OUTLINE FOR Chapter 3
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1 013/4/ OUTLINE FOR Chapter 3 AERODYNAMICS (W-1-1 BERNOULLI S EQUATION & integration BERNOULLI S EQUATION AERODYNAMICS (W-1-1
2 013/4/ BERNOULLI S EQUATION FOR AN IRROTATION FLOW AERODYNAMICS (W-1-.1 VENTURI TUBE AERODYNAMICS (W-1-3
3 013/4/ PITOT-STATIC TUBE for susonic compressile flow (see Ch8 for detail for supersonic compressile flow (see Ch8 for detail AERODYNAMICS (W_1_4 Pressure coefficient: PRESSURE COEFFICIENT C p AERODYNAMICS (W_1_5 3
4 013/4/ REVIEW FOR IRROTATIONAL, INCOMPRESSIBLE FLOW: Continuit equation Momentum equation Irrotational flow = 0 GOVERNING EQUATION FOR IRROTATIONAL, INCOMPRESSIBLE FLOW: LAPLACE S EQUATION Continuit equation Incompressile: constant For incompressile flow: there eists a streamfunction For irrotational flow: there eists a velocit potential Laplace s equation For irrotational, incompressile flow: Laplace s equation For irrotational, incompressile flow, there are velocit potential ti and streamfunction ti that oth satisf Laplace s equation. 0 0 AERODYNAMICS (W_1_6 4
5 013/4/ LAPLACE S EQUATION Laplace s equation is a second-order linear partial differential equation. If 1,, 3,, n represent n separate solutions of Laplace s equation, then = n is also a solution of Laplace s equation Boundar Conditions: Infinite oundar conditions: Wall oundar conditions: or or AERODYNAMICS (W-1-7 SUMMARY AERODYNAMICS (W-1-8 5
6 013/4/ OUTLINE FOR Chapter 3 AERODYNAMICS (W--1 LAPLACE S EQUATION: GOVERNING EQUATION FOR IRROTATIONAL, INCOMPRESSIBLE FLOW Some elementar flows: Laplace s equation is a second-order linear partial differential equation. If 1,, 3,, n represent n separate solutions of Laplace s equation, then = n is also a solution of Laplace s equation. Therefore, the solution of a comple flow are usuall in the form of a sum of elementar flow solutions. Uniform flow (1st elementar flow Source and Sink (nd elementar flow Comine Uniform flow with a Source and Sink. Doulet flow (3rd elementar flow Comine Uniform flow with a Doulet. Vorte flow (4th elementar flow Comine Uniform flow with Doulet and Vorte flows AERODYNAMICS (W-- 6
7 013/4/ 1st ELEMENTARY FLOW - UNIFORM FLOW Velocit potential Cartesian coordinates Basic Flow u = V v = 0 Satisf incompressile flow Satisf irrotational flow Stream function Cartesian coordinates or Clinderical coordinates AERODYNAMICS (W--3 nd ELEMENTARY FLOW - SOURCE & SINK FLOW Basic flow: Stif Satisf = 0 Satisf incompressile flow = 0 irrotational flow Velocit potential Polar coordinates Stream function Polar coordinates AERODYNAMICS (W--4 7
8 013/4/ THE COMBINATION OF A UNIFORM FLOW WITH A SOURCE - THE SEMI-INFINITE BODY W= /V Stagnation point: Stagnation streamline: 0 Width of semi-infinite od: r sin (1 V 1 W ( 00 V W= /V AERODYNAMICS (W--5 THE PRESSURE DISTRIBUTION OVER THE SEMI-INFINITE BODY Pressure coefficient: Stream function: Streamline equation of the surface: 1 V Vr V ( V cos ( V sin V (cos sin ( V cos ( r 4 r r r o r V V o (r V r V V V o ( V cos ( o 4 r r V r r 1 o (cos ( o V r r V r r C 1 [ o (cos ( o P ] V r r AERODYNAMICS (W--6 8
9 013/4/ 9 THE COMBINATION OF A UNIFORM FLOW WITH A SOURCE AND SINK - THE RANKINE OVAL ln( ln( r 1 r V ( ln( ( ln( V ln(( ln(( V Stagnation points: ( ( V u ln(( 4 ln(( 4 V ( ( v 0 ( ( V u 0 v AERODYNAMICS (W--7 Stagnation streamline: 0 ( ( v =0 V DOUBLET FLOW AERODYNAMICS (W--8
10 013/4/ NONLIFTING FLOW OVER A CIRCULAR CYLINDER Velocit Field: On the surface of the clinder Stagnation points and streamline: Circle with radius AERODYNAMICS (W--9 PRESSURE COEEFICIENT DISTRBUTION OVER THE SURFACE OF A CIRCULAR CYLINDER Pressure coefficient: On the surface of the clinder = 0 = 0 = 0 = 0 L (lift = D (drag = 0 AERODYNAMICS (W
11 013/4/ OUTLINE FOR Chapter 3 AERODYNAMICS (W-3-1 4th ELEMENTARY FLOW - VORTEX FLOW Basic Flow 0 = 0 incompressile flow = 0 Velocit potential irrotational flow ecept the origin What happens at r=0? Stream function AERODYNAMICS (W-3-11
12 013/4/ LIFTING FLOW OVER A CIRCULAR CYLINDER Velocit Field: Stagnation points: On the surface of the clinder AERODYNAMICS (W-3-3 PRESSURE COEEFICIENT DISTRBUTION OVER THE SURFACE OF A LIFTING CIRCULAR CYLINDER On the surface of the clinder Pressure coefficient: Drag coefficient: = C a D (drag = 0 AERODYNAMICS (W-3-4 1
13 013/4/ LIFT CREATION ON A SPINNING CIRCULAR CYLINDER Lift: = C n Creation of lift on a spinning clinder AERODYNAMICS (W-3-5 on the surface of the clinder. Stream function for a lifting flow over a circular clinder On the surface of the clinder r=r = 0 =-V sin - /(R Peak (negative pressure coefficient appears at =/ = 1-(- - /(RV( = 5 C p = 1-(- - 5/( = -6.8 AERODYNAMICS (W
14 013/4/ =5 Point B AERODYNAMICS (W-3-5. KUTTA JOUKOWSKI THEOREM For a closed two-dimensional od of aritrar shape, the lift per unit span is L = V AERODYNAMICS (W
15 013/4/ SUMMARY UNIFORM FLOW SOURCE & SINK DOUBLET VORTEX AERODYNAMICS (W-3-7 Source Panel Method (I ds ds d ln r 15
16 013/4/ Source Panel Method (II Source Panel Method (III 16
17 013/4/ Source Panel Method (IV Source Panel Method (V 17
18 013/4/ Source Panel Method (VI Source Panel Method (VII 18
19 013/4/ Source Panel Method (VIII Source Panel Method (IX 19
20 013/4/ Source Panel Method (X 0
21 013/4/ 1
22 013/4/ sucritical supercritical
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