On a finite element CFD algorithm for compressible, viscous and turbulent aerodynamic flows

Baker, A. J.; Kim, J. W.; Freels, James D; Orzechowski, J. A.

doi:10.1002/fld.1650071107

Cited by 10 publications

(6 citation statements)

References 36 publications

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“…1) Here a denominator of a second part of (3)(4)(5)(6)(7)(8) increases if ξ > 1. 1) Here a denominator of a second part of (3)(4)(5)(6)(7)(8) increases if ξ > 1.…”

Section: Some Particular Cases Of 1d2c Flowsmentioning

confidence: 99%

“…Combining equations (3)(4)(5)(6)(7)(8)(9)(10) and (1-12), the expression for the radial velocity is obtained in the following form:…”

Section: (3-10)mentioning

confidence: 99%

“…(3)(4)(5)(6)(7)(8)(9)(10)(11)(12)(13) Calculation results are shown in Fig. (3)(4)(5)(6)(7)(8)(9)(10)(11)(12)(13) Calculation results are shown in Fig.…”

Section: Equation (2-3) Yieldsmentioning

confidence: 99%

“…f/fo-ψξ = tana 0 tan 2 α 0 )-1/ξ 2 ' (3)(4)(5)(6)(7)(8)(9)(10)(11)(12)(13)(14) i.e. cross section area of the channel diminishes as radius increases.…”

Section: ) By Multiplying Into ξmentioning

confidence: 99%

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One-dimensional Steady-state Radial Swirling Gas Flow

Levy¹,

Sherbaum²,

Hekhamkin³

2002

International Journal of Turbo and Jet Engines

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It is well known that in the case of one-dimensional ideal isentropic flows, Hugoniot's equation enables to analyze the effect of the nozzle geometry on the flow regime. In such flows it is essential that the velocity vector coincides with the longitudinal channel axis.A class of one-dimensional flows, namely axisymmetric swirling radial flows, that are typical for radial turbines and compressors, is described. A generalized Hugoniot equation was developed. Some limiting cases are analyzed and the influence of the channel configuration on the flow characteristics is examined. Four particular cases were considered: (I) flow with constant radial velocity, (2) flow with constant absolute velocity, (3) flow in a channel with parallel walls, and (4) flow with radial Mach number equal to 1.It was established that in the first case the required channel width depends only on a single parameter -the tangential Mach number Μ φ and in the second -only on the swirling angle a a (swirling parameter κ 0 ). Regarding the third case, it was found that there are limiting values of the swirling parameter κ, corresponding to M r * 0 that in turn depend on their initial values κ 0 . It was also found that increase of κ enhances the dependence of M r = M r (r). If radial Mach number equal to 1, (case 4), channel cross section area grows smaller as the channel radius increases.A set of equations relating the channel radius and its width with the gas flow parameters is derived. This set can serve as basis for determination of the channel profile.

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“…1) Here a denominator of a second part of (3)(4)(5)(6)(7)(8) increases if ξ > 1. 1) Here a denominator of a second part of (3)(4)(5)(6)(7)(8) increases if ξ > 1.…”

Section: Some Particular Cases Of 1d2c Flowsmentioning

confidence: 99%

“…Combining equations (3)(4)(5)(6)(7)(8)(9)(10) and (1-12), the expression for the radial velocity is obtained in the following form:…”

Section: (3-10)mentioning

confidence: 99%

“…(3)(4)(5)(6)(7)(8)(9)(10)(11)(12)(13) Calculation results are shown in Fig. (3)(4)(5)(6)(7)(8)(9)(10)(11)(12)(13) Calculation results are shown in Fig.…”

Section: Equation (2-3) Yieldsmentioning

confidence: 99%

“…f/fo-ψξ = tana 0 tan 2 α 0 )-1/ξ 2 ' (3)(4)(5)(6)(7)(8)(9)(10)(11)(12)(13)(14) i.e. cross section area of the channel diminishes as radius increases.…”

Section: ) By Multiplying Into ξmentioning

confidence: 99%

See 2 more Smart Citations

One-dimensional Steady-state Radial Swirling Gas Flow

Levy¹,

Sherbaum²,

Hekhamkin³

2002

International Journal of Turbo and Jet Engines

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“…Although considerable success has been achieved by using the methods such as the streamline-upwind Petrov-Galerkin method [8], the Taylor-Galerkin method [55,7], the Taylor-Galerkin method with flux-corrected transpose(FCT) and mesh refinement[5659], the block relaxation via Godunov's method [60] ,the characteristic Galerkin method [61], and the non-osillatory discontinuous Galerkin method [62], more investigation is still needed to compare the efficiency and accuracy of these methods and alternative schemes.…”

Section: High-speed Compressible Flowmentioning

confidence: 99%

Least-squares finite element method for fluid dynamics

Jiang

Povinelli

1990

Computer Methods in Applied Mechanics and Engineering

146

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Least‐squares finite element methods for compressible Euler equations

Jiang

Carey

1990

Numerical Methods in Fluids

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SUMMARYA method based on backward finite differencing in time and a least-squares finite element scheme for firstorder systems of partial differential equations in space is applied to the Euler equations for gas dynamics. The scheme minimizes the L2-norm of the residual within each time step. The method naturally generates numerical dissipation proportional to the time step size. An implicit method employing linear elements has been implemented and proves robust. For high-order elements, computed solutions based on the L2-method may have oscillations for calculations at similar time step sizes. To overcome this difficulty, a scheme which minimizes the weighted If'-norm of the residual is proposed and leads to a successful scheme with highdegree elements. Finally, a conservative least-squares finite element method is also developed. Numerical results for two-dimensional problems are given to demonstrate the shock resolution of the methods and compare different approaches. KEY WORDS Compressible Euler equations Finite element Least-squares method Shock resolution

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On a finite element CFD algorithm for compressible, viscous and turbulent aerodynamic flows

Cited by 10 publications

References 36 publications

One-dimensional Steady-state Radial Swirling Gas Flow

One-dimensional Steady-state Radial Swirling Gas Flow

Least-squares finite element method for fluid dynamics

Least‐squares finite element methods for compressible Euler equations

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