L: according to p =Wherein k is 1 Is a constant of proportionality and is used for the control of the temperature,
the deformation can be achieved by a combination of the two,
5. the cavitation water jet nozzle structural design method according to claim 1, wherein: in the case of a linear variation of the fluid pressure p with the neck length L, the nozzle cross-sectional internal diameter d is a function of the neck length L: l=k 2 -k 3 p 2 Or (b)Wherein k is 2 ，k 3 Is a constant value, and is used for the treatment of the skin,
then
It is possible to obtain a solution,
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