Three-dimensional shock-wave/boundary-layer interactions with bleed
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Shih, T. I.-P.↗
Engineering topics
Chyu, W. J.
Publications and source records attributed to Chyu, W. J..
Numerical study of shock-wave/boundary-layer interactions with bleed
A numerical study was conducted to investigate how bleed through a two-dimensional slot affects shock-wave induced, boundary-layer separation on a flat plate. This study is based on the ensemble-averaged, compressible, Navier-Stokes equations closed by the Baldwin-Lomax, algebraic turbulence model. The algorithm used to obtain solutions was the implicit, partially split, two-factored scheme of Steger. This study examined the effects of the following parameters in controlling shock-wave induced flow separation: location of slot in relation to where the incident shock wave impinged on the boundary layer, size of slot in relation to the boundary-layer thickness, number of slots, spacings between slots, and strength of the incident shock wave. This study also showed the nature of the very complex flowfield about the slot or slots and how the plenum affects the bleed process. The results of this study are relevant to problems where bleed is used to control shock-wave induced, boundary-layer separation (e.g., inside jet engine inlets and wind tunnels).
Hahn, T. O.↗
Implicit treatment of diffusion terms in lower-upper algorithms
A method is presented which allows diffusion terms to be treated implicitly in the lower-upper (LU) algorithm (which is a commonly used method for solving 'compressible' Euler and Navier-Stokes equations) so that the algorithm's good stability properties will not be impaired. The new method generalizes the concept of LU factorization from that associated with the sign of eigenvalues to that associated with backward- and forward-difference operators without regard to eigenvalues. The method is verified in a turbulent boundary layer study.
Shih, T. I.-P.↗
Bleed-boundary conditions for numerically simulated mixed-compression supersonic inlet flow
A numerical study was performed to investigate boundary conditions for bleed openings that are needed in the numerical simulation of critical flow through turbojet inlets with bleed. Nine different boundary conditions (BCs) were devised and examined. Of the BCs examined, three were able to stabilize the terminal shock near the inlet's throat. This numerical study was based on the ensemble-averaged, unsteady, three-dimensional, compressible Navier-Stokes equations closed by the Baldwin-Lomax algebraic turbulence model. Solutions to the Navier-Stokes equations were obtained by using a hybrid implicit-explicit method (Beam and Warming/MacCormack). The multiblock grid system used in the solution procedure was generated by solving a set of elliptic partial differential equations. Solutions obtained were compared with available experimental data.
Chyu, W. J.↗
Three-dimensional shock-wave/boundary-layer interactions with bleed through a circular hole
Computations were performed to study three-dimensional (3-D), shock-wave/boundary-layer interactions on a flat plate in which fluid in the boundary layer was bled through a circular hole into a plenum to control shock-wave induced separation. Results are presented which show the details of the 3-D flowfield about the bleed hole and how bleed-hole placement relative to shock-wave impingement affect upstream, spanwise, and downstream influence lengths. This study revealed an underlying mechanisms by which bleed holes can affect shock-wave/boundary-layer interactions. This investigation is based on the ensemble-averaged, "full-compressible" Navier-Stokes equations closed by the Baldwin-Lomax turbulence model. Solutions to these equations were obtained by an implicit finite-volume method based on the partially-split, two-factored algorithm of Steger.
Rimlinger, M. J.↗
Navier-Stokes simulation of flow through a highly contoured subsonic diffuser
The flow through a highly offset subsonic diffuser with cross-sectional profiles that varied from rectangular at the duct entrance to circular at the engine face was numerically simulated. A multizonal approach combined with a two-grid topology was used to represent both the internal and external flowfields, and an implicit, approximately-factored, partially flux-split finite-difference algorithm was used to solve the three-dimensional thin-layer Navier-Stokes equations. The computed static pressures along the inlet wall and total pressures on the engine face were compared with experimental data. In addition, the overall flowfield within the duct was examined in detail. Good agreement is shown between experiment and computations, with the limiting factor being the lack of a reliable turbulence model for internal flow problems.
Chyu, W. J.↗
Approximate factorization with source terms
A comparative evaluation is made of three methodologies with a view to that which offers the best approximate factorization error. While two of these methods are found to lead to more efficient algorithms in cases where factors which do not contain source terms can be diagonalized, the third method used generates the lowest approximate factorization error. This method may be preferred when the norms of source terms are large, and transient solutions are of interest.
Shih, T. I.-P.↗
Navier-Stokes solutions for mixed compression axisymmetric inlet flow with terminal shock
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Chyu, W. J.↗
Calculation of external-internal flow fields for mixed-compression inlets
Supersonic inlet flows with mixed external-internal compressions were computed using a combined implicit-explicit (Beam-Warming-Steger/MacCormack) method for solving the three-dimensional unsteady, compressible Navier-Stokes equations in conservation form. Numerical calculations were made of various flows related to such inlet operations as the shock-wave intersections, subsonic spillage around the cowl lip, and inlet started versus unstarted conditions. Some of the computed results were compared with wind tunnel data.
Chyu, W. J.↗
Numerical simulation of three-dimensional supersonic inlet flow fields
Supersonic inlet flows with mixed external-internal compressions of an axisymmetric inlet model were computed using a combined implicit-explicit (Beam-Warming-Steger/MacCormack) method for solving the three-dimensional unsteady, compressible Navier-Stokes equations in conservation form. Numerical calculations were made of various flows typically found in supersonic inlets such as shock-wave intersections, flow spillage around the cowl lip, shock-wave/boundary-layer interactions, control of shock-induced flow separation by means of boundary layer bleed, internal normal (terminal) shocks, and the effects of flow incidence. Computed results were compared with available wind tunnel data.
Kawamura, T.↗
Calculation of external-internal flow fields for mixed-compression inlets
Supersonic inlet flows with mixed external-internal compressions were computed using a combined implicit-explicit (Beam-Warming-Steger/MacCormack) method for solving the three-dimensional unsteady, compressible Navier-Stokes equations in conservation form. Numerical calculations were made of various flows related to such inlet operations as the shock-wave intersections, subsonic spillage around the cowl lip, and inlet started versus unstarted conditions. Some of the computed results were compared with wind tunnel data.
Chyu, W. J.↗
Computation of flow around a circular cylinder in a supercritical regime
Compressible flows around a circular cylinder in a supercritical regime at Mach number 0.3 have been calculated by using the Beam-Warming-Steger scheme based on the full Navier-Stokes equations with improved accuracy. The flow patterns are visualized extensively to observe the characteristics in this regime. The computations show that the flow at certain Reynolds numbers in a supercritical regime becomes rather steady and irregular with small drag coefficients. This may correspond to the experimental observations that the Strouhal number can not be measured clearly at a certain Reynolds number range in the supercritical regime.
Ishii, K.↗
Numerical studies of unsteady transonic flow over oscillating airfoil
A finite difference solution to the Navier-Stokes equations combined with a time varying grid generation technique was used to compute unsteady transonic flow over an oscillating airfoil. These computations were compared with experimental data (obtained at Ames Research Center) which form part of the AGARD standard configuration for aeroelastic analysis. A variety of approximations to the full Navier-Stokes equations was used to determine the effect of frequency, shock wave motion, flow separation, and airfoil geometry on unsteady pressures and overall air loads. Good agreement is shown between experiment and theory with the limiting factor being the lack of a reliable turbulence model for high Reynolds number, unsteady transonic flows.
Chyu, W. J.↗
Numerical studies of unsteady transonic flow over an oscillating airfoil
A finite-difference solution to the Navier-Stokes equations combined with a time-varying grid-generation technique was used to compute unsteady transonic flow over an oscillating airfoil. These computations were compared with experimental data (obtained at Ames Research Center) which form part of the AGARD standard configuration for aeroelastic analysis. A variety of approximations to the full Navier-Stokes equations was used to determine the effect of frequency, shock-wave motion, flow separation, and airfoil geometry on unsteady pressures and overall air loads. Good agreement is shown between experiment and theory with the limiting factor being the lack of a reliable turbulence model for high-Reynolds-number, unsteady transonic flows.
Chyu, W. J.↗
Nonlinear aerodynamic modeling of flap oscillations in transonic flow - A numerical validation
The regime of validity of a nonlinear aerodynamic force and moment formulation, based on concepts from nonlinear functional analysis and applicable to a transonic airfoil with a deflecting flap, is investigated. A time-dependent finite difference technique is used to evaluate the aerodynamic data of the formulation in terms of specified, characteristic motions. Flap-motion histories are generated from the flap inertial equations of motion, with aerodynamic reactions specified by the moment formulation. The motion histories depicting the cases of decaying and growing flap oscillations are compared with histories generated through simultaneous, coupled solution of the fluid-dynamic equations and flap inertial equations of motion. The range of applicability of the formulation is discussed.
Chyu, W. J.↗
Computations of transonic flow over an oscillating airfoil with shock-induced separation
A numerical study is presented on unsteady transonic flow over an airfoil in pitching oscillation at a moderately high incidence. The study was focused on the effects of unsteady shock-wave/boundary-layer interactions and subsequent flow separations. An implicit finite-difference scheme was used to solve the full time-dependent compressible Navier-Stokes equations in conservation-law form. The algorithm adopted for this study is the Beam-Warming spatially factored scheme. It is, however, constructed in a body-fitted curvilinear coordinate system for efficient unsteady flow computations. The computational results are compared with experimental data measured in the Ames 11- by 11-Foot Transonic Wind Tunnel.
Chyu, W. J.↗
Computation of simple three-dimensional wing-vortex interaction in transonic flow
An implicit delta form finite-difference algorithm for Euler equations in conservation law form has been used in preliminary calculations of three-dimensional wing-vortex interactions. Both steady and unsteady transonic flow wing-vortex interactions are computed. The computations themselves are meant to guide upcoming wind tunnel experiments of the same flow field. Various modifications to the numerical method that are intended to improve computational efficiency are also described and tested in both two- and three-dimensions.
Srinivasan, G. R.↗
Calculation of Unsteady Transonic Flow over an Airfoil
An implicit finite-difference solver for either the Euler equations or the "thin-layer" Navier-Stokes equations was used to calculate a transonic flow over the NACA 64A010 airfoil pitching about its one-quarter chord. An unsteady automatic grid-generation procedure that will improve significantly the computational efficiency of various unsteady flow problems is described. The calculated results for both inviscid and viscous flows at Much number 0.8 over the airfoil oscillating with reduced frequency referenced to one-half chord, 0.2, are compared with experimental data measured in the Ames 11 x 11-ft Transonic Wind Tunnel. Nonlinear, unsteady effects of the flow on the surface pressure variations, shock-wave excursions, and overall airloads are examined. Good agreements between the results of computations and experiments were obtained. In the shock-wave region, however, the results of the viscous-flow computations showed closer agreement with the experimental data.
Chyu, W. J.↗