Determination of aerodynamic sensitivity coefficients based on the transonic small perturbation formulation

Elbanna, Hesham M.; Carlson, Leland A.

doi:10.2514/3.25312

Cited by 16 publications

(5 citation statements)

References 4 publications

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“…In general, primarily due to wing sweep and finite span, all the section sensitivity values are smaller in magnitude than corresponding values for the two-dimensional problem. 2 Finally, the agreement between the FD and QA section sensitivities is excellent. Figure 3 shows representative section and wing lift sensitivity derivative results for some of the nonbasic design variables.…”

Section: Resultsmentioning

confidence: 82%

“…In addition, the results followed the trend of the two-dimensional study. 2 Representative results for the chordwise variation of the pressure coefficient and its sensitivity derivatives for a supercritical case (M x = 0.84, a = 3 deg) are shown on Fig. 1 for 56.4% semispan.…”

Section: Resultsmentioning

confidence: 98%

“…1 for the lower surface are typical of subcritical flow. 2 However, the upper surface results exhibit large variations in the vicinity of the shock wave that reflect the influence on the pressure of the sensitivity of the upper surface shock wave location to various design parameters. As can be seen by noting the differences in vertical scale, the pressures and lift coefficient at this mid-semi-span location are most sensitive to camber and least sensitive to camber location.…”

Section: Resultsmentioning

confidence: 99%

“…The best method to obtain these subexpressions was to consider the governing equation and the involved intermediate expressions in the original form given in Eqs. (2)(3)(4)(5)(6)(7)(8)(9)(10)(11)(12)(13)(14). This splitting or nesting of expressions with various intermediate dependencies declared in advance allowed each subexpression to be handled efficiently by the symbolic manipulator, in this case MACSYMA.…”

Section: Symbolic and Numerical Treatmentmentioning

confidence: 99%

“…Application of the QA method to the full potential equation yields the sensitivity equation dXDj where the residual expression in the computational plane in terms of backward differences is (2) The retarded density coefficients in Eq. (2) are Pi +1/2,/,* = (1 ~ ^i + 1/2,7, *)Pi+ 1/2,7,* ~1~ I/ /+l/2,7,*Pi-1/2,7,* Pi, 7+ 1/2,* = HP* + 1/2,/,* ~^~ P/+ 1/2,7+1,* ~^~ P/-1/2,7,* + Pi-l/2,y+l,*) P/,7,*+l/2 = HP/ +1/2,/,* "*" P/+ 1/2,7,*+!…”

Section: Problem Statementmentioning

confidence: 99%

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Aerodynamic sensitivity coefficients using the three-dimensional full potential equation

Elbanna

Carlson

1994

Journal of Aircraft

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The quasianalytical (QA) approach is applied to the three-dimensional full potential equation to compute wing aerodynamic sensitivity coefficients in the transonic regime. Symbolic manipulation is used and is crucial in reducing the effort associated with obtaining sensitivity equations, and the large sensitivity system is solved using sparse solver routines such as the iterative conjugate gradient method. The results obtained are almost identical to those obtained by the finite difference (FD) approach and indicate that obtaining the sensitivity derivatives using the QA approach is more efficient than computing the derivatives by the FD method, especially as the number of design variables increases. It is concluded that the QA method is an efficient and accurate approach for obtaining transonic aerodynamic sensitivity coefficients in three dimensions.

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Section: Resultsmentioning

confidence: 82%

Section: Resultsmentioning

confidence: 98%

Section: Resultsmentioning

confidence: 99%

Section: Symbolic and Numerical Treatmentmentioning

confidence: 99%

Section: Problem Statementmentioning

confidence: 99%

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Aerodynamic sensitivity coefficients using the three-dimensional full potential equation

Elbanna

Carlson

1994

Journal of Aircraft

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Discrete shape sensitivity equations for aerodynamic problems

Hou

Taylor

Korivi

1994

Numerical Meth Engineering

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Intensive research and development in Computational Fluid Dynamics (CFD) has recently produced many powerful CFD codes to simulate complex aerodynamic phenomena. However, in order to enhance the usefulness of these CFD codes for design practice, development of design sensitivity equations compatible to these codes becomes very important. This paper represents a part of such an effort to develop a sensitivity analysis methodology that enables the sensitivity equations to be implemented into existing CFD codes with minimal code modification. The methodology is based upon a pre-elimination procedure which accounts for consistently linearized boundary conditions. Formulations of both the direct differentiation and the adjoint variable methods will be presented in the paper.

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