ENERGY TRANSFER BETWEEN FLUID AND ROTOR. Dr. Ir. Harinaldi, M.Eng Mechanical Engineering Department Faculty of Engineering University of Indonesia
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1 ENERGY TRANSFER BETWEEN FLUID AND ROTOR Dr. Ir. Harinaldi, M.Eng Mechanical Engineering Department Faculty of Engineering University of Indonesia
2 Basic Laws and Equations Continuity Equation m m ρ mass C A ρ C A flow rate ( kg / s)
3 Basic Laws and Equations Basic Laws and Equations Steady Flow Energy Equation (First Law of Thermodynamics) ( ) ( ) ( ) u u Z Z g C C p p m W Q ρ ρ
4 Basic Laws and Equations Newton s Second Law of Motion - Linear F x ( C ) m C x x
5 Basic Laws and Equations Newton s Second Law of Motion - Angular Torque ( r C) ρ C n da ( r F) cv content T cs
6 Basic Laws and Equations Newton s Second Law of Motion - Angular Power (Euler Equation for Turbomachinery) W For Power Machine (Turbine) W < 0 For Working Machine (Pump) W > 0
7 Basic Laws and Equations Entropy Turbine Pump dq T s In the absence of motion, gravity and any other effects Tds Tds du dh + pdv vdp
8 Flow Idealization through a Turbomachinery a. Working Machine C W + U
9 Flow Idealization through a Turbomachinery b. Power Machine C W + U
10 Flow Idealization through a Turbomachinery a. Working Machine Energy is transferred from rotor to the fluid The increase of tangential component of absolute velocity in the same direction with rotation of rotor b. Power Machine Energy is transferred from fluid to the rotor The increase of tangential component of absolute velocity in the opposite direction to rotation of rotor
11 Analysis of Velocity Triangle Relation of Absolute, Blade and Relative Velocity C x tangential component of absolute velocity (whirl velocity) C r radial component of absolute velocity
12 Analysis of Velocity Triangle Relation of Blade Angle and Relative Flow Angle Nomenclatures: β blade angle β relative flow angle inlet/entry outlet/exit Ideal Condition : - No schock at entry - No slip at exit β β β β
13 Analysis of Velocity Triangle Euler Equation of Turbomachinery Power Specific W Tω m ( U C ) m ( U C ) x x m m m continuity U r ω ; U rω W m ( ) ( ) Power w U C U C ( r ω C ) ( r ω C ) x x x x Note: π n π D ω U rω n ω (rad/s) n (rpm)
14 Analysis of Velocity Triangle Analysis of Velocity Triangle r C x C C ( ) U C W C x r W U C UC x + ( ) ( ) ( ) W W U U C C w + Another approach Large triangle : Small triangle : Therefore :
15 Analysis of Velocity Triangle Energy Head Relation between rotor power and fluid energy W h ( C ) ( U C ) mg h m U x x Change of Fluid energy Head ( U C ) ( U C ) g x [( ) ( ) ( )] C C + U U W W g x 3
16 Analysis of Velocity Triangle Energy Head. Change of head caused by change of kinetic energy of the fluid. Change of head that develops across the impeller due to the centrifugal effect, 3. Chage of head caused by the diffusion of relative flow in the blade passages
17 Analysis of Velocity Triangle in Turbomachinery. An inward flow power turbomachinery, having an external diameter of.5 m and internal diameter of 0.5 m runs at 400 rpm. The radial component of absolute velocity of flow at inlet is 0 m/s. If the absolute flow angle is 5 o find : (a) Absolute velocity of water (b) Tangential component of absolute velocity (whirl velocity) at inlet (c) Relative velocity at inlet (d) Relative flow angle at inlet Solution: Given D.5 m ; n 400 rpm; C r 0 m/s ; 5 o Velocity triangle: U D n/ m/s C x? 5 o? C? W? C r 0 m/s
18 Analysis of Velocity Triangle in Turbomachinery U 3.4 m/s C x 37.3 m/s 5 o 0.5o 59.5 o W.6 m/s C r 0 m/s C m/s C C r / sin 5 o m/s C x C cos 5 o 37.3 m/s W [C r + (C x U ) ] /.6 m/s (a) (b) (c) Sin C r / W o 80 o 59.5 o 0.5 o (d)
19 Analysis of Velocity Triangle in Turbomachinery. An outward flow working turbomachinery, having an external diameter of 0.6 m and internal diameter of 0.3 m. The water enters the impeller radially with absolute velocity at.5 m/s. The relative flow angle at inlet is 30 o and at outlet is 45 o. If the water leave the impeller with radial component of absolute velocity equal to absolute velocity at inlet, find : (a) Rotating speed of impeller (b) Specific work of the rotor shaft Solution: Given D 0.3 m ; D 0.6 m ; C C r.5 m/s ; 30o ; 45 o Velocity triangle at inlet: 30 o W U 4.33 m/s C.5 m/s tan V / U U V / tan 30 o 4.33 m/s U D n/60 n 60U / ( D ) 75.8 rpm (a)
20 Analysis of Velocity Triangle in Turbomachinery Velocity triangle at outlet: U D n/ m/s C x 6.6 m/s 45 o W C r.5 m/s C C x U (C r / tan 45 o ) 6.6 m/s w shaft U C x - U C x (8.66)(6.6) kj/kg (b)
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