IMPLEMENTATION OF THE EQUIVALENT DIAMETER APPROACH TO CHARACTERIZING SI ENGINE FUEL SPRAYS

The theory of this m ethod has been covered in the previous sections of this chapter. This section aim s to cover its im plem entation and integration w ith the M alvern particle sizer.

A program w as w ritten in MS GWBASIC, w hich could be run on the Olivetti PC supplied w ith the M alvern 2600c particle sizer, in o rd er to gain d irect access to the resu lt files produced by this device.

The late st versions of this p ro g ram are DL-V5-1A a n d DL-V5-1B, (for injector and carburettor sprays respectively), and m ay be selected from the M alvern m enu w hen required. A flow chart, program listing and details of constants, variables and arrays used w ithin the program s are included w ith this report. A version w hich om its the graphical routines and sim ply calculates de o[10], de,o[50] and de o[90] is also available.

The flow chart and program listing for program DL-V5-1A are given in appendix A.

2.5.1 O perating principles

The m ain inform ation that the program extracts from the M alvern result file is the 33 size boundaries of the 32 bands, and the percentage volum e w eighting in each of these bands. As the size boundaries are dictated by the incom ing file, the program needs no prior know ledge of lens (and thus m easurem ent range) of the instrum ent, and could easily be adapted to accept d a ta from o th er so u rces/in stru m en ts. The num ber of sizebands could also be adjusted if required.

From the size boundary inform ation the program calculates the geometric m ean diam eter of each sizeband, an d as a check it also calculates the Sm d of the sp ray (w hich m ay be com pared to the value given by the M alvern instrum ent for the sam e spray). The (geometric m ean diam eter)^ of each band is then decayed at a given fixed rate according to the d^-law,

ie, for each band di^=do^ - (constant x time)

The value of the constant is arbitrary, so a value of u n ity is assum ed for sim plicity. The value of tim e is increm ented by an am ount a t each iteration and (as show n in the theory) values for % volum e evaporated y, and equivalent diam eter de,o[y] m ay be evaluated for each value of time.

A t approxim ately every 2% by volum e evaporated the program is instructed to plot a point on a grap h of y versus de,o[y] and this progresses until in excess of 99% of the spray has evaporated, pro v id in g a useful graphical representation of the likely evaporation history. In addition, the values of de,o[10], de,o[50] and de,o[90] are recorded as a concise sum m ary of the spray.

2.5.2 Value of tim estep DT

The feature central to the effective operation of the program is the determ ination of the tim estep value, DT. A suitable value m ust be obtained th a t w ill p rovide a tim e-efficient calculation, w ith sufficient resolution to yield the required inform ation. It m ust do this for a range of sprays, w hich could have quite diverse likely evaporation histories.

The m ethod used in this p rogram has been to link the value of DT w ith the cu rren t (geom etric m ean diam eter)^ of the smallest surviving d ro p size band. This link is m ade so

th at w h en there are small drops present (and high evaporation rates) the value of DT is small in order that the resolution rem ains sufficiently high. W hen there are only large drops present the value of DT is large preventing w asted com puter time.

The equation used by the program is

DT=(DIASQ1(NU M )+A)/B

DIASQl(NUM ) is the current value of the (geom etric m ean diam eter)^ in sizeband NUM, w here NUM is the n u m ber rep resenting the sm allest su rv iv in g sizeband. A an d B are constants. W hilst DIASQl(NUM ) provides the link w ith d ro p size, th e actual num erical value m ay not be appropriate and the constant B is required to ensure that a sensible value for DT is produced. The constant A w as included after a certain am o u n t of testing had taken place. It becam e evident that for som e types of sp ray (particularly injector sprays), w hilst the step size w as appropriate for m uch of the evaporation period, there w ere tim es w hen it w as too small (ie w hen DIASQl(NUM ) w as small). This caused unnecessary slow ing of the program . The constant A is positioned so that it m ay m ake a significant increase to the value of DT w hen DIASQl(NUM) is small, but becomes insignificant w hen DIASQl(NUM ) is large.

2.53 Saving discrete values of de

The a im of the program w as to p ro d u ce a grap h ical re p re se n ta tio n of the likely evaporation history, together w ith the discrete values dg o[10]/ de,o[50] and de,o[90]. The graphical history did not require an exact value of y for any given point, as long as the diam eter and y values corresponded and sufficient points w ere plotted. H ow ever, to obtain discrete values for dg o[y]/ exact values of y to w ithin some given tolerance w ere required.

A solution-seeking procedure (such as N ew ton-R aphson) w ould have been possible, b ut w ould have added greatly to the complexity of the program . Instead it w as decided to adapt the calculation of DT, thus using the existing iterative program structure.

Let us consider the program as it progresses by one tim estep DT, from tim e ti to tim e t2- The value of de,o[y] is desired for a specified value of y, a n d actually occurs at tim e t j . It is possible th at this target value m ay actually be found to w ithin the specified tolerance as the tim e steps forw ard (figure 2.7a).

How ever, if the target value of y is exceeded, then the tim e value m ust be decrem ented by some fraction of the last tim estep until the target is reached (figure 2.7b). This is done in the program by changing the value of B in the equation for DT. B is given the value B1 in the forw ard (normal) direction and -Blx4+B2 in the reverse direction. The -Blx4 term in isolation w ould effectively produce a tim e decrem ent 1 /4 of the last tim e increm ent in value. The addition of B2 avoids this decrem ent being an exact m ultiple of that last increm ent. Thus, if by d e c re m e n tin g the tim e th e so lu tio n is still m isse d , th e n th e p ro ce ss of increm enting/decrem enting is repeated w ith an offset (due to B2) so th at the solution will eventually be found (figure 2.7c).

W hilst the description is probably long-w inded, the am ount of com puter code required for this solution is small, and its execution is fairly quick (especially as only three values are sought).

2.5.4 Smallest surviving drop size band

It has been described in the preceding text how the step size DT is related to the sm allest surviving drop size band. It follows that this band m ust be determ ined.

The program initially assum es th at the sm allest band size is band 1, ie. the sm allest band m easured by the Malvern. Thus INUM=1. W hen this band has evaporated com pletely INUM is increm ented and the next band becom es the sm allest. This relies on the fact th at if all bands contain some volume, then according to the d^ law, 100% evaporation will occur in each band sequentially from the smallest to the largest. A ny em pty bands are 'flagged' (both those w hich are em pty at the start and those w hich become em pty d u rin g execution). Flagged bands are rem oved from further calculations and hence this also speeds up the execution of the program .

2.5.5 Limitations of the program

The fundam ental lim itation of the program is the theory upon w hich it is based, the d^ law . T hus, it calculates a likely evap o ratio n h isto ry for the sp ray based on this law. H ow ever, the previous sections have suggested this to be a reasonable assu m p tio n for characterizing sprays within the manifolds of SI engines.

The program also relies on the good quality of in p u t data from the M alvern result files. An assessm ent m ust be m ade of the v alidity of the d a ta before using w ithin this program otherw ise the evaporation characteristic produced will clearly be m eaningless.

The basis of the program is to apply the d^ law to the existing size bands of some result file. W ith d a ta from a source such as the M alvern these bands vary considerably in size. Thus, w hen a large percentage of the spray has ev ap orated, one m ay have only sm all drops rem aining, b u t in a single band of considerable w idth. This is really a lim itation of the m easuring device, which is carried across to the subsequent analysis. W hilst the bands could be further subdivided w ith greater program complexity, to do so w ould give a false level of accuracy. The current size range using the 300 m m lens of the M alvern instrum ent gives largest and sm allest size bands of 564 - 487 pm and 5.8 -1 .5 p.m respectively, w hilst w ith the 100 m m lens these become 188 -162 pm and 1.93 - 0.5 pm.

2.5.6 Tolerance

The tolerance for the equivalent diam eters de,o[10]/ de,o[50] and de,o[90] is y+0.3y, y-0.01% These lim its w ere found to be acceptable d u rin g the validation process, in term s of both accuracy an d com puter time. They should be m ore than adequate given the accuracy of the

incom ing data. Because of this limited accuracy it w as felt th at the results should be given w ith only one decimal place.

2.5.7 T ine tuning*

Values for the constants A, B1 and B2 are required for the program to function. It w as found that d u e to the large difference in spray distributions produced by injectors and carburettors, one set of values w ould not suffice for all sprays.

Two sets of values were found, giving tw o versions, DL-V5-1A and DL-V5-1B. These w ere optim ized or fine tuned' for injector and carburettor sprays respectively. The values used for each are given in table 2.2.

It sh o u ld be em phasized that these constants h av e little effect on the accuracy of the results; they prim arily affect the resolution of the plots and the speed at which the program converges on solutions for the equivalent diam eters. Typically, the program takes 1-2 m inutes to com pute the results for a typical' injector spray using the (rather slow and dated) M alvern O liv e tti.

2.5.8 Program validation

V alidation of the program was carried out by three m ethods.

Firstly, distributions were created w hich com prised 100% volum e in only o ne sizeband (figures 2.8 and 2.10). The effect of this should be to give a vertical line on a y versus dg o[y] plot, w ith de,o[y] equal in value to the geometric m ean diam eter of the chosen sizeband (the Smd also equals this value).

The p rogram correctly predicted this result for a single band in both 300 and 100 m m lens cases (figures 2.9 and 2.11), w ith values of 89.0 and 29.7 pm respectively. The slight deviation in the num erical value quoted for de,o[50] in the 300 m m case w as d u e to the tolerance involved. The routine optim ized for injector sprays w as used in this case, although this was not ideal for a single band spray.

The second m ethod of validation used was to m ake an in dependent check on an artificial d istribution using a simplified routine on a second com puter. The test case (figure 2.12) had four adjacent bands, covering the range 129 - 715 pm , each band containing 25% of the volume. The results from DL-V5-1A can be seen in figure 2.13, the results of the independent check agreed w ith these values.

The th ird m ethod used w as to take a m easured spray distribution (figure 2.14) and then perform som e calculations w ith the aid of a spreadsheet. The DL-V5-1A program w as ru n and values for dg o[10], de,o[50] and de,o[90] w ere obtained (figure 2.15). The program w as then m odified slightly so that the time values corresponding to these equivalent diam eters w ere printed (figure 2.16). A spreadsheet was constructed which used the size band boundaries, the w eighting in each band and the time values to w ork back and calculate the value of y, and then calculate the equivalent diam eter. The results for the three cases can be seen in tables 2.3, 2.4 and 2.5 respectively. There was no significant discrepancy in the results.

It is felt that this series of validation checks show ed that the program w as functioning as intended, and was free of major errors.