CN113987694A - Rotary detonation engine flow field parameter distribution prediction method based on space propulsion algorithm - Google Patents

Rotary detonation engine flow field parameter distribution prediction method based on space propulsion algorithm Download PDF

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CN113987694A
CN113987694A CN202111092248.1A CN202111092248A CN113987694A CN 113987694 A CN113987694 A CN 113987694A CN 202111092248 A CN202111092248 A CN 202111092248A CN 113987694 A CN113987694 A CN 113987694A
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李锐
徐惊雷
黄帅
陈匡世
俞凯凯
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Nanjing University of Aeronautics and Astronautics
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Abstract

The invention discloses a method for predicting the distribution of flow field parameters of a rotary detonation engine based on a space propulsion algorithm, which comprises the following steps: pre-estimating the flow parameters of the front of the detonation wave; determining a flowing parameter after a detonation wave according to a CJ detonation model with a single specific heat ratio; assigning the flow parameters after the detonation wave and the far downstream flow parameters to an initial value line; determining flow parameters under a shock wave coordinate system through a space propulsion algorithm; determining the initial position and the final position of combustible gas mixture injection; and (3) iteratively converging the flow field parameters of the rotary detonation engine, and obtaining the flow parameters in a laboratory coordinate system through coordinate conversion. According to the method, the flow parameters under a laboratory coordinate system are obtained through a coupling space propulsion algorithm and a CJ detonation wave model through coordinate conversion, the flow field structure and the outlet flow parameter distribution of the rotary detonation engine can be rapidly obtained, the defects that the conventional algorithm is long in time consumption for obtaining the flow field of the rotary detonation engine and the like are overcome, and the design cycle of the rotary detonation engine is shortened.

Description

Rotary detonation engine flow field parameter distribution prediction method based on space propulsion algorithm
Technical Field
The invention belongs to the field of numerical calculation of a flow field of a rotary detonation engine, and particularly relates to a rotary detonation engine flow field parameter distribution prediction method based on a space propulsion algorithm.
Background
As a novel propelling device, as shown in FIG. 2, a common structure of a rotary detonation engine is a concentric ring column, and a combustible mixture injection notch is formed in the bottom end of the ring column. Within the annular chamber there are single or multiple detonation waves inclined towards the injection plane and propagating circumferentially. The gas immediately after detonation wave is subjected to rapid heat release, the temperature and pressure are obviously improved, and then a series of expansion waves accelerate the expansion of the gas flow. The combustible mixture is injected into the annular chamber when the pressure of the combustion products close to the injection plane is lower than the total injection pressure of the combustible mixture. The detonation wave and the combustible mixture/combustion product discontinuity enclose a triangular area filled with the combustible mixture, so that the sustainability of detonation combustion is ensured. In the flow field structure, the detonation wave, the shear layer and the induced shock wave intersect at the upper vertex of the triangular region. Most of the airflow is discharged axially along the outlet of the rotary detonation engine, but the variation of the flow parameters along the circumferential direction is still significant.
Compared with a gas turbine engine and a ramjet engine, the rotary detonation engine has the advantages of smaller entropy increase and higher thermal efficiency in work, and is widely concerned by various research organizations. In order to obtain complete information of a flow field of the rotary detonation engine, a high-precision numerical simulation technology is indispensable. The kinetic shock wave and the chemical exothermic reaction are strongly coupled in the detonation combustion process, so that the traditional numerical simulation grid scale and discrete time step based on time advance are too small. In order to obtain the aerodynamic performance of a rotary detonation engine, much time and computing resources are consumed.
Disclosure of Invention
The technical purpose is as follows: in order to solve the technical problems, the invention provides a method for predicting the distribution of flow field parameters of a rotary detonation engine based on a space propulsion algorithm.
The technical scheme is as follows: in order to achieve the purpose, the invention adopts the technical scheme that:
a method for predicting the distribution of flow field parameters of a rotary detonation engine based on a space propulsion algorithm is characterized by comprising the following steps of: the method comprises the following steps:
(1) estimating the average speed of an inlet of an injection surface in advance, and determining the flow parameters of the detonation wave front according to a compressible flow relation;
(2) substituting the flow parameters of the detonation wave front into a CJ detonation model with a single specific heat ratio to determine the flow parameters of the detonation wave front;
(3) assigning the flow parameters after the detonation wave and the flow parameters far downstream to an initial value line; the flow parameters far downstream of the detonation wave in the first iteration are obtained by expanding the pressure after the detonation wave to the pressure before the detonation wave, and the flow parameters far downstream of the detonation wave in the later iteration are obtained according to the calculation result of the previous iteration;
(4) substituting the initial value line into a space propulsion algorithm, and determining a flow field structure and flow parameter distribution of the rotary detonation engine under a shock wave coordinate system;
(5) comparing the pressure value of the solution point of the injection surface with the total injection pressure, when the pressure value of the solution point is smaller than the total injection pressure, performing coupled solution on the injection flow field and the detonation wave downstream flow field, and when the pressure value of the solution point is larger than the total injection pressure, only solving the detonation wave downstream flow field;
(6) determining the area average value of the flow parameters of the detonation wave front at the far downstream position of the detonation wave, returning to the step (2) to the step (5) for iteration, jumping out of a loop until the average airflow angle at the far downstream is 0, and executing the step (7);
(7) and determining the rotation angle of the shock wave coordinate system according to the inclination angle of the detonation wave, and determining the flow parameter distribution of the rotary detonation engine under the laboratory coordinate system according to the velocity triangle.
Further, the step (1) comprises the following steps:
(11) determining the total pressure Pt and the total temperature Tt of the combustible mixture at the rotary detonation inlet according to the flight condition of the rotary detonation engine, and estimating the average speed at the inlet of the rotary detonation engine
Figure BDA0003267983790000021
(12) Determining the average static temperature of the detonation wave front according to the compressible flow relation
Figure BDA0003267983790000022
Mean static pressure
Figure BDA0003267983790000023
And average density
Figure BDA0003267983790000024
Further, the step (2) comprises the following steps:
(21) constructing a CJ knock model with a single specific heat ratio, wherein a model equation is in the form of:
Figure BDA0003267983790000025
Figure BDA0003267983790000026
wherein M isCJRepresenting the Mach number of the detonation wave, H representing the dimensionless heat release amount, Q representing the heat of chemical reaction, RgRepresenting a gas constant, gamma is the specific heat ratio of the combustible mixture and the combustion products;
(22) determining post-detonation wave flow parameters including post-detonation wave static pressure parameters according to the mass conservation law, momentum conservation law and energy conservation law before and after the detonation wave
Figure BDA0003267983790000031
Density after detonation wave
Figure BDA0003267983790000032
And post detonation wave temperature
Figure BDA0003267983790000033
Further, the step (4) comprises the following steps:
(41) determining an intermediate variable chi through the non-viscous flux E in the main flow direction, and further obtaining a state quantity Q on an initial value line, wherein the expression of the intermediate variable chi is in the following form:
Figure BDA0003267983790000034
(42) determining downstream solution point coordinates according to the velocity distribution on the initial value line
Figure BDA0003267983790000035
A streamline grid is established, and the streamline grid is established,
Figure BDA0003267983790000036
representing the x coordinate of the jth downstream solution point in the x direction,
Figure BDA0003267983790000037
representing the x coordinate of the jth initial value line point in the x direction;
(43) obtaining step by step half-steps along the x-direction according to an essentially oscillationless interpolation method and a limiting function
Figure BDA0003267983790000038
And
Figure BDA0003267983790000039
to obtain the state quantity of 1/2 position of step length
Figure BDA00032679837900000310
And
Figure BDA00032679837900000311
(44) according to the shock wave polar curve theory, the solution point pressure and the airflow angle of the space propulsion algorithm at the position 1/2 in the stepping length are determined through two adjacent points of which the stepping length in the space x direction is 1/2 set values, and then a Riemann self-similarity solution is obtained, wherein the expression of the state curve of the two adjacent points is as follows:
Figure BDA00032679837900000312
Figure BDA00032679837900000313
wherein phiBA state curve representing the lower side point of the initial value line, thetaBAir flow angle, f (M), representing the lower side point of the initial value lineB,αB) Rankine allowances relation, alpha, representing the lower side point of the initial value lineBDenotes the ratio of pressure at any point in the downstream space to pressure at the lower side of the initial value line, v (M)B) Prandtl-Meyer function, phi, representing the lower side point of the initial lineTA state curve representing the upper point of the initial value line, thetaTAirflow angle, f (M), representing the upper point of the initial value lineT,αT) Rankine allowances relation, alpha, representing upper side point of initial value lineTDenotes the ratio of pressure at any point in the downstream space to pressure at a point on the initial line, v (M)T) A planter-meier function representing an upper point of the initial value line;
(45) obtaining flow parameters under a single space progressive step length by carrying out differential dispersion on a compressible Euler equation, wherein the downstream differential equation along the flow x direction is in the following form:
Figure BDA0003267983790000041
wherein the content of the first and second substances,
Figure BDA0003267983790000042
represents the difference value of y coordinates of two adjacent points of the initial value line,
Figure BDA0003267983790000043
the y coordinate difference of two adjacent solution points at the downstream is shown,
Figure BDA0003267983790000044
the inviscid flux in the y-direction of the upper grid point representing the length position of spatial step 1/2,
Figure BDA0003267983790000045
the slope of the upper grid edge representing the length position of spatial step 1/2,
Figure BDA0003267983790000046
the unbounded flux in the x-direction of the upper grid point representing the length position of spatial step 1/2,
Figure BDA0003267983790000047
the inviscid flux in the y-direction of the lower grid point representing the length position of spatial step 1/2,
Figure BDA0003267983790000048
the slope of the lower lattice edge representing the length position of spatial step 1/2,
Figure BDA0003267983790000049
the non-viscous flux in the x-direction of the lower grid point representing the length position of spatial step 1/2.
Further, the step (6) comprises the following steps:
(61) identifying the interval of the combustible mixed gas in the detonation wave front according to the flow parameter distribution of the far downstream along the y direction;
(62) determining the area average value of the flow parameters of the interval where the detonation wave front combustible mixed gas is located, wherein the area average formula is as follows:
Figure BDA00032679837900000410
Figure BDA00032679837900000411
Figure BDA00032679837900000412
Figure BDA00032679837900000413
wherein the content of the first and second substances,
Figure BDA00032679837900000414
an x component representing the mean velocity of the detonation wave front,
Figure BDA00032679837900000415
y component representing mean velocity of detonation wave front, nxX component, n, representing the normal vector of the detonation wave frontyRepresents the y-component of the normal vector of the knock wave front,
Figure BDA00032679837900000416
expressing the internal energy contained in unit mass, simultaneously solving four equations of an area average formula according to a Newton-Laverson multivariate iterative method to obtain a detonation wave front flow parameter
Figure BDA0003267983790000051
And
Figure BDA0003267983790000052
further, the step (7) comprises the following steps:
(71) and correcting the inclination angle of the detonation wave relative to the injection plane according to the airflow angle of the detonation wave front, wherein the correction formula is as follows:
Figure BDA0003267983790000053
wherein the content of the first and second substances,
Figure BDA0003267983790000054
indicating the inclination of the modified detonation wave relative to the injection plane,
Figure BDA0003267983790000055
representing the inclination of the uncorrected detonation wave relative to the injection plane;
(72) determining the rotation angle of a shock wave coordinate system according to the inclination angle of the detonation wave corrected by multiple iterations relative to the injection plane, and converting the outlet direction into the horizontal direction through a two-dimensional rotation matrix, wherein the rotation angle and the two-dimensional rotation matrix are in the following forms:
Figure BDA0003267983790000056
Figure BDA0003267983790000057
Figure BDA0003267983790000058
wherein the content of the first and second substances,
Figure BDA0003267983790000059
representing the rotation angle, x, of the shock coordinate systemnewRepresenting the x coordinate and y coordinate of any point in the flow field after the rotation of the shock wave coordinate systemnewThe y coordinate and x of any point in the flow field after the shock wave coordinate system rotates are expressedoldRepresenting the x coordinate, y, of any point in the non-rotating flow field of the shock coordinate systemoldY-coordinate, u, representing any point in the non-rotating flow field of the shock coordinate systemnewRepresenting the velocity x component, v, of any point in the flow field after the rotation of the shock wave coordinate systemnewRepresenting the velocity y component u of any point in the flow field after the rotation of the shock wave coordinate systemoldIndicating shock wave seatThe velocity x component, v, of any point in the non-rotating flow fieldoldRepresenting the velocity y component of any point in the non-rotating flow field of the shock wave coordinate system;
(73) converting the speed in the shock wave coordinate system into the speed in the laboratory coordinate system by a speed triangle method according to the vector addition and subtraction principle, wherein the conversion relation is as follows:
Figure BDA0003267983790000061
vlab＝vnew
wherein u islabX component, v, representing the velocity at any point in the laboratory coordinate systemlabThe y component represents the velocity at any point in the laboratory coordinate system.
Further, in the step (6), the airflow angle in the upper section of the section where the knock wavefront combustible mixture is located is corrected to be 0 in the shock coordinate system of the new iteration.
Has the advantages that: due to the adoption of the technical scheme, the invention has the following technical effects:
according to the method for predicting the distribution of the parameters of the flow field of the rotary detonation engine based on the space propulsion algorithm, through coupling the space propulsion algorithm and a single gamma CJ detonation wave model, by utilizing the flow following characteristics of a streamline grid corresponding to the space propulsion algorithm, the flow parameters after the detonation wave and the far and downstream flow parameters of the detonation wave under a shock wave coordinate system are determined, and the flow parameters under a laboratory coordinate system are obtained through coordinate conversion, so that the flow field of the rotary detonation engine can be rapidly solved, the pneumatic performance of the rotary detonation engine can be rapidly evaluated, meanwhile, the flow structures such as the detonation wave, a shear layer and an induced shock wave in the flow field can be accurately captured, and the configuration design period of the rotary detonation engine is greatly shortened.
Drawings
FIG. 1 is a calculation domain under a shock wave coordinate system determined in steps (1) to (6) in a method for predicting the distribution of flow field parameters of a rotary detonation engine based on a space propulsion algorithm;
FIG. 2 is a physical schematic diagram of a rotary detonation engine;
FIG. 3 is the intersection process of the shock polar curves of two adjacent points on the initial line;
FIG. 4 is a step process from an initial line to a solution point of a space propulsion algorithm, wherein E-P represents a grid edge point, C-P represents a grid center point, Const X represents a straight line where the initial line and the solution point are located, P-M represents a Plantt-Meyer expansion wave, Sh represents a shock wave, and Sl represents a non-stick slip line;
FIG. 5 is a detonation wave parameter convergence process in a flow field of a rotary detonation engine;
FIG. 6 is a streamline grid of a rotary detonation engine under a shock wave coordinate system;
FIG. 7 is a rotational knock engine temperature field obtained by a spatial boosting algorithm;
FIG. 8 is a rotating detonation engine speed field in a laboratory coordinate system obtained by a spatial boosting algorithm;
in the figure, 11-an upstream detonation wave corresponds to an initial value line, 12-a far downstream flow field of the detonation wave corresponds to an initial value line, 13-a redundancy section of the far downstream flow field of the detonation wave corresponds to an initial value line, 14-an imaginary non-adhesive wall surface with an inclination angle consistent with the airflow deflection angle of the redundancy section, 15-an injection plane blocking section with an inclination angle equal to the inclination angle of the detonation wave, 16-a combustible mixed gas modeling air inlet section, 17-a far downstream flow field of the detonation wave corresponds to a straight line where a solution point is located, 18-a downstream detonation wave corresponds to a position where the solution point is located, and 19-an imaginary non-adhesive wall surface with an inclination angle consistent with the airflow deflection angle of the combustible mixed gas modeling air inlet section.
Detailed Description
The present invention will be further described with reference to the accompanying drawings and examples.
The invention discloses a method for predicting the distribution of flow field parameters of a rotary detonation engine based on a space propulsion algorithm, which comprises the following steps: estimating a flow parameter of the detonation wave front in advance; determining a flowing parameter after a detonation wave according to a CJ detonation model with a single specific heat ratio; assigning the flow parameters after the detonation wave and the far downstream flow parameters to an initial value line; determining flow parameters under a shock wave coordinate system through a space propulsion algorithm; determining the initial position and the final position of combustible gas mixture injection; and (3) iteratively converging the flow field parameters of the rotary detonation engine, and obtaining the flow parameters in a laboratory coordinate system through coordinate conversion.
Referring to fig. 1, 11 is an initial value line corresponding to an upstream detonation wave, 12 is an initial value line corresponding to a far downstream flow field of the detonation wave, and 13 is an initial value line corresponding to a redundancy section of the far downstream flow field of the detonation wave. The method comprises the following steps that 14 a virtual non-adhesive wall surface with an inclination angle consistent with an airflow folding angle of a redundant section is corresponding to the virtual non-adhesive wall surface, 15 an injection plane blocking section with an inclination angle equal to an inclination angle of a detonation wave is corresponding to the injection plane blocking section, 16 a combustible mixture modeling air inlet section is corresponding to the injection plane blocking section, 17 a straight line with a far downstream flow field corresponding to the detonation wave is corresponding to the point, 18 a position with a downstream detonation wave corresponding to the point, and 19 a virtual non-adhesive wall surface with an inclination angle consistent with an airflow folding angle of a combustible mixture modeling air inlet section is corresponding to the virtual non-adhesive wall surface.
The shock wave coordinate system is a coordinate system formed by assuming that a moving detonation wave line segment AB is kept still, taking the direction of the line segment AB as a y coordinate direction and taking the direction vertical to the line segment AB as an x coordinate direction. The laboratory coordinate system is a coordinate system formed by taking a set of line segment AM directions of the injection plane as an x coordinate direction and taking a direction perpendicular to the line segment AM as a y coordinate direction.
θaveThe angle is the average flow angle and is located slightly upstream of the line segment IJ, and the angle θ is the complement of the angle between the injection plane (line segment AJ inclined in the case of a shock coordinate system) and the detonation wave AB.
The prediction method specifically comprises the following steps:
step (1), estimating the average speed of an injection surface inlet in advance, and determining the flow parameters of the detonation wave front according to a compressible flow relation;
substituting the flow parameters of the detonation wave front into a CJ detonation model with a single specific heat ratio gamma to determine the flow parameters of the detonation wave front;
step (3), the flow parameters far downstream of the detonation wave in the first iteration are obtained by expanding the pressure after the detonation wave to the pressure before the detonation wave, and the flow parameters far downstream of the detonation wave in the later iteration are assigned to an initial value line according to the previous calculation result; as shown in fig. 1, the initial value line is composed of line segments AB and BD, the flow parameter after the detonation wave AB is consistent with the flow parameter after the detonation wave of the line segment IJ calculated in the previous time, the flow parameter distribution of the line segment BD above the detonation wave is consistent with the flow parameter distribution of the line segment IE calculated in the previous time, and the specific value is obtained by linear interpolation.
Substituting the initial value line into a space propulsion algorithm to determine a flow field structure and flow parameter distribution of the rotary detonation engine under a shock wave coordinate system;
step (5), comparing the pressure value of the solution point of the injection surface with the injection total pressure, and when the pressure value of the solution point is smaller than the injection total pressure, performing coupling solution on an injection flow field and an explosion wave downstream flow field; and if the solution point pressure value is greater than or equal to the total pressure, the injection flow field does not exist, and only the solution of the detonation wave downstream flow field is carried out at the moment.
Step (6), determining the area average value of the flow parameters of the detonation wave front at the far downstream position of the detonation wave, returning to the step (2) for iteration, and jumping out of the cycle until the average airflow angle of the far downstream position is 0;
determining the rotation angle of a shock wave coordinate system according to the size of the detonation wave inclination angle, and determining the flow parameter distribution of the rotary detonation engine in a laboratory coordinate system according to the speed triangle;
and (8) outputting the flow parameter distribution of the rotary detonation engine in the laboratory coordinate system into a data file.
With reference to fig. 3, in the present invention, the intersection point parameters of the state curves of two adjacent points are obtained by a newton-raphson iteration method. With reference to fig. 4, in the present invention, in the process of advancing from the initial line to the downstream solution point, the flow parameters are obtained by directly calculating the interaction between the shock wave and the expansion wave, without the need of additional construction of unit point process, and the streamline mesh is formed by adaptively changing the slope of the lattice edge.
The method comprises the following steps of (1):
(11) determining the total pressure Pt and the total temperature Tt of the combustible mixture at the rotary detonation inlet according to the flight condition of the rotary detonation engine, and estimating the average speed at the inlet of the rotary detonation engine
Figure BDA0003267983790000081
(12) Determining a detonation wave front flow parameter, including an average static temperature, from the compressional flow relationship
Figure BDA0003267983790000082
Mean static pressure
Figure BDA0003267983790000083
And average density
Figure BDA0003267983790000084
The following relationships exist:
Figure BDA0003267983790000085
Figure BDA0003267983790000091
Figure BDA0003267983790000092
wherein, the CpAnd gamma is the constant pressure specific heat and specific heat ratio of the combustible mixture and the combustion product, RgRepresenting the gas constant.
The step (2) specifically comprises the following steps:
(21) according to the CJ knock model with double gamma, the CJ knock model with a single specific heat ratio gamma is simplified and obtained:
Figure BDA0003267983790000093
Figure BDA0003267983790000094
(22) determining an expression of a flow parameter after the detonation wave as follows according to a mass conservation law, a momentum conservation law and an energy conservation law before and after the detonation wave is crossed:
Figure BDA0003267983790000095
Figure BDA0003267983790000096
Figure BDA0003267983790000097
wherein M isCJRepresenting the Mach number of the detonation wave, H representing the dimensionless heat release amount, Q representing the heat of chemical reaction, RgWhich represents the constant of the gas,
Figure BDA0003267983790000098
represents the average static temperature of the detonation wave front,
Figure BDA0003267983790000099
represents the average density of the detonation wave front,
Figure BDA00032679837900000910
represents the mean static pressure of the detonation wave front,
Figure BDA00032679837900000911
which represents the static pressure after the detonation wave,
Figure BDA00032679837900000912
which represents the density after the detonation wave,
Figure BDA00032679837900000913
indicating the post-detonation temperature.
The step (4) specifically comprises the following steps:
(41) determining an intermediate variable chi through the non-viscous flux E in the main flow direction, and further obtaining a state quantity Q on an initial value line, wherein the expression of the intermediate variable chi is in the following form:
Figure BDA00032679837900000914
E1、E2、E3、E4the main flow direction has no adhesive flux;
(42) determining downstream solution point coordinates according to the velocity distribution on the initial value line, and establishing a streamline grid, wherein the expression of the downstream solution point is in the following form:
Figure BDA0003267983790000101
Figure BDA0003267983790000102
Figure BDA0003267983790000103
representing the x coordinate of the jth downstream solution point in the x direction,
Figure BDA0003267983790000104
represents the x coordinate of the jth initial value line point in the x direction, deltax represents the stepping length of the grid along the x direction,
Figure BDA0003267983790000105
the y coordinate representing the jth downstream solution point in the y direction,
Figure BDA0003267983790000106
representing the x coordinate of the jth initial line point in the y direction,
Figure BDA0003267983790000107
the y-direction velocity component representing the jth initial line point in the y-direction,
Figure BDA0003267983790000108
representing the x-direction velocity component of the jth initial value line point in the y direction;
(43) obtaining step by step half-steps along the x-direction according to an essentially oscillationless interpolation method and a limiting function
Figure BDA0003267983790000109
And
Figure BDA00032679837900001010
to obtain the state quantity of 1/2 position of step length
Figure BDA00032679837900001011
And
Figure BDA00032679837900001012
(44) according to the shock wave polar curve theory, the solution point pressure and the airflow angle of the space propulsion algorithm at the position with the stepping length of 1/2 are determined through two adjacent points with the stepping length of 1/2 in the x direction of the space, so that the Riemann self-similarity solution is obtained, and the state curves of the two adjacent points comprise the following shock wave polar curve equations:
Figure BDA00032679837900001013
Figure BDA00032679837900001014
wherein phiBA state curve representing the lower side point of the initial value line, thetaBAir flow angle, f (M), representing the lower side point of the initial value lineB,αB) Rankine allowances relation, alpha, representing the lower side point of the initial value lineBDenotes the ratio of pressure at any point in the downstream space to pressure at the lower side of the initial value line, v (M)B) Prandtl-Meyer function, phi, representing the lower side point of the initial lineTA state curve representing the upper point of the initial value line, thetaTAirflow angle, f (M), representing the upper point of the initial value lineT,αT) Rankine allowances relation, alpha, representing upper side point of initial value lineTTo representThe ratio of the pressure at any point in the downstream space to the pressure at the side point on the initial value line, v (M)T) A plantt-meier function representing the upper point of the initial line.
(45) Obtaining flow parameters under a single space progressive step length by carrying out differential dispersion on a compressible Euler equation, wherein the downstream differential equation along the flow x direction is in the following form:
Figure BDA0003267983790000111
wherein the content of the first and second substances,
Figure BDA0003267983790000112
represents the difference value of y coordinates of two adjacent points of the initial value line,
Figure BDA0003267983790000113
the y coordinate difference of two adjacent solution points at the downstream is shown,
Figure BDA0003267983790000114
the inviscid flux in the y-direction of the upper grid point representing the length position of spatial step 1/2,
Figure BDA0003267983790000115
the slope of the upper grid edge representing the length position of spatial step 1/2,
Figure BDA0003267983790000116
the unbounded flux in the x-direction of the upper grid point representing the length position of spatial step 1/2,
Figure BDA0003267983790000117
the inviscid flux in the y-direction of the lower grid point representing the length position of spatial step 1/2,
Figure BDA0003267983790000118
the slope of the lower lattice edge representing the length position of spatial step 1/2,
Figure BDA0003267983790000119
the non-viscous flux in the x-direction of the lower grid point representing the length position of spatial step 1/2.
In step (5), the pressure value of the injection surface solution point is compared with the injection total pressure, and the solution point is the downstream point of the n +1 st line obtained by the steps (44) and (45) at the upstream point on the nth ConstX line in the flow field area. Wherein ConstX represents a straight line parallel to the detonation wave AB in fig. 1.
The step (6) comprises the following steps:
step (61), identifying an interval where the detonation wave front combustible mixed gas is located according to the flow parameter distribution of far downstream along the y direction;
step (62), determining the area average value of the flow parameters of the interval where the detonation wave front combustible mixed gas is located, wherein the area average formula is as follows:
Figure BDA00032679837900001110
Figure BDA00032679837900001111
Figure BDA00032679837900001112
Figure BDA0003267983790000121
wherein the content of the first and second substances,
Figure BDA0003267983790000122
an x component representing the mean velocity of the detonation wave front,
Figure BDA0003267983790000123
y component representing mean velocity of detonation wave front, nxX component, n, representing the normal vector of the detonation wave frontyRepresents the y-component of the normal vector of the knock wave front,
Figure BDA0003267983790000124
the internal energy per unit mass is shown, and A is the area occupied by the detonation wave. According to a Newton-Laverson multivariate iterative method, simultaneously solving four equations of an area average formula to obtain a detonation wave front flow parameter
Figure BDA0003267983790000125
And
Figure BDA0003267983790000126
during iteration, the previous calculation result used in the assignment of the step (3) refers to the knock wave front flow parameter obtained by further calculating the knock wave front flow parameter obtained in the step (62) through the step (2).
The step (7) comprises the following steps:
(71) and correcting the inclination angle of the detonation wave relative to the injection plane according to the airflow angle of the detonation wave front, wherein the correction formula is as follows:
Figure BDA0003267983790000127
wherein the content of the first and second substances,
Figure BDA0003267983790000128
indicating the inclination of the modified detonation wave relative to the injection plane,
Figure BDA0003267983790000129
representing the inclination of the uncorrected detonation wave relative to the injection plane;
(72) determining the rotation angle of a shock wave coordinate system according to the inclination angle of the detonation wave corrected by multiple iterations relative to the injection plane, and converting the outlet direction into the horizontal direction through a two-dimensional rotation matrix, wherein the rotation angle and the two-dimensional rotation matrix are in the following forms:
Figure BDA00032679837900001210
Figure BDA00032679837900001211
Figure BDA00032679837900001212
wherein the content of the first and second substances,
Figure BDA00032679837900001213
representing the rotation angle, x, of the shock coordinate systemnewRepresenting the x coordinate and y coordinate of any point in the flow field after the rotation of the shock wave coordinate systemnewThe y coordinate and x of any point in the flow field after the shock wave coordinate system rotates are expressedoldRepresenting the x coordinate, y, of any point in the non-rotating flow field of the shock coordinate systemoldY-coordinate, u, representing any point in the non-rotating flow field of the shock coordinate systemnewRepresenting the velocity x component, v, of any point in the flow field after the rotation of the shock wave coordinate systemnewRepresenting the velocity y component u of any point in the flow field after the rotation of the shock wave coordinate systemoldRepresenting the x component, v, of the velocity at any point in the non-rotating flow field of the shock coordinate systemoldRepresenting the velocity y component of any point in the non-rotating flow field of the shock wave coordinate system;
(73) converting the speed in the shock wave coordinate system into the speed in the laboratory coordinate system by a speed triangle method according to the vector addition and subtraction principle, wherein the conversion relation is as follows:
Figure BDA0003267983790000131
vlab＝vnew
wherein u islabX component, v, representing the velocity at any point in the laboratory coordinate systemlabThe y component represents the velocity at any point in the laboratory coordinate system. The velocity triangle is shown in figure 1 and,
Figure BDA0003267983790000132
and the flow field speed in the AMLKED area under the shock wave coordinate system is represented, and the conversion between the speeds is obtained by vector addition and subtraction. Because the space position of the shock wave in the shock wave coordinate system is fixed, and the flow structures such as the shock wave in the actual flow (laboratory coordinate system) move at high speed along the tangential direction of the injection plane, the flow field of the actual rotary detonation engine is obtained through coordinate conversion according to the transformation rule of relative movement.
Further, in the step (6), the airflow angle in the upper section of the section where the knock wavefront combustible mixture is located is corrected to be 0 in the shock coordinate system of the new iteration.
The method can be used for rapidly evaluating the pneumatic performance of the rotary detonation engine, namely, the characteristics that the traditional time propulsion algorithm consumes time and computing resources are avoided by establishing a mathematical model of a detonation process and a downstream flow field structure of the detonation process.
For better illustration of the invention, and to facilitate understanding of the technical solutions thereof, typical but non-limiting examples of the invention are as follows:
the total injection pressure of combustible mixture at the inlet of the rotary detonation engine is 5 multiplied by 105Pa, total injection temperature of 300K, initial value of inlet average speed of 450m/s, specific heat ratio of the combustible premixed gas of 1.3961, and gas constant of the combustible premixed gas of 395.75J-kg-1·K-1The specific heat ratio of the combustion product is 1.1653, and the gas constant of the combustion product is 346.20J-kg-1·K-1The heat release per unit mass is 5.4704X 106J·kg-1Activation temperature of combustible gas mixture 15100K, single-step chemical reaction front factor 1.0X 109s-1. The ring expansion length of the rotary detonation engine is 314mm, and the axial length of the rotary detonation engine is 75 mm.
FIG. 5 is a graph showing the convergence course, θ, of each parameter of the detonation wave in the fast solution iteration of the present inventionincRepresenting the angle of inclination of the detonation wave, HDIndicating the length of the detonation wave, P1/P2Representing the detonation wave front wave-to-wave static pressure ratio, UlabRepresenting the knock wave velocity. FIG. 6 shows the shock coordinate system during fast resolving of the present inventionA grid of streamlines. FIG. 7 shows the temperature field of the rotary detonation engine obtained by the invention, and accurately captures the shock wave supercharging process and the post-detonation gas flow expansion acceleration process. Fig. 8 is a speed field of the rotary detonation engine obtained by the invention in a laboratory coordinate system, which is defined as a coordinate system formed by taking a line segment AM direction group of a jetting plane as an x coordinate direction and taking a direction perpendicular to the line segment AM as a y coordinate direction, and accurately capturing the airflow direction change process of the rotary detonation engine.
Table 1 shows the comparative data between the detonation wave parameters obtained by the rapid calculation and the detonation wave parameters obtained by the conventional time-marching algorithm.
TABLE 1
Figure BDA0003267983790000141
Compared with the detonation wave parameters of the rotary detonation engine obtained by the traditional time propulsion algorithm, the relative deviation of the height of the detonation wave obtained by the method is 1.38%, the relative deviation of the inclination angle of the detonation wave is 1.35%, the relative deviation of the front static pressure and the rear static pressure of the detonation wave is 1.05%, the relative deviation of the wave speed of the detonation wave is 0.97%, and the visible space propulsion algorithm has the same precision of resolving the rotary detonation flow field by the time propulsion algorithm.
Table 2 is data comparing the time spent in resolving the flow field of the rotary detonation engine and the time spent in resolving the flow field of the traditional time-marching algorithm in the 4-core 8-thread i7CPU environment.
TABLE 2
Algorithm Number and model of CPU Time consuming
Space-marching algorithm 4 core 8 threads, i7 5h
Traditional time advance algorithm 4 core 8 threads, i7 48h
The invention discloses a method for predicting the distribution of flow field parameters of a rotary detonation engine based on a space propulsion algorithm, which uses a CPU (central processing unit) of a 4-core 8-thread i7 to carry out solving operation, and the total time consumption is 5 h. And the traditional time advance algorithm uses 4 cores and 8 threads to carry out solving operation, and the total time consumption is 48 h. Compared with the traditional time propulsion algorithm, the method has the advantage that the solving speed is 8.6 times faster, and the configuration design and the selection period of the rotary detonation engine can be effectively reduced.
The above description is only of the preferred embodiments of the present invention, and it should be noted that: it will be apparent to those skilled in the art that various modifications and adaptations can be made without departing from the principles of the invention and these are intended to be within the scope of the invention.

Claims (7)

1. A method for predicting the distribution of flow field parameters of a rotary detonation engine based on a space propulsion algorithm is characterized by comprising the following steps of: the method comprises the following steps:
(1) estimating the average speed of an inlet of an injection surface in advance, and determining the flow parameters of the detonation wave front according to a compressible flow relation;
(2) substituting the flow parameters of the detonation wave front into a CJ detonation model with a single specific heat ratio to determine the flow parameters of the detonation wave front;
(3) assigning the flow parameters after the detonation wave and the flow parameters far downstream to an initial value line; the flow parameters far downstream of the detonation wave in the first iteration are obtained by expanding the pressure after the detonation wave to the pressure before the detonation wave, and the flow parameters far downstream of the detonation wave in the later iteration are obtained according to the calculation result of the previous iteration;
(4) substituting the initial value line into a space propulsion algorithm, and determining a flow field structure and flow parameter distribution of the rotary detonation engine under a shock wave coordinate system;
(5) comparing the pressure value of the solution point of the injection surface with the total injection pressure, when the pressure value of the solution point is less than the total injection pressure, performing coupled solution on the injection flow field and the detonation wave downstream flow field, and when the pressure value of the solution point is more than or equal to the total injection pressure, only performing solution on the detonation wave downstream flow field;
(6) determining the area average value of the flow parameters of the detonation wave front at the far downstream position of the detonation wave, returning to the step (2) to the step (5) for iteration, jumping out of a loop until the average airflow angle at the far downstream is 0, and executing the step (7);
(7) and determining the rotation angle of the shock wave coordinate system according to the inclination angle of the detonation wave, and determining the flow parameter distribution of the rotary detonation engine under the laboratory coordinate system according to the velocity triangle.
2. A method for predicting distribution of flow field parameters of a rotary detonation engine based on a spatial propelling algorithm according to claim 1, wherein the step (1) comprises the following steps:
(11) determining the total pressure Pt and the total temperature Tt of the combustible mixture at the rotary detonation inlet according to the flight condition of the rotary detonation engine, and estimating the average speed at the inlet of the rotary detonation engine
Figure FDA0003267983780000011
(12) Determining the average static temperature of the detonation wave front according to the compressible flow relation
Figure FDA0003267983780000012
Mean static pressure
Figure FDA0003267983780000013
And average density
Figure FDA0003267983780000014
3. The method for predicting the distribution of the flow field parameters of the rotary detonation engine based on the spatial propelling algorithm is characterized in that the step (2) comprises the following steps:
(21) constructing a CJ knock model with a single specific heat ratio, wherein a model equation is in the form of:
Figure FDA0003267983780000021
Figure FDA0003267983780000022
wherein M isCJRepresenting the Mach number of the detonation wave, H representing the dimensionless heat release amount, Q representing the heat of chemical reaction, RgRepresenting a gas constant, gamma is the specific heat ratio of the combustible mixture and the combustion products;
(22) determining post-detonation wave flow parameters including post-detonation wave static pressure parameters according to the mass conservation law, momentum conservation law and energy conservation law before and after the detonation wave
Figure FDA0003267983780000023
Density after detonation wave
Figure FDA0003267983780000024
And post detonation wave temperature
Figure FDA0003267983780000025
4. A method for predicting distribution of flow field parameters of a rotary detonation engine based on a spatial propelling algorithm according to claim 3, wherein the step (4) comprises the following steps:
(41) determining an intermediate variable chi through the non-viscous flux E in the main flow direction, and further obtaining a state quantity Q on an initial value line, wherein the expression of the intermediate variable chi is in the following form:
Figure FDA0003267983780000026
(42) determining downstream solution point coordinates according to the velocity distribution on the initial value line
Figure FDA0003267983780000027
A streamline grid is established, and the streamline grid is established,
Figure FDA0003267983780000028
representing the x coordinate of the jth downstream solution point in the x direction,
Figure FDA0003267983780000029
representing the x coordinate of the jth initial value line point in the x direction;
(43) obtaining step by step half-steps along the x-direction according to an essentially oscillationless interpolation method and a limiting function
Figure FDA00032679837800000210
And
Figure FDA00032679837800000211
to obtain the state quantity of 1/2 position of step length
Figure FDA00032679837800000212
And
Figure FDA00032679837800000213
(44) according to the shock wave polar curve theory, the solution point pressure and the airflow angle of the space propulsion algorithm at the position 1/2 in the stepping length are determined through two adjacent points of which the stepping length in the space x direction is 1/2 set values, and then a Riemann self-similarity solution is obtained, wherein the expression of the state curve of the two adjacent points is as follows:
Figure FDA00032679837800000214
Figure FDA00032679837800000215
wherein phiBA state curve representing the lower side point of the initial value line, thetaBAir flow angle, f (M), representing the lower side point of the initial value lineB,αB) Rankine allowances relation, alpha, representing the lower side point of the initial value lineBDenotes the ratio of pressure at any point in the downstream space to pressure at the lower side of the initial value line, v (M)B) Prandtl-Meyer function, phi, representing the lower side point of the initial lineTA state curve representing the upper point of the initial value line, thetaTAirflow angle, f (M), representing the upper point of the initial value lineT,αT) Rankine allowances relation, alpha, representing upper side point of initial value lineTDenotes the ratio of pressure at any point in the downstream space to pressure at a point on the initial line, v (M)T) A planter-meier function representing an upper point of the initial value line;
(45) obtaining flow parameters under a single space progressive step length by carrying out differential dispersion on a compressible Euler equation, wherein the downstream differential equation along the flow x direction is in the following form:
Figure FDA0003267983780000031
wherein the content of the first and second substances,
Figure FDA0003267983780000032
represents the difference value of y coordinates of two adjacent points of the initial value line,
Figure FDA0003267983780000033
the y coordinate difference of two adjacent solution points at the downstream is shown,
Figure FDA0003267983780000034
the inviscid flux in the y-direction of the upper grid point representing the length position of spatial step 1/2,
Figure FDA0003267983780000035
the slope of the upper grid edge representing the length position of spatial step 1/2,
Figure FDA0003267983780000036
the unbounded flux in the x-direction of the upper grid point representing the length position of spatial step 1/2,
Figure FDA0003267983780000037
the inviscid flux in the y-direction of the lower grid point representing the length position of spatial step 1/2,
Figure FDA0003267983780000038
the slope of the lower lattice edge representing the length position of spatial step 1/2,
Figure FDA0003267983780000039
the non-viscous flux in the x-direction of the lower grid point representing the length position of spatial step 1/2.
5. A method for predicting distribution of flow field parameters of a rotary detonation engine based on a spatial propelling algorithm according to claim 4, characterized in that the step (6) comprises the following steps:
(61) identifying the interval of the combustible mixed gas in the detonation wave front according to the flow parameter distribution of the far downstream along the y direction;
(62) determining the area average value of the flow parameters of the interval where the detonation wave front combustible mixed gas is located, wherein the area average formula is as follows:
Figure FDA00032679837800000310
Figure FDA00032679837800000311
Figure FDA0003267983780000041
Figure FDA0003267983780000042
wherein the content of the first and second substances,
Figure FDA0003267983780000043
an x component representing the mean velocity of the detonation wave front,
Figure FDA0003267983780000044
y component representing mean velocity of detonation wave front, nxX component, n, representing the normal vector of the detonation wave frontyRepresents the y-component of the normal vector of the knock wave front,
Figure FDA0003267983780000045
expressing the internal energy contained in unit mass, simultaneously solving four equations of an area average formula according to a Newton-Laverson multivariate iterative method to obtain a detonation wave front flow parameter
Figure FDA0003267983780000046
And
Figure FDA0003267983780000047
a represents the area occupied by the detonation wave.
6. A method for predicting distribution of flow field parameters of a rotary detonation engine based on a spatial propelling algorithm according to claim 5, characterized in that the step (7) comprises the following steps:
(71) and correcting the inclination angle of the detonation wave relative to the injection plane according to the airflow angle of the detonation wave front, wherein the correction formula is as follows:
Figure FDA0003267983780000048
wherein the content of the first and second substances,
Figure FDA0003267983780000049
indicating the inclination of the modified detonation wave relative to the injection plane,
Figure FDA00032679837800000410
representing the inclination of the uncorrected detonation wave relative to the injection plane;
(72) determining the rotation angle of a shock wave coordinate system according to the inclination angle of the detonation wave corrected by multiple iterations relative to the injection plane, and converting the outlet direction into the horizontal direction through a two-dimensional rotation matrix, wherein the rotation angle and the two-dimensional rotation matrix are in the following forms:
Figure FDA00032679837800000411
Figure FDA00032679837800000412
Figure FDA00032679837800000413
wherein the content of the first and second substances,
Figure FDA00032679837800000414
representing the rotation angle, x, of the shock coordinate systemnewRepresenting the x coordinate and y coordinate of any point in the flow field after the rotation of the shock wave coordinate systemnewThe y coordinate and x of any point in the flow field after the shock wave coordinate system rotates are expressedoldRepresenting the x coordinate, y, of any point in the non-rotating flow field of the shock coordinate systemoldY-coordinate, u, representing any point in the non-rotating flow field of the shock coordinate systemnewRepresenting the velocity x component, v, of any point in the flow field after the rotation of the shock wave coordinate systemnewRepresenting the velocity y component u of any point in the flow field after the rotation of the shock wave coordinate systemoldRepresenting the x component, v, of the velocity at any point in the non-rotating flow field of the shock coordinate systemoldRepresenting the velocity y component of any point in the non-rotating flow field of the shock wave coordinate system;
(73) converting the speed in the shock wave coordinate system into the speed in the laboratory coordinate system by a speed triangle method according to the vector addition and subtraction principle, wherein the conversion relation is as follows:
Figure FDA0003267983780000051
vlab＝vnew
wherein u islabX component, v, representing the velocity at any point in the laboratory coordinate systemlabThe y component represents the velocity at any point in the laboratory coordinate system.
7. The method for predicting the distribution of the flow field parameters of the rotary detonation engine based on the spatial propelling algorithm according to claim 1, wherein the method comprises the following steps: and (4) correcting the airflow angle of the upper side interval of the detonation wave front combustible mixed gas in the step (6) to be 0 in a new iteration shock wave coordinate system.
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CN117688697A (en) * 2024-02-02 2024-03-12 中国人民解放军空军工程大学 Design method of rotary detonation engine air inlet channel
CN117688697B (en) * 2024-02-02 2024-04-26 中国人民解放军空军工程大学 Design method of rotary detonation engine air inlet channel

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