CN112199787A - Elliptical partition plate nozzle shaping method for increasing acoustic energy dissipation - Google Patents

Elliptical partition plate nozzle shaping method for increasing acoustic energy dissipation Download PDF

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CN112199787A
CN112199787A CN202011016185.7A CN202011016185A CN112199787A CN 112199787 A CN112199787 A CN 112199787A CN 202011016185 A CN202011016185 A CN 202011016185A CN 112199787 A CN112199787 A CN 112199787A
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energy dissipation
acoustic
acoustic energy
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杨立军
李敬轩
朱烁烁
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Beihang University
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    • G06—COMPUTING; CALCULATING OR COUNTING
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    • G06F30/00—Computer-aided design [CAD]
    • G06F30/20—Design optimisation, verification or simulation
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    • G06F2119/14—Force analysis or force optimisation, e.g. static or dynamic forces

Abstract

The invention relates to an elliptical diaphragm nozzle modification method for increasing acoustic energy dissipation, which is mainly used for controlling the combustion instability of a rocket engine. The calculation method is that the average value of disturbance parameters is calculated on the cross section to obtain the fluctuation equation of the pressure, and the fluctuation equation can be calculated by a numerical method. The length of the longitudinal half shaft is fixed to be unchanged, the eccentricity of the elliptical partition plate nozzle is changed by changing the length of the transverse half shaft, and the maximum value of the sound wave dissipation coefficient under different minimum gaps is calculated. The invention is suitable for various rocket engine partition plate nozzles, can increase sound energy dissipation and is beneficial to controlling unstable combustion.

Description

Elliptical partition plate nozzle shaping method for increasing acoustic energy dissipation
Technical Field
The invention relates to an elliptical diaphragm nozzle modification method for increasing acoustic energy dissipation, which is mainly applied to unstable combustion control of a liquid rocket engine.
Background
In the working process of the liquid rocket engine, the problem of unstable combustion is easily caused in the combustion chamber, the unstable combustion brings great harm, severe fluctuation of the pressure in the combustion chamber is caused, even the structure is damaged, and the normal operation of system tasks is influenced. Acoustic instability is a form of combustion instability in a combustion chamber, where the sound waves continue to gain energy due to the coupling of heat release and the combustion chamber acoustic system, ultimately producing severe pressure oscillations. Therefore, the combustor acoustic system has been studied to help understand and control the combustion instability problem.
The acoustic instability in the combustion chamber has three modes of longitudinal instability, tangential instability and radial instability, wherein the harm caused by the tangential instability and the radial instability of high frequency is the largest. To control tangential and radial instabilities, baffles are often employed in practice to convert the more destructive tangential and radial instabilities at high frequencies to less destructive longitudinal instabilities at low frequencies. Later research shows that the control effect on unstable combustion can be better by replacing the partition plates with the partition plate nozzle cylindrical rows with gaps to form a columnar-grid type sound absorption channel. In order to obtain a better sound absorption effect, the acoustic characteristics of the diaphragm nozzle need to be studied.
The invention provides a modification method of an elliptical diaphragm nozzle for increasing sound energy dissipation, which is of great significance for deeply researching a combustion instability mechanism and controlling a combustion instability phenomenon.
Disclosure of Invention
Against this background, the present invention provides an elliptical diaphragm nozzle profiling method that increases acoustic energy dissipation.
The technical scheme adopted by the invention is as follows:
elliptical partition plate nozzle trimming type for increasing acoustic energy dissipationMethod, characterized in that the longitudinal half-axis length L1Unchanged by varying the transverse half-axis length L2The eccentricity e is changed, so that the gap of the partition plate nozzle is changed, as shown in fig. 1, the sound energy dissipation is increased, and a better sound absorption effect is realized. The expression for eccentricity e is:
Figure BDA0002699148590000021
calculation of acoustic energy dissipation:
the diaphragm nozzle model is simplified into a rectangular slit pipe internal acoustic wave propagation model with an area gradient. A plane sound wave is transmitted in the tube with a rectangular slit with variable cross section, the height of the rectangular slit is 2a, the width of the rectangular slit is 2b, the cross section area of the rectangular slit is 2a multiplied by 2b, wherein a > b, and the tube has no average flow. Assuming that the pipe wall is rigid, the velocity of the medium particles near the pipe wall is 0, and the farther away from the pipe wall, the less the medium particles are constrained by the pipe wall, the higher the velocity, and then a velocity gradient is generated in the pipe, relative motion is generated between the media layers, and the medium particles are acted by viscous force. Similarly, assuming the wall is constant, there is a heat exchange effect between the medium particles and the medium particles are thus subjected to heat transfer.
According to the momentum equation of the N-S equation, because the viscous force mainly acts on the cross section direction, neglecting the action of the viscous force on the slit length direction, the following can be obtained:
Figure BDA0002699148590000031
wherein ρ is density, η is dynamic viscosity, u is velocity, y is slit width direction, i is imaginary unit, ω is acoustic frequency, p is pressure, x is slit length direction, subscript 0 parameter represents balance value, and parameters not labeled with 0 are all disturbance parameters.
Similarly, neglecting the effect of thermal conduction in the direction of the slit length x, the energy equation can be derived:
Figure BDA0002699148590000032
wherein κ is heat transfer coefficient, T is gas temperature, CpIs the specific heat at constant pressure.
The boundary conditions of the velocity and temperature on the cross section are that when y ═ b, u ═ 0, and T ═ 0, the velocity and temperature distributions on the cross section are determined, and then averaged over the cross section:
Figure BDA0002699148590000033
Figure BDA0002699148590000034
wherein the subscript a represents the average value of the disturbance parameter in the cross-section, F (delta)1)、F(δ2) Are respectively delta1、δ2Function of (c):
Figure BDA0002699148590000035
Figure BDA0002699148590000036
wherein, delta1、δ2Acoustic viscous dissipation boundary layer thickness and acoustic thermal conduction dissipation boundary layer thickness, respectively, defined as:
Figure BDA0002699148590000037
Figure BDA0002699148590000041
the expression of the half width b of the variable cross-section rectangular slit along the length x direction is as follows:
Figure BDA0002699148590000042
parameter bmIs the minimum gap value between adjacent diaphragm nozzles.
According to an ideal gas state equation:
Figure BDA0002699148590000043
the continuity equation can be written as:
Figure BDA0002699148590000044
where t is the time variable and c is the speed of sound.
Substituting the calculated average speed and temperature of the cross section into a continuity equation to obtain a wave equation:
Figure BDA0002699148590000045
wherein γ is a specific heat ratio.
After the wave equation is obtained, the distribution of the sound wave pressure in the axial space position can be analyzed through numerical calculation, and the pressure disturbance is the sound wave A which is propagated downstream+And an acoustic wave A propagating upstream-I.e. p ═ a++A-And the velocity is disturbed ua＝kF(δ1)(A++A-)/ρ0ω, wave number of acoustic wave:
Figure BDA0002699148590000046
by solving the pressure disturbance and the speed disturbance, the acoustic wave amplitude A propagating downstream can be obtained+And the amplitude A of the acoustic wave propagating upstream-。
Defining a dissipation coefficient:
Figure BDA0002699148590000047
subscripts 1 and 2 represent the energy loss at the inlet and outlet, respectively, and the dissipation factor E represents the loss of acoustic energy due to hot tack, with higher values indicating higher losses.
Under the conditions of certain working frequency, gas temperature and environmental pressure of the rocket engine, different minimum gaps have different acoustic energy dissipation coefficients, and an optimal gap exists, so that the acoustic energy dissipation coefficient is maximum, as shown in fig. 2. FIG. 2 illustrates the variation rule of the acoustic energy dissipation coefficient with different minimum clearances under the conditions of the working frequency of 1000Hz, the length of the longitudinal half shaft of 10mm and the eccentricity of 0 at normal temperature and normal pressure. And calculating the maximum dissipation under the optimal clearance when the eccentricity of the nozzles of different elliptical partition plates is calculated.
In the invention, aiming at the longitudinal half shaft lengths of different partition plate nozzles, the maximum sound energy dissipation can be increased by increasing the eccentricity.
In the invention, aiming at different working frequencies, the maximum sound energy dissipation can be increased by increasing the eccentricity.
According to the invention, the maximum sound energy dissipation can be increased by increasing the eccentricity aiming at different gas temperatures.
The invention has the advantages and effects that: the baffle nozzle can effectively increase acoustic energy dissipation, and has the advantages of simple structure, convenient installation, low cost and easy processing.
Drawings
FIG. 1 is a schematic view of an elliptical diaphragm nozzle.
Fig. 2 shows the dissipation factor of the acoustic energy at different gaps.
Fig. 3 maximum acoustic energy dissipation factor as a function of eccentricity.
FIG. 4 shows the variation of the maximum sound energy dissipation factor with eccentricity for different longitudinal half-axis lengths.
Fig. 5 maximum acoustic energy dissipation factor as a function of eccentricity for different operating frequencies.
FIG. 6 maximum acoustic energy dissipation factor as a function of eccentricity for different combustion gas temperatures.
The symbols in the figure are as follows: l is1Longitudinal half-axis length, L2Length of transverse half-axis, half width of slit between partitions bmMinimum gap of the partition plate, E elliptical eccentricity, E acoustic energy dissipation coefficient, f working frequency and T fuel gas temperature.
The specific implementation mode is as follows:
the present invention will be described in detail below with reference to the accompanying drawings. In this embodiment, the acoustic energy dissipation is effectively increased by changing the eccentricity of the elliptical diaphragm nozzle, and the specific implementation is described as follows:
in this embodiment, the working frequency f is 1000Hz and the longitudinal half-axis length L of the nozzle is selected under normal temperature and pressure110mm, eccentricity of 0-0.9, and minimum gap bmThe variation range is 0-0.5 mm, and the rule that the maximum sound energy dissipation changes along with the eccentricity is obtained by calculating a wave equation, as shown in the figure. FIG. 3 shows the rule that the working frequency is 1000Hz, the length of the longitudinal half shaft of the partition plate nozzle is 10mm, the change range of the minimum clearance is 0-0.5 mm, and the maximum sound energy dissipation changes with the elliptical eccentricity. It can be seen that as the elliptical eccentricity increases, the maximum acoustic energy dissipation increases, demonstrating that the elliptical diaphragm nozzle is effective in increasing acoustic energy dissipation.
Because rocket engines of different models are different, conditions such as the length of a longitudinal half shaft of the clapboard nozzle, working frequency, gas temperature and the like are different, and in order to verify that the elliptical clapboard nozzle can effectively increase sound energy dissipation under various conditions, the sound energy dissipation under different conditions needs to be calculated.
FIG. 4 shows the change rule of the maximum acoustic energy dissipation with the eccentricity when the working frequency is 1000Hz and the lengths of the longitudinal half shafts are 2.5mm, 5mm, 7.5mm, 10mm, 12.5mm and 15mm respectively, and the elliptical eccentricity is changed within the range of 0-0.9. It can be seen that the maximum sound energy dissipation increases with increasing eccentricity for different longitudinal half-axis lengths. Therefore, the elliptical diaphragm nozzle can effectively increase the acoustic energy dissipation under the condition of different longitudinal half-axis lengths.
FIG. 5 shows the change rule of the maximum acoustic energy dissipation with the eccentricity when the longitudinal half-axis length is 10mm at normal temperature and pressure and the working frequencies are 400Hz, 800Hz, 1000Hz, 1200Hz, 1600Hz, and 2000Hz, respectively, and the elliptical eccentricity is changed within the range of 0-0.9. It can be seen that the maximum acoustic energy dissipation increases with increasing eccentricity at different operating frequencies. Therefore, the elliptical diaphragm nozzle can effectively increase the acoustic energy dissipation under different working frequency conditions.
FIG. 6 shows the change rule of the maximum acoustic energy dissipation with the eccentricity when the working frequency is 1000Hz and the gas temperature is 293K, 500K, 1000K, 1500K, 2000K and 2500K respectively under the condition that the length of the vertical half shaft under normal pressure is 10 mm. It can be seen that the maximum sound energy dissipation increases with increasing eccentricity under different gas temperature conditions. Therefore, the elliptical diaphragm nozzle can effectively increase the acoustic energy dissipation under different gas temperature conditions.
Correspondingly, according to the above results, the diaphragm nozzles are composed of a series of diaphragm nozzles extending to the combustion chamber, and the diaphragm nozzles are arranged in an elliptic cylindrical row according to a certain arrangement mode to form a cylindrical grid type sound absorption channel, so that the sound energy dissipation can be effectively increased under the conditions of different longitudinal half shaft lengths, working frequencies and gas temperatures.
The specific implementation process of the invention is as follows with reference to the attached drawings: substituting the parameter values in each embodiment into a wave equation, solving the wave equation numerically to obtain the distribution condition of the pressure disturbance on the space, obtaining the distribution condition of the speed disturbance on the space through a relational expression of the speed disturbance and the pressure disturbance, combining the relational expressions of the pressure disturbance, the speed disturbance and the sound wave amplitude to obtain the sound wave amplitude propagated downstream and the sound wave amplitude propagated upstream, and further obtaining the loss condition of the energy of the sound wave under the action of thermal viscous dissipation through a dissipation coefficient definition expression.
The above description of the invention and its embodiments is not intended to be limiting, and the illustrations in the drawings are intended to represent only one embodiment of the invention. Without departing from the spirit of the invention, it is within the scope of the invention to design structures or embodiments similar to the technical solution without creation.

Claims (5)

1. An elliptical diaphragm nozzle modification method for increasing acoustic energy dissipation is characterized in that: longitudinal half axis length L1Unchanged by varying the transverse half-axis length L2The eccentricity e is changed, so that the gap of the nozzle of the partition plate is changed, the sound energy dissipation is increased, and the sound absorption effect is realized; the expression for eccentricity e is:
Figure FDA0002699148580000011
2. the elliptical diaphragm nozzle contouring method of claim 1 for increasing acoustic energy dissipation, wherein: the acoustic energy dissipation is calculated by simplifying the diaphragm nozzle model into a rectangular slit tube internal acoustic wave propagation model with an area gradient.
3. The elliptical diaphragm nozzle contouring method of claim 2 for increasing acoustic energy dissipation, wherein: the plane sound wave is transmitted in the tube of the variable cross-section rectangular slit, the height of the rectangular slit is 2a, the width of the rectangular slit is 2b, the cross-sectional area of the rectangular slit is 2a multiplied by 2b, wherein a > b, and no average flow exists in the tube; the pipe wall is rigid, medium particles near the pipe wall adhere to the pipe wall and have a velocity of 0, and the farther away from the pipe wall, the medium particles are restrained by the pipe wall to be small and have a high velocity, so that a velocity gradient is generated in the pipe, relative motion is generated among the media of the layers, and the medium particles are acted by viscous force.
4. The elliptical diaphragm nozzle profiling method of increasing acoustic energy dissipation of claim 1 or 2, wherein: according to the momentum equation of the N-S equation, because viscous force acts on the cross section direction, neglecting the action of the viscous force on the slit length direction, the method obtains:
Figure FDA0002699148580000012
wherein ρ is density, η is dynamic viscosity, u is speed, y is slit width direction, i is imaginary unit, ω is acoustic frequency, p is pressure, x is slit length direction, subscript 0 parameter represents balance value, parameters not labeled with 0 are disturbance parameters;
similarly, neglecting the effect of thermal conduction in the direction of the slit length x, we obtain the energy equation:
Figure FDA0002699148580000021
wherein κ is heat transfer coefficient, T is gas temperature, CpIs the specific heat at constant pressure;
the boundary conditions of the velocity and temperature on the cross section are that when y ═ b, u ═ 0, and T ═ 0, the velocity and temperature distributions on the cross section are determined, and then averaged over the cross section:
Figure FDA0002699148580000022
Figure FDA0002699148580000023
wherein the subscript a represents the average value of the disturbance parameter in the cross-section, F (delta)1)、F(δ2) Are respectively delta1、δ2Function of (c):
Figure FDA0002699148580000024
Figure FDA0002699148580000025
wherein, delta1、δ2Acoustic viscous dissipation boundary layer thickness and acoustic thermal conduction dissipation boundary layer thickness, respectively, defined as:
Figure FDA0002699148580000026
Figure FDA0002699148580000027
the expression of the half width b of the variable cross-section rectangular slit along the length x direction is as follows:
Figure FDA0002699148580000028
parameter bmIs the minimum gap value between adjacent baffle nozzles;
according to an ideal gas state equation:
Figure FDA0002699148580000031
the continuity equation is written as:
Figure FDA0002699148580000032
wherein t is a time variable, and c is a sound velocity;
substituting the obtained average speed and temperature of the cross section into a continuity equation to obtain a wave equation:
Figure FDA0002699148580000033
wherein γ is the specific heat ratio;
after the wave equation is solved, the distribution of the sound wave pressure in the axial space position is analyzed through numerical calculation, and the pressure disturbance is the sound wave A which is propagated downstream+And an acoustic wave A propagating upstream-I.e. p ═ a++A-And the velocity is disturbed ua＝kF(δ1)(A++A-)/ρ0ω, wave number of acoustic wave:
Figure FDA0002699148580000034
obtaining the acoustic wave amplitude A propagated downstream by solving the pressure disturbance and the speed disturbance+And the amplitude A of the acoustic wave propagating upstream-。
5. The elliptical diaphragm nozzle profiling method of increasing acoustic energy dissipation of claim 1 or 4, wherein: defining an acoustic energy dissipation coefficient:
Figure FDA0002699148580000035
subscripts 1 and 2 represent the energy loss at the inlet and outlet, respectively, and the dissipation factor E represents the loss of acoustic energy due to hot tack, with higher values indicating higher losses.
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Citations (4)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
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CN109073221A (en) * 2016-05-03 2018-12-21 通用电气公司 The high-frequency acoustic damper of combustion chamber lining
CN109057995A (en) * 2018-08-03 2018-12-21 北京航空航天大学 The partition nozzle best clearance design method and partition nozzle that can be dissipated based on sound
CN109604829A (en) * 2018-12-25 2019-04-12 常州中车通用电气柴油机有限公司 Diesel engine of locomotive booster nozzle ring laser repair welding device and its repair welding method

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* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
US6509081B1 (en) * 2000-09-28 2003-01-21 The Boeing Company No-septum acoustic sandwich panel, and apparatus and method for suppressing noise in a nozzle
CN109073221A (en) * 2016-05-03 2018-12-21 通用电气公司 The high-frequency acoustic damper of combustion chamber lining
CN109057995A (en) * 2018-08-03 2018-12-21 北京航空航天大学 The partition nozzle best clearance design method and partition nozzle that can be dissipated based on sound
CN109604829A (en) * 2018-12-25 2019-04-12 常州中车通用电气柴油机有限公司 Diesel engine of locomotive booster nozzle ring laser repair welding device and its repair welding method

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Title
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