Gated Neural Network-Based Unsteady Aerodynamic Modeling for Large Angles of Attack

Modeling of unsteady aerodynamic loads at high angles of attack using a small amount of experimental or simulation data to construct predictive models for unknown states can greatly improve the efficiency of aircraft unsteady aerodynamic design and flight dynamics analysis.In this paper,aiming at the problems of poor generalization of traditional aerodynamic models and intelligent models,an intelligent aerodynamic modeling method based on gated neural units is proposed.The time memory characteristics of the gated neural unit is fully utilized,thus the nonlinear flow field characterization ability of the learning and training process is enhanced,and the generalization ability of the whole prediction model is improved.The prediction and verification of the model are carried out under the maneuvering flight condition of NACA0015 airfoil.The results show that the model has good adaptability.In the interpolation prediction,the maximum prediction error of the lift and drag coefficients and the moment coefficient does not exceed 10%,which can basically represent the variation characteristics of the entire flow field.In the construction of extrapolation models,the training model based on the strong nonlinear data has good accuracy for weak nonlinear prediction.Furthermore,the error is larger,even exceeding 20%,which indicates that the extrapolation and generalization capabilities need to be further optimized by integrating physical models.Compared with the conventional state space equation model,the proposed method can improve the extrapolation accuracy and efficiency by 78%and 60%,respectively,which demonstrates the applied potential of this method in aerodynamic modeling.

Numerical Investigation of the Unsteady Flow in a Transonic Compressor with Curved Rotors

The unsteady 3D flow fields in a single-stage transonic compressor under designed conditions are simulated numerically to investigate the effects of the curved rotors on the stage performance and the aerodynamic interaction between the blade rows. The results show that, compared to the compressor with unurved rotors, the compressor under scrutiny acquires remarkable increases in efficiency with significantly reduced amplitudes of the time-dependent fluctuation. The amplitude of the pressure fluctuation around the stator leading edge decreases at both endwalls, but increases at the mid-span in the curved rotors. The pressure fluctuation near the stator leading edge, therefore, becomes more uniform in the radial direction of this compressor. Except for the leading edge area, the pressure fluctuatinn amplitude declines remarkably in the tip region of stator surface downstream of the curved rotor, but hardly changes in the middle and at the hub.

GRIDLESS METHOD FOR UNSTEADY VISCOUS FLOWS

Gridless method is developed for unsteady viscous flows involving moving boundaries. The point distri- bution of gridless method is implemented in an isotropic or anisotropic way according to the features of viscous flows. In the area far away from the body, the traditional cloud of isotropic points is used, while in the adjacent area, the cloud of anisotropic points is distributed. In this way, the point spacing normal to the wall can be small enough for simulating the boundary layer, and meanwhile, the total number of points in the computational do- main can be controlled due to large spacing in other tangential direction through the anisotropic way. A fast mov- ing technique of clouds of points at each time-step is presented based on the attenuation law of disturbed motion for unsteady flows involving moving boundaries. In the mentioned cloud of points, a uniform weighted least- square curve fit method is utilized to discretize the spatial derivatives of the Navier-Stokes equations. The pro- posed gridless method, coupled with a dual time-stepping method and the Spalart-Allmaras turbulence model, is implemented for the Navier-Stokes equations. The computational results of unsteady viscous flows around a NLR7301 airfoil with an oscillating flap and a pitching NACA0012 airfoil are presented in a good agreement with the available experimental data.

Unsteady Turbulent Simulation and Pressure Fluctuation Analysis for Centrifugal Pumps

The pressure fluctuation in the flow passage of both impeller and casing is addressed on design condition. The initial conditions for the unsteady turbulent simulation are resulted from the steady calculations, and the three dimensional unsteady turbulent simulation concerning the rotor-stator interaction is executed by a Navier-Stoke solver embedded with k -ε turbulence model and with appropriate moving interface boundary conditions. Detecting points are distributed in the flow passage in different radial and circumferential positions to capture the static pressure fluctuation character for one cycle of the impeller. The time-domain spectrums show that the static pressure curves are periodic and have five peaks and five valleys. With the radius increasing, the pressure fluctuation peak-to-peak values in the impeller are increasing, and reach the maximum value on the interface. In the casing flow passage, those values are about 7% of local static pressure except some ones near the tongue. The values become decreasingly in the diffuser pipe. The frequency spectrums transformed by fast Fourier transform （FFT） show that the dominant frequency is approximate with the blade passing frequency, and the pressure fluctuations in impeller passage have high frequency content while those in casing ones have no such information.

UNSTEADY FLOWS OF A GENERALIZED SECOND GRADE FLUID WITH THE FRACTIONAL DERIVATIVE MODEL BETWEEN TWO PARALLEL PLATES

The fractional calculus approach in the constitutive relationship model of a generalized second grade fluid is introduced.Exact analytical solutions are obtained for a class of unsteady flows for the generalized second grade fluid with the fractional derivative model between two parallel plates by using the Laplace transform and Fourier transform for fractional calculus.The unsteady flows are generated by the impulsive motion or periodic oscillation of one of the plates.In addition,the solutions of the shear stresses at the plates are also determined.

Studies of the unsteady supersonic base flows around three afterbodies

Unsteady supersonic base flows around three afterbodies, cylindrical （Cy）, boattailed （BT） and three-step （MS）, are investigated in this paper. Reynolds-averaged Navier-Stokes （RANS） and two RANS/LES （large-eddy simulation） hybrid methods, detached eddy simulation （DES） and delayed-DES （DDES）, are used to predict the base flow characteristics around the baseline Cy afterbody. All the RANS and hybrid methods are based on the two-equation SST （shear-stress transport） model with compressible corrections （CC）. According to the comparison of measurements, both DES and DDES can produce more satisfactory results than RANS. RANS can only present the ＂stable＂ flow pat- terns, while the hybrid methods can demonstrate unsteady flow structures. DDES and DES results are little different from one another although the latter exhibits better agreement with the experiment. DES is taken to investigate the 5° BT and three-step afterbodies. The mean flow data and the instantaneous turbulent coherent structures are compared against available measurements.

Unsteady rotating flows of a viscoelastic fluid with the fractional Maxwell model between coaxial cylinders

The fractional calculus is used in the constitutive relationship model of viscoelastic fluid. A generalized Maxwell model with fractional calculus is considered. Based on the flow conditions described, two flow cases are solved and the exact solutions are obtained by using the Weber transform and the Laplace transform for fractional calculus.

Unsteady Flow and Structural Behaviors of Centrifugal Pump under Cavitation Conditions

Cavitation has a significant e ect on the flow fields and structural behaviors of a centrifugal pump. In this study, the unsteady flow and structural behaviors of a centrifugal pump are investigated numerically under di erent cavitation conditions. A strong two-way coupling fluid-structure interaction simulation is applied to obtain interior views of the e ects of cavitating bubbles on the flow and structural dynamics of a pump. The renormalization-group k-ε turbulence model and the Zwart–Gerbe–Belamri cavitation model are solved for the fluid side, while a transient structural dynamic analysis is employed for the structure side. The di erent cavitation states are mapped in the head-net positive suction head(H-NPSH) curves and flow field features inside the impeller are fully revealed. Results indicate that cavitating bubbles grow and expand rapidly with decreasing NPSH. In addition, the pressure fluctuations, both in the impeller and volute, are quantitatively analyzed and associated with the cavitation states. It is shown that influence of the cavitation on the flow field is critical, specifically in the super-cavitation state. The e ect of cavitation on the unsteady radial force and blade loads is also discussed. The results indicate that the averaged radial force increased from 8.5 N to 54.4 N in the transition progress from an onset cavitation state to a super-cavitation state. Furthermore, the structural behaviors, including blade deformation, stress, and natural frequencies, corresponding to the cavitation states are discussed. A large volume of cavitating bubbles weakens the fluid forces on the blade and decreases the natural frequencies of the rotor system. This study could enhance the understanding of the e ects of cavitation on pump flow and structural behaviors.

Numerical simulation of unsteady interaction of centrifugal impeller with its diffuser using Lagrangian discrete vortex method

In this study, an advanced Lagrangian vortex- boundary element method is applied to simulate the unsteady impeller-diffuser interactions in a diffuser pump not only for design but also for off-design considerations. In velocity calculations based on the Biot-Savart law we do not have to grid large portions of the flow field and the calculation points are concentrated in the regions where vorticity is present. Lagrangian representation of the evolving vorticity field is well suited to moving boundaries. An integral pressure equation shows that the pressure distribution can be estimated directly from the instantaneous velocity and vorticity field. The numerical results are compared with the experimental data and the comparisons show that the method used in this study can provide us insight into the complicated unsteady impeller-diffuser interaction phenomena in a diffuser pump.

Unsteady aerodynamic forces and power requirements of a bumblebee in forward flight

Aerodynamic forces and power requirements in forward flight in a bumblebee （Bombus terrestris） were studied using the method of computational fluid dynamics. Actual wing kinematic data of free flight were used in the study （the speed ranges from 0 m/s to 4.5 m/s; advance ratio ranges from 0-0.66）. The bumblebee employs the delayed stall mechanism and the fast pitching-up rotation mechanism to produce vertical force and thrust. The leading-edge vortex does not shed in the translatory phase of the half-strokes and is much more concentrated than that of the fruit fly in a previous study. At hovering and low-speed flight, the vertical force is produced by both the half-strokes and is contributed by wing lift; at medium and high speeds, the vertical force is mainly produced during the downstroke and is contributed by both wing lift and wing drag. At all speeds the thrust is mainly produced in the upstroke and is contributed by wing drag. The power requirement at low to medium speeds is not very different from that of hovering and is relatively large at the highest speed （advance ratio 0.66）, i.e. the power curve is Jshaped. Except at the highest flight speed, storing energy elastically can save power up to 20%-30%. At the highest speed, because of the large increase of aerodynamic torque and the slight decrease of inertial torque （due to the smaller stroke amplitude and stroke frequency used）, the power requirement is dominated by aerodynamic power and the effect of elastic storage of energy on power requirement is limited.

Unsteady boundary layer flow and heat transfer over an exponentially shrinking sheet with suction in a copper-water nanofluid

An analysis of unsteady boundary layer flow and heat transfer over an exponentially shrinking porous sheet filled with a copper-water nanofluid is presented.Water is treated as a base fluid.In the investigation,non-uniform mass suction through the porous sheet is considered.Using Keller-box method the transformed equations are solved numerically.The results of skin friction coefficient,the local Nusselt number as well as the velocity and temperature profiles are presented for different flow parameters.The results showed that the dual non-similar solutions exist only when certain amount of mass suction is applied through the porous sheet for various unsteady parameters and nanoparticle volume fractions.The ranges of suction where dual non-similar solution exists,become larger when values of unsteady parameter as well as nanoparticle volume fraction increase.So,due to unsteadiness of flow dynamics and the presence of nanoparticles in flow field,the requirement of mass suction for existence of solution of boundary layer flow past an exponentially shrinking sheet is less.Furthermore,the velocity boundary layer thickness decreases and thermal boundary layer thickness increases with increasing of nanoparticle volume fraction in both non-similar solutions.Whereas,for stronger mass suction,the velocity boundary layer thickness becomes thinner for the first solution and the effect is opposite in the case of second solution.The temperature inside the boundary layer increases with nanoparticle volume fraction and decreases with mass suction.So,for the unsteadiness and for the presence of nanoparticles,the flow separation is delayed to some extent.

NUMERICAL STUDY ON THE UNSTEADY INTERACTION FLOW IN A CENTRIFUGAL COMPRESSOR STAGE

Numerical simulation on the unsteady flow in a centrifugal compressor isperformed, and compared with the experimental data. The influence of the impeller-diffuserinteraction on the flow-fields is discussed, and the reasons for the losses are also explored.Results show that qualitative and quite fair quantitative agreements are achieved between thepredicted and measured flowfields. The influence of the impeller wake on the convexity surface ofdiffuser is great. The potential repercussion of the diffuser on the suction surface of the impelleris much larger than on the pressure surface. Effect of the unsteady interaction is strongest in theradial gap. The unsteady flow itself may compensate for the loss generated in stage, and the stageefficiency is inversely proportional to the entropy production.

An analytical study of unsteady heat transfer in the rock surrounding a deep airway

The heat transfer between an airway and the air flowing though it is an unsteady problem. The governing equation of unsteady heat transfer was solved using the method of separation of variables. The solution is an infinite series including Bessel functions. The theoretical solution was analyzed by solving for the positive roots of the transcendental equation by iteration. The dimensionless surface temperature of the sur- rounding rock is only affected by the Bi number but not by the thermo-physical coefficients of the rock. The dimensionless coefficient of heat transfer, k, decreases with the Fo number similarly to the influence of the Bi number on k. A formula for determining the fully developed stage (FDS) suitable for unsteady heat transfer in the airway is proposed. The FDS from theoretical analysis occurs with Fo from 1.6 to 2. The ratio of excess temperature in the surrounding rock is independent of the initial conditions and only dependent on the Bi number and the relative position in the airway, at the FDS. The calculation error is large when using just the first term from the complete series when Fo is from 2 to 12. Five terms give a solution approximately equal to that found using the complete series. The first term could replace the complete series only when Fo is greater than 12. The FDS plays an important role in predication of the temperature field of the surrounding rock and in simplified calculations.

Mechanism of unsteady aerodynamic heating with sudden change in surface temperature

The characteristics and mechanism of unsteady aerodynamic heating of a transient hypersonic boundary layer caused by a sudden change in surface temperature are studied. The complete time history of wall heat flux is presented with both analytical and numerical approaches. With the analytical method, the unsteady compressible boundary layer equation is solved. In the neighborhood of the initial and final steady states, the transient responses can be expressed with a steady-state solution plus a perturbation series. By combining these two solutions, a complete solution in the entire time domain is achieved. In the region in which the analytical approach is applicable, numerical results are in good agreement with the analytical results, showing reliability of the methods. The result shows two distinct features of the unsteady response. In a short period just after a sudden increase in the wall temperature, the direction of the wall heat flux is reverted, and a new inflexion near the wall occurs in the profile of the thermal boundary layer. This is a typical unsteady characteristic. However, these unsteady responses only exist in a very short period in hypersonic flows, meaning that, in a long-term aerodynamic heating process considering only unsteady surface temperature, the unsteady characteristics of the flow can be ignored, and the traditional quasi-steady aerodynamic heating prediction methods are still valid.

Study of modeling unsteady blade row interaction in a transonic compressor stage part 1:code development and deterministic correlation analysis

The average-passage equation system （APES） provides a rigorous mathematical framework for account- ing for the unsteady blade row interaction through multi- stage compressors in steady state environment by introduc- ing deterministic correlations （DC） that need to be modeled to close the equation system. The primary purpose of this study is to provide insight into the DC characteristics and the influence of DC on the time-averaged flow field of the APES. In Part 1 of this two-part paper, firstly a 3D viscous unsteady and time-averaging flow CFD solver is developed to investi- gate the APES technique. Then steady and unsteady simu- lations are conducted in a transonic compressor stage. The results from both simulations are compared to highlight the significance of the unsteady interactions. Furthermore, the distribution characteristics of DC are studied and the DC at the rotor/stator interface are compared with their spatial cor- relations （SC）. Lastly, steady and time-averaging （employing APES with DC） simulations for the downstream stator alone are conducted employing DC derived from the unsteady re- suits. The results from steady and time-averaging simula- tions are compared with the time-averaged unsteady results. The comparisons demonstrate that the simulation employing APES with DC can reproduce the time-averaged field and the 3D viscous time-averaging flow solver is validated.

Study of modeling unsteady blade row interaction in a transonic compressor stage part 2:influence of deterministic correlations on time-averaged flow prediction

The average-passage equation system （APES） provides a rigorous mathematical framework for account- ing for the unsteady blade row interaction through multistage compressors in steady state environment by introducing de- terministic correlations （DC） that need to be modeled to close the equation system. The primary purpose of this study was to provide insight into the DC characteristics and the in- fluence of DC on the time-averaged flow field of the APES. In Part 2 of this two-part paper, the influence of DC on the time-averaged flow field was systematically studied; Several time-averaging computations boundary conditions and DC were conducted with various for the downstream stator in a transonic compressor stage, by employing the CFD solver developed in Part 1 of this two-part paper. These results were compared with the time-averaged unsteady flow field and the steady one. The study indicat;d that the circumferential- averaged DC can take into account major part of the unsteady effects on spanwise redistribution of flow fields in compres- sors. Furthermore, it demonstrated that both deterministic stresses and deterministic enthalpy fluxes are necessary to reproduce the time-averaged flow field.

An application of interacting shear flows theory: exact solution for unsteady oblique stagnation point flow

An analytical solution of the governing equations of the interacting shear flows for unsteady oblique stagnation point flow is obtained. It has the same form as that of the exact solution obtained from the complete NS equations and physical analysis and relevant discussions are then presented.

Effects of unsteady deformation of flapping wing on its aerodynamic forces

Effects of unsteady deformation of a＇flapping model insect wing on its aerodynamic force production are studied by solving the Navier-Stokes equations on a dynamically deforming grid. Aerodynamic forces on the flapping wing are not much affected by considerable twist, but affected by camber deformation. The effect of combined camber and twist deformation is similar to that of camber deformation. With a deformation of 6% camber and 20% twist （typical values observed for wings of many insects）, lift is increased by 10% - 20% and lift-to-drag ratio by around 10% compared with the case of a rigid fiat-plate wing. As a result, the deformation can increase the maximum lift coefficient of an insect, and reduce its power requirement for flight. For example, for a hovering bumblebee with dynamically deforming wings （6% camber and 20% twist）, aerodynamic power required is reduced by about 16% compared with the case of rigid wings.

Analysis of Unsteady Flow over Offshore Wind Turbines in Combination with Different types of Foundations

Environmental effects have an important influence on Offshore Wind Turbine (OWT) power generation efficiency and the structural stability of such turbines. In this study, we use an in-house Boundary Element (BEM)-panMARE code-to simulate the unsteady flow behavior of a full OWT with various combinations of aerodynamic and hydrodynamic loads in the time domain. This code is implemented to simulate potential flows for different applications and is based on a three-dimensional first-order panel method. Three different OWT configurations consisting of a generic 5 MW NREL rotor with three different types of foundations (Monopile, Tripod, and Jacket) are investigated. These three configurations are analyzed using the RANSE solver which is carried out using ANSYS CFX for validating the corresponding results. The simulations are performed under the same environmental atmospheric wind shear and rotor angular velocity, and the wave properties are wave height of 4 m and wave period of 7.16 s. In the present work, wave environmental effects were investigated firstly for the two solvers, and good agreement is achieved. Moreover, pressure distribution in each OWT case is presented, including detailed information about local flow fields. The time history of the forces at inflow direction and its moments around the mudline at each OWT part are presented in a dimensionless form with respect to the mean value of the last three loads and the moment amplitudes obtained from the BEM code, where the contribution of rotor force is lower in the tripod case and higher in the jacket case and the calculated hydrodynamic load that effect on jacket foundation type is lower than other two cases.