CN117150969B - Method for analyzing internal cavitation point of liquid drop in combustion chamber of scramjet engine - Google Patents
Method for analyzing internal cavitation point of liquid drop in combustion chamber of scramjet engine Download PDFInfo
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Abstract
The invention discloses a method for analyzing cavitation points inside liquid drops in a combustion chamber of a scramjet engine, and relates to the technical field of combustion chambers. The liquid fuel in the combustion chamber of the scramjet engine interacts with the shock wave, and when the shock wave acts on the liquid drops, the position and the propagation direction of disturbance in the liquid drops under the high gas-liquid wave velocity ratio are determined by secondary atomization; the generation speed of the disturbance is larger than the propagation speed, and the angle range of the influence of the inside of the liquid drop on the transmission wave generated by the disturbance is calculated; obtaining the position of the internal disturbance of the liquid drop when the internal disturbance of the liquid drop touches the side wall of the liquid drop for the first time and the position of the internal disturbance of the liquid drop when the internal disturbance of the liquid drop touches the side wall of the liquid drop for the second time; calculating the disturbance propagation time; repeating the steps to obtain the positions reached in all disturbance propagation time, obtaining the position of the negative pressure point, and judging whether cavitation reaction occurs to the liquid drop. The invention adopts the steps, is beneficial to acquiring the related information of the cavitation point in the liquid drop and improves the combustion efficiency of the combustion chamber.
Description
Technical Field
The invention relates to the technical field of combustion chambers, in particular to a method for analyzing cavitation points in liquid drops in a combustion chamber of a scramjet engine.
Background
Unlike conventional engines, scramjet engines will not come from the oxidant carried by their own equipment, but will directly react with oxygen in the incoming atmosphere. In the process, shock waves are generated, the pressure, density and temperature of the gas are all suddenly increased through the shock waves, and the flow rate is suddenly reduced. After the liquid fuel in the combustion chamber of the scramjet engine is injected, the liquid fuel collides with supersonic air to be crushed to form liquid drops, the interaction of shock wave liquid drops is an important link with very tiny time scale and space scale in the process, and the crushing degree of the liquid drops determines the combustion efficiency of the scramjet engine. The injected liquid fuel interacts with shock wave, and the process is divided into two parts, namely primary atomization and secondary atomization, wherein the primary atomization represents the process of generating larger fuel liquid drops after the liquid fuel interacts with the shock wave; secondary atomization represents the process of generating smaller droplets of fuel after further interaction with shock waves.
In the early stage of the interaction process of the shock wave liquid drops, the shock wave forms a transmission wave in the liquid drops after touching the liquid drops, the transmission wave continuously moves to contact with the side walls of the liquid drops along the motion direction of the shock wave and is reflected in the form of expansion waves, and the reflected expansion waves are converged to one point in the liquid drops to form negative pressure due to the concave shape of the side walls of the liquid drops, cavitation reaction is possibly generated, and cavitation, noise, vibration and other phenomena are generated due to collapse of cavitation bubbles. It is possible to promote the breakage of the fuel droplets and thus the combustion efficiency, and also to accelerate the corrosion breakage of the mechanical structure inside the combustion chamber. When a single cavitation bubble comes into contact with the wall and breaks, pressures up to several GPa are generated and damage to the soft aluminum sample can occur. When the number of cavitation bubbles reaches 100, brass, mild steel and other materials generate measurable indentations.
The existing analysis model related to the wave system movement inside the liquid drop only discusses the condition of lower gas-liquid wave speed ratio, meanwhile, the analysis result of the existing analysis model under the condition of higher gas-liquid wave speed ratio is compared with the numerical simulation result to be larger in and out, and the related information of cavitation points formed by the convergence of the expansion waves is inconvenient to obtain.
Disclosure of Invention
The invention aims to provide a method for analyzing the cavitation point inside liquid drops in a combustion chamber of a scramjet engine, which can further understand the mutual collision process of shock wave liquid drops and is beneficial to acquiring the related information of the cavitation point inside the liquid drops.
In order to achieve the purpose, the invention provides a method for analyzing the cavitation point inside liquid drops in a combustion chamber of a scramjet engine, which comprises the following specific analysis steps:
s1, carrying out primary atomization and secondary atomization by interaction of liquid fuel in a combustion chamber of a scramjet engine and shock waves, and finding out the position and the propagation direction of disturbance in liquid drops under a high gas-liquid wave velocity ratio when the shock waves act on the liquid drops in the secondary atomization;
s2, calculating an angle range of influence of the inside of the liquid drop on the transmission wave generated by disturbance when the generation speed of the disturbance in S1 is larger than the propagation speed;
s3, obtaining the position of the internal disturbance of the liquid drop when the internal disturbance of the liquid drop touches the side wall of the liquid drop for the first time and the position of the internal disturbance of the liquid drop when the internal disturbance of the liquid drop touches the side wall of the liquid drop for the second time according to the angle range in the S2;
s4, calculating disturbance propagation time according to the position obtained in the S3;
s5, repeating the steps S2-S4 to obtain positions reached in all disturbance propagation time, namely a wave system envelope surface formed by disturbance, obtaining a negative pressure point position, and judging whether cavitation reaction occurs to the liquid drop.
Preferably, in S1, the position and propagation direction of the disturbance generated in the droplet under the high gas-liquid wave velocity ratio are:
;
;
wherein,is the included angle between the connecting line of the disturbance starting position on the liquid drop and the center of the liquid drop and the motion direction of shock wave, +.>For the propagation direction of the transmitted wave disturbance in each interaction of the droplet surface +.>Is the ratio of gas-liquid wave and ∈>For the propagation speed of shock waves in air, < +.>Is the propagation velocity of the shock wave in the liquid.
Preferably, in S2, the angle of the influence of the inside of the droplet on the transmitted waveThe range is as follows:
;
wherein,is a critical angle that can affect the transmitted wave.
Preferably, in S3, the position of the first time the internal disturbance of the droplet touches the edge wall of the droplet is obtained according to the angle in S2：
;
Obtaining the position of the internal disturbance of the liquid drop when the internal disturbance of the liquid drop touches the side wall of the liquid drop for the second time according to the angle in S2：
。
Preferably, in S4, the disturbance propagation time t is obtained from the position in S3:
;
wherein,for the radius of the drop>Generating the first->The distance between the point of the secondary reflection and the current arrival location of the transmitted wave disturbance,kthe number of reflections occurring for the disturbance of the transmitted wave inside the droplet.
Preferably, in S4,at the moment, the track of the mach rod reaching the droplet position is:
;
;
wherein,time required for Mach rod to reach drop position, < >>For the time step size of the time step,Mais Mach number;
。
therefore, the method for analyzing the cavitation point inside the liquid drop in the combustion chamber of the scramjet engine by adopting the steps has the beneficial effects that:
1. the analysis method provided by the invention is fit with the motion track of the Mach rod in the interaction process of shock waves and liquid drops to analyze the internal wave system motion of the liquid drops, so that the analysis method can be suitable for a wider range of gas-liquid wave velocity ratio;
2. the analysis method provided by the invention can obtain the internal wave system structure of the liquid drop similar to the numerical simulation result in a larger application range, and provides an analysis tool for exploring the formation process and the reason of the negative pressure point;
3. the analysis method provided by the invention can analyze the mutual collision process of shock wave liquid drops, obtain the related information of the cavitation points in the liquid drops, further calculate the ignition time or ignition mode for promoting the combustion efficiency of the combustion chamber, and avoid the damage of cavitation bubbles to the combustion chamber.
The technical scheme of the invention is further described in detail through the drawings and the embodiments.
Drawings
Figure 1 is a graph of the results of numerical simulations of shock drop action under different conditions,
(a), (b), (c) and (d) are simulation results during rightward movement of an incident shock wave;
figure 2 is a graph of the motion profile of a mach-bar with time steps for different mach-number embodiments,
(a) Is the space position of the Mach rod motion track under a rectangular coordinate system,
(b) The spatial position of the motion track of the Mach rod under the polar coordinate system;
figure 3 is a graph comparing the analysis method with the numerical simulation with respect to the position of the negative pressure point,
at a lower gas-liquid wave speed ratio, (a) is a numerical simulation result of the occurrence time of the negative pressure point, (b) is an analysis result of the analysis method provided by the invention at the occurrence time of the negative pressure point, (c) is an enlarged graph of (b),
when the gas-liquid wave velocity ratio is higher, (A) is a numerical simulation result of the occurrence time of the negative pressure point, (B) is an analysis result of the analysis method provided by the invention at the occurrence time of the negative pressure point, and (C) is an enlarged graph of (B);
figure 4 is a graph comparing example 3 and comparative example 1 with the results of numerical simulation,
at a low gas-liquid wave ratio, (a) is a numerical simulation result, (b) is an analysis result of comparative example 1, (c) is an analysis result of example 3,
at higher gas-liquid wave velocity ratios, (a) is a numerical simulation result, (B) is an analysis result of comparative example 1, and (C) is an analysis result of example 3;
fig. 5 is a schematic diagram of the analytical application in comparative example 1.
Detailed Description
The technical scheme of the invention is further described below through the attached drawings and the embodiments.
The present invention will be explained in more detail by the following examples, and the purpose of the present invention is to protect all changes and modifications within the scope of the present invention, and the present invention is not limited to the following examples.
Example 1
As shown in fig. 1, (a) in fig. 1, (b) in fig. 1, (c) in fig. 1, and (d) in fig. 1 are equally divided into an upper half and a lower half, wherein the upper half is a numerical schlieren chart, and the lower half is a pressure cloud chart.
Fig. 1 (a), fig. 1 (b), fig. 1 (c) and fig. 1 (d) are simulation results during rightward movement of an incident shock wave, and it can be seen that the mach rod continuously develops along with rightward movement of the incident shock wave, and when the mach rod passes over the surface of the droplet, the corresponding points on the droplet start to be disturbed and jointly form a shock wave envelope surface, i.e. a transmission wave.
As can be seen from fig. 1 (a), the critical angle that can affect the transmitted wave is relatively small due to the relatively small gas-liquid sound velocityThe smaller the Mach bar is, the more distant the transmitted wave is, indicating that the newly generated disturbance after the critical angle cannot affect the composition of the transmitted wave. Therefore, under the condition of low gas-liquid wave velocity ratio, the factors for controlling the disturbance initiation are not greatly different from the internal wave system structure of the liquid drop no matter whether the incident shock wave or the Mach rod is selected.
As can be seen from fig. 1 (b), fig. 1 (c) and fig. 1 (d), as the gas-liquid wave velocity ratio increases, the degree of the concave of the transmitted wave gradually increases before the transmitted wave first touches the right side wall of the droplet, and the distance between the incident shock wave and the position of the mach rod on the droplet gradually increases, and the mach rod plays a key role in controlling the start of disturbance.
As can be seen from fig. 1 (d), the vertical position of the incident shock wave is marked by the dashed line, and it can be seen that the mach rod is still attached to the droplet, and that the point on the droplet is still not disturbed, and that the theoretical analysis only uses the incident shock wave as a factor for controlling the disturbance initiation, which is not the same as the actual situation. At this time, the factor controlling the onset of disturbance is changed from an incident shock wave to a mach-zender.
Example 2
As shown in fig. 2, (a) in fig. 2 is a spatial position of a mach-bar motion locus in a rectangular coordinate system, and (b) in fig. 2 is a spatial position of a mach-bar motion locus in a polar coordinate system.
Fig. 2 (a) shows the spatial position of the mach-rod motion trajectory, and the general shape of the trajectory is a ring shape surrounding the droplet. The leftmost point is the first time at which the mach bar can be observed, corresponding to time step 200, and the mach bar is separated from the right end of the droplet to the lowest end point, corresponding to time step 950.
The rough estimation of the motion trajectory of the mach-zender may be expressed by multiplying the formula time by the velocity, the time in the numerical calculation being equal to the time step times the time step, whereas the time step in the present invention varies with the mach number of the example, and is approximately inversely proportional to the mach number, and the velocity of the mach-zender is approximately proportional to the mach number.
Therefore, in the numerical simulation result of the present invention, the mach-number effect is eliminated by multiplying the time steps by the movement speed, so that the mach-number movement trace of the example at different mach numbers as shown in fig. 2 (a) and fig. 2 (b) is approximately at the same spatial position at the same time step. Therefore, the Mach rod track expression formulas under different working conditions are the same.
Example 3
S1, carrying out primary atomization and secondary atomization by interaction of liquid fuel in a combustion chamber of a scramjet engine and shock waves, and determining the position and the propagation direction of disturbance in liquid drops under a high gas-liquid wave velocity ratio when the shock waves act on the liquid drops in the secondary atomization;
the position of disturbance generation and the propagation direction in the liquid drop under the high gas-liquid wave velocity ratio are as follows:
;
wherein,is the included angle between the connecting line of the disturbance starting position on the liquid drop and the center of the liquid drop and the motion direction of shock wave, +.>For the propagation direction of the transmitted wave disturbance in each interaction of the droplet surface +.>Is the ratio of gas-liquid wave and ∈>For the propagation speed of shock waves in air, < +.>Is the propagation velocity of shock waves in the liquid;
s2, calculating the angle of influence of the inside of the liquid drop on the transmission wave when the generation speed of disturbance in S1 is larger than the propagation speedA range;
;
wherein,is a critical angle that can affect the transmitted wave;
s3, obtaining the position of the internal disturbance of the liquid drop when the internal disturbance of the liquid drop touches the side wall of the liquid drop for the first time and the position of the internal disturbance of the liquid drop when the internal disturbance of the liquid drop touches the side wall of the liquid drop for the second time according to the angle range in the S2;
obtaining the position when the internal disturbance of the liquid drop touches the side wall of the liquid drop for the first time according to the angle in S2:
;
obtaining the position of the internal disturbance of the liquid drop when the internal disturbance of the liquid drop touches the side wall of the liquid drop for the second time according to the angle in S2:
；
s4, obtaining disturbance propagation time t according to the position in S3:
;
wherein,for the radius of the drop>Generating the first->The distance between the point of secondary reflection and the current arrival position of the transmission wave disturbance is k, and k is the number of times of reflection of the transmission wave disturbance in the liquid drop;
the first term is the time required for the mach rod to reach the drop position;
the second term is that the disturbance is in the pathThe time required for propagation;
the third term is disturbance in the thirdAfter touching the droplet edge again and at +.>The time required for propagation before touching the droplet edge wall once;
in S4, when the gas-liquid wave speed ratio is changed from low to high, the initial factor for controlling the disturbance in the liquid drop is Mach rod.
In S4, the processing unit is configured to,at the moment, the locus of the mach lever reaching the droplet position is,
;
wherein,time required for Mach rod to reach drop position, < >>For the time step size of the time step,Mais Mach number;
。
s5, repeating the steps S2-S4 to obtain positions reached in all disturbance propagation time, namely a wave system envelope surface formed by disturbance, obtaining a negative pressure point position, and judging whether cavitation reaction occurs to the liquid drop.
In the secondary atomization process of shock wave droplet interaction, cavitation bubbles generated after cavitation reaction occur in the droplets can be broken, and a series of shock waves are generated. Meanwhile, the existence of cavitation bubbles can promote the deformation of liquid drops so as to accelerate the cracking, the combustion efficiency of the combustion chamber is closely related to the deformation degree of fuel liquid drops, and the ignition time or the ignition mode capable of promoting the combustion efficiency can be further calculated after the deformation degree of the fuel liquid drops is obtained. The analysis method provided by the invention further knows the mutual collision process of shock wave liquid drops, is beneficial to acquiring the related information of cavitation points formed by the convergence of expansion waves, calculates the ignition moment or ignition mode for promoting the combustion efficiency of the combustion chamber, and can also avoid the damage of cavitation bubbles to the combustion chamber.
As shown in fig. 3, when (a) in fig. 3, (b) in fig. 3, and (c) in fig. 3 are lower gas-liquid wave speed ratios, fig. 3 (a) is a numerical simulation result of the occurrence time of the negative pressure point, fig. 3 (b) is an analysis result of the analysis model provided by the present invention at the occurrence time of the negative pressure point, and fig. 3 (c) is an enlarged view of fig. 3 (b).
When (a) in fig. 3, (B) in fig. 3, and (C) in fig. 3 are high gas-liquid wave velocity ratios, fig. 3 (a) is a numerical simulation result of the occurrence time of the negative pressure point, and it can be seen from the pressure cloud image (lower half) that there is a small-range dark region near the right side wall of the droplet at the current time, that is, the position where the negative pressure point is located.
Fig. 3 (B) shows an analysis result of the analysis model provided by the present invention at the occurrence time of the negative pressure point, where the dot is the position of the extreme value of the negative pressure obtained by numerical simulation, and the arc black line is the envelope surface formed by each disturbance, and represents the reflected expansion wave.
Fig. 3 (C) is an enlarged view of fig. 3 (B), and it can be seen that a larger number of disturbances after primary reflection are concentrated in a certain range of the dots, that is, the negative pressure points, and the numerical simulation result is better matched with the position of the negative pressure point obtained by the theoretical analysis result.
As can be seen from FIG. 3, the negative pressure point obtained by the analysis model provided by the invention is in good agreement with the numerical simulation result in the internal wave system structure of the liquid drop at the moment of occurrence.
Comparative example 1
As shown in fig. 5, when a shock wave acts on a droplet, a disturbance propagating along a certain direction is generated at a corresponding position of the droplet, and the position where the disturbance is generated and the propagation direction thereof should be as follows:
;
;
wherein,the direction of the shock wave motion is the connection line between the starting position of disturbance on the liquid drop and the center of the liquid dropIncluded angle between directions, add>For the propagation direction of the transmitted wave disturbance in each interaction of the droplet surface +.>Is the ratio of gas-liquid wave and ∈>For the propagation speed of shock waves in air, < +.>Is the propagation velocity of the shock wave in the liquid.
S2, only when the disturbance propagation speed is larger than the disturbance generation speed, partial disturbance can affect the internal transmission wave envelope surface of the liquid drop:
;
wherein,is a critical angle that can affect the transmitted wave.
S3, the position of the edge wall of the liquid drop is reached for the first time and the second time by the disturbance in the liquid drop:
;
;
s4, the change relation of the disturbance propagation path along with time:
;
wherein,for the radius of the drop>Generating the first->The distance between the point of the secondary reflection and the current arrival location of the transmitted wave disturbance,kthe number of reflections occurring for the disturbance of the transmitted wave inside the droplet.
Wherein the first term is the time required for the corresponding position of the drop to start to disturb, i.e. the incident shock wave moves toThe time required for this is set up to be,
the second term is that the disturbance is in the pathThe time required for the propagation is set,
the third term is disturbance in the thirdAfter touching the droplet edge again and at +.>The time required for propagation before touching the droplet edge wall once.
By determining the time at which each disturbance point is selectedTo determine the locations where all disturbances arrive at the current moment, i.e. the formed wave system envelope.
As shown in fig. 4, at a low gas-liquid wave ratio, fig. 4 (a) shows the numerical simulation result, fig. 4 (b) shows the analysis result of comparative example 1, and fig. 4 (c) shows the analysis result of example 3.
At a higher ratio of gas-liquid waves, fig. 4 (a) shows the numerical simulation results, fig. 4 (B) shows the analysis results of comparative example 1, and it is clear from fig. 4 (a) and fig. 4 (B) that some points on the liquid droplets are still in an undisturbed state.
Fig. 4 (C) shows the analysis result of example 3, which shows that the mach lever can be used as a factor for controlling the start of disturbance, so that the distribution state of disturbance in the droplet at the current time can be restored well.
Finally, it should be noted that: the above embodiments are only for illustrating the technical solution of the present invention and not for limiting it, and although the present invention has been described in detail with reference to the preferred embodiments, it will be understood by those skilled in the art that: the technical scheme of the invention can be modified or replaced by the same, and the modified technical scheme cannot deviate from the spirit and scope of the technical scheme of the invention.
Claims (1)
1. The method for analyzing the cavitation point inside the liquid drop in the combustion chamber of the scramjet engine is characterized by comprising the following steps of:
s1, carrying out primary atomization and secondary atomization by interaction of liquid fuel in a combustion chamber of a scramjet engine and shock waves, and finding out the position and the propagation direction of disturbance in liquid drops under a high gas-liquid wave velocity ratio when the shock waves act on the liquid drops in the secondary atomization;
in S1, the position and the propagation direction of disturbance in liquid drops under high gas-liquid wave velocity ratio are as follows:
；
；
wherein,is the included angle between the connecting line of the disturbance starting position on the liquid drop and the center of the liquid drop and the motion direction of shock wave, +.>For the propagation direction of the transmitted wave disturbance in each interaction of the droplet surface +.>Is the ratio of gas-liquid wave and ∈>For the propagation speed of shock waves in air, < +.>Is the propagation velocity of shock waves in the liquid;
s2, calculating an angle range of influence of the inside of the liquid drop on the transmission wave generated by disturbance when the generation speed of the disturbance in S1 is larger than the propagation speed;
s2, the angle of the influence of the inside of the droplet on the transmitted waveThe range is as follows:
；
wherein,is a critical angle that can affect the transmitted wave;
s3, obtaining the position of the internal disturbance of the liquid drop when the internal disturbance of the liquid drop touches the side wall of the liquid drop for the first time and the position of the internal disturbance of the liquid drop when the internal disturbance of the liquid drop touches the side wall of the liquid drop for the second time according to the angle range in the S2;
s3, obtaining the position when the internal disturbance of the liquid drop touches the side wall of the liquid drop for the first time according to the angle in S2：
；
Obtaining the position of the internal disturbance of the liquid drop when the internal disturbance of the liquid drop touches the side wall of the liquid drop for the second time according to the angle in S2：
；
S4, calculating disturbance propagation time according to the position obtained in the S3;
in S4, the disturbance propagation time t is obtained according to the position in S3:
；
wherein,for the radius of the drop>Generating the first->The distance between the point of the secondary reflection and the current arrival location of the transmitted wave disturbance,kthe number of times of reflection occurs for the disturbance of the transmission wave in the liquid drop;
in S4, the processing unit is configured to,at the moment, the locus of the mach lever reaching the droplet position is,
；
；
wherein,time required for Mach rod to reach drop position, < >>For the time step size of the time step,Mais Mach number;
；
s5, repeating the steps S2-S4 to obtain positions reached in all disturbance propagation time, namely a wave system envelope surface formed by disturbance, obtaining a negative pressure point position, and judging whether cavitation reaction occurs to the liquid drop.
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Citations (2)
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| CN108763800A (en) * | 2018-06-04 | 2018-11-06 | 北京理工大学 | A kind of cavitation compressible flows shock-wave dynamics method for numerical simulation |
| CN110837688A (en) * | 2019-09-30 | 2020-02-25 | 西安电子科技大学 | Total field/scattered field plane wave source generation method in plasma sheath 3D-FDTD modeling |
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