How to find the given point is inside or outside or lying on circle boundary ?

What is the standard equation of a circle?

(x- h)^2+(y- k)^2= r^2 

This is the general standard equation for the circle centered at (h,k) with radius r. When you center point and radius, then substitute any point (x,y)in the equation. 

• If LHS=RHS, then the point is in the boundary of the circle 
• If LHS <RHS, then the point is inside the circle   
• If LHS > RHS, then the point is outside the circle  

Effect of Stator Leading and Trailing Edge Coolant Flow on Performance of Typical High Pressure Turbine Stage of a Gas Turbine Engine

Effect of Stator Leading and Trailing Edge Coolant Flow on Performance of Typical High Pressure Turbine Stage of a Gas  Turbine Engine:

The Nozzle Guide Vane (NGV) of High Pressure (HP) turbine of modern military gas turbine is extensively cooled to reap the benefits of using higher cycle temperatures and to ensure longer life of the turbine components. NGV of the HP turbine encounters the maximum temperature from the combustion chamber. Hence, cooling of the NGV is essential from creep and thermal fatigue points of view. Compressor Bleed air is used for cooling the NGV and due to addition of mass, leads to decrease in turbine efficiency and increase in losses. The objective of the present study is to determine numerically using 3D Navier Stokes (NS) solver, the effect of Leading edge (LE) and Trailing Edge (TE) coolant ejection on the performance of the NGV via blade loading, efficiency and exit flow angles for different mass ratios

LARGE EDDY SIMULATION OF FLOW OVER NOZZLE GUIDE VANE OF A TRANSONIC HIGH PRESSURE TURBINE

LARGE EDDY SIMULATION OF FLOW OVER NOZZLE GUIDE VANEOF A TRANSONIC HIGH PRESSURE TURBINE

Fifth generation fighter aircraft engines demand thrust to weight ratios in excess of 8 and moderate Specific Fuel Consumption. This calls for lower weight and higher component efficiencies. To improve turbine efficiency, it is necessary to understand the aerodynamic loss generation mechanism in the flow field. Since most such mechanisms are unsteady in nature, it is often necessary to carry out unsteady analysis of the turbine stage. It is desirable to study the loss generation mechanisms in the stationary Nozzle Guide Vanes (NGVs) and the rotor blades through unsteady analysis. In this paper, NGV of a transonic high pressure turbine has been analysed using Large Eddy Simulation (LES) and the results have been compared with Reynolds Averaged Navier Stokes (RANS) simulations and Unsteady RANS (URANS) simulations. The investigation is focused on the mechanisms of loss generation in the NGV at low Reynolds number condition of 1.5x106 (high altitude low Mach number condition) where shock boundary layer interactions are predominant.

Perforated Wall in Controlling the Separation Bubble Due to Shock Wave –Boundary Layer Interaction

Perforated Wall in Controlling the Separation Bubble Due to Shock Wave –Boundary Layer Interaction: 

The shock wave boundary layer interaction (SWBLI) induced separation bubble formation (SB) and its control has been investigated numerically in the mixed compression type of intake in the scramjet engine. The external compression has occurred due to the three successive oblique shocks formed from the three successive ramps of the forebody with the semi-wedge angle of 7.6, 7.0, and 9.4 respectively. The intake is designed in such a way that all three shocks converge and impinge on the leading edge of the cowl lip for the operating Mach number of 5.0. The numerical simulation is carried out by solving steady, compressible 2-D RANS equations using transitional SST k-ω turbulence model to capture the influence of SWBLI in the performance of supersonic intake. The formation of SB and its control by establishing the perforated wall in its proximity are investigated for three different cases based on the perforation with respect to SSB. Findings of the numerical simulation have concluded that the size of the SB decreases to an acceptable level while establishing the perforation in the entire fore-body wall in the isolator region. The feedback loop established between the upstream and downstream of SB could be a possible reason for

reducing its size.