Optical Measurement of the Speed of Sound in Air Over the Temperature Range K

Transcription

1 NASA/CR ICASE Report No Optcal Measurement of the Speed of Sound n Ar Over the Temperature Range K Roger C. Hart ICASE, Hampton, Vrgna R. Jeffrey Balla and G.C. Herrng NASA Langley Research Center, Hampton, Vrgna Insttute for Computer Applcatons n Scence and Engneerng NASA Langley Research Center Hampton, VA Operated by Unverstes Space Research Assocaton Natonal Aeronautcs and Space Admnstraton Langley Research Center Hampton, Vrgna Prepared for Langley Research Center under Contract NAS Aprl 2000

2 OPTICAL MEASUREMENT OF THE SPEED OF SOUND IN AIR OVER THE TEMPERATURE RANGE 300{650 K ROGER C. HART, R. JEFFREY BALLA y, AND G. C. HERRING z Abstract. Usng laser-nduced thermal acoustcs (LITA), the speed of sound n room ar (1 atm) s measured over the temperature range 300{650 K. Snce the LITA apparatus mantans a xed sound wavelength as temperature s vared, ths temperature range smultaneously corresponds to a sound frequency range 10{15 MHz. The data are compared to a publshed model and typcally agree wthn 0.1{0.4% at each of 21 temperatures. Key words. laser thermometry, speed of sound, optcal dagnostcs Subject classcaton. Flud Mechancs 1. Introducton. The speed of sound n ar near room temperature has been ntensely studed over a range of varous parameters such as frequency, humdty, and pressure. Ths body of work, stretchng back three centures, has been revewed by Wong [1]. Most of ths work was conducted n the audo (20{ 20,000 Hz) or hundreds-of-khz frequency range. Less frequently, work was carred out n the MHz range. At room temperature, sound speed models for ar [1] and pure gases [2] agree wth measurement to 0.03% or better. However, prevous work on the speed of sound n ar s lmted to temperatures of 300 K and below. In ths letter we present measurements of the speed of sound (10{15 MHz) n ar at 1 atm over the 300{650 K temperature range and compare these data wth theoretcal values. Ths letter s an outgrowth of our earler work [3] ndevelopng remote dagnostcs for ow temperature n wnd tunnels. We compare our expermental data to a model syntheszed by Zuckerwar [4]. The speed of sound s wrtten n the standard Laplacan form wth correctons for varous gas-phase phenomena. Thus, (1.1) V sound =[( o RT=M)(1 + C 1 )(1 + C 2 )(1 + C 3 )] 0:5 where 0 s the rato of specc heats, R s the unversal gas constant, T s the temperature, and M s the molecular mass. C 1 s a correcton for the temperature varaton of o, C 2 s a correcton for vral (non-deal gas) eects, and C 3 s a combned correcton for the vbratonal, rotatonal, and translatonal (classcal thermal and vscous) relaxatons. For our expermental condtons, C 1, C 2, and C 3 are each 0:05. Addtonal detals of these correctons are descrbed n Refs. [3] and [4]. 2. Expermental Method. The expermental method s laser-nduced thermal acoustcs (LITA) [5]. Detaled descrptons of the LITA apparatus, procedure, and data analyss are descrbed n Ref. [3]. Sound waves are produced by crossng two hgh-peak-power pulsed laser beams (532 nm) at 1 deg, formng nterference frnges at the crossng nsde an oven. Two counter-propagatng ultrasonc sound wave packets are launched by electrostrcton. The propagaton of these two acoustc waves s montored by probng them wth a long-duraton laser pulse (750 nm) that s Bragg-dracted nto a fast optcal detector. Ths probe sgnal decays as the wave packets propagate out of the sample volume (dened by the probe beam) and ICASE, NASA Langley Research Center, Hampton, VA Ths research was supported by the Natonal Aeronautcs and Space Admnstraton under NASA Contract No. NAS whle the rst author was n resdence at the Insttute for Computer Applcatons n Scence and Engneerng (ICASE), NASA Langley Research Center, Hampton, VA y AMDB, NASA Langley Research Center, Hampton, VA z AMDB, NASA Langley Research Center, Hampton, VA

3 Table 3.1 Summary of Model and Measurement for the Speed of Sound n Ar from 300 to 650 K Usng LITA T N N r H f LIT A V LIT A V mod V m V K % MHz m/s m/s m/s m/s m/s as the waves are attenuated through relaxaton. In prncple, the speed of sound can be determned from the wavelength (derved from beam crossng angle) and frequency of the temporal modulaton of the sgnal. Ths modulaton arses from the beatng of two ndvdual dracted lght beams (one from each sound wave packet) that are Doppler shfted relatve to each other. Snce we cannot measure our 1-deg crossng angle to 0.1% accuracy geometrcally, we eectvely measure t wth another LITA apparatus. We smultaneously generate a second LITA sgnal wth the same crossng angle n a reference cell at known temperature of 295 K. The sound speed n the oven s then determned from the rato of the LITA frequences observed n the oven, f LIT A, and reference cell, f ref, and the known sound speed V ref n the reference cell. Oven temperatures were read wth a precson of 0.2 K wth a thermocouple, whch had been calbrated by comparson wth a precson NIST-traceable Pt thermometer. Allowng for small temperature gradents n the oven, we estmate an absolute uncertanty n the measurement of the oven temperature of 0.33% (1 K at 300 K, growng to 2 K at 600 K). The small day-to-dayvaratons n atmospherc pressure produce neglgble changes n the speed of sound, relatve to the accuracy that we acheve here. 3. Expermental Results. The results of our experment are summarzed n Table 3.1. In what follows, quanttes assocated wth a sngle laser shot use subscrpt, quanttes averaged over a sngle run (100 shots n 2 mn) use subscrpt j, and all quanttes appearng n the table (wthout a subscrpt or j) 2

4 are averaged over a temperature bn of 3{15 runs. A total of 107 one-hundred-shot runs were made, of whch more than 9500 shots yelded usable data. The data shown have been bnned nto 21 temperatures, the wdth of the bns varyng from 0 K (all runs at the same temperature) to 5.0 K. The reason for consoldatng the 107 runs nto 21 temperature bns s to reduce the length of Table 3.1. For each good shot of each run, the oven sound speed V LIT A V LIT A j =(f LIT A =f ref )V ref was determned, and for each run, an unweghted average was found. Usng the observed oven temperature, humdty, and the unweghted average of measured sound frequency f LIT A j for each run, we calculated V mod j from the model (Eq. (1.1)). Fg Velocty derence (V from Table 3.1) between the measurements and the model as a functon of temperature. Uncertantes due to temperature uncertantes and sound velocty uncertantes (m from Table 3.1) were added n quadrature to obtan the total 1 uncertantes, ndcated by the error bars. In Table 3.1, N r s the number of runs and N s the total number of shots used n each bn. average temperature T, relatve humdty H, and model velocty V mod for each bn were calculated as the average of per run values weghted by the number of good shots n each run, e.g. T = (N j T j )=N j. Average values of f LIT A and V LIT A were weghted wth the per run standard devatons of the mean j. The quantty m was calculated from the per run standard devatons of the mean j The weghted by N j accordng to m = (N j (N j, 1) 2 j )=(N j (N j, 1)) 1=2 ; thus, m s the standard devaton of the mean of the dstrbuton f all the runs n a bn are normalzed to have the same mean value. The average of the derences V j = Vj LIT A, Vj mod, weghted by per run standard devatons, s denoted by V, whle the standard devaton of the V j, agan weghted by per run standard devatons, s denoted by V. Comparson of the m and V allows evaluaton of the short ( 10 mn) and long-term ( 1 day) repeatablty of the method. All bns contanng three runs comprse data taken over a ten mnute perod; here V s only a few tmes m (average value = 2.7 for N r = 3). Bns contanng more than three runs contan data from more than one day and show substantally hgher values of V = m ( 30 for the N r = 15 bn). Clearly our mplementaton of the reference cell technque does not provde long-term stablty comparable to the short-term precson. The uncertanty due to temperature and the statstcal uncertanty m are comparable, and addng them n quadrature results n the total uncertantes (1 ) shown as error bars n Fg Our measurements are n complete agreement wth the model, and sgncantly smaller 3

5 uncertantes wll be necessary to nd devatons from the model. 4. Concluson. Our results lead us to beleve that ths nonnvasve method for generatng and detectng free-eld ultrasonc waves s promsng for future work n gas-phase acoustcs. The statstcs of our sound speed measurements can be mproved by averagng more laser shots. In addton, mprovements n future LITA apparatus and ovens are possble. Thus, we antcpate that LITA can be used for characterzaton of the speed of sound for a varety of gases, frequences, and temperatures wth mproved uncertantes compared to those we have acheved here. We gratefully thank A. Zuckerwar for helpful dscussons. REFERENCES [1] G.S.K. Wong, Speed of Sound n Standard Ar, J. Acoust. Soc. Am. 79 (1986), pp. 1359{1366. [2] A.J. Zuckerwar, Speed of Sound n Real Gases. II. Comparson wth Experment, J. Acoust. Soc. Am. 100 (1996), p [3] R.C. Hart, R.J. Balla, and G.C. Herrng, Nonresonant Referenced Laser Induced Thermal Acoustcs Thermometry n Ar, Appl. Opt. 38 (1999), pp. 577{584. [4] A.J. Zuckerwar, Speed of Sound n Real Gases. I. Theory, J. Acoust. Soc. Am. 100 (1996), p [5] E.B. Cummngs, H.G. Hornung, M.S. Brown, and P.A. DeBarber, Measurement of Gas-Phase Sound Speed and Thermal Dusvty Over a Broad Pressure Range Usng Laser-Induced Thermal Acoustcs, Opt. Lett. 20 (1994), pp. 1577{