Transition study of 3D aerodynamic configures using improved transport equations modeling

As boundary layer transition plays an important role in aerodynamic drag prediction,the proposal and study of transition prediction methods simulating the complex flow phenomena are prerequisite for aerodynamic design. In this paper, with the application of the linear stability theory based on amplification factor transport transition equations on the two-equation shear stress transport(SST) eddy-viscosity model, a new method, the SST-N TS-N CF model, is yielded. The new amplification factor transport equation for the crossflow instability induced transition is proposed to add to the N TS equation proposed by Coder, which simulates Tollmien–Schlichting wave transition. The turbulent kinetic energy equation is modified by introducing a new source term that simulates the transition process without the intermittency factor equation. Finally, coupled with these two amplification factor transport equations and SST turbulence model, a four-equation transition turbulence model is built. Comparisons between predictions using the new model and wind-tunnel experiments of NACA64(2)A015, NLF(2)-0415 and ONERA-D infinite swept wing and ONERAM6 swept wing validate the predictive quality of the new SST-N_(TS)-N_(CF) model.     

ON THE PERTURBATION EQUATION OF NAVIER-STOKES EQUATION

The perturbation equation of the Navier-Stokes equation is obtained by superimposing a noise field on to a flow field. Because of the interaction between viscosity and the perturbation displacement,the equation simultaneously the properties of dissipation and dispersion. It reveals the following important physical features of turbulence: the mechanism of transition and intermittency, which arises from a composite spatio-temporai instability mainly due to the interaction between viscosity and positive dispersion; and the relationship between negative dispersion and turbulent energy inversion.     

DIGITAL GENERATION OF TWO-DIMENSIONAL FIELD OF TURBULENCE FOR FLIGHT SIMULATION

In some special cases of flight simulation (e.g. for formation flight, in-flight tanking) it is required to generate a two-dimensional field of turbulence, in which the turbulent wind speeds are stochastic functions of two coordinates (e.g. x in the flight direction and y in the wing span direction). For this purpose a simple and efficient technique for the digital generation of a two-dimensional field of turbulence,i.e. for the production of turbulent speed sequences on a rectangular network, is proposed in this paper. The correlation of the turbulent field so generated is found to be in good agreement with the theoretical correlation of the turbulence model, and thus the feasibility of the proposed method is verified. Two possible operation modes (off-line and on-line) of the turbulence generator in flight simulation are also discussed.     

Boundary-layer transition prediction using a simplified correlation-based model

This paper describes a simplified transition model based on the recently developed correlation-based c ? Reht transition model. The transport equation of transition momentum thick-ness Reynolds number is eliminated for simplicity, and new transition length function and critical Reynolds number correlation are proposed. The new model is implemented into an in-house com-putational fluid dynamics (CFD) code and validated for low and high-speed flow cases, including the zero pressure flat plate, airfoils, hypersonic flat plate and double wedge. Comparisons between the simulation results and experimental data show that the boundary-layer transition phenomena can be reasonably illustrated by the new model, which gives rise to significant improvements over the fully laminar and fully turbulent results. Moreover, the new model has comparable features of accuracy and applicability when compared with the original c ? Reht model. In the meantime, the newly proposed model takes only one transport equation of intermittency factor and requires fewer correlations, which simplifies the original model greatly. Further studies, especially on separation-induced transition flows, are required for the improvement of the new model.     

NUMERICAL CALCULATIONS OF GASEOUS REACTING FLOWS IN A MODEL OF GAS TURBINE COMBUSTORS

This paper describes the numerical calculations of gaseous reaction flows in a model of gas turbine combustors. The profiles of hydrodynamic and thermodynamic patterns in a three-dimensional combustor model are obtained by solving the governing differential transport equations. The well-established numerical prediction algorithm SIMPLE, the modified k-ε turbulence model and k-ε-g turbulent diffusion flame model have been adopted in computations. The β function has been selected as probability density function. The effect of combustion process on flow patterns has been investigated. The calculated results have been verified by experiments. They are in remarkably good agreement.     

Numerical study of compression corner flowfield using Gao-Yong turbulence model

A numerical simulation of shock wave turbulent boundary layer interaction induced by a 24° compression corner based on Gao-Yong compressible turbulence model was presented.The convection terms and the diffusion terms were calculated using the second-order AUSM (advection upstream splitting method) scheme and the second-order central difference scheme,respectively.The Runge-Kutta time marching method was employed to solve the governing equations for steady state solutions.Significant flow separation-region which indicates highly non-isotropic turbulence structure has been found in the present work due to intensity interaction under the 24° compression corner.Comparisons between the calculated results and experimental data have been carried out,including surface pressure distribution,boundary-layer static pressure profiles and mean velocity profiles.The numerical results agree well with the experimental values,which indicate Gao-Yong compressible turbulence model is suitable for the prediction of shock wave turbulent boundary layer interaction in two-dimensional compression corner flows.      

A study on turbulence transportation and modification of Spalart–Allmaras model for shock-wave/turbulent boundary layer interaction flow

It is of great significance to improve the accuracy of turbulence models in shock-wave/ boundary layer interaction flow. The relationship between the pressure gradient, as well as the shear layer, and the development of turbulent kinetic energy in impinging shock-wave/turbulent boundary layer interaction flow at Mach 2.25 is analyzed based on the data of direct numerical simulation(DNS). It is found that the turbulent kinetic energy is amplified by strong shear in the separation zone and the adverse pressure gradient near the separation point. The pressure gradient was non-dimensionalised with local density, velocity, and viscosity. Spalart–Allmaras(S–A) model is modified by introducing the non-dimensional pressure gradient into the production term of the eddy viscosity transportation equation. Simulation results show that the production and dissipation of eddy viscosity are strongly enhanced by the modification of S–A model. Compared with DNS and experimental data, the wall pressure and the wall skin friction coefficient as well as the velocity profile of the modified S–A model are obviously improved. Thus it can be concluded that the modification of S–A model with the pressure gradient can improve the predictive accuracy for simulating the shock-wave/turbulent boundary layer interaction.     

ALGEBRAIC TURBULENCE MODEL WITH MEMORY FOR COMPUTATION OF 3-D TURBULENT BOUNDARY LAYERS WITH VALIDATION

Additional equations were found based on experiments for an algebraic turbulence model to improve the prediction of the behavior of three dimensional turbulent boundary layers by taking account of the effects of pressure gradient and the historical variation of eddy viscosity, so the model is with memory. Numerical calculation by solving boundary layer equations was carried.out for the five pressure driven three dimensional turbulent boundary layers developed on flat plates, swept-wing, and prolate spheroid in symmetrical plane. Comparing the computational results with the experimental data, it is obvious that the prediction will be more accurate if the proposed closure equations are used, especially for the turbulent shear stresses.     

Evaluation of Turbulence Models in Predicting Hypersonic and Subsonic Base Flows Using Grid Adaptation Techniques

The flows behind the base of a generic rocket, at both hypersonic and subsonic flow conditions, are numerically studied. The main concerns are addressed to the evaluation of turbulence models and the using of grid adaptation techniques. The investiga- tion focuses on two configurations, related to hypersonic and subsonic experiments. The applicability tests of different turbulence models are conducted on the level of two-equation models calculating the steady state solution of the Reynolds-averaged Navier-Stokes(RANS) equations. All used models, the original Wilcox k-ω, the Menter shear-stress transport (SST) and the explicit algebraic Reynolds stress model(EARSM) formulation, predict an asymmetric base flow in both cases caused by the support of the models. A comparison with preliminary experimental results indicates a preference for the SST and EARSM results over the results from the older k-ω model. Sensitivity studies show no significant influence of the grid topology or the location of the laminar to turbulent transition on the base flow field, but a strong influence of even small angles of attack is reported from the related experiments.     

Numerical study of transonic separation flow using an anisotropic turbulence model

A transonic turbulent separation flow in a converging-diverging transonic diffuser was studied, when there existed a separation bubble on the top wall of the diffuser triggered by strong shock-wave-boundary-layer-interaction (SWBLI). To capture the essential behavior of this complex flow, the current study utilized an anisotropic turbulence model developed on the basis of a statistical partial average scheme. The first order moment of turbulent fluctuations, retained by a novel average scheme, and the turbulent length scale, can be determined from the momentum equations and mechanical energy equation of the fluctuation flow, respectively. The two physical quantities were readily used to construct the nonlinear anisotropic eddy viscosity tensor and to significantly improve the computational results. Comparisons between the computational results and experimental data were carried out for velocity profiles, pressure distribution, skin friction coefficient, Reynolds stress as well as streamline vectors distribution. Without using any empirical coefficients and wall functions, the numerical results were in good agreement with the available experimental data, further confirming that the nonlinear anisotropic eddy viscosity tensor is the decisive factor for the success of the computational results.     

NUMERICAL MODELING OF TURBULENTEVAPORATING GAS-DROPLET TWO-PHASE FLOWS IN AN AFTERBURNER DIFFUSOR OF TURBO-FAN JET ENGINES

The two-dimensional turbulent evaporating gas-droplet two-phase flows in an afterburner diffusor of turbo-fan jet engines are simulated by the k-ε turbulence model and the particle trajectory model. Comparison of predicted gas velocity and temperature distributions with experimental results for the cases without liquid spray shows pretty good agreement. Gas-droplet two-phase flow predictions give plausible droplet trajectories, fuel-vapor concentration distribution, gas-phase velocity and temperature field in presence of liquid droplets. One run of computation with this method is made for a particular afterburner. The results indicate that the location of the atomizers is not favorable to flame stabilization and combustion efficiency. The proposed numerical modeling can also be adopted for optimization design and performance evaluation of afterburner combustors of turbo-fan jet engines.     

Modeling and Control for Magnetostrictive Hysteresis

To deal with the rate-dependent hysteresis presented in a magnetostrictive actuator, a new method of modeling and control is pro-posed. The relationship between inputs and outputs of the actuator is approximately described by a dynamic differential equation with two rate-dependent coefficients, each expressed as a polynomial of frequency. For a given frequency, the coefficients will be able to be estimated by approximating the experimental data of the outputs of the magnetostrictive actuator. Based on this model, a quasi-PID con-troller is designed. In the space of the coefficients and frequency, the stable domain of closed loop system with hysteresis is analyzed. The numerical simulation and experiments have born witness to the feasibility of the proposed new method.     

Secondary instability of separated shear layers

The process through which a laminar flow undergoes transition to turbulence is of great fundamental and practical interest. Such a process is hugely complex as there are many diverse routes for a laminar flow to become turbulent flow. The transition process is usually initiated by flow instabilities—a primary instability stage followed by a secondary instability stage. This forms a rational framework for the early stage of a transition process and it is crucially important to understand the physics of instabilities leading to turbulence. This article reviews the results of studies on secondary instability of separated shear layers in separation bubbles and summaries the current status of our understanding in this area.     

基于静强度分布的复合材料疲劳寿命分布的预测模型(英文)

The reasons of the static strength dispersion and the fatigue life dispersion of composite laminates are analyzed in this article. It is concluded that the inner original defects, which derived from the manufacturing process of composite laminates, are the common and major reason of causing the random distributions of the static strength and the fatigue life. And there is a correlative relation between the two distributions. With the study of statistical relationship between the fatigue loading and the fatigue life in the uniform confidence level and the same survival rate S-N curves of material, the relationship between the static strength distribution and the fatigue life distribution through a material S-N curve model has been obtained. And then the model which is used to describe the distributions of fatigue life of composites, based on their distributions of static strength, is set up. This model reasonably reflects the effects of the inner original defects on the static strength dispersion and on the fatigue life dispersion of composite laminates. The experimental data of three kinds of composite laminates are employed to verify this model, and the results show that this model can predict the random distributions of fatigue life for composites under any fatigue loads fairly well.     

On developing data-driven turbulence model for DG solution of RANS

High-order Discontinuous Galerkin(DG) methods have been receiving more and more attentions in the area of Computational Fluid Dynamics(CFD) because of their high-accuracy property. However, it is still a challenge to obtain converged solution rapidly when solving the Reynolds Averaged Navier–Stokes(RANS) equations since the turbulence models significantly increase the nonlinearity of discretization system. The overall goal of this research is to develop an Artificial Neural Networks(ANNs) model with low complexity acting as an algebraic turbulence model to estimate the turbulence eddy viscosity for RANS. The ANN turbulence model is off-line trained using the training data generated by the widely used Spalart–Allmaras(SA) turbulence model before the Optimal Brain Surgeon(OBS) is employed to determine the relevancy of input features.Using the selected relevant features, a fully connected ANN model is constructed. The performance of the developed ANN model is numerically tested in the framework of DG for RANS, where the‘‘DG+ANN" method provides robust and steady convergence compared to the ‘‘DG+SA" method. The results demonstrate the promising potential to develop a general turbulence model based on artificial intelligence in the future given the training data covering a large rang of flow conditions.     

Characteristics of reattached boundary layer in shock wave and turbulent boundary layer interaction

The reattached boundary layer in the interaction of an oblique shock wave with a flatplate turbulent boundary layer at Mach number 2.25 is studied by means of Direct Numerical Simulation(DNS). The numerical results are carefully compared with available experimental and DNS data in terms of turbulence statistics, wall pressure and skin friction. The coherent vortex structures are significantly enhanced due to the shock interaction, and the reattached boundary layer is characterized by large-scale...     

Numerical study of corner separation in a linear compressor cascade using various turbulence models

Three-dimensional corner separation is a common phenomenon that significantly affects compressor performance.Turbulence model is still a weakness for RANS method on predicting corner separation flow accurately.In the present study,numerical study of corner separation in a linear highly loaded prescribed velocity distribution(PVD) compressor cascade has been investigated using seven frequently used turbulence models.The seven turbulence models include Spalart–Allmaras model,standard k–e model,realizable k–e model,standard k–x model,shear stress transport k–x model,v~2–f model and Reynolds stress model.The results of these turbulence models have been compared and analyzed in detail with available experimental data.It is found the standard k–e model,realizable k–e model,v~2–f model and Reynolds stress model can provide reasonable results for predicting three dimensional corner separation in the compressor cascade.The Spalart–Allmaras model,standard k–x model and shear stress transport k–x model overestimate corner separation region at incidence of 0°.The turbulence characteristics are discussed and turbulence anisotropy is observed to be stronger in the corner separating region.     

Dynamic modeling of a hose-drogue aerial refueling system and integral sliding mode backstepping control for the hose whipping phenomenon

Dynamic modeling of a hose-drogue aerial refueling system（HDARS） and an integral sliding mode backstepping controller design for the hose whipping phenomenon（HWP） during probe-drogue coupling are studied. Firstly, a dynamic model of the variable-length hose-drogue assembly is built for the sake of exploiting suppression methods for the whipping phenomenon.Based on the lumped parameter method, the hose is modeled by a series of variable-length links connected with frictionless joints. A set of iterative equations of the hose＇s three-dimensional motion is derived subject to hose reeling in/out, tanker motion, gravity, and aerodynamic loads accounting for the effects of steady wind, atmospheric turbulence, and tanker wake. Secondly,relying on a permanent magnet synchronous motor and high-precision position sensors, a new active control strategy for the HWP on the basis of the relative position between the tanker and the receiver is proposed. Considering the strict-feedback configuration of the permanent magnet synchronous motor, a rotor position control law based on the backstepping method is designed to insure global stability. An integral of the rotor position error and an exponential sliding mode reaching law of the current errors are applied to enhance control accuracy and robustness. Finally,the simulation results show the effectiveness of the proposed model and control laws.     

Improvement of Baldwin-Lomax turbulence model for supersonic complex flows

Entropy represents the dissipation rate of energy. Through direct numerical simulation (DNS) of supersonic compression ramp flow, we find the value of entropy is monotonously decreasing along the wall-normal direction no matter in the attached or the separated region. Based on this feature, a new version of Baldwin-Lomax turbulence model (BL-entropy) is proposed in this paper. The supersonic compression ramp and cavity-ramp flows in which the original Baldwin-Lomax model fails to get convergent solutions are chosen to evaluate the performance of this model. Results from one-equation Spalart-Allmaras model (SA) and two-equation Wilcox k-x model are also included to compare with available experimental and DNS data. It is shown that BLentropy could conquer the essential deficiency of the original version by providing a more physically meaningful length scale in the complex flows. Moreover, this method is simple, computationally efficient and general, making it applicable to other models related with the supersonic boundary layer.     

CFD Study of NO_x Emissions in a Model Commercial Aircraft Engine Combustor

Air worthiness requirements of the aircraft engine emission bring new challenges to the combustor research and design. With the motivation to design high performance and clean combustor, computational fluid dynamics (CFD) is utilized as the powerful design approach. In this paper, Reynolds averaged Navier-Stokes (RANS) equations of reactive two-phase flow in an experimental low emission combustor is performed. The numerical approach uses an implicit compressible gas solver together with a Lagrangian liquid-phase tracking method and the extended coherent flamelet model for turbulence-combustion interaction. The NOx formation is modeled by the concept of post-processing, which resolves the NOx transport equation with the assumption of frozen temperature distribution. Both turbulence-combustion interaction model and NOx formation model are firstly evaluated by the comparison of experimental data published in open literature of a lean direct injection (LDI) combustor. The test rig studied in this paper is called low emission stirred swirl (LESS) combustor, which is a two-stage model combustor, fueled with liquid kerosene (RP-3) and designed by Beihang University (BUAA). The main stage of LESS combustor employs the principle of lean prevaporized and premixed (LPP) concept to reduce pollutant, and the pilot stage depends on a diffusion flame for flame stabili-zation. Detailed numerical results including species distribution, turbulence performance and burning performance are qualita-tively and quantitatively evaluated. Numerical prediction of NOx emission shows a good agreement with test data at both idle condition and full power condition of LESS combustor. Preliminary results of the flame structure are shown in this paper. The flame stabilization mechanism and NOx reduction effort are also discussed with in-depth analysis.