Small unsteady perturbations in transonic flows

Fung, K.-Y.; Yu, N. J.; Seebass, R.

doi:10.2514/6.1977-675

Cited by 8 publications

(5 citation statements)

References 5 publications

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“…These assumptions along with appropriate independent-variable scalings provide a linearized theory which formally applies at free-stream Mach numbers close to one, but only for low-frequency unsteady motions. Finite-difference methods have been developed for solving the time-linearized transonic equations in either the time (Fung, Yu & Seebass 1978) or frequency (Ehlers & Weatherill 1982) domain. But these methods have been applied only to the prediction of unsteady transonic flows around isolated airfoils.…”

Section: Introductionmentioning

confidence: 99%

A linearized unsteady aerodynamic analysis for transonic cascades

Verdon¹,

Caspar²

1984

J. Fluid Mech.

142

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A linearized potential-flow analysis is presented for predicting the unsteady airloads produced by the vibrations of turbomachinery blades operating at transonic Mach numbers. The unsteady aerodynamic model includes the effects of blade geometry, non-zero mean-pressure variation across the blade row, high-frequency blade motion, and shock motion within the framework of a linearized frequency-domain formulation. The unsteady equations are solved using an implicit least-squares finite-difference approximation which is applicable on arbitrary grids. A numerical solution for the entire unsteady flow field is determined by matching a solution determined on a rectilinear-type cascade mesh, which covers an extended blade-passage region, to a solution determined on a detailed polar-type local mesh, which covers and extends well beyond the supersonic region(s) adjacent to a blade surface. Results are presented for cascades of double-circular-arc and flat-plate blades to demonstrate the unsteady analysis and to partially illustrate the effects of blade geometry, inlet Mach number, blade-vibration frequency and shock motion on unsteady response.

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Section: Introductionmentioning

confidence: 99%

A linearized unsteady aerodynamic analysis for transonic cascades

Verdon¹,

Caspar²

1984

J. Fluid Mech.

142

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“…The aerofoil functions required in the flow tangency boundary condition are obtained by least-square interpolation (using low-order polynomials) of the aerofoil coordinates, taking into account of the square root behaviour at the aerofoil nose. Any shock wave that exists in the flowfield must satisfy the shock jump condition (Fung et al (12) and Ly et al (13) ) derived from the conservation law form of Equation (1), namely, together with the condition derived from the assumption of irrotationality,…”

Section: General-frequency Tsd Equation and Boundary Conditionsmentioning

confidence: 99%

“…The shock wave motion is time-linearised (Ly and Gear (2) and Fung et al (12) ) as, to first-order approximation and for |Λ u | << 1,…”

Section: Inclusion Of Shock Wave Motion Effectsmentioning

confidence: 99%

“…In general, their results compared reasonably with the experimental data, except in the regions where shock wave motion is anticipated. Fung et al (12) computed the time-linearised time-domain solution including shock wave motion effects, but because they solved the low-frequency TSD equation, their theory cannot be applied to model transonic flows in moderate to high-frequency range.…”

Section: Introductionmentioning

confidence: 99%

“…This results in a coupled flow problem for the steady and first-order unsteady reduced velocity potentials. The steady flow problem is governed by the usual nonlinear steady TSD equation (Ly and Gear (2) , Traci et al (7,8) , Fung et al (12) and Ly et al (13) ) and shockgenerated entropy and vorticity effects are incorporated. The governing equation for the first-order unsteady reduced potential is linear, locally of mixed elliptic/hyperbolic type depending upon the nature of the steady-state solution, and solved in conjunction with the shock jump correction procedure.…”

Section: Introductionmentioning

confidence: 99%

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Time-linearised transonic computations including entropy, vorticity and shock wave motion effects

Nakamichi²

2003

Aeronaut. j.

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The effect of small perturbations on steady nonlinear transonic small disturbance flowfields, in the context of two-dimensional flows governed by the general-frequency transonic small disturbance equation with nonreflecting far-field boundary conditions, is investigated. This paper presents a time-linearised time-domain solution method that includes effects due to the shock-generated entropy and vorticity and shock wave motions. The solution procedure correctly accounts for the small-amplitude shock wave motion due to small unsteady changes in the aerofoil boundary conditions, and correctly models a flowfield with embedded strong shock waves. Steady and first harmonic pressure distributions for the NACA 0003 aerofoil with a harmonically oscillating flap, and NACA 0012 aerofoil undergoing a sinusoidal pitching oscillation, are predicted and compared with the Euler results.

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Implicit Shock-Fitting Scheme for Unsteady Transonic Flow Computations

Seebass

Ballhaus

1978

AIAA Journal

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Small unsteady perturbations in transonic flows

Cited by 8 publications

References 5 publications

A linearized unsteady aerodynamic analysis for transonic cascades

A linearized unsteady aerodynamic analysis for transonic cascades

Time-linearised transonic computations including entropy, vorticity and shock wave motion effects

Implicit Shock-Fitting Scheme for Unsteady Transonic Flow Computations

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