On artificial dissipation models for viscous airfoil computations

Frew, K.; Zingg, David W.

doi:10.2514/6.1996-1970

Cited by 3 publications

(3 citation statements)

References 7 publications

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“…It should be noted that the large errors resulting from the scalar arti cial dissipation model without preconditioning can also be reduced using matrix dissipation or cell Reynolds number scaling. 13 For the second case, with = 6 o and transition at 5% and 80% chord on the upper and lower surfaces, respectively, a grid-independent drag coe cient of 0.00779 was determined. 12 Using the grid with the smaller o -wall spacing, a drag coe cient of 0.01018 is computed by the unpreconditioned algorithm, an error of 24 counts or 31%.…”

Section: Resultsmentioning

confidence: 99%

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Viscous airfoil computations using local preconditioning

Unrau¹

1997

13th Computational Fluid Dynamics Conference

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A local preconditioning technique for compressible ows at low Mach number is examined in the context of turbulent ows over airfoils. The preconditioning technique is implemented in an approximately-factored algorithm for the steady thin-layer Navier-Stokes equations. Parametric studies are presented showing trade-o s between accuracy and convergence rates. Excellent convergence rates and solution accuracy are demonstrated for freestream Mach numbers as low as 0.01. Improvements in accuracy, especially in drag prediction, are seen for Mach numbers as high as 0.4. Thus the present approach is useful in the computation of low-speed airfoil ows, including those typically encountered during take-o and landing of aircraft. Graduate Student.

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Section: Resultsmentioning

confidence: 99%

“…Note that the di culties associated with the scalar model, discussed for example in Ref 13,. are greatly reduced due to the improved conditioning of the preconditioned ux Jacobian matrices.The second-and fourth-di erence arti cial dissipation terms on the right-hand-side of eq.…”

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confidence: 99%

Viscous airfoil computations using local preconditioning

Unrau¹

1997

13th Computational Fluid Dynamics Conference

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“…Second-and fourth-difference scalar artificial dissipation are used to maintain stability. The algorithm has been well validated for steady [21][22][23][24] and unsteady 4, 7 flows and has been the subject of several grid convergence studies. 25,26…”

Section: Spatial Discretizationmentioning

confidence: 99%

Efficient Implicit Time-Marching Methods Using a Newton-Krylov Algorithm

Tabeshand

Zingg

2009

47th AIAA Aerospace Sciences Meeting Including the New Horizons Forum and Aerospace Exposition

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The numerical behavior of two implicit time-marching methods is investigated in solving two-dimensional unsteady compressible flows. The two methods are the second-order multistep backward differencing formula and the fourth-order multistage explicit first stage, single-diagonal coefficient, diagonally implicit Runge-Kutta scheme. A Newton-Krylov method is used to solve the nonlinear problem arising from the implicit temporal discretization. The methods are studied for two test cases: laminar flow over a cylinder and turbulent flow over a NACA0012 airfoil with a blunt trailing edge. Parameter studies show that the subiteration termination criterion plays a major role in the efficiency of time-marching methods. Efficiency studies show that when only modest global accuracy is needed, the second-order method is preferred. The fourth-order method is more efficient when high accuracy is required. The Newton-Krylov method is seen to be an efficient choice for implicit time-accurate computations.

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Artificial Dissipation Schemes for Viscous Airfoil Computations

1998

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where there is a pressure peak as seen in the theoretical model of the roller-type structure and recent experimental measurements. 12 This supports the idea that the excitation causes a pressure peak in the mixing layer that induces the roller-type structure.Instantaneous and average images were also taken for a Mach 2 jet (M c D 0:85) with no excitation and with laser excitation (Figs. 4d and 4e) having a delay time of 100 ¹s between the excitation and imaging pulses. For the unforced case, the decrease in mixing layer growth rate is clearly observed compared to the lower-convective-Mach-numbercase shown earlier. Also there is no indicationof organizedlarge-scale,roller-typestructures.With laser excitation, however, a spatially stable, roller-type structure is observed in the instantaneousand average images with distinct core (39 § 4% thicker than the unforced case) and braid regions, as observed for the lower-Mach-number case. The convective velocity measured for this case is 365 m/s for the core and 309 m/s for the braid region, with an uncertainty of §4 m/s. Again the measured convective velocity from the braid region is closer to the theoretical convectivevelocity of 297 § 5 m/s, with the measured value slightly higher as already discussed.The forcing mechanism for the large-scale structures in the present study may be similar to wall heating used to force TollmienSchlichting waves in subsonic boundary layers 13 and subsequent Kelvin-Helmholtz waves in free shear layers. 14 Liepmann et al. 13 reported that the forcing of the instability can be explained by the boundary-layer momentum equation and by observing that heating the surface (for a gas) has the same effect as an adverse pressure gradient. If the temperature is large enough, this could lead to a local region of separation, which may force the large-scale structures observedin the present experiments.Note, however, that the forcing was not large enough to cause the nozzle to unstart or create strong shocks, which would have appeared in instantaneous schlieren images that were taken. Further experiments are needed, however, to con rm this explanation. IV. ConclusionAn innovative method of controlling and forcing the creation of large roller-type structures in compressible mixing layers is presented. A laser beam from a pulsed Nd:YAG laser is focused on the nozzle exit of axisymmetric supersonic jets with Mach numbers of 1.36 and 2, resulting in convective Mach numbers of 0.63 and 0.85, respectively. Laser excitation causes a thermal bump at the wall, which induces the formation of a roller-type structure in the mixing layer. Instantaneous and phase-averaged images were taken of the mixing layer to investigatethe ability to induce the large-scalestructure and measure its characteristics.The convectivevelocitiesof the core and braid regions of the structure were found to be higher than the theoretical values. The thickness of the core region was found to be from 32 to 38% greater than the shear layer thicknesswithout excitation. Future experiments will ...

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On artificial dissipation models for viscous airfoil computations

Cited by 3 publications

References 7 publications

Viscous airfoil computations using local preconditioning

Viscous airfoil computations using local preconditioning

Efficient Implicit Time-Marching Methods Using a Newton-Krylov Algorithm

Artificial Dissipation Schemes for Viscous Airfoil Computations

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