Lecture # 12: Shock Waves and De Laval Nozzle

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1 ere 3L & ere343l Lecture Notes Lecture # : Shock Waves and De Laval Nozzle Dr. Hui Hu Dr. Rye Waldman Department of erospace Engineering Iowa State University mes, Iowa 5, U.S. Sources/ Further reading: nderson, Fundamentals of erodynamics Part 3 Chs 7 & 8

2 Subsonic, Transonic, Supersonic and hypersonic Flows Subsonic flows: Transonic flows: Supersonic flows: Hypersonic flows: >5. <.. >. Sonic boom

Source moving with V source = V sound ( ach - breaking the

3 Subsonic and Supersonic Flow a. Stationary sound source b. Source moving with V source < V sound c. Source moving with V source = V sound ( ach - breaking the sound barrier ) d. Source moving with V source > V sound (ach.4 - supersonic)

4 Shock Waves Normal Shock Wave (The airstream slows to subsonic) Oblique Shock Wave (The airstream slows down, but remains supersonic) Expansion Wave (The airsteam accelerates, and the air behind the shock wave is higher supersonic)

5 Review of Quasi-D Nozzle Flow

6 Review of Quasi-D Nozzle Flow ssumptions: Steady-state Inviscid No body forces X Quasi-D: rea is allowed to vary but flow variables are considered a function of x only ass conservation V dv t U nds S omentum conservation t UdV U n UdS pds fdv Fviscous V S S V Energy conservation t U U q e dv e U nds pu nds dv f U dv t V S S V V

7 Review of Quasi-D Nozzle Flow ssumptions: Steady-state Inviscid No body forces, u, r +d u+du r +d r Quasi-D: rea is allowed to vary but flow variables are considered a function of x only V dv U nds t ass conservation u u du d d S u u ud du du higher order terms u Const. d d du u

8 Review of Quasi-D Nozzle Flow ssumptions: Steady-state, Inviscid, No body forces Quasi-D: rea is allowed to vary but flow variables are considered a function of x only omentum conservation t, u, r UdV U n UdS pds fdv Fviscous V S S V +d u+du r +d r Pd u d u d udu udu P P Pd dp Pd u d u du u du d P P dp d u u Since: d udu dp u ud ud du dp dp d dp d dp udu udu a d du u d du u d du d d d du u du u a d u a u ( ) u s u du a du

9 Review of Quasi-D Nozzle Flow d ( ) du u Throat = u increasing < > Throat = u decreasing > <

10 Review of Quasi-D Nozzle Flow Isentropic relations (Thermodynamics) : Energy Equation : P P P C T T T P P T ( ) ( ) T V T V V CPT T C T RT ( ) ( ) P

11 Review of Quasi-D Nozzle Flow )] ( [ ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( u section : y a a u a u a P P T T relation isentropic a u a at u u < > Throat P,T = u=a=(krt) / P,T, u )] ( [ ) ( y

a tube that is pinched in the middle, making an hourglass-shape.

12 Review of Quasi-D Nozzle Flow < > Throat P,T = u=a=(krt) / P,T, u ( ) [ ( )] y T T P P ( ( ) ) de Laval nozzle (or convergent-divergent nozzle, CD nozzle) is a tube that is pinched in the middle, making an hourglass-shape. It is used as a means of accelerating the flow of a gas passing through it to a supersonic speed

13 Test Section Test section Tank with compressed air

14 ere344 Lab: Pressure easurements in a de Laval Nozzle Tank with compressed air Test section Tap No. Distance downstream of throat (inches) rea (Sq. inches)

15 P increasing P increasing st, nd, and 3 rd critical conditions st critical condition st critical condition 3st critical condition

16 ere344 Lab: Pressure easurements in a de Laval Nozzle. Under-expanded flow. 3rd critical 3. Over-expanded flow with oblique shocks 4. nd critical 5. Normal shock existing inside the nozzle 6. st critical

17 st, nd, and 3 rd critical conditions Underexpanded flow nd critical shock is at nozzle exit Flow close to 3 rd critical Over-expanded flow with shock between nozzle exit and throat Overexpanded flow st critical shock is almost at the nozzle throat.

18 Pressure Distribution Prediction within a De Laval Nozzle by using Numerical pproach Throat, or t P T P P < > Shock S P T < e Pe P atm Pe P atm Using the area ratio, the ach number at any point up to the shock can be determined: fter finding ach number at front of shock, calculate ach number after shock using: Then, calculate the s which allows us calculate the remaining ach number distribution

19 Pressure Distribution Prediction within a De Laval Nozzle by using Numerical pproach Throat, or t Shock S e P P T P P T Pe P atm < > < Pe P atm a.for 3rd Critical

20 Pressure Distribution Prediction within a De Laval Nozzle by using Numerical pproach Throat, or t < > Shock S P P T P P T < e Pe P atm Pe P atm ethod #, by using equations: If the shockwave is located at position of tap#: ethod #: by using Isentropic Flow properties table (ppendix- of nderson s textbook)

21 Pressure Distribution Prediction within a De Laval Nozzle by using Table ethod By using the normal shock tables with =.64 we find that =.686. (ppendix-b of nderson s textbook) Next, we find the sonic reference area behind the shock using the area-ach relation. i.e., =.686 (ppendix- of nderson s textbook) Find sonic reference behind the shock using the area-ach relationship: i.e., =.557sq. Inches If the shockwave is located at position of tab#:

22 Pressure Distribution Prediction within a De Laval Nozzle by using Table ethod With the exit pressure to be sealevel standard pressure. We now calculate the total pressure behind the shock using this value of exit pressure and the pressure ratio at the exit: Pt Pt P P.758 Our last major task is to find the total pressure ahead of the shock, P t P P P P P t t t P P Pt

23 Gauge Pressure, psi Pressure (PSI) Gauge Pressure, psi Examples of the previous lab reports 5 Theoretical Data - Gauge Pressure vs. Position Position along Nozzle xis, inches 3rd Critical nd Critical Normal Shock st Critical Experimental -D Theory Experimental Results - Pressure vs. Nozzle Location Nozzle location, inches 5 Total Pressure = PSI Distance from Troat (in) Under-Expanded Flow pproximately nd Critical Normal Shock

24 ere344 Lab#: Set up Schlieren and Shadowgraph Systems to Visualize a Thermal Plume Flow of a Burning Candle Before the candle is on fter the candle is on Schlieren image of a the thermal plume of a burning candle

25 ere344 Lab#: Set up Schlieren and Shadowgraph Systems to Visualize a Thermal Plume Flow of a Burning Candle Set up Schlieren and Shadowgraph Systems to visualize a thermal plume flow. Sign-in sheet signature. No lab report.

AerE 344: Undergraduate Aerodynamics and Propulsion Laboratory. Lab Instructions. Pressure Measurements in a de Laval Nozzle

AerE 344: Undergraduate Aerodynamics and ropulsion Laboratory Lab Instructions Lab #0: ressure easurements in a de Laval Nozzle Instructor: Dr. Hui Hu Department of Aerospace Engineering Iowa State University