ch,实验模拟研究
Twenty-Seventh Symposium(International)on Combustion/The Combustion Institute,1998/pp.615–623 EXPERIMENTAL AND COMPUTATIONAL STUDY OF CH,CH*,AND OH*IN AN AXISYMMETRIC LAMINAR DIFFUSION FLAME
K.T.WALSH,M.B.LONG,M.A.TANOFF and M.D.SMOOKE
Department of Mechanical Engineering
Yale University
New Haven,CT06520-8284,USA
In this study,we extend the results of previous combined numerical and experimental investigations of
an axisymmetric laminar diffusion?ame in which difference Raman spectroscopy,laser-induced?uores-
cence(LIF),and a multidimensional?ame model were used to generate pro?les of the temperature and
major and minor species.A procedure is outlined by which the number densities of ground-state CH
(X2P),excited-state CH(A2D,denoted CH*),and excited-state OH(A2R,denoted OH*)are measured
and modeled.CH*and OH*number densities are deconvoluted from line-of-sight?ame-emission mea-
surements.Ground-state CH is measured using linear LIF.The computations are done with GRI Mech
2.11as well as an alternate hydrocarbon mechanism.In both cases,additional reactions for the production
and consumption of CH*and OH*are added from recent kinetic studies.Collisional quenching and
spontaneous emission are responsible for the de-excitation of the excited-state radicals.
As with our previous investigations,GRI Mech2.11continues to produce very good agreement with
the overall?ame length observed in the experiments,while signi?cantly under predicting the?ame lift-
off height.The alternate kinetic scheme is much more accurate in predicting lift-off height but overpredicts
the overall?ame length.Ground-state CH pro?les predicted with GRI Mech2.11are in excellent agree-
ment with the corresponding measurements,regarding both spatial distribution and absolute concentration
(measured at4ppm)of the CH radical.Calculations of the excited-state species show reasonable agree-
ment with the measurements as far as spatial distribution and overall characteristics are concerned.For
OH*,the measured peak mole fraction,1.3?10?8,compared well with computed peaks,while the
measured peak level for CH*,2?10?9,was severely underpredicted by both kinetic schemes,indicating
that the formation and destruction kinetics associated with excited-state species in?ames require further
research.
Introduction
CH has long been recognized as a key reactant in NO x formation through the prompt NO mechanism. Given that CH is a short-lived trace species that ex-ists in a narrow spatial and temperature region within a?ame,its concentration and spatial distri-bution are very sensitive tests of the detailed chem-ical kinetics needed to model pollutant formation. The oxidation of CH plays a central role in the pro-duction of chemically excited OH(A2R,denoted OH*),which emits in the ultraviolet.This ultraviolet emission has been suggested as a measure of the ?nal steps of the CH x reduction chain[1].Chemi-
cally excited CH(A2D,denoted CH*)is responsible for the blue light in low-soot?ames and may provide insight into the C2reaction chain[1].Despite the prevalence of CH*and OH*chemiluminescence, little quantitative work has been done either exper-imentally or computationally in predicting the ab-solute concentrations of these species.In this study, quantitative measurements of CH,CH*,and OH* are performed and comparisons are made with com-putational predictions.
The?ame under investigation is a lifted axisym-metric laminar diffusion?ame,which has been char-acterized previously both experimentally and com-putationally[2–5].The fuel is nitrogen-diluted methane surrounded by an air co?ow.Experimen-tally,temperature and major species(CH4,N2,O2, H2O,CO,CO2,H2)concentrations were measured simultaneously with Rayleigh and Raman scattering [2].Laser-induced?uorescence(LIF)measure-ments were performed to measure number densities of minor species.Quantitative,linear LIF measure-ments were made for OH[3]and NO[4],and qual-itative measurements of CH have been made[3]. Modeling work has employed different kinetics schemes,including a26-species C2hydrocarbon mechanism[3]and GRI Mech2.11.Both produced excellent agreement for temperature and major spe-cies[5].Computed peak concentrations for NO and OH were within30%and15%,respectively,of their measured values.
In the following sections,the experimental con?g-uration is described,and the details of the measure-ments of CH,CH*,and OH*are presented.The
615
616LAMINAR DIFFUSION FLAMES
computational model and the various kinetics schemes used to predict the measured species are then described.Finally,the experimental results are compared with computations based on different ki-netics schemes.
Burner Con?guration
The burner used in this experiment consisted of a central fuel jet(4mm diameter)surrounded by cof-lowing air(50mm diameter).The fuel was com-posed of65%methane diluted with35%nitrogen by volume to reduce soot,and the plug?ow exit velocity of both fuel and co?ow was35cm/s.This produces a blue?ame roughly3cm in length with a lift-off height https://www.wendangku.net/doc/1b17428550.html,plete burner speci-?cations are given elsewhere[2].The burner was mounted on a stepper motor to allow measurements to be taken at different heights.
Laser-Induced Fluorescence Measurement
of CH
The third harmonic of a Nd:YAG laser,operating at10Hz,pumped a dye laser containing Coumarin 440dye.The R(7)line in the(0,0)band of the A–X system,near426.8nm,was selected for excitation. The dye beam was split for power measurement,at-tenuated,shaped into a sheet,and passed across the jet centerline.Typical energies were1l J per pulse. The laser sheet dimensions were measured to be5.5 mm?300l m.The measured line width Dm of the beam was0.16cm?1,and the pulse duration was10 ns,which corresponds to a spectral density of order 104W/(cm2cm?1),well below the saturation value [6].Imaging was done with a cooled charged-cou-pled device(CCD)camera and a lens-coupled image intensi?er.The CH?uorescence was isolated with an interference?lter that transmitted from400to 440nm.An f/2camera lens collected the CH?uo-rescence,and a pair of f/1.4camera lenses focused the light from the back end of the intensi?er onto the CCD chip.The imaged pixel volume was30?30?300l m3.The laser was set to426.777nm to record on-resonance images(I on)and to426.671nm for off-resonance images(I off).A?ame luminosity image was also taken with the laser turned off(I lum). Typical images were integrated over6000laser shots.The on-resonance image contained LIF and Rayleigh scattering on top of the?ame luminosity background,while the off-resonance image had only Rayleigh scattering and?ame luminosity.Because the laser energy differed by a small known amount between the on-and off-resonance measurements (E on and E off),the?nal LIF images were created as follows:S LIF?I on?I lum?(I off?I lum)*E on/E off. Measurements were made at each of eight heights above the burner surface,and these images were later tiled together.
To convert the measured LIF signal into a quan-titative concentration measurement,a number of calibrations and corrections must be made.For a two-level model,the LIF signal per pulse in the lin-ear regime is given by
1E LIF
S?b n f C
LIF12CH B
4p A Dm
LIF
A21
?V Xeg(1)
LIF
A?Q
2121
14243
U
where b12is the absorption rate,E LIF is the laser energy per pulse,Dm is the laser line width,A LIF is the cross-sectional area of the laser beam,n CH is the number density of ground-state CH,f B is the frac-tion of the ground state in the state being pumped, C is a dimensionless overlap integral,A21is the spon-taneous emission rate,Q21is the collisional quench-ing rate,V LIF is the LIF pixel volume,X is the solid angle over which light is collected,e is the ef?ciency of the collection optics,and g is the detector ef?-ciency in counts per photon[7].The quantity that we are interested in determining is n CH.The factors in equation1must be measured directly or deter-mined from the literature.The quantity A21/(A21?Q21)represents the fraction of excited molecules that emit a photon and is called the?uorescence yield,U.The total collisional quenching rate for the excited state is Q21??c i k i,where c i is the concen-tration of species i and k i is the collisional quenching rate for species i.Values for k i(which are tempera-ture dependent)were computed from the functional form given by Tamura et al.[8].Concentration pro-?les of the major species(CH4,N2,O2,H2O,CO, CO2,H2)were computed previously[5]and used for these calculations.The temperature in the thin region where CH is present is nearly constant at 1900K.This quenching calculation resulted in a spa-tially constant?uorescence yield U of1/176.In this ?ame,N2was responsible for more than60%of the quenching.Unfortunately,the CH/N2quenching rate has not been measured above1300K making the extrapolation to?ame temperatures a source of uncertainty.The Boltzmann factor,f B,is calculated based on the molecule probed,temperature,and the excitation/detection scheme used.Given our choice of the R(7)line,f B?0.07.Spectroscopic rotational and vibrational constants were taken from Huber and Herzberg[9].C is a spectral integral of the over-lap between the CH absorption pro?le and the laser beam.The laser pro?le was?t to a Gaussian distri-bution centered at426.777nm with a full width at half-maximum(FWHM)of Dm?0.16cm?1,mea-sured previously.The absorption spectrum of CH(at
CH,CH*,OH*IN LAMINAR FLAME
617
F ig .1.CH mole fraction pro?les determined by measurement,GRI Mech 2.11,and an alternate hydrocarbon mechanism.
atmospheric pressure with resolution Dm )was cal-culated with the LIFBASE program [10]and re-sulted in C ?0.17.The calculated absorption pro?le was needed because a CH excitation spectrum could not be measured practically in the linear regime given the long integration times needed to obtain reasonable signal levels.A saturated CH excitation scan was performed,however,and compared well to a computed absorption pro?le for a larger line width.When evaluating the integral,both the computed absorption pro?le (with line width Dm )and ?t beam pro?le had narrow features.Small variations in the peak of the Gaussian,hence small changes in the laser wavelength,affect C .Given that the resetta-bility of the dye laser is ?0.02A
?,the uncertainty in C is estimated at 20%.
Rayleigh Calibration
Calibration of CH LIF is somewhat problematic.CH is highly reactive,preventing reference to a known concentration,and is present in a very thin (?500l m wide)region,making absorption calibra-tion dif?cult.However,Luque and Crosley [7]have demonstrated that Rayleigh scattering can be used on the same optical setup to relate the measured signal to an absolute light level and thus solve for the overall calibration product (Xeg )in equation 1.For scattering from a homogeneous gas,the Ray-leigh signal per pulse is given by
?r NE V R R
??
?X
S ?
Xeg (2)
R A h m
R where N is the number density of the gas ?ow used for calibration,E R is the laser energy per pulse pro-ducing the Rayleigh signal,V R is the Rayleigh vol-ume,(?r /?X )is the Rayleigh cross section,h m is the photon energy,and A R is the cross-sectional area of the laser beam.After Rayleigh measurements are made,the calibration product can be eliminated,re-sulting in a single expression for number density.Given that the ?uorescence beam occupies the same spatial region as the Rayleigh beam (A R ?A LIF and V R ?V LIF ),we now have
?r
4p S Dm NE LIF R
??
?X n ?
(3)
CH b E C f U h m S 12LIF B R
as an expression for absolute number density of ground-state CH.
Rayleigh calibration was done on a ?ow of clean air with the same optical setup and beam dimensions as used in LIF.Although calibration can be done with a single Rayleigh image,measurements were made over a range of energies to verify the linear relationship between the signal and laser energy and to con?rm a zero intercept.The measured calibra-tion was linear and had an intercept within a few percent of the origin.Energy per pulse was varied between 0.1and 1.2mJ,with an integration of 300to 1500shots.
These calibrations and calculations,in conjunction with previous temperature measurements,resulted in a two-dimensional pro?le of CH mole fraction that can be seen in Fig.1.The measured peak mole fraction was 4ppm.
618LAMINAR DIFFUSION FLAMES
Chemiluminescence of CH*and OH* Measurements of chemically excited?ame radi-cals,such as CH*and OH*,are relatively easy to make but have calibration dif?culties similar to those of ground-state CH.Fortunately,the same Rayleigh calibrations can be applied to determine absolute in-tensity levels,and quenching corrections can be made to quantify the measured signals.The space and power constraints imposed by microgravity ex-periments have generated a renewed interest in making such emission measurements as quantitative as possible.Although?ame emissions were exam-ined spectrally decades ago and CH*has been rec-ognized as the primary source of the ubiquitous “blue light”in low-soot?ames[11],the reactions that produce CH*are not well understood.Chemi-luminescent OH(OH*)is another common?ame emitter whose kinetics deserve investigation.A goal of this study was to measure the absolute number densities of these?ame radicals to assess the current state of CH*and OH*kinetics.
OH*chemiluminescence peaks at307.8nm.Ex-cited-state OH measurements were made with a cooled CCD camera using an f/4.5UV camera lens; the camera/lens system was placed50cm away to ensure a wide depth of?eld.A narrow bandpass UV ?lter was used(center307nm,10nm bandwidth). High emission signal levels were collected with10s integration times.Rayleigh calibration was done with a Nd:YAG-pumped dye laser utilizing sulfar-hodamine640dye.The612nm output was fre-quency doubled to perform calibration measure-ments on clean air.Beam energy in the UV was varied from0.3to2.0mJ per pulse and integration times were600shots.
For CH*?ame emission,the A2D→X2P tran-sition at431.2nm was imaged with the camera and lens system detailed above.An interference?lter (center431nm,10nm bandwidth)was used to iso-late the CH*emission.Again,good signal levels were collected over10s integration times.The cal-ibration measurements were again performed with a Nd:YAG-pumped dye laser.During Rayleigh cali-bration,the energy of the431.5-nm beam was varied between0.5and2.5mJ,with signal collected over 600shots.
The?ame emission signal,in detector counts,is given by
1
S?A s V N Xeg(4)
em21em em
4p
where s is the integration time,V em is the pixel vol-ume of the emission signal,and N em is the number of molecules that emit a photon.The spontaneous emission rate and integration time are known,and the emission volume can be determined directly.As with the?uorescence measurement,the calibration constants of the optical system,Xeg,are accounted for with Rayleigh scattering.Furthermore,a quenching calculation is needed to relate the num-ber density of emitting molecules to the total popu-lation of the chemically excited radical.To obtain an absolute number density of a chemically excited rad-ical,N*,we recognize that N*?N em/U.Equations (2)and(4)can be combined with this to yield
?r
4p S NE?
em R???X
N*?(5)
S A s V U h m
R21em
where?is the length along the beam in the Rayleigh volume under consideration.
Emission measurements are integrated through the collection optics along the line of sight.Appro-priate background images,taken for both CH*and OH*with the?ame extinguished,are subtracted from the raw emission signal.Given that our?ame is axisymmetric and that the imaging optics are con-?gured so that the magni?cation changes by only1% over the?ame width,we can recover a two-dimen-sional,in-plane intensity distribution proportional to number density with the use of an algorithm that is equivalent to a two-point Abel deconvolution[12]. After inversion,pixel volumes were determined to be cubes of side length68l m for both CH*and OH*.The quenching correction for CH*was per-formed using the cross sections and temperature de-termined for ground-state CH.This resulted in a peak CH*mole fraction of2?10?9,as seen in Fig.
2.For OH*,quenching rates for OH were taken from Tamura et al.[8]and combined with major species and temperature computations performed previously[5].OH*appears at a nearly constant temperature of1900K and is highly localized.The quenching calculation resulted in a?uorescence yield U of1/327that did not vary spatially.Water, the only important individual collider,is responsible for about2/3of the OH*quenching in this?ame. Cross sections for OH have been measured over a large range of temperatures and have agreed with low-pressure quenching measurements to within5% [8].The measured OH*pro?le is displayed in Fig. 3;the peak mole fraction was1.3?10?8.
Computational Model
The computational model used to compute the temperature?eld,velocities,and species concentra-tions solves the full set of elliptic two-dimensional governing equations for mass,momentum,species, and energy conservation on a two-dimensional mesh [13].The resulting nonlinear equations are then solved on an IBM RS/6000Model590computer by a combination of time integration and Newton’s method.The chemical mechanisms employed were GRI Mech2.11[14]and an alternate hydrocarbon mechanism(used,for example,in Ref.[3]).
CH,CH*,OH*IN LAMINAR FLAME
619 F ig.2.CH*mole fraction pro?les determined by measurement,GRI Mech2.11,and an alternate hydro-carbon mechanism.The ground-state CH pro?le is shown to illustrate the thin features of both the mea-sured and computed CH*pro?les.
Accurate computations of the CH,CH*,and OH* radicals pose a dif?cult numerical problem.For ex-ample,the concentration of CH can change by an order of magnitude within0.1mm.This requires that the adaptive grid be re?ned to an extremely small mesh size in the vicinity of high spatial activity.
Kinetics Modeling
To model chemiluminescence,the species CH* and OH*must be added to the kinetic mechanisms, along with a set of formation and destruction reac-tions with appropriate rate constants.All CH*/OH*-related rate constants used in this study are detailed in Table1.
CH*is produced chemically via the reaction of the ethynyl radical with monatomic and diatomic oxy-gen:
C H?O?CH*?CO
I)222
C H?O?CH*?CO
II)2
The rate constants have been reported as k I?3.6?10?14cm3molecule?1s?1and k II?1.8?10?11 cm3molecule?1s?1[15].The uncertainties associ-ated with these reaction rates are about40%.De-struction reactions occur by spontaneous emission (CH*→CH?h m)and collisional quenching. Quenching was modeled with seven different reac-tions,each involving CH*and a major chemical spe-cies in the?ame(CH4,N2,O2,H2O,CO,CO2,H2). Species-speci?c,temperature-dependent quenching rates were taken from Tamura et al.[8].The heat of formation of CH*was set at66.3kcal/mole above that of ground-state CH,based on the energy of the spontaneously emitted photon.
OH*formation was modeled with a single reac-tion:
620LAMINAR DIFFUSION
FLAMES
F ig .3.OH*mole fraction pro?les determined by measurement,GRI Mech 2.11,and an alternate hydrocarbon mechanism.
CH ?O ?OH*?CO
III)
2The rate constant for the reaction CH ?O 2→All Products was measured by Berman [16].This mea-surement was used for k III by Marchese et al.[17]and will be used here as well.Uncertainty in this rate constant is likely to be large but is not readily estimated.Spontaneous emission and collisional quenching reactions were added to the mechanism in the same manner as previously described.The heat of formation of OH*was set at 93kcal/mole above that of ground-state OH.Note that chemi-excitation reactions I–III all have other channels that form ground-state species,which are included in both kinetic schemes.
Results and Discussion
As with our previous investigations,GRI Mech 2.11continues to produce very good agreement with the overall ?ame length observed in the experi-ments,while signi?cantly underpredicting the ?ame lift-off height.The alternate kinetic scheme is much more accurate in predicting lift-off height but ov-erpredicts the overall ?ame length.Note that the predicted lift-off height is related to the extinction strain rate obtained in the corresponding counter-?ow diffusion ?ame.The extinction strain rate com-puted with GRI Mech 2.11is nearly 20%higher than that obtained with the alternate mechanism,and thus the ?ame can anchor itself in a region of higher strain.
The character of the CH distribution within the GRI-computed pro?le is in excellent agreement
with the measurements;that is,the highest CH con-centration appears near the ?ame anchoring region,falling off to a nearly constant level throughout the ?ame front,up to and including the tip of the ?ame front.The peak measured ground-state CH number density was 1.53?1013cm ?3.Given that the tem-perature was measured in this ?ame previously,we can easily calculate mole fractions from measured concentrations.Hence,the measured peak mole fraction of CH is 4?10?6,nearly 20%higher than the prediction of GRI Mech 2.11.
Other than a better prediction of the lift-off height,the computed CH results are not as good with the alternate hydrocarbon kinetic mechanism.The location and distribution of CH is still within reasonable agreement,but the CH pro?le no longer appears to close at the ?ame tip.Additionally,the peak CH concentration is predicted to be 42%lower than the measured concentration.The dependence of the spatial characteristics and absolute concentra-tions on the choice of kinetic scheme reveals CH to be an important test of our rather well-validated ?ame model,as subtle differences are not seen be-tween the two kinetic schemes for the prediction of major species and temperature pro?les.
The CH*pro?le is thinner than that of ground-state CH when comparing measured CH to mea-sured CH*,as seen in Fig.2.The difference in peak concentration of the experimental pro?les of CH and CH*is of order 1000,similar to the ratio mea-sured by other researchers [18].A relationship simi-lar to that discussed with CH exists between the computed pro?les of CH*and the measurements,as far as spatial distribution and overall characteris-tics.However,the measured peak mole fraction of
CH,CH*,OH*IN LAMINAR FLAME621
TABLE1
Reactions added for CH*and OH*kinetics.Units for rate constants are centimeters,moles,and seconds,with the formulation k?AT B exp[?E a/RT]?E a in cal mole?1and R in cal mole?1K?1
Reaction A B E a Ref. C2H?O?CH*?CO 1.08E?130.000[15] C2H?O2?CH*?CO2 2.17E?100.000[15] CH*→CH 1.85E?060.000[8] CH*?N2?CH?N2 3.03E?02 3.40?381[8] CH*?O2?CH?O2 2.48E?06 2.14?1720[8] CH*?H2O?CH?H2O 5.30E?130.000[8] CH*?H2?CH?H2 1.47E?140.001361[8] CH*?CO2?CH?CO2 2.40E?01 4.30?1694[8] CH*?CO?CH?CO 2.44E?120.500[8] CH*?CH4?CH?CH4 1.73E?130.00167[8] CH?O2?OH*?CO 3.25E?130.000[16] OH*→OH 1.45E?060.000[8] OH*?N2?OH?N2 1.08E?110.50?1238[8] OH*?O2?OH?O2 2.10E?120.50?482[8] OH*?H2O?OH?H2O 5.92E?120.50?861[8] OH*?H2?OH?H2 2.95E?120.50?444[8] OH*?CO2?OH?CO2 2.75E?120.50?968[8] OH*?CO?OH?CO 3.23E?120.50?787[8] OH*?CH4?OH?CH4 3.36E?120.50?635[8]
CH*,2?10?9,is a factor of17and33greater than the predictions of the alternate mechanism and GRI Mech2.11,respectively.
As with CH and CH*,the highest concentration of OH*is found at the anchoring region,as seen in Fig.3.The measured OH*concentration pro?le ap-pears somewhat broader than predicted by either set of kinetics,and the measured peak mole fraction is within15%of the peak computed with the alternate mechanism.
Conclusions
In this study,we extended the results of previous combined numerical and experimental investiga-tions of an axisymmetric laminar diffusion?ame in which difference Raman spectroscopy,laser-induced ?uorescence,and a multidimensional?ame model were used to generate pro?les of the temperature and major and minor species.We discussed issues related to the computation and measurement of CH, CH*,and OH*in an uncon?ned laminar?ame in which a cylindrical fuel stream is surrounded by a co?owing oxidizer jet.Experimentally,CH radical concentrations were measured with laser-induced ?uorescence,whereas CH*and OH*concentrations were measured with?ame emission.
The results of this study indicate that GRI Mech 2.11does an excellent job of predicting peak CH concentration,considering the ppm concentration levels and narrow spatial extent of the CH radical’s pro?le,as well as the overall characteristics and shape of the CH pro?le.Other than a better predic-tion of?ame lift-off height,the CH results are not nearly as good with our alternate hydrocarbon ki-netic scheme.
As far as spatial distribution and overall character-istics are concerned,relationships similar to those observed between calculated and measured CH were observed for calculated and measured CH* and OH*,as well.Peak concentration levels for CH* were severely underpredicted with both kinetic schemes,while peak concentration levels of OH* agreed to within15%(alternate mechanism)and a factor of2(GRI Mech2.11)of the predicted peaks. Still,this indicates that although overall?ame struc-ture is well understood and well characterized,the formation and destruction kinetics associated with excited-state species in?ames requires further re-search.The reasonable uncertainties in the excita-tion reaction rate constants for CH*production in-dicate it is likely that new formation pathways,such as C2?OH→CH*?CO[11],need to be pos-tulated and investigated.
Acknowledgments
We would like to thank https://www.wendangku.net/doc/1b17428550.html,ler of George Wash-ington University and Dr.J.B.Jeffries of SRI for helpful discussions.The support of NASA under Grant NAG3-1939is gratefully acknowledged.
622LAMINAR DIFFUSION FLAMES
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COMMENTS
David R.Crosley,SRI International,USA.You predicted the CH concentration quite well,and of course you know O2even better.Thus,the correspondence between mea-sured and predicted OH*depends only on a single rate coef?cient and suggests some adjustment is needed.Does the predicted OH*,which differs between the two mech-anisms,track directly the predicted CH?
Author’s Reply.The peak mole fractions of both CH and OH*were greater using GRI Mech2.11than with the alternate mechanism(see table).However,if one forms the ratio of peak CH to peak OH*mole fractions using the two different mechanisms,the ratios differ by nearly a fac-tor of2.The location of the peak CH mole fraction in the GRI Mech calculation corresponds to a region with higher O2mole fraction compared to the calculation using the alternate mechanism.In regions where the CH exists,the CO mole fractions and temperatures are nearly the same for both calculations.As a result,when the effects of all four species are taken into account,the ratio X CH/
X O
2 X CO is essentially the same for the two mechanisms. X OH*Peak Mole
Fraction GRI Mech2.11
Alternate
Mechanism X CH 3.30E-06 2.30E-06 X OH* 2.70E-08 1.10E-08
●
Steve Hasko,BG Technology plc,UK.
1.Did the authors use the same rate data in their alternate
reaction scheme as they used in their implementation of GRI Mech?Otherwise,what was that scheme opti-mized against?
2.On the experimental and computed maps of tempera-
ture,the tip of the inner cone of the computed result seems to be sharper than that of the measured?ame, which appears more rounded.It has been our experi-ence that the strength of the tip can affect the lower edges and,thus,also the standoff height.Have the au-thors any thoughts about what might be happening at the tip,such as thermal diffusion of M atoms,that might cause this difference between the measured and com-puted results?
CH,CH*,OH*IN LAMINAR FLAME623
Author’s Reply.The two mechanisms did not use the same rate data.The alternate mechanism was compared against experimental measurements for temperature and species in a variety of?ame con?gurations(Ref.[3]in the paper and references therein).
The apparent sharpness at the tip of the inner cone seen in the computed temperature maps is due,in part,to the lower spatial resolution of the calculations at this down-stream location.We note that the calculations using the two different mechanisms display a similar degree of sharp-ness,despite having quite different lift-off heights.Your observation is an interesting one,but we have not had an opportunity to investigate this further.
●
H.F.Calcote,ChemIon,Inc.,USA.Ions in hydrocar-bon–oxygen?ames are due to the chemi-ionization reac-tion:CH?O→HCO?where the CH is usually con-sidered to be the excited state CH(A2D).Your work is thus of relevance toward quantitatively accounting for chemi-ions.The rate coef?cient for the foregoing reaction with CH(A2D)has been reported as4.8E?14[1]as measured in a?ame by Cool and Tjossem[2].How would the inclu-sion of this reaction in Table1affect your results?
Table1includes three reactions with negative activation energies.Could you comment on these reactions in terms of Benson and Dobis recent discussion[3]of negative ac-tivation energy reactions?They argue that such reactions are an artifact of the experiment or they are due to a mul-tistep transition-state mechanism.
REFERENCES
1.Filakov,A.B.,Prog.Energy Combust.Sci.23:399–528
(1997).
2.Cool,T.A.and Tjossem,P.J.H.,Chem.Phys.Lett.
111:82–88(1984).3.Benson,S.W.and Dobis,O.,J.Phys.Chem.A
102:5175–5181(1998).
Author’s Reply.The rate constant for the chemi-ioniza-tion step is approximately a factor of4(for CO and H2)to an order of magnitude(for O2,N2,and CO2)higher than the rate constants we used in our CH*collisional deacti-vation steps in the region of the?ame where CH*is pres-ent.However,considering the magnitude of the O-atom concentration compared with the concentration of the col-lisional partners in this region(e.g.,N2),the chemi-ioni-zation step will have little impact on the consumption of CH*.
Benson and Dobis discuss the apparent nature of neg-ative activation energies for certain bimolecular metathesis reactions.However,the negative activation energies quoted for three of the CH*collisional deactivation steps (as well as the OH*collisional deactivation steps)are nei-ther an experimental artifact nor due to a multistep tran-sition-state mechanism.The three parameter pseudo-Ar-rhenius forms used by Tamura et al.(our Ref.[8]),are taken from the compilation of Heinrich and Stuhl[1],who determined best?ts of their experimentally determined quenching rate constants grouped with a variety of previ-ously quoted literature values in alternate temperature ranges.Indeed,Heinrich and Stuhl noted the dif?culty in ?tting the observed temperature dependencies with phys-ically meaningful rate parameters.While the sum of two Arrhenius forms was observed to be a good representation of the date,the authors found no indication that the quenching reactions occurred via two paths with distinct activation energies and thus opted for the more general three-parameter pseudo-Arrhenius form.
REFERENCE
1.Heinrich,P.and Stuhl,F.,Chem.Phys.199:105–118
(1995).
系统仿真综合实验指导书(2011.6)
系统仿真综合实验指导书 电气与自动化工程学院 自动化系 2011年6月
前言 电气与自动化工程学院为自动化专业本科生开设了控制系统仿真课程，为了使学生深入掌握MATLAB语言基本程序设计方法，运用MATLAB语言进行控制系统仿真和综合设计，同时开设了控制系统仿真综合实验，30学时。为了配合实验教学，我们编写了综合实验指导书，主要参考控制系统仿真课程的教材《自动控制系统计算机仿真》、《控制系统数字仿真与CAD》、《反馈控制系统设计与分析——MATLAB语言应用》及《基于MATLAB/Simulink的系统仿真技术与应用》。
实验一MATLAB基本操作 实验目的 1．熟悉MATLAB实验环境，练习MATLAB命令、m文件、Simulink的基本操作。 2．利用MATLAB编写程序进行矩阵运算、图形绘制、数据处理等。 3．利用Simulink建立系统的数学模型并仿真求解。 实验原理 MATLAB环境是一种为数值计算、数据分析和图形显示服务的交互式的环境。MATLAB有3种窗口，即：命令窗口（The Command Window）、m-文件编辑窗口（The Edit Window）和图形窗口（The Figure Window），而Simulink另外又有Simulink模型编辑窗口。 1．命令窗口（The Command Window） 当MATLAB启动后，出现的最大的窗口就是命令窗口。用户可以在提示符“>>”后面输入交互的命令，这些命令就立即被执行。 在MATLAB中，一连串命令可以放置在一个文件中，不必把它们直接在命令窗口内输入。在命令窗口中输入该文件名，这一连串命令就被执行了。因为这样的文件都是以“.m”为后缀，所以称为m-文件。 2．m-文件编辑窗口（The Edit Window） 我们可以用m-文件编辑窗口来产生新的m-文件，或者编辑已经存在的m-文件。在MATLAB 主界面上选择菜单“File/New/M-file”就打开了一个新的m-文件编辑窗口；选择菜单“File/Open”就可以打开一个已经存在的m-文件，并且可以在这个窗口中编辑这个m-文件。 3．图形窗口（The Figure Window） 图形窗口用来显示MATLAB程序产生的图形。图形可以是2维的、3维的数据图形，也可以是照片等。 MATLAB中矩阵运算、绘图、数据处理等内容参见教材《自动控制系统计算机仿真》的相关章节。 Simulink是MATLAB的一个部件，它为MATLAB用户提供了一种有效的对反馈控制系统进行建模、仿真和分析的方式。 有两种方式启动Simulink:
控制系统仿真与CAD 实验报告
《控制系统仿真与CAD》 实验课程报告
一、实验教学目标与基本要求 上机实验是本课程重要的实践教学环节。实验的目的不仅仅是验证理论知识，更重要的是通过上机加强学生的实验手段与实践技能，掌握应用 MATLAB/Simulink 求解控制问题的方法，培养学生分析问题、解决问题、应用知识的能力和创新精神，全面提高学生的综合素质。 通过对MATLAB/Simulink进行求解，基本掌握常见控制问题的求解方法与命令调用，更深入地认识和了解MATLAB语言的强大的计算功能与其在控制领域的应用优势。 上机实验最终以书面报告的形式提交，作为期末成绩的考核内容。 二、题目及解答 第一部分：MATLAB 必备基础知识、控制系统模型与转换、线性控制系统的计算机辅助分析 1. >>f=inline('[-x(2)-x(3);x(1)+a*x(2);b+(x(1)-c)*x(3)]','t','x','flag','a','b','c');[t,x]=ode45( f,[0,100],[0;0;0],[],0.2,0.2,5.7);plot3(x(:,1),x(:,2),x(:,3)),grid,figure,plot(x(:,1),x(:,2)), grid
2. >>y=@(x)x(1)^2-2*x(1)+x(2);ff=optimset;https://www.wendangku.net/doc/1b17428550.html,rgeScale='off';ff.TolFun=1e-30;ff.Tol X=1e-15;ff.TolCon=1e-20;x0=[1;1;1];xm=[0;0;0];xM=[];A=[];B=[];Aeq=[];Beq=[];[ x,f,c,d]=fmincon(y,x0,A,B,Aeq,Beq,xm,xM,@wzhfc1,ff) Warning: Options LargeScale = 'off' and Algorithm = 'trust-region-reflective' conflict. Ignoring Algorithm and running active-set algorithm. To run trust-region-reflective, set LargeScale = 'on'. To run active-set without this warning, use Algorithm = 'active-set'. > In fmincon at 456 Local minimum possible. Constraints satisfied. fmincon stopped because the size of the current search direction is less than twice the selected value of the step size tolerance and constraints are satisfied to within the selected value of the constraint tolerance.
典型环节的模拟研究-实验分析报告
典型环节的模拟研究-实验报告
————————————————————————————————作者：————————————————————————————————日期：
第三章 自动控制原理实验 3.1 线性系统的时域分析 3.1.1典型环节的模拟研究 一. 实验目的 1． 了解和掌握各典型环节模拟电路的构成方法、传递函数表达式及输出时域函数表达 式 2． 观察和分析各典型环节的阶跃响应曲线，了解各项电路参数对典型环节动态特性的 影响 二．典型环节的结构图及传递函数 方 框 图 传递函数 比例 （P ） K (S) U (S) U (S)G i O == 积分 （I ） TS 1(S)U (S)U (S)G i O == 比例积分 （PI ） )TS 11(K (S)U (S)U (S)G i O +== 比例微分 （PD ） )TS 1(K (S) U (S) U (S)G i O +== 惯性环节 （T ） TS 1K (S)U (S)U (S)G i O += = 比例积分微分（PID ） S T K S T K K (S)U (S)U (S)G d p i p p i O ++ == 三．实验内容及步骤 观察和分析各典型环节的阶跃响应曲线，了解各项电路参数对典型环节动态特性的影响.。 改变被测环节的各项电路参数，画出模拟电路图，阶跃响应曲线，观测结果，填入实验报告 运行LABACT 程序，选择自动控制菜单下的线性系统的时域分析下的典型环节的模拟研究中的相应实验项目，就会弹出虚拟示波器的界面，点击开始即可使用本实验机配套的虚拟示波器（B3）单元的CH1测孔测量波形。具体用法参见用户手册中的示波器部分。
系统仿真实验报告
中南大学系统仿真实验报告 指导老师胡杨 实验者 学号 专业班级 实验日期 2014.6.4 学院信息科学与工程学院
目录 实验一MATLAB中矩阵与多项式的基本运算 (3) 实验二MATLAB绘图命令 (7) 实验三MATLAB程序设计 (9) 实验四MATLAB的符号计算与SIMULINK的使用 (13) 实验五MATLAB在控制系统分析中的应用 (17) 实验六连续系统数字仿真的基本算法 (30)
实验一MATLAB中矩阵与多项式的基本运算 一、实验任务 1．了解MATLAB命令窗口和程序文件的调用。 2．熟悉如下MATLAB的基本运算： ①矩阵的产生、数据的输入、相关元素的显示； ②矩阵的加法、乘法、左除、右除； ③特殊矩阵：单位矩阵、“1”矩阵、“0”矩阵、对角阵、随机矩阵的产生和运算； ④多项式的运算：多项式求根、多项式之间的乘除。 二、基本命令训练 1．eye(m) m=3; eye(m) ans = 1 0 0 0 1 0 0 0 1 2．ones(n)、ones(m,n) n=1;m=2; ones(n) ones(m,n) ans = 1 ans = 1 1
3．zeros(m,n) m=1,n=2; zeros(m,n) m = 1 ans = 0 0 4．rand(m,n) m=1;n=2; rand(m,n) ans = 0.8147 0.9058 5．diag(v) v=[1 2 3]; diag(v) ans = 1 0 0 0 2 0 0 0 3 6．A\B 、A/B、inv(A)*B 、B*inv(A) A=[1 2;3 4];B=[5 6;7 8]; a=A\B b=A/B c=inv(A)*B d=B*inv(A) a = -3 -4 4 5 b = 3.0000 -2.0000 2.0000 -1.0000
《控制系统计算机仿真》实验指导书
实验一 Matlab使用方法和程序设计 一、实验目的 1、掌握Matlab软件使用的基本方法； 2、熟悉Matlab的数据表示、基本运算和程序控制语句 3、熟悉Matlab绘图命令及基本绘图控制 4、熟悉Matlab程序设计的基本方法 二、实验内容 1、帮助命令 使用help命令，查找sqrt（开方）函数的使用方法； 2、矩阵运算 （1）矩阵的乘法 已知A=[1 2;3 4]; B=[5 5;7 8]; 求A^2*B （2）矩阵除法 已知A=[1 2 3;4 5 6;7 8 9]; B=[1 0 0;0 2 0;0 0 3]; A\B,A/B （3）矩阵的转置及共轭转置 已知A=[5+i,2-i,1;6*i,4,9-i]; 求A.', A' （4）使用冒号选出指定元素 已知：A=[1 2 3;4 5 6;7 8 9]; 求A中第3列前2个元素；A中所有列第2，3行的元素； （5）方括号[] 用magic函数生成一个4阶魔术矩阵，删除该矩阵的第四列 3、多项式 （1）求多项式p(x) = x3 - 2x - 4的根 （2）已知A=[1.2 3 5 0.9;5 1.7 5 6;3 9 0 1;1 2 3 4] ， 求矩阵A的特征多项式; 求特征多项式中未知数为20时的值； 4、基本绘图命令 （1）绘制余弦曲线y=cos(t)，t∈[0，2π] （2）在同一坐标系中绘制余弦曲线y=cos(t-0.25)和正弦曲线y=sin(t-0.5)，t∈[0，2π] 5、基本绘图控制 绘制[0，4π]区间上的x1=10sint曲线，并要求： （1）线形为点划线、颜色为红色、数据点标记为加号； （2）坐标轴控制：显示范围、刻度线、比例、网络线 （3）标注控制：坐标轴名称、标题、相应文本； 6、基本程序设计 （1）编写命令文件：计算1+2+?+n<2000时的最大n值； （2）编写函数文件：分别用for和while循环结构编写程序，求2的0到n次幂的和。 三、预习要求 利用所学知识，编写实验内容中2到6的相应程序，并写在预习报告上。
矩形蒸汽灭菌器强度数值模拟与试验研究
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控制系统仿真实验报告
哈尔滨理工大学实验报告 控制系统仿真 专业：自动化12-1 学号：1230130101 姓名：
一．分析系统性能 课程名称控制系统仿真实验名称分析系统性能时间8.29 地点3# 姓名蔡庆刚学号1230130101 班级自动化12-1 一．实验目的及内容： 1. 熟悉MATLAB软件的操作过程； 2. 熟悉闭环系统稳定性的判断方法； 3. 熟悉闭环系统阶跃响应性能指标的求取。 二．实验用设备仪器及材料： PC, Matlab 软件平台 三、实验步骤 1. 编写MATLAB程序代码； 2. 在MATLAT中输入程序代码，运行程序； 3.分析结果。 四．实验结果分析： 1.程序截图
得到阶跃响应曲线 得到响应指标截图如下
2.求取零极点程序截图 得到零极点分布图 3.分析系统稳定性 根据稳定的充分必要条件判别线性系统的稳定性最简单的方法是求出系统所有极点,并观察是否含有实部大于0的极点，如果有系统不稳定。有零极点分布图可知系统稳定。
二．单容过程的阶跃响应 一、实验目的 1. 熟悉MATLAB软件的操作过程 2. 了解自衡单容过程的阶跃响应过程 3. 得出自衡单容过程的单位阶跃响应曲线 二、实验内容 已知两个单容过程的模型分别为 1 () 0.5 G s s =和5 1 () 51 s G s e s - = + ，试在 Simulink中建立模型，并求单位阶跃响应曲线。 三、实验步骤 1. 在Simulink中建立模型，得出实验原理图。 2. 运行模型后，双击Scope，得到的单位阶跃响应曲线。 四、实验结果 1．建立系统Simulink仿真模型图，其仿真模型为
典型环节的模拟研究实验报告
第三章自动控制原理实验 3.1 线性系统的时域分析 3.1.1典型环节的模拟研究 一. 实验目的 1．了解和掌握各典型环节模拟电路的构成方法、传递函数表达式及输出时域函数表达式 2．观察和分析各典型环节的阶跃响应曲线，了解各项电路参数对典型环节动态特性的影响 二．典型环节的结构图及传递函数 三．实验容及步骤 观察和分析各典型环节的阶跃响应曲线，了解各项电路参数对典型环节动态特性的影响.。 改变被测环节的各项电路参数，画出模拟电路图，阶跃响应曲线，观测结果，填入实验报告 运行LABACT程序，选择自动控制菜单下的线性系统的时域分析下的典型环节的模拟研究中的相应实验项目，就会弹出虚拟示波器的界面，点击开始即可使用本实验机配套的虚拟示波器（B3）单元的CH1测孔测量波形。具体用法参见用户手册中的示波器部分。 1)．观察比例环节的阶跃响应曲线 典型比例环节模拟电路如图3-1-1所示。
图3-1-1 典型比例环节模拟电路 传递函数： 1 (S) (S) (S) R R K K U U G i O= = = ；单位阶跃响应：K )t( U= 实验步骤：注：‘S ST’用短路套短接！ （1）将函数发生器（B5）所产生的周期性矩形波信号（OUT），作为系统的信号输入（Ui）； 该信号为零输出时，将自动对模拟电路锁零。 ①在显示与功能选择（D1）单元中，通过波形选择按键选中‘矩形波’（矩形波指示灯亮）。 ②量程选择开关S2置下档，调节“设定电位器1”，使之矩形波宽度＞1秒（D1单元左显示）。 ③调节B5单元的“矩形波调幅”电位器使矩形波输出电压= 4V（D1单元右显示）。（2）构造模拟电路：按图3-1-1安置短路套及测孔联线，表如下。 （a）安置短路套（b）测孔联线 模块号跨接座号 1 A5 S4，S12 2 B5 ‘S-ST’ （3）运行、观察、记录： 打开虚拟示波器的界面，点击开始，按下信号发生器（B1）阶跃信号按钮（0→+4V阶跃），观测A5B输出端（Uo）的实际响应曲线Uo（t）见图3-1-2。示波器的截图详见虚拟示波器的使用。 图3-1-2 比例环节阶跃响应曲线图图3-1-3 惯性环节阶跃响应曲线 实验报告要求：按下表改变图3-1-1所示的被测系统比例系数，观测结果，填入实验报告。 R0 R1 输入Ui 比例系数K 计算值测量值 200K 100K 4V 0.5 0.51 200K 4V 1 1.02 50K 100K 2V 2 1.93 200K 1V 4 4.06 1 信号输入（Ui）B5（OUT）→A5（H1） 2 示波器联接 ×1档 A6（OUT）→B3（CH1） 3 B5（OUT）→B3（CH2）
第一章系统仿真的基本概念与方法
第一章控制系统及仿真概述 控制系统的计算机仿真是一门涉及到控制理论、计算数学与计算机技术的综合性新型学科。这门学科的产生及发展差不多是与计算机的发明及发展同步进行的。它包含控制系统分析、综合、设计、检验等多方面的计算机处理。计算机仿真基于计算机的高速而精确的运算，以实现各种功能。 第一节控制系统仿真的基本概念 1．系统： 系统是物质世界中相互制约又相互联系着的、以期实现某种目的的一个运动整体，这个整体叫做系统。 “系统”是一个很大的概念，通常研究的系统有工程系统和非工程系统。 工程系统有：电力拖动自动控制系统、机械系统、水力、冶金、化工、热力学系统等。 非工程系统：宇宙、自然界、人类社会、经济系统、交通系统、管理系统、生态系统、人口系统等。 2．模型： 模型是对所要研究的系统在某些特定方面的抽象。通过模型对原型系统进行研究，将具有更深刻、更集中的特点。 模型分为物理模型和数学模型两种。数学模型可分为机理模型、统计模型与混合模型。 3．系统仿真： 系统仿真，就是通过对系统模型的实验，研究一个存在的或设计中的系统。更多的情况是指以系统数学模型为基础，以计算机为工具对系统进行实验研究的一种方法。 要对系统进行研究，首先要建立系统的数学模型。对于一个简单的数学模型，可以采用分析法或数学解析法进行研究，但对于复杂的系统，则需要借助于仿真的方法来研究。 那么，什么是系统仿真呢？顾名思义，系统仿真就是模仿真实的事物，也就是用一个模型（包括物理模型和数学模型）来模仿真实的系统，对其进行实验研究。用物理模型来进行仿真一般称为物理仿真，它主要是应用几何相似及环境条件相似来进行。而由数学模型在计算机上进行实验研究的仿真一般则称为数字仿真。我们这里讲的是后一种仿真。 数字仿真是指把系统的数学模型转化为仿真模型，并编成程序在计算机上投入运行、实验的全过程。通常把在计算机上进行的仿真实验称为数字仿真，又称计算机仿真。
控制系统仿真实验报告1
昆明理工大学电力工程学院学生实验报告 实验课程名称：控制系统仿真实验 开课实验室：年月日
实验一 电路的建模与仿真 一、实验目的 1、了解KCL 、KVL 原理； 2、掌握建立矩阵并编写M 文件； 3、调试M 文件，验证KCL 、KVL ； 4、掌握用simulink 模块搭建电路并且进行仿真。 二、实验内容 电路如图1所示，该电路是一个分压电路，已知13R =Ω，27R =Ω，20S V V =。试求恒压源的电流I 和电压1V 、2V 。 I V S V 1 V 2 图1 三、列写电路方程 （1）用欧姆定律求出电流和电压 （2）通过KCL 和KVL 求解电流和电压
四、编写M文件进行电路求解（1）M文件源程序 （2）M文件求解结果 五、用simulink进行仿真建模（1）给出simulink下的电路建模图（2）给出simulink仿真的波形和数值
六、结果比较与分析
实验二数值算法编程实现 一、实验目的 掌握各种计算方法的基本原理，在计算机上利用MATLAB完成算法程序的编写拉格朗日插值算法程序，利用编写的算法程序进行实例的运算。 二、实验说明 1．给出拉格朗日插值法计算数据表； 2．利用拉格朗日插值公式，编写编程算法流程，画出程序框图，作为下述编程的依据； 3．根据MATLAB软件特点和算法流程框图，利用MATLAB软件进行上机编程； 4．调试和完善MATLAB程序； 5．由编写的程序根据实验要求得到实验计算的结果。 三、实验原始数据 上机编写拉格朗日插值算法的程序，并以下面给出的函数表为数据基础，在整个插值区间上采用拉格朗日插值法计算(0.6) f，写出程序源代码，输出计算结果： 四、拉格朗日插值算法公式及流程框图
工作面相似模拟实验方案研究
工作面相似模拟实验方案研究 1 试验研究内容 （1）顶板的初次来压步距、冒落带裂隙带高度及分布形态； （2）煤层上山煤柱的留设。 （3）沿煤层推进方向支承压力的分布曲线。 2 相似模拟试验原理 相似材料模拟试验结果的可靠性取决于模型与原型之间的相似程度。相似材料模拟试验的基本原理是相似理论，其主要原理是三个基本相似定律：（1）相似第一定律（相似定律）：对于两个相似的力学系统，在任一力学过程中，它们对应的长度、时间、力和质量等基本物理量应当具有：几何相似、动力相似和运动相似。 （2）相似第二定律（Π定律）：两个相似现象的基本物理方程可以用量纲分析的方法进行转换。对于所研究的对象，尚无法建立描述其特性的表达式，但知道决定其意义的物理量，就可以通过量纲分析的方法，确定相似判据，从而为建立模型与原型之间的相似关系提供依据。 （3）相似第三定律（相似存在定律）：只有具有相同的单值条件和相同的主导相似判据时，现象才互相相似。其中，单值条件为：①原型与模型的几何条件相似；②在所研究的过程中具有显著意义的物理常数成比例；③二个系统的初始状态相似；④在研究期间两个系统的边界条件相似。主导相似判据为系统中具有重要意义的物理常数和几何性质组成的判据。 本方案依据相似定律，对于两个相似的力学系统，在任一过程中，它们相对应的长度、时间、力及质量的基本物理量满足如下关系： 在同一特征和现象中，如表征现象的所有物理量在空间上所对应的各点和在时间上对应的瞬间各自互成一定比例，则现象相似。相似现象的基本性质和被研究对象之间的相似特征可以用相似定理或理论来表示。 鉴于相似材料模拟的特点，模拟试验应满足：几何相似、运动相似、动力相似、边界条件相似、对应的物理量成比例，因此： (1) 岩石的变形特征相似，即模型上任一点、任一时刻的应变与原型上的点应变相似。 (2) 根据试验目的，在选择相似材料的要求上，由于条件限制，仅以强度（抗拉或抗压）指标作为主导特征。 (3) 模型线比
控制系统数字仿真实验报告
控制系统数字仿真实验报告 班级：机械1304 姓名：俞文龙 学号： 0801130801
实验一数字仿真方法验证1 一、实验目的 1.掌握基于数值积分法的系统仿真、了解各仿真参数的影响； 2.掌握基于离散相似法的系统仿真、了解各仿真参数的影响； 3.熟悉MATLAB语言及应用环境。 二、实验环境 网络计算机系统（新校区机电大楼D520），MATLAB语言环境 三实验内容 （一）试将示例1的问题改为调用ode45函数求解，并比较结果。 实验程序如下； function dy = vdp(t,y) dy=[y-2*t/y]; end [t,y]=ode45('vdp',[0 1],1); plot(t,y); xlabel('t'); ylabel('y');
（二）试用四阶RK 法编程求解下列微分方程初值问题。仿真时间2s ，取步长h=0.1。 ?????=-=1 )0(2y t y dt dy 实验程序如下: clear t0=0; y0=1; h=0.1; n=2/h; y(1)=1; t(1)=0; for i=0:n-1 k1=y0-t0^2; k2=(y0+h*k1/2)-(t0+h/2)^2; k3=(y0+h*k2/2)-(t0+h/2)^2;
k4=(y0+h*k3)-(t0+h)^2; y1=y0+h*(k1+2*k2+2*k3+k4)/6; t1=t0+h; y0=y1; t0=t1; y(i+2)=y1; t(i+2)=t1; end y1 t1 figure(1) plot(t,y,'r'); xlabel('t'); ylabel('y'); （三）试求示例3分别在周期为5s的方波信号和脉冲信号下的响应，仿真时间20s，采样周期Ts=0.1。
扭动微动的模拟及其试验研究
第28卷 第1期摩擦学学报V o l28, N o1 2008年1月TRI BOLOGY Jan,2008扭动微动的模拟及其试验研究 蔡振兵,朱旻昊,俞 佳,周仲荣 (西南交通大学牵引动力国家重点实验室摩擦学研究所,四川成都 610031) 摘要:在CETR UM T 2型多功能摩擦磨损试验机上配置高精度低速往复转动台,构成新型试验装置并成功实现了球/平面接触条件下的扭动微动;在低速往复转动台上进行了GC r15钢球(直径10mm)与LZ50钢在扭动角位移幅值为 3 ~20 和法向载荷10N时的扭动微动试验,并在分析其摩擦动力学行为的基础上对LZ50钢的扭动微动损伤特征进 行探讨.结果表明:角位移幅值和循环次数对扭动微动行为影响很大;可以通过摩擦力矩 角位移(T )曲线表征扭动微动行为;随着循环次数变化,T 曲线呈3种基本类型,即平行四边形状、椭圆状和直线状.扭动微动损伤在低角位移幅值时较轻微,随着角位移幅值增加,出现塑性流动、氧化磨损和剥层. 关键词:微动模式;扭动微动;试验装置;微动磨损 中图分类号:TG174.4;TH117.3文献标识码:A文章编号:1004 0595(2008)01 0018 05 微动运动非常复杂,按球/平面接触模型可分为切向微动、径向微动、滚动微动和扭动微动4种基本运行模式[1,2],目前微动摩擦学的研究主要集中于切向模式.扭动微动是在交变载荷下接触副发生微幅扭动的相对运动,并大量存在于机械装备和器械中.例如,从4000余年前苏美尔文明时期受扭动磨损的门斗[3],到机车车辆转向架与车体连接的心盘磨损,再到人体植入器械中的人工心脏瓣膜、髋关节和肘关节杵臼状接触区内发生的失效[4].Lubkin 等[5~7]对扭动条件下的力学行为早有研究,但目前针对扭动微动的研究还十分有限,实验研究仅见B riscoe等[8~10]对医用关节材料P MMA的扭动磨损行为的报导.由于扭动微动存在重要的工程应用背景,因此深入研究材料在扭动微动条件下的运行和损伤机理具有重要的学术和工程应用价值.本文作者在新型高精度低速转动试验台上实现了球/面接触方式的扭动微动,对其动力学特性和损伤特征进行了初步探讨. 1 实验部分 1.1 扭动微动的实现 在CETR UMT 2型多功能摩擦磨损试验机上,配置高精度低速往复转动试验台(转速为0.001~30.000r/m in),实现了球/平面接触条件下的扭动微动.扭动微动试验装置主要由平动机构、旋转机构以及基架组成,其主要结构如图1所示.高精度六维传感器连接在平动机构上,上试样球及其夹持结构通过弹性缓冲装置与六维传感器连接;平面试样及其夹具连接在机架上,通过高精度低速马达驱动旋转.扭动微动试验前,运动机构沿X、Y轴方向移动,使得对摩球的中心线和马达的旋转轴重合在同一条轴线上,同轴度2 m.采用高精度ATI六维F/T 传感器对力和扭矩的6个分量(F x,F y,F z,T x,T y, T z)随循环次数变化的情况进行实时记录,用ATI DAQ软件对结果进行分析.该试验装置的法向载荷范围处于5~580N之间;扭转运动的最小角位移幅值为0.36 ;角速度控制范围在0.01~5( )/s之间;切向力测量范围为1.8~180N,扭矩测量范围为10~10000N!mm,测量精度为4N!mm. 1.2 试验材料和方法 试验材料选用铁道车辆用LZ50车轴钢,主要成分(质量分数计)为0.55%C,0.26%~0.32%S,i 0.78%M n,<0.03%P,<0.03%S,<0.30%N,i HV50g352,s=330MPa.将其加工成尺寸10mm?10mm?20mm的块试样,经研磨和抛光至表面粗糙度R a=0.04 m,试验前依次用酒精和丙酮对其 基金项目:国家自然科学基金委创新研究群体科学基金资助项目(50521503,50775192);国家973计划资助项目(2007CB714704);教育部优秀博士论文基金资助项目(200536). 收稿日期:2007 05 10;修回日期:2007 08 30/联系人朱旻昊,e m ai:l z hum i nhao@ho m e.s w jt https://www.wendangku.net/doc/1b17428550.html, 作者简介:朱旻昊,男,1968年生,博士,教授,博士生导师,目前主要从事摩擦学及表面工程研究.