Axially symmetric potential flow around a slender body

Handelsman, Richard A.; Keller, Joseph B.

doi:10.1017/s0022112067001946

Cited by 76 publications

(58 citation statements)

References 4 publications

(4 reference statements)

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“…where ~(e) and fl(e) determine the extent of the singularities distribution along the body axis and are the same as given by Handelsman andKeller (1967) andGeer (1975;see also Hassan 1992a, b). The components of the SSD function can be found, as shown by Geer (1975) …”

Section: Methods Yieldsmentioning

confidence: 99%

“…when used with the VP equations of the oscillating sphere and of the body yields a linear integral equation for each singularity order n. From the leading terms of the uniform asymptotic solutions of the integral equations, the SSD function g,(z, e) can be determined as (Handelsman and Keller 1967;Geer 1975):…”

Section: Methods Yieldsmentioning

confidence: 99%

“…This function was chosen to fulfil the requirement that the derivatives of the cross-sectional function of the body S(z) with respect to z at the body ends may not equal zero to ensure that the SSD function will be analytic for the interval between z = 0 and 1 (Handelsman and Keller 1967). The value of the factor q was taken to be equal to e, the slenderness ratio, which was chosen to be 0.05.…”

Section: Ij(z O Z) = F-js(z O Z) + Ij:(z)mentioning

confidence: 99%

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Mathematical description of the stimuli to the lateral line system of fish, derived from a three-dimensional flow field analysis. III. The case of an oscillating sphere near the fish

Hassan

1993

Biol. Cybern.

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Abstract. The three-dimensional potential flow field of an oscillating sphere near a fish with an axially symmetric body was investigated mathematically. The spatial distributions of the stimuli to the lateral line system are derived from the flow-field analysis, taking into consideration the hydrodynamical interaction between the fish body and the flow of the oscillating sphere. This was done dependent on the location and the direction of oscillation of the sphere relative to the fish. The theoretical results are compared with measurements of the flow on the surface of a fish model.

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Section: Methods Yieldsmentioning

confidence: 99%

Section: Methods Yieldsmentioning

confidence: 99%

Section: Ij(z O Z) = F-js(z O Z) + Ij:(z)mentioning

confidence: 99%

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Mathematical description of the stimuli to the lateral line system of fish, derived from a three-dimensional flow field analysis. III. The case of an oscillating sphere near the fish

Hassan

1993

Biol. Cybern.

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“…It has been applied successfully to various canonical constantcoefficient equations, including Laplace (Handelsman & Keller 1967), Stokes (Batchelor 1970;Cox 1970), Helmholtz (Geer 1978), and Maxwell equations (Geer 1980). In contrast, the possibility of devising similar schemes for the advection-diffusion equation has been largely overlooked.…”

Section: Introductionmentioning

confidence: 99%

Slender-body approximations for advection–diffusion problems

Schnitzer

2015

J. Fluid Mech.

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We consider steady advection-diffusion about a slender ( 1) body of revolution at arbitrary O(1) Péclet numbers (Pe). The transported scalar attenuates at large distances, and is governed by axisymmetric (either Dirichlet or Neumann) data prescribed at the body boundary. The advecting field is assumed to be an axisymmetric Stokes flow approaching a uniform stream at large distances and satisfying impermeability at the boundary; otherwise, the interfacial distribution of tangential velocity is assumed arbitrary, irrotational and no-slip Stokes flows being particular cases. Employing the method of matched asymptotic expansions, we develop a systematic scheme for calculating the scalar concentration in increasing powers of ln −1 (1/ ). The leading term in the inner expansion coincides with the pure diffusion case, the second term depends nonlinearly on the magnitude of the far-field stream, and higher-order terms depend on the boundary distribution of tangential velocity. In the special case of irrotational flow and Neumann boundary conditions the logarithmic expansion terminates, leaving an algebraic error in . The general formulae developed can be directly applied to numerous physical scenarios. We here consider the classical problem of forced heat convection from an isothermal body, finding a two-term expansion for Nu( , Pe)/Nu( , 0), the ratio of the Nusselt number to its value at Pe = 0. This ratio is insensitive to the particle shape at the asymptotic orders considered; at moderately large Pe ( −1 ) its deviation from unity is O [ln(Pe)/ ln(1/ )], marking the poor effectiveness of advection about slender bodies. The expansion is compared to a numerical computation in the case of a prolate spheroid in both irrotational and no-slip Stokes flows.

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“…the blind Mexican cave fish produces (Handelsman and Keller 1967;Geer 1975;Hassan 1985Hassan , 1992aHassan , b, 1993 to sense its environment. The flow field in front of and besides the blind Mexican cave fish may be treated irrotational as long it is moving through nearly undisturbed water.…”

Section: Introductionmentioning

confidence: 99%

Snookie: An Autonomous Underwater Vehicle with Artificial Lateral-Line System

Vollmayr¹,

Sosnowski

Urban³

et al. 2014

Flow Sensing in Air and Water

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In this work we present Snookie, an autonomous underwater vehicle with an artificial lateral-line system. Integration of the artificial lateral-line system with other sensory modalities is to enable the robot to perform behaviors as observed in fish, such as obstacle detection and geometrical-shape reconstruction by means of hydrodynamic images. The present chapter consists of three sections devoted to design of the robot, its lateral-line system, and processing of the ensuing flowsensory data. The artificial lateral-line system of Snookie is presented in detail, together with a simple version of a flow reconstruction algorithm applicable to both the artificial lateral-line system and, e.g. the blind Mexican cave fish. More in particular, the first section deals with the development of the autonomous underwater vehicle Snookie, which provides the functionality and is tailored to the requirements of the artificial lateral-line system. The second section is devoted to the implementation of the artificial lateral-line system that consists of an array of hot thermistor anemometers to be integrated in the nozzle. In the final section, the information processing ensuing from the flow sensors and leading to conclusions about the environment is presented. The measurement of the tangential velocities at the artificial lateral-line system together with the no-penetration condition provides

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Axially symmetric potential flow around a slender body

Cited by 76 publications

References 4 publications

Mathematical description of the stimuli to the lateral line system of fish, derived from a three-dimensional flow field analysis. III. The case of an oscillating sphere near the fish

Mathematical description of the stimuli to the lateral line system of fish, derived from a three-dimensional flow field analysis. III. The case of an oscillating sphere near the fish

Slender-body approximations for advection–diffusion problems

Snookie: An Autonomous Underwater Vehicle with Artificial Lateral-Line System

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