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Farassat, F.

Publications and source records attributed to Farassat, F..

At least 73 records · Page 4
All sourcesNASA NTRSDOE OSTI
NASA NTRS1996

A study of wave propagation in a duct and mode radiation

In this paper we discuss two problems of classical duct acoustics: (1) wave propagation in infinite ducts with uniform flow based on a graphical approach, and (2) detection of mode radiation from a duct by an external circular microphone array. In (1) we show that the wave number vectors for a given flow Mach number form an ellipse whose center and shape depend on the Mach number only. We construct graphically the upstream and downstream wave number vectors of modes that propagate in the duct. We then show how one can infer from this graphical approach many known results in duct propagation such as the mode cut-off concept, the direction of energy propagation, the angle of the radiation lobe at peak directivity using Rice' s cutoff ratio concept, and other qualitative results. In (2) we give the mathematics behind the experimental detection of mode radiation from a duct by a circular array of microphones whose axis coincides with the engine axis. Since the external microphone array does not introduce additional noise sources inside the engine, as does a rotating rake of microphones positioned at the inlet, this measurement technique may be preferable to use of a rotating rake. The simplicity afforded by the lack of sophisticated rotating parts is an additional advantage over the rotating array.

Farassat, F.↗
NASA NTRS1996

The Kirchhoff Formula for a Supersonically Moving Surface

The Kirchhoff formula for radiation from stationary surfaces first appeared in 1882, and it has since found many applications in wave propagation theory. In 1930, Morgans extended the formula to apply to surfaces moving at speeds below the wave propagation speed; we refer to Morgans formula as the subsonic formulation. A modern derivation of Morgans result was published by Farassat and Myers in 1988, and it has now been used extensively in acoustics, particularly for high speed helicopter rotor noise prediction. Under some common conditions in this application, however, the appropriate Kirchhoff surface must be chosen such that portions of it travel at supersonic speed. The available Kirchhoff formula for moving surfaces is not suitable for this situation. In the current paper we derive the Kirchhoff formula applicable to a supersonically moving surface using some results from generalized function theory. The new formula requires knowledge of the same surface data as in the subsonic case. Complications that arise from apparent singularities in the new formulation are discussed briefly in the paper.

Farassat, F.↗
NASA NTRS1995

Scattering Of Nonplanar Acoustic Waves

Report presents theoretical study of scattering of nonplanar acoustic waves by rigid bodies. Study performed as part of effort to develop means of predicting scattering, from aircraft fuselages, of noise made by rotating blades. Basic approach was to model acoustic scattering by use of boundary integral equation to solve equation by the Galerkin method.

Gillman, Judith M.↗
NASA NTRS1994

Introduction to Generalized Functions with Applications in Aerodynamics and Aeroacoustics

Generalized functions have many applications in science and engineering. One useful aspect is that discontinuous functions can be handled as easily as continuous or differentiable functions and provide a powerful tool in formulating and solving many problems of aerodynamics and acoustics. Furthermore, generalized function theory elucidates and unifies many ad hoc mathematical approaches used by engineers and scientists. We define generalized functions as continuous linear functionals on the space of infinitely differentiable functions with compact support, then introduce the concept of generalized differentiation. Generalized differentiation is the most important concept in generalized function theory and the applications we present utilize mainly this concept. First, some results of classical analysis, are derived with the generalized function theory. Other applications of the generalized function theory in aerodynamics discussed here are the derivations of general transport theorems for deriving governing equations of fluid mechanics, the interpretation of the finite part of divergent integrals, the derivation of the Oswatitsch integral equation of transonic flow, and the analysis of velocity field discontinuities as sources of vorticity. Applications in aeroacoustics include the derivation of the Kirchhoff formula for moving surfaces, the noise from moving surfaces, and shock noise source strength based on the Ffowcs Williams-Hawkings equation.

Farassat, F.↗
NASA NTRS1994

An introduction to generalized functions with some applications in aerodynamics and aeroacoustics

In this paper, we start with the definition of generalized functions as continuous linear functionals on the space of infinitely differentiable functions with compact support. The concept of generalization differentiation is introduced next. This is the most important concept in generalized function theory and the applications we present utilize mainly this concept. First, some of the results of classical analysis, such as Leibniz rule of differentiation under the integral sign and the divergence theorem, are derived using the generalized function theory. It is shown that the divergence theorem remains valid for discontinuous vector fields provided that the derivatives are all viewed as generalized derivatives. This implies that all conservation laws of fluid mechanics are valid as they stand for discontinuous fields with all derivatives treated as generalized deriatives. Once these derivatives are written as ordinary derivatives and jumps in the field parameters across discontinuities, the jump conditions can be easily found. For example, the unsteady shock jump conditions can be derived from mass and momentum conservation laws. By using a generalized function theory, this derivative becomes trivial. Other applications of the generalized function theory in aerodynamics discussed in this paper are derivation of general transport theorems for deriving governing equations of fluid mechanics, the interpretation of finite part of divergent integrals, derivation of Oswatiitsch integral equation of transonic flow, and analysis of velocity field discontinuities as sources of vorticity. Applications in aeroacoustics presented here include the derivation of the Kirchoff formula for moving surfaces,the noise from moving surfaces, and shock noise source strength based on the Ffowcs Williams-Hawkings equation.

Farassat, F.↗
NASA NTRS1992

Advanced propeller noise prediction in the time domain

The time domain code ASSPIN gives acousticians a powerful technique of advanced propeller noise prediction. Except for nonlinear effects, the code uses exact solutions of the Ffowcs Williams-Hawkings equation with exact blade geometry and kinematics. By including nonaxial inflow, periodic loading noise, and adaptive time steps to accelerate computer execution, the development of this code becomes complete.

Farassat, F.↗
NASA NTRS1992

Helicopter noise prediction - The current status and future direction

The paper takes stock of the progress, assesses the current prediction capabilities, and forecasts the direction of future helicopter noise prediction research. The acoustic analogy approach, specifically, theories based on the Ffowcs Williams-Hawkings equations, are the most widely used for deterministic noise sources. Thickness and loading noise can be routinely predicted given good plane motion and blade loading inputs. Blade-vortex interaction noise can also be predicted well with measured input data, but prediction of airloads with the high spatial and temporal resolution required for BVI is still difficult. Current semiempirical broadband noise predictions are useful and reasonably accurate. New prediction methods based on a Kirchhoff formula and direct computation appear to be very promising, but are currently very demanding computationally.

Brentner, Kenneth S.↗
NASA NTRS1991

Development of a shock noise prediction code for high-speed helicopters - The subsonically moving shock

A previously defined airfoil subsonic shock-noise prediction formula whose result depends on a mapping of the time-dependent shock surface to a time-independent computational domain is presently coded and incorporated in the NASA-Langley rotor-noise prediction code, WOPWOP. The structure and algorithms used in the shock-noise prediction code are presented; special care has been taken to reduce computation time while maintaining accuracy. Numerical examples of shock-noise prediction are presented for hover and forward flight. It is confirmed that shock noise is an important component of the quadrupole source.

Tadghighi, H.↗
NASA NTRS1991

High-speed helicopter rotor noise - Shock waves as a potent source of sound

In this paper we discuss the problem of high speed rotor noise prediction. In particular, we propose that from the point of view of the acoustic analogy, shocks around rotating blades are sources of sound. We show that, although for a wing at uniform steady rectilinear motion with shocks the volume quadrupole and shock sources cancel in the far field to the order of 1/r, this cannot happen for rotating blades. In this case, some cancellation between volume quadrupoles and shock sources occurs, yet the remaining shock noise contribution is still potent. A formula for shock noise prediction is presented based on mapping the deformable shock surface to a time independent region. The resulting equation is similar to Formulation 1A of Langley. Shock noise prediction for a hovering model rotor for which experimental noise data exist is presented. The comparison of measured and predicted acoustic data shows good agreement.

Farassat, F.↗
NASA NTRS1991

The influence of quadrupole sources in the boundary layer and wake of a blade on helicopter rotor noise

It is presently noted that, for an observer in or near the plane containing a helicopter rotor disk, and in the far field, part of the volume quadrupole sources, and the blade and wake surface quadrupole sources, completely cancel out. This suggests a novel quadrupole source description for the Ffowcs Williams-Hawkings equation which retain quadrupoles with axes parallel to the rotor disk; in this case, the volume and shock surface sourse terms are dominant.

Farassat, F.↗
NASA NTRS1990

State-of-the-art of high-speed propeller noise prediction - A multidisciplinary approach and comparison with measured data

The results of NASA's Propeller Test Assessment program involving extensive flight tests of a large-scale advanced propeller are presented. This has provided the opportunity to evaluate the current capability of advanced propeller noise prediction utilizing principally the exterior acoustic measurements for the prediction of exterior noise. The principal object of this study was to evaluate the state-of-the-art of noise prediction for advanced propellers utilizing the best available codes of the disciplines involved. The effects of blade deformation on the aerodynamics and noise of advanced propellers were also studied. It is concluded that blade deformation can appreciably influence propeller noise and aerodynamics, and that, in general, centrifugal and blade forces must both be included in the calculation of blade forces. It is noted that the present capability for free-field noise prediction of the first three harmonics for advanced propellers is fairly good. Detailed data and diagrams of the test results are presented.

Dunn, Mark H.↗
NASA NTRS1990

A boundary integral approach to the scattering of nonplanar acoustic waves by rigid bodies

The acoustic scattering of an incident wave by a rigid body can be described by a singular Fredholm integral equation of the second kind. This equation is derived by solving the wave equation using generalized function theory, Green's function for the wave equation in unbounded space, and the acoustic boundary condition for a perfectly rigid body. This paper will discuss the derivation of the wave equation, its reformulation as a boundary integral equation, and the solution of the integral equation by the Galerkin method. The accuracy of the Galerkin method can be assessed by applying the technique outlined in the paper to reproduce the known pressure fields that are due to various point sources. From the analysis of these simpler cases, the accuracy of the Galerkin solution can be inferred for the scattered pressure field caused by the incidence of a dipole field on a rigid sphere. The solution by the Galerkin technique can then be applied to such problems as a dipole model of a propeller whose pressure field is incident on a rigid cylinder. This is the groundwork for modeling the scattering of rotating blade noise by airplane fuselages.

Gallman, Judith M.↗
NASA NTRS1990

Can shock waves on helicopter rotors generate noise? - A study of the quadrupole source

An analysis has previously established that local shock surfaces attached to helicopter rotor blades moving at high subsonic speeds are potent noise generators; in pursuit of this insight, a novel formulation is presented for the prediction of the noise of a deformable shock, whose area changes as a function of the azimuthal position of the blade. The derivation of this formulation has its basis in a mapping of the moving shock to a time-independent region. In virtue of this mapping, the implementation of the main result on a computer becomes straightforward enough for incorporation into the available rotor-noise prediction code. A problem illustrating the importance of rotor shocks in the generation of high-intensity noise is presented.

Farassat, F.↗
NASA NTRS1989

High speed propeller acoustics and aerodynamics - A boundary element approach

The Boundary Element Method (BEM) is applied in this paper to the problems of acoustics and aerodynamics of high speed propellers. The underlying theory is described based on the linearized Ffowcs Williams-Hawkings equation. The surface pressure on the blade is assumed unknown in the aerodynamic problem. It is obtained by solving a singular integral equation. The acoustic problem is then solved by moving the field point inside the fluid medium and evaluating some surface and line integrals. Thus the BEM provides a powerful technique in calculation of high speed propeller aerodynamics and acoustics.

Farassat, F.↗
NASA NTRS1989

On the possibility of singularities in the acoustic field of supersonic sources when BEM is applied to a wave equation

Using a time domain method based on the Ffowcs Williams-Hawkings equation, a reliable explanation is provided for the origin of singularities observed in the numerical prediction of supersonic propeller noise. In the last few years Tam and, more recently, Amiet have analyzed the phenomenon from different points of view. The method proposed here offers a clear interpretation of the singularities based on a new description of sources, relating to the behavior of lines where the propeller blade surface exhibit slope discontinuity.

De Bernardis, E.↗
NASA NTRS1988

Extension of Kirchhoff's formula to radiation from moving surfaces

Kirchhoff's formula for radiation from a closed surface has been used recently for prediction of the noise of high speed rotors and propellers. Because the closed surface on which the boundary data are prescribed in these cases is in motion, an extension of Kirchhoff's formula to this condition is required. In this paper such a formula, obtained originally by Morgans for the interior problem, is derived for regions exterior to surfaces moving at speeds below the wave propagation speed by making use of some results of generalized function theory. It is shown that the usual Kirchhoff formula is a special case of the main result of the paper. The general result applies to a deformable surface. However, the special form it assumes for a rigid surface in motion is also noted. In addition, Morgans' result is further extended by showing that edge line integrals appear in the formula when applied to a surface that is piecewise smooth. Some possible areas of application of the formula to problems of current interest in aeroacoustics are discussed.

Farassat, F.↗