Gerald J. Franz. Naval Ship Research and Development Center Washington, D.C

Transcription

1 '"im-l i l i i um»!»«) GO ROUGHNESS CRITERIA AND THE RELATIONSHIPS BETWEEN SURFACE ROUGHNESS AND FLOW NOISE by Gerald J. Franz Naval Ship Researh and Development Center Washington, D.C S UJ OCT ACT * i«ni i / B I Paper CC10 at Seventy-fifth Meeting of the Aoustial Soiety of Ameria, Ottawa, Ontario, Canada, May pnduad by NATIONAL TECHNICAL INFORMATION SERVICE SpringMd, Vs. 221S1 ^^Tfor pubu release; 1

2 ROUGHNESS CRITERIA AND THE RELATIONSHIPS BETWEEN SURFACE ROUGHNESS AND FLOW NOISE Gerald J. Franz Naval Ship Researh and Development Center Washington, D.C V ABSTRACT Roughness riteria are usually given for the surfaes of strutures to prevent premature strutural failure, added drag, and added flow noise, Strutural roughness riteria usually deal only with long wavelength roughness, or wavlness, whih is speified in terms of learane under a batten of a partiular length. Drag roughness riteria usually deal only with the short wavelength roughness as measured by a profile meter. Flow noise roughness riteria, however, must inlude both the long and short wavelength omponents of the roughness and. In the ase of water, separate riteria are needed for boundary layer turbulene and avitatlon indued noise. A more unified desription of roughness and roughness riteria is given in terms of Its wavenumber spetrum. Hydraullally smooth surfaes are believed to have no roughness related omponent of drag or turbulene indued flow noise. In water, for instane, the surfae is onsidered to be hydraullally smooth If the roughness height in inhes is less than about 0.01 divided by the free stream veloity in knots. The expeted Inrease in turbulene Indued flow noise In water and in air as a funtion of roughness and flow speed Is then determined from available data on loal akin frition.

3 The surfae of any real body ontains deviations from the average ontour that are desribed In terms of roughness and wavlness. These deviations are of Interest in the field of strength, fatigue, frition, wear, drag, and noise generation. The strength of- pressure vessels, for Instane, depends on out-of-roundness and fatigue strength an depend on Initial roughness or raks In the surfae. Frition and wear are Influened by the fine grain roughness, bearing length, et. The drag of bodies moving in fluids is known to depend on the roughness. Flow noise generated by bodies moving in fluids is also known to be dependent on roughness and wavlness. This noise and its dependene on the properties of the wavlness and roughness of the body are the main onern of this paper. Surfae flaws with wavelengths greater than about 1/32 Inhes are onsidered to be wavlness. Those with wavelength less than this are onsidered to be roughness. Wavlness is onventionally desribed in terms of learane under a batten of a partiular span, say 1/8 inh in 4 inhes. This peak-to-valley distane is defined here as 2h end the wavelength or span as X. If one plots wave amplitude h as a funtion of reiproal wavelength 1/X, points of onstant ratio X/2h lie on a line having a -6 db/otave slope as shown in Slide 1. This line moves down 6 db eah time the X/2h ratio is doubled and up 6 db eah time it is ut in half. These are speifiations of a line spetrum. Roughness is onventionally desribed in terms of average height or rms height and is measured using one of a number of available profile measuring devies. These devies move over the surfae with a stylus and produe an eletrial signal proportional to the transverse displaement of the surfae. This signal an be read diretly on an averaging or on an rms meter to give readings of average or rms roughness height. This signal an also be reorded or traed to give a profile of the surfae itself when properly alibrated and normalizeu in terms of the veloity of travel over the surfae. A typial traversing speed of 0.1 in/se ^- over roughness wavelengths from 10"* to 10" 3 Inhes gives frequenies - ^ between 10 and 1000 Hz. This trae is not unlike a trae of sound pressure as a funtion of time and an be analyzed in the same way. We are seldom satisfied with Just the rms amplitude of suh a signal. Aousti pressures are usually desribed in terms of their spetral density beause their frequeny ontent is of Interest. Indeed we are.interested in the "frequeny" ontent of the roughness also. Suh an Idealized roughness spetral density is also shown on the slide. Sine the spetral density is the square of the amplitude per yle/inh bandwidth, the slope of the onstant X/2h lines are -9 db/otave Instead of the -6 db/otave for the wavlness points whih are essentially line omponents whih have not been divided by the bandwidth. The levels of these lines are a measure of the peakiness of the roughness, i.e., the

4 lower the X/2h ratio is, the peakler the roughness is. A value of 2 indiates a double amplitude equal to half a wavelength whih is roughly what one would obtain for losely paked sand grains glued to a flat surfae. It should be noted that the frequeny response of the profile meter eletronis, the radius of the stylus tip of the profile meter, the length of the sample, and the "wheelbase" of the profile meter all limit the frequeny limits of the spetra that an be measured. The frequeny alibration of the profile meter an be used to orret for defiienies in the eletronis but the others are inherent limitations for a partiular instrument. One an obtain the rms roughness from the spetral density in the usual way by integration or using the bandwidth at the 3 db down points. Typially a hand ground surfae ranges from about 250 to 1000 miroinhes rms and a highly polished surfae is in the few miroinh range. Turbulene stimulator pins used on models are typially about 1/8 inh in diameter and inh high. In order to determine the ineption of avitation on roughnesses on the wall of an underwater body, one must know the loal pressure around the roughness relative to the vapor pressure of water. Cavitation an our on roughness with a low X/2h ratio and large enough to protrude well out into the boundary layer. The important veloity to be used in the avitation number and Reynolds number is the loal veloity at the height of the roughness. Cavitation ineption speeds for rough hydrodynami bodies have been omputed by Borden (6th Naval Hydrodynamis Symposium, Vol. 1, Sep 28 - Ot 4, 1966, Washington, D.C.). As expeted, sharp roughnesses are more prone (by several knots) to avitate than rounded ones. On typial streamlined bodies at reasonable depths, the roughness must be almost stiking out of the boundary layer before it will avitate. At shallow depths, on blunt bodies, or at high speeds avitation an our at relatively small roughnesses. For prediting avitation ineption, individual roughnesses are best desribed by their size and shape rather than in spetral form but if their size and shape are randomly distributed over an extended area, a spetral desription is appropriate. In this ase, as in fatigue problems, the statistis of ourrene of peak values are also important. It is assumed, of ourse, that if avitation is present, signifiant noise is produed. Waviness with X/2h ratio of some 32 or more is not expeted to enhane the flow noise from a body. Suh a gradual hange in ontour would alternately slightly inrease and then slightly derease the pressure gradient along the body and have a slight net effet on the boundary layer. If X/2h dereased from this, however, separation of the

5 flow will eventually our behind the peaks and Inreased turbulene, drag, and boundary layer pressure flutuations will result. Roughness is known to Inrease the drag or loal skin frition If It exeeds the so alled hydraulially smooth ondition. In Shllhting's Ath edition of Boundary Layer Theory, plots are given of loal skin frition oeffiient as a funtion of Reynolds number and roughness height ratio. Shlihting also gives an expression for the admissible roughness to be h a( j m ^ loov/u where v is the kinemati visosity and U is the free stream veloity. One should note that this expression is independent of distane x along the body but holds only for Reynolds number, R x» xua», between the values of 10 7 and l(f. Above ICP the admissible roughness height is slightly lower. A value of 3(l(f ) is onsidered a typial value for transition from laminar to turbulent flow. For water at typial temperatures and the veloity in knots, the admissible rms roughness height in inhes is given simply by hadm (Inhes) 0.01/U (knots). For air at typial onditions and the veloity In feet per seond, the expression beomes h a d m (inhes) < 0.2/ U (ft/se). If one now makes the assumption that the rms pressure flutuations at the wall are proportional to the loal skin frition oeffiient (whih in turn is proportional to the loal shear stress at the wall), one an then determine inreases in rms wall pressure for roughness above the hydraulially smooth value. This has been done on Slide 2. For approximately 10 knots in water or 200 ft/se in air, a surfae is onsidered hydraulially smooth If it has an rms roughness less than 1000 mlroinhes. For a roughness some ten times this value, an inrease of about 3 db in the rms pressure over the smooth surfae value Is to be expeted. Curves for other speeds are also shown. Sine It Is expeted that fine grain roughness influenes the high frequeny pressures and large grain roughness and waviness Influenes the low frequeny pressure, it is essential that we know the frequeny spetrum of the roughness before we an expet to predit the influene of roughness on the frequeny spetrum of the flutuating pressures at the wall. Considering the assumptions made for the slide, an auray better than a db or an otave in roughness or veloity is not likely. It is obvious then that for flow noise work related to roughness, we'need a spetral desription of surfae roughness and waviness. A spetral density using reiproal wavelength or wave number is proposed here for suh a unified desription. Profile meters with a wide frequeny response are needed for this. The low frequeny response espeially, needs to be extended several deades. The line omponent

6 speifiation Is not really appropriate beause very few surfaes have a sinusoidal harater but have broad-band spetral ontent. This wavenumber spetrum of the surfae roughness seems espeially appropriate for onvolving with the wavenumber spetrum of the onveting boundary layer pressure flutuations.

7 .j b 1 I "T~ r~ r" "T- r" 1 r~ r~ I "T"] * tz 5 m k "j U 3 «~* j u o x: -] L ^^ J i! g / «* <*- 1 /M JA SU L. "^ " - 1 C\J TT.y ü _^ p ^j 1 // o >, L. A-^ // / 13 U V v' > 7 / H w # f" x f -j > / > *^ ß r CM fo i i / L '/ n / o ^^3 P / / y ^ -5 V 3 L / / / X «j ^^ / i r / o J «0-0> i n // i H L, ^l^ r / x: w L / «J o A to * ""»s M *-< «3 II O o \ i o w 3s p u Pi y r MB V II H z v. L. "o A y ml O? H! '^" <M / LJOO >» ^ f-s CM o 3 3 t "-' /< "7 / ro 3 JC a 1 i/? -1 C, A u. E ^ /s» JC ^* ^-^ «J ^ 1 ^"^ VJ / > k = = (A i mi r* /s \ ^L Iß -J 1 3 N 1 * id hi N > A 01 ^^ mm At 1 3 t 5 / 1 u> ^~ ^^ / 1 O 3 i r 0 (0 o *i to / r / «r / ^? f s P N >. >v JL r ^ r _ E. w 3 tr > '"- ES20 d f D«1 H 2 L r 1 w / a C -4 z O r / > 2 *i! I w i J 1 1 1,.j JL_ L«L_ JL- ij OOOO O O o o o o o g CO CD 5^ CM CM.^ro CO ildui/ap^d/ ( ii Ty )9j.p U! AIISUSQ idjpsds ssaugßnoy T/ 9J qp UJ 0 M apnüiduiv ssoui/vo/w i o o io O (M I»4 I

8 o o CM «u 3 60 CVJ O o v ^r dsoq MiOOUJS X DD! ndjpäh JSAQ djnssdjj simd u i ösdojouj qp 0 s^