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It was found that new concepts and methods were needed to develop a statistical theory of turbulence. The group kinetic method was devised for the transformation of the dynamical system into a kinetic system as the basis for a statistical treatment of turbulence. Spectral structure is used as a basis for turbulence modeling.
Past efforts to develop methods for objective wind analysis and to provide turbulence estimates to pilots are reviewed. The present approach involves a wind module and a turbulence module. The wind module extends the critical dividing streamline concept and past developments in mass-conserving wind interpolation schemes. The turbulence module is based on recent efforts to develop practical atmospheric turbulence parameterization schemes based on lapse rate, wind shear, surface heating, and surface roughness. The lapse rate and wind shear are readily obtained from the wind module. Surface roughness and heating come from land use information and net radiation estimates derived from cloud cover, terrain slope, local time, and latitude. This system is argued to have considerable potential for providing useful online information for many kinds of aircraft operations.
Enhancements to the previously reported mixed-element USM3D Hierarchical Adaptive Nonlinear Iteration Method (HANIM) framework have been made to further improve robustness, efficiency, and accuracy of computational fluid dynamic simulations. The key enhancements include a multi-color line-implicit preconditioner, a discretely consistent symmetry boundary condition, and a line-mapping method for the turbulence source term discretization. The USM3D iterative convergence for the turbulent flows is assessed on four configurations. The configurations include a two-dimensional (2D) bump-in-channel, the 2D NACA 0012 airfoil, a three-dimensional (3D) bump-in-channel, and a 3D hemisphere cylinder. The Reynolds Averaged Navier Stokes (RANS) solutions have been obtained using a Spalart-Allmaras turbulence model and families of uniformly refined nested grids. Two types of HANIM solutions using line- and point-implicit preconditioners have been computed. Additional solutions using the point-implicit preconditioner alone (PA) method that broadly represents the baseline solver technology have also been computed. The line-implicit HANIM shows superior iterative convergence in most cases with progressively increasing benefits on finer grids.
A novel approach to compute affordable approximate sensitivities in a large-eddy simulation (LES) is proposed and assessed. The approach is based on solving a Reynolds-averaged Navier–Stokes (RANS) problem that has been linearized around the mean LES solution, with closure modeling required for the linearized changes in turbulent Reynolds stresses. In the present study, the closure modeling is based on a linearized algebraic turbulence model. The method is assessed for the flow over a NACA0012 airfoil at a fixed angle of attack, with the Reynolds number as the variable parameter. The results show that, provided an accurate linearized closure model, the method predicts the correct sensitivity of the skin friction coefficient and the mean velocity field at the cost of a linearized RANS, which provides an important proof-of-concept for this approach. Here, the linearized algebraic turbulence model with standard model coefficients produces a reasonably accurate sensitivity, but the results also suggest that accuracy could be gained from recalibrating the model coefficients for this new use of the model.
This paper describes a fully spectral, Polynomial Chaos method for the propagation of uncertainty in numerical simulations of compressible, turbulent flow, as well as a novel stochastic collocation algorithm for the same application. The stochastic collocation method is key to the efficient use of stochastic methods on problems with complex nonlinearities, such as those associated with the turbulence model equations in compressible flow and for CFD schemes requiring solution of a Riemann problem. Both methods are applied to compressible flow in a quasi-one-dimensional nozzle. The stochastic collocation method is roughly an order of magnitude faster than the fully Galerkin Polynomial Chaos method on the inviscid problem.
A one-dimensional electron fluid model is investigated using the mathematical methods of modern fluid turbulence theory. Non-dissipative equilibrium canonical distributions are determined in a phase space whose co-ordinates are the real and imaginary parts of the Fourier coefficients for the field variables. Spectral densities are calculated, yielding a wavenumber electric field energy spectrum proportional to k to the negative second power for large wavenumbers. The equations of motion are numerically integrated and the resulting spectra are found to compare well with the theoretical predictions.
A one-dimensional electron fluid model is investigated using the mathematical methods of modern fluid turbulence theory. Nondissipative equilibrium canonical distributions are determined in a phase space whose coordinates are the real and imaginary parts of the Fourier coefficients for the field variables. Spectral densities are calculated, yielding a wavenumber electric field energy spectrum proportional to 1/k squared for large wavenumbers. The equations of motion are numerically integrated and the resulting spectra are found to compare well with the theoretical predictions.
The observed large reduction in spreading rate of adiabatic high-Mach-number free turbulent shear layers has been predicted successfully for the first time by a mean turbulent energy closure method using a new model for a specified pressure-dilitation correlation. A physical mechanism that produces this correlation has been hypothesized based on an eddy shock wave concept. This hypothesis indicates that the correlation would act like a turbulence energy sink or source according to whether the transverse gradients of mean Mach number and mean density have the same or opposite signs, respectively.
Simulating separated flows at high Reynolds numbers using Reynolds Averaged Navier-Stokes (RANS) modeled equations remains a challenge in aeronautics. The main hindrance to progress stems from the lack of extended de- tailed data pertinent to the root cause of failure of RANS models, as well as the little progress in RANS modeling innovations in the past several decades. The goal of the current effort is to generate data for separated flow at a Reynolds numbers where conventional models are challenged. We use Direct Numerical Simulations to model turbulent flow over the wall-mounted hump configuration to investigate the physics of flow separation and boundary layer recovery, as well as provide data relevant to the modeling community. A chord-based Reynolds number of Re(sub c) = 47,500 is considered with a turbulent inflow profile of Re(sub θ) = 1,400 (θ /c = 3%). We use FDL3DI, a code that solves the compressible Navier-Stokes equations using high-order compact-difference scheme and filter, with the standard re- cycling/rescaling method of generating turbulent boundary layers as inflow to the computational domain. Two differ- ent configurations of the upper-wall are analyzed for two sets of boundary conditions (slip and no-slip). The results are compared with the available higher Re(sub c) (= 936,000, Re(sub θ) = 7,200, θ /c = 0.77%) experiment for major flow features. The simulated lower Rec allows for DNS-like mesh resolutions, and adequately wide spans. The results from these simulations show earlier separation and delayed reattachment compared to Re(sub c) = 936,000, and significantly higher skin friction in the forebody of the hump. We also find that the upper-wall shape and boundary condition influence pressure distribution over the hump, whereas skin friction is only influenced by the boundary condition.
We present a deep probabilistic convolutional neural network (PCNN) model for predicting local values of small-scale mixing properties in stratified turbulent flows, namely the dissipation rates of turbulent kinetic energy and density variance, $\varepsilon$ and $\chi$ . Inputs to the PCNN are vertical columns of velocity and density gradients, motivated by data typically available from microstructure profilers in the ocean. The architecture is designed to enable the model to capture several characteristic features of stratified turbulence, in particular the dependence of small-scale isotropy on the buoyancy Reynolds number $Re_b:=\varepsilon /(\nu N^2)$ , where $\nu$ is the kinematic viscosity and $N$ is the background buoyancy frequency, the correlation between suitably locally averaged density gradients and turbulence intensity and the importance of capturing the tails of the probability distribution functions of values of dissipation. Empirically modified versions of commonly used isotropic models for $\varepsilon$ and $\chi$ that depend only on vertical derivatives of density and velocity are proposed based on the asymptotic regimes $Re_b\ll 1$ and $Re_b\gg 1$ , and serve as an instructive benchmark for comparison with the data-driven approach. When trained and tested on a simulation of stratified decaying turbulence which accesses a range of turbulent regimes (associated with differing values of $Re_b$ ), the PCNN outperforms assumptions of isotropy significantly as $Re_b$ decreases, and additionally demonstrates improvements over the fitted empirical models. A differential sensitivity analysis of the PCNN facilitates a comparison with the theoretical models and provides a physical interpretation of the features enabling it to make improved predictions.
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Turbulent boundary layer measurements on axisymmetric hypersonic nozzle walls
Methods of measuring the three dimensional flow field using a three-sensor, hot-wire probe is described in this paper, with emphasis on the techniques developed by the author's group at The Pennsylvania State University. The hot wire equations, data processing procedure, calibration techniques, and a discussion of various errors in the measurement are included. Some typical data acquired by this probe is also included.
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A design method has been developed by which an airfoil with a substantial amount of natural laminar flow can be designed, while maintaining other aerodynamic and geometric constraints. After obtaining the initial airfoil's pressure distribution at the design lift coefficient using an Euler solver coupled with an integml turbulent boundary layer method, the calculations from a laminar boundary layer solver are used by a stability analysis code to obtain estimates of the transition location (using N-Factors) for the starting airfoil. A new design method then calculates a target pressure distribution that will increase the larninar flow toward the desired amounl An airfoil design method is then iteratively used to design an airfoil that possesses that target pressure distribution. The new airfoil's boundary layer stability characteristics are determined, and this iterative process continues until an airfoil is designed that meets the laminar flow requirement and as many of the other constraints as possible.
A design method has been developed by which an airfoil with a substantial amount of natural laminar flow can be designed, while maintaining other aerodynamic and geometric constraints. After obtaining the initial airfoil's pressure distribution at the design lift coefficient using an Euler solver coupled with an integral turbulent boundary layer method, the calculations from a laminar boundary layer solver are used by a stability analysis code to obtain estimates of the transition location (using N-Factors) for the starting airfoil. A new design method then calculates a target pressure distribution that will increase the laminar flow toward the desired amount. An airfoil design method is then iteratively used to design an airfoil that possesses that target pressure distribution. The new airfoil's boundary layer stability characteristics are determined, and this iterative process continues until an airfoil is designed that meets the laminar flow requirement and as many of the other constraints as possible.
A developed method has been applied to calculate accurately the viscous flow about airfoils normal to the free-stream flow. This method has special application to the analysis of tilt rotor aircraft in the evaluation of download. In particular, the flow about an XV-15 airfoil with and without deflected leading and trailing edge flaps at -90 degrees incidence is evaluated. The multi-element aspect of the method provides for the evaluation of slotted flap configurations which may lead to decreased drag. The method solves for turbulent flow at flight Reynolds numbers. The flow about the XV-15 airfoil with and without flap deflections has been calculated and compared with experimental data at a Reynolds number of one million. The comparison between the calculated and measured pressure distributions are very good, thereby, verifying the method. The aerodynamic evaluation of multielement airfoils will be conducted to determine airfoil/flap configurations for reduced airfoil drag. Comparisons between the calculated lift, drag and pitching moment on the airfoil and the airfoil surface pressure will also be presented.
An investigation was made to determine the feasibility of using a boundary layer integral method to study the separation of a turbulent boundary layer on a two dimensional ramp at supersonic speeds. The numerical calculations were made for a free stream Mach number of 3, a Reynolds number of 10 million, and over a ramp angle range from 0 deg to 30 deg. For ramp angles where no flow separation was indicated, theoretical calculations were in reasonable agreement with experimental data except for a somewhat belated rise in pressure. For larger ramp angles, where separation was present, the investigation produced results that were not in agreement with experiment or with results calculated by time dependent Navier-Stokes methods. This apparently was true because no provision had been made for a proper shock boundary layer interaction where strong normal pressure gradients are induced within the boundary layer under the shock independent of surface curvature effects.