Computed Hypersonic Viscous Flows Over Delta Wings
Report describes development of algorithm for finite-volume solution of conical Navier-Stokes equations of hypersonic viscous flow over conical delta wing.
Ruffin, Stephen M.↗
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A computational and experimental investigation of a delta wing with vertical tails
The flow over an aspect ratio 1 delta wing with twin vertical tails is studied in a combined computational and experimental investigation. This research is conducted in an effort to understand the vortex and fin interaction process. The computational algorithm used solves both the thin-layer Navier-Stokes and the inviscid Euler equations and utilizes a chimera grid-overlapping technique. The results are compared with data obtained from a detailed experimental investigation. The laminar case presented is for an angle of attack of 20 deg and a Reynolds number of 500,000. Good agreement is observed for the physics of the flow field, as evidenced by comparisons of computational pressure contours with experimental flow-visualization images, as well as by comparisons of vortex-core trajectories. While comparisons of the vorticity magnitudes indicate that the computations underpredict the magnitude in the wing primary-vortex-core region, grid embedding improves the computational prediction.
Krist, Sherrie L.↗
Spatial simulation of secondary instability in plane channel flow - Comparison of K- and H-type disturbances
This study involves a numerical simulation of spatially evolving secondary instability in plane channel flow. The computational algorithm integrates the time-dependent, 3D, incompressible Navier-Stokes equations by a mixed finite-difference/spectral technique. In particular, we are interested in the differences between instabilities instigated by Klebanoff (K-) type and Herbert (H-) type inflow conditions, and in comparing the present spatial results with previous temporal models. It is found that for the present inflow conditions, H-type instability is biased towards one of the channel walls, while K-type instability evolves on both walls. For low initial perturbation amplitudes, H-type instability exhibits higher growth rates than K-type instability, while higher initial amplitudes lead to comparable growth rates of both H- and K-type instability. In H-type instability, spectral analysis reveals the presence of the subharmonic 2D mode which promotes the growth of the 3D spanwise and fundamental modes through nonlinear interactions. An intermodal energy transfer study demonstrates that there is a net energy transfer from the 3D modes to the 2D mode. This analysis also indicates that the mean mode transfers net energy to the 2D subharmonic mode and to the 3D modes.
Saiki, E. M.↗
A Computational and Experimental Investigation of a Delta Wing with Vertical Tails
The flow over an aspect ratio 1 delta wing with twin vertical tails is studied in a combined computational and experimental investigation. This research is conducted in an effort to understand the vortex and fin interaction process. The computational algorithm used solves both the thin-layer Navier-Stokes and the inviscid Euler equations and utilizes a chimera grid-overlapping technique. The results are compared with data obtained from a detailed experimental investigation. The laminar case presented is for an angle of attack of 20 and a Reynolds number of 500; 000. Good agreement is observed for the physics of the flow field, as evidenced by comparisons of computational pressure contours with experimental flow-visualization images, as well as by comparisons of vortex-core trajectories. While comparisons of the vorticity magnitudes indicate that the computations underpredict the magnitude in the wing primary-vortex-core region, grid embedding improves the computational prediction.
Krist. Sherrie L.↗
Conservative Patch Algorithm and Mesh Sequencing for PAB3D
A mesh-sequencing algorithm and a conservative patched-grid-interface algorithm (hereafter Patch Algorithm ) have been incorporated into the PAB3D code, which is a computer program that solves the Navier-Stokes equations for the simulation of subsonic, transonic, or supersonic flows surrounding an aircraft or other complex aerodynamic shapes. These algorithms are efficient, flexible, and have added tremendously to the capabilities of PAB3D. The mesh-sequencing algorithm makes it possible to perform preliminary computations using only a fraction of the grid cells (provided the original cell count is divisible by an integer) along any grid coordinate axis, independently of the other axes. The patch algorithm addresses another critical need in multi-block grid situation where the cell faces of adjacent grid blocks may not coincide, leading to errors in calculating fluxes of conserved physical quantities across interfaces between the blocks. The patch algorithm, based on the Stokes integral formulation of the applicable conservation laws, effectively matches each of the interfacial cells on one side of the block interface to the corresponding fractional cell area pieces on the other side. This approach is comprehensive and unified such that all interface topology is automatically processed without user intervention. This algorithm is implemented in a preprocessing code that creates a cell-by-cell database that will maintain flux conservation at any level of full or reduced grid density as the user may choose by way of the mesh-sequencing algorithm. These two algorithms have enhanced the numerical accuracy of the code, reduced the time and effort for grid preprocessing, and provided users with the flexibility of performing computations at any desired full or reduced grid resolution to suit their specific computational requirements.
Pao, S. P.↗
Grid Sensitivity and Aerodynamic Optimization of Generic Airfoils
An algorithm is developed to obtain the grid sensitivity with respect to design parameters for aerodynamic optimization. The procedure is advocating a novel (geometrical) parameterization using spline functions such as NURBS (Non-Uniform Rational B- Splines) for defining the airfoil geometry. An interactive algebraic grid generation technique is employed to generate C-type grids around airfoils. The grid sensitivity of the domain with respect to geometric design parameters has been obtained by direct differentiation of the grid equations. A hybrid approach is proposed for more geometrically complex configurations such as a wing or fuselage. The aerodynamic sensitivity coefficients are obtained by direct differentiation of the compressible two-dimensional thin-layer Navier-Stokes equations. An optimization package has been introduced into the algorithm in order to optimize the airfoil surface. Results demonstrate a substantially improved design due to maximized lift/drag ratio of the airfoil.
Sadrehaghighi, Ideen↗
Grid and aerodynamic sensitivity analyses of airplane components
An algorithm is developed to obtain the grid sensitivity with respect to design parameters for aerodynamic optimization. The procedure is advocating a novel (geometrical) parameterization using spline functions such as NURBS (Non-Uniform Rational B-Splines) for defining the wing-section geometry. An interactive algebraic grid generation technique, known as Two-Boundary Grid Generation (TBGG) is employed to generate C-type grids around wing-sections. The grid sensitivity of the domain with respect to geometric design parameters has been obtained by direct differentiation of the grid equations. A hybrid approach is proposed for more geometrically complex configurations such as a wing or fuselage. The aerodynamic sensitivity coefficients are obtained by direct differentiation of the compressible two-dimensional thin-layer Navier-Stokes equations. An optimization package has been introduced into the algorithm in order to optimize the wing-section surface. Results demonstrate a substantially improved design due to maximized lift/drag ratio of the wing-section.
Sadrehaghighi, Ideen↗
On recent advances and future research directions for computational fluid dynamics
This paper highlights some recent accomplishments regarding CFD numerical algorithm constructions for generation of discrete approximate solutions to classes of Reynolds-averaged Navier-Stokes equations. Following an overview of turbulent closure modeling, and development of appropriate conservation law systems, a Taylor weak-statement semi-discrete approximate solution algorithm is developed. Various forms for completion to the final linear algebra statement are cited, as are a range of candidate numerical linear algebra solution procedures. This development sequence emphasizes the key building blocks of a CFD RNS algorithm, including solution trial and test spaces, integration procedure and added numerical stability mechanisms. A range of numerical results are discussed focusing on key topics guiding future research directions.
Baker, A. J.↗
Applications of the Navier-Stokes equations to wings and complex configurations using a zonal approach
The simulation of a transonic viscous flow over a series of 3-D configurations, ranging from isolated wings to relatively complete aircraft, is presented. A fast, diagonalized Beam-Warming algorithm is used in conjunction with a zonal approach to solve the Euler/Navier-Stokes equations for these applications. The computer code, called Transonic Navier-Stokes, uses four zones for wing configurations and up to 19 zones for more complete aircraft configurations. For the inner zones adjacent to no-slip surfaces, the thin-layer Navier-Stokes equations are solved, while in the outer zones the Euler equations are solved. Numerical results are presented and compared with experiment (when available) for wing calculations and a more complete configuration based on the F-16A aircraft.
Flores, Jolen↗
Enhancements to Program LAURA for computation of three-dimensional hypersonic flow
Changes to Program Laura (Langley Aerothermodynamic Upwind Relaxation Algorithm) are presented which enhance both stability and accuracy of the algorithm. A discussion of iteration/sweeping strategies and their relation to computer architectures is included to best exploit the capabilities of serial, vector, and parallel processor machines. Test cases for Mach 10 perfect gas flow and Mach 32 real gas flow in chemical nonequilibrium over a blunt, raked elliptic cone using the thin-layer Navier-Stokes equations are presented in order to demonstrate the current improved capabilities. Algorithm changes include the use of volume averaging, application of a symmetric total variation diminishing (TVD) scheme, and stronger interaction between the grid/shock alignment routine and the relaxation algorithm. Good comparisons with heat transfer and pitching moment data at three different angles of attack for the Mach 10 tests serve to further validate the present algorithm. Parameters are defined which control the coupling of the specie continuity equations with the solution of the mixture conservation equations. A discussion of the consequences involved in the choice of strong versus weak coupling is presented, and a sample nonequilibrium calculation on a fine grid over a full scale model of the Aeroassist Flight Experiment (AFE) demonstrates current capabilities.
Gnoffo, Peter A.↗
Computationally Efficient Control Co-Design Optimization Framework with Mixed-Fidelity Fluid and Structure Analysis: OpenTurbineCoDe (OTCD) - ARPA-E ATLANTIS Phase I Project (Final Technical Report)
The goal of the Department of Energy (DOE) Advanced Research Projects Agency-Energy (ARPA-E) Aerodynamic Turbines Lighter and Afloat with Nautical Technologies and Integrated Servo-control (ATLANTIS) Program is to develop new technologies for floating offshore wind turbines, or wind farms, using the discipline of control co-design (CCD.) In this context, our goal is to develop a computationally efficient optimization framework for design of floating offshore wind turbines. Our specific aim is to utilize high-fidelity structural, aerodynamic, aero-structural tools, and to derive control-oriented reduced- or low-order models directly from the high-fidelity tools. We proposed a mixed-fidelity modeling approach which means that we are also using low- and mid-fidelity tools when necessary. This research is conducted by a multidisciplinary team consisting of Rutgers University, University of Michigan, Brigham Young University, and the National Renewable Energy Laboratory (NREL). The computational framework, called OpenTurbineCoDe, is designed to integrate, where possible, traditional structural, aerodynamic, aeroelastic models (e.g., OpenFAST) and advanced control algorithms with higher fidelity simulation tools including Reynolds-averaged Navier–Stokes (RANS) solvers, and three-dimensional structural finite element solvers. All the high-fidelity tools used in this research provide numerically exact gradients to facilitate both efficient optimization and local linearization for control implementation.
17 WIND ENERGY↗
Finite element computational fluid mechanics
Finite element analysis as applied to the broad spectrum of computational fluid mechanics is analyzed. The finite element solution methodology is derived, developed, and applied directly to the differential equation systems governing classes of problems in fluid mechanics. The heat conduction equation is used to reveal the essence and elegance of finite element theory, including higher order accuracy and convergence. The algorithm is extended to the pervasive nonlinearity of the Navier-Stokes equations. A specific fluid mechanics problem class is analyzed with an even mix of theory and applications, including turbulence closure and the solution of turbulent flows.
Baker, A. J.↗
Three-dimensional flow over a conical afterbody containing a centered propulsive jet - A numerical simulation
The supersonic flow field over a body of revolution incident to the free stream is simulated numerically on a large, array processor (the CDC Cyber 205). The configuration is composed of a cone-cylinder forebody followed by a conical afterbody from which emanates a centered, supersonic propulsive jet. The free-stream Mach number is 2, the jet-exit Mach number is 2.5, and the jet-to-free-stream static pressure ratio is 3. Both the external flow and the exhaust are ideal air at a common total temperature. The thin-layer approximation to the time-dependent, compressible, Reynolds-averaged Navier-Stokes equations are solved using an implicit finite-difference algorithm. The data base, of 5 million words, is structured in a 'pencil' format so that efficient use of the array processor can be realized. The computer code is completely vectorized to take advantage of the data structure. Turbulence closure is achieved using an empirical algebraic eddy-viscosity model. The configuration and flow conditions correspond to published experimental tests and the computed solutions are consistent with the experimental data.
Deiwert, G. S.↗
Time-dependent finite-difference simulation of unsteady interactive flows
The solution of the time-dependent, Reynolds-averaged, Navier-Stokes equations for unsteady, interacting flows by finite-difference algorithms is discussed. Specific examples include (1) unsteady transonic flow over a thick biconvex airfoil, (2) determination of buffet boundaries for a transonic lifting airfoil, (3) the simulation of aileron buzz and (4) dynamic stall. Algorithms considered include explicit methods, mixed (or hybrid) methods, and fully implicit methods. Consideration of time scales for computational stability, computational accuracy, and physical accuracy and the use of time-dependent adaptive meshing to realize computational efficiency are also discussed.
Deiwert, G. S.↗
Theoretical analysis of aircraft afterbody flow
The strongly interactive flow field about aircraft afterbodies is investigated using computational techniques by which the thin-shear-layer formulation of the compressible, Reynolds-averaged Navier-Stokes equations is solved. A time-dependent implicit numerical algorithm is used to obtain solutions for a variety of afterbody and nozzle geometries, within the class of bodies of revolution, for both subsonic and supersonic external flow, and for sonic and supersonic underexpanded jets. Only centered nozzles with either a sharp lip or a blunt base are considered. In all cases, computed results are compared with experimental data taken at flight Reynolds numbers for like-flow conditions. Turbulence closure is realized using algebraic eddy-viscosity concepts. A new and unique adaptive-grid technique is used to resolve flow regimes with large gradients and to improve the accuracy and efficiency of the computational scheme. Special singular point boundary conditions are used for similar purposes, and are especially effective for highly under-expanded jets. For all cases considered, except one with a very large base-to-nozzle-exit-diameter ratio, the agreement with experimental measurements is excellent. For geometries with large base regions, enhancements in the turbulence transport model are necessary to support improvements in the flow-field simulation.
Deiwert, G. S.↗
High-resolution shock-capturing schemes for inviscid and viscous hypersonic flows
A class of implicit Total Variation Diminishing (TVD) type algorithms suitable for transonic and supersonic multidimensional Euler and Navier-Stokes equations was extended to hypersonic computations. The improved conservative shock-capturing schemes are spatially second- and third-order, and are fully implicit. They can be first- or second-order accurate in time and are suitable for either steady or unsteady calculations. Enhancement of stability and convergence rate for hypersonic flows is discussed. With the proper choice of the temporal discretization and suitable implicit linearization, these schemes are fairly efficient and accurate for very complex two-dimensional hypersonic inviscid and viscous shock interactions. This study is complimented by a variety of steady and unsteady viscous and inviscid hypersonic blunt-body flow computations. Due to the inherent stiffness of viscous flow problems, numerical experiments indicated that the convergence rate is in general slower for viscous flows than for inviscid steady flows.
Yee, H. C.↗
Embedded adaptation for time dependent real fluid/gas flows
An embedded adaptation algorithm is used to illustrate applications and requirements for Navier-Stokes and nonequilibrium unsteady two-dimensional flow fields. Both grid refinement and equation modification are included for unstructured distributions of quadrilateral cells. Multiple refinement parameters for distinct physical phenomena serve to monitor the evolving nonuniform field and to recognize flow features in isolated and overlapping subdomains. Examples from subsonic, hypersonic, internal, and external fields show substantial advantages for the adaptive approach.
Baron, Judson R.↗
Suppression of pressure oscillations in an open cavity by passive pneumatic control
A computational investigation has been conducted to determine the effectiveness of a passive control technique in suppressing the oscillations in an open cavity exposed to a supersonic flow. Time-accurate solutions of the unsteady, Reynolds-averaged, Navier-Stokes equations were obtained with an explicit predictor-corrector algorithm; the passive control was implemented through the use of a simple linear pressure-velocity law along the porous cavity floor. The computational code was validated by comparisons with experimental data for the cavity flow without control. The computational results with control demonstrate that the oscillations are suppressed; the fluid dynamic mechanism of the control is seen to be a stabilization of the free-shear layer. Spectral analysis of the unsteady data shows that the resonant frequencies are essentially unchanged by the control. Beneficial reductions in the cavity resonant drag are also observed.
Chokani, N.↗