Turbulent boundary layer thickness estimation method and apparatus

A method for determining turbulent boundary layer thickness, comprising the steps of:

• mounting a pair of sensors to a solid surface interfacing with a fluid at two separate stream wise locations;
• recording a voltage output from said pair of sensors;
• computing a real non-dimensional value of a correlation coefficient from said recorded voltage;
• independently determining a laboratory non-dimensional value of the correlation coefficient from laboratory data;
• and
• comparing the real non-dimensional value with the laboratory non-dimensional value to obtain a boundary layer thickness having a value which minimizes a difference between the values of the real non-dimensional value and the laboratory non-dimensional value;
• wherein said correlation coefficient is defined as:
• R τ 1 ⁢ ⁢ τ 2 ⁢ ⁢ ( ξ n , T ) = ⟨ τ 1 ⁢ ⁢ ( x , t ) ⁢ ⁢ τ 2 ⁢ ⁢ ( x + ξ n , t + T ⟩ ⟨ τ 1 ⁢ ⁢ ( x , t ) 2 ⟩ ⁢ ⁢ ⟨ τ 2 ⁢ ⁢ ( x + ξ n , t + T ) 2 ⟩
• where τ1 and τ2 are the wall shear stress values at the sensor mounting locations, x is the stream wise coordinate, ξn is the discrete sensor spacing, and the < > indicate temporal mean quantities.

A turbulent boundary layer thickness sensor for use in a flowing fluid comprising:

• a first wall stress shear sensor positionable in contact with said flowing fluid to provide a first wall shear stress measurement;
• a second wall stress shear sensor positionable in contact with said flowing fluid relatively downstream from said first wall stress shear sensor to provide a second wall shear stress measurement;
• a first analog to digital converter joined to said first wall stress shear sensor to receive said first wall shear stress measurement and to provide a first digital stress measurement;
• a second analog to digital converter joined to said second wall stress shear sensor to receive said second wall shear stress measurement and to provide a second digital stress measurement;
• a memory element containing tabulated values of the correlation coefficient;
• and
• a computer joined to said first and second analog to digital converters to receive the first and second digital stress measurements and to said memory element to estimate said boundary layer value by calculating a real correlation coefficient from the first and second digital stress measurements and comparing the real correlation coefficient with tabulated values of the correlation coefficient from said memory element.