Modeling of dielectric barrier discharge plasma actuators considering uncertainties
By modifying the dielectric barrier discharge plasma actuator model through static ion wind experiments and interval optimization theory, the problem of parameter uncertainty was solved, the prediction accuracy and robustness of the model were improved, and it is suitable for flow control and drag reduction and noise reduction.
Patent Information
- Authority / Receiving Office
- CN · China
- Patent Type
- Applications(China)
- Current Assignee / Owner
- JILIN UNIVERSITY
- Filing Date
- 2026-02-06
- Publication Date
- 2026-05-29
AI Technical Summary
Existing dielectric barrier discharge plasma actuator models suffer from parameter uncertainties when excitation conditions change, leading to a decrease in model prediction accuracy and versatility. There is a lack of systematic methods to handle model parameter uncertainties, which affects flow control and drag reduction/noise reduction effects.
The volume force distribution was obtained through static ion wind experiments, a parameterized plasma equivalent model was constructed, uncertain design variables were identified, sample point combinations were generated, a surrogate model was established, and a nested optimization strategy was used to solve the interval multi-objective optimization problem, thereby correcting the plasma model.
It significantly improves the prediction accuracy and robustness of the model under different operating conditions, enhances the reliability and engineering applicability of flow control, and is suitable for aerospace and vehicle engineering fields.
Smart Images
Figure CN122113729A_ABST
Abstract
Description
Technical Field
[0001] This invention relates to the fields of computational fluid dynamics, flow control, and aeroacoustics, and more specifically to a method for establishing a model of a dielectric barrier discharge plasma exciter that takes into account uncertainties. Background Technology
[0002] DBD plasma actuators, due to their simple structure, fast response, and low power consumption, have shown great potential in fields such as flow separation control, drag reduction, and noise reduction. A dielectric barrier discharge plasma actuator consists of exposed electrodes, buried electrodes, an insulating dielectric layer, and a high-voltage excitation power supply. The exposed electrodes are exposed to the air, while the buried electrodes are covered by the insulating dielectric layer. Both electrode layers are connected to the two ends of the high-voltage excitation power supply. Under high-voltage excitation, the air around the exposed electrodes is ionized, thus forming plasma. The actuator produces a quasi-steady glow during operation. Currently, commonly used excitation power supplies include sinusoidal AC, microsecond pulse, and nanosecond pulse power supplies. Under different high-voltage power supply excitations, the airflow around the upper electrode will undergo different changes. To study its mechanism of action, an accurate numerical model needs to be established. Currently, the mainstream phenomenological plasma equivalent model typically equates the effect of plasma on the airflow to a volume force source term in the momentum equation, and determines the spatial distribution and magnitude of the volume force through simplification assumptions.
[0003] However, the core parameters of these models (such as charge density and the boundary of the electric field region) largely rely on empirical formulas or experimental calibrations under specific operating conditions, resulting in inherent empirical errors and uncertainties. When excitation conditions (such as excitation voltage) change, fixed model parameters struggle to accurately predict changes in the plasma-induced flow field, leading to a decrease in model versatility and prediction accuracy. This uncertainty stems from various factors, including the complexity of the physical process and experimental measurement errors.
[0004] In existing technologies, improvements to plasma models mostly focus on fitting specific parameters with more experimental data or increasing the physical complexity of the model. The former lacks a systematic approach to parameter uncertainties, resulting in poor model robustness; the latter significantly increases computational costs. Currently, there is a lack of a method that can systematically quantify model parameter uncertainties and perform global, robust corrections to the model based on limited experimental data. This method would significantly improve the model's prediction accuracy and generalization ability under different operating conditions while ensuring computational efficiency, thus meeting the needs of engineering applications.
[0005] The technical problem to be solved by the present invention is to overcome the above-mentioned defects of the prior art and provide a method that can effectively handle the uncertainty of model parameters and use interval optimization theory to perform efficient and accurate calibration of plasma models. Summary of the Invention
[0006] In view of the above problems, the present invention is proposed to provide a method for establishing a dielectric barrier discharge plasma actuator model that considers uncertainty, which overcomes or at least partially solves the above problems, effectively overcomes the influence of parameter uncertainty, and significantly improves the model prediction accuracy and engineering applicability.
[0007] To achieve the above objectives, the present invention adopts the following technical solution:
[0008] In a first aspect, embodiments of the present invention provide a method for establishing a dielectric barrier discharge plasma actuator model considering uncertainties, comprising: S1: The time-averaged velocity field of plasma-induced flow field under different excitation voltages was obtained through static ion wind experiments, and the corresponding spatial distribution of volume force was deduced based on the principle of momentum balance. S2: Construct a parameterized initial plasma equivalent model, identify parameters that are sensitive to excitation voltage and difficult to determine precisely as uncertain design variables, and determine the initial value range of the uncertain design variables based on the spatial distribution of the volume force. S3: Generate a combination of sample points within the initial value range of the uncertain design variables, obtain the simulated values of the key evaluation indicators corresponding to each sample point through high-fidelity numerical simulation, and construct a surrogate model that has passed cross-validation. S4: Divide the uncertain design variables into interval variables and deterministic design variables. Within the interval variables, establish an interval multi-objective optimization problem based on the surrogate model, and solve it using a nested optimization strategy to obtain the Pareto optimal solution set. S5: Select the optimal compromise solution from the Pareto optimal solution set, determine the final boundary shape parameters and charge density-excitation voltage relationship, and substitute them into the initial plasma equivalent model to form the modified plasma model; S6: The modified plasma model is embedded as a momentum source term in the computational fluid dynamics solver for use in actual engineering flow control simulation.
[0009] Preferably, S1 includes: S101: Under no-flow conditions, a static ion wind experiment was conducted on the dielectric barrier discharge plasma exciter to measure the time-averaged velocity field of the induced flow field under different excitation voltages. S102: Based on the principle of momentum balance, the following two assumptions are introduced to simplify the inversion model: a) Assuming the dielectric barrier discharge plasma actuator is in a steady state, the flow induced by the dielectric barrier discharge plasma actuator is considered as a two-dimensional steady flow along the longitudinal symmetry plane of the actuator center, and the spanwise cross section of the body force along the z direction is uniformly distributed. b) Treat the fluid in the entire measurement area as an incompressible fluid; S103: Under the above assumptions, the two-dimensional incompressible Navier-Stokes equations are simplified to a balance form containing viscous terms and volume force terms, and the spatial distribution of volume force generated by plasma is inverted based on the measured mean velocity field. S104: Extract experimental values of key evaluation indicators from the spatial distribution of the volume force and the time-averaged velocity field.
[0010] Preferably, the spatial distribution of the volume force is as follows:
[0011]
[0012] Where x is the coordinate axis along the width direction of the dielectric barrier discharge plasma actuator, and y is the coordinate axis perpendicular to the surface of the dielectric barrier discharge plasma actuator. u The velocity along the x-axis exciter width direction, v The velocity is perpendicular to the exciter surface along the y-axis. It is dynamic viscosity. It is the density of the gas. T x It is the x-axis volume force component. T y It is the y-axis volume force component.
[0013] Preferably, S2 includes: S201: Construct a parameterized initial plasma equivalent model: The plasma-induced fluid forcing is equivalent to an electric force, and the electric field intensity is linearly distributed along the x and y directions, with the electric field intensity gradually decreasing from the origin to the boundary. S202: Based on the initial plasma equivalent model, the plasma active region is defined, and the boundary of the plasma active region is discretized and represented as a segmented boundary defined by multiple control endpoint coordinates. The geometry of the active region is flexibly described by adjusting the control endpoint coordinates. S203: Establish electric field intensity and local volume force within the discretized plasma active region; S204: Identify parameters in the initial plasma equivalent model that are sensitive to the excitation voltage and difficult to determine precisely as uncertain design variables. The uncertain design variables include at least the charge density and the coordinates of the control endpoints of the segment boundary. S205: Based on the spatial distribution of volume forces, extract the contour of the core action area of the volume forces and determine the initial value range of each uncertain design variable.
[0014] Preferably, the formula for calculating the electric field strength is:
[0015] in, The peak electric field intensity is represented by , and 'n' represents the segment number of the boundary discretization, used to distinguish different boundary segments. and This represents the electric field attenuation cutoff rate corresponding to the nth boundary segment. Indicates electric field strength; The formula for calculating the local volume force is:
[0016] In the formula, Indicates the excitation voltage and excitation frequency. It is the effective coefficient for elastic collisions between electrons and neutral particles. It is the amount of charge per unit charge. It is charge density. For effective breakdown time, The electric field intensity vector, This is a local volume force vector.
[0017] Preferably, S3 includes: S301: Within the initial value range of the uncertain design variables, a certain number of sample point combinations are generated using the OLHD method; S302: For the uncertain design variable values corresponding to each sample point, based on the electric field strength and local volume force under the framework of the initial plasma equivalent model, the Navier-Stokes equation is solved by high-fidelity numerical simulation to obtain the simulated value of the key evaluation index corresponding to the sample point. S303: Using the uncertain design variables as input and the difference between the simulated values and experimental values of the key evaluation indicators as output, construct a proxy model describing the nonlinear mapping relationship between input and output; S304: Perform cross-validation on the surrogate model. If R² > 0.9: the surrogate model is validated and proceed to the next step; if R² < 0.9: use the OLHD method again to supplement sample points or adjust the surrogate model type.
[0018] Preferably, S4 includes: S401: Divide the uncertain design variables into two categories: set the coordinates of the control endpoints of the segmented boundary of the electric field force action region as deterministic design variables, and set the excitation voltage and charge density as interval variables; S402: Establish an interval multi-objective optimization problem based on the surrogate model within the interval variables, the objective function of which is to simultaneously minimize the midpoint value and radius of the interval for peak velocity error and peak volume force error. S403: The nested optimization strategy is used to solve the interval multi-objective optimization problem: the outer optimization uses a multi-objective optimization algorithm to iteratively search the deterministic design variables, while the inner evaluation uses the interval variables to quickly calculate the maximum and minimum values of the peak velocity error and peak volume force error within the entire interval for each set of deterministic design variables, thereby determining the interval range. S404: Based on minimizing the maximum and minimum values of peak velocity error and peak volume force error, the interval multi-objective optimization problem is transformed into a deterministic optimization problem. A comprehensive objective function is constructed by weighted summation to obtain the Pareto optimal solution set.
[0019] Preferably, the objective function for:
[0020]
[0021] in, These are the weighting coefficients. Indicates the midpoint value. Indicates the radius of the interval. and This is the regularization coefficient.
[0022] As can be seen from the above technical solution, compared with the prior art, the present invention discloses a method for establishing a dielectric barrier discharge plasma actuator model that considers uncertainties, which has the following effects: High precision: By using an experimental data-driven approach combined with interval uncertainty optimization, systematic errors caused by empirical parameters are eliminated, and the consistency between the model's predicted velocity field and volume force and the experimental data is greatly improved.
[0023] High robustness: This invention systematically introduces interval uncertainty theory into the establishment of plasma models, quantifying the influence of uncertainties such as structure, excitation, and boundaries. By simultaneously minimizing the "average value" and "fluctuation range" of model errors, the corrected model not only achieves high accuracy under specific operating conditions but also maintains stable and reliable predictive performance over a wide range of operating conditions.
[0024] Practical engineering value: This invention provides a complete technical process from experimentation to model correction and then to engineering application, which significantly improves the credibility of numerical simulation of plasma actuators and helps to accelerate their design and optimization process in flow control applications in aerospace, vehicle engineering and other fields.
[0025] Good scalability: This method can be extended to DBD plasma actuators with different structures. Only the experimental parameters and constraint range need to be adjusted to achieve rapid model correction and adaptation. Attached Figure Description
[0026] To more clearly illustrate the technical solutions in the embodiments of the present invention or the prior art, the drawings used in the description of the embodiments or the prior art will be briefly introduced below. Obviously, the drawings described below are only embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on the provided drawings without creative effort.
[0027] Figure 1 This is a flowchart of the method for establishing a dielectric barrier discharge plasma actuator model considering uncertainties provided in the embodiments of the present invention; Figure 2 This is a schematic diagram of the dielectric barrier discharge plasma exciter structure provided in an embodiment of the present invention; Figure 3 This refers to the static ion wind experimental PIV measurement area provided in this embodiment of the invention. Figure 4 This is a flowchart illustrating the process of establishing a parameterized initial plasma model and identifying uncertainty parameters, as provided in this embodiment of the invention. Figure 5 This is a schematic diagram of the discretization and parameterization of the boundary of the electric field force action region provided in the embodiments of the present invention; Figure 6 This is a flowchart illustrating the construction of the experimental design sample space and surrogate model provided in this embodiment of the invention. Figure 7 This is a flowchart illustrating the multi-objective optimization based on interval uncertainty provided in this embodiment of the invention. Figure 8 These are the optimal deterministic boundary shape parameters provided in the embodiments of the present invention; Figure 9 This is the optimal charge density parameter relationship related to the excitation voltage provided in the embodiments of the present invention; Figure 10 The root mean square values of the relative errors of peak velocity and peak volume force provided in the embodiments of the present invention; Figure 11 The accuracy of the downstream velocity profile provided in the embodiments of the present invention. Detailed Implementation
[0028] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.
[0029] This invention discloses a method for establishing a dielectric barrier discharge plasma actuator model that considers uncertainties, such as... Figure 1 As shown, it includes: S1: The time-averaged velocity field of plasma-induced flow field under different excitation voltages was obtained through static ion wind experiments, and the corresponding spatial distribution of volume force was deduced based on the principle of momentum balance. S2: Construct a parameterized initial plasma equivalent model, identify parameters that are sensitive to excitation voltage and difficult to determine precisely as uncertain design variables, and determine the initial value range of uncertain design variables based on the spatial distribution of volume forces. S3: Generate a combination of sample points within the initial range of uncertain design variables, obtain the simulated values of key evaluation indicators corresponding to each sample point through high-fidelity numerical simulation, and construct a surrogate model that has passed cross-validation. S4: Divide the uncertain design variables into interval variables and deterministic design variables. Within the interval variables, establish an interval multi-objective optimization problem based on the surrogate model and solve it using a nested optimization strategy to obtain the Pareto optimal solution set. S5: Select the optimal compromise solution from the Pareto optimal solution set, determine the final boundary shape parameters and charge density-excitation voltage relationship, and substitute them into the initial plasma equivalent model to form the modified plasma model; S6: The modified plasma model is embedded as a momentum source term into the computational fluid dynamics solver for use in practical engineering flow control simulation.
[0030] The implementation process of this invention is described in detail below: S1: The time-averaged velocity field of the plasma-induced flow field under different excitation voltages was obtained through static ion wind experiments, and the corresponding spatial distribution of body forces was deduced based on the momentum balance principle. S101: Obtain the mean velocity field induced by the plasma actuator. Under no-flow conditions, conduct a static ion wind experiment on the DBD plasma actuator (e.g., using particle image velocimetry, PIV) to measure different excitation voltages. V pp The time-averaged velocity field of the induced flow field under the peak value of the excitation voltage.
[0031] S102: Based on the principle of momentum balance, the following two assumptions are proposed to deduce the spatial distribution of volume force generated by plasma from the time-averaged velocity field.
[0032] Assumption 1: The PIV measurement in the experiment was performed during the stabilization process of the dielectric barrier discharge plasma actuator. Considering the difference in time scale between the excitation half-cycle and the flow acceleration response, the flow induced by the plasma actuator can be regarded as a two-dimensional (xy section) steady flow along the longitudinal symmetry plane of the actuator center. That is, the volume force is quasi-steady, and the volume force is uniformly distributed along the spanwise cross section in the z-direction. Figure 2 direction shown; Assumption 2: The exciter-induced flow field velocity is low during the experiment, and the pressure pulsation change in the measurement area can be ignored. Therefore, the fluid in the entire measurement area is regarded as an incompressible fluid.
[0033] S103: Obtain the average volume force field induced by the plasma actuator. Based on the above assumptions, the velocity field is analyzed using the Navier-Stokes (NS) equations to obtain the volume forces. According to the assumption that volume forces exist, the 2D incompressible NS equations can be expressed as:
[0034] In the formula, It is a two-dimensional velocity vector, containing the x-axis velocity component u (velocity along the width of the exciter) and the y-axis velocity component v (velocity perpendicular to the surface of the exciter). It is static pressure. It is dynamic viscosity. It is the density of the gas; The volume force vector generated by the plasma includes an x-component. T x and y-component T y The x-axis is the coordinate axis along the width of the dielectric barrier discharge plasma actuator (parallel to the extension direction of the actuator electrodes); the y-axis is the coordinate axis perpendicular to the actuator surface (perpendicular to the plane where the electrodes are located, pointing towards the flow field region); the xy plane is the longitudinally symmetrical plane at the center of the actuator (perpendicular to the z-axis (spanwise), the z-axis extending along the length of the actuator), consistent with the "two-dimensional steady flow plane" in assumption S102. The directions are defined as follows... Figure 3 As shown.
[0035] Based on the two-dimensional steady assumption, under the condition of zero initial velocity, the above equation simplifies to:
[0036] Further, the volume force components in the x and y directions are obtained:
[0037]
[0038] S104: Extract experimental values of key evaluation indicators from the spatial distribution of volumetric forces and the time-averaged velocity field, and use them as the benchmark and verification basis for model correction.
[0039] The key evaluation indicators specifically include the experimental values of: 1) the experimental value of induced peak velocity U. max 1) The maximum velocity in the flow field (the peak value of the combined velocity components in the x and y directions); 2) The experimental value of the peak volume force T max 3) The maximum value of volume force (the resultant peak value of the combined x and y volume force components); 4) The contour range of the core action area of volume force: the spatial boundary range where the volume force amplitude is greater than the set threshold (usually 10%-20% of the peak volume force).
[0040] S2: Establish a parameterized initial plasma model and identify uncertain parameters, such as Figure 4 As shown.
[0041] S201: Determine the parameterized initial plasma equivalent model as the foundation model. This model equates plasma-induced fluid forcing to electro-body forces, with the electric field intensity linearly distributed along the x and y directions, providing a basic framework for subsequent calculations of electric field intensity and volume forces. Plasma-induced fluid forcing is equivalently modeled as electro-body forces within the activation region, with the electric field intensity gradually decreasing from the origin to the boundary, as shown below. Figure 5 direction shown; S202: Based on the above parameterized initial plasma equivalent model, the plasma active region (i.e., the region where the electric field force core acts, referring to the volume force range in S104) is defined, and this plasma active region is discretized along the boundary so that the region shape can be accurately described by the coordinates of the boundary control points. For example... Figure 5 As shown: The simple boundary (such as a straight line or a single boundary) in the initial plasma equivalent model is discretized into a segmented boundary defined by multiple control endpoint coordinates (such as x2, x3, x4, y1, y2, y3, n=3 corresponding to 3 boundary segments and 4 control points). These endpoint coordinates can move within a certain range to change the shape of the action area.
[0042] S203: Within the discretized plasma active region, considering the linear distribution characteristics of the electric field intensity, the following mathematical expression is established: Electric field intensity distribution:
[0043] Peak electric field intensity:
[0044] In the formula It represents the peak electric field intensity (the maximum electric field intensity generated by the excitation voltage in the direction of the electrode spacing). This represents the peak excitation voltage, while d is the electrode spacing between the exposed electrode and the covered electrode. The segment number of the boundary discretization is used to distinguish different boundary segments (e.g., n=3 corresponds to 3 discrete boundary segments). and Let represent the electric field strength attenuation cutoff rate corresponding to the nth boundary segment, controlling the attenuation rate of the electric field strength along the x and y directions. The resulting local body force is calculated as follows:
[0045] In the formula, This indicates the excitation frequency of the excitation power supply. It is the effective coefficient of elastic collision between electrons and neutral particles. It is the amount of charge per unit. It is charge density. For effective breakdown time. is the electric field intensity vector.
[0046] S204: Identify parameters in the initial plasma equivalent model that are sensitive to excitation voltage and difficult to determine precisely as design variables for uncertainty. These variables include at least: excitation voltage. Charge density And the coordinates of the control endpoints of the segment boundaries.
[0047] S205: Determine the initial range of values for design variables with uncertainties.
[0048] Based on the spatial distribution data of volume forces obtained by back-calculating the x- and y-axis volume force components in S1, the contour of the core action region of the volume forces is extracted (as described in S104), and the initial value range of each uncertain design variable is determined. The initial value range of the charge density is determined by the horizontal body force field. T x Divided by the horizontal component of the electric field E x The core region distribution of the charge density field is obtained as the initial range of charge density values.
[0049] S3: Generate sample point combinations within the initial value range of the uncertain design variables, obtain simulated values of key evaluation indicators corresponding to each sample point through high-fidelity numerical simulation, and construct a surrogate model that has passed cross-validation, such as... Figure 6 As shown: S301: Within the initial range of uncertain design variables, use an experimental design method with good space-filling characteristics (such as the optimal Latin hypercube design OLHD) to generate a certain number of sample point combinations.
[0050] S302: For each sample point (i.e. a set of defined design variable values), under the initial plasma equivalent model framework of S2, the simulated values of the key evaluation indicators corresponding to the sample point are obtained through high-fidelity numerical simulation (based on the numerical solution of the NS equation), including the simulated values of induced peak velocity and peak volume force.
[0051] S303: Using uncertain design variables as input and the difference (such as difference or relative error) between the simulated value and the experimental value of the key evaluation index as output, construct a surrogate model to describe the nonlinear mapping relationship between input and output, such as a radial basis function (RBF) neural network model, to establish the nonlinear mapping relationship between input and output.
[0052] S304: Perform cross-validation on the surrogate model to ensure that its prediction accuracy meets the requirements (e.g., coefficient of determination R² > 0.9).
[0053] If R² > 0.9: The surrogate model is validated and proceed to the next step; If R² < 0.9: Use the OLHD method again to supplement sample points or adjust the surrogate model type, and return to the sample point generation step (S301) to re-execute the subsequent process.
[0054] S4: Divide the uncertain design variables into interval variables and deterministic design variables. Within the interval variables, establish an interval multi-objective optimization problem based on a surrogate model, and solve it using a nested optimization strategy to obtain the Pareto optimal solution set, such as... Figure 7 As shown: S401: Define variable types for interval multi-objective optimization. Optimization variables: Deterministic design variables (coordinates of the control endpoints of the segmented boundary of the electric field force application region); Uncertainty variables: Interval variables (excitation voltage) Charge density It changes continuously within a certain range; S402: Establishing an Interval Multi-Objective Optimization Problem Objective function: Minimize the peak velocity error predicted by the model within the range of changes in the uncertain variables. Y 1 and peak volume force error Y The range of 2. Specifically, the goal is to simultaneously minimize the midpoint value of each objective function interval. (Representing average error) and interval radius (This represents sensitivity to changes in uncertainty, i.e., robustness). Here, i represents the number of objective functions; there are two objective functions in this case. Y 1 and Y 2.
[0055] Constraints: The range of values for deterministic design variables (defined by the contour of the S1 volumetric force core region). S403: Solve the above problem using a nested optimization strategy. Outer layer optimization: Use multi-objective optimization algorithms (such as the non-dominated sorting genetic algorithm NSGA-II) to iteratively optimize deterministic design variables.
[0056] Inner layer evaluation: For each set of deterministic design variables given by the outer layer, within the interval of uncertainty variables ( , Throughout the entire range of variation, the objective function is quickly evaluated using the surrogate model established by S3. Y 1 and Y The range of 2 (i.e., the maximum and minimum values).
[0057] S404: By transforming the interval multi-objective optimization problem into a deterministic optimization problem, a weighted sum is performed on the midpoint and radius of the interval:
[0058]
[0059] In the formula These are the weighting coefficients, used to obtain a more robust electric field boundary. Take values of 0.6, 0.7, and 0.8 respectively. and This is the regularization coefficient, used to avoid... Y im and Y iw The difference in magnitude is significant. The multi-objective optimization interval optimization problem is transformed into a deterministic optimization problem, namely, finding the objective function in the sample space. The minimum value.
[0060] S405: Iterative optimization until the Pareto front converges, resulting in a set of Pareto optimal solutions, each solution corresponding to an optimized boundary shape and a matching charge density-voltage relationship.
[0061] S5: Select the optimal compromise solution from the Pareto optimal solution set, determine the final boundary shape parameters and charge density-excitation voltage relationship, and substitute them into the initial plasma equivalent model to form the modified plasma model: S501: Select an optimal compromise solution from the Pareto optimal solution set. This solution provides: A set of optimal deterministic boundary shape parameters (fixed values), such as Figure 8 As shown.
[0062] An optimal charge density parameter relationship related to the excitation voltage, such as Figure 9 As shown.
[0063] S502: Substitute the above optimization results into the initial plasma equivalent model to obtain the corrected plasma model.
[0064] S503: Verifying the accuracy of the modified model. Under the full range of excitation voltages, the induced flow field is calculated using the modified plasma model and compared with the experimental data from S1 to verify the model's accuracy in predicting peak velocity and peak volumetric force (e.g., Figure 10 (as shown) and downstream velocity profile (as shown) Figure 11 The accuracy of aspects such as (as shown) has been improved.
[0065] S504: Accuracy Judgment. If the root mean square value of the predicted relative error meets engineering requirements (refer to...). Figure 10 If the accuracy level shown is met, the model validation is successful; otherwise, return to S3 to adjust the surrogate model or S4 to re-optimize.
[0066] S6: The modified plasma model is embedded as a momentum source term into the computational fluid dynamics solver for practical engineering flow control simulation. S601: The modified plasma model is embedded as a momentum source term into the computational fluid dynamics (CFD) solver; S602: Simulation of active flow control effects for practical engineering problems (such as cavity flutter noise control, airfoil flow separation control, etc.); S603: Based on simulation results, analyze the mechanism of plasma's influence on key flow characteristics such as shear layer evolution, vortex structure, and pressure feedback.
[0067] The various embodiments in this specification are described in a progressive manner, with each embodiment focusing on its differences from other embodiments. Similar or identical parts between embodiments can be referred to interchangeably. For the apparatus disclosed in the embodiments, since they correspond to the methods disclosed in the embodiments, the description is relatively simple; relevant parts can be referred to the method section.
[0068] The above description of the disclosed embodiments enables those skilled in the art to make or use the invention. Various modifications to these embodiments will be readily apparent to those skilled in the art, and the general principles defined herein may be implemented in other embodiments without departing from the spirit or scope of the invention. Therefore, the invention is not to be limited to the embodiments shown herein, but is to be accorded the widest scope consistent with the principles and novel features disclosed herein.
Claims
1. A method for establishing a model of a dielectric barrier discharge plasma actuator considering uncertainties, characterized in that, include: S1: The time-averaged velocity field of plasma-induced flow field under different excitation voltages was obtained through static ion wind experiments, and the corresponding spatial distribution of volume force was deduced based on the principle of momentum balance. S2: Construct a parameterized initial plasma equivalent model, identify parameters that are sensitive to excitation voltage and difficult to determine precisely as uncertain design variables, and determine the initial value range of the uncertain design variables based on the spatial distribution of the volume force. S3: Generate a combination of sample points within the initial value range of the uncertain design variables, obtain the simulated values of the key evaluation indicators corresponding to each sample point through high-fidelity numerical simulation, and construct a surrogate model that has passed cross-validation. S4: Divide the uncertain design variables into interval variables and deterministic design variables. Within the interval variables, establish an interval multi-objective optimization problem based on the surrogate model, and solve it using a nested optimization strategy to obtain the Pareto optimal solution set. S5: Select the optimal compromise solution from the Pareto optimal solution set, determine the final boundary shape parameters and charge density-excitation voltage relationship, and substitute them into the initial plasma equivalent model to form the modified plasma model; S6: The modified plasma model is embedded as a momentum source term in the computational fluid dynamics solver for use in actual engineering flow control simulation.
2. The method as described in claim 1, characterized in that, S1 includes: S101: Under no-flow conditions, a static ion wind experiment was conducted on the dielectric barrier discharge plasma exciter to measure the time-averaged velocity field of the induced flow field under different excitation voltages. S102: Based on the principle of momentum balance, the following two assumptions are introduced to simplify the inversion model: a) Assuming the dielectric barrier discharge plasma actuator is in a steady state, the flow induced by the dielectric barrier discharge plasma actuator is considered as a two-dimensional steady flow along the longitudinal symmetry plane of the actuator center, and the spanwise cross section of the body force along the z-direction is uniformly distributed. b) Treat the fluid in the entire measurement area as an incompressible fluid; S103: Under the above assumptions, the two-dimensional incompressible Navier-Stokes equations are simplified to a balance form containing viscous terms and volume force terms, and the spatial distribution of volume force generated by plasma is inverted based on the measured mean velocity field. S104: Extract experimental values of key evaluation indicators from the spatial distribution of the volume force and the time-averaged velocity field.
3. The method as described in claim 2, characterized in that, The spatial distribution of the volume force is as follows: Where x is the coordinate axis along the width direction of the dielectric barrier discharge plasma actuator, and y is the coordinate axis perpendicular to the surface of the dielectric barrier discharge plasma actuator. u The velocity along the x-axis exciter width direction, v The velocity is perpendicular to the exciter surface along the y-axis. It is dynamic viscosity. It is the density of the gas. T x It is the x-axis volume force component. T y It is the y-axis volume force component.
4. The method as described in claim 2, characterized in that, S2 includes: S201: Construct a parameterized initial plasma equivalent model: The plasma-induced fluid forcing is equivalent to an electric force, and the electric field intensity is linearly distributed along the x and y directions, with the electric field intensity gradually decreasing from the origin to the boundary. S202: Based on the initial plasma equivalent model, the plasma active region is defined, and the boundary of the plasma active region is discretized and represented as a segmented boundary defined by multiple control endpoint coordinates. The geometry of the active region can be flexibly described by adjusting the control endpoint coordinates. S203: Establish electric field intensity and local volume force within the discretized plasma active region; S204: Identify parameters in the initial plasma equivalent model that are sensitive to the excitation voltage and difficult to determine precisely as uncertain design variables. The uncertain design variables include at least the charge density and the coordinates of the control endpoints of the segment boundary. S205: Based on the spatial distribution of volume forces, extract the contour of the core action area of the volume forces and determine the initial value range of each uncertain design variable.
5. The method as described in claim 4, characterized in that, The formula for calculating the electric field strength is: in, The peak electric field intensity is represented by , and 'n' represents the segment number of the boundary discretization, used to distinguish different boundary segments. and This represents the electric field attenuation cutoff rate corresponding to the nth boundary segment. Indicates electric field strength; The formula for calculating the local volume force is: In the formula, Indicates the excitation voltage and excitation frequency. It is the effective coefficient for elastic collisions between electrons and neutral particles. It is the amount of charge per unit charge. It is charge density. For effective breakdown time, The electric field intensity vector, This is a local volume force vector.
6. The method as described in claim 4, characterized in that, S3 includes: S301: Within the initial value range of the uncertain design variables, a certain number of sample point combinations are generated using the OLHD method; S302: For each sample point, the design variable value is determined based on the electric field strength and local volume force. Under the framework of the initial plasma equivalent model, the Navier-Stokes equation is solved by high-fidelity numerical simulation to obtain the simulated value of the key evaluation index corresponding to the sample point. S303: Using the uncertain design variables as input and the difference between the simulated values and experimental values of the key evaluation indicators as output, construct a proxy model describing the nonlinear mapping relationship between input and output; S304: Perform cross-validation on the surrogate model. If R² > 0.9: the surrogate model is validated and proceed to the next step; if R² < 0.9: use the OLHD method again to supplement sample points or adjust the surrogate model type.
7. The method as described in claim 1, characterized in that, S4 includes: S401: Divide the uncertain design variables into two categories: set the coordinates of the control endpoints of the segmented boundary of the electric field force action region as deterministic design variables, and set the excitation voltage and charge density as interval variables; S402: Establish an interval multi-objective optimization problem based on the surrogate model within the interval variables, the objective function of which is to simultaneously minimize the midpoint value and radius of the interval for peak velocity error and peak volume force error. S403: The nested optimization strategy is used to solve the interval multi-objective optimization problem: the outer optimization uses a multi-objective optimization algorithm to iteratively search the deterministic design variables, while the inner evaluation uses the interval variables to quickly calculate the maximum and minimum values of the peak velocity error and peak volume force error within the entire interval for each set of deterministic design variables, thereby determining the interval range. S404: Based on minimizing the maximum and minimum values of peak velocity error and peak volume force error, the interval multi-objective optimization problem is transformed into a deterministic optimization problem. A comprehensive objective function is constructed by weighted summation to obtain the Pareto optimal solution set.
8. The method as described in claim 7, characterized in that, The objective function for: in, These are the weighting coefficients. Indicates the midpoint value. Indicates the radius of the interval. and This is the regularization coefficient.