Measurements in Fluid Mechanics 058:180 (ME:5180) Time & Location: 2:30P - 3:20P MWF 3315 SC Office Hours: 4:00P – 5:00P MWF 223B-5 HL Instructor: Lichuan Gui lichuan-gui@uiowa.edu Phone: 319-384-0594 (Lab), 319-400-5985 (Cell) http://lcgui.net

Lecture 17. Flow visualization with optical techniques

Flow visualization with optical techniques Refractive index c – light speed in vacuum v – light speed in medium 𝑛= 𝑐 𝑣 Gladstone-Dale formula (T=273K, =589nm) - relation between refractive index and density of gases n – refractive index K – Gladstone-Dale constant  – density e – charge of an electron me – mass of an electron L – Loschmidt’s number m – molecular weight  – frequency of visualizing light i – resonant frequency of distorted electron fi – oscillator strength of distorted electron In gas mixture of N components: Kn – value of the n-th component n – density of the n-th component = 1+2+3++N

Flow visualization with optical techniques Light deflection in variable refractive-index media Medium 1 & 3 with uniform refractive index n0 Medium 2 with variable refractive index n(x,y) for very small : 𝑟𝛿𝜑 𝛿𝑡 = 𝑟𝛿𝑣 𝛿𝑟 𝑣= 𝑟𝛿𝑣 𝛿𝑟 with geometrical simplification: Differential equation for the ray path: Light deflection angle:

Flow visualization with optical techniques Light deflection in variable refractive-index media - Undisturbed light ray would arrive at Q - Deflected light ray arrives at point Q* - Optical length covered by deflected ray different from that of undisturbed i.e. t* t Quantities can be measured in photographic film: - The displacement Shadowgraph - The angular deflection Schlieren method - The phase shift between both rays Interferometry

Flow visualization with optical techniques The shadowgraph method Schematic arrangement of two typical shadowgraph systems Photo film or screen Light source Spherical mirrors or lenses Optical disturbance (test section) Focus plane Camera lens

Flow visualization with optical techniques The shadowgraph method Working principle: detecting second derivatives z y Ph Object Uniform illumination Uniform illumination Non-uniform illumination

Flow visualization with optical techniques The shadowgraph method APLLICATION: DETACHED SHOCK WAVE The shadowgraph of a supersonic flow around a finned hemisphere The bow shock is detached Because of the blunt body. The flow behind the nearly normal portion of the shock is subsonic. Thus, no Mach waves are seen near the line of symmetry. As the subsonic flow sweeps over the body, it accelerates, ultimately becomes sonic and then supersonic. The position of the transition to supersonic flow can be estimated by noting the position of the first appearance of Mach lines on the body. Data from http://www.eng.vt.edu/fluids/msc/gallery/shocks/

Flow visualization with optical techniques The shadowgraph method APPLICATION: A .308 CALIBER BULLET Shadowgraph of Winchester .308 caliber bullet traveling at about 2800 ft/sec, M=2.5. Curvature of the Mach lines generated at the nose Data from http://www.eng.vt.edu/fluids/msc/gallery/shocks/

Flow visualization with optical techniques The shadowgraph method APPLICATION: SHOCK WAVES AROUND THE X-15 Classical shock wave pattern around a free-flight model of the X-15 at M=3.5. In the lower half of the image, the convergence of the downstream shocks with the main bow shock is clearly seen. Data from http://www.eng.vt.edu/fluids/msc/gallery/shocks/

Imaging techniques for fluid flow measurements Flow visualization with optical techniques The Schlieren method Schematic arrangement of a Toeplor Schlieren system Optical disturbance (test section) Photo film or screen Light source Spherical mirrors or lenses Detecting 1st derivatives Imaging techniques for fluid flow measurements

Flow visualization with optical techniques The Schlieren method Different configurations of Schlieren system Double-path systems Z-shaped system

Flow visualization with optical techniques The Schlieren method APPLICATION: PENETRATION OF ALUMINUM FOIL BY A BULLET Pattern of waves generated as a .222 caliber bullet passes through a hanging sheet of aluminum foil. The reflected shock is clearly seen at the left of the foil. A second spherical shock surface can be seen on the right side of the foil. The small disturbances just behind the shock are bits of the foil ejected at impact. Data from http://www.eng.vt.edu/fluids/msc/gallery/shocks/

Flow visualization with optical techniques The Schlieren method APPLICATION: REFRACTION OF SHOCK WAVES The Schlieren photo at the right reveals the pattern of waves generated by a .222 caliber bullet traveling at about Mach 3. The bullet has just passed through the plume of a candle and the different densities in the heated plume have refracted the lower set of shock waves. Data from http://www.eng.vt.edu/fluids/msc/gallery/shocks/

Shock waves from a .44 Magnum Flow visualization with optical techniques The Schlieren method Full-Scale Schlieren Shock waves from a .44 Magnum

Flow visualization with optical techniques The Schlieren method Full-Scale Schlieren Images Heat released from gas grill Heat from space heater, lamp& person Cold air dragged from a freezer From http://www.mne.psu.edu/psgdl/FSSPhotoalbum/index1.htm

Flow visualization with optical techniques Interferometry 𝑥 1 𝑥 2 𝑛 0 𝑛 𝑥,𝑦 𝑡 0 𝑡 ∆𝜃 𝐼 2 𝐼 1 𝐼 𝑡𝑜𝑡 𝑚𝑖𝑟𝑟𝑜𝑟 𝑏𝑒𝑎𝑚 𝑠𝑝𝑙𝑖𝑡𝑡𝑒𝑟 Phase difference: Light intensity: 𝐼 1 =𝐴∙sin 2𝜋𝑣𝑡 𝐼 2 =𝐴∙sin 2𝜋𝑣𝑡−∆𝜃 𝐼 𝑡𝑜𝑡 = 𝐼 1 + 𝐼 2 =𝐴 sin 2𝜋𝑣𝑡 +sin 2𝜋𝑣𝑡−∆𝜃 =2𝐴cos ∆𝜃 2 sin 2𝜋𝑣𝑡− ∆𝜃 2

Flow visualization with optical techniques Mach-Zehnder interferometer

Flow visualization with optical techniques Mach-Zehnder interferometer EXAMPLE the interference pattern of a horizontal annulus filled with air when the inner cylinder is heated isothermally. The outer tube is cooled by water at constant temperature. http://www.thermopedia.com/content/932/

- Read textbook 10.3-10.5 on page 231 - 244 Homework - Read textbook 10.3-10.5 on page 231 - 244 Questions and Problems: 6 on page 246 (optional, but may add credit to midterm examination ) - Due on 10/05

Try to write a Matlab program to select an image sample in a 64×64-pixel window from an image at x=400, y=200 S1.bmp S2.bmp Example of Matlab program: clear; A1=imread('A001_1.bmp'); G1=img2xy(A1); M=64; N=64; x=400; y=200; g1=sample01(G1,M,N,x,y); Sx=1.6; Sy=2.3; g2=sample01(G1,M,N,x+Sx,y+Sy); S1=xy2img(g1); S2=xy2img(g2); imwrite(S1,'S1.bmp','bmp'); imwrite(S2,'S2.bmp','bmp'); http://lcgui.net/ui-lecture2012/hw/00/A001_1.BMP to select another image sample with a window shift of S = ( 1.6, 2.3 )