Design of Passive Adiabatic Control Volumes P M

Design of Passive (Adiabatic) Control Volumes P M V Subbarao Professor Mechanical Engineering Department A Comprehensive Design Method for Overall Fuel Savings…. .

Geometric Design of Intakes & Nozzles

One–Dimensional Frictional Flow through Variable Area

Conservation Laws for a Real Fluid

Conservation of Mass Applied to 1 D Steady Flow Conservation of Mass: Conservation of Mass for Steady Flow: Integrate from inlet to exit :

One Dimensional Stead Flow A, V A+d. A, V+d. V r+dr r dl

Governing Equations for 1 D Steady flow Non reaction, no body forces, viscous work negligible Conservation of mass for steady flow: Conservation of momentum for frictional steady flow: Conservation of energy for ideal steady flow:

Additional Equations Ideal Gas law : Mach number equation :

Wall Shear Stress & Friction Factor Convenient to write the friction induced shear force, x, in terms of a friction factor Darcy Friction Factor Hydraulic Diameter

Design Model thru momentum equation

Design Equations for 1 D Steady flow Non reaction, no body forces, viscous work negligible Conservation of mass for steady flow: Conservation of momentum for frictional steady flow: Conservation of energy for ideal steady flow:

Other Equations Ideal Gas law : Mach number equation :

Design Equation for Variable Area Conduit Combine conservation, state equations– to get design equations for steady one dimensional frictional flow : So we have three ways to change the Mach number of a flow – area change (d. A): – friction: f > 0, same effect as –d. A – heat transfer: heating, q’’’ > 0, like –d. A cooling, q’’’ < 0, like +d. A

Effect of Shape of duct on Flow Consider an isentropic flow through a variable area duct: Pure shape effects :

Pure Shape Effects …. . A truth Beyond Common Sense

Control of Mach Number in Subsonic Flows Subsonic Nozzle: M <1 d. A < 0 So, d. V > 0 & dp <0 Subsonic Diffuser : M <1 d. A > 0 So, d. V < 0 & dp>0

Control of Mach Number in Supersonic Flows Supersonic Diffuser Supersonic Nozzle d. A < 0 & M >1 So, d. V < 0 & dp >0 d. A > 0 & M >1 So, d. V >0 & dp<0

Generation of High Pressure from Supersonic velocity : Isentropic Devices

Occurrence of Maximum Allowable Velocity Section At M =1 Minimum Area = A* : Also called throat For a given mass flow rate:

Geometry of Isentropic Diffuser