CN115859482A - Aircraft flow field steady-state elementary stream rapid calculation method - Google Patents
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Abstract
The invention discloses a method for quickly calculating a steady-state elementary stream of an aircraft flow field, which relates to the field of computational fluid dynamics and comprises the following steps: step 1: obtaining a control equation of an aircraft flow field; step 2: decomposing the control equation to obtain a nonlinear term and a linear term in the control equation; and step 3: solving the nonlinear term to obtain a first calculation result; and 4, step 4: and obtaining a control coefficient and a filtering time width for calculating the linear term, and solving the control equation based on the control coefficient, the filtering time width and the first calculation result to obtain a steady-state elementary flow calculation result of the aircraft flow field.
Description
Technical Field
The invention relates to the field of computational fluid dynamics, in particular to a method for rapidly calculating a steady-state elementary stream of an aircraft flow field.
Background
The transition process of the aircraft bypass flow from laminar flow to turbulent flow is a complex physical phenomenon of multi-factor coupling, which can cause the friction resistance and heat flow of the aircraft to be obviously increased, and the century difficult problem which is not solved is still existed so far. Researches show that the boundary layer transition process is often triggered by unstable disturbance (or called mode) in the boundary layer, the modes have various types, such as a first mode, a second mode, a cross flow mode and the like, a shape function and characteristic parameters of the modes can be obtained by solving a stability equation, and then a dominant mode for triggering the boundary layer transition is analyzed.
When solving the boundary layer stability equation, a steady-state elementary stream of the flow field is obtained first. For simple geometric configurations such as flat panels, the Booth (Blasius) solution can be directly computed to obtain an approximate elementary stream. However, for complex flows such as high-speed cylinders and steps, a steady-state basic flow can be obtained only by long-time iterative solution of a Navier-Stokes equation (an N-S equation), but the flows belong to global unstable flows, and the iterative solution of the N-S equation requires a very long time to obtain the steady-state flow, so that the method is basically not operable.
Disclosure of Invention
The invention aims to quickly calculate and obtain the steady-state elementary stream of an aircraft flow field.
In order to achieve the above object, the present invention provides a method for rapidly calculating a steady-state elementary stream of an aircraft flow field, the method comprising:
step 1: obtaining a control equation of an aircraft flow field;
and 2, step: decomposing the control equation to obtain a nonlinear term and a linear term in the control equation;
and step 3: solving the nonlinear term to obtain a first calculation result;
and 4, step 4: and obtaining a control coefficient and a filtering time width for calculating the linear term, and solving the control equation based on the control coefficient, the filtering time width and the first calculation result to obtain an aircraft flow field steady-state elementary stream calculation result.
The method can be used for processing disturbance of specific frequency and quickly attenuating the components, so that an expected steady-state basic flow field can be quickly obtained, the process of rebuilding a model and an algorithm can be avoided based on the existing large vortex simulation or direct numerical simulation program, the workload of program development is saved, and the steady-state basic flow field of the aircraft can be more conveniently obtained.
Preferably, the step 4 specifically includes:
obtaining a control coefficient and a filtering time width for calculating the linear term;
calculating a nonlinear term in the control equation by adopting large eddy simulation or direct numerical simulation to obtain a first calculation result;
solving a linear term in the control equation by adopting a Runge-Kutta time iteration method based on the control coefficient and the filtering time width to obtain a second calculation result;
obtaining an aircraft flow field steady state elementary stream calculation result based on the first calculation result and the second calculation result.
The large vortex simulation or the direct numerical simulation is an existing mature means and can be directly utilized, the nonlinear terms in the control equations can be directly calculated by the large vortex simulation or the direct numerical simulation to obtain a first calculation result, and the linear terms in the rest control equations are solved by a Runge-Kutta time iteration method.
Preferably, the governing equation is decomposed using the following formula:
wherein,
for a non-linear term in the governing equation, <' >>
For a linear term in the governing equation, <' > H>
For a certain variable of the aircraft flow field>
Represents->
In the time derivative of (D), in>
For a matrix representing the nonlinear term of the equation, I is the unit operator, and>
for the duration of the filtering time +>
For controlling the coefficient>
Is->
Low-pass filtering of>
Is->
Low pass filtering of (1).
Preferably, when the mode of dominant transition in the laminar boundary layer of the aircraft flow field is one, the mode of obtaining the control coefficient and the filtering time width is as follows:
estimating the frequency of dominant unstable modes
And a growth rate->
Wherein c represents a dominant unstable mode, r is a real part, and i is an imaginary part;
based on estimated frequency
And a growth rate->
Obtaining the value ranges of the control coefficient and the filtering time width;
and obtaining the values of the control coefficient and the filtering time width from the value range.
To reject the most unstable mode using low-pass filtering, the frequency (reciprocal of time width) is controlled
Must be less than the frequency of the unstable mode->
Attenuation ratio (control coefficient)>
Must be greater than the growth rate of the unstable mode>
. Therefore, the value ranges of the control coefficient and the filtering time width are respectively as follows:
，
For the duration of the filtering>
Is a control coefficient.
Preferably, when the mode of dominant transition in the laminar boundary layer of the aircraft flow field is one, the mode of obtaining the control coefficient and the filtering time width is as follows:
obtaining a frequency of a dominant unstable mode by performing stability analysis on a Brahous' solution
And a growth rate->
Wherein c is a dominant unstable mode, r is a real part, and i is an imaginary part;
based on frequency
And a growth rate->
And calculating the values of the control coefficient and the filtering time width.
Preferably, based on frequency
And a growth rate->
The numerical values of the control coefficient and the filtering time width are calculated by the following formulas:
wherein,
for the duration of the filtering>
For controlling the coefficient>
，
For time information which dominates the unstable mode, is asserted>
Based on the frequency of the unstable mode>
Is the growth rate that dominates the unstable mode.
Preferably, when the modes of dominant transition in the aircraft flow field laminar boundary layer are multiple, the modes of obtaining the control coefficient and the filtering time width are as follows:
and respectively estimating and obtaining a control coefficient and a filtering time width corresponding to each mode aiming at multiple modes of dominant transition in a laminar boundary layer of the aircraft flow field, and obtaining multiple groups of control coefficients and filtering time widths.
The manner of estimating and obtaining the control coefficient and the filtering time width corresponding to each mode can adopt one of the manners described above: estimating the frequency of dominant unstable modes
And a growth rate>
Based on the estimated frequency->
And a growth rate->
Obtaining the value ranges of the control coefficient and the filtering time width; obtaining values of the control coefficient and the filtering time width from the value range; another approach may also be used: obtaining a frequency of dominant unstable modes by performing stability analysis on a Brahous' solutionRatio->
And a growth rate->
(ii) a Based on frequency->
And a growth rate->
And calculating the values of the control coefficient and the filtering time width.
Preferably, the control equation is solved based on the multiple groups of control coefficients and the filtering time width until the residual error of the control equation is smaller than a set critical value, and a calculation result of the aircraft flow field steady-state elementary stream is obtained based on the final calculation result.
Preferably, the solving the control equation based on the plurality of sets of control coefficients and the filtering time width until a residual error of the control equation is smaller than a set critical value, and obtaining a calculation result of a steady-state elementary stream of the aircraft flow field based on a final calculation result specifically includes:
step a: obtaining a first array based on the plurality of groups of control coefficients and the filtering time width;
step b: randomly selecting a group of control coefficients and filtering time width from the first array, inputting the control coefficients and the filtering time width into the control equation for calculation to obtain an intermediate calculation result, and deleting the selected group of control coefficients and the filtering time width from the first array to update the first array;
step c: on the basis of the intermediate calculation result obtained in the step b, randomly selecting a group of control coefficients and filtering time width from the updated first array to input the control equation for calculation, updating the intermediate calculation result based on the current calculation result, and judging whether the residual error of the control equation at the moment is smaller than a set critical value; if the current calculation result is smaller than the set critical value, obtaining an aircraft flow field steady-state elementary stream calculation result based on the updated current calculation result; if the set of control coefficients and the filter time width are larger than or equal to the set critical value, deleting the selected set of control coefficients and the filter time width from the first array to update the first array, and returning to execute the step b.
One or more technical schemes provided by the invention at least have the following technical effects or advantages:
the method can quickly obtain the steady-state flow field of the aircraft, and provides a data basis for the stability and transition analysis of the aircraft flow field.
Drawings
The accompanying drawings, which are included to provide a further understanding of the embodiments of the invention and are incorporated in and constitute a part of this specification, illustrate embodiments of the invention and together with the description serve to explain the principles of the invention;
FIG. 1 is a schematic flow chart of a method for rapidly calculating a steady-state elementary stream of an aircraft flow field;
FIG. 2 is a flow chart of an aircraft flow field steady state elementary stream solution;
FIG. 3 is a schematic diagram of a geometry and computational domain;
FIG. 4 is a schematic diagram of method-residual versus propulsion time;
FIG. 5 is a graph showing the variation of the second residual error with the advancing time;
fig. 6 is a schematic diagram of method triple residual error as a function of propulsion time.
Detailed description of the preferred embodiments
In order that the above objects, features and advantages of the present invention can be more clearly understood, a more particular description of the invention will be rendered by reference to the appended drawings. It should be noted that the embodiments of the present invention and features of the embodiments may be combined with each other without conflicting with each other.
In the following description, numerous specific details are set forth in order to provide a thorough understanding of the present invention, however, the present invention may be practiced in other ways than those specifically described and thus the scope of the present invention is not limited by the specific embodiments disclosed below.
The first embodiment;
referring to fig. 1, fig. 1 is a schematic flow chart of a method for rapidly calculating a steady-state elementary stream of an aircraft flow field, and the method for rapidly calculating a steady-state elementary stream of an aircraft flow field according to the present invention includes:
step 1: obtaining a control equation of an aircraft flow field;
step 2: decomposing the control equation to obtain a nonlinear term and a linear term in the control equation;
and step 3: solving the nonlinear term to obtain a first calculation result;
and 4, step 4: and obtaining a control coefficient and a filtering time width for calculating the linear term, and solving the control equation based on the control coefficient, the filtering time width and the first calculation result to obtain an aircraft flow field steady-state elementary stream calculation result.
The method in the embodiment can quickly obtain the steady-state flow field of the aircraft, provides a data basis for the stability and transition analysis of the aircraft flow field, can calculate the steady-state basic flow of the flow field with the complex geometric configuration, is suitable for the aircraft flow fields with different speed ranges, can accelerate the flow field convergence process, greatly saves the calculation time, and can realize quick development based on the existing large vortex simulation or direct numerical simulation program.
In the practical application process, the applicant finds that the mode of the dominant transition in the laminar boundary layer is usually one or more fixed modes, and the modes have corresponding frequencies, so that a solving algorithm can be set to process the disturbance of a specific frequency and quickly attenuate the components, and an expected steady-state basic flow field is obtained. In addition, the method can realize rapid calculation based on the existing large vortex simulation or direct numerical simulation program, and the specific technical scheme is as follows:
1. decomposing a control equation to obtain nonlinear and linear terms;
consider a nonlinear N-S governing equation:
wherein
Is a variable of the flow field such as velocity, pressure, temperature, etc. The steady-state base stream is the steady-state solution (in +) to the control equation>
Expressed), i.e. a solution whose time derivative is zero, is asserted>
(operator-representation of derivative over time), ->
Represents->
Represents a non-temporal term of the governing equation.
The governing equation for the steady state solution can be expressed as:
wherein,
the expressed function represents the non-temporal term of the governing equation, if so>
Low-pass filtering->
To approximate>
Wherein G is a convolution kernel, and represents a convolution operation. For steady state de- ->
And/or is present in>
I.e. when->
When the temperature of the water is higher than the set temperature,
. Will subsequently use->
Represents->
。
Will be provided with
Adding the obtained product into an original control equation (1) as a penalty term to obtain a new control equation:
wherein,
is a control coefficient; when +>
Then, equation (3) is still true;
The time derivative of (d) can be expressed as:
wherein,
is the filtering time width; if so>
To approximate>
Then when
Both equations (3) and (4) will be true.
The combinations of formulae (3) and (4) give:
wherein,
is a matrix representing the nonlinear term of the equation>
Is->
Is low-pass filtered, and>
is->
The low-pass filtering of (a) is performed,
i is a unit operator, i.e. < >>
。
In order to fully utilize the existing large vortex simulation or direct numerical simulation solver, equation (5) can be further decomposed into:
the first term on the right side of the formula (6) is a nonlinear term, contains an original N-S equation, and can be solved by adopting the existing large vortex simulation or direct numerical simulation routine; the second term on the right is a linear term and can be solved by adopting a traditional Longge-Kutta time iteration method.
2. Determining a control coefficient
And a filter time width->
：
In equation (6), there are 2 parameters which are respectively control coefficients
And a filter time width->
The values of these two parameters must be given before solving, and three methods are given below to obtain the values of these two parameters:
the first method is to empirically estimate the values of these two parameters, control the coefficients
The filter time width->
Depending on the frequency of the unstable mode, the frequency ≥ of the dominant unstable mode can be estimated empirically for different flows, such as subsonic, supersonic and hypersonic>
And a growth rate->
Then take any
Is solved by substituting in equation (6), in the usual case, based on>
The smaller the steady state solution convergence rate is;
The smaller the steady state solution converges faster.
The second method is obtained by accurate calculation, firstly obtaining the growth rate and the frequency of the flow field dominant unstable mode, obtaining the growth rate and the frequency by performing stability analysis on the Brahous solution, and then obtaining a control coefficient by calculating the following formula
And a filter time width->
：/>
Wherein,
the method is suitable for boundary layer transition dominated by a single mode.
The third method mainly aims at the condition that multiple unstable modes exist, if multiple modes exist in the flow field, the control coefficient corresponding to each mode needs to be estimated respectively
And a filter time width->
The calculation is performed in steps and then a smaller group is selected>
And &>
Storing the result after the flow field tends to be stable, and then solving the equationIn the steady-state control equation, the multiple modes can be considered as a single mode, and then the control coefficient->
And a filter time width->
。
3. Solving an equation steady state control equation:
obtaining a control coefficient
And a filter time width>
Then, the global residual (the difference between the left-hand estimated value and the actual value of the equation obtained in the iteration) of the control equation is substituted into equation (6) for iterative calculation until the global residual (the difference between the left-hand estimated value and the actual value of the equation obtained in the iteration) of the control equation falls below a set critical value (the critical value is generally ≧ greater than or equal to @)>
) The calculation can be stopped, and the result output in the last step is the steady-state elementary stream of the flow field.
For the flow field with single mode dominance, adopting a method I or a method II, and obtaining a final result through one-time calculation;
for a multi-modal dominant flow field, a third method is adopted, and a group is selected firstly
And &>
Calculating in an equation (6) in a substituted mode, and storing the result of the last step after equation residual is stable; then input into another group>
And &>
And continuing to calculate on the basis of the result of the last step until the equation residual is lower than a set critical value, and finishing the calculation, wherein the result output by the last step is the steady-state elementary stream of the flow field.
Example two;
on the basis of the first embodiment, the second embodiment combines specific examples and data to describe the technical scheme in the invention in detail.
Referring to fig. 2, fig. 2 is a flow chart of solving a steady elementary stream of an aircraft flow field.
Decomposing a control equation corresponding to the aircraft to obtain nonlinear and linear terms of the control equation:
the control equation of the aircraft flow field is obtained by the principles of mass conservation, momentum conservation and energy conservation, the control equation of the aircraft flow field can be obtained in a manner of referring to John D-Anderson-computational fluid mechanics basis and application thereof-mechanical industry Press-2007, and the control equation can be expressed in a unified nonlinear form (namely, an N-S equation):
wherein
A variable of the aircraft flow field, such as velocity, pressure, temperature, etc.;
Represents->
Is the steady-state solution (in @) of the control equation>
Expressed), i.e. a solution whose time derivative is zero, is asserted>
(operator ·)Representing a derivative over time).
Will be provided with
Adding the control function as a penalty term into the original control equation (1) to obtain a new control equation:
wherein,
g is the convolution kernel of the low-pass filter, which represents the convolution operation.
For is to
By time differencing, we can get: />
Wherein,
is the filtering temporal width.
The combinations of formulae (3) and (4) give:
wherein,
i is a unit operator, i.e. < >>
。
Further decomposition can yield:
the first term on the right side is a nonlinear term, comprises an original N-S equation, and can be solved by adopting the existing large vortex simulation and direct numerical simulation programs, and the specific solving method can refer to the John D-Anderson-computational fluid mechanics basis and the application thereof-mechanical industry Press-2007; the second term on the right is a linear term, which can be solved by using a traditional Longge-Kutta time iteration method, and a specific solving method can refer to John D-Anderson-computational fluid mechanics basis and application thereof-mechanical industry Press-2007.
2. Determination of control coefficient in equation (6)
And a filter time width->
Solving the equation steady state control equation (6):
the example of a stepped flow is shown, and the selected example is a supersonic stepped flow, and the geometry is shown in fig. 3.
First, according to the characteristics of supersonic flow, the dominant unstable mode of flow before the step can be estimated in advance as the first mode, and the frequency is about
The increase rate is approximately->
According to formula (I)
Available>
If so, pick up>
Substituting the equation into the formula (6) to solve to obtain equation residual errorThe curve of the advancing time t is shown in fig. 4, fig. 4 is a graph showing the change of a residual error with the advancing time in the method, and the rapid decrease of the residual error can be seen.
The second method, because there is actually a shear mode in the step flow, has a frequency of about
With a growth rate of approximately +>
Then, a more accurate control coefficient is calculated and obtained through the following formula>
And a filter time width->
：
The equation residual error is substituted into the equation (6) to be solved, so that a change curve of the equation residual error along with the propulsion time can be obtained, as shown in fig. 5, fig. 5 is a schematic diagram of the change of the method residual error along with the propulsion time, and as more accurate control parameters and filtering time width are adopted, the decrease is faster compared with the method residual error.
In a third method, the steps of the first method are repeated first, when
When the iteration convergence speed is lower, the result is saved and the control coefficient is replaced when t =1300>
And when filteringInterval width->
Then, continuing to calculate to obtain a curve of the equation residual along with the propulsion time, as shown in fig. 6, fig. 6 is a schematic diagram of the variation of the method three residual along with the propulsion time, and it can be seen that the method three residual decreases faster than the method two residual.
While preferred embodiments of the present invention have been described, additional variations and modifications in those embodiments may occur to those skilled in the art once they learn of the basic inventive concepts. Therefore, it is intended that the appended claims be interpreted as including preferred embodiments and all such alterations and modifications as fall within the scope of the invention.
It will be apparent to those skilled in the art that various changes and modifications may be made in the present invention without departing from the spirit and scope of the invention. Thus, if such modifications and variations of the present invention fall within the scope of the claims of the present invention and their equivalents, the present invention is also intended to include such modifications and variations.
Claims (10)
1. A method for rapidly calculating a steady-state elementary stream of an aircraft flow field, the method comprising:
step 1: obtaining a control equation of an aircraft flow field;
step 2: decomposing the control equation to obtain a nonlinear term and a linear term in the control equation;
and step 3: solving the nonlinear term to obtain a first calculation result;
and 4, step 4: and obtaining a control coefficient and a filtering time width for calculating the linear term, and solving the control equation based on the control coefficient, the filtering time width and the first calculation result to obtain an aircraft flow field steady-state elementary stream calculation result.
2. The method for rapidly calculating the steady-state elementary stream of the aircraft flow field according to claim 1, wherein the step 4 specifically comprises:
obtaining a control coefficient and a filtering time width for calculating the linear term;
calculating a nonlinear term in the control equation by adopting large eddy simulation or direct numerical simulation to obtain a first calculation result;
solving a linear term in the control equation by adopting a Runge-Kutta time iteration method based on the control coefficient and the filtering time width to obtain a second calculation result;
and obtaining an aircraft flow field steady-state elementary stream calculation result based on the first calculation result and the second calculation result.
3. The method for rapidly calculating the steady-state elementary stream of the aircraft flow field according to claim 1, wherein the control equation is decomposed by adopting the following formula:
4. The method for rapidly calculating the steady-state elementary stream of the aircraft flow field according to claim 1, wherein when the mode of dominant transition in a laminar boundary layer of the aircraft flow field is one, the mode of obtaining the control coefficient and the filter time width is as follows:
estimating the frequency of dominant unstable modes
And a growth rate->
Wherein c is a dominant unstable mode, r is a real part, and i is an imaginary part;
based on estimated frequency
And a growth rate>
Obtaining the value ranges of the control coefficient and the filtering time width;
and obtaining the values of the control coefficient and the filtering time width from the value range.
5. The method for rapidly calculating the steady-state elementary stream of the aircraft flow field according to claim 4, wherein the value ranges of the control coefficient and the filter time width are respectively as follows:
，
in order to filter the temporal width of the filtering,
is a control coefficient.
6. The method for rapidly calculating the steady-state elementary stream of the aircraft flow field according to claim 1, wherein when the mode of dominant transition in a laminar boundary layer of the aircraft flow field is one, the mode of obtaining the control coefficient and the filter time width is as follows:
obtaining a frequency of a dominant unstable mode by performing stability analysis on a Brahous' solution
And a growth rate->
Wherein c is a dominant unstable mode, r is a real part, and i is an imaginary part;
based on frequency
And a growth rate->
And calculating the values of the control coefficient and the filtering time width.
7. The method for rapidly calculating the steady-state elementary stream of the aircraft flow field according to claim 6, wherein the method comprises the step of calculating the steady-state elementary stream of the aircraft flow field according to the steady-state elementary streamCharacterised by being based on frequency
And a growth rate->
The numerical values of the control coefficient and the filtering time width are calculated by the following formulas:
8. The method for rapidly calculating the steady-state elementary stream of the aircraft flow field according to claim 1, wherein when the dominant transition mode in the laminar boundary layer of the aircraft flow field is multiple, the modes for obtaining the control coefficient and the filtering time width are as follows:
and respectively estimating and obtaining a control coefficient and a filtering time width corresponding to each mode aiming at multiple modes of dominant transition in a laminar boundary layer of the aircraft flow field, and obtaining multiple groups of control coefficients and filtering time widths.
9. The method for rapidly calculating the steady-state elementary stream of the aircraft flow field according to claim 8, wherein the control equation is solved based on a plurality of groups of control coefficients and filtering time widths until the residual error of the control equation is smaller than a set critical value, and a calculation result of the steady-state elementary stream of the aircraft flow field is obtained based on the final calculation result.
10. The method according to claim 9, wherein the step of solving the control equation based on the plurality of sets of control coefficients and the filtering time width until a residual error of the control equation is smaller than a set critical value and obtaining a calculation result of the steady-state elementary stream of the aircraft flow field based on a final calculation result specifically comprises:
step a: obtaining a first array based on the plurality of groups of control coefficients and the filtering time width;
step b: randomly selecting a group of control coefficients and filtering time width from the first array, inputting the control coefficients and the filtering time width into the control equation for calculation to obtain an intermediate calculation result, and deleting the selected group of control coefficients and the filtering time width from the first array to update the first array;
step c: on the basis of the intermediate calculation result obtained in the step b, randomly selecting a group of control coefficients and filtering time width from the updated first array to input the control equation for calculation, updating the intermediate calculation result based on the current calculation result, and judging whether the residual error of the control equation at the moment is smaller than a set critical value; if the current calculation result is smaller than the set critical value, obtaining an aircraft flow field steady-state elementary stream calculation result based on the updated current calculation result; if the set of control coefficients and the filter time width are larger than or equal to the set critical value, deleting the selected set of control coefficients and the filter time width from the first array to update the first array, and returning to execute the step b.
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