A method for predicting the cleaning performance of jet impact flat plate based on dimensional analysis

Abstract

The present invention discloses a method for predicting the cleaning performance of a jet impacting a flat plate based on dimensional analysis, which specifically includes the following steps: Step 1, establishing a mathematical model of a circular water film formed by a jet impacting a flat plate; Step 2, defining a dimensionless water film radius and a dimensionless impact power based on dimensional analysis; Step 3, defining a dimensionless wetting angle based on dimensional analysis; Step 4, applying the Bernoulli equation to the jet impacting the flat plate upward, and deriving the expressions of the jet velocity and the jet radius at the jet impact point under the influence of gravity; Step 5, deriving the theoretical impact force of the jet impacting the flat plate, and deriving the relationship between the jet impact force coefficient and the dimensionless impact power. The present invention adopts the above-mentioned method for predicting the cleaning performance of a jet impacting a flat plate based on dimensional analysis, combines the flow state and impact force formed by the jet impacting the flat plate, theoretically derives various physical quantities related to the cleaning performance, has high prediction accuracy, and is of great significance for the prediction of the jet cleaning performance.

Description

Technical Field

[0001] The invention relates to the technical field of jet cleaning, and in particular to a method for predicting the cleaning performance of a jet impacting a flat plate based on dimensional analysis. Background Art

[0002] Cleaning operations have always been an indispensable field in the civil and industrial fields, and jet cleaning uses its high-pressure, impact and other high-energy processes to clean the surface, and plays an important role in cleaning operations. The flow pattern generated by the jet hitting the flat plate has an important impact on the jet cleaning performance. When a continuous water jet hits a flat plate, a circular water jump phenomenon can be generated, and the circular water film generated when the jet hits upward has a high similarity to the circular water jump structure. In addition, in the process of destroying and removing the scale layer on the surface of the cleaning object, the impact of impact, erosion, penetration and shearing on the cleaning effect cannot be ignored.

[0003] According to the survey, foreign scholars have done a lot of research on the shear force generated on the jet surface and proposed a series of empirical and semi-empirical formulas on shear force. Shear force is an important physical parameter when dealing with sticky scale. However, there is little research on the application of jet impact force in cleaning performance. Therefore, how to quickly and accurately predict the circular water film area and impact force formed by the jet impacting the horizontal flat plate is of great significance to the jet cleaning operation. Summary of the invention

[0004] The purpose of the present invention is to provide a method for predicting the cleaning performance of a jet impacting a flat plate based on dimensional analysis. It combines the flow state and impact force formed by the jet impacting the flat plate, theoretically derives various physical quantities related to the cleaning performance, has high prediction accuracy, and is of great significance for the prediction of jet cleaning performance.

[0005] To achieve the above object, the present invention provides a method for predicting the cleaning performance of a jet impact plate based on dimensional analysis, which specifically comprises the following steps:

[0006] Step 1, establish a mathematical model of a circular water film formed by a jet impacting a flat plate, establish a polar coordinate system with the jet impact point as the coordinate origin, and use the impact jet geometric parameters to describe the model;

[0007] Step 2, defining the dimensionless water film radius and the dimensionless impact power based on dimensional analysis, and deriving the relationship between the dimensionless water film radius and the dimensionless impact power;

[0008] Step 3, defining the dimensionless wetting angle based on dimensional analysis, and deriving the relationship between the dimensionless wetting angle and the nozzle diameter;

[0009] Step 4, apply Bernoulli's equation to the jet impacting the plate upward, and derive expressions for the jet velocity and the jet radius at the jet impact point under the influence of gravity;

[0010] Step 5, derive the theoretical impact force of the jet impacting the flat plate, define the ratio of the impact force to the circular water film area as the jet impact force coefficient, and derive the relationship between the jet impact force coefficient and the dimensionless impact power.

[0011] Preferably, in step 1, if ψ is used to represent the cleaning performance objective function of the jet impacting the flat plate, its main influencing physical quantities can be expressed as:

[0012] ψ=f(ρ,d,w0,H,g,υ,σ,r wf ,F z );

[0013] Where ρ is the liquid density, kg / m 3 ; d is the nozzle outlet diameter, m; w0 is the initial velocity of the jet outlet, m / s; H is the vertical distance from the jet nozzle outlet to the plate, m; g is the gravitational acceleration, m / s 2 ; υ is the kinematic viscosity of the liquid, m 2 / s; σ is the surface tension coefficient of the liquid, N / m; r wf is the radius of the circular water film, m; F z is the jet impact force, N;

[0014] Based on the dimensional analysis method, the objective function can be transformed into:

[0015] ψ=f(Re,Fr,We,r wf / d,I p * ,θ,C f );

[0016] Where Re is the jet Reynolds number, Re = w0d / υ; Fr is the jet Froude number, Fr = w0 / (gd) 1 / 2 ; We is the jet Weber number, We=ρw0 2 d / σ;r wf / d is the dimensionless water film radius; Ip* is the dimensionless impact power, Ip*=πw0 3 d 2 / 8υ 7 / 3 g 1 / 3 ; θ is the dimensionless wetting angle, θ = 2r wf / H;C f is the jet impact force coefficient.

[0017] Preferably, the relationship between the dimensionless water film radius and the dimensionless impact power in step 2 is specifically:

[0018]

[0019] Among them, C1 and C2 are correction coefficients, C1 = (π / 8) 1 / 4 C2.

[0020] Preferably, the relationship between the dimensionless wetting angle and the nozzle diameter in step 3 is specifically:

[0021]

[0022] Preferably, the ratio of the velocity at the impact point to the velocity at the nozzle outlet in step 4 is specifically:

[0023]

[0024] Among them, w (H) and R (H) Respectively represent the velocity and jet radius at the impact point; R0 represents the jet radius at the nozzle outlet, R0 = d / 2; the unit is m;

[0025] According to the law of conservation of mass, the flow rate of the jet at the nozzle outlet and the impact point is equal, that is,

[0026]

[0027] Therefore, the ratio of the jet radius at the impact point to the jet radius at the nozzle outlet is:

[0028]

[0029] Preferably, the striking force coefficient in step 5 is defined as:

[0030]

[0031] in, Indicates the jet impact force; It represents the pressure drop between the stagnation point of the jet impact surface and the surrounding environment; represents the area of ​​the circular water film;

[0032] Therefore, the relationship between the jet impact force coefficient and the dimensionless impact power can be expressed as:

[0033]

[0034] Compared with the existing prediction methods, the present invention has the following advantages: a prediction model for the dimensionless water film radius on the surfaces of different materials is given; the relationship between the dimensionless wetting angle and the nozzle diameter is derived; and an empirical formula between the jet impact force coefficient and the dimensionless impact power is established. The impact power of the jet is an important indicator for measuring the operating cost of jet cleaning. This method combines the flow state and impact force formed by the jet impacting the flat plate, and theoretically derives various physical quantities related to the cleaning performance, which is of great significance for the prediction of the jet cleaning performance.

[0035] The technical solution of the present invention is further described in detail below through the accompanying drawings and embodiments. BRIEF DESCRIPTION OF THE DRAWINGS

[0036] Figure 1 It is a flow chart of an embodiment of a method for predicting the cleaning performance of a jet impact flat plate based on dimensional analysis of the present invention;

[0037] Figure 2 It is a general physical model diagram of a jet vertically impacting a horizontal flat plate in an embodiment of a jet impacting a flat plate cleaning performance prediction method based on dimensional analysis of the present invention;

[0038] Figure 3 It is a structural diagram of a jet test bench in an embodiment of a method for predicting the cleaning performance of a jet impacting a flat plate based on dimensional analysis of the present invention;

[0039] Figure 4 It is a graph showing the variation of dimensionless impact radius with dimensionless impact power under different nozzle diameters in an embodiment of a method for predicting the cleaning performance of a jet impacting a flat plate based on dimensional analysis of the present invention;

[0040] Figure 5 is a diagram showing the change of the dimensionless wetting angle with the nozzle diameter in an embodiment of a method for predicting the cleaning performance of a jet impacting a flat plate based on dimensional analysis of the present invention;

[0041] Figure 6 It is a graph showing the variation of the jet impact force coefficient with the dimensionless impact power in an embodiment of a jet impact flat plate cleaning performance prediction method based on dimensional analysis of the present invention. DETAILED DESCRIPTION

[0042] The technical solution of the present invention is further described below through the accompanying drawings and embodiments.

[0043] Embodiment 1

[0044] like Figure 1 As shown, in an embodiment of the present invention, a flow chart of a method for predicting the cleaning performance of a jet impact plate based on dimensional analysis is provided, which specifically includes the following steps:

[0045] Step 1: Establish a general mathematical and physical model of jet impacting a horizontally placed flat plate, and describe the jet geometric parameters based on the polar coordinate system.

[0046] In the embodiment of the present invention, the general model of the jet impacting the horizontal flat plate is as follows: Figure 2 As shown, the test was conducted with clean water, the nozzle diameter range was 1.5-5mm, and the indoor temperature was kept at 20℃. If ψ is used to represent the cleaning performance objective function of the jet impacting the flat plate, its main influencing physical quantities can be expressed as:

[0047] ψ=f(ρ,d,w0,H,g,υ,σ,r wf ,F z ) (1)

[0048] In the embodiment of the present invention, ρ, υ and σ are the density, kinematic viscosity and surface tension coefficient of water, respectively, which are all physical parameters of water and have specific values ​​under given test conditions (20°C), ρ = 998 kg / m 3 ,υ=1.01×10 －6 m 2 / s, σ=0.072N / m; g is the gravitational acceleration under the test conditions, g=9.81m / s 2 ; d, w0 and H are the nozzle outlet diameter, the jet outlet initial velocity and the vertical distance from the jet nozzle outlet to the plate, respectively; r wf 、F z They are respectively the radius of the circular water film formed by the jet impacting the flat plate and the jet impact force, which are important parameters for judging the jet cleaning performance.

[0049] Based on the dimensional analysis method, the objective function can be transformed into the formula form:

[0050]

[0051] Step 2: Define the dimensionless water film radius r based on dimensional analysis wf / d and the dimensionless impact power Ip* of the jet, and derive r wf The relationship between / d and Ip*.

[0052] formula The definitions of dimensionless numbers in the formula are as follows: As shown:

[0053]

[0054] Where Re is the jet Reynolds number; Fr is the jet Froude number; We is the jet Weber number; θ is the dimensionless wetting angle; C f is the jet impact force coefficient; θ and C f The definition of will be given later.

[0055] In the embodiment of the present invention, considering the axial symmetry of the jet, the fully developed area in the circular water film is The boundary layer equation is:

[0056]

[0057]

[0058] Among them, U r and Uz are the components of the average velocity in the circular water film in the r and z directions, respectively, and h(r) is the thickness of the fully developed region.

[0059] For U in the above formula r , U z , r and z, we can know that the dimensionless water film radius and dimensionless impact power always follow the following relationship:

[0060]

[0061] Among them, C1 and C2 are correction coefficients, C1 = (π / 8) 1 / 4 C2.

[0062] In the embodiment of the present invention, a Figure 3 The jet test bench shown in the figure has the characteristics of both circular water film recording and jet impact force measurement. The self-priming pump provides the power source for the jet; the turbine flowmeter with an accuracy standard of 0.1% is used to measure the volume flow in the pipe; the valve opening controls the jet flow; the model selected is The circular water film was photographed by a C110-5.6μm high-speed camera; the jet impact force was measured by a Kistler model, Type 9371B force sensor. In addition, an organic glass plate was used as a target plate in the test, and the contact angle between water and organic glass was 55°.

[0063] In the embodiment of the present invention, the circular water film radius of each nozzle is measured under the condition that the dimensionless impact power range is 3.3×109﹤Ip*﹤2.1×1011. The circular water film photographed by the high-speed camera has a nozzle diameter of 5mm. After measuring the circular water film radius under multiple flow conditions of 5mm in the experiment, the circular water film radius of the remaining nozzle diameters under different flow rates is measured in turn. Different flow conditions are converted into their corresponding dimensionless impact powers. Figure 4 The dimensionless water film radius r is shown in wf / d varies with dimensionless impact power Ip*, thus the formula By correcting the coefficient in, we can get r when organic glass is used as the target plate. wf The specific relationship between / d and Ip* is:

[0064]

[0065] Step 3, define the dimensionless wetting angle based on dimensional analysis, and derive the relationship between the dimensionless wetting angle and the nozzle diameter.

[0066] Based on the principle of momentum and surface tension balance at the edge of the water jump, foreign scholars have established the following dimensionless wetting angle prediction model:

[0067]

[0068] Wherein, β is the contact angle between water and organic glass plate, β = 55°; is the jet mass flow rate, kg / s; μ is the dynamic viscosity of water, μ = 1.01 × 10 －3 Pas.

[0069] The formula Substitute the definition of Ip* into the formula The relationship can be transformed into:

[0070]

[0071] By multiplying both ends of the above formula by d / H, we can obtain the dimensionless relationship between the wetting angle and the nozzle diameter:

[0072]

[0073] In the embodiment of the present invention, the comparison formula and formula The effect of the jet power source on the dimensionless wetting angle is the same, the formula is middle formula Middle θ~Re 3 / 4 Although the formula The relationship between the dimensionless wetting angle and the contact angle is not given, but the formula itself has been corrected for the coefficients C1 and C2. The relationship between the dimensionless wetting angle and the nozzle diameter is given. Figure 5 It can be clearly seen that the dimensionless wetting angle θ is positively correlated with the 3 / 4 power of the nozzle diameter d.

[0074] Step 4, apply the steady-state Bernoulli equation along the polar coordinate z-axis direction to derive the jet velocity and jet radius at the impact point under the effect of gravity.

[0075] Mode The steady-state Bernoulli equation is:

[0076]

[0077] Where z1=0 is the nozzle exit position, z2=H is the impact point. p1 and p2 are the pressures at z1 and z2, respectively. The pressure can be calculated using the Yang-Laplace equation:

[0078]

[0079] Where p0 is the ambient pressure, is the normal vector of the jet free surface.

[0080] In the embodiment of the present invention, assuming that the axial curvature 1 / R2 is much smaller than the azimuthal curvature 1 / R1=1 / R(H), then

[0081]

[0082] Among them, R0=R1=d / 2. According to the formula The ratio of the jet velocity at the impact point z2 to the jet velocity at the nozzle outlet z1 can be obtained:

[0083]

[0084] Among them, w (H) and R (H) Represent the velocity and jet radius at the impact point respectively. According to the law of mass conservation, the flow rate of the jet at the two positions is equal, that is:

[0085]

[0086] Therefore, the ratio of the jet radius at the impact point z2 to the jet radius at the nozzle outlet z1 can be obtained as:

[0087]

[0088] In the embodiment of the present invention, the range of the jet Weber number We is 227-2618, and the influence of We on the jet radius and jet velocity is ignored here, so the formula is and formula It can be expressed as follows:

[0089]

[0090]

[0091] It can be seen that the vertical jet hits the horizontal plate upward. Under the action of gravity, the jet velocity decreases with the square root of the axial distance z. Correspondingly, the jet radius increases radially at the power of 1 / 4.

[0092] Step 5, define the ratio of the jet impact force to the circular water film area as the jet impact force coefficient, and derive the relationship between the jet impact force coefficient and the dimensionless impact power.

[0093] According to the analysis of jet velocity and jet diameter in step 4, the impact force of the vertical jet hitting the flat plate can be theoretically derived using the principle of conservation of momentum:

[0094]

[0095] Relating the impact force to the pressure drop Δp and the circular water film area A, the jet impact force coefficient C f is defined as follows:

[0096]

[0097] in, The formula Substitute into the formula The striking force coefficient C can be obtained f and the dimensionless water film radius r wf / The relationship of d:

[0098]

[0099] Furthermore, the formula The jet impact force coefficient C can be obtained f Regarding the relationship of dimensionless impact power Ip*:

[0100]

[0101] In the embodiment of the present invention, the effect of Fr and H / d on the impact force coefficient C is not considered. f The influence of the dimensionless impact power Ip* of the jet is considered, so the formula It can be written as follows:

[0102]

[0103] Figure 6 Shows the impact coefficient C for different nozzle diameters f The relationship between the dimensionless impact power Ip* and the test value of the jet impact force coefficient and the empirical formula The above test data and theoretical formulas all have good agreement, indicating that the present invention can well predict the striking performance of a jet vertically upward impacting a horizontal flat plate.

[0104] Therefore, the present invention adopts the above-mentioned jet impact plate cleaning performance prediction method based on dimensional analysis, combines the flow state and impact force formed by the jet impacting the plate, theoretically derives various physical quantities related to the cleaning performance, has high prediction accuracy, and is of great significance for the prediction of jet cleaning performance.

[0105] Finally, it should be noted that the above embodiments are only used to illustrate the technical solution of the present invention rather than to limit it. Although the present invention has been described in detail with reference to the preferred embodiments, those skilled in the art should understand that they can still modify or replace the technical solution of the present invention with equivalents, and these modifications or equivalent replacements cannot cause the modified technical solution to deviate from the spirit and scope of the technical solution of the present invention.

Claims

1. A method for predicting the cleaning performance of a jet impact plate based on dimensional analysis, characterized in that: The specific steps include: Step 1, establish a mathematical model of a circular water film formed by a jet impacting a flat plate, establish a polar coordinate system with the jet impact point as the coordinate origin, and use the impact jet geometric parameters to describe the model; If you use ψ Represents the cleaning performance objective function of the jet impacting the flat plate, and the influencing physical quantity is expressed as: ； in, ρ is the liquid density, kg / m 3 ; d is the nozzle outlet diameter, m; w 0 is the initial velocity of the jet outlet, m / s; H is the vertical distance from the jet nozzle outlet to the flat plate, m; g is the acceleration due to gravity, m / s 2 ; υ is the kinematic viscosity of the liquid, m 2 / s; σ is the surface tension coefficient of the liquid, N / m; r wf is the radius of the circular water film, m; F z is the jet impact force, N; Based on the dimensional analysis method, the objective function is transformed into: ； Where Re is the jet Reynolds number, Re= w 0 d / υ ; Fr is the jet Froude number, Fr= w 0 / (gd) 1 / 2 ; We is the jet Weber number, We= ρw 0 2 d / σ ; r wf / d is the dimensionless water film radius; Ip * is the dimensionless impact power, Ip *= πw 0 3 d 2 / 8 υ 7 / 3 g 1 / 3 ; θ is the dimensionless wetting angle, θ =2 r wf / H ; C f is the jet impact force coefficient; Step 2, defining the dimensionless water film radius and the dimensionless impact power based on dimensional analysis, and deriving the relationship between the dimensionless water film radius and the dimensionless impact power; The relationship between the dimensionless water film radius and the dimensionless impact power in step 2 is: ； in, C 1 and C 2 is the correction factor, C 1=( π / 8) 1 / 4 C 2; Step 3, defining the dimensionless wetting angle based on dimensional analysis, and deriving the relationship between the dimensionless wetting angle and the nozzle diameter; The relationship between the dimensionless wetting angle and the nozzle diameter in step 3 is as follows: ； Step 4, apply Bernoulli's equation to the jet impacting the plate upward, and derive expressions for the jet velocity and the jet radius at the jet impact point under the influence of gravity; The ratio of the velocity at the impact point to the velocity at the nozzle outlet in step 4 is specifically: ； in, w (H) and R (H) represent the velocity and jet radius at the impact point, respectively; R 0 represents the jet radius at the nozzle outlet, R 0= d / 2; all units are m; According to the law of conservation of mass, the flow rate of the jet at the nozzle outlet and the impact point is equal, that is, ； Therefore, the ratio of the jet radius at the impact point to the jet radius at the nozzle outlet is: ； Step 5, derive the theoretical impact force of the jet impacting the flat plate, define the ratio of the impact force to the circular water film area as the jet impact force coefficient, and derive the relationship between the jet impact force coefficient and the dimensionless impact power; The impact force coefficient in step 5 is defined as: ； in, , Indicates the jet impact force; , It represents the pressure drop between the stagnation point of the jet impact surface and the surrounding environment; , represents the area of ​​the circular water film; Therefore, the relationship between the jet impact force coefficient and the dimensionless impact power is expressed as: 。

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