Generation of Dynamic Grids and Computation of Unsteady Transonic Flows around Assemblies

Algebraic methods and rapid deforming techniques are used to generate three-dimensional boundary-fitted dynamic grids for assemblies. The conservative full-potential equation is solved by a time-accurate approximate factorization algorithm and internal Newton iterations. An integral boundary layer method based on the dissipation integral is used to account for viscous effects. The computational results about unsteady transonic forces on wings, bodies and control surfaces are in agreement with experimental data.

Aerodynamic Design for Three-Dimensional Multi-lifting Surfaces at Transonic Flow

An aerodynamic design method and corresponding codes are developed for three-dimensional multi lifting surfaces at transonic flow. It is based on the ＂iterative residual correction＂ concept that is successfully used for transonic wing design and subsonic multi-lifting surface design. The up-wind scheme is introduced into governing equations of multi-lifting surface design method and automatically acted when supersonic flow appears on the surface. A series of interface codes are programmed, including a target-pressure modification tool. Using the improved inverse aerodynamic design code, TAU code and interface codes, the transonic multi-lifting aerodynamic design software system is founded. Two cases of canard-wing configuration have been performed to validate the method and codes. The results show that the convergence of analysis/design iteration is very good at higher speed transonic flow.

Numerical investigation of transonic flow over deformable airfoil with plunging motion

In this article, the transonic inviscid flow over a deformable airfoil with plunging motion is studied numerically. A finite volume method based on the Roe scheme developed in a generalized coordinate is used along with an arbitrary Lagrangian-Eulerian method and a dynamic mesh algorithm to track the instantaneous position of the airfoil. The effects of different governing parameters such as the phase angle, the deformation amplitude, the initial angle of attack, the flapping frequency, and the Mach number on the unsteady flow field and aerodynamic coefficients are investigated in detail. The results show that maneuverability of the airfoil under various flow conditions is improved by the deformation. In addition, as the oscillation frequency of the airfoil increases, its aerodynamic performance is significantly improved.

Solution Method for Singular Initial Value Problems of One-dimensional Steady Transonic Flow in a Dual-mode Scramjet

Singular initial value problems arise in solving one-dimensional steady transonic flow of dualmode scramjet. The existing solution method has the problems of large initial value errors in principles. This paper puts forward an improved algorithm based on variable transformation, and constructs a nonsingular one-dimensional steady transonic flow equation by defining a new variable. The improved algorithm can eliminate the singularity of the differential equation, and can solve the singular initial value problems of one-dimensional steady transonic flow of dual-mode scramjet.

ANISOTROPIC MULTISTAGE FINITE ELEMENT METHOD FOR TWO DIMENSIONAL VISCOUS TRANSONIC FLOW IN TURBOMACHINERY

A new method based on the anisotropic tensor force finite element and Taylor-Galerkin finite element is presented in the present paper.Its application to two-dimensional viscous transonic flow in turbomachinery improves the conver- gence rate and stability of calculation,and the results obtained agree well with the experimental measurements.

Recent Developments of Image Based Measurement Methods for Application to Transonic Flows in Industrial Wind Tunnels

The experimental investigation of unsteady complex flow fields in wind tunnels requires advanced measurement techniques. The most important of such image based measurement techniques are those for the measurement of planar flow velocity fields, planar pressure distribution, model location and deformation, model temperature and quantitative high speed flow visualization. The applications as carried out by DLR range from low speed flows to transonic flows, from high lift configurations to propellers and rotors, from wake vortex investigations in catapult facilities and water towing tanks to investigations of vortex break down phenomena on delta wings. The capability to use image based measurement techniques in transonic flows requires dedicated technical developments and experienced scientists due to the special environment of a transonic wind tunnel. In this paper an overview of the state-of-the art of the application of image based measurement techniques in transonic flows as performed by DLR＇s Institute of Aerodynamics and Flow Technology will be given.

HIGH ORDER ACCURACY SCHEME FOR 2-D TRANSONIC FLOWS

According to Taylor's expansion formula, a kind of derivatives computation method is presented, which can achieve arbitrary order of accuracy. Then it is combined with a flux difference splitting technique and a flux limiter to construct the desiredscheme that is suitable for non-oscillatory shock-capturing calculation. TVD typeRunge-Kutta method is used for temporal discretization. Several steady and unsteadynumerical experiments demonstrate that the scheme is a robust solver for transonicflows with high accuracy and high resolution of shock wave structures.

TIME MARCHING INTEGRAL EQUATION METHOD FOR UNSTEADY TRANSONIC FLOWS

In this paper,we have proposed a time marching intregral equation method which does not have the limitation of the time linearized integral equation method in that the latter method can not satisfac- torily simulate the shock-wave motions.Firstly,a model problem——one dimensional initial and boundary value wave problem is treated to clarify the basic idea of the new method.Then the method is implemented for 2-D and 3-D unsteady transonic flow problems.The introduction of the concept of a qua- si-velocity-potential simplifies the time marching integral equations and the treatment of trailing vortex sheet condition.The numerical calculations show that the method is reasonable and reliable.

NUMERICAL METHOD FOR SOLVING THE EULER EQUATION FOR UNSTEADY TRANSONIC FLOWS OVER OSCILLATING AIRFOILS

Through transformations, the time-dependent boundary condition on the airfoil contour and the boundary condition at infinity are brought fixed to the boundaries of a finite domain. The boundary conditions can thus be satisfied exactly without increasing the computational time. The novel scheme is useful for computing transonic, strong disturbance, unsteady flows with high reduced frequencies. The scheme makes use of curvefitted orthogonal meshes and the lattice control technique to obtain the optimal grid distribution. The numerical results are satisfactory.

TRANSONIC FLOW CALCULATION OF EULER EQUATIONS BY IMPLICIT ITERATING SCHEME WITH FLUX SPLITTING

Three dimensional Euler equations are solved in the finite volume form with van Leer's flux vector splitting technique. Block matrix is inverted by Gauss-Seidel iteration in two dimensional plane while strongly implicit alternating sweeping is implemented in the direction of the third dimension. Very rapid convergence rate is obtained with CFL number reaching the order of 100. The memory resources can be greatly saved too. It is verified that the reflection boundary condition can not be used with flux vector splitting since it will produce too large numerical dissipation. The computed flow fields agree well with experimental results. Only one or two grid points are there within the shock transition zone.

Numerical Analysis of Transonic Flow around Cones

A new solver is presented for transonic flow around cone-cylinder, axisymmetric bodies. Ground experiments almost always suffer from uncertainty due to operating in the presence of high levels of facility noise. Besides, experimental measurements of these mechanisms are not available at high-speed flows. Direct Numerical Simulations have made it possible to compute details of the transonic mechanisms but still a significant challenge due to the cost. This study aims to present a new solver to model transonic flows. To assess the new solver, the surface Mach number and the drag coefficient are investigated as the freestream Mach number varies. The results are in excellent agreement with experimental data, indicating the new model is capable of accurately predicting the aerodynamics coefficients at transonic flow regimes.

A LIMITING VISCOSITY APPROACH TO THE RIEMANN PROBLEM FOR TRANSONIC FLOW

In this paper we have obtained the existence of weak solutions of the small disturbance equations of steady two-dimension flow [GRAPHICS] with Riemann date [GRAPHICS] where v+ greater-than-or-equal-to 0, v- greater-than-or-equal-to 0 and u- less-than-or-equal-to u+ by introducing 'artificial' viscosity terms and employing Helley's theorem. The setting under our consideration is a nonstrictly hyperbolic system. our analysis in this article is quite fundamental.

Fourier time spectral method for subsonic and transonic flows

The time accuracy of the exponentially accurate Fourier time spectral method（TSM） is examined and compared with a conventional 2nd-order backward difference formula（BDF） method for periodic unsteady flows. In particular, detailed error analysis based on numerical computations is performed on the accuracy of resolving the local pressure coefficient and global integrated force coefficients for smooth subsonic and non-smooth transonic flows with moving shock waves on a pitching airfoil. For smooth subsonic flows, the Fourier TSM method offers a significant accuracy advantage over the BDF method for the prediction of both the local pressure coefficient and integrated force coefficients. For transonic flows where the motion of the discontinuous shock wave contributes significant higherorder harmonic contents to the local pressure fluctuations,a sufficient number of modes must be included before the Fourier TSM provides an advantage over the BDF method.The Fourier TSM, however, still offers better accuracy than the BDF method for integrated force coefficients even for transonic flows. A problem of non-symmetric solutions for symmetric periodic flows due to the use of odd numbers of intervals is uncovered and analyzed. A frequency-searching method is proposed for problems where the frequency is not known a priori. The method is tested on the vortex shedding problem of the flow over a circular cylinder.

Improved local amplification factor transport equation for stationary crossflow instability in subsonic and transonic flows

Transition prediction is a hot research topic of fluid mechanics.For subsonic and transonic aerodynamic flows,e^(N) method based on Linear Stability Theory(LST)is usually adopted reliably to predict transition.In 2013,Coder and Maughmer established a transport equation for Tollmien-Schlichting(T-S)instability so that the e^(N) method can be applied to general Reynolds-Average-Navier-Stokes(RANS)solvers conveniently.However,this equation focuses on T-S instability,and is invalid for crossflow instability induced transition which plays a crucial role in flow instability of three-dimensional boundary layers.Subsequently,a transport equation for crossflow instability was developed in 2016,which is restricted to wing-like geometries.Then,in 2019,this model was extended to arbitrarily shaped geometries based on local variables.However,there are too many tedious functions and parameters in this version,and it can only be used for incompressible flows.Hence,in this paper,after a large amount of LST analyses and parameter optimization,an improved version for subsonic and transonic boundary layers is built.The present improved model is more robust and more concise,and it can be applied widely in aeronautical flows,which has great engineering application value and significance.An extensive validation study for this improved transition model will be performed.

Effects of Heterogeneous Condensation on the Transonic Flow Fields on a Bump Model

In the present study, effect of the heterogeneous condensation on the characteristics of shock wave generated on the bump model in the transonic flow field was investigated numerically. As a result, it was found that, for the flow field with steady adiabatic shock wave on the bump model, the condensation with heterogeneous nucleation has a strong effect on the whole flow field, and it reduced the strength of the shock. Furthermore, the total pressure loss was dependent on the concentration of the solid particles per unit volume.

Liquid Phase Evaporation on the Normal Shock Wave in Moist Air Transonic Flows in Nozzles

This paper presents a numerical analysis of the atmospheric air transonic flow through de Laval nozzles. By nature, atmospheric air always contains a certain amount of water vapor. The calculations were made using a Laval nozzle with a high expansion rate and a convergent-divergent(CD) "half-nozzle", referred to as a transonic diffuser, with a much slower expansion rate. The calculations were performed using an in-house CFD code. The computational model made it possible to simulate the formation of the liquid phase due to spontaneous condensation of water vapor contained in moist air. The transonic flow calculations also take account of the presence of a normal shock wave in the nozzle supersonic part to analyze the effect of the liquid phase evaporation.

Computations of unsteady transonic flow over airfoil at low Reynolds number

Transonic flow over a thin airfoil at low Reynolds number was studied numerically by directly solving two-dimensional full Navier-Stokes equations through 5th order weighted essentially non-oscillatory(WENO) scheme without using any turbulence model.A series of distinguished unsteady phenomena for a thin 2-D transonic airfoil flow were presented.Due to continuous adverse pressure gradient in the subsonic flow downstream of the sonic line,the unsteady separated boundary layer with main vortex and secondary vortex was developed at the rear of the airfoil.At the trailing edge,the vortex-shedding was characterized by periodical connection of the main vortex and secondary vortex on the other side of the airfoil.The unsteady separation and vortex-shedding occurred with the same period.On the airfoil surface,the average pulse pressure related to the unsteady supersonic region was obviously smaller than that related to the vortex-shedding at the trailing edge.With the attack angle increasing from 0°to 2°,the frequency of vortex-shedding decreases about 4.2%.At last,the turbulence intensity and many second-order statistics in the wake region were investigated.

AN EFFICIENT METHOD FOR SOLVING THE MIXED DIRECT-INVERSE PROBLEM OF THE TRANSONIC ROTATIONAL FLOW IN PLANE CASCADES

The method in [1] has been extended to the case of rotational flow in this paper. A new method for dealing with the shock wave is presented. This method has the advantages of both the shock-fitting and the shock capturing methods. The direct problem and the mixed direct-inverse prob- lem of the rotational flow in a transonic plane cascade at both design and off design conditions are solved, and the results show that the present method has rapid convergence rate and high accuracy even for the flow with moderately strong shocks. The calculations have been carried out on the DPS-8 computer, and for the direct problem, only 50-80 iterations are needed, and 50-80 seconds of CPU time are required.

Control of Transonic Flow Fields Using Local Occurrence of Non-Equilibrium Condensation

Control of supersonic flow fields with shock wave is important for some industrial fields. There are many studies for control of the supersonic flow fields using active or passive control. When non-equilibrium condensation occurs in a supersonic flow field, the flow is affected by latent heat released. Many studies for the condensation have been conducted and the characteristics have been almost clarified. Further, it was found that non-equilibrium condensation can control the flow field. In these studies, the condensation occurs across the passage of the flow field and it causes the total pressure loss in the flow field. However, local occurrence of non-equilibrium condensation in the flow field may change the characteristics of total pressure loss compared with that by the condensation across the passage of the nozzle and there are few for researches of locally occurred non-equilibrium condensation in supersonic flow field. The purpose in the present study is to clarify the effect of local occurrence of non-equilibrium condensation on the transonic flow field in a nozzle with a circular bump. As a result, local occurrence of non-equilibrium condensation reduced the shock strength and total pressure loss in the transonic flow field by flowing the moist air from trailing edge of the circular bump to the mainstream.

Influence of Air Humidity on Transonic Flows with Weak Shock Waves

The paper presents CFD results for the transonic flow of dry and moist air through a diffuser and a compressor rotor.In both test geometries,i.e.the Sajben transonic diffuser and the NASA Rotor 37,the air humidity impact on the structure of flows with weak shock waves was examined.The CFD simulations were performed by means of an in-house CFD code,which was the RANS-based modelling approach to compressible flow solutions.It is shown that at high values of relative humidity,above 70%,the modelling of the transonic flow field with weak shock waves by means of the dry air model may produce wrong results.