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One-equation model of turbulence based on standard equations of k-epsilon model of turbulence, where k is turbulent energy and e is rate of dissipation of k. Derivation of one-equation model motivated partly by inaccuracies of flows computed by some Navier-Stokes-equations-solving algorithms incorporating algebraic models of turbulence. Satisfies need to avoid having to determine algebraic length scales.
Report discusses aspects of development of CENS3D computer code, solving three-dimensional Navier-Stokes equations of compressible, viscous, unsteady flow. Implements implicit finite-difference or finite-volume numerical-integration scheme, called "lower-upper symmetric-Gauss-Seidel" (LU-SGS), offering potential for very low computer time per iteration and for fast convergence.
The LU-SGS (lower upper symmetric Gauss Seidel) algorithm has been implemented into the Compressible Navier-Stokes, Finite Volume (CNSFV) code and validated with a multizonal Navier-Stokes simulation of a transonic turbulent flow around an Onera M6 transport wing. The convergence rate and robustness of the code have been improved and the computational cost has been reduced by at least a factor of 2 over the diagonal Beam-Warming scheme.
This paper presents a description and verification of RVC3D (rotor viscous code 3-D) which provides a Euler or Navier-Stokes analysis for steady three dimensional flows in turbomachinery. A motivation for this analysis is the calculation of turbine endwall heat transfer. Features of the turbulence model code include thin-layer formulation, Baldwin-Lomax or Cebeci-Smith turbulence models, node-centered finite difference formulation, and explicit four-stage Runge-Kutta time marching scheme. Results for flat plate, annular turbine cascade, turbine endwall heat transfer, and supersonic compressor blade test cases are presented.
An efficient steady analysis for predicting strong inviscid/viscid interaction phenomena such as viscous-layer separation, shock/boundary-layer interaction, and trailing-edge/near-wake interaction in turbomachinery blade passages is needed as part of a comprehensive analytical blade design prediction system. Such an analysis is described. It uses an inviscid/viscid interaction approach, in which the flow in the outer inviscid region is assumed to be potential, and that in the inner or viscous-layer region is governed by Prandtl's equations. The inviscid solution is determined using an implicit, least-squares, finite-difference approximation, the viscous-layer solution using an inverse, finite-difference, space-marching method which is applied along the blade surfaces and wake streamlines. The inviscid and viscid solutions are coupled using a semi-inverse global iteration procedure, which permits the prediction of boundary-layer separation and other strong-interaction phenomena. Results are presented for three cascades, with a range of inlet flow conditions considered for one of them, including conditions leading to large-scale flow separations. Comparisons with Navier-Stokes solutions and experimental data are also given.
The viewgraphs and discussion of linear stability theory and three dimensional boundary layer transition are provided. The ability to predict, using analytical tools, the location of boundary layer transition over aircraft-type configurations is of great importance to designers interested in laminar flow control (LFC). The e(sup N) method has proven to be fairly effective in predicting, in a consistent manner, the location of the onset of transition for simple geometries in low disturbance environments. This method provides a correlation between the most amplified single normal mode and the experimental location of the onset of transition. Studies indicate that values of N between 8 and 10 correlate well with the onset of transition. For most previous calculations, the mean flows were restricted to two-dimensional or axisymmetric cases, or have employed simple three-dimensional mean flows (e.g., rotating disk, infinite swept wing, or tapered swept wing with straight isobars). Unfortunately, for flows over general wing configurations, and for nearly all flows over fuselage-type bodies at incidence, the analysis of fully three-dimensional flow fields is required. Results obtained for the linear stability of fully three-dimensional boundary layers formed over both wing and fuselage-type geometries, and for both high and low speed flows are discussed. When possible, transition estimates form the e(sup N) method are compared to experimentally determined locations. The stability calculations are made using a modified version of the linear stability code COSAL. Mean flows were computed using both Navier Stokes and boundary-layer codes.
Time accurate Navier-Stokes computations were performed to study a class 2 (acoustic) whistle, the edge tone, and to gain knowledge of the vortex-acoustic coupling mechanisms driving production of these tones. Results were obtained by solving the full Navier-Stokes equations for laminar compressible air flow of a two dimensional jet issuing from a slit interacting with a wedge. Cases considered were determined by varying the distance from the slit to the wedge. Flow speed was kept constant at 1,750 cm/s as was the slit thickness of 0.1 cm, corresponding to conditions in the experiments of Brown. The analytical computations revealed edge tones to be present in four harmonic stages of jet flow instability over the wedge as the jet length was varied from 0.3 to 1.6 cm. Excellent agreement was obtained in all four edge tone stage cases between the present computational results and the experimentally obtained frequencies and flow visualization results of Brown. Specific edge tone generation phenomena and further confirmation of certain theories and empirical formulas concerning these phenomena were brought to light in this analytical simulation of edge tones.
Aeroacoustic noise generation in a supersonic round jet is studied to understand in particular the effect of turbulence structure on the noise without numerically compromising the turbulence itself. This means that direct numerical simulations (DNS's) are needed. In order to use DNS at high enough Reynolds numbers to get sufficient turbulence structure we have decided to solve the temporal jet problem, using periodicity in the direction of the jet axis. Physically this means that turbulent structures in the jet are repeated in successive downstream cells instead of being gradually modified downstream into a jet plume. Therefore in order to answer some questions about the turbulence we will partially compromise the overall structure of the jet. The first section of chapter 1 describes some work on the linear stability of a supersonic round jet and the implications of this for the jet noise problem. In the second section we present preliminary work done using a TVD numerical scheme on a CM5. This work is only two-dimensional (plane) but shows very interesting results, including weak shock waves. However this is a nonviscous computation and the method resolves the shocks by adding extra numerical dissipation where the gradients are large. One wonders whether the extra dissipation would influence small turbulent structures like small intense vortices. The second chapter is an extensive discussion of preliminary numerical work using the spectral method to solve the compressible Navier-Stokes equations to study turbulent jet flows. The method uses Fourier expansions in the azimuthal and streamwise direction and a 1-D B-spline basis representation in the radial direction. The B-spline basis is locally supported and this ensures block diagonal matrix equations which are solved in O(N) steps. A very accurate highly resolved DNS of a turbulent jet flow is expected.
This work addresses the significant differences in compressor rotor wake mixing loss which exist in a stage environment relative to a rotor in isolation. The wake decay for a rotor in isolation is due solely to viscous dissipation which is an irreversible process and thus leads to a loss in both total pressure and efficiency. Rotor wake decay in the stage environment is due to both viscous mixing and the inviscid strain imposed on the wake fluid particles by the stator velocity field. This straining process, referred to by Smith (1993) as recovery, is reversible and for a 2D rotor wake leads to an inviscid reduction of the velocity deficit of the wake. A model for the rotor wake decay process is developed and used to quantify the viscous dissipation effects relative to those of inviscid wake stretching. The model is verified using laser anemometer measurements acquired in the wake of a transonic rotor operated in isolation and in a stage configuration at near peak efficiency and near stall operating conditions. Additional insight is provided by a time-accurate 3D Navier-Stokes simulation of the compressor stator flow field at the corresponding stage loading levels. Results from the wake decay model exhibit good agreement with the experimental data. Data from the model, laser anemometer measurements, and numerical simulations indicate that for the rotor/stator spacing used in this work, which is typical of core compressors, rotor wake straining (stretching) is the primary decay process in the stator passage with viscous mixing playing only a minor role. The implications of these results on compressor stage design are discussed.
The present study uses two dimensional numerical simulations to study unsteady low-Reynolds-number separation bubbles. The numerical study is in two parts: (1) a two dimensional time-accurate Navier-Stokes solver is used to simulate flows over the APEX airfoil, and (2) a numerical procedure is developed for localized simulations of transitional separation bubbles. The 2-D computations of flow over the APEX airfoil show that the flow is unsteady with periodic vortex shedding. A linear stability analysis of the separated flow shows that the vortex shedding is caused due to the instability of the separated flow. For transonic flows over the APEX airfoil the vortex shedding is additionally influenced by the presence of shocks. The flowfield has two characteristic time scales, one corresponding to the vortex shedding and another corresponding to the movement of the shocks. The two dimensional (2-D) airfoil simulations also showed the presence of nonlinear effects in the separated region. To better understand the characteristics of separation bubbles a numerical procedure has been developed for localized separation bubble calculations. This procedure is used to perform computations for a flat plate separation bubble test case. The separation bubble is induced by specifying a velocity gradient in the freestream. The growth of disturbances in the separation bubble is analyzed by introducing disturbances upstream of the separation bubble.
A new reduced-order model of multidimensional synthetic jet actuators that combines the accuracy and conservation properties of full numerical simulation methods with the efficiency of simplified zero-order models is proposed. The multidimensional actuator is simulated by solving the time-dependent compressible quasi-1-D Euler equations, while the diaphragm is modeled as a moving boundary. The governing equations are approximated with a fourth-order finite difference scheme on a moving mesh such that one of the mesh boundaries coincides with the diaphragm. The reduced-order model of the actuator has several advantages. In contrast to the 3-D models, this approach provides conservation of mass, momentum, and energy. Furthermore, the new method is computationally much more efficient than the multidimensional Navier-Stokes simulation of the actuator cavity flow, while providing practically the same accuracy in the exterior flowfield. The most distinctive feature of the present model is its ability to predict the resonance characteristics of synthetic jet actuators; this is not practical when using the 3-D models because of the computational cost involved. Numerical results demonstrating the accuracy of the new reduced-order model and its limitations are presented.
A numerically calculated Green's function is used to predict jet noise spectrum and its far-field directivity. A linearized form of Lilley's equation governs the non-causal Green s function of interest, with the non-linear terms on the right hand side identified as the source. In this paper, contributions from the so-called self- and shear-noise source terms will be discussed. A Reynolds-averaged Navier-Stokes solution yields the required mean flow as well as time- and length scales of a noise-generating turbulent eddy. A non-compact source, with exponential temporal and spatial functions, is used to describe the turbulence velocity correlation tensors. It is shown that while an exact non-causal Green's function accurately predicts the observed shift in the location of the spectrum peak with angle as well as the angularity of sound at moderate Mach numbers, at high subsonic and supersonic acoustic Mach numbers the polar directivity of radiated sound is not entirely captured by this Green's function. Results presented for Mach 0.5 and 0.9 isothermal jets, as well as a Mach 0.8 hot jet conclude that near the peak radiation angle a different source/Green's function convolution integral may be required in order to capture the peak observed directivity of jet noise.
This work studies pressurization and pressure control of a large liquid hydrogen storage tank. A finite element model is developed that couples a lumped thermodynamic formulation for the vapor region with a complete solution of the Navier-Stokes and energy equations for the flow and temperature fields in the liquid. Numerical results show that buoyancy effects are strong, even in microgravity, and can reposition a vapor bubble that is initially at the center of the tank to a region near the tank wall in a relatively short time. Long-term tank pressurization with the vapor bubble at the tank wall shows that after an initial transient lasting about a week, the final rate of pressure increase agrees with a purely thermodynamic analysis of the entire tank. However, the final pressure levels are quite different from thermodynamic predictions. Numerical results also show that there is significant thermal stratification in the liquid due to the effects of natural convection. A subcooled jet is used to provide simultaneous cooling and mixing in order to bring the tank pressure back down to its initial value. Three different jet speeds are examined. Although the lowest jet speed is ineffective at controlling the pressure because of insufficient penetration into the liquid region, the highest jet speed is shown to be quite effective at disrupting thermal stratification and reducing the tank pressure in reasonable time.
A research project is underway at NASA Glenn to produce computer software that can accurately predict ice growth under any meteorological conditions for any aircraft surface. This report will present results from version 3.0 of this software, which is called LEWICE. This version differs from previous releases in that it incorporates additional thermal analysis capabilities, a pneumatic boot model, interfaces to computational fluid dynamics (CFD) flow solvers and has an empirical model for the supercooled large droplet (SLD) regime. An extensive comparison of the results in a quantifiable manner against the database of ice shapes and collection efficiency that have been generated in the NASA Glenn Icing Research Tunnel (IRT) has also been performed. The complete set of data used for this comparison will eventually be available in a contractor report. This paper will show the differences in collection efficiency between LEWICE 3.0 and experimental data. Due to the large amount of validation data available, a separate report is planned for ice shape comparison. This report will first describe the LEWICE 3.0 model for water collection. A semi-empirical approach was used to incorporate first order physical effects of large droplet phenomena into icing software. Comparisons are then made to every single element two-dimensional case in the water collection database. Each condition was run using the following five assumptions: 1) potential flow, no splashing; 2) potential flow, no splashing with 21 bin drop size distributions and a lift correction (angle of attack adjustment); 3) potential flow, with splashing; 4) Navier-Stokes, no splashing; and 5) Navier-Stokes, with splashing. Quantitative comparisons are shown for impingement limit, maximum water catch, and total collection efficiency. The results show that the predicted results are within the accuracy limits of the experimental data for the majority of cases.
The convergence of a Runge-Kutta (RK) scheme with multigrid is accelerated by preconditioning with a fully implicit operator. With the extended stability of the Runge-Kutta scheme, CFL numbers as high as 1000 could be used. The implicit preconditioner addresses the stiffness in the discrete equations associated with stretched meshes. Numerical dissipation operators (based on the Roe scheme, a matrix formulation, and the CUSP scheme) as well as the number of RK stages are considered in evaluating the RK/implicit scheme. Both the numerical and computational efficiency of the scheme with the different dissipation operators are discussed. The RK/implicit scheme is used to solve the two-dimensional (2-D) and three-dimensional (3-D) compressible, Reynolds-averaged Navier-Stokes equations. In two dimensions, turbulent flows over an airfoil at subsonic and transonic conditions are computed. The effects of mesh cell aspect ratio on convergence are investigated for Reynolds numbers between 5.7 x 10(exp 6) and 100.0 x 10(exp 6). Results are also obtained for a transonic wing flow. For both 2-D and 3-D problems, the computational time of a well-tuned standard RK scheme is reduced at least a factor of four.
Insights and lessons learned from the aerodynamic analysis of the High Wing Transport (HWT) high-lift configuration are presented. Three-dimensional Navier-Stokes CFD simulations using the OVERFLOW flow solver are compared with high Reynolds test data obtained in the NASA Ames 12 Foot Pressure Wind Tunnel (PWT) facility. Computational analysis of the baseline HWT high-lift configuration with and without Externally Blown Flap (EBF) jet effects is highlighted. Several additional aerodynamic investigations, such as nacelle strake effectiveness and wake vortex studies, are presented. Technical capabilities and shortcomings of the computational method are discussed and summarized.
Two Reynolds-averaged Navier-Stokes codes were used to compute flow over the NASA Trapezoidal Wing at high lift conditions for the 1st AIAA CFD High Lift Prediction Workshop, held in Chicago in June 2010. The unstructured-grid code FUN3D and the structured-grid code CFL3D were applied to several different grid systems. The effects of code, grid system, turbulence model, viscous term treatment, and brackets were studied. The SST model on this configuration predicted lower lift than the Spalart-Allmaras model at high angles of attack; the Spalart-Allmaras model agreed better with experiment. Neglecting viscous cross-derivative terms caused poorer prediction in the wing tip vortex region. Output-based grid adaptation was applied to the unstructured-grid solutions. The adapted grids better resolved wake structures and reduced flap flow separation, which was also observed in uniform grid refinement studies. Limitations of the adaptation method as well as areas for future improvement were identified.
An acoustic analogy is developed based on the Euler equations for broadband shock- associated noise (BBSAN) that directly incorporates the vector Green's function of the linearized Euler equations and a steady Reynolds-Averaged Navier-Stokes solution (SRANS) as the mean flow. The vector Green's function allows the BBSAN propagation through the jet shear layer to be determined. The large-scale coherent turbulence is modeled by two-point second order velocity cross-correlations. Turbulent length and time scales are related to the turbulent kinetic energy and dissipation. An adjoint vector Green's function solver is implemented to determine the vector Green's function based on a locally parallel mean flow at streamwise locations of the SRANS solution. However, the developed acoustic analogy could easily be based on any adjoint vector Green's function solver, such as one that makes no assumptions about the mean flow. The newly developed acoustic analogy can be simplified to one that uses the Green's function associated with the Helmholtz equation, which is consistent with the formulation of Morris and Miller (AIAAJ 2010). A large number of predictions are generated using three different nozzles over a wide range of fully expanded Mach numbers and jet stagnation temperatures. These predictions are compared with experimental data from multiple jet noise labs. In addition, two models for the so-called 'fine-scale' mixing noise are included in the comparisons. Improved BBSAN predictions are obtained relative to other models that do not include the propagation effects, especially in the upstream direction of the jet.