Computation of Unsteady Viscous Marine-Propulsor Blade Flows—Part 1: Validation and Analysis

1997 ◽  
Vol 119 (1) ◽  
pp. 145-154 ◽  
Author(s):  
E. G. Paterson ◽  
F. Stern
Keyword(s):  
Stokes Equations ◽  
External Flow ◽  
Navier Stokes ◽  
Massachusetts Institute Of Technology ◽  
Propeller Blade ◽  
Navier Stokes Equations ◽  
Displacement Thickness ◽  
Unsteady Interaction ◽  
Institute Of Technology ◽  
Marine Propulsor

In this two-part paper, time-accurate solutions of the Reynolds-averaged Navier-Stokes equations are presented, which address through model problems, the response of turbulent propeller-blade boundary layers, and wakes to external-flow traveling waves. In Part 1, the Massachusetts Institute of Technology flapping-foil experiment is simulated and the results validated through comparisons with data. The physics of unsteady blade flows are shown to be complex with analogy to Stokes layers and are explicated through visualization and Fourier analysis. It is shown that convection induced steady/unsteady interaction causes deformation of the external-flow waves and is responsible for the upstream- and downstream-traveling pressure-gradient waves over the foil and in the wake, respectively. The nature of the unsteady displacement thickness suggests viscous-inviscid interaction as the mechanism for the response. In Part 2, a parametric study is undertaken to quantify the effects of frequency, foil geometry, and waveform.

Computation of Unsteady Viscous Marine-Propulsor Blade Flows—Part 2: Parametric Study

1999 ◽  
Vol 121 (1) ◽  
pp. 139-147 ◽  
Author(s):  
Eric G. Paterson ◽  
Fred Stern
Keyword(s):  
Boundary Layer ◽  
Frequency Response ◽  
High Frequency ◽  
Stokes Equations ◽  
Low Frequency ◽  
Driving Mechanism ◽  
Massachusetts Institute Of Technology ◽  
Flapping Foil ◽  
Displacement Thickness ◽  
Institute Of Technology

In this two-part paper, time-accurate solutions of the Reynolds-averaged Navier-Stokes equations are presented, which address through model problems, the response of turbulent propeller-blade boundary layers and wakes to external-flow traveling waves. In Part 1, the Massachusetts Institute of Technology flapping-foil experiment was simulated and the results validated through comparisons with data. The response was shown to be significantly more complex than classical unsteady boundary layer and unsteady lifting flows thus motivating further study. In Part 2, the effects of frequency, waveform, and foil geometry are investigated. The results demonstrate that uniquely different response occurs for low and high frequency. High-frequency response agrees with behavior seen in the flapping-foil experiment, whereas low-frequency response displays a temporal behavior which more closely agrees with classical inviscid-flow theories. Study of waveform and geometry show that, for high frequency, the driving mechanism of the response is a viscous-inviscid interaction created by a near-wake peak in the displacement thickness which, in turn, is directly related to unsteady lift and the oscillatory wake sheet. Pressure waves radiate upstream and downstream of the displacement thickness peak for high frequency flows. Secondary effects, which are primarily due to geometry, include gust deformation due to steady-unsteady interaction and trailing-edge counter-rotating vortices which create a two-layered amplitude and phase-angle profile across the boundary layer.

scholarly journals The numerical solution of the asymptotic equations of trailing edge flow

1974 ◽  
Vol 340 (1620) ◽  
pp. 91-111 ◽  
Keyword(s):  
Boundary Layer ◽  
Outer Layer ◽  
Numerical Solutions ◽  
Stokes Equations ◽  
Navier Stokes ◽  
Trailing Edge ◽  
Navier Stokes Equations ◽  
Boundary Layer Equations ◽  
Asymptotic Equations ◽  
Displacement Thickness

According to Stewartson (1969, 1974) and to Messiter (1970), the flow near the trailing edge of a flat plate has a limit structure for Reynolds number Re →∞ consisting of three layers over a distance O (Re -3/8 ) from the trailing edge: the inner layer of thickness O ( Re -5/8 ) in which the usual boundary layer equations apply; an intermediate layer of thickness O ( Re -1/2 ) in which simplified inviscid equations hold, and the outer layer of thickness O ( Re -3/8 ) in which the full inviscid equations hold. These asymptotic equations have been solved numerically by means of a Cauchy-integral algorithm for the outer layer and a modified Crank-Nicholson boundary layer program for the displacement-thickness interaction between the layers. Results of the computation compare well with experimental data of Janour and with numerical solutions of the Navier-Stokes equations by Dennis & Chang (1969) and Dennis & Dunwoody (1966).

Laminar Boundary Layers and Their Separation From Curved Surfaces

1965 ◽  
Vol 87 (2) ◽  
pp. 483-493 ◽  
Author(s):  
B. S. Massey ◽  
B. R. Clayton
Keyword(s):  
Stokes Equations ◽  
Equation Of Motion ◽  
Navier Stokes ◽  
Curved Surfaces ◽  
Integration Technique ◽  
Navier Stokes Equations ◽  
Laminar Boundary Layers ◽  
Displacement Thickness ◽  
Order Of Magnitude ◽  
Similar Solutions

The equation of motion in a laminar boundary layer on curved surfaces has been developed from the Navier-Stokes equations. After an order-of-magnitude analysis terms of highest and next order have been retained and a single ordinary differential equation of motion derived by the method of “similar solutions.” An iteration procedure has been used to determine effects of displacement thickness and surface curvature up to and including separation. The equation of motion has been solved by a digital computer using the Runge-Kutta step-by-step integration technique.

Effects of stator splitter blades on aerodynamic performance of a single-stage transonic axial compressor

2020 ◽  
Vol 14 (4) ◽  
pp. 7369-7378
Author(s):  
Ky-Quang Pham ◽  
Xuan-Truong Le ◽  
Cong-Truong Dinh
Keyword(s):  
Stokes Equations ◽  
Three Dimensional ◽  
Axial Compressor ◽  
Aerodynamic Performance ◽  
Numerical Results ◽  
Single Stage ◽  
Navier Stokes ◽  
Navier Stokes Equations ◽  
Operating Stability ◽  
Length Coverage

Splitter blades located between stator blades in a single-stage axial compressor were proposed and investigated in this work to find their effects on aerodynamic performance and operating stability. Aerodynamic performance of the compressor was evaluated using three-dimensional Reynolds-averaged Navier-Stokes equations using the k-e turbulence model with a scalable wall function. The numerical results for the typical performance parameters without stator splitter blades were validated in comparison with experimental data. The numerical results of a parametric study using four geometric parameters (chord length, coverage angle, height and position) of the stator splitter blades showed that the operational stability of the single-stage axial compressor enhances remarkably using the stator splitter blades. The splitters were effective in suppressing flow separation in the stator domain of the compressor at near-stall condition which affects considerably the aerodynamic performance of the compressor.

Sensitivity analysis for Navier-Stokes equations on unstructured meshes using complex variables

AIAA Journal ◽  
2001 ◽  
Vol 39 ◽  
pp. 56-63
Author(s):  
W. Kyle Anderson ◽  
James C. Newman ◽  
David L. Whitfield ◽  
Eric J. Nielsen
Keyword(s):  
Sensitivity Analysis ◽  
Stokes Equations ◽  
Unstructured Meshes ◽  
Complex Variables ◽  
Navier Stokes ◽  
Navier Stokes Equations

Numerical solution of the reduced Navier-Stokes equations for internal incompressible flows

AIAA Journal ◽  
2000 ◽  
Vol 38 ◽  
pp. 1603-1614
Author(s):  
Martin Scholtysik ◽  
Bernhard Mueller ◽  
Torstein K. Fannelop
Keyword(s):  
Numerical Solution ◽  
Incompressible Flows ◽  
Stokes Equations ◽  
Navier Stokes ◽  
Navier Stokes Equations
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