An Initial Investigation of the Effects of Turbulence Models on the Convergence of the RK/Implicit Scheme

A three-stage Runge-Kutta (RK) scheme with multigrid and an implicit preconditioner has been shown to be an effective solver for the fluid dynamic equations. This scheme has been applied to both the compressible and essentially incompressible Reynolds-averaged Navier-Stokes (RANS) equations using the algebraic turbulence model of Baldwin and Lomax (BL). In this paper we focus on the convergence of the RK/implicit scheme when the effects of turbulence are represented by either the Spalart-Allmaras model or the Wilcox k-! model, which are frequently used models in practical fluid dynamic applications. Convergence behavior of the scheme with these turbulence models and the BL model are directly compared. For this initial investigation we solve the flow equations and the partial differential equations of the turbulence models indirectly coupled. With this approach we examine the convergence behavior of each system. Both point and line symmetric Gauss-Seidel are considered for approximating the inverse of the implicit operator of the flow solver. To solve the turbulence equations we use a diagonally dominant alternating direction implicit (DDADI) scheme. Computational results are presented for three airfoil flow cases and comparisons are made with experimental data. We demonstrate that the two-dimensional RANS equations and transport-type equations for turbulence modeling can be efficiently solved with an indirectly coupled algorithm that uses the RK/implicit scheme for the flow equations

Convergence speeding up in the calculation of the viscous flow about an airfoil

A finite volume method to solve the three dimensional Navier-Stokes equations was developed. It is based on a cell-vertex scheme with central differences and explicit Runge-Kutta time steps. A good convergence for a stationary solution was obtained by the use of local time steps, implicit smoothing of the residues, a multigrid algorithm, and a carefully controlled artificial dissipative term. The method is illustrated by results for transonic profiles and airfoils. The method allows a routine solution of the Navier-Stokes equations

Convergence Acceleration of Runge-Kutta Schemes for Solving the Navier-Stokes Equations

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 can be used. The implicit preconditioner addresses the stiffness in the discrete equations associated with stretched meshes. This RK/implicit scheme is used as a smoother for multigrid. Fourier analysis is applied to determine damping properties. Numerical dissipation operators based on the Roe scheme, a matrix dissipation, and the CUSP scheme are considered in evaluating the RK/implicit scheme. In addition, the effect of the number of RK stages is examined. 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. Turbulent flows over an airfoil and wing at subsonic and transonic conditions are computed. The effects of the cell aspect ratio on convergence are investigated for Reynolds numbers between 5:7 x 10(exp 6) and 100 x 10(exp 6). It is demonstrated that the implicit preconditioner can reduce the computational time of a well-tuned standard RK scheme by a factor between four and ten

Using Malware Analysis to Evaluate Botnet Resilience

Bos, H.J. [Promotor]Steen, M.R. van [Promotor

Convergence Acceleration for Multistage Time-Stepping Schemes

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

Factors Related to Average Concentric Velocity of Four Barbell Exercises at Various Loads

The resistance exercise load is the primarily determinant of the average concentric velocity (ACV) during a repetition. It is unknown whether individual factors such as training experience or anthropometrics also influence the ACV. Previous research has shown the ACV during the 1 repetition maximum (1RM) varies between exercises, but it is not clear whether ACV is different between exercises at various percentages of the 1RM. This information could provide practical guidelines for trainees using ACV to select training loads. Therefore, the purpose of this study was to determine whether training age, current training frequency, limb length, height, and relative strength are related to ACV at loads between 35 and 100% of the 1RM for the squat, bench press, deadlift, and overhead press. A secondary purpose was to compare the ACV values between the 4 lifts at each relative load. Fifty-one (18 women and 33 men) completed 2 testing sessions in which the squat, bench press, deadlift, and overhead press ACV were measured during a modified 1RM protocol. Average concentric velocity values were significantly different among the 4 lifts (p \u3c 0.05) at all relative loads between 35 and 100% 1RM except for 55% 1RM (p = 0.112). Generally, compared at the same relative loads, the overhead press exhibited the greatest ACV followed by the squat, bench press, and deadlift (in order). In addition, relative strength level was inversely related to ACV at maximal loads (≥95% 1RM) for the squat, bench press, and deadlift while height was positively related to ACV at moderate loads (55% 1RM) for all lifts (p \u3c 0.05). These results suggest that the load-velocity profile is unique for each of these exercises, and that velocity ranges used for exercise prescription should be specific to the exercise. A trainee\u27s relative strength and height may be a primary influence on the ACV

14C-Cobalamin Absorption from Endogenously Labeled Chicken Eggs Assessed in Humans Using Accelerator Mass Spectrometry.

Traditionally, the bioavailability of vitamin B-12 (B12) from in vivo labeled foods was determined by labeling the vitamin with radiocobalt (57Co, 58Co or 60Co). This required use of penetrating radioactivity and sometimes used higher doses of B12 than the physiological limit of B12 absorption. The aim of this study was to determine the bioavailability and absorbed B12 from chicken eggs endogenously labeled with 14C-B12 using accelerator mass spectrometry (AMS). 14C-B12 was injected intramuscularly into hens to produce eggs enriched in vivo with the 14C labeled vitamin. The eggs, which provided 1.4 to 2.6 μg of B12 (~1.1 kBq) per serving, were scrambled, cooked and fed to 10 human volunteers. Baseline and post-ingestion blood, urine and stool samples were collected over a one-week period and assessed for 14C-B12 content using AMS. Bioavailability ranged from 13.2 to 57.7% (mean 30.2 ± 16.4%). Difference among subjects was explained by dose of B12, with percent bioavailability from 2.6 μg only half that from 1.4 μg. The total amount of B12 absorbed was limited to 0.5-0.8 μg (mean 0.55 ± 0.19 μg B12) and was relatively unaffected by the amount consumed. The use of 14C-B12 offers the only currently available method for quantifying B12 absorption in humans, including food cobalamin absorption. An egg is confirmed as a good source of B12, supplying approximately 20% of the average adult daily requirement (RDA for adults = 2.4 μg/day)

Playing with nonuniform grids

Numerical experiments with discretization methods on nonuniform grids are presented for the convection-diffusion equation. These show that the accuracy of the discrete solution is not very well predicted by the local truncation error. The diagonal entries in the discrete coefficient matrix give a better clue: the convective term should not reduce the diagonal. Also, iterative solution of the discrete set of equations is discussed. The same criterion appears to be favourable.

Experimental study of flow deflectors designed to alleviate ground winds induced by exhaust of 80-by 120-foot wind tunnel

An experimental study directed at finding a deflector ramp that will reduce to an acceptable level the ground winds under the exhaust jet of the 80 by 120 Foot Wind Tunnel at NASA Ames Center is described. A one-fifieth scale model of the full-scale facility was used to investigate how the jet flow field was modified by the various design parameters of the ramp. It was concluded that the ground winds were alleviated sufficiently by a ramp with end plates located next to the wind tunnel building along the ground edge of the exhaust opening. At full scale, the ramp should have a slant length of 7.62 m (25 ft) or more, and would be elevated at about 45 degrees to the ground plane. The material should have holes less than 15.2 (6 in) in diameter distributed uniformly over its surface to produce a porosity of about 30%

Multi-Fidelity Design Optimization of a Long-Range Blended Wing Body Aircraft with New Airframe Technologies

The German Cluster of Excellence SE²A (Sustainable and Energy Efficient Aviation) is established in order to investigate the influence of game-changing technologies on the energy efficiency of future transport aircraft. In this paper, the preliminary investigation of the four game-changing technologies active flow control, active load alleviation, boundary layer ingestion, and novel materials and structure concepts on the performance of a long-range Blended Wing Body (BWB) aircraft is presented. The BWB that was equipped with the mentioned technologies was designed and optimized using the multi-fidelity aircraft design code SUAVE with a connection to the Computational Fluid Dynamics (CFD) code SU2. The conceptual design of the BWB aircraft is performed within the SUAVE framework, where the influence of the new technologies is investigated. In the second step, the initially designed BWB aircraft is improved by an aerodynamic shape optimization while using the SU2 CFD code. In the third step, the performance of the optimized aircraft is evaluated again using the SUAVE code. The results showed more than 60% reduction in the aircraft fuel burn when compared to the Boeing 77