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 for Steady Flow: Integrate from inlet to exit :

One Dimensional Stead Flow V r A+dA, V+dV r+dr dl

Governing Equations for 1D 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 1D 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 (dA): – friction: f > 0, same effect as –dA – heat transfer: heating, q’’’ > 0, like –dA cooling, q’’’ < 0, like +dA

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 Subsonic Diffuser : M <1 dA < 0 dA > 0 So, dV > 0 & dp <0 So, dV < 0 & dp>0

Control of Mach Number in Supersonic Flows Supersonic Diffuser Supersonic Nozzle dA < 0 & M >1 So, dV < 0 & dp >0 dA > 0 & M >1 So, dV >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