CN110727251B - Pogo system modeling method of gas-liquid path coupling propulsion system carrier rocket - Google Patents
Pogo system modeling method of gas-liquid path coupling propulsion system carrier rocket Download PDFInfo
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- QVGXLLKOCUKJST-UHFFFAOYSA-N atomic oxygen Chemical compound [O] QVGXLLKOCUKJST-UHFFFAOYSA-N 0.000 claims description 4
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- MYMOFIZGZYHOMD-UHFFFAOYSA-N Dioxygen Chemical compound O=O MYMOFIZGZYHOMD-UHFFFAOYSA-N 0.000 description 1
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Abstract
The invention discloses a Pogo system modeling method of a gas-liquid path coupling propulsion system carrier rocket, which comprises the steps of establishing a second-order kinetic model of gas components such as a gas generator, a turbine, a gas guide pipe, a gas-liquid type thrust chamber and the like, and assembling the second-order kinetic model and an established second-order kinetic equation of a liquid path part into a complete propulsion system, thereby establishing a Pogo state space model containing gas path characteristics based on a state space method. Compared with the traditional transfer matrix method, the damping ratio can be given while the frequency of the propulsion system is calculated; compared with the traditional iteration method, the state space method has higher calculation efficiency, is not influenced by the initial value of the iteration, and cannot leak roots; the state equation method can consider more factors such as multimode, multi-coupling points, core-stage and boosting coupling effects, and the result is more accurate.
Description
Technical Field
The invention belongs to the field of dynamic modeling, and particularly relates to a Pogo system modeling method containing gas path characteristics based on a state space method.
Background
The Pogo vibration modeling method comprises a single transmission method, a critical damping method, a matrix method and the like, wherein a state equation method proposed by Rubin is more advanced. However, the methods are all researches on a liquid path system, and the heavy carrier rockets and the like in China adopt novel high-pressure low-temperature liquid oxygen/kerosene afterburning cycle engines with gas path characteristics, the influence of the gas path entropy wave characteristics on the Pogo vibration modeling and stability is not negligible, and the literature data in the aspect is very lacking. According to the Liujin code, a transfer matrix method is used for carrying out stability analysis on a Pogo system with gas path characteristics, although the stability of the Pogo of the rocket can be well predicted, the method is only suitable for the stability analysis of the Pogo of a single-path carrier rocket, and can only be equivalently treated as a single path for the rocket with multiple paths, so that the analysis effect is poor.
In the modeling method for liquid rocket Pogo vibration, an equation of state method is a relatively perfect method at present. The method comprises the steps of dividing a pipeline into a plurality of basic units by using a finite element modeling thought for reference, uniformly describing the basic units and elements such as a pump, a pressure accumulator, a thrust chamber and the like by using a second-order differential equation, and constructing a second-order differential equation of Pogo vibration of the whole system by coupling with a structural vibration equation, so that Pogo stability analysis is converted into a characteristic value problem of a generalized matrix. The method is easy to popularize to the modeling of a complex three-dimensional pipeline, has strong universality, can conveniently analyze the bundled liquid rocket with a plurality of boosters and a plurality of engines, and is successfully applied to the Atlas-II/Centaurand rocket in the United states and the research on the problem of CZ-2F rocket Pogo in China. The state space model established by the method can be directly used for frequency domain analysis, and compared with the traditional transfer matrix method, the method can calculate the frequency of a propulsion system and give a damping ratio; compared with the traditional iteration method, the state space method has higher calculation efficiency, is not influenced by the initial value of the iteration, and cannot leak roots; the state equation method can consider more factors such as multimode, multi-coupling points, core-stage and boosting coupling effects, and the result is more accurate. But the equation of state method has no relevant report for Pogo modeling of a gas-liquid path propulsion system.
Disclosure of Invention
The application provides a Pogo system modeling method of a gas-liquid path coupling propulsion system carrier rocket, which comprises the steps of establishing a second-order kinetic model of gas components such as a gas generator, a turbine, a gas guide pipe and a gas-liquid type thrust chamber, and assembling the second-order kinetic model and an established second-order kinetic equation of a liquid path part into a complete propulsion system, so that a Pogo state space model containing gas path characteristics based on a state space method is established.
In order to achieve the purpose, the technical scheme of the invention is as follows: a Pogo system modeling method of a gas-liquid path coupling propulsion system carrier rocket comprises the following steps:
step 1: establishing a second-order dynamic model of a liquid path part of the propulsion system;
step 2: establishing a second-order dynamic model of each unit and boundary conditions of the gas path part;
and step 3: assembling the units of the gas circuit and the second order kinetic equation of the boundary condition according to the selection sequence of the state variables;
and 4, step 4: in order to enable the liquid circuit and the gas circuit to be assembled, the liquid circuit and the gas circuit need to be made to have the same state variable;
and 5: adjusting a gas path second-order kinetic equation of the propulsion system into a form suitable for being connected with a liquid path part;
step 6: assembling the liquid path second order kinetic equation coefficient matrix and the gas path second order kinetic equation coefficient matrix according to the selection sequence of the state variables, and assembling the two matrixes in the RGAnd filling 1 in a place corresponding to the pressure at the tail end of the matrix liquid path, and deriving a second-order kinetic equation of the propulsion system containing the gas path characteristics.
And 7: solving first derivative on two sides of the structural vibration equation, and adjusting the structural vibration equation into a form suitable for being assembled with a propulsion system;
and 8: and coupling a second-order kinetic equation of the propulsion system with a structural vibration equation to derive a Pogo system model containing gas path characteristics.
Further, the step 1 of establishing a second-order dynamic model of the liquid path part of the propulsion system specifically comprises the following steps:
wherein the mass displacement uLIs a state variable of the liquid path system,
is the flow velocity of the fluid relative to the wall of the tube, PLIs the pressure at each node of the liquid path unit, and uL＝[u1u2 … ui …]T，u1u2 … ui… is the mass displacement at each node; pG0The pressure intensity of the tail end node of the liquid path is also the pressure intensity of the initial end of the gas path; q. q.ssModal displacement of the structural system;
is uLA first derivative;
is uLA second derivative;
is qsA first derivative;
is qsA second derivative; mLIs a mass array; rLIs a damping array; kLIs a stiffness matrix; u shape0L，U1L，U2LCoefficient matrixes for different sections of the propulsion system; rho is mass density; a is the sectional area of the pipeline.
Further, step 2, carrying out Taylor second-order expansion on the pre-combustion chamber, the turbine, the rectifier grid, the gas guide pipe, the thrust chamber unit of the gas path system and the transfer matrix model of the boundary condition, carrying out Laplace inverse transformation to convert the pre-combustion chamber, the turbine, the rectifier grid, the gas guide pipe and the thrust chamber unit into second-order kinetic equation description, and deriving the second-order kinetic equation description of each unit of the gas path part and the boundary condition.
Further, (1) the dimensionalized second order kinetic equation of the prechamber unit is described as:
wherein
τ1＝τgg，τ2＝-τΓ，τ3＝-(τgg+τΓ)，
Respectively the steady state gas pressure, flow, temperature and mixing ratio at the outlet of the pre-combustion chamber,
steady state pressure and flow, p, respectively, of the prechamber inletG2、qG2、TG2、KG2Respectively representing the pressure, flow, temperature and mixing ratio of the gas at the outlet of the precombustion chamber; kggThe rated mixing ratio of the gas generator; tau isΓCombustion time lag of the gas generator; psi is the slope of the combustion product temperature versus propellant component mixing ratio curve, and
PG0，qG0for the pressure at the end of the liquid path and the pulsating quantity, τ, of liquid oxidant flow entering the generator through the nozzleggTime from gas formation to gas generator outlet; k is a radical ofggIs a gas adiabatic index; t is the combustion product temperature;
are the partial derivative symbols. (2) The dimensional second order kinetic equation for a turbine unit is described as:
in the formula:
respectively the steady state gas pressure, flow, temperature and mixing ratio at the turbine inlet,
respectively steady state gas pressure, flow, temperature and mixing ratio, p, at the turbine outletG2、qG2、TG2、KG2Turbine inlet gas pressure, flow, temperature and mixing ratio, respectively; p is a radical ofG3、qG3、TG3、KG3Respectively turbine outlet gas pressure, flow, temperature and mixing ratio;
and
respectively the static temperature of the inlet and the outlet of the turbine; ε is the slope of the gas flow through the turbine versus pressure.
(3) The dimensional second order kinetic equation of the gas conduit unit is described as:
in the formula:
respectively the steady state gas pressure, flow, temperature and mixing ratio at the inlet of the gas conduit,
respectively, steady state gas pressure, flow, temperature and mixing ratio, p, of the gas conduit outletG3、qG3、TG3、KG3Respectively the gas pressure, flow, temperature and mixing ratio at the inlet of the gas guide pipe; p is a radical ofG4、qG4、TG4、KG4Respectively the pressure, flow, temperature and mixing ratio of the gas at the outlet of the gas conduit; k is a radical ofgdBeing gas conduitsA gas adiabatic index; tau isgdThe residence time of the fuel gas in the fuel gas guide pipe;
(4) the dimensional second order kinetic equation of the rectifier grid unit is described as follows:
in the formula:
respectively the steady state gas pressure, flow, temperature and mixing ratio at the inlet of the flow straightener,
respectively the steady state gas pressure, flow, temperature and mixing ratio, p, of the outlet of the rectifier gridG4、qG4、TG4、KG4Respectively the pressure, flow, temperature and mixing ratio of the gas at the inlet of the rectifier grid, pG5、qG5、TG5、KG5Respectively the pressure, flow, temperature and mixing ratio of the gas at the outlet of the rectifier grid; epsilon is the slope of the gas flow rate-pressure ratio curve passing through the rectifier grid.
(5) The dimensionalized second order kinetic equation of the thrust cell unit is described as:
the gas-liquid type thrust chamber is different from other gas circuit units, and has the acting force on the structure besides the kinetic equation, and the acting force on the structure is described as follows:
wherein Qp′＝[-AthCf]，CfIs the thrust coefficient, Ath is the thrust chamber throat area;
in the formula:
respectively the steady state gas pressure, flow, temperature and mixing ratio at the inlet of the thrust chamber,
respectively the steady state gas pressure, flow, p of the outlet of the thrust chambercFor pulsating pressure in the combustion chamber, qmcIs the total pulsating flow of the combustion chamber; p is a radical ofG5、qG5、TG5、KG5Respectively the pressure, flow, temperature and mixing ratio of the gas at the inlet of the thrust chamber; kggThe gas mixing ratio is the rated gas mixing ratio entering the combustion chamber from the gas conduit through the nozzle; tau iscThe residence time of the fuel gas in the combustion chamber; k is a radical ofcIs the adiabatic index of the gas in the combustion chamber; psicIs the slope of the curve of the gas temperature in the combustion chamber as a function of the mixing ratio of the components, and
qmfgis a steady oxygen-enriched gas flow entering the combustion chamber from a gas conduit through a nozzle; kmcThe rated mixing ratio of the combustion chamber; q. q.smfcIs the steady state liquid fuel flow into the combustion chamber; a. theq＝qmfg+(1+Kgg)qmfc；τTcThe time for the liquid fuel to convert to gas in the combustion chamber.
(6) Boundary conditions need to be added at the tail end of the gas circuit, and the boundary conditions with dimension basic variables are as follows:
further, the gas path part equation of the propulsion system including the boundary conditions after the assembly in step 3 is as follows:
wherein M'G，R′G，K′GRespectively a mass array, a damping array and a rigidity array of the gas circuit system q'GState variables of the gas circuit:
further, step 4, solving first derivatives on both sides of the liquid path propulsion system equation by changing the state variable of the liquid path to be the same as the state variable of the gas path, and adjusting the second order kinetic equation of the liquid path of the propulsion system to be suitable for being connected with the gas path part;
make equation (1) of the liquid path portion become
Wherein M isLIs a mass array; rLIs a damping array; kLIs a stiffness matrix; pLIs the pressure intensity and mass flow q of each node of the liquid path unitLAnd mass displacement uLIn a relationship of
Namely, it is
The flow rate of the fluid relative to the pipe wall is shown, and A is the sectional area of the pipeline.
Further, step 5 is to M'G，R′G，K′GExchanging two columns of 1 and 2 of the matrix, and replacing the original two columns with the original two columns
q′G＝[PG0,qG0,PG2,qG2,TG2,KG2…PG5,qG5,TG5,KG5]T
Coefficient matrix M 'derived for state variables'G，R′G，K′GWritten as state variables
qG＝[qG0,PG0,PG2,qG2,TG2,KG2…PG5,qG5,TG5,KG5]T
Coefficient matrix M derived for basic variablesG，RG，KG。
Further, the specific implementation manner of step 6 is:
the liquid path and the gas path are assembled as follows:
wherein
Variable of state
qL＝[qL1,qL2,qL3…qLn,qG0]TIs the mass flow state variable of the liquid path;
qG0，PG0，q″G＝[PG2,qG2,TG2,KG2…PG5,qG5,TG5,KG5]Tis the state variable of the gas circuit;
the outlet quantity of the liquid path is the inlet quantity of the gas path, and the state variables of the liquid path and the gas path both contain qG0I.e. the state variables of the liquid path and the gas path overlap.
Further, the specific implementation manner of step 7 is:
equation of vibration of structure
Two ends are derived to obtain
Ms，Rs，KsA structural system mass array, a damping array and a rigidity array; q0，Q1，Q2For coupling system matrices, QpTo be composed of
When being state variables Qp' spreading matrix, qsModal displacement of the structural system; v is a coupling system coefficient matrix; wherein the relationship between the q mass flow and the u mass displacement is
Namely, it is
Further, the specific implementation manner of step 8 is: taking state variables
Coupling a second order kinetic equation (11) of the propulsion system with a structural vibration equation (13) to obtain a Pogo system model can be written as:
wherein
Through the technical scheme, the invention can obtain the following effects: compared with the traditional transfer matrix method, the damping ratio can be given while the frequency of the propulsion system is calculated; compared with the traditional iteration method, the state space method has higher calculation efficiency, is not influenced by the initial value of the iteration, and cannot leak roots; the state equation method can consider more factors such as multimode, multi-coupling points, core-stage and boosting coupling effects, and the result is more accurate.
Drawings
In order to more clearly illustrate the embodiments of the present invention or the technical solutions in the prior art, the drawings required for the present invention will be briefly described below.
FIG. 1 is a layout diagram of units of a liquid path system in which only an oxygen path is considered by a rocket of a certain type in the embodiment;
FIG. 2 is a layout diagram of the units of the air path system in the embodiment.
The sequence numbers in the figures illustrate: 1 a first section of corrugated pipe, 2 a second section of straight pipe, 3 a third section of corrugated pipe, 4 a fourth section of straight pipe, 5 a three-way-accumulator super unit, 6 a swinging hose corrugated pipe, 7 a pre-pressurizing pump, 8 a pump pipe, 9 a pump pipe, 10 a main pump, 11 a pump rear pipe, 12 a pump rear pipe, b-valve super unit, 13 a pre-combustion chamber, 14 a turbine, 15 a gas guide pipe, 16 a flow straightener and 17 a thrust chamber.
Detailed Description
In this embodiment, the above steps are explained by taking a certain type of gas-liquid path coupled propulsion carrier rocket as an example:
step 1: establishing a second-order dynamic model of a liquid path part of a propulsion system: the layout of each unit of the liquid path system of a certain rocket only considering an oxygen path is shown in figure 1: the device comprises a first section of corrugated pipe, a second section of straight pipe, a third section of corrugated pipe, a fourth section of straight pipe, a three-way-accumulator super unit, a swinging hose corrugated pipe, a prepressing pump, an inter-pump pipe, a main pump, a post-pump pipe and a post-pump pipe b-valve super unit which are arranged in sequence;
the liquid path part model is
Wherein the second straight tube section is divided into 3 units, so ML，RL，KLIs a 15 × 15 matrix, U0L，U1L，U2LIs a 15 × 4 matrix, uL＝[uL1 uL2 … uL15]T Dimension 15 × 1. q. q.ss＝[qs1 qs2 qs3 qs4]TDimension 4 × 1.
Step 2: and establishing a second-order dynamic model of each unit and boundary conditions of the gas path part. The layout of each unit of the gas circuit system is shown in fig. 2, and a second-order kinetic equation of each unit of the gas circuit system is written as follows:
(1) the second order kinetic equation of the precombustion chamber is
(2) The second order kinetic equation of the turbine is
(3) The second order kinetic equation of the gas conduit is
(4) The second order kinetic equation of the rectifier grid is
(5) The second order kinetic equation of the thrust chamber is
The force of the thrust chamber on the structure is described as follows:
wherein Qp′＝[-AthCf]。
(6) The second order kinetic equation of the boundary condition is
And step 3: and assembling the units of the gas circuit and the second order kinetic equation of the boundary condition according to the selection sequence of the state variables.
The assembled gas path part model is as follows:
wherein q'GState variables of the gas circuit:
q′G＝[PG0 qG0 pG2 qG2 TG2 KG2 pG3 qG3 TG3 KG3 pG4 qG4 TG4 KG4 pG5 qG5 TG5 KG5 pcqmc]T
and 4, step 4: in order to enable the assembly of the liquid and gas circuit parts, the same state variables are required for the liquid and gas circuit parts.
Solving the first derivative on both sides of the equation of the liquid path part to make the state variable of the equation of the liquid path part consistent with that of the gas path part, i.e.
Wherein
qs＝[qs1 qs2 qs3qs4]T。
And 5: and adjusting a gas path second-order kinetic equation of the propulsion system into a form suitable for being connected with the liquid path part. To M'G，R′G，K′GThe two columns 1 and 2 of the matrix are interchanged.
The gas circuit part model at this moment is:
MGqG+RGqG+KGqG＝0
wherein
qG＝[qG0 PG0 pG2 qG2 TG2 KG2 pG3 qG3 TG3 KG3 pG4 qG4 TG4 KG4 pG5 qG5 TG5 KG5 pcqmc]T
Step 6: assembling the liquid path second order kinetic equation coefficient matrix and the gas path second order kinetic equation coefficient matrix according to the selection sequence of the state variables, and assembling the two matrixes in the RGAnd filling 1 in a place corresponding to the pressure at the tail end of the matrix liquid path, and deriving a second-order kinetic equation of the propulsion system containing the gas path characteristics. The liquid path and the gas path are assembled as follows:
wherein
Variable of state
The dimension is 34 × 1. ML，RL，KLIs a 15 × 15 matrix, MG，RG，KGIs a 19 × 20 matrix, Mp，Rp，KpIs a 34 × 34 matrix, U0，U1，U2Is a 34 × 4 matrix, qL＝[qL1,qL2,qL3…,qG0]TIs a state variable of mass flow of the fluid path, qG0＝qL15；qG0，PG0，q″G＝[PG2,qG2,TG2,KG2…PG5,qG5,TG5,KG5]TIs the state variable of the gas circuit;
and 7: and solving first derivative on two sides of the structural vibration equation, and adjusting the structural vibration equation into a form suitable for being assembled with the propulsion system.
Equation of vibration of structure
Two ends are derived to obtain
In this example, the first four modes of the structure are selected to couple with the propulsion system, so Ms，Rs，KsV is a 4X 4 matrix, Q0，Q1，Q2，QpA 4 x 34 matrix.
And 8: and coupling a second-order kinetic equation of the propulsion system with a structural vibration equation to derive a Pogo system model containing gas path characteristics.
Coupling a second order kinetic equation of the propulsion system with a structural vibration equation to obtain a Pogo system model can be written as:
wherein
So far, the Pogo system modeling including the gas path characteristics based on the state equation method is completed by taking a certain type of gas-liquid path coupling propulsion carrier rocket as an example.
Claims (10)
1. A Pogo system modeling method of a gas-liquid path coupling propulsion system carrier rocket is characterized by comprising the following steps:
step 1: establishing a second-order dynamic model of a liquid path part of the propulsion system;
step 2: establishing a second-order dynamic model of each unit and boundary conditions of the gas path part;
and step 3: assembling the units of the gas circuit and the second order kinetic equation of the boundary condition according to the selection sequence of the state variables;
and 4, step 4: in order to enable the liquid circuit and the gas circuit to be assembled, the liquid circuit and the gas circuit need to be made to have the same state variable;
and 5: adjusting a gas path second-order kinetic equation of the propulsion system into a form suitable for being connected with a liquid path part;
step 6: assembling the liquid path second order kinetic equation coefficient matrix and the gas path second order kinetic equation coefficient matrix according to the selection sequence of the state variables, and assembling the two matrixes in the RGFilling 1 in a place corresponding to the pressure at the tail end of the matrix liquid path, and deriving a second-order kinetic equation of the propulsion system containing the gas path characteristics;
and 7: solving first derivative on two sides of the structural vibration equation, and adjusting the structural vibration equation into a form suitable for being assembled with a propulsion system;
and 8: and coupling a second-order kinetic equation of the propulsion system with a structural vibration equation to derive a Pogo system model containing gas path characteristics.
2. The Pogo system modeling method of a gas-liquid path coupled propulsion system launch vehicle of claim 1, wherein the step 1 of establishing a propulsion system liquid path part second order dynamics model specifically comprises:
wherein the mass displacement uLIs a state variable of the liquid path system,
is the flow velocity of the fluid relative to the wall of the tube, PLIs the pressure at each node of the liquid path unit, and uL＝[u1u2 … ui …]T，u1u2 … ui… are nodesThe mass displacement of (d); pG0The pressure intensity of the tail end node of the liquid path is also the pressure intensity of the initial end of the gas path; q. q.ssModal displacement of the structural system;
is uLA first derivative;
is uLA second derivative;
is qsA first derivative;
is qsA second derivative; mLIs a mass array; rLIs a damping array; kLIs a stiffness matrix; u shape0L，U1L，U2LCoefficient matrixes for different sections of the propulsion system; rho is mass density; a is the sectional area of the pipeline.
3. The Pogo system modeling method of the gas-liquid path coupling propulsion system carrier rocket of claim 1, wherein in the step 2, Taylor second-order expansion is performed on a transmission matrix model of a gas path system precombustion chamber, a turbine, a rectifier grid, a gas guide pipe, a thrust chamber unit and boundary conditions, Laplace inverse transformation is performed to convert the expansion into second-order kinetic equation description, and the second-order kinetic equation description of each unit of a gas path part and the boundary conditions is derived.
4. The method of claim 3, wherein the Pogo system modeling of the gas-liquid path coupled propulsion system launch vehicle,
(1) the dimensional second order kinetic equation for the prechamber unit is described as:
wherein
τ1＝τgg，τ2＝-τΓ，τ3＝-(τgg+τΓ)，
Respectively the steady state gas pressure, flow, temperature and mixing ratio at the outlet of the pre-combustion chamber,
steady state pressure and flow, p, respectively, of the prechamber inletG2、qG2、TG2、KG2Respectively representing the pressure, flow, temperature and mixing ratio of the gas at the outlet of the precombustion chamber; kggThe rated mixing ratio of the gas generator; tau isΓCombustion time lag of the gas generator; psi is the slope of the combustion product temperature versus propellant component mixing ratio curve, and
PG0，qG0for the pressure at the end of the liquid path and the pulsating quantity, τ, of liquid oxidant flow entering the generator through the nozzleggTime from gas formation to gas generator outlet; k is a radical ofggIs a gas adiabatic index; t is the combustion product temperature;
is a partial derivative symbol;
(2) the dimensional second order kinetic equation for a turbine unit is described as:
in the formula:
respectively the steady state gas pressure, flow, temperature and mixing ratio at the turbine inlet,
respectively steady state gas pressure, flow, temperature and mixing ratio, p, at the turbine outletG2、qG2、TG2、KG2Turbine inlet gas pressure, flow, temperature and mixing ratio, respectively; p is a radical ofG3、qG3、TG3、KG3Respectively turbine outlet gas pressure, flow, temperature and mixing ratio;
and
respectively the static temperature of the inlet and the outlet of the turbine; epsilon is the slope of the gas flow rate and pressure ratio curve passing through the turbine;
(3) the dimensional second order kinetic equation of the gas conduit unit is described as:
in the formula:
respectively the steady state gas pressure, flow, temperature and mixing ratio at the inlet of the gas conduit,
respectively, steady state gas pressure, flow, temperature and mixing ratio, p, of the gas conduit outletG3、qG3、TG3、KG3Respectively gas pressure at inlet of gas conduitFlow rate, temperature and mixing ratio; p is a radical ofG4、qG4、TG4、KG4Respectively the pressure, flow, temperature and mixing ratio of the gas at the outlet of the gas conduit; k is a radical ofgdIs the gas insulation index of the gas conduit; tau isgdThe residence time of the fuel gas in the fuel gas guide pipe;
(4) the dimensional second order kinetic equation of the rectifier grid unit is described as follows:
in the formula:
respectively the steady state gas pressure, flow, temperature and mixing ratio at the inlet of the flow straightener,
respectively the steady state gas pressure, flow, temperature and mixing ratio, p, of the outlet of the rectifier gridG4、qG4、TG4、KG4Respectively the pressure, flow, temperature and mixing ratio of the gas at the inlet of the rectifier grid, pG5、qG5、TG5、KG5Respectively the pressure, flow, temperature and mixing ratio of the gas at the outlet of the rectifier grid; epsilon is the slope of the gas flow and pressure ratio curve passing through the rectifier grid;
(5) the dimensionalized second order kinetic equation of the thrust cell unit is described as:
the force of the thrust chamber on the structure is described as follows:
wherein Qp′＝[-AthCf]，CfIs the thrust coefficient, Ath is the thrust chamber throat area;
in the formula:
respectively the steady state gas pressure, flow, temperature and mixing ratio at the inlet of the thrust chamber,
respectively the steady state gas pressure, flow, p of the outlet of the thrust chambercFor pulsating pressure in the combustion chamber, qmcIs the total pulsating flow of the combustion chamber; p is a radical ofG5、qG5、TG5、KG5Respectively the pressure, flow, temperature and mixing ratio of the gas at the inlet of the thrust chamber; kggThe gas mixing ratio is the rated gas mixing ratio entering the combustion chamber from the gas conduit through the nozzle; tau iscThe residence time of the fuel gas in the combustion chamber; k is a radical ofcIs the adiabatic index of the gas in the combustion chamber; psicIs the slope of the curve of the gas temperature in the combustion chamber as a function of the mixing ratio of the components, and
qmfgis a steady oxygen-enriched gas flow entering the combustion chamber from a gas conduit through a nozzle; kmcThe rated mixing ratio of the combustion chamber; q. q.smfcIs the steady state liquid fuel flow into the combustion chamber; a. theq＝qmfg+(1+Kgg)qmfc；τTcThe time for converting the liquid fuel into gas in the combustion chamber;
(6) boundary conditions need to be added at the tail end of the gas circuit, and the boundary conditions with dimension basic variables are as follows:
5. the Pogo system modeling method of a gas-liquid path coupled propulsion system launch vehicle of claim 1, wherein the propulsion system gas path portion equation including boundary conditions after the step 3 assembly is completed is:
wherein M'G，R′G，K′GRespectively a mass array, a damping array and a rigidity array of the gas circuit system q'GState variables of the gas circuit:
6. the Pogo system modeling method of a launch vehicle of a gas-liquid path coupled propulsion system according to claim 1, characterized in that step 4 is implemented by solving first derivatives on both sides of the propulsion system equation of the liquid path in such a way that the state variables of the liquid path become the same as the state variables of the gas path, and adjusting the second order kinetic equation of the liquid path of the propulsion system to a form suitable for connection with the gas path portion;
make the equation of the liquid path part become
Wherein M isLIs a mass array; rLIs a damping array; kLIs a stiffness matrix; pLIs the pressure intensity and mass flow q of each node of the liquid path unitLAnd mass displacement uLIn a relationship of
Namely, it is
The flow rate of the fluid relative to the pipe wall is shown, and A is the sectional area of the pipeline.
7. The method of modeling the Pogo system of a gas-liquid coupled propulsion system launch vehicle of claim 1, wherein step 5 is to M'G，R′G，K′GTwo columns 1 and 2 of the matrix are interchanged to
q′G＝[PG0,qG0,PG2,qG2,TG2,KG2…PG5,qG5,TG5,KG5]T
Coefficient matrix M 'derived for state variables'G，R′G，K′GWritten as state variables
qG＝[qG0,PG0,PG2,qG2,TG2,KG2…PG5,qG5,TG5,KG5]T
Coefficient matrix M derived for basic variablesG，RG，KG。
8. The Pogo system modeling method of a gas-liquid path coupled propulsion system launch vehicle of claim 1, wherein the specific implementation manner of step 6 is as follows:
the liquid path and the gas path are assembled as follows:
wherein
Variable of state
qL＝[qL1,qL2,qL3…qLn,qG0]TIs the mass flow state variable of the liquid path;
qG0，PG0，q″G＝[PG2,qG2,TG2,KG2…PG5,qG5,TG5,KG5]Tis the state variable of the gas circuit;
the outlet quantity of the liquid path is the inlet quantity of the gas path, and the state variables of the liquid path and the gas path both contain qG0I.e. the state variables of the liquid path and the gas path overlap.
9. The Pogo system modeling method of a gas-liquid path coupled propulsion system launch vehicle of claim 2, wherein the specific implementation manner of step 7 is as follows:
equation of vibration of structure
Two ends are derived to obtain
Ms，Rs，KsA structural system mass array, a damping array and a rigidity array; q0，Q1，Q2For coupling system matrices, QpTo be composed of
When being state variables Qp' spreading matrix, qsModal displacement of the structural system; v is a coupling system coefficient matrix; wherein the relationship between the q mass flow and the u mass displacement is
Namely, it is
10. The Pogo system modeling method of a gas-liquid path coupled propulsion system launch vehicle of claim 1, wherein the specific implementation manner of step 8 is: taking state variables
Coupling a second order kinetic equation of the propulsion system with a structural vibration equation to obtain a Pogo system model can be written as:
wherein
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