##### Author

Virk, Akashdeep Singh

##### Other Contributors

Rusak, Zvi; Borca-Tasçiuc, Diana-Andra; Gandhi, Farhan; Kapila, Ashwani K.;

##### Date Issued

2019-08

##### Subject

Mechanical engineering

##### Degree

PhD;

##### Terms of Use

This electronic version is a licensed copy owned by Rensselaer Polytechnic Institute, Troy, NY. Copyright of original work retained by author.;

##### Abstract

A small-disturbance asymptotic theory which simplifies the governing equations of flow and thermodynamics is derived to describe the complex nature of pure water vapour flow with homogeneous and non-equilibrium condensation around a thin airfoil. Flow is assumed to be steady, compressible and inviscid. The thermodynamics of water vapour is described by a general equation of state. Classical nucleation and droplet growth rate theory is used to model the condensation process. The theoretical model is derived from an asymptotic analysis of the flow and condensation equations in terms of proximity of upstream flow Mach number to 1, small thickness ratio and angle of attack of airfoil and small quantity of condensate. The flow field of water vapour may be described by a non-homogeneous and nonlinear transonic small-disturbance (TSD) equation coupled with a set of four ordinary differential equations to describe the condensation field. The analysis provides a list of similarity parameters that describe the flow physics. A numerical scheme which is composed of Cole and Cook's algorithm for the computation of flow parameters and Simpson's integration method for calculation of condensate mass fraction is applied.; This small-disturbance theory provides a simple and effective tool to model physics of steam flow with homogeneous and non-equilibrium condensation around blades/airfoils operating at high pressures and temperatures and near the vapour-liquid saturation dome. The theory captures the complex interactions between global scale flow phenomena (such as supersonic zone and shock waves) and nanoscale condensation phenomena.; It was found that at low Mach numbers (less than the critical Mach number), all gas models are essentially reduced to the classical Prandtl-Glauert model and result in similar solutions for the flow fields irrespective of free-stream properties. For transonic flows at low temperatures and pressures, the solutions of the gas models are close to each other. However, for transonic flows at high temperatures and pressures, the difference between the solutions produced by various models became more pronounced, suggesting a significant sensitivity of transonic flows of real gases to their thermodynamic modeling.; Using the general equation of state asymptotic analysis, specific TSD models are derived for a perfect gas, a van der Waals gas and a cubic virial gas. The various gas models are used to study effects of independent variation of the upstream flow and thermodynamic conditions of water vapour and of the airfoil's geometry and angle of attack on the fields of pressure and condensate mass fraction, and consequent effect on the wave drag and lift coefficients. Increasing upstream temperature at fixed values of upstream supersaturation ratio and Mach number at zero angle of attack results in increased condensation and higher wave drag coefficient, except for free-stream temperatures higher than 450 K, where the wave drag was found to decrease within the range of 450-500 K. Increasing upstream supersaturation ratio at fixed values of upstream temperature and Mach number at zero angle of attack also results in increased condensation and the wave drag coefficient increases nonlinearly. The effects of increasing upstream Mach number at fixed values of upstream supersaturation ratio and temperature at zero angle of attack are the downstream movement and strengthening of shock wave. Increasing the angle of attack for fixed values of upstream conditions, results in higher condensation compression effects on the suction surface. Comparing the flow and condensation fields of wet steam around airfoils with the same chord length and thickness ratio at zero angle of attack but with different geometries, reveals that NACA0012 airfoil produces the strongest shock wave and the highest condensation compared to the circular arc, a modified airfoil and the sonic arc.;

##### Description

August 2019; School of Engineering

##### Department

Dept. of Mechanical, Aerospace, and Nuclear Engineering;

##### Publisher

Rensselaer Polytechnic Institute, Troy, NY

##### Relationships

Rensselaer Theses and Dissertations Online Collection;

##### Access

Restricted to current Rensselaer faculty, staff and students. Access inquiries may be directed to the Rensselaer Libraries.;