Radial Mode Analysis of Ducted Sound Fields with Sensor Rakes and Wall Flush Sensor Arrays under Consideration of a Radial Flow Profile

2016 ◽  
Author(s):  
Mirko Spitalny ◽  
Ulf Tapken
Keyword(s):  
Radial Flow ◽  
Sensor Arrays ◽  
Radial Mode ◽  
Mode Analysis ◽  
Flow Profile ◽  
Sound Fields

An Acoustic Excitation System for the Generation of Turbomachinery Specific Sound Fields: Part I — Design and Methodology

2016 ◽  
Author(s):  
Akif Mumcu ◽  
Christian Keller ◽  
C. Mandanna Hurfar ◽  
Joerg R. Seume
Keyword(s):  
Sound Propagation ◽  
Microphone Array ◽  
Sound Field ◽  
Radial Mode ◽  
Mode Analysis ◽  
Acoustic Excitation ◽  
Axial Distribution ◽  
Excitation System ◽  
Sound Fields ◽  
Duct Wall

A strong focus in the development of modern aircraft engines is the reduction of the engine tonal core noise. For the development of efficient noise reduction techniques, a detailed understanding of the sound transmission throughout all turbomachinery components of the engine is mandatory. In this paper an excitation system is developed to generate turbomachinery-specific sound fields by controlling their circumferential and radial mode order. The excitation system consists of two rows of eight loudspeakers distributed circumferentially around the outer duct wall. This paper gives a detailed description of the analytically- and numerically-supported design methodology of an optimized excitation system, as well as an optimized microphone array mounted flush with the outer duct wall. A sensitivity analysis of the loudspeaker array and of the microphone array with respect to distance and frequency is then carried out numerically. To analyze the microphone signals and to deconstruct the propagating sound field into its modal components, a Radial Mode Analysis (RMA) is carried out. To ensure high-quality RMA results, the axial distribution of the microphones is optimized with respect to the condition number of the array’s transfer matrix. The procedure explained in this paper shall help guide the development of acoustic excitation and microphone array systems for experiments to better understand sound propagation in turbomachinery and flow ducts.

Unsteady-State Spherical Flow With Storage and Skin

1985 ◽  
Vol 25 (06) ◽  
pp. 804-822 ◽  
Author(s):  
Jeffrey A. Joseph ◽  
Leonard F. Koederitz
Keyword(s):  
Boundary Condition ◽  
Radial Flow ◽  
Linear Partial Differential Equation ◽  
Flow Profile ◽  
Unsteady State ◽  
Well Test ◽  
Linear Flow ◽  
Dimensionless Groups ◽  
Short Time ◽  
Suitable Expression

Abstract This paper presents short-time interpretation methods for radial-spherical (or radial-hemispherical) flow in homogeneous and isotropic reservoirs inclusive of wellbore storage, wellbore phase redistribution, and damage skin effects. New dimensionless groups are introduced to facilitate the classic transformation from radial flow in the sphere to linear flow in the rod. Analytical expressions, type curves (in log-log and semilog format), and tabulated solutions are presented, both in terms of pressure and rate, for all flow problems considered. A new empirical equation to estimate the duration of wellbore and near-wellbore effects under spherical flow is also proposed. Introduction The majority of the reported research on unsteady-state flow theory applicable to well testing usually assumes a cylindrical (typically a radial-cylindrical) flow profile because this condition is valid for many test situations. Certain well tests, however, are better modeled by assuming a spherical flow symmetry (e.g., wireline formation testing, vertical interference testing, and perhaps even some tests conducted in wellbores that do not fully penetrate the productive horizon or are selectively penetrate the productive horizon or are selectively completed). Plugged perforations or blockage of a large part of an openhole interval may also promote spherical flow. Numerous solutions are available in the literature for almost every conceivable cylindrical flow problem; unfortunately, the companion spherical problem has not received as much attention, and comparatively few papers have been published on this topic. papers have been published on this topic. The most common inner boundary condition in well test analysis is that of a constant production rate. But with the advent of downhole tools capable of the simultaneous measurement of pressures and flow rates, this idealized inner boundary condition has been refined and more sophisticated models have been proposed. Therefore, similar methods must be developed for spherical flow analysis, especially for short-time interpretations. This general problem has recently been addressed elsewhere. Theory The fundamental linear partial differential equation (PDE) describing fluid flow in an infinite medium characterized by a radial-spherical symmetry is (1) The assumptions incorporated into this diffusion equation are similar to those imposed on the radial-cylindrical diffusivity equation and are discussed at length in Ref. 9. In solving Eq. 1, the classic approach is illustrated by Carslaw and Jaeger (later used by Chatas, and Brigham et al.). According to Carslaw and Jaeger, mapping b=pr will always reduce the problem of radial flow in the sphere (Eq. 1) to an equivalent problem of linear flow in the rod for which general solutions are usually known. (For example, see Ref. 17 for particular solutions in petroleum applications.) Note that in this study, we assumed that the medium is spherically isotropic; hence k in Eq. 1 is the constant spherical permeability. This assumption, however, does not preclude analysis in systems possessing simple anisotropy (i.e., uniform but unequal horizontal and vertical permeability components). In this case, k as used in this paper should be replaced by k, an equivalent or average (but constant) spherical permeability. Chatas presented a suitable expression (his Eq. 10) obtained presented a suitable expression (his Eq. 10) obtained from a volume integral. It is desirable to transform Eq. 1 to a nondimensional form, thereby rendering its applicability universal. The following new, dimensionless groups accomplish this and have the added feature that solutions are obtained directly in terms of the dimensionless pressure drop, PD, not the usual b (or bD) groups. ......................(2) .......................(3) .........................(4) The quantity rsw is an equivalent or pseudospherical wellbore radius used to represent the actual cylindrical sink (or source) of radius rw. SPEJ p. 804

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