Gecheng Zha

Improvement of Stability and Accuracy for Weighted Essentially Nonoscillatory Scheme

This paper studies the weights stability and accuracy of the implicit fifth-order weighted essentially nonoscillatory finite difference scheme. It is observed that the weights of the Jiang-Shu weighted essentially nonoscillatory scheme oscillate even for smooth flows. An increased e value of 10 -2 is suggested for the weighted essentially nonoscillatory smoothness factors, which removes the weights oscillation and significantly improves the accuracy of the weights and solution convergence. With the improved e value, the weights achieve the optimum value with minimum numerical dissipation in smooth regions and maintain the sensitivity to capture nonoscillatory shock profiles for the transonic flows. The theoretical justification of this treatment is given in the paper. The wall surface boundary condition uses a half-point mesh so that the conservative differencing can be enforced. A third-order accurate finite difference scheme is given to treat wall boundary conditions. The implicit time-marching method with unfactored Gauss-Seidel line relaxation is used with the high-order schemes to achieve a high convergence rate. Several transonic cases are calculated to demonstrate the robustness, efficiency, and accuracy of the methodology.

High-Performance Supersonic Missile Inlet Design Using Automated Optimization

A multilevel design strategy for supersonic missile inlet design is developed. The multilevel design strategy combines an efe cient simple physical model analysis tool and a sophisticated computational e uid dynamics (CFD) Navier ‐ Stokes analysis tool. The efe cient simple analysis tool is incorporated into the optimization loop, and the sophisticated CFD analysis tool is used to verify, select, and e lter the e nal design. The genetic algorithms and multistart gradient line search optimizers are used to search the nonsmooth design space. A geometry model for the supersonic missile inlet is developed. A supersonic missile inlet that starts at Mach 2.6 and cruises at Mach 4 was designed. Signie cant improvement of the inlet total pressure recovery has been obtained. Detailed e owe eld analysis is also presented.

General Subdomain Boundary Mapping Procedure for Structured Grid Implicit CFD Parallel Computation

In the present work, a general subdomain boundary mapping procedure has been developed for arbitrary topology multiblock structured grids with grid points matched on subdomain boundaries. The interface of two adjacent blocks is uniquely defined according to each local mesh index system, which is specified independently.A pack/unpack procedure basedonthedefinitionoftheinterfaceisdevelopedtoexchangethedatainaone-dimensional array to minimize data communication. A secure send/receive procedure is employed to remove the possibility of blocked communication and achieve optimum parallel computationefficiency.Twoterms,“order”and“orientation”,areintroducedasthelogicsdefiningthe relationship of adjacent blocks. The procedure is applied to parallelize a three-dimensional Navier‐Stokes code, which uses an implicit time marching scheme with line Gauss‐Seidel iteration. The partitioning of the implicit matrix is done by discarding the corner matrices, which is easily implemented and is shown to have a small negative effect on the convergence rate. The message passing interface protocol is used for communicating the data. The numerical experiments presented in this paper include two- and three-dimensional flows using Reynolds averaged Navier‐Stokes equations and a detached eddy simulation with a fifth-orderweightedessentiallynon-oscillatoryscheme.Numericalexperimentsonamessage passing interface based computer cluster show that this general mapping algorithm is robust and has high parallel computing efficiency.

Calculation of Transonic Internal Flows Using an Efficient High-Resolution Upwind Scheme

A new efficient upwind scheme based on the concept of convective upwind and split pressure is developed. The upwinding of the convective term and the pressure split are consistent with their characteristic directions. The scheme has low diffusion to resolve accurately wall boundary layers and is able to capture crisp shock waves and exact contact discontinuities. The accuracy of the scheme is compared with other popularly used schemes including the Roe scheme, the Lious latest advection upstream splitting method scheme (AUSM + ), the Van Leer scheme, and the Van Leer-Hanel scheme. The new scheme is tested for the one-dimensional Sod shock tube problem, one-dimensional slowly moving contact surface, supersonic flat plate laminar boundary layer, a transonic nozzle with oblique shock waves and reflections that do not align with the mesh lines, and a transonic inlet diffuser with shock wave/turbulent boundary-layer interaction

Calculation of transonic flows using WENO method with a low diffusion E-CUSP upwind scheme

A low difiusion E-CUSP (LDE) scheme is applied with 5th order WENO scheme in this paper. The E-CUSP scheme can capture crisp shock proflle and exact contact surface. Several numerical cases are presented to demonstrate the accuracy and robustness for the E-CUSP scheme to be used with the WENO strategy.

Large eddy simulation using a new set of sixth order schemes for compressible viscous terms

A set of conservative sixth order central differencing schemes is suggested for compressible flows with variable viscosity coefficient. This new set of central differencing schemes has the stencil width matching that of the seventh order weighted essentially non-oscillatory scheme (WENO). This feature is important to maintain the compactness of the seventh order WENO scheme and facilitate boundary condition treatment. As an application example, a large eddy simulation (LES) is conducted for a cylinder flow using the seventh order WENO scheme for the convective terms and the new set of sixth order central differencing scheme for the viscous terms. The results are compared with those from other research groups and those obtained using the fifth order WENO scheme and fourth order central differencing.

High-Performance Airfoil Using Coflow Jet Flow Control

T O ACHIEVE revolutionary aircraft performance, advanced technologies should be pursued to drastically reduce the weight of aircraft and fuel consumption and significantly increase aircraft mission payload and maneuverability. Both the military and commercial aircraft will benefit from the same technology. Flow control is a promising technology to break through the limits of the conventional aerodynamic concepts. Recently, a novel active airfoil flow control concept with zero-net mass flux, the coflow jet (CFJ) airfoil, has been developed by Zha et al. [1–5]. The CFJ airfoil achieves three effects simultaneously in a dramatic fashion: lift augmentation, stall margin increase, and drag reduction. The energy expenditure of the CFJ airfoil is low [1], and the CFJ airfoil concept is straightforward to implement. The CFJ airfoil may create a new concept of an “engineless” airplane, which uses the CFJ to generate both lift and thrust without conventional propulsion systems of propellers or jet engines [6]. A CFJ airfoil [1–5] uses an injection slot near the leading edge (LE) and a suction slot near the trailing edge (TE) on the airfoil suction surface. Similar to tangential blowing, the LE jet is in the same direction of the main flow, but the same amount of mass flow that is injected is removed via suction near the TE, resulting in zeronet mass-flux flow control. A proposed fundamental mechanism [2] is that the severe adverse pressure gradient on the suction surface strongly augments turbulent mixing between the main flow and the jet [7]. The mixing then creates the lateral transport of energy from the jet to the main flow and enables the main flow to overcome the large adverse pressure gradient and remain attached at high angle of attack (AOA). The stall margin is hence significantly increased. At the same time, the high-momentum jet drastically increases the circulation, which significantly augments lift, reduces drag, or even generates thrust (negative drag). The objective of this paper is to demonstrate the high performance of the CFJ airfoil with the windtunnel test results.

Effect of Injection Slot Size on the Performance of Coflow Jet Airfoil

Two coflowjet airfoils with injection slot size differing by a factor of 2 are tested in a wind tunnel to study the effect of injection slot size. At the same angle of attack, the larger injection slot size airfoil passes about twice the jet mass flow rate of the smaller injection slot size airfoil. The smaller injection slot size airfoil is more effective in increasing the stall margin and maximum lift, whereas the larger slot coflow jet airfoil is more effective in reducing drag. To achieve the same lift, the smaller injection slot size airfoil has much less energy expenditure than the larger injection slot airfoil. A coefficient of jet kinetic energy is introduced, which appears to correlate well with the maximum lift and stall margin when coflow jet airfoil geometry varies. Both the jet kinetic energy coefficient and the momentum coefficient correlate well with drag reduction. No optimization of the airfoil configuration is pursued in this research, and the results indicate that there is a great potential for coflow jet airfoil performance improvement.

Experimental Investigation of Jet Mixing Mechanism of Co-Flow Jet Airfoil

The jet mixing of a co-flow jet (CFJ) airfoil is investigated to understand the mechanism of lift enhancement, drag reduction, and stall margin increase. Digital Particle Image Velocimetry, flow visualization and aerodynamic forces measurements are used to reveal the insight of the CFJ airfoil mixing process. At low AoA and low momentum coefficient, the mixing between the wall jet and mainflow is dominant with large structure coherent structures for the attached flows. When the momentum coefficient is increased, the large vortex structure disappears. At high AoA with flow separation, the CFJ creates a upstream flow strip between two counter rotating vertical shear layer, i.e., the outer shear layer and inner flow induced by CFJ. The UFS is characterized with large vortex free region. The co-flow wall jet is deflected normal to the airfoil surface characterized with a saddle point. With increased momentum coefficient of the CFJ, the saddle point moves downstream and eventually disappears when the flow is attached. Turbulence plays a key role in mixing the CFJ with mainflow to transport high kinetic energy from the jet to mainflow so that the mainflow can remain attached at high AoA to generate high lift. When the flow is separated, increased CFJ momentum coefficient also increases the turbulence intensity at jet injection mixing region.

A general sub-domain boundary mapping procedure for structured grid CFD parallel computation

In the present work, a general sub-domain boundary mapping procedure has been developed for arbitrary topology multi-block structured grids with grid points matched on sub-domain boundaries. The interface of two adjacent blocks is uniquely deflned according to each local meshing index system (MIS) which is specifled independently. A pack/unpack procedure based on the deflnition of the interface is developed to exchange the data in 1D array to minimize the communication amount. A safe send/receive procedure is built to remove the possibility of communication block and achieve an optimum parallel computation e‐ciency. The procedure is applied to parallelize an in house 3D Navier-Stokes code. The message passing interface (MPI) protocol is used for the data communication. The implementation of this newly developed parallelization procedure is straightforward. The programming work to convert a sequential code to parallel code using this procedure is minimal. The numerical experiments on an MPI based computer cluster show that the general mapping algorithm is robust and has high parallel computation e‐ciency.