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TRANSEP Calculates flow field about low-speed single-element airfoil at high-angle-of-attack and high-lift conditions with massive boundary-layer separation. TRANSEP includes effects of weak viscous interactions and can be used for subsonic/transonic airfoil design and analysis. The approach used in TRANSEP is based on direct-inverse method and its ability to use either displacement surface or pressure as airfoil boundary condition.
A finite difference method is developed for making detailed predictions of three dimensional subsonic turbulent flow in turbofan lobe mixers. The governing equations are solved by a forward-marching solution procedure which corrects an inviscid potential flow solution for viscous and thermal effects, secondary flows, total pressure distortion and losses, internal flow blockage and pressure drop. Test calculations for a turbulent coaxial jet flow verify that the turbulence model performs satisfactorily for this relatively simple flow. Lobe mixer flows are presented for two geometries typical of current mixer design. These calculations included both hot and cold flow conditions, and both matched and mismatched Mach number and total pressure in the fan and turbine streams.
Numerical simulations of the time-dependent, Reynolds averaged, Navier-Stokes equations, employing various eddy viscosity turbulence models, are presented and compared with measurements from an investigation of a transonic trailing-edge flow at a high Reynolds number. Comparisons are made for mean surface quantities as well as mean and fluctuating flow-field quantities. Solutions employing two-equation turbulence models correctly predict all the major features of the flow field. Viscous-inviscid interaction effects were found to be extremely important for predicting this flow field and equally important to the turbulence modeling employed.
A wind tunnel investigation was conducted to determine the aerodynamic interference associated with the installation of a long duct, flow-through nacelle on a straight unswept untapered supercritical wing. Experimental data was obtained for the verification of computational prediction techniques. The model was tested in the 16-Foot Transonic Tunnel at Mach numbers from 0.20 to 0.875 and at angles of attack from about 0 deg to 5 deg. The results of the investigation show that strong viscous and compressibility effects are present at the transonic Mach numbers. Numerical comparisons show that linear theory is adequate for subsonic Mach number flow prediction, but is inadequate for prediction of the extreme flow conditions that exist at the transonic Mach numbers.
A method and program called TRANSEP is presented that can be used for the analysis of the flow about a low speed airfoil under high lift, massive separation conditions. Since the present program is a modification of the direct-inverse TRANDES code, it can also be used for the design and analysis of transonic airfoils, including the effects of weak viscous interaction. Interactions on program usage, program modifications to convert TRANDES to TRANSEP, and sample cases and results are given.
Wind-tunnel measurements of steady and unsteady pressures for a high-aspect-ratio supercritical wing model are compared with calculations by the linear unsteady aerodynamic lifting-surface theory, known as the Doublet Lattice method, at Mach numbers of 0.650 (subsonic) and 0.78 (transonic). The steady-pressure data comparisons are made for incremental changes in angle of attack and control-surface deflection. The unsteady-pressure data comparisons are made for oscillating control-surface deflections. Some differences between the measured and calculated aerodynamics are attributed to viscous and transonic effects that are not accounted for in the Doublet Lattice analysis. Comparisons of the transonic unsteady-pressure data for the oscillating control surfaces are improved by applying empirical corrections based on the steady-pressure measurements to the unsteady Doublet Lattice calculations.
The unsteady aerodynamic lifting surface theory, the Doublet Lattice method, with experimental steady and unsteady pressure measurements of a high aspect ratio supercritical wing model at a Mach number of 0.78 were compared. The steady pressure data comparisons were made for incremental changes in angle of attack and control surface deflection. The unsteady pressure data comparisons were made at set angle of attack positions with oscillating control surface deflections. Significant viscous and transonic effects in the experimental aerodynamics which cannot be predicted by the Doublet Lattice method are shown. This study should assist development of empirical correction methods that may be applied to improve Doublet Lattice calculations of lifting surface aerodynamics.
The dynamics of magnetic fibrils in the convective zone of a star is investigated analytically, deriving mean-field equations for the two-dimensional transverse motion of an incompressible fluid containing numerous small widely spaced circular cylinders. The equations of Parker (1982) are extended to account for the inertial effects of local flow around the cylinders. The linear field equation for the stream function at the onset of convection is then rewritten, neglecting large-scale heat transport, and used to construct a model of convective counterflow. The Kelvin impulse and fluid momentum, convective motion initiated by a horizontal impulse, and the effects of a viscous boundary layer are considered in appendices.
This paper contributes to the understanding of the noise generation process of an airfoil encountering an unsteady upwash. By using a fast Fourier transform together with accurate airfoil response functions, the lift-time waveform for an airfoil encountering a delta function gust (the indicial function) is calculated for a flat plate airfoil in a compressible flow. This shows the interesting property that the lift is constant until the generated acoustic wave reaches the trailing edge. Expressions are given for the magnitude of this constant and for the pressure distribution on the airfoil during this time interval. The case of an airfoil cutting through a line vortex is also analyzed. The pressure-time waveform in the far field is closely related to the left-time waveform for the above problem of an airfoil entering a delta function gust. The effects of varying the relevant parameters in the problem are studied, including the observed position, the core diameter of the vortex, the vortex orientation and the airfoil span. The far field sound varies significantly with observer position, illustrating the importance of non-compactness effects. Increasing the viscous core diameter tends to smooth the pressure-time waveform. For small viscous core radius and infinite span, changing the vortex orientation changes only the amplitude of the pressure-time waveform, and not the shape.
A numerical study of the effects of viscous-inviscid interactions in three-dimensional duct flows is presented. In particular interacting flows for which the oncoming flow is not fully-developed were considered. In this case there is a thin boundary layer still present upstream of the surface distortion, as opposed to the fully-developed pipe flow situation wherein the flow is viscous across the cross section.
A general method is presented for determining the dynamic torsional/axial response of linear structures composed of either tapered bars or shafts to transient excitations. The method consists of formulating and solving the dynamic problem in the Laplace transform domain by the finite element method and obtaining the response by a numerical inversion of the transformed solution. The derivation of the torsional and axial stiffness matrices is based on the exact solution of the transformed governing equation of motion, and it consequently leads to the exact solution of the problem. The solution permits treatment of the most practical cases of linear tapered bars and shafts, and employs modeling of structures with only one element per member which reduces the number of degrees of freedom involved. The effects of external viscous or internal viscoelastic damping are also taken into account.
Navier-Stokes simulations are used to study the phenomena of wing lift augmentation with spanwise tip blowing. Flowfields calculated for varying blowing conditions are analyzed to determine the mechanisms responsible for providing lift augmentation. It is found that both viscous and inviscid effects are important.
An interactive boundary-layer method previously developed and tested for steady flows is used here in a quasi-steady manner to examine the evolution of the flow behavior around oscillating airfoils operating inlight stall conditions. The calculations encompass the airfoil and wake flows at angles of attack which lead to flow separation. The location of the onset of transition is represented by a correlation based on steady flows. The results show the large effects of the viscous layer on the variation of lift coefficient with angle of attack and reduced frequency.
Based on previous observations of glaze ice accretion, a 'Multi-Zone' model with distinct zones of different surface roughness is demonstrated. The use of surface roughness in the LEWICE ice accretion prediction code is examined. It was found that roughness is used in two ways: to determine the laminar to turbulent transition location and to calculate the turbulent heat transfer coefficient. A two zone version of the Multi-Zone model is implemented in the LEWICE code, and compared with experimental heat transfer coefficient and ice accretin results. The analysis of the boundary layer transition, surface roughness, and viscous flow field effects significantly increased the accuracy in predicting heat transfer coefficients. The Multi-Zone model was found to greatly improve the ice accretion prediction for the cases compared.
The Rai method of single-stage rotor/stator flow interaction is extended to handle multistage configurations. In this study, a two-dimensional Navier-Stokes multi-zone approach was used to investigate unsteady flow interactions within two multistage axial turbines. The governing equations are solved by an iterative, factored, implicit finite-difference, upwind algorithm. Numerical accuracy is checked by investigating the effect of time step size, the effect of subiteration in the Newton-Raphson technique, and the effect of full viscous versus thin-layer approximation. Computer results compared well with experimental data. Unsteady flow interactions, wake cutting, and the associated evolution of vortical entities are discussed.
A k-epsilon model that accounts for viscous and wall effects is presented. The proposed formulation does not contain the local wall distance thereby making very simple the application to complex geometries. The formulation is based on an existing k-epsilon model that proved to fit very well with the results of direct numerical simulation. The new form is compared with nine different two-equation models and with direct numerical simulation for a fully developed channel flow at Re = 3300. The simple flow configuration allows a comparison free from numerical inaccuracies. The computed results prove that few of the considered forms exhibit a satisfactory agreement with the channel flow data. The model shows an improvement with respect to the existing formulations.
Three solution algorithms, explicit underrelaxation, point implicit, and lower upper symmetric Gauss-Seidel (LUSGS), are used to compute nonequilibrium flow around the Apollo 4 return capsule at 62 km altitude. By varying the Mach number, the efficiency and robustness of the solution algorithms were tested for different levels of chemical stiffness. The performance of the solution algorithms degraded as the Mach number and stiffness of the flow increased. At Mach 15, 23, and 30, the LUSGS method produces an eight order of magnitude drop in the L2 norm of the energy residual in 1/3 to 1/2 the Cray C-90 computer time as compared to the point implicit and explicit under-relaxation methods. The explicit under-relaxation algorithm experienced convergence difficulties at Mach 23 and above. At Mach 40 the performance of the LUSGS algorithm deteriorates to the point it is out-performed by the point implicit method. The effects of the viscous terms are investigated. Grid dependency questions are explored.
Computational fluid dynamics (CFD) was used to study some transient flow features that can occur during the startup process of a shoch tunnel. The investigation concentrated on two areas: (1) the flow near the endwall of the driven tube during shock reflection and (2) the transient flow in the nozzle. The driven tube calculations were inviscid and focused on the study of a vortex system that was seen to form at the driven tube's axis of symmetry. The nozzle flow calculations examined viscous and inviscid effects during nozzle startup. The CFD solutions of the nozzle flows were compared with experimental data to demonstrate the effectiveness of the numerical analysis.