Unsteady aerodynamics modeling for flight dynamics application

In view of engineering application, it is practicable to decompose the aerodynamics into three components： the static aerodynamics, the aerodynamic increment due to steady rotations, and the aerodynamic increment due to unsteady separated and vortical flow. The first and the second components can be presented in conventional forms, while the third is described using a one-order differential equation and a radial-basis-function （RBF） network. For an aircraft configuration, the mathematical models of 6- component aerodynamic coefficients are set up from the wind tunnel test data of pitch, yaw, roll, and coupled yawroll large-amplitude oscillations. The flight dynamics of an aircraft is studied by the bifurcation analysis technique in the case of quasi-steady aerodynamics and unsteady aerodynam- ics, respectively. The results show that： （1） unsteady aerodynamics has no effect upon the existence of trim points, but affects their stability; （2） unsteady aerodynamics has great effects upon the existence, stability, and amplitudes of periodic solutions; and （3） unsteady aerodynamics changes the stable regions of trim points obviously. Furthermore, the dynamic responses of the aircraft to elevator deflections are inspected. It is shown that the unsteady aerodynamics is beneficial to dynamic stability for the present aircraft. Finally, the effects of unsteady aerodynamics on the post-stall maneuverability

Numerical investigation on aerodynamic performance of a bionic flapping wing

This paper numerically studies the aerodynamic performance of a bird-like bionic flapping wing.The geometry and kinematics are designed based on a seagull wing,in which flapping,folding,swaying,and twisting are considered.An in-house unsteady flow solver based on hybrid moving grids.is adopted for unsteady flow simulations.We focus on two main issues in this study,i.e.,the influence of the proportion of down-stroke and the effect of span-wise twisting.Numerical results show that the proportion of downstroke is closely related to the efficiency of the flapping process.The preferable proportion is about 0.7 by using the present geometry and kinematic model,which is very close to the observed data.Another finding is that the drag and the power consumption can be greatly reduced by the proper span-wise twisting.Two cases with different reduced frequencies are simulated and compared with each other.The numerical results show that the power consumption reduces by more than 20%,and the drag coefficient reduces by more than 60% through a proper twisting motion for both cases.The flow mechanism is mainly due to controlling of unsteady flow separation by adjusting the local effective angle of attack.These conclusions will be helpful for the high-performance micro air vehicle (MAV) design.

Hypersonic Shock Wave/Boundary Layer Interactions by a Third-Order Optimized Symmetric WENO Scheme

A novel third-order optimized symmetric weighted essentially non-oscillatory(WENO-OS3)scheme is used to simulate the hypersonic shock wave/boundary layer interactions.Firstly,the scheme is presented with the achievement of low dissipation in smooth region and robust shock-capturing capabilities in discontinuities.The Maxwell slip boundary conditions are employed to consider the rarefied effect near the surface.Secondly,several validating tests are given to show the good resolution of the WENO-OS3 scheme and the feasibility of the Maxwell slip boundary conditions.Finally,hypersonic flows around the hollow cylinder truncated flare(HCTF)and the25°/55°sharp double cone are studied.Discussions are made on the characteristics of the hypersonic shock wave/boundary layer interactions with and without the consideration of the slip effect.The results indicate that the scheme has a good capability in predicting heat transfer with a high resolution for describing fluid structures.With the slip boundary conditions,the separation region at the corner is smaller and the prediction is more accurate than that with no-slip boundary conditions.

Impacts of NBTI/PBTI on power gated SRAM

A signal probability and activity probability (SPAP) model was proposed firstly, to estimate the impacts of the negative bias temperature instability (NBTI) and positive bias temperature instability (PBTI) on power gated static random access memory (SRAM). The experiment results show that PBTI has significant influence on the read and write operations of SRAM with power gating, and it deteriorates the NBTI effects and results in a up to 39.38% static noise margin reduction and a 35.7% write margin degradation together with NBTI after 106 s working time. Then, a circuit level simulation was used to verify the assumption of the SPAP model, and finally the statistic data of CPU2000 benchmarks show that the proposed model has a reduction of 3.85% for estimation of the SNM degradation after 106 s working time compared with previous work.

Aircraft parameter estimation using a stacked long short-term memory network and Levenberg-Marquardt method

To effectively estimate the unknown aerodynamic parameters from the aircraft’s flight data,this paper proposes a novel aerodynamic parameter estimation method incorporating a stacked Long Short-Term Memory(LSTM)network model and the Levenberg-Marquardt(LM)method.The stacked LSTM network model was designed to realize the aircraft dynamics modeling by utilizing a frame of nonlinear functional mapping based entirely on the measured input-output data of the aircraft system without requiring explicit postulation of the dynamics.The LM method combines the already-trained LSTM network model to optimize the unknown aerodynamic parameters.The proposed method is applied by using the real flight data,generated by ATTAS aircraft and a bio-inspired morphing Unmanned Aerial Vehicle(UAV).The investigation reveals that for the two different flight data,the designed stacked LSTM network structure can maintain the efficacy of the network prediction capability only by appropriately adjusting the dropout rates of its hidden layers without changing other network parameters(i.e.,the initial weights,initial biases,number of hidden cells,time-steps,learning rate,and number of training iterations).Besides,the proposed method’s effectiveness and potential are demonstrated by comparing the estimated results of the ATTAS aircraft or the bio-inspired morphing UAV with the corresponding reference values or wind-tunnel results.

Aerodynamic configuration optimization by the integration of aerodynamics, aerothermodynamics and trajectory for hypersonic vehicles

The problem of aerodynamic configuration design optimization is a multidisciplinary design optimization(MDO) problem, and recently the MDO method is widely adopted in the field of hypersonic vehicle configuration design. From the aerodynamic point of view, the aerodynamics, aerothermodynamics and trajectory are considered in this paper. Generally speaking, the aerodynamic characteristics, aerodynamic heating and trajectory are determined by the aerodynamic configuration and the design of flight trajectory. The design method considering these three disciplines is proposed. The parametric geometrical configurations are proposed, and the aerodynamic characteristics are predicted by the rapid and effective engineering method. The optimization of aerodynamic configuration considering the integration of aerodynamics,aerothermodynamics and trajectory is investigated based on the parametric geometrical configuration. Maximum lift-to-drag ratio, maximum range of the trajectory and minimum total heat load of the stagnation point are chosen as the three optimal goals. The detailed research indicates that the optimal configurations and trajectories with different weighting factors can be obtained by the optimization, and there are obvious differences between them. The optimal configuration and flight trajectory obtained by the optimization can be used as the feasible schemes in the future work.

Virtual flight test of pitch and roll attitude control based on circulation control of tailless flying wing aircraft without rudders

Circulation Control(CC) realizes rudderless flight control by driving compressed air jet to generate a virtual rudder surface, which significantly improves low detectability. The layout plan of combined control rudder surface is proposed based on the tailless flying wing aircraft. The closed-loop jet actuator system and stepless rudder surface switching control strategy are used to quantitatively study the control characteristics of circulation actuator for pitch and roll attitude through 3-DOF virtual flight test in a wind tunnel with a powered model at wind speed of 40 m/s. The results show that the combined use of circulation actuators can achieve bidirectional continuous and stable control of the aircraft’s pitch and roll attitude, with the maximum pitch rate of 12.3(°)/s and the maximum roll rate of 21.5(°)/s;the response time of attitude angular rate varying with the jet pressure ratio is less than 0.02 s, which can satisfy the control response requirements of aircraft motion stability for the control system;the jet rudder surface has a strong moment control ability, and the pitch moment of the jet elevator with a pressure ratio of 1.28 is the same as that of the mechanical elevator with 28° rudder deflection, which can expand the flight control boundary.

A practical filter error method for aerodynamic parameter estimation of aircraft in turbulence

It is common for aircraft to encounter atmospheric turbulence in flight tests.Turbulence is usually modeled as stochastic process noise in the flight dynamics equations.In this paper,parameter estimation of nonlinear dynamic system with both process and measurement noise was studied,and a practical filter error method was proposed.The linearized Kalman filter of first-order approximation was used for state estimation,in which the filter gain,along with the system parameters and the initial states,constituted the parameter vector to be estimated.The unknown parameters and measurement noise covariance were estimated alternately by a relaxation iteration method,and the sensitivities of observations to unknown parameters were calculated by finite difference approximation.Some practical aspects of the method application were discussed.The proposed filter error method was validated by the flight simulation data of a research aircraft.Then,the method was applied to the flight tests of a subscale aircraft,and the aerodynamic stability and control derivatives were estimated.All the estimation results were compared with the results of the output error method to demonstrate the effectiveness of the approach.It is shown that the filter error method is superior to the output error method for flight tests in atmospheric turbulence.

Hypersonic shock wave and turbulent boundary layer interaction in a sharp cone/flare model

A direct numerical simulation of hypersonic Shock wave and Turbulent Boundary Layer Interaction(STBLI)at Mach 6.0 on a sharp 7.half-angle circular cone/flare configuration at zero angle of attack is performed.The flare angle is 34.and the momentum thickness Reynolds number based on the incoming turbulent boundary layer on the sharp circular cone is Re θ=2506.It is found that the mean flow is separated and the separation bubble occurring near the corner exhibits unsteadiness.The Reynolds analogy factor changes dramatically across the interaction,and varies between 1.06 and 1.27 in the downstream region,while the QP85 scaling factor has a nearly constant value of 0.5 across the interaction.The evolution of the reattached boundary layer is characterized in terms of the mean profiles,the Reynolds stress components,the anisotropy tensor and the turbulence kinetic energy.It is argued that the recovery is incomplete and the near-wall asymptotic behavior does not occur for the hypersonic interaction.In addition,mean skin friction decomposition in an axisymmetric turbulent boundary layer is carried out for the first time.Downstream of the interaction,the contributions of transverse curvature and body divergence are negligible,whereas the positive contribution associated with the turbulence kinetic energy production and the negative spatial-growth contribution are dominant.Based on scale decomposition,the positive contribution is further divided into terms with different spanwise length scales.The negative contribution is analyzed by comparing the convective term,the streamwise-heterogeneity term and the pressure gradient term.

Accurately predicting hypersonic transitional flow on cone via a symmetry approach

A new algebraic transition model is proposed based on a Structural Ensemble Dynamics(SED)theory of wall turbulence,for accurately predicting the hypersonic flow heat transfer on cone.The model defines the eddy viscosity in terms of a two-dimensional multi-regime distribution of a Stress Length(SL)function,and hence is named as SED-SL.This paper presents clear evidence of precise predictions of transition onset location and peak heat flux of a wide range of hypersonic Transitional Boundary Layers(TrBL)around straight cone at zero incidence,to an unprecedented accuracy as validated by over 70 measurements for varying five crucial influential factors(Mach number,temperature ratio,cone half angle,nose Reynolds number and noise level).The results demonstrate the universality of the postulated multi-regime similarity structure,in characterizing not only the spatial non-uniform distribution of the eddy viscosity in hypersonic TrBL on cone,but also the dependence of the transition onset location on the five influential factors.The latter yields a novel correlation formula for transition center Reynolds number which takes similar functional form as the SL function within the symmetry approach.It is concluded that the SED-SL model simulates TrBL around cone with uniformly high accuracy,and then points out to an optimistic alternative way to construct hypersonic transition model.

Solution Remapping Method with Lower Bound Preservation for Navier-Stokes Equations in Aerodynamic Shape Optimization

It is found that the solution remapping technique proposed in[Numer.Math.Theor.Meth.Appl.,2020,13(4)]and[J.Sci.Comput.,2021,87(3):1-26]does not work out for the Navier-Stokes equations with a high Reynolds number.The shape deformations usually reach several boundary layer mesh sizes for viscous flow,which far exceed one-layer mesh that the original method can tolerate.The direct application to Navier-Stokes equations can result in the unphysical pressures in remapped solutions,even though the conservative variables are within the reasonable range.In this work,a new solution remapping technique with lower bound preservation is proposed to construct initial values for the new shapes,and the global minimum density and pressure of the current shape which serve as lower bounds of the corresponding variables are used to constrain the remapped solutions.The solution distribution provided by the present method is proven to be acceptable as an initial value for the new shape.Several numerical experiments show that the present technique can substantially accelerate the flow convergence for large deformation problemswith 70%-80%CPU time reduction in the viscous airfoil drag minimization.

Unsteady aerodynamic modeling at high angles of attack using support vector machines

Abstract Accurate aerodynamic models are the basis of flight simulation and control law design. Mathematically modeling unsteady aerodynamics at high angles of attack bears great difficulties in model structure determination and parameter estimation due to little understanding of the flow mechanism. Support vector machines （SVMs） based on statistical learning theory provide a novel tool for nonlinear system modeling. The work presented here examines the feasibility of applying SVMs to high angle.-of-attack unsteady aerodynamic modeling field. Mainly, after a review of SVMs, several issues associated with unsteady aerodynamic modeling by use of SVMs are discussed in detail, such as sele, ction of input variables, selection of output variables and determination of SVM parameters. The least squares SVM （LS-SVM） models are set up from certain dynamic wind tunnel test data of a delta wing and an aircraft configuration, and then used to predict the aerodynamic responses in other tests. The predictions are in good agreement with the test data, which indicates the satisfving learning and generalization performance of LS-SVMs.

Progress in application of CFD techniques

Computational Fluid Dynamics (CFD) is an important branch of fluid mechanics, and will continue to play great roles on the design of aerospace vehicles, explora- tion of new concept vehicles and new aerodynamic technology. This paper will present the progress of CFD from point of view of engineering application in recent years at CARDC, including the software integration, grid technique, speeding up of convergence, unsteady fluid computation,etc., and also give some engineering application examples of CFD at CARDC.

Aerodynamic Modeling and Parameter Estimation from QAR Data of an Airplane Approaching a High-altitude Airport

Aerodynamic modeling and parameter estimation from quick accesses recorder （QAR） data is an important technical way to analyze the effects of highland weather conditions upon aerodynamic characteristics of airplane. It is also an essential content of flight accident analysis. The related techniques are developed in the present paper, including the geometric method for angle of attack and sideslip angle estimation, the extended Kalman filter associated with modified Bryson-Frazier smoother （EKF-MBF） method for aerodynamic coefficient identification, the radial basis function （RBF） neural network method for aerodynamic mod- eling, and the Delta method for stability/control derivative estimation. As an application example, the QAR data of a civil air- plane approaching a high-altitude airport are processed and the aerodynamic coefficient and derivative estimates are obtained. The estimation results are reasonable, which shows that the developed techniques are feasible. The causes for the distribution of aerodynamic derivative estimates are analyzed. Accordingly, several measures to improve estimation accuracy are put forward.

Inverse design of low boom configurations using proper orthogonal decomposition and augmented Burgers equation

Mitigation of sonic boom to an acceptable stage is a key point for the next generation of supersonic transports. Meanwhile, designing a supersonic aircraft with an ideal ground signature is always the focus of research on sonic boom reduction. This paper presents an inverse design approach to optimize the near-field signature of an aircraft, making it close to the shaped ideal ground signature after the propagation in the atmosphere. Using the Proper Orthogonal Decomposition(POD) method, a guessed input of augmented Burgers equation is inversely achieved. By multiple POD iterations, the guessed ground signatures successively approach the target ground signature until the convergence criteria is reached. Finally, the corresponding equivalent area distribution is calculated from the optimal near-field signature through the classical Whitham F-function theory. To validate this method, an optimization example of Lockheed Martin 1021 is demonstrated. The modified configuration has a fully shaped ground signature and achieves a drop of perceived loudness by 7.94 PLdB. This improvement is achieved via shaping the original near-field signature into wiggles and damping it by atmospheric attenuation. At last, a nonphysical ground signature is set as the target to test the robustness of this inverse design method and shows that this method is robust enough for various inputs.

Calibration of a γ-Re_θ transition model and its validation in low-speed flows with high-order numerical method

Abstract Based on the Reynolds-averaged Navier--Stokes （RANS） equations and structured grid technology, the calibration and validation of Y-Reo transition model is preformed with fifth-order weighted compact nonlinear scheme （WCNS）, and the purpose of the present work is to improve the numerical accuracy for aerodynamic characteristics simulation of low-speed flow with transition model on the basis of high-order numerical method study. Firstly, the empirical correlation functions involved in the Y-Reo transition model are modified and calibrated with experimental data of turbulent flat plates. Then, the grid convergence is studied on NLR-7301 two-element airfoil with the modified empirical correlation. At last, the modified empirical correlation is validated with NLR-7301 two-element airfoil and high-lift trapezoidal wing from transition location, velocity pro- file in boundary layer, surface pressure coefficient and aerodynamic characteristics. The numerical results illustrate that the numerical accuracy of transition length and skin friction behind transition location are improved with modified empirical correlation function, and obviously increases the numerical accuracy of aerodynamic characteristics prediction for typical transport configurations in low-speed range.

A CFD-based numerical virtual flight simulator and its application in control law design of a maneuverable missile model

A CFD-based Numerical Virtual Flight(NVF)simulator is presented,which integrates an unsteady flow solver on moving hybrid grids,a Rigid-Body Dynamics(RBD)solver and a module of the Flight Control System(FCS).A technique of dynamic hybrid grids is developed to control the active control surfaces with body morphing,with a technique of parallel unstructured dynamic overlapping grids generating proper moving grids over the deflecting control surfaces(e.g.the afterbody rudders of a missile).For the flow/kinematic coupled problems,the 6 Degree-Of-Freedom(DOF)equations are solved by an explicit or implicit method coupled with the URANS CFD solver.The module of the control law is explicitly coupled into the NVF simulator and then improved by the simulation of the pitching maneuver process of a maneuverable missile model.A nonlinear dynamic inversion method is then implemented to design the control law for the pitching process of the maneuverable missile model.Simulations and analysis of the pitching maneuver process are carried out by the NVF simulator to improve the flight control law.Higher control response performance is obtained by adjusting the gain factors and adding an integrator into the control loop.

Validation of a RANS transition model using a high-order weighted compact nonlinear scheme

A modified transition model is given based on the shear stress transport (SST) turbulence model and an intermittency transport equation. The energy gradient term in the original model is replaced by flow strain rate to saving computational costs. The model employs local variables only, and then it can be conveniently implemented in modern computational fluid dynamics codes. The fifth-order weighted compact nonlinear scheme and the fourth-order staggered scheme are applied to discrete the governing equations for the purpose of minimizing discretization errors, so as to mitigate the confusion between numerical errors and transition model errors. The high-order package is compared with a second-order TVD method on simulating the transitional flow of a flat plate. Numerical results indicate that the high-order package give better grid convergence property than that of the second-order method. Validation of the transition model is performed for transitional flows ranging from low speed to hypersonic speed.

An improved adaptive sampling and experiment design method for aerodynamic optimization

Experiment design method is a key to construct a highly reliable surrogate model for numerical optimization in large-scale project. Within the method, the experimental design criterion directly affects the accuracy of the surrogate model and the optimization efficient. According to the shortcomings of the traditional experimental design, an improved adaptive sampling method is proposed in this paper. The surrogate model is firstly constructed by basic sparse samples. Then the supplementary sampling position is detected according to the specified criteria, which introduces the energy function and curvature sampling criteria based on radial basis function （RBF） network. Sampling detection criteria considers both the uniformity of sample distribution and the description of hypersurface curvature so as to significantly improve the prediction accuracy of the surrogate model with much less samples. For the surrogate model constructed with sparse samples, the sample uniformity is an important factor to the interpolation accuracy in the initial stage of adaptive sam- pling and surrogate model training. Along with the improvement of uniformity, the curvature description of objective function surface gradually becomes more important. In consideration of these issues, crowdness enhance function and root mean square error （RMSE） feedback function are introduced in C criterion expression. Thus, a new sampling method called RMSE and crowd- ness enhance （RCE） adaptive sampling is established. The validity of RCE adaptive sampling method is studied through typical test function firstly and then the airfoil/wing aerodynamic opti- mization design problem, which has high-dimensional design space. The results show that RCE adaptive sampling method not only reduces the requirement for the number of samples, but also effectively improves the prediction accuracy of the surrogate model, which has a broad prospects for applications.

An efficient large-scale mesh deformation method based on MPI/Open MP hybrid parallel radial basis function interpolation

An efficient MPI/OpenMP hybrid parallel Radial Basis Function (RBF) strategy for both continuous and discontinuous large-scale mesh deformation is proposed to reduce the computational cost and memory consumption.Unlike the conventional parallel methods in which all processors use the same surface displacement and implement the same operation,the present method employs different surface points sets and influence radius for each volume point movement,accompanied with efficient geometry searching strategy.The deformed surface points,also called Control Points (CPs),are stored in each processor.The displacement of spatial points is interpolated by using only 20-50 nearest control points,and the local influence radius is set to 5-20 times the maximum displacement of control points.To shorten the searching time for the nearest control point clouds,an Alternating Digital Tree (ADT) algorithm for 3D complex geometry is designed based on an iterative bisection technique.Besides,an MPI/OpenMP hybrid parallel approach is developed to reduce the memory cost in each High-Performance Computing (HPC) node for large-scale applications.Three 3D cases,including the ONERA-M6 wing and a commercial transport airplane standard model with up to 2.5 billion hybrid elements,are used to test the present mesh deformation method.The robustness and high parallel efficiency are demonstrated by a wing deflection case with a maximum bending angle of 450 and more than 80% parallel efficiency with 1024 MPI processors.In addition,the availability for both continuous and discontinuous surface deformation is verified by interpolating the projecting displacement with opposite directions surface points to the spatial points.