A New Turbulence Model For External Flow Simulation Of Aircraft

Most of the aircraft external flow fields are turbulent, so an accurate mathematical physicsmodel of turbulent flows is necessary for increasing the simulate precision. Currently, aircraftexternal flows are mainly simulated with Reynolds Averaged Navier-Stokes (RANS) methodto model the turbulence, where turbulence models play a very important role on enhancing thesimulate accuracy of turbulent flows. Most of turbulence models are conventionallymathematical models and the natural physical mechanism of turbulence flows are technicallylimited or even neglectd.In recent years, for the purpose of increasing the simulation precision of turbulent flows,an evolution of turbulence models and Reynolds stress constitutive equation: from algebraicmodels to differential equations models and linear hypothesis to nonlinear hypothesis, hasenhanced the fidelity of simulation results of flows with separation, transition and strongcurvature. However, all of these enhancements are usually at the cost of reducing robustnessand adding equations to be solved. Meanwhile, with the help of fast development of highperformance computing technology, optimization design system can be sometimes used inaircraftdesign.Optimizationsystemusuallyneedstoruntheflowsimulationmodulefrequentlyin order to decide the optimum searching direction. Consequently, flow simulation methods areimportant segment of aircraft aerodynamic shape design, the aircraft design period and costmust be reduced and the optimization process must be accelerated by enhancing the precisionandefficiencyofflowsimulation.Foroptimizationsystems,turbulenceflowequationreductiongains little reduction of time cost, while it significantly affects the number of iterations inoptimization process. Constructing a turbulent model balancing the calculation efficiency andprecision is necessary and important for aircraft design.In this paper the author tried to construct a one-equation high precision turbulent modelapplying to aircraft design. This dissertation finishes the works as following:1.The closed problem about Reynolds stress is discussed base on the introduction of somefrequently used turbulent models for aircraft external flows simulation. Moreover, the crossdiffusion term in two-equation turbulent model is particularly deduced in this paper in orderto show the effect of this term in reducing the freestream sensibility of the original model;2. A scale-adaptive kinetic energy transport equation is raised. The turbulent kinetictransport equation obtained by Prandtl is closed using algebraic diffusion rate of turbulentkinetic energy. The turbulent diffusion rate is divided into two parts including regions near wallboundary and regions in far field. Von Karman length scale is adopted to automatically adapt the scale of flow during iterations;3. An improved Bradshaw assumption is put forward. The hypothesis of Bradshaw isdemarcated using the DNS data of turbulent plate and the demarcated curve is fitted by usingthe structural ensemble theory to get the new hypothesis of Bradshaw. An improved Reynoldsstrain constitutive equation can be obtained based on this new hypothesis. While this newhypothesis is based on standard boundary layer flows, the posterior results also indicate thatthis hypothesis can be used to various complex steady and unsteady flows;4. A Kinetic energy Dependent Only (KDO) model is raised and validated by some test-cases. The fully turbulent flat plate test case shows that the KDO model can precisely reflectlog-law in the turbulent boundary layer, and also demonstrates that the KDO model has lowergrid sensitivity and better convergence ability compared with other pertinent turbulent models.Some numerical experimental tests support that the KDO model meets the basic requirementsof a turbulent model;5. Many classic aircraft external flow test cases are simulated by the KDO model. In two-dimension external flow test-cases, the computation of the NACA0012airfoil and the RAE2822airfoil in the transonic condition shows that the KDO model can capture the shock wavesat an acceptable precision. The lift coefficient curve of airfoil NACA0012computed using theKDO model at low Mach number condition has showed a favorably good agreement withexperimental data at the linear segment. The test case of the A-foil shows that the KDO modelis able to predict the free shear flow at a high precision; The test case of three-element airfoiland the NACA4412with separation bubble at the trailing edge indicates that the KDO modelhas a good prediction in terms of flows with little and middle separation regions and adversepressure gradient. In three-dimensional external flowtestcases,the computationofthe M6wingand the DLR-F6shows that the KDO model is competent to precisely predict the complex threedimensional flows, such as the interaction between shock waves and boundary layer; the VFE-2triangle wing test case shows that the KDO model is able to simulate the stability of turbulentvortices. The test case of blended pipe flow demonstrates that the KDO model can reflect thecurvature effect to some extent, which indicates that the improved Reynolds strain constitutiveequation has wide adaptability;6. A transition prediction framework base on the KDO model is rasied. The von Karmanlength scale can be changed accordingly to simulate the intermittency factor and dampingfunction. The KDO model is able to predict some simple transition phenomenon. The test casesofnaturaltransitionplateandbypasstransitionplateshowtheacceptablecomputationprecisionof the KDO model, which implies the potential of future development of the KDO model to adapt to the transition problems;7.Amethod for Detached Eddy Simulation (or DES) named DFSM method is put forward.The two classic branches of the DES and FSM method included in the hybrid RANS/LESmethod have been verified and the flaws the two methods are fixed. The DFSM with delayedeffect is presented as well. The test-case of plate boundary layer simulation demonstrates thatthis method can reduce the modelled stress dissipation and has a good computational precisionfor unsteady turbulent flow;8. Satisfactory results of wing at stall angle can be obtained by using the unsteady KDOmodel, which indicates that the KDO model has the ability of solving both the steady andunsteady flow. The SAS method is also introduced and test cases show that SAS model canavoid the flaw of modelled stress dissipation with well corrected source term.