CN109753698B - Method for establishing liquid shaking model in horizontal cylindrical liquid tank with longitudinal baffle - Google Patents
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Abstract
The invention discloses a method for establishing a liquid shaking model in a horizontal cylindrical liquid tank with a longitudinal baffle, which belongs to the field of kinematics and dynamics modeling, and is based on the equivalence of a horizontal shaking model of a horizontal cylindrical container, and the method utilizes a boundary element method to divide a liquid semi-free liquid level into grids and calculates a generalized coordinate vector gamma of a grid unit i And beta i Velocity profileAnd establishing a constraint equation of the grid unit, establishing a system dynamics and kinematics equation based on the Laplace equation and the Green equation, and solving to obtain lateral force and rolling moment generated by liquid shaking on the tank wall and the baffle. The boundary element method adopted by the invention improves the calculation efficiency, and the established multi-mode model effectively solves the dynamics analysis problem of the tank truck with the longitudinal baffle.
Description
Technical Field
The invention belongs to the technical field of kinematics and dynamics modeling, and particularly relates to a method for establishing a liquid shaking model in a horizontal cylindrical liquid tank with a longitudinal baffle.
Background
Sloshing of the liquid in the tank refers to movement of the free surface of the liquid due to an applied disturbance or excitation. The liquid shaking analysis is of great significance to the aspects of spaceflight and ships and is also of great significance to the transportation of the tank truck. In recent years, the side turning accidents of the oil tank truck are increased year by year, so that the casualties and property losses are serious. Along with the development of economy, the tank truck is one of main transportation vehicles for transporting dangerous chemicals, and the goods transported by the tank truck are generally dangerous chemicals in liquid state, so that the side turning accidents are easier to be caused compared with the common transportation vehicles when the tank truck is subjected to lateral force due to the shaking characteristic of liquid. External excitation generates obvious shaking power and moment for the tank truck, so an anti-shaking device must be introduced to analyze the influence of liquid shaking on the stability of the tank truck.
The effect of annular, transverse baffles on liquid sloshing in rectangular and ellipsoidal shaped containers has been studied heretofore. The liquid in the horizontal cylindrical liquid tank with the longitudinal baffle is relatively less in shaking analysis. Moreover, the related literature shows that the dynamic research of the rigid body part of the tank truck tends to be mature, and the mechanical model is effective mainly by means of a spring mass model, a simple pendulum model and the like. Research on interactions between sloshing liquid and vehicle systems is mostly limited to quasi-static fluid sloshing models, ignoring the effects of dynamic loads. The study of the liquid dynamics in the tank truck is still lacking. Therefore, a novel multi-mode model of liquid shaking in a horizontal cylindrical liquid tank with a longitudinal baffle is needed to be established. The natural frequency and the mode shape of each-order mode during liquid impact can be obtained by utilizing mode analysis, so that the relation between the mode parameters and the height of the baffle and the liquid filling ratio can be further studied, and the action mechanism of liquid impact in the tank can be further known.
Disclosure of Invention
Aiming at the defects of a modeling method for liquid dynamics research in the prior art, the invention provides a method for establishing a liquid shaking model in a horizontal cylindrical liquid tank with a longitudinal baffle, and the method effectively solves the dynamics analysis problem of a tank truck with the longitudinal baffle by establishing a multi-mode model.
In order to achieve the above purpose, the invention adopts the following technical scheme:
a method for establishing a liquid shaking model in a horizontal cylindrical liquid tank with a longitudinal baffle plate comprises the following steps:
step one: establishing a two-dimensional coordinate system yoz of the horizontal cylinder, and defining parameters according to the fluid domain, the free liquid level and the height of the baffle, wherein Q represents the fluid domain, s f Represent the free liquid level s w and sb Respectively representing the wetted tank wall surface area and baffle area, Γ representing the fluid boundary;
step two: under the condition that the fluid is set to be non-viscous, incompressible and non-rotational flow, a Laplace equation of a fluid domain velocity potential function phi and a free liquid level boundary condition are established according to the Laplace equation;
step three: decomposing the velocity potential into a relative velocity potential phi S And absolute velocity potential phi R By generalized coordinates gamma i and βi Respectively represent the relative velocity potential phi s (y, z, t) and the free liquid level delta (y, t) as follows:
wherein For normalized natural shaking mode, z 0 Is the distance from the free liquid level to the origin of coordinates;
step four: obtaining the generalized coordinate beta by utilizing the orthogonality of the modes and the relation between the relative velocity potential and the absolute velocity potential i Is as follows:
wherein ,σi Is the natural frequency of the liquid sloshing,g is the gravitational acceleration, k i and λi Is hydrodynamic coefficient>Is the lateral acceleration of the tank, < >>Is the generalized coordinate beta i Second derivative with respect to time t;
step five: integrating the differential equation (2) in the fourth step, and initializing the condition beta i (0)＝β 0i ，Periodic excitation Y (t) =y a Obtaining second derivative of sin sigma t to obtain +.>Then the second derivative is carried into a differential equation of (2), and the second constant coefficient differential equation is solved to obtain +.>The steady-state wave height of the periodic steady-state equation is:
wherein ,ya Is the amplitude of the periodic excitation Y (t), and σ is the frequency of the periodic excitation Y (t); so far, the solving of the generalized coordinate vector of the grid unit is completed;
step six: dividing the fluid boundary Γ into three-node secondary units, dividing the fluid domain intoQ I and QII Neglecting the thickness of the baffle, the boundary integral equation of the boundary point p obtained by the green second equation is as follows:
wherein When the boundary point p is at a smooth boundary, +.>When the boundary point p is a corner point, α p Is the included angle between boundary tangents at the p position;
step seven: discretizing the boundary integral equation (4), configuring according to nodes on the boundary, and rewriting the equation (4) into:
wherein i is the node number, j is the unit number, and the integral on each unit is related to only the node i and the unit j, so that
Then the formula (5) becomes
When the point coincides with the source point, i.e. i=j,the rest are all 0, let
Then the formula (7) becomes
Calculating an influence coefficient matrix H using a quadratic interpolation function according to equation (9) Ι and GΙ Boundary quantity on each element of (3) and qi Obtaining the speed potential->
Step eight: all defined parameters are solved, the pressure distribution on the wall surface of the tank body and the baffle plate is derived according to a linearized Bernoulli equation, the lateral force and the rolling moment are obtained by integrating the pressures distributed on the wall of the wetting tank and the baffle plate according to mechanical knowledge, and the parameters are solved to obtain complete kinematics and dynamics equations of the lateral force and the rolling moment, namely a multi-modal model of liquid shaking in the horizontal cylindrical liquid tank with the longitudinal baffle plate.
Preferably, in the first step, the step of establishing a two-dimensional coordinate system of the horizontal cylinder further includes: the origin o of the two-dimensional coordinate system oyz is established at the center of the can, and the horizontal flat-head cylindrical can with radius R is stimulated laterally along the y-axis and vertically upwards along the z-axis to fill the height h with liquid.
Preferably, in the first step, the baffles comprise three bottom baffles and three top baffles, the heights of each baffle are different, and the three bottom baffles and the three top baffles are distributed at the middle longitudinal surface of the tank body.
Preferably, in the second step, the Laplace equation of the fluid domain velocity potential function phi and the boundary condition of the free liquid surface are respectively:
where δ (y, t) is the free liquid level height and g is the gravitational acceleration.
Further, in step three, decomposing the velocity potential phi in the boundary condition of the free liquid surface of the formula (11) into an absolute velocity potential phi R And relative velocity potential phi S Facilitate determination of the generalized coordinate beta i Is a differential equation of (a). The absolute velocity potential, i.e. the rigid motion of the fluid, is the same as the velocity potential of the tank motion. The relative velocity potential is the motion of the fluid relative to the tank, i.e., the velocity potential of the fluid sloshing.
Preferably, in the third step, for facilitating calculation, the normalized natural shaking modeThe concrete steps are as follows:
wherein Ni Is the number of elements on the semi-free liquid surface.
Preferably, in the fourth step, the orthogonality of the modes and the relation between the relative velocity potential and the absolute velocity potential specifically refer to:
modal orthogonality:
wherein ,sf Indicating the length of the free liquid level, i is the node number, j is the unit number,the velocity potential of the node and the cell, respectively;
relation of relative velocity potential to absolute velocity potential:
wherein ,is the lateral velocity of the tank body, gamma i (t) is generalized coordinates, s f Indicating the length of the free liquid level, i is the node number, j is the unit number, +.>The velocity potential of the node and the cell, respectively.
Preferably, in step four, the hydrodynamic coefficient λ i Further comprises: for symmetric modes, i.e. even-order modes, λ 2i =0; for asymmetric modes, i.e. odd-order modes, then
Preferably, in step six, the fluid domain is divided into Q I and QII Due to the fluid field Q I and QII Is symmetrical, so that a fluid sloshing mode matrix equation is obtained:
wherein ,is->The unknown vector at each node affects the coefficient matrix H Ι and GΙ Calculating the boundary quantity on each element from the rewritten boundary integral formula (9) using a quadratic interpolation function> and qi The method comprises the steps of carrying out a first treatment on the surface of the Subscripts f, c, b, and w refer to the free liquid surface, the internal interface, respectively,A baffle and a tank boundary; h Ι and GΙ The first subscript of (2) represents the position of the source point, i.e., point p in the boundary integration equation, and the second subscript represents the position of the element performing the boundary integration.
Preferably, in step eight, the specific expression of the lateral force and the roll moment solved after the parameter is brought in is as follows:
lateral force:
roll moment:
wherein S w ,S b Is the wetted tank wall and baffle area, F y Indicating the total lateral force applied by the tank body in the y-axis direction, F y,s ，F y,R Respectively representing the relative lateral force and absolute lateral force to which the tank body wall surface and the baffle are subjected, ρ represents the density of the liquid, m represents the mass of the liquid in the tank body, and k i and λi Is hydrodynamic coefficient>Is the lateral acceleration of the tank, < >>Is the generalized coordinate beta i Regarding the second derivative of time t, M o (t) represents the total lateral force F y Total moment of origin of coordinates O, M s (t) represents the relative lateral force F y,s Relative moment to origin O of coordinates, M R (t) represents absolute lateral force F y,R Absolute moment of origin O of coordinates, y 0 Indicating the length of the semi-free liquid surface.
Compared with the prior art, the invention has the beneficial effects that: the invention provides a liquid in a horizontal cylindrical liquid tank with a longitudinal baffle plateThe shaking model establishment method can be used for an actual liquid shaking model in a horizontal cylindrical liquid tank, is based on the equivalent of a horizontal shaking model of the horizontal cylindrical liquid tank, divides a liquid semi-free liquid level into grids by using a boundary element method, and calculates a generalized coordinate vector gamma of a grid unit i and βi Velocity profileAnd establishing a constraint equation of the grid unit, establishing a system dynamics and kinematics equation by using a Laplace equation and a Grignard equation, and solving to obtain lateral force and rolling moment generated by liquid shaking on the tank wall and the baffle. The boundary element method adopted by the method improves the calculation efficiency, and the established multi-mode model effectively solves the dynamics analysis problem of the tank truck with the longitudinal baffle.
Drawings
FIG. 1 is a schematic illustration of two-dimensional fluid movement within a partially baffled circular cross-section can;
FIG. 2 is a schematic illustration of a separated fluid domain;
figure 3 is a bottom longitudinal baffle height of 0.25R,
figure 4 is a bottom longitudinal baffle height of 0.5R,
figure 5 is a bottom longitudinal baffle height of 0.75R,
figure 6 is a top longitudinal baffle height of 1.75R,
figure 7 is a top longitudinal baffle height of 1.5R,
figure 8 is a top longitudinal baffle height of 1.25R,
Detailed Description
The following description of the embodiments of the present invention will be made more apparent and fully hereinafter with reference to the accompanying drawings, in which some, but not all embodiments of the invention are shown. All other embodiments, which can be made by one of ordinary skill in the art without undue burden on the person of ordinary skill in the art based on embodiments of the present invention, are within the scope of the present invention.
The invention provides a method for establishing a liquid shaking model in a horizontal cylindrical liquid tank with a longitudinal baffle, which is shown in figure 1, wherein a two-dimensional coordinate system of a horizontal cylindrical tank body is established, an origin o of a two-dimensional coordinate system oyz is established at the center of the tank body, the radius of the horizontal flat-head cylindrical tank body is R, the radius is stimulated by the lateral direction along a y axis, the z axis is vertically upwards, the liquid filling height h (namely the height from a tank bottom B point to a free liquid level) is equal to m in mass of liquid in unit length, and the length of a semi-free liquid level is equal to y 0 Baffle length l b . FIG. 2 is a schematic illustration of a separated fluid domain.
In a specific implementation, six longitudinal baffles of different heights are provided, including three bottom baffles and three top baffles, which are all distributed at the middle longitudinal surface of the tank, as shown in fig. 3 to 8.Is the lateral speed of the tank body, < >>Is the lateral acceleration of the tank. The force and moment generated by the liquid shaking on the tank body and the baffle plate are F respectively y and MO . The i th order natural shaking mode is +.>From the symmetry of the separated fluid domains, the hydrodynamic coefficient λ of the symmetric mode is obtained (2i) =0, antisymmetric modal hydrodynamic coefficient +.>γ i and βi Is generalized coordinates.
The model building method comprises the following steps:
step one: a two-dimensional coordinate system yoz of the horizontal cylinder is established, and parameters are defined according to the fluid field, the free liquid level and the height of the baffle. Q represents a fluid domain, s f Represent the free liquid level s w and sb Respectively the wetted tank wall surface area and the baffle area, Γ representing the fluid boundary. h represents the height from the point B at the bottom of the tank body to the free liquid level, y 0 Indicating the length of the semi-free liquid level, z 0 Representing the height of the free liquid surface from the origin of coordinates, g represents the gravitational acceleration.
Step two: and under the condition that the fluid is set to be non-viscous, incompressible and non-rotational flow, establishing a Laplace equation of a fluid domain velocity potential function phi and a free liquid level boundary condition according to the Laplace equation.
Specifically, the Laplace equation of the fluid domain velocity potential function phi and the boundary conditions of the free liquid surface are respectively:
where δ (y, t) is the free liquid level height and g is the gravitational acceleration.
Step three: decomposing the velocity potential into a relative velocity potential phi S And absolute velocity potential phi R By generalized coordinates gamma i and βi Respectively represent the relative velocity potential phi s (y, z, t) and the free liquid level delta (y, t) as follows:
wherein For normalized natural shaking mode, z 0 Is the distance of the free liquid surface from the origin of coordinates.
In particular, for ease of calculation, the normalized natural shaking modeThe concrete steps are as follows:
wherein Ni Is the number of elements on the semi-free liquid surface.
Step four: obtaining the generalized coordinate beta by utilizing the orthogonality of the modes and the relation between the relative velocity potential and the absolute velocity potential i Is as follows:
wherein ,σi Is the natural frequency of the liquid sloshing,g is the gravitational acceleration, k i and λi Is hydrodynamic coefficient>Is the lateral acceleration of the tank; />Is the generalized coordinate beta i Second derivative with respect to time t.
Wherein, the orthogonality of the modes and the relation between the relative velocity potential and the absolute velocity potential are specifically:
modal orthogonality:
relation of relative velocity potential to absolute velocity potential:
wherein ,is the lateral velocity of the tank body, gamma i (t) is generalized coordinates, s f Indicating the length of the free liquid level, i is the node number, j is the unit number, +.>The velocity potential of the node and the cell, respectively.
Further, the hydrodynamic coefficient lambda i Further comprises: for symmetric modes, i.e. even-order modes, λ 2i =0; for asymmetric modes, i.e. odd-order modes, then
Step five: integrating the differential equation (5) in the fourth step, and initializing the condition beta i (0)＝β 0i ，Periodic excitation Y (t) =y a Obtaining second derivative of sin sigma t to obtain +.>The second derivative is then brought into the micro-scale of equation (5)Solving a second-order constant coefficient differential equation to obtain +.>The steady-state wave height of the periodic steady-state equation is:
wherein ,ya Is the amplitude of the periodic excitation Y (t), and σ is the frequency of the periodic excitation Y (t); and thus, the solving of the generalized coordinate vector of the grid unit is completed.
Step six: dividing the fluid boundary Γ into three-node secondary units, dividing the fluid domain into Q I and QII Neglecting the thickness of the baffle, the boundary integral equation of the boundary point p obtained by the green second equation is as follows:
wherein When the boundary point p is at a smooth boundary, +.>When the boundary point p is a corner point, α p Is the angle between the boundary tangents at p.
Specifically, the fluid domain is divided into Q I and QII Due to the fluid field Q I and QII Is symmetrical, so that a fluid sloshing mode matrix equation is obtained:
wherein ,is->The unknown vector at each node affects the coefficient matrix H Ι and GΙ Calculating the boundary quantity +.for each element from the rewritten boundary integral formula using a quadratic interpolation function> and qi The method comprises the steps of carrying out a first treatment on the surface of the Subscripts f, c, b, and w refer to the free liquid surface, the internal interface, the baffle, and the tank boundary, respectively; h Ι and GΙ The first subscript of (2) represents the position of the source point, i.e., point p in the boundary integration equation, and the second subscript represents the position of the element performing the boundary integration.
Step seven: discretizing the boundary integral equation (7), and configuring according to nodes on the boundary, wherein the equation (7) can be rewritten as follows:
in the formula, i is a node sequence number, and j is a unit sequence number. The integral over each cell is only related to node i and cell j. Order the
Then the formula (5) becomes
When the point coincides with the source point i.e. i=j,the balance being 0. Thus making the lead
Then the formula (11) can be changed into
Calculating the influence coefficient matrix H using a quadratic interpolation function according to equation (13) Ι and GΙ Boundary quantity on each element of (3) and qi I.e. speed potential->And (5) obtaining the solution.
Step eight: solving all defined parameters, deriving dynamic pressure distribution on the wall surface of the tank body and the baffle according to a linearized Bernoulli equation, integrating to obtain lateral force and rolling moment, and carrying the parameters into solution; and obtaining complete kinematics and dynamics equations of the lateral force and the side-tipping moment, namely a multi-mode model of liquid shaking in the horizontal cylindrical liquid tank with the longitudinal baffle.
Specifically, the specific expression of the lateral force and the roll moment solved after the parameter is brought in is as follows:
lateral force:
roll moment:
wherein S w ,S b Is the wetted tank wall and baffle area, F y Indicating the total lateral force applied by the tank body in the y-axis direction, F y,s ，F y,R Respectively representing the relative lateral force and absolute lateral force to which the tank body wall surface and the baffle are subjected, ρ represents the density of the liquid, m represents the mass of the liquid in the tank body, and k i and λi Is hydrodynamic coefficient>Is the lateral acceleration of the tank; />Is the generalized coordinate beta i Regarding the second derivative of time t, M o (t) represents the total lateral force F y Total moment of origin of coordinates O, M s (t) represents the relative lateral force F y,s Relative moment to origin O of coordinates, M R (t) represents absolute lateral force F y,R Absolute moment of origin O of coordinates, y 0 Indicating the length of the semi-free liquid surface.
The invention provides a method for establishing a liquid shaking model in a horizontal cylindrical liquid tank with a longitudinal baffle, which belongs to the field of kinematics and dynamics modeling, and the method is based on the equivalence of a horizontal shaking model of a horizontal cylindrical container, utilizes a boundary element method to divide a liquid semi-free liquid level into grids, and calculates a generalized coordinate vector gamma of a grid unit i and βi Velocity profileAnd establishing a constraint equation of the grid unit, establishing a system dynamics and kinematics equation based on the Laplace equation and the Green equation, and solving to obtain lateral force and rolling moment generated by liquid shaking on the tank wall and the baffle. The boundary element method adopted by the invention improves the calculation efficiency, and the established multi-mode model effectively solves the dynamics analysis problem of the tank truck with the longitudinal baffle.
Although embodiments of the present invention have been shown and described, it will be understood by those skilled in the art that various changes, modifications, substitutions and alterations can be made therein without departing from the principles and spirit of the invention, the scope of which is defined in the appended claims and their equivalents.
Claims (9)
1. The method for establishing the liquid shaking model in the horizontal cylindrical liquid tank with the longitudinal baffle is characterized by comprising the following steps of:
step one: establishing a two-dimensional coordinate system yoz of the horizontal cylinder, and defining parameters according to the fluid domain, the free liquid level and the height of the baffle, wherein Q represents the fluid domain, s f Representing the length of the free liquid level, s w and sb Respectively representing the wetted tank wall surface area and baffle area, Γ representing the fluid boundary;
step two: under the condition that the fluid is set to be non-viscous, incompressible and non-rotational flow, a Laplace equation of a fluid domain velocity potential function phi and a free liquid level boundary condition are established according to the Laplace equation;
step three: decomposing the velocity potential into a relative velocity potential phi S And absolute velocity potential phi R By generalized coordinates gamma i and βi Respectively represent the relative velocity potential phi s (y, z, t) and the free liquid level delta (y, t) as follows:
wherein For normalized natural shaking mode, z 0 Is the distance from the free liquid level to the origin of coordinates;
step four: obtaining the generalized coordinate beta by utilizing the orthogonality of the modes and the relation between the relative velocity potential and the absolute velocity potential i Is as follows:
wherein ,σi Is the natural frequency of the liquid sloshing,g is the gravitational acceleration, k i and λi As a result of the coefficient of fluid dynamics,is the lateral acceleration of the tank, < >>Is the generalized coordinate beta i Second derivative with respect to time t;
step five: integrating the differential equation (2) in the fourth step, and initializing the condition beta i (0)＝β 0i ，Periodic excitation Y (t) =y a Obtaining second derivative of sin sigma t to obtain +.>Then the second derivative is carried into a differential equation of (2), and the second constant coefficient differential equation is solved to obtain +.>The steady-state wave height of the periodic steady-state equation is:
wherein ,ya Is the amplitude of the periodic excitation Y (t), and σ is the frequency of the periodic excitation Y (t); so far, the solving of the generalized coordinate vector of the grid unit is completed;
step six: dividing the fluid boundary Γ into three-node secondary units, dividing the fluid domain into Q I and QII Neglecting the thickness of the baffle, the boundary integral equation of the boundary point p obtained by the green second equation is as follows:
wherein When the boundary point p is located at a smooth boundary,when the boundary point p is a corner point, α p Is the included angle between boundary tangents at the p position;
step seven: discretizing the boundary integral equation (4), configuring according to nodes on the boundary, and rewriting the equation (4) into:
wherein i is the node number, j is the unit number, and the integral on each unit is related to only the node i and the unit j, so that
Then the formula (5) becomes
When the point coincides with the source point, i.e. i=j,the rest are all 0, let
Then the formula (7) becomes
Calculating an influence coefficient matrix H using a quadratic interpolation function according to equation (9) I and GI Boundary quantity on each element of (3) and qi Obtaining the speed potential->
Step eight: all defined parameters are solved, the pressure distribution on the wall surface of the tank body and the baffle plate is derived according to a linearized Bernoulli equation, the lateral force and the rolling moment are obtained by integrating the pressures distributed on the wall of the wetting tank and the baffle plate according to mechanical knowledge, and the parameters are solved to obtain complete kinematics and dynamics equations of the lateral force and the rolling moment, namely a multi-modal model of liquid shaking in the horizontal cylindrical liquid tank with the longitudinal baffle plate.
2. The method for creating a sloshing model of liquid in a horizontal cylinder tank with a longitudinal baffle according to claim 1, wherein in the step one, the step of creating a two-dimensional coordinate system yoz of the horizontal cylinder further comprises: the origin o of the two-dimensional coordinate system yoz is established at the center of the tank body, the horizontal flat-head cylindrical tank body with the radius R is stimulated laterally along the y axis, the z axis is vertically upwards, and the liquid filling height is h.
3. The method for building a liquid shaking model in a horizontal cylindrical liquid tank with longitudinal baffles according to claim 1, wherein in the first step, the baffles comprise three bottom baffles and three top baffles, the heights of each baffle are different, and the three bottom baffles and the three top baffles are distributed at the middle longitudinal surface of the tank body.
4. The method for establishing a liquid sloshing model in a horizontal cylindrical liquid tank with a longitudinal baffle according to claim 1, wherein in the second step, the Laplace equation of the velocity potential function phi of the fluid domain and the boundary conditions of the free liquid level are respectively:
▽ 2 φ＝0 (10)
where δ (y, t) is the free liquid level height and g is the gravitational acceleration.
5. The method for building a liquid shaking model in a horizontal cylindrical liquid tank with a longitudinal baffle according to claim 1, wherein in the third step, for facilitating calculation, the normalized natural shaking modeThe concrete steps are as follows:
wherein Ni Is the number of elements on the semi-free liquid level,is the i-th order natural shaking mode.
6. The method for establishing a liquid shaking model in a horizontal cylindrical liquid tank with a longitudinal baffle according to claim 1, wherein in the fourth step, the orthogonalization of the mode and the relation between the relative velocity potential and the absolute velocity potential specifically refer to:
modal orthogonality:
wherein ,sf Indicating the length of the free liquid level, i is the node number, j is the unit number,the velocity potential of the node and the cell, respectively;
relation of relative velocity potential to absolute velocity potential:
wherein ,is the lateral velocity of the tank body, gamma i (t) generalized coordinates, < >>The velocity potential of the node and the cell, respectively.
7. The method for establishing a liquid sloshing model in a horizontal cylindrical liquid tank with a longitudinal baffle according to claim 1, wherein in the fourth step, the hydrodynamic coefficient λ is i Further comprises: for symmetric modes, i.e. even-order modes, λ 2i =0; for asymmetric modes, i.e. odd-order modes, thens f Indicating the length of the free liquid surface.
8. The method for building a sloshing model of liquid in a horizontal cylindrical liquid tank with longitudinal baffle according to claim 1, wherein in step six, the fluid domain is divided into Q I and QII Due to the fluid field Q I and QII Is symmetrical, so that a fluid sloshing mode matrix equation is obtained:
wherein ,is->The unknown vector at each node affects the coefficient matrix H I and GI Calculating the boundary quantity on each element from the rewritten boundary integral formula (9) using a quadratic interpolation function> and qi The method comprises the steps of carrying out a first treatment on the surface of the Subscripts f, c, b, and w refer to the free liquid surface, the internal interface, the baffle, and the tank boundary, respectively; h I and GI The first subscript of (2) represents the position of the source point, i.e., point p in the boundary integration equation, and the second subscript represents the position of the element performing the boundary integration; q I Is q i An unknown vector at each node.
9. The method for building a liquid sloshing model in a horizontal cylindrical liquid tank with a longitudinal baffle according to claim 1, wherein in the eighth step, the specific expression of the lateral force and the rolling moment solved after the parameters are brought in is as follows:
lateral force:
roll moment:
wherein S w ,S b Is the wetted tank wall and baffle area, F y Indicating the total lateral force applied by the tank body in the y-axis direction, F y,s ，F y,R Respectively representing the relative lateral force and absolute lateral force to which the tank body wall surface and the baffle are subjected, ρ represents the density of the liquid, m represents the mass of the liquid in the tank body, and k i and λi Is hydrodynamic coefficient>Is the lateral acceleration of the tank, < >>Is the generalized coordinate beta i Regarding the second derivative of time t, M o (t) represents the total lateral force F y Total moment of origin of coordinates O, M s (t) represents the relative lateral force F y,s Relative moment to origin O of coordinates, M R (t) represents absolute lateral force F y,R Absolute moment of origin O of coordinates, y 0 Indicating the length of the semi-free liquid surface.
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| CN107436981A (en) * | 2017-07-27 | 2017-12-05 | 中国人民解放军后勤工程学院 | Oil plant rocks the method for building up of numerical model inside vehicle-mounted metallic oil tank |
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