CN114861134B - Step length determination method for calculating water drop motion track and storage medium - Google Patents
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Abstract
The embodiment of the application discloses a step length determining method for calculating a water drop motion track and a storage medium, and relates to the technical field of water drop impact characteristic research. The method comprises the following steps: acquiring a single step error under the current time step according to the last time step of the water drop and the motion parameter variation of the current time step, wherein the motion parameter variation comprises position variation and/or speed variation; if the single step error under the current time step is smaller than the minimum value of the preset interval, increasing the value of the current time step as the value of the next time step; and if the single step error under the current time step is within a preset interval, taking the value of the current time step as the value of the next time step. And if the single step error under the current time step is larger than the maximum value of the preset interval, reducing the value of the current time step as the value of the next time step. Therefore, the problem that the motion trail of the water drop cannot meet the requirements of high precision and small calculated amount at the same time can be solved.
Description
Technical Field
The present disclosure relates to the field of research technologies for water drop impact characteristics, and more particularly, to a method for determining a step length for calculating a water drop motion trajectory and a storage medium.
Background
When the plane passes through the cloud layer, supercooled water drops impact the plane body, phase change may occur and icing may be caused. Icing can change the appearance and the streaming flow field of the airplane, destroy the pneumatic performance, reduce the maneuverability and the stability, threaten the flight safety and cause air crash accidents in severe cases. The water drop collection rate can quantitatively represent water drops impacting on an object and is an important parameter for researching the impact characteristics of the water drops. Therefore, the water drop collection rate can be used for researching the icing characteristic of the airplane and can also be used for designing an anti-icing system of the airplane.
At present, a numerical simulation method can be adopted to study the water drop collection rate, wherein the lagrangian method is one of the common methods for studying the water drop collection rate. And obtaining the motion trail of the water drop released by the far field plane by using a Lagrange method, thereby obtaining the condition that the water drop impacts the object plane. The water drop collection rate can then be obtained by using an area ratio method or a particle statistical method.
In the prior art, when a motion trajectory of a water drop released from a far-field plane is obtained, the same time step is usually adopted, if the accuracy of the obtained motion trajectory of the water drop is high enough to obtain the accuracy of the obtained water drop collection rate, the time step needs to be very small, and when the motion trajectory of the water drop is obtained, the number of calculated steps is very large, which results in a large calculation amount; if the calculation amount for obtaining the movement trajectory of the water droplet is to be reduced, the time step needs to be increased, but this will result in insufficient accuracy of the obtained movement trajectory of the water droplet.
Therefore, the prior art has the problem that high precision and small calculation amount cannot be simultaneously met when the motion trail of the water drop is obtained.
Disclosure of Invention
The application provides a step length determining method for calculating a water drop motion track, which is characterized by obtaining a single-step error under a current time step according to a motion parameter variation of the last time step of a water drop and a motion parameter variation of the current time step, wherein the motion parameter variation comprises a position variation and/or a speed variation, and the single-step error comprises a position variation error and/or a speed variation error; and if the single step error under the current time step is smaller than the minimum value of the preset interval, increasing the value of the current time step as the value of the next time step. And if the single step error under the current time step is larger than the maximum value of the preset interval, reducing the value of the current time step as the value of the next time step. And if the single step error under the current time step is within a preset interval, taking the value of the current time step as the value of the next time step. According to the method provided by the application, the value of the next time step is determined according to the error in each time step, when the error is small, namely the calculation precision of the water drop motion track can be ensured, the time step is increased, the times of calculating the water drop motion track are reduced, and therefore the calculation amount is reduced under the condition of ensuring the precision; when the error is large, the time step length is reduced, and the calculation precision of the movement track of the water drop is improved; and when the error is proper, keeping the original time step to continue the calculation. Therefore, the problem that in the prior art, when the motion trail of the water drop is obtained, high precision and small calculated amount cannot be met simultaneously can be effectively solved.
In a first aspect, an embodiment of the present application provides a step size determining method for calculating a movement trajectory of a water droplet, where the method includes: s110, obtaining a single step error under the current time step according to the motion parameter variation of the last time step of the water drop and the motion parameter variation of the current time step, wherein the motion parameter variation comprises position variation and/or speed variation, and the single step error comprises position variation errorAnd/or speed variance error(ii) a S120, if the single step error under the current time step is smaller than the minimum value of the preset interval, increasing the value of the current time step as the value of the next time step, wherein the preset interval is,For the purpose of the upper limit of the single-step error,is an error control factor, and(ii) a And S130, if the single step error under the current time step is within a preset interval, taking the value of the current time step as the value of the next time step.
In a second aspect, the present application further provides a computer-readable storage medium, in which a program code is stored, where the program code can be called by a processor to execute the above method.
In summary, the present application has at least the following technical effects:
1. the value of the next time step is determined according to the error in each time step, when the error is small, namely the calculation precision of the water drop motion track can be guaranteed, the time step is increased, the number of times of calculating the water drop motion track is reduced, and therefore the calculation amount is reduced under the condition of guaranteeing the precision.
2. This application is through the error in according to every time step, confirms the value of next time step, and when the error is great, reduces the time step, improves the computational accuracy of water droplet movement track.
3. The value of the next time step is determined according to the error in each time step, when the error is appropriate, the original time step is kept to continue to be calculated, and meanwhile, high precision and small calculated amount are met.
Therefore, the scheme provided by the application can effectively solve the problem that the prior art cannot meet the requirements of high precision and small calculated amount at the same time when the motion trail of the water drop is obtained.
Drawings
In order to more clearly illustrate the technical solutions in the embodiments of the present application, the drawings needed to be used in the description of the embodiments are briefly introduced below, and it is obvious that the drawings in the following description are only some embodiments of the present application, and it is obvious for those skilled in the art to obtain other drawings based on these drawings without creative efforts.
Fig. 1 is a schematic flow chart illustrating a step size determining method for calculating a water drop motion trajectory, provided by embodiment 1 of the present application;
fig. 2 shows a schematic diagram of a far field plane releasing water droplets provided in example 1 of the present application;
fig. 3 is a schematic diagram illustrating a last time step and a next time step provided in embodiment 1 of the present application;
FIG. 4 is a schematic diagram showing the current time step provided in embodiment 1 of the present application;
fig. 5 shows a storage unit for storing or carrying program codes for implementing the step size determining method for calculating a water drop motion trajectory according to the embodiment of the present application, provided in embodiment 2 of the present application.
Detailed Description
In order to make the technical solutions of the present application better understood, the technical solutions in the embodiments of the present application will be clearly and completely described below with reference to the drawings in the embodiments of the present application, and it is obvious that the described embodiments are only a part of the embodiments of the present application, and not all of the embodiments. All other embodiments, which can be derived by a person skilled in the art from the embodiments given herein without making any creative effort, shall fall within the protection scope of the present application.
Currently, the lagrangian method is one of the common methods for studying the water droplet collection rate. And obtaining the motion trail of the water drop released by the far field plane by using a Lagrange method, thereby obtaining the condition that the water drop impacts the object plane. And then the water drop collection rate can be obtained by adopting an area ratio method or a particle statistical method. When the motion trail of the water drop released from the far-field plane is obtained, the same time step is usually adopted, if the precision of the obtained motion trail of the water drop is high enough to ensure that the precision of the obtained water drop collection rate is high enough, the time step needs to be very small, and when the motion trail of the water drop is obtained, the number of calculated steps is very large, so that the calculation amount is very large; if the calculation amount for obtaining the movement trajectory of the water droplet is to be reduced, the time step needs to be increased, but this will result in insufficient accuracy of the obtained movement trajectory of the water droplet.
Therefore, in order to solve the above-mentioned drawback, an embodiment of the present application provides a step size determining method for calculating a movement trajectory of a water droplet, where the method includes: obtaining a single step error under the current time step according to the motion parameter variation of the last time step of the water drop and the motion parameter variation of the current time step, wherein the motion parameter variation comprises a position variation and/or a speed variation, and the single step error comprises a position variation error and/or a speed variation error; if the single step error under the current time step is smaller than the minimum value of the preset interval, increasing the value of the current time step as the value of the next time step; and if the single step error under the current time step is within a preset interval, taking the value of the current time step as the value of the next time step. When the error is small, namely the calculation precision of the water drop motion track can be ensured, the time step length is increased, the frequency of calculating the water drop motion track is reduced, and when the error is appropriate, the original time step length is kept to continue calculation, so that the calculation amount is reduced under the condition of ensuring the precision.
The following describes a step length determination method for calculating a water drop motion trajectory according to the present application.
Example 1
Referring to fig. 1, fig. 1 is a schematic flowchart of a method for determining a step length for calculating a motion trajectory of a water droplet according to embodiment 1 of the present application. In this embodiment, the step length determining method for calculating the movement trajectory of the water drop may include the following steps:
step S110: obtaining a single step error under the current time step according to the motion parameter variation of the last time step and the motion parameter variation of the current time step of the water drop, wherein the motion parameter variation comprises a position variation and/or a speed variation, and the single step error comprises a position variation errorAnd/or speed variation error。
In the embodiment of the present application, far field flat is shown in FIG. 2The Lagrange method judges whether each water drop can impact the object plane or not by obtaining the motion trail of each water drop released by the far field plane. The movement locus of the water drop can be obtained according to the stress condition of the water drop. Specifically, depending on the gravity, buoyancy and resistance to which the water droplets are subjected, it is possible to obtain:wherein, in the process,is the density of the air flow field and,is the density of the water droplets and,is the volume of the water droplets,is the displacement of the water droplet or droplets,is the velocity of the air flow field and,is the speed of the water droplets,is the area of the water drop facing the wind,is the acceleration of the force of gravity,is a water drop resistance coefficient, and,is the relative reynolds number for the gas,and is made of,Is the equivalent diameter of the water drops,is the air viscosity coefficient. From the above formula, one can obtain:wherein, in the step (A),is the acceleration of the water droplet. According to the acceleration of the water drop, the position of the water drop in each time step can be obtained until the water drop moves from a far-field plane to an object plane or moves from the far-field plane to the periphery of the object plane, and then the movement track of the water drop can be obtained.
As an alternative, the variation of the motion parameter includes a variation of a position or a variation of a speed, and the single step error is a variation of a position errorOr error in variation of speed。
As another alternative, the motion parameter variation includes a position variation and a speed variation, and the single-step error is a position variation errorAnd velocityError of variation。
As still another alternative, the motion parameter variation includes a position variation and a speed variation, and the single-step error is a position variation errorAnd error in speed variationMaximum value of (2).
In the embodiment of the present application,may be a relative error of the amount of position change, i.e.,It may also be the absolute error of the amount of change in position, i.e.Wherein, in the step (A),is the amount of position change of the current time step,the position variation of the last time step is used as the position variation of the last time step.
In the embodiment of the present application,may be a relative error in the amount of speed change, i.e.,It may also be the absolute error of the speed variation, i.e.Wherein, in the process,is the speed variation of the current time step,the speed variation of the last time step is adopted.
In an exemplary embodiment, if the last time step is followed by the next time step, step S110 may include sub-step S111 and sub-step S112.
Substep S111: and obtaining the acceleration of the last time step of the water drop and the acceleration in the current time step after the last time step of the water drop according to the stress condition of the water drop, wherein the current time step is equal to the current time step.
Substep S112: and obtaining the motion parameter variation of the previous time step according to the acceleration of the previous time step on the water drop and the value of the previous time step, and obtaining the motion parameter variation of the current time step according to the acceleration in the current time step after the previous time step on the water drop and the value of the current time step.
In the embodiment of the present application, as shown in fig. 3, the last time step has a value ofThe next time step has a value of. The last time step is followed by the next time step. In this embodiment, the current time stepThe length is not the time step actually used in the process of acquiring the motion track of the water drop, but is an assumed value used for determining the next time step, and the value of the current time step is equal to the value of the previous time step.
In an exemplary embodiment, if the last time step is followed by the current time step and the current time step is followed by the next time step, step S110 may further include substeps S113 and S114.
Substep S113: and obtaining the acceleration of the last time step of the water drop and the acceleration of the current time step according to the stress condition of the water drop, wherein the current time step is determined by the single step error of the last time step.
Substep S114: and obtaining the motion parameter variation of the previous time step according to the acceleration of the previous time step of the water drop and the value of the previous time step, and obtaining the motion parameter variation of the current time step according to the acceleration of the current time step of the water drop and the value of the current time step.
In the embodiment of the present application, as shown in fig. 4, the last time step has a value ofThe current time step has a value ofThe next time step has a value of. The last time step is followed by the current time step, and the next time step is followed by the current time step. In this embodiment, the current time step is a time step actually used in the process of obtaining the movement trajectory of the water drop, and the current time step is determined by a single-step error in the previous time step, if the single-step error in the previous time step is within a preset interval, the current time step is equal to the previous time step, and if the single-step error in the previous time step is not within the preset interval, the current time step is not within the preset intervalThe time step may not be equal to the previous time step, but the value of the previous time step is decreased or increased according to the single step error as the value of the current time step.
Step S120: if the single step error under the current time step is smaller than the minimum value of the preset interval, increasing the value of the current time step as the value of the next time step, wherein the preset interval is,For the purpose of the upper limit of the single-step error,is an error control factor, and。
in an exemplary embodiment, the value of the upper limit of the single step error and the value of the error control factor may be set empirically, for example, the value of the upper limit of the single step error may beThe value of the error control factor may be 1.3.
As an alternative, the current time step value may be increased empirically.
As another alternative, the value of the current time step may be increased by using a binary method.
For example: if the last time step is later than the next time step, setting,,. The last time step has a value ofLet the current time step have a value ofAnd at this timeIf the single-step error in the current time step is smaller than the minimum value of the preset interval, the implementation manner may be: order to,Then give an order againIncrease the current time step toAnd is used as the value of the next time step; the implementation may also be: order to,Then give an order againIncreasing the value of the current time step toAnd at this timeRepeating the steps until the single step error under the increased current time step is in a preset interval, and increasing the current time step to the current time stepAs the value of the next time step.
Another example is: if the last time step is followed by the current time step and the next time step is followed by the current time step, setting,,. Current step of time and that timeIf the single step error in the current time step is smaller than the minimum value of the preset interval, the embodiment may be: order to,Then give an order againIncrease the current time step toAnd is used as the value of the next time step; the implementation may also be: order to,Then give an order againIncreasing the value of the current time step toAnd at this timeRepeating the above steps until the single step error of the increased current time step is within a preset interval, and increasing the current time step to the current time stepAs the value of the next time step.
The value of the next time step is determined according to the error in each time step, when the error is small, namely the calculation precision of the water drop motion track can be guaranteed, the time step is increased, the number of times of calculating the water drop motion track is reduced, and therefore the calculation amount is reduced under the condition of guaranteeing the precision.
Step S130: and if the single step error under the current time step is within a preset interval, taking the value of the current time step as the value of the next time step.
The value of the next time step is determined according to the error in each time step, when the error is appropriate, the original time step is kept to continue to be calculated, and meanwhile, high precision and small calculated amount are met.
Step S140: and if the single step error under the current time step is larger than the maximum value of the preset interval, reducing the value of the current time step as the value of the next time step.
As an alternative, the current time step value may be reduced by empirically reducing the current time step value.
As another alternative, the current time step value may be decreased by a binary method. The step of decreasing the value of the current time step by the bisection method may refer to the step of increasing the value of the current time step by the bisection method, which is not described in detail herein.
This application is through the error in according to every time step, confirms the value of next time step, and when the error is great, reduces the time step, improves the computational accuracy of water droplet movement track.
As an alternative embodiment, step S110, step S120, step S130 and step S140 are performed once every n time steps have elapsed, wherein,。
in the present embodiment, the first time step during the movement of the water droplet may be determined empirically.
In the embodiment of the present application, the first time step in the movement process of the water drop can also be determined by using a dichotomy.
For example, set,,,Can be any time value set according to experience, and the value of the first time step isAnd at this timeLet us orderThe value of two time steps is alsoAnd obtaining the motion parameter variation of the first time step according to the value of the first time step and the acceleration of the water drop in the first time step, obtaining the motion parameter variation of the second time step according to the value of the second time step and the acceleration of the water drop in the second time step, and obtaining the single-step error under the first time step according to the motion parameter variation of the first time step and the motion parameter variation of the second time step.
If the single step error is less than the minimum value of the preset interval, the order is given,Then give a new orderRepeating the steps until the single step error under the increased first time step is within a preset interval, and adding the increased single step error at the momentAs the value of the first time step.
If the single step error is within a preset interval, the error will be detectedAs the value of the first time step, and this time。
If the single step error is larger than the minimum value of the preset interval, order,Then give an order againRepeating the steps until the single step error under the reduced first time step is within a preset interval, and reducing the reduced single step error at the momentAs the value of the first time step.
The method for determining the step length for calculating the movement track of the water drops is suitable for calculating the water drop collection rate on the airplane and also suitable for calculating the water drop collection rate on other equipment such as a wind driven generator.
Example 2
Referring to fig. 5, fig. 5 is a block diagram illustrating a structure of a computer-readable storage medium according to embodiment 2 of the present application. The computer-readable storage medium 600 has stored therein program code that can be called by a processor to execute the method described in the above-described method embodiments.
The computer-readable storage medium 600 may be an electronic memory such as a flash memory, an EEPROM (electrically erasable programmable read only memory), an EPROM (erasable programmable read only memory), a hard disk, or a ROM. Alternatively, the computer-readable storage medium 600 includes a non-volatile computer-readable storage medium. The computer readable storage medium 600 has storage space for program code 610 for performing any of the method steps of the method described above. The program code can be read from or written to one or more computer program products. The program code 610 may be compressed, for example, in a suitable form.
Finally, it should be noted that: the above embodiments are only used to illustrate the technical solutions of the present application, and not to limit the same; although the present application has been described in detail with reference to the foregoing embodiments, it will be understood by those of ordinary skill in the art that: the technical solutions described in the foregoing embodiments may still be modified, or some technical features may be equivalently replaced; such modifications and substitutions do not necessarily depart from the spirit and scope of the corresponding technical solutions in the embodiments of the present application.
Claims (6)
1. A step length determination method for calculating a movement locus of a water drop is characterized by comprising the following steps:
s110, obtaining a single step error under the current time step according to the motion parameter variation of the last time step of the water drop and the motion parameter variation of the current time step, wherein the motion parameter variation comprises position variation and/or speed variation, and the single step error comprises position variation errorAnd/or speed variance error;
S120, if the single step error under the current time step is smaller than the minimum value of a preset interval, increasing the value of the current time step as the value of the next time step, wherein the preset interval is,For the purpose of the upper limit of the single-step error,is an error control factor, and;
s130, if the single step error under the current time step is within the preset interval, taking the value of the current time step as the value of the next time step;
s140, if the single step error under the current time step is larger than the maximum value of the preset interval, reducing the value of the current time step as the value of the next time step.
2. The method for determining step length for calculating trajectory of water droplet according to claim 1, wherein if the previous time step is followed by the next time step, step S110 further comprises:
obtaining the acceleration of the last time step of the water drop and the acceleration in the current time step after the last time step of the water drop according to the stress condition of the water drop, wherein the value of the current time step is equal to the value of the last time step;
and obtaining the motion parameter variation of the last time step according to the acceleration of the last time step of the water drop and the value of the last time step, and obtaining the motion parameter variation of the current time step according to the acceleration of the water drop in the current time step after the last time step and the value of the current time step.
3. The method as claimed in claim 1, wherein if the previous time step is followed by the current time step, and the current time step is followed by the next time step, step S110 further includes:
obtaining the acceleration of the last time step of the water drop and the acceleration of the current time step according to the stress condition of the water drop, wherein the current time step is determined by the single step error under the last time step;
and obtaining the motion parameter variation of the previous time step according to the acceleration of the previous time step of the water drop and the value of the previous time step, and obtaining the motion parameter variation of the current time step according to the acceleration of the current time step of the water drop and the value of the current time step.
6. a computer-readable storage medium, characterized in that a program code is stored in the computer-readable storage medium, which program code can be called by a processor to execute the method of any of claims 1-5.
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