# Accession Number:

## ADA156993

# Title:

## A Differential Prediction Method for Three-Dimensional Laminar and Turbulent Boundary Layers of Rotating Propeller Blades.

# Descriptive Note:

## Final rept.,

# Corporate Author:

## DAVID W TAYLOR NAVAL SHIP RESEARCH AND DEVELOPMENT CENTER BETHESDA MD

# Personal Author(s):

# Report Date:

## 1985-06-01

# Pagination or Media Count:

## 27.0

# Abstract:

A general mathematical formulation is given for the three dimensional boundary-layer flow on a rotating propeller blade. The basic equations are presented in a nonorthogonal coordinate system which rotates with the blade. Finite difference methods are used to develop a computer code for solving the laminar and turbulent boundary-layer equations. The Reynolds stress tensor is modeled by an algebraic eddy-viscosity formulation. In general, the equations are solved numerically using the standard Keller box method. However, regions of flow reversal across the boundary-layer are computed by the characteristics box method. A companion geometry computer code, developed to model propeller geometry characteristics, and an existing inviscid flow code for computing propeller blade pressures are combined with the boundary-layer computer code to form an efficient computation scheme. For a given potential-flow solution, a typical boundary-layer solution of 690 grid points requires 64 seconds CPU time on a CYBER 176 computer. Computed results are presented for several propeller blade geometries. The rotating segment solution compares well with analytical and experimental data. Predictions for a model propeller also compare favorably with experimental data and illustrate that two-dimensional theory may provide adequate predictions for applications where crossflow effects are not important. Geometry effects of warp and skew are shown to be small for the boundary-layer predictions on three model propellers.

# Descriptors:

- *COMPUTER PROGRAMS
- *BOUNDARY LAYER FLOW
- *PROPELLER BLADES
- STRESSES
- COMPUTATIONS
- PREDICTIONS
- TWO DIMENSIONAL
- THEORY
- ALGEBRA
- BOUNDARY LAYER
- TURBULENCE
- EDDIES(FLUID MECHANICS)
- TURBULENT BOUNDARY LAYER
- CODING
- FINITE DIFFERENCE THEORY
- SOLUTIONS(GENERAL)
- MATHEMATICAL PREDICTION
- REVERSIBLE
- COORDINATES
- PRESSURE
- DIFFERENTIAL EQUATIONS
- GEOMETRY
- TENSORS
- EQUATIONS
- INVISCID FLOW
- ROTATION
- VISCOSITY
- POTENTIAL FLOW
- FORMULAS(MATHEMATICS)
- MOMENTUM TRANSFER
- CROSS FLOW
- THREE DIMENSIONAL FLOW
- LAMINAR BOUNDARY LAYER
- METHOD OF CHARACTERISTICS

# Subject Categories:

- Theoretical Mathematics
- Fluid Mechanics