Freely propgting jet Introduction Gseous rectnts re frequently introduced into combustion chmbers s jets. Chemicl, therml nd flow processes tht re tking plce in the jets re so complex tht nlyticl description of the jet propgtion is very difficult to solve. Only the simplest cses of jets cn be described by nlyticl nd empiricl reltionships. Exmples of such jets re free strem isotherml nd non-isotherml jets. The jet hs higher momentum thn the surrounding fluid nd it propgtes in such wy tht the surrounding fluid is entrined by the jet. Scheme of freely propgting jet is presented in Figure 1. Fig. 1. Isotherml freely propgting jet Velocity distribution in n isotherml jet is described by empiricl equtions [1, 2]: w = [1 ( y 3 2 2 ) ] R j (1) = 0.96 x o (2) R + 0.29 o where: x the distnce from the injection nozzle outlet, y the distnce from the xis of the jet for the primry section nd distnce from the border of the constnt speed cone for the initil section, R o the rdius of the outlet nozzle, R j the hlf width of jet for the primry section or the width of the Instytut Techniki Cieplnej, Politechnik Śląsk, Gliwice 1
boundry lyer for the initil section, xil velocity (t the xis), w o the injection nozzle outlet velocity, the number of the structure of jet (0.066-0.08). The non-isotherml jet (jet temperture different from the temperture of the surrounding medium), in ddition to the velocity distribution, is lso chrcterized by temperture distribution. Bsed on the nlogy of turbulent het nd momentum trnsfer phenomen, in the non-isotherml jets the temperture surplus distribution is similr to the velocity distribution: T T ~ w = C 1 w (3) T T o ~ w o = C 2 w o (4) In equtions (3) nd (4) the indices nd o concern the prmeters on the xis nd in the initil cross section of the nozzle outlet, respectively, nd the symbol Δ stnds for the difference between the temperture t the certin loction within the jet nd the temperture of the surrounding medium. The im of the exercise The im of the exercise is to study the structure, size nd prmeters of the rel jets nd to verify these prmeters distributions obtined from the mesurements with empiricl reltionships outlined bove. Description of the test rig Figure 2 shows the test stnd which cn be used to mesure the prmeters of freely propgting isotherml nd non-isotherml jets. The ir from the compressed ir network is delivered through reducing vlve, flow meter, heter nd short metl tube into the surrounding ir, where it forms jet. Electric heter, powered by n utotrnsformer, hets the ir flond therefore non-isotherml jet is formed. Moveble mesurement sensor comprised of thermocouple nd Pitot tube llows mesuring the temperture nd dynmic pressure, nd thus the velocity of gs, within the jet t selected points situted in horizontl plne pssing through the xis of the jet. The mesured flow prmeters cn be red form the temperture guge nd micromnometer [1]. Instytut Techniki Cieplnej, Politechnik Śląsk, Gliwice 2
12 13 0000000000 1 2 3 4 5 6 8 7 11 Powietrze z sieci Air from the compressed ir network 10 9 Fig. 2. Test stnd for mesurements of the jet prmeters. 1. control vlve; 2. mnometer; 3. rotmeter; 4. electric heter; 5. utotrnsformer; 6. nozzle; 7. Pitot tube; 8. thermocouple; 9. moveble bse; 10. ruler; 11. ril system; 12. temperture guge; 13. micromnometer Gs velocity t point, where the dynmic pressure is mesured, is clculted from w = 2p d ρ (5) where ρ is the density of gs t the mesuring point. Mesurement procedure After generl inspection of the test fcility, the circuits nd connections of mesuring instruments, perform the following steps: 1) open the ir control vlve nd (by using the reduction vlve) set the ir flow in such wy tht the gs velocity t the outlet of the nozzle is pproximtely equl to w o 15 (it corresponds to the vlue of 17 of liquid displcement in the mnometer), 2) tke mesurements of the velocity vlues on the xis t four points ccording to the progrm given in Tble 1 3) Repet the bove steps for the two other speeds: w o 20 ( 30 column of liquid) nd w o 25 ( 45 ), 4) set the ir flot similr level to set the mesurements for w o 20 nd switch the ir flow heter on (using utotrnsformer). The power should be set such tht fter determining n equilibrium therml stte, the temperture t the outlet of the nozzle will be slightly bove 150 C. This cn be chieved when powered heting element voltge will be pproximtely 90 V. Be wre tht too high voltge my destroy the heting element, Instytut Techniki Cieplnej, Politechnik Śląsk, Gliwice 3
x2= x1= LABORATORY OF COMBUSTION FUNDAMENTALS 5) fter reching stedy stte tke mesurements of velocity nd temperture t the outlet of the nozzle, the width of the strem R j, velocity nd temperture t the points t horizontl hlf-plne pssing through the xis of the strem ccording to the progrm given in Tble 2. Tb. 1. The mesurement results for isotherml jets. The jet dt = = = The distnce from the nozzle outlet x, 30 60 90 120 Tb. 2. The mesurements results for non-isotherml jets The jet dt T = T o T tm = K t tm = C w o = R o = loction of mesurement R j T K kg/m 3 w C 1 C 2 y = 0 y = 0,25 R j y = 0,50 R j y = 0,75 R j y = 0 y = 0,25 R j y = 0,50 R j y = 0,75 R j Hints Stbility of velocity w o during the velocity nd temperture mesurements inside the jet hs to be ensured by mintining stbility of the flot of the rotmeter Instytut Techniki Cieplnej, Politechnik Śląsk, Gliwice 4
When mesuring velocity t the outlet of the nozzle, mke sure tht the tip of the probe hs not been inserted into the nozzle. This will reduce the cross-section of the outlet nd cuse flsifiction of reding. The tip of the sensor should be offset bout 2 from the nozzle outlet. Anlysis nd evlution of the results Bsed on the mesurements, perform pproprite clcultions ccording to formule 2-4 nd use the bove-mentioned formuls to clculte the results by filling in Tbles 1 nd 2. For given mesurement point clculte the error of determining the constnt. On the bsis of the vlues of constnts, C 1 nd C 2, check the degree of similrity of the velocity nd temperture distributions of the exmined jet. Determine the effect of Reynolds number on the obtined constnt. References [1] Splnie i pliw (W. Kordylewski - editor), Oficyn Wydwnicz Politechniki Wrocłwskiej, Issue II, Wrocłw, 1999 [2] Teori turbulentnych strug (G.N. Abrmowicz - editor), Nuk, Moskw, 1984 Instytut Techniki Cieplnej, Politechnik Śląsk, Gliwice 5