On the Edge Singularity of an Actuator Disk with Large Constant Normal Load

1977 ◽  
Vol 21 (02) ◽  
pp. 125-131
Author(s):  
G. H. Schmidt ◽  
J. A. Sparenberg
Keyword(s):  
Potential Theory ◽  
Normal Load ◽  
Curved Surface ◽  
Singular Behavior ◽  
Nonlinear Potential Theory ◽  
Edge Singularity ◽  
Actuator Disk ◽  
Nonlinear Potential ◽  
Constant Normal Load ◽  
Special Case

In this paper some aspects of the nonlinear potential theory of actuator disks are considered. A rather general formulation of the problem for a prescribed load on a curved surface is given. For the special case of constant normal load and no incoming velocity the singular behavior of the flow at the edge of the disk is discussed.

scholarly journals Weak Barriers in Nonlinear Potential Theory

2007 ◽  
Vol 27 (4) ◽  
pp. 381-387 ◽  
Author(s):  
Anders Björn
Keyword(s):  
Potential Theory ◽  
Nonlinear Potential Theory ◽  
Nonlinear Potential

scholarly journals Nonlinear potentials in function spaces

2002 ◽  
Vol 165 ◽  
pp. 91-116 ◽  
Author(s):  
Murali Rao ◽  
Zoran Vondraćek
Keyword(s):  
Banach Space ◽  
Potential Theory ◽  
Finite Energy ◽  
Duality Mapping ◽  
Quadratic Functional ◽  
Continuous Linear ◽  
Linear Functionals ◽  
Nonlinear Potential Theory ◽  
Nonlinear Potential ◽  
Nonlinear Potentials

We introduce a framework for a nonlinear potential theory without a kernel on a reflexive, strictly convex and smooth Banach space of functions. Nonlinear potentials are defined as images of nonnegative continuous linear functionals on that space under the duality mapping. We study potentials and reduced functions by using a variant of the Gauss-Frostman quadratic functional. The framework allows a development of other main concepts of nonlinear potential theory such as capacities, equilibrium potentials and measures of finite energy.

The Edge Singularity of an Actuator Disc With a Constant Normal Load

2003 ◽  
Author(s):  
Gijs A. M. van Kuik
Keyword(s):  
Normal Load ◽  
Leading Edge ◽  
Radial Component ◽  
Pressure Jump ◽  
Axial Component ◽  
Field Calculation ◽  
Edge Singularity ◽  
Momentum Theory ◽  
Actuator Disc ◽  
Constant Normal Load

All rotor and propeller design methods using momentum theory are based on the concept of the actuator disc, formulated by Froude. In this concept, the rotor load is represented by a uniform pressure jump. This pressure jump generates infinite pressure gradients at the edge of the disc, leading to a velocity singularity. The subject of this paper is the characterization of this velocity singularity assuming inviscid flow. The edge singularity is also the singular leading edge of the vortex sheet emanating from the edge. The singularity is determined as a simple bound vortex of order O(1), carrying an edge force Fedge = −ρ Vedge × Γ. The order of Fedge equals the order of Vedge. This order is determined by a radial momentum analysis. The classical momentum theory for actuators with a constant, normal load Δp appears to be inconsistent: the axial balance provides a value for the velocity at the actuator, with which the radial balance cannot be satisfied. The only way to obtain consistency is to allow the radial component of Fedge to enter the radial balance. The analysis does not resolve on the axial component of Fedge. A quantitative analysis by a full flow field calculation has to assess the value of Fedge for the various actuator disc flow states. Two other solutions for the edge singularity have been published. It is shown that both solutions do not comply with the governing boundary conditions.

scholarly journals Thin sets in nonlinear potential theory

1983 ◽  
Vol 33 (4) ◽  
pp. 161-187 ◽  
Author(s):  
Lars-Inge Hedberg ◽  
Thomas H. Wolff
Keyword(s):  
Potential Theory ◽  
Nonlinear Potential Theory ◽  
Nonlinear Potential ◽  
Thin Sets
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