CN112597609A - One-dimensional modeling method for transient response of multistage sealed disc cavity - Google Patents

One-dimensional modeling method for transient response of multistage sealed disc cavity Download PDF

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CN112597609A
CN112597609A CN202011576743.5A CN202011576743A CN112597609A CN 112597609 A CN112597609 A CN 112597609A CN 202011576743 A CN202011576743 A CN 202011576743A CN 112597609 A CN112597609 A CN 112597609A
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王磊
毛军逵
潘进
王飞龙
何辉
毕帅
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Nanjing University of Aeronautics and Astronautics
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Abstract

The invention discloses a one-dimensional modeling method for transient response of a multi-stage sealed disc cavity, which considers the coupling effect of a sealed labyrinth and the disc cavity, establishes a corresponding one-dimensional transient mathematical model by analyzing the volume effect in a labyrinth element and a disc cavity element, and obtains the time-dependent response rule of fluid parameters in the multi-stage sealed disc cavity under the transient working condition by solving a one-dimensional transient network of a disc cavity air system after inputting element geometric parameters and transient boundary working conditions. Compared with the prior art, the method can accurately describe the response changes of the temperature and the pressure of the fluid in the multistage sealing disc cavity along with time under the transient working condition, thereby providing an important theoretical basis for the design and the test of an air system of an aircraft engine.

Description

One-dimensional modeling method for transient response of multistage sealed disc cavity
Technical Field
The invention relates to a one-dimensional modeling method for transient response of a multistage sealing disc cavity, and belongs to the field of modeling and simulation of air systems in aerospace propulsion theory and engineering.
Background
When the aircraft engine is in a transition working condition (such as starting, accelerating, stopping, rapid maneuvering process and the like), especially under an extreme working condition (such as main shaft breakage, air stopping and the like), a complex transient response phenomenon can occur inside an air system. When boundary disturbance generated in the transient state and the extreme working condition of the engine acts on the air system, short-time dangerous transient load can be induced under the action of the volume effect and the unsteady internal flow of each chamber, so that the safe operation and the service life of the engine are threatened, and therefore the transient response problem of the air system gradually becomes one of the important points in the development of modern aircraft engines.
In 2015, Liu Legend is published in a paper 'modular simulation modeling of a strong transient air system' in the journal of the aeronautical dynamics, a simulation method of the strong transient process of an air system is provided, the air system is decomposed into four basic elements, namely a cavity, a node, a pipeline and a throttle, a nonlinear equation set of the air system is established by considering the cavity effect and the fluid inertia of the elements, a residual point method is adopted for solving, and an air system simulation program is developed based on the method. In 2017, in a doctor thesis of "numerical simulation and experimental research on transient process of air system of aircraft engine", jupeng flying at northwest industrial university, a pipeline and a disc cavity are regarded as transient response elements, a transient network algorithm of the air system is provided, cross-sectional flow relational expressions of various elements are obtained, further, a transient network node pressure residual equation is established, and flow distribution, pressure and temperature distribution of the air system at different moments are finally obtained through iterative solution and calculation. In 2019, the masha states that the delay time of the flow field at the outlet of the disc cavity is related to the working conditions of the inlet boundary and the geometric characteristics of the disc cavity in a text of a transient response characteristic research of a static disc cavity under a typical air inlet function published by a propulsion technology.
However, in the above research, transient heat exchange characteristics of fluid in the element are not considered, errors possibly caused by an internal volume effect of the labyrinth element are ignored, and transient response of fluid parameters in the multi-stage sealed disc cavity air system along with time cannot be accurately described. In the actual operation of the engine, the flow rate and the temperature of cold air in the high-temperature turbine disk cavity deviate from the design requirements, and serious thermal load can be caused to influence the normal operation of the engine. Therefore, the establishment of the one-dimensional model of the transient response of the multistage sealing disc cavity has important significance for designing and testing the air system and reducing the research and development cost.
Disclosure of Invention
The technical problem to be solved by the invention is as follows: the one-dimensional modeling method for the transient response of the multistage sealed disc cavity can accurately describe the volume effect of the disc cavity and the labyrinth element, further calculate the transient response of fluid parameters in the multistage sealed disc cavity air system along with time, and has important significance for the design, test and research and development cost reduction of the air system of the aero-engine.
The invention adopts the following technical scheme for solving the technical problems:
the method comprises the steps of taking a rotating and static disc cavity in a multi-stage sealing disc cavity structure as a disc cavity element, taking a sealing labyrinth as a labyrinth element, and providing a labyrinth splitting model for splitting the labyrinth element, wherein the labyrinth splitting model splits the labyrinth element into a pressure loss element without considering transient effect and a tooth cavity element with volume effect needing to be considered, and defines the pressure loss element as a region between a labyrinth tooth top and a bush, the width of the region is the tooth thickness, and the tooth cavity element is a cavity region between two adjacent teeth;
and establishing a one-dimensional transient mathematical model for the disc cavity element and the tooth cavity element, inputting the geometric parameters of the element and the transient boundary working condition into the model, and solving the one-dimensional transient network of the disc cavity air system to obtain the response change of the fluid parameters in the disc cavity along with time.
As a preferable scheme of the present invention, the one-dimensional transient mathematical models established for the disc cavity element and the tooth cavity element are the same, and the one-dimensional transient mathematical model includes an average pressure change rate in the cavity and an average temperature change rate in the cavity;
the calculation formula of the intracavity average pressure change rate is as follows:
Figure BDA0002864391990000021
in the formula (I), the compound is shown in the specification,
Figure BDA0002864391990000022
and
Figure BDA0002864391990000023
average static pressure and average static temperature, V, respectively, in the chambercvIs the volume of the chamber and is,
Figure BDA0002864391990000024
and
Figure BDA0002864391990000025
inlet and outlet flows of the chamber, t is time, and R is a gas constant;
the calculation formula of the average temperature change rate in the cavity is as follows:
Figure BDA0002864391990000031
in the formula, Tt,inAnd Tt,outTotal temperature of the fluid at the inlet and outlet of the chamber, Cp,inAnd Cp,outConstant pressure specific heat capacity, C, of the fluid at the inlet and outlet of the chamber, respectivelyvIs constant specific heat capacity, QnetFor convective heat transfer Q of fluid and wheel discnet,HTHeat Q of wind resistance temperature risenet,discThe sum of (a);
wherein, the heat exchange quantity Q of the convection of the fluid and the wheel discnet,HTThe calculation formula of (2) is as follows:
Qnet,HT＝havAw(Tw-Tref)
in the formula, AwTo heat exchange surface area, TwIs the average temperature, T, of the surface of the wheel discrefIs the average temperature of the fluid, havIs the convective heat transfer coefficient of the surface of the wheel disc; h isavThe calculation formula of (a) is as follows:
Figure BDA0002864391990000032
wherein y is the structural coefficient, ReΩReynolds number of rotation, L geometric characteristic length, λfIs the thermal conductivity of the stationary fluid, CwIs a dimensionless flow coefficient defined as
Figure BDA0002864391990000033
Where μ is the aerodynamic viscosity, routIs the outer edge radius of the rotating disc cavity;
wind resistance temperature rise heat Qnet,discThe calculation formula of (2) is as follows:
Qnet,disc＝Md·ωd
in the formula, ωdRotational angular velocity of the wheel disc, MdIs a wheel moment, MdThe calculation formula of (a) is as follows:
Figure BDA0002864391990000034
where K is a moment coefficient factor, ρ is the cold gas density, r is the local radius, and Cm,diskFor the disk moment coefficient, ω (r) represents the angular velocity of the cold air relative to the disk at the local radius, and sgn (·) is a sign function.
As a preferred aspect of the present invention, the calculation formula of the inlet and outlet flow rates of the chamber is as follows:
Figure BDA0002864391990000035
Figure BDA0002864391990000041
wherein, CdIs the flow coefficient of the chamber outlet, PinAnd poutTotal inlet pressure and static outlet pressure, p, of the chamberoAnd prStatic pressure at the center and outer edge radius of the chamber, AinAnd AoutThe flow areas of the inlet and the outlet of the chamber are respectively, and k is an isentropic index.
In the multi-stage sealing disc cavity structure, cooling air in an engine flows into the static disc cavity from the upstream sealing labyrinth to cool the turbine disc, and then flows out of the static disc cavity through the downstream sealing labyrinth.
In a preferred embodiment of the present invention, the mass flow rate in the pressure loss element is set to be lower than the mass flow rate in the case of the pressure loss element
Figure BDA0002864391990000044
To total pressure ratio PRtThe relationship between them is:
Figure BDA0002864391990000042
wherein A is the area of the region of the pressure loss element, CDIs the flow coefficient of the grate, PinIs the total pressure at the inlet of the chamber, Tt,inThe total temperature of fluid at the inlet of the chamber is shown, R is a gas constant, n is the number of teeth, gamma is a ventilation effect correction coefficient, and the calculation formula of gamma is as follows:
Figure BDA0002864391990000043
in the formula, B is the distance between the grid teeth, and c is the tooth top clearance.
Compared with the prior art, the invention adopting the technical scheme has the following technical effects:
1. the multistage sealing disc cavity transient response one-dimensional modeling method provided by the invention considers the influence of the volume effect of the labyrinth, establishes a one-dimensional transient mathematical model and a labyrinth splitting model of the cavity element, has small error between a one-dimensional transient calculation result and a numerical simulation result, and has good calculation precision and reliability.
2. The method can accurately simulate the volume effect of the grate and the parameter response in the disc cavity, the studied coupling effect of the grate and the disc cavity is an important problem to be considered in a transient air system, and the method has important significance for designing and testing the air system and reducing the research and development cost.
Drawings
FIG. 1 is a schematic flow path of a multi-stage packing disk chamber of the present invention.
Fig. 2 is a schematic view of a grate splitting model.
FIG. 3 is a simplified schematic of the disk chamber air system flow path.
Fig. 4 is a flow chart of a transient fluid network algorithm.
Figure 5 is a schematic view of a sealing labyrinth geometry model.
FIG. 6 is a schematic diagram of inlet pressure changes during transient conditions.
FIG. 7 is a graph of the response of the disc chamber flow parameter for a step inlet pressure condition, where (a) is the pressure parameter and (b) is the temperature parameter.
FIG. 8 is a graph of response time versus step amplitude for a disc chamber fluid parameter, where (a) is a pressure parameter and (b) is a temperature parameter.
FIG. 9 is a graph of the response of the disk chamber temperature during inlet pressure step/ramp conditions.
FIG. 10 is a graph of response time of disk chamber temperature as a function of disturbance amplitude for inlet pressure ramp conditions.
FIG. 11 is a temperature overshoot plot for an inlet pressure step condition.
FIG. 12 is a temperature overshoot plot for inlet pressure ramp conditions.
Detailed Description
Reference will now be made in detail to embodiments of the present invention, examples of which are illustrated in the accompanying drawings. The embodiments described below with reference to the accompanying drawings are illustrative only for the purpose of explaining the present invention, and are not to be construed as limiting the present invention.
The invention provides a one-dimensional modeling method for transient response of a multi-stage sealed disc cavity, which aims at performing transient calculation analysis on an air system by taking the multi-stage sealed disc cavity as an example.
Firstly, according to the structure of the sealed disc cavity shown in FIG. 1, relevant geometric characteristic parameters and flow path structures are determined. The sealing disc cavity can be divided into a rotating and static disc cavity and a sealing labyrinth, wherein the sealing labyrinth can be divided into a pressure loss element and a tooth cavity element according to the internal structure. And establishing a conservation equation set according to the one-dimensional transient mathematical model of each element, performing time dispersion on the conservation equation, and solving the equation by using a transient fluid network method.
The relationship between the inlet and outlet flow of the rotor and stator disc cavity and the pressure is as follows:
Figure BDA0002864391990000061
Figure BDA0002864391990000062
in the formula
Figure BDA0002864391990000063
And
Figure BDA0002864391990000064
inlet and outlet flow of the chamber, CdIs the flow coefficient, PinAnd poutTotal inlet pressure and static outlet pressure, p, of the chamberoAnd prStatic pressure, T, at the center and outer edge radius of the chamber, respectivelyt,inIs the total temperature of the inlet, and the temperature of the inlet,
Figure BDA0002864391990000065
mean resting temperature in the cavity, AinAnd AoutRespectively the flow areas of the inlet and the outlet of the chamber, k is equalAn entropy index.
For a chamber element with larger volume, the disturbance of the boundary inlet pressure cannot be instantaneously transmitted to the outlet of the chamber, the flow of the inlet and the outlet of the chamber is discontinuous due to the volume effect of the chamber, and gas is retained in the chamber, so that the transient response change of the gas flow density, the pressure and the temperature in the chamber is realized.
For a cavity with unchanged volume, neglecting spatial uneven distribution of parameter variables, only considering mass average parameters in the cavity, and deriving from a mass conservation formula and an ideal gas state equation to obtain the change rate of the average pressure in the cavity:
Figure BDA0002864391990000066
in the formula
Figure BDA0002864391990000067
And
Figure BDA0002864391990000068
respectively representing the average static pressure and static temperature, V, in the chambercvRepresenting the chamber volume, R is the gas constant.
The average temperature change rate in the cavity is derived from an energy conservation equation:
Figure BDA0002864391990000069
in the formula Tt,inAnd Tt,outIs the total temperature of the fluid at the inlet and outlet of the chamber, Cp,inAnd Cp,outIs the constant pressure specific heat capacity of the fluid at the inlet and outlet of the cavity, CvIs constant specific heat capacity, QnetFor convective heat transfer Q of fluid and wheel discnet,HTAnd heat Q brought by wind resistance temperature risenet,discThe sum of (a) and (b). Wherein Qnet,HTThe calculation formula is as follows:
Qnet,HT＝havAw(Tw-Tref) (5)
in the formula AwTo heat exchange surface area, TwIs the average temperature, T, of the surface of the wheel discrefIs the average temperature of the fluid, havExpressing the convective heat transfer coefficient of the disk surface, h for an axially through-flowing rotating disk cavityavThe specific calculation formula of (2) is as follows:
Figure BDA0002864391990000071
where y is the structural coefficient, related only to the geometric dimensions of the disk cavity, ReΩReynolds number of rotation, L geometric characteristic length, λfIs the thermal conductivity of the stationary fluid. CwIs a dimensionless flow coefficient defined as
Figure BDA0002864391990000072
Wherein μ is the aerodynamic viscosity, routIs the radius of the outer edge of the cavity of the rotating disc.
In transient calculation, the flow coefficient CwWill change with the change of the flow in the cavity, thereby leading to the heat exchange coefficient havChange of fluid mean temperature TrefWill also change accordingly, so the convection heat exchange quantity Qnet,HTChanges in transient calculations will vary with time.
Wind resistance temperature rise heat Qnet,discThe calculation formula of (2) is as follows:
Qnet,disc＝Md·ωd (7)
in the formula of omegadRotational angular velocity of the wheel disc, MdThe wheel moment is calculated by the following formula:
Figure BDA0002864391990000073
where K represents a moment coefficient factor, K is constant for a given physical system, ρ represents the cold gas density, and r is the local radius. Cm,diskIs the disk moment coefficient and is a function of the Reynolds number of rotation. Omega (r) represents the angular velocity of cold air at the local radius relative to the disk, and the magnitudeRelated to the disc chamber inlet tangential velocity and local radius. In transient calculations, changes in the disc chamber inlet flow will result in changes in the inlet velocity, affecting the value of ω (r), the disc moment M, in the equationdWill change accordingly, so the wind resistance temperature rise heat quantity Qnet,discAnd is also a transient variation.
The modeling method considers the volume effect in the tooth cavity of the sealed labyrinth and provides a labyrinth splitting model. The split model simplifies the tooth tip gap into a pressure loss element and a tooth cavity element with negligible transient effect, and the split sealing labyrinth model is shown in fig. 2.
For pressure loss elements, mass flow
Figure BDA0002864391990000075
To total pressure ratio PRt(ratio of downstream total pressure to upstream total pressure) is:
Figure BDA0002864391990000074
in the formula, A is the area of an annular area between the tip of the grate and the lining, and the width of the annular area is the tooth thickness; cDIs the flow coefficient of the grate, the size of which depends on the clearance thickness ratio (the ratio of the tooth top clearance C to the tooth thickness w), when the clearance thickness ratio is 1.3 to 2.3, CDMay be taken to be 0.71; r is a gas constant; Γ is the air permeability correction coefficient, which can be determined for a straight-through grate by:
Figure BDA0002864391990000081
in the formula, n is the number of the grid teeth; b is the distance between the grid teeth; and c is the tooth top clearance.
Regarding the tooth cavity element as a rotary chamber element with a volume effect, when the boundary inlet pressure generates disturbance, the tooth cavity element in the grate has a gas retention phenomenon under the action of the volume effect, so that the inlet and outlet flow of each tooth cavity element is unequal, and the density, the pressure and the temperature of the fluid in each tooth cavity generate complex transient response.
When solving the air system, the complex flow path is generally simplified into a network system composed of nodes and elements, the distribution of parameters along the path of the air system is obtained by solving a continuity equation and a momentum and energy conservation equation system of the network system, and fig. 3 shows a simplified model of the flow path of the disc cavity air system.
Because the flow rates upstream and downstream of the chamber are not equal due to the influence of the volume effect, the chamber elements need to be divided separately, the combination of the elements upstream of the chamber is regarded as one flow path, and the combination of the elements downstream of the chamber is regarded as the other flow path, so that a conservation equation system is established.
When a conservation equation is established at a response element, the transient mathematical models of the disc cavity and the grate are subjected to time term dispersion, corresponding boundary working conditions are read in each time step, and a Newton-Raphson method is adopted to iteratively solve the conservation equation set subjected to time dispersion to obtain parameters such as node pressure, flow, temperature and the like, so that the solution of the transient air system fluid network is completed.
The transient calculation adopts a calculation method of solving time step by time step, and the specific flow is as follows: giving a system initial field at an initial moment, assigning the air system network parameters at the t-delta t moment as the network initial field at the t moment, reading in boundary node parameters at the t moment, expanding a conservation equation set at the t moment to solve until the node pressure P (t) and the flow m (t) at the t moment are converged to obtain the air system network parameters at the t moment, using the air system network parameters as the network initial field at the t + delta t moment, and circularly calculating until a convergence coefficient lambda is smaller than a set value in a transient process, wherein the specific calculation flow is shown in figure 4.
Wherein the convergence factor λ is defined as:
Figure BDA0002864391990000082
and c (t), c (t-delta t) and c (t-delta t) are flow field parameter values at the time t and the time t-delta t respectively, delta t is a time step, when lambda is smaller than a set value, the system parameter is considered to be stable, and the response process is finished.
In order to verify the effect of the method, the one-dimensional modeling method is compared with the traditional one-dimensional calculation method under the transient working condition aiming at the flow path structure of the multi-stage sealing disc cavity of a certain engine.
The specific flow path structure is shown in fig. 1, cooling air flows into the static disc cavity from a downstream sealing part to cool the turbine disc, and then flows out of the static disc cavity through an upstream sealing labyrinth. The main geometric parameters of the model disc cavity and the grate element of the multi-stage sealing disc cavity are shown in the table 1, wherein the geometric characteristic dimension parameters of the grate 1 and the grate 2 are consistent. The structure of the specific grid is shown in figure 5.
TABLE 1 model geometry parameters
Parameter(s) Value of
Axial width/mm of disc cavity 50
Inlet radius of rotation/mm 40
Radius of rotation of the outlet/mm 100
Tip clearance c/mm 0.5
Tooth thickness w/mm 0.3
Pitch B/mm 6
Height H/mm of tooth 5.5
Table 2 shows the transient boundary conditions for the inlet and outlet of the multi-stage sealed disk cavity. The transient working conditions are divided into two typical working conditions of inlet pressure step and inlet pressure slope, which respectively correspond to extreme working conditions (such as main shaft fracture, air parking and the like) and transition working conditions (such as starting, accelerating, parking, rapid maneuvering processes and the like) of an actual engine. And the traditional one-dimensional transient calculation example is named as a cavity example, and the calculation example considering the influence of the volume effect of the grate teeth in the invention is named as a seal-cavity example.
TABLE 2 boundary conditions settings
Figure BDA0002864391990000091
Figure BDA0002864391990000101
Wherein
Figure BDA0002864391990000102
Denotes the initial inlet pressure, PoutIndicating the outlet pressure, Tt,inIndicating the initial cold air inlet temperature, omegadWhich represents the rotational speed of the rotor,
Figure BDA0002864391990000103
representing the ratio of the transient inlet pressure to the initial pressure, trIs the ramp time, TwIs the solid wall mean temperature. Under the step working condition, the inlet pressure is suddenly increased to 1.1 to 1.3 times of the initial pressure; under the working condition of a slope, the inlet pressure is at the time t of the sloperWithin 0.15s over timeLinearly increasing to 1.1 to 1.3 times. Fig. 6 shows schematic changes of the inlet pressure under the slope condition and the step condition when the disturbance amplitude is 1.2, in which the ordinate is the ratio of the inlet pressure to the initial value in the transient response process and the abscissa is the time value at the moment when the transient condition is applied as 0.
Transient parameter changes under the same structural parameters and working conditions as those in the final-cavity example of the method are utilized to compare with the results of the cavity example of the traditional one-dimensional transient algorithm.
When the aircraft engine is accelerated or braked in an emergency, the fluctuation caused by the aircraft engine to the air inlet parameter of the air system can be generally reduced to a step function, wherein the dimensionless step amplitude is an important parameter of the step function, and the size of the dimensionless step amplitude reflects the disturbance intensity of the inlet pressure. In fig. 7, (a) and (b) show the average pressure in the cavity of the stationary disk in equations (3) and (4) when the step amplitude is 1.1, 1.2, and 1.3 respectively under the condition of step change of the inlet pressure
Figure BDA0002864391990000104
And average temperature
Figure BDA0002864391990000105
Response curve over time.
In fig. 7, (a) and (b) have abscissa axes representing time values at the start time of the applied pressure step condition, and ordinate axes represent average pressure and temperature values in the chamber, respectively. Under different step amplitudes, the change trend of the average pressure of the chamber in the graph along with time is gradually increased firstly and then gradually eased to a stable value, and the average temperature in the chamber is obviously increased in the first 0.05s or so and then gradually decreased. The response speed of the cavity temperature is obviously lower than the cavity pressure, the pressure and the temperature in the cavity are stable within 0.08s and 0.5s respectively, and the cavity pressure and the cavity temperature response of the disk obtained by the seal-cavity example are obviously delayed from the calculation results of the cavity example.
In order to quantitatively analyze the response speed of the cavity pressure and the cavity temperature, the shortest time for the response residual error of the flow parameter to reach and keep within 5 percent in the transient response process is defined as the response time tsAnd will tsSize of (2)As an evaluation index of the response speed of the transient process.
Wherein the response residual etIs defined as:
Figure BDA0002864391990000111
wherein c istAs the value of the fluid parameter at time t, c0As initial steady state parameter value, c*In response to reaching the stabilized parameter value. The changes of the chamber pressure and the temperature response time with the step amplitude are shown in (a) and (b) of fig. 8. The abscissa of fig. 8 (a) and (b) represents the magnitude of the inlet pressure step and the ordinate represents the response time representing the average pressure and temperature in the disc chamber, respectively. It can be seen from the graph that as the step amplitude increases, the response time of the chamber pressure gradually increases, while the response time of the average temperature of the chamber is not sensitive to changes in the step amplitude.
And after considering the volume effect of the grate, the response time of the cavity pressure and the cavity temperature of the seal-cavity example is obviously higher than that of the cavity example. When the step amplitude is 1.3, compared with the result of the cavity example, the cavity pressure response time of the seal-cavity example is relatively improved by 24.4%. The response time of the cavity temperature is relatively improved by 9.3 percent.
When the aircraft engine is in the transition working conditions of takeoff, acceleration or deceleration and the like, the fluctuation of the air inlet parameters of the air system can be simplified into a slope function. Under the working condition of inlet pressure slope, the response time of the disk cavity pressure is far shorter than the slope time trThe transient characteristic of the cavity pressure in the example is negligible as 0.15s, and only the transient characteristic of the cavity temperature is specifically analyzed subsequently. FIG. 9 shows the response of the temperature in the chamber over time for inlet pressure step and ramp conditions at a disturbance amplitude of 1.2. As can be seen from FIG. 9, compared with the pressure step condition, the difference between the cavity temperature response curve of the seal-cavity example under the pressure slope condition and the cavity temperature response curve of the cavity example under the pressure slope condition is larger, which indicates that the response of the cavity temperature under the pressure slope condition is more sensitive to the labyrinth volume effect.
The response time of the disc chamber temperature with the disturbance amplitude under the ramp condition is shown in fig. 10, and it can be seen that the response time of the chamber temperature gradually increases with the increase of the disturbance amplitude. When the disturbance amplitude is 1.3, the cavity temperature response time of the seal-cavity calculation example is 0.385s, which is 10.6% higher than that of the cavity calculation example.
When the inlet pressure is increased, the flow of cold air entering the disc cavity is increased, the temperature of the air in the cavity is in a gradually-decreasing trend, and in the result, the response of the temperature of the disc cavity under different boundary working conditions is in a obvious rising phenomenon in the early stage of transient. This increase in chamber temperature with increased cold gas flow is defined herein as a temperature overshoot phenomenon.
The invention defines the parameter temperature overshoot value sigmaTFor quantitative analysis of the overshoot, sigma, of the cavity temperatureTIs defined as follows:
σT＝Tmax-T* (13)
in the formula TmaxIndicates the maximum value, T, reached by the chamber temperature during the response*The steady state average temperature value in the cavity before the transient working condition is applied. The changes of the cavity temperature overshoot values with disturbance amplitude under the inlet pressure step and the slope working condition are shown in the figures 11 and 12. As can be seen from FIGS. 11 and 12, as the amplitude of the disturbance increases, the cavity temperature overshoot value also increases, and σ under the step condition increasesTIs obviously higher than sigma under the working condition of slopeT。
Temperature overshoot value σ in the seal-timing calculation example in fig. 11 and 12TThe temperature overshoot value is obviously higher than the result of the cavity example, because a certain temperature overshoot phenomenon is generated in the labyrinth tooth cavity in the transient response process, and due to the interaction of elements in the flow path, the temperature overshoot of the outlet of the upstream labyrinth 1 can cause the inlet temperature of the rotating and static disc cavity to rise, and the temperature in the cavity rises, so that the temperature overshoot value of the seal-cavity example is higher than the result of the cavity example. In fig. 12, when the disturbance amplitude is 1.3, the temperature overshoot of the cavity example is 1.02K, and the temperature overshoot of the seal-cavity example is 3.2K, which is relatively increased by 213.7%.
Compared with the traditional one-dimensional transient calculation, the multi-stage sealing disc cavity one-dimensional transient mathematical model considers the coupling effect of the sealing labyrinth and the disc cavity, can accurately simulate the labyrinth volume effect and the parameter response in the disc cavity, and has important engineering reference value for the design of an air system.
The above embodiments are only for illustrating the technical idea of the present invention, and the protection scope of the present invention is not limited thereby, and any modifications made on the basis of the technical scheme according to the technical idea of the present invention fall within the protection scope of the present invention.

Claims (5)

1. The one-dimensional modeling method for the transient response of the multi-stage sealing disc cavity is characterized in that a rotating and static disc cavity in a multi-stage sealing disc cavity structure is taken as a disc cavity element, a sealing labyrinth is taken as a labyrinth element, a labyrinth splitting model is provided for splitting the labyrinth element, the labyrinth splitting model splits the labyrinth element into a pressure loss element without considering the transient effect and a tooth cavity element with the volume effect needing to be considered, the pressure loss element is defined as an area between a labyrinth tooth top and a lining, the width of the area is the tooth thickness, and the tooth cavity element is a cavity area between two adjacent teeth;
and establishing a one-dimensional transient mathematical model for the disc cavity element and the tooth cavity element, and solving a one-dimensional transient network of the disc cavity air system to obtain the response variation of fluid parameters in the disc cavity along with time after inputting element geometric parameters and transient boundary working conditions.
2. The one-dimensional modeling method for transient response of multi-stage sealed disc cavity according to claim 1, characterized in that the one-dimensional transient mathematical models established for the disc cavity element and the tooth cavity element are the same, and the one-dimensional transient mathematical model comprises an average pressure change rate in the cavity and an average temperature change rate in the cavity;
the calculation formula of the intracavity average pressure change rate is as follows:
Figure FDA0002864391980000011
in the formula (I), the compound is shown in the specification,
Figure FDA0002864391980000012
and
Figure FDA0002864391980000013
average static pressure and average static temperature, V, respectively, in the chambercvIs the volume of the chamber and is,
Figure FDA0002864391980000014
and
Figure FDA0002864391980000015
inlet and outlet flows of the chamber, t is time, and R is a gas constant;
the calculation formula of the average temperature change rate in the cavity is as follows:
Figure FDA0002864391980000016
in the formula, Tt,inAnd Tt,outTotal temperature of the fluid at the inlet and outlet of the chamber, Cp,inAnd Cp,outConstant pressure specific heat capacity, C, of the fluid at the inlet and outlet of the chamber, respectivelyvIs constant specific heat capacity, QnetFor convective heat transfer Q of fluid and wheel discnet,HTHeat Q of wind resistance temperature risenet,discThe sum of (a);
wherein, the heat exchange quantity Q of the convection of the fluid and the wheel discnet,HTThe calculation formula of (2) is as follows:
Qnet,HT＝havAw(Tw-Tref)
in the formula, AwTo heat exchange surface area, TwIs the average temperature, T, of the surface of the wheel discrefIs the average temperature of the fluid, havIs the convective heat transfer coefficient of the surface of the wheel disc; h isavThe calculation formula of (a) is as follows:
Figure FDA0002864391980000021
wherein y is the structural coefficient, ReΩReynolds number of rotation, L geometric characteristic length, λfIs the thermal conductivity of the stationary fluid, CwIs a dimensionless flow coefficient defined as
Figure FDA0002864391980000022
Where μ is the aerodynamic viscosity, routIs the outer edge radius of the rotating disc cavity;
wind resistance temperature rise heat Qnet,discThe calculation formula of (2) is as follows:
Qnet,disc＝Md·ωd
in the formula, ωdRotational angular velocity of the wheel disc, MdIs a wheel moment, MdThe calculation formula of (a) is as follows:
Figure FDA0002864391980000023
where K is a moment coefficient factor, ρ is the cold gas density, r is the local radius, and Cm,diskFor the disk moment coefficient, ω (r) represents the angular velocity of the cold air relative to the disk at the local radius, and sgn (·) is a sign function.
3. The one-dimensional modeling method for transient response of the multi-stage sealed disc cavity according to claim 2, characterized in that the calculation formula of the inlet and outlet flow of the chamber is as follows:
Figure FDA0002864391980000024
Figure FDA0002864391980000025
wherein, CdIs the flow coefficient of the chamber outlet, PinAnd poutTotal pressure at the inlet of the chamberAnd static outlet pressure, poAnd prStatic pressure at the center and outer edge radius of the chamber, AinAnd AoutThe flow areas of the inlet and the outlet of the chamber are respectively, and k is an isentropic index.
4. The one-dimensional modeling method for transient response of the multistage sealing disk cavity according to claim 1, characterized in that in the multistage sealing disk cavity structure, cooling air in an engine flows into the rotating-static disk cavity from an upstream sealing labyrinth to cool a turbine disk, and then flows out of the rotating-static disk cavity through a downstream sealing labyrinth.
5. The method of one-dimensional modeling of transient response of a multi-stage sealed disk cavity of claim 1, wherein mass flow in said pressure loss element
Figure FDA0002864391980000031
To total pressure ratio PRtThe relationship between them is:
Figure FDA0002864391980000032
wherein A is the area of the region of the pressure loss element, CDIs the flow coefficient of the grate, PinIs the total pressure at the inlet of the chamber, Tt,inThe total temperature of fluid at the inlet of the chamber is shown, R is a gas constant, n is the number of teeth, gamma is a ventilation effect correction coefficient, and the calculation formula of gamma is as follows:
Figure FDA0002864391980000033
in the formula, B is the distance between the grid teeth, and c is the tooth top clearance.
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