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Surface Pressure Fluctuations Near an Axisymmetric Stagnation Point

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Surface Pressure Fluctuations Near an Axisymmetric Stagnation Point KM m Vk I •/•*.*.•* .^ >.,*.' . i • I H H '**<J2 MITED STATES \RTMENT OF 1MERCE NBS TECHNICAL NOTE 563 JUCATION If"' Surface Pressure Fluctuations Near an Axisymmetric Stagnation Point U.S. VRTMENT OF MMERCE National Bureau of -. ndards Lz UI — NATIONAL BUREAU OF STANDARDS 1 The National Bureau of Standards was established by an act of Congress March 3, 1901. The Bureau's overall goal is to strengthen and advance the Nation's science and technology and facilitate their effective application for public benefit. To this end, the Bureau conducts research and provides: (1) a basis for the Nation's physical measure- ment system, (2) scientific and technological services for industry and government, (3) a technical basis for equity in trade, and (4) technical services to promote public safety. 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THE OFFICE FOR INFORMATION PROGRAMS promotes optimum dissemination and accessibility of scientific information generated within NBS and other agencies of the Federal Government; promotes the development of the National Standard Reference Data System and a system of information analysis centers dealing with the broader aspects of the National Measurement System; provides appropriate services to ensure that the NBS staff has optimum accessibility to the scientific information of the world, and directs the public information activities of the Bureau. The Office consists of the following organizational units: Office of Standard Reference Data—Office of Technical Information and Publications—Library—Office of Public Information—Office of International Relations. 1 Headquarters and Laboratories at Gaithersburg, Maryland, unless otherwise noted; mailing address Washing- ton, D.C. 20234. 2 Part of the Center for Radiation Research. 8 Located at Boulder. Colorado 80302. it A UNITED STATES DEPARTMENT OF COMMERCE Maurice H. Stans, Secretary NATIONAL BUREAU OF STANDARDS • Lewis M. Branscomb, Director ^O^i D^ ft i „„. i, NBS TECHNICAL NOTE 563 ISSUED AUGUST 1971 Nat. Bur. Stand. (U.S.), Tech. Note 563, 67 pages (Aug. 1971) CODEN: NBTNA Surface Pressure Fluctuations Near an Axisymmetric Stagnation Point Richard D. Marshall Building Research Division Institute for Applied Technology National Bureau of Standards Washington. D.C. 20234 " V„u of NBS Technical Notes are designed to supplement the Bureau's regular publications program. They provide a means for making available scientific data that are of transient or limited interest. Technical Notes may be listed or referred to in the open literature. For sale by the Superintendent of Documents, U.S. Government Printing Office, Washington, D.C, 20402. (Order by SD Catalog No. C 13.46:563). Price .70 cents. Stock Number 0303-0896 CONTENTS Page List of Symbols v 1. Introduction 2 2. Theoretical Background 3 3. Experimental Techniques 18 4. Experimental Results 21 5. Conclusions 34 6. Bibliography 37 in LIST OF SYMBOLS Symbol Definition Dimensions 2 A Area L C Contraction ratio C Drag coefficient D CM Virtual mass coefficient °p Pressure coefficient cpf RMS pressure coefficient D Disk diameter L D' Maximum wake diameter L f Coefficient of spatial, longitudinal velocity correlation ,2 m_l _2 T Jf m fAB (n) Cross-spectrum function L T ,F L T f (n) = 4 f r ( T )cos(27rnT) dx. etc Q AB Coefficient of spatial, lateral velocity correlation Hz Symbol for cycles per second Intensity, etc. P U K1} K Modified Bessel functions of the second kind Lx , Ly, Lz , Lr Integral scales of turbulence in x, y, z and r directions L M Grid mesh size L Frequency i-l Total pressure, average load per unit area FL" -2 Mean pressure FL Symbol Definition Dimensions P Stagnation pressure FL o _2 P Fluctuating pressure FL" R Radius of disk L R(n) Narrow-band correlation function R (n) Normalized form of cross-spectral AB function f fa - AB > R (n),, « " V^~~ R(t) Space-time correlation function Re Reynolds number Radial distance L Spatial separation L "AB _u 2 2 2 4 : Cross-correlation function l t" ,f l" AB u AB u (t) * u (t T etc - A B + ) t Time U Total velocity in x direction LT U Mean velocity in x direction LT" u,v,w Velocity fluctuation in x,y and z directions lt" _1 J ' J~T 2 * 2 RMS of velocity fluctuations lt" _1 W Local mean velocity in z direction lt"I _1 W Convection velocity lt" c w Free-stream velocity lt" x,y,z Space coordinates L Lateral separation L yAB VI Symbol Definition Dimensions (1) Non-dimensional function (2) Normalization factor (1) Non-dimensional function (2) Angle Angular separation of hot wire and pressure tap (1) Non-dimensional function (2) Radial separation of hot wire and pressure tap Ndn- dimensional function Mass density of air FL hT 2 Time delay T *(n) Spectral density function, /°°$ (n) dn = 1 o T 2m-1 T,2T -4m <f>(n) Spectrum function L T ,F L T oo u 2 °° P 2 = = / <£ (n)dn u ,/ <J> (n)dn p etc. X*(n) Aerodynamic admittance fu _1 to Angular velocity Subscripts A Denotes point A B Denotes point B r Radial direction 3 Circumferential direction Superscripts P Denotes pressure u,w Denotes velocity vn Symbol Definition Dimensions ( ) Denotes time- aver aged quantity 2 u = lim 1 T 2 r U (t)dt4 _ T— T I J o Other symbols are defined as they occur in the text. VI 11 SURFACE PRESSURE FLUCTUATIONS NEAR AN AXISYMMETRIC STAGNATION POINT Richard D. Marshall Structural Research Engineer National Bureau of Standards Washington, D. C. Surface pressure fluctuations on a circular disk placed normal to a turbulent air stream have been investigated. Turbulence intensities of approximately 10% were produced by a coarse grid installed at the test- section entrance. The turbulent field in the neighborhood of the disk was homogeneous and nearly isotropic. Experimental results indicate that existing linear theories which do not consider distortion of the flow fail to predict the nature of sur- face pressure fluctuations on a bluff body. Only for wavelengths which are large compared to the body do these theories yield satisfactory results. A strong attenuation of the high frequency components occurs as the flow stagnates. This is accompanied by a transfer of energy from short to long wavelengths. The opposite effect is observed as the flow attains a radial direction and approaches the edge of the disk. A neu- tral wavelength which undergoes little change in energy was observed. Integral scales of surface pressure fluctuations are much larger than the lateral integral scale of the free-stream turbulence. Pressure-velocity correlations indicate the existence of two distinct
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