BUREAU OF RECLAMATION DENVER LIBRARY 92098804
9 20 9 88 0 4
MISCELLANEOUS PAPER H-69-1 c-
TRENDS IN BAFFLED, HYDRAULIC JUMP STILLING BASIN DESIGNS OF THE CORPS OF ENGINEERS SINCE 1947 by
D. R. Basco I *
□ID 1 0!
January 1969
Sponsored by
Assistant Secretary of the Army (R6-D) * Department of the Army
Conducted by
U. S. Army Engineer Waterways Experiment Station CORPS OF ENGINEERS Vicksburg, Mississippi
ARMY-MRC VICK8BURO. MISS.
THIS DOCUMENT HAS BEEN APPROVED FOR PUBLIC RELEASE AND SALE; ITS DISTRIBUTION IS UNLIMITED
w FOREWORD
» This report grew out of the need for a general, experimental study
of drag coefficients for baffle blocks in hydraulic jump type spillway
energy dissipators. Sponsored by the U. S. Army Engineer Waterways Experi
ment Station (WES) (In-House Laboratory Independent Research), the general
study wiil be published in a lati r WES technical report. This survey of
the trends of Corps designs has provided the investigator with greater
perspective when viewing the Corps of Engineers work with that of other
investigations throughout the world.
The report was prepared by David R. Basco, Research Hydraulic Engineer,
Locks Section, Structures Branch, of the Hydraulics Division. Colonel Levi A.
Brown, CE, was director of the Waterways Experiment Station during the
preparation. Mr. E. P. Fortson, Jr., was Chief of the Hydraulics Division.
♦
1X1
manm CONTENTS Page FOREWORD ...... iii NOTATION ...... vii SUMMARY...... v Introduction . . , . 1 Limitations. . . . . 1 Tabulated Results. . 1 $ 2 Analysis of Results. 2 General...... 2 Tailwater Depths 11 i Basin Length' . . 16 .1 Baffle Blocks. . 17 General . Location. 17 Height. . 18 Width . . 20 Spacing . 20 20 Distance between Rows...... 23 • End Sill ...... 25 Comparison with Current WES Design Criteria. 25 Conclusions...... 29 REFERENCES
to
'»'■•WiMWJigiJ" ».'w.w u p m 1 li t . NOTATION
Maximum spillway discharge, cfs
Width of rectangular stilling basin, ft
Maximum unit discharge, cfs/ft
Average velocity at inlet section to hydraulic jump, ft/sec
Average inlet depth, ft
Inlet Froude number
Average depth of tailwater immediately downstream of forced hydraulic jump,ft
Sequent or conjugate depth of free hydraulic jump, ft
Critical open channel flow depth, ft
Downstream depth when jump begins to sweep-out of the basin, ft
Length of the stilling basin, ft
Location of the baffle blocks (first row) on the stilling basin floor, ft
Vertical height of the baffle block, ft
Horizontal width of the baffle block, ft
Horizontal spacing between baffle blocks in a particular row, ft
Horizontal distance between front faces of two rows of baffle blocks, ft
Vertical height of end sill, ft.
Horsepower SUMMARY
This report summarizes the last twenty-one years of Corps of Engineer hydraulic model tests on spillways with hydraulic jump type energy dissipators using baffle blocks and end sills. From the averages, maximums and minimums, general trends, and other information presented it is hoped that the reader will obtain a general picture of Corps of Engineer designs.
No attempt was made to completely compare the results with those of other hydraulic laboratories. TRENDS IN BAFFLED, HYDRAULIC JUMP, STILLING BASIN DESIGNS
OF THE CORPS OF ENGINEERS SINCE 1947
Introduction
♦ 1. It is often important in any evolutionary design process to review
previous designs in order to gain clearer insight into future trends.
Surveys of this type are also necessary to place the designs of one organization
in proper perspective with those of similar U. S. organizations and also with
those throughout the world.
2. The object of this report, therefore, is to summarize the last twenty-
one years of hydraulic model tests on spillways with hydraulic jump type
energy dissipators using baffle blocks and end sills. From the averages,
maximums and minimums, general trends, and other information presented it is
hoped that the reader will obtain a general picture of Corps of Engineer
designs. No attempt was made to completely compare the results with those of other hydraulic laboratories.
Limitations
3. The study was limited to baffled, approximately rectangular, stilling basins that were used below high, concrete and earth dam spillways where the hydraulic jumps formed are either free or only slightly submerged. Low head spillways that are often connected with navigation dams usually have highly submerged jumps. Because of the physical difference in these jumps,.' this group lends itself to an independent study. Similarly, outlet works stilling basins were not included because of the three-dimensional affects of the diverging channel walls. Also, the large run-of-river projects model
w - iv ’ mum*. ... . * it I I * iI jtested at the Bonneville Hydraulic Laboratory were kept separate from those ! I 1 tested at .the Waterways Experiment Station. i 4. The currently revised "List of Publications" of the U. S. Army Engineer
Waterways Experiment Station^- was used as the source for available Technical « i Reports. Any omissions were unintentional. The twenty-two projects model 1 tested at the Waterways Experiment Station (WES) with Technical Reports dating
from 1947 were of primary interest.
Tabulated Results
5. The complete tabulation of all primary and computed information is
shown as Table 1. The nomenclature used in Table 1 is defined in Fig. 1 and
under Notation, p.vii. Many of the similar dimensionless ratios were included
because of their appearance in the literature and because none alone has gained
widespread use.
6. Each column in Table 1 is c.onsectively numbered and because of its
size and complexity Table 2 has been prepared to simplify explanation. The
values shown in Table 1 for baffle block and end sill geometry were those
chosen for the final design and represent the ultimate engineering compromise
between hydraulic performance and economics. «
7. Where applicable, Table 1 also lists the maximum, minimum and mean
values. Average values are greatly distorted by extremes and therefore
must be observed with caution. They do, however, give some idea of the
magnitude and geometry of a typical project.
Analysis of Results
8. General . Some indication of the prototype size of the projects tested . * 9 i , *¡¡> , ' smw
TABLE 1 - TABULATED RESULTS 1 i MAX. SASIN A/AX. 1 7»/¿|se?. ¿»a? ¥ MAX. /2!¿¿ MAX. b a v h ce/r ÍAS/V ) 639.2 575. e 62.4 51 3.0 162,500 (5 6 1048 74-7 13.5 3.6 51.0 62.8 32 5 0-9( 54.0 o.so 4.2 I2S.O 2 0 76 é 665 STOCKTON (05) 904.8 800-0 104.0 738.0 174,000 184 950 950 lo.O 5.3 62.0 73.0 3 0 .5 0.85 5¿.o o.76 6 2 225 0 3. ( 56 7 673 SED ROCK (65) 19 7 3 7 /7 -2 74./ 6 5 4 0 362,600 241 . 1.295 92 3 (8.2 3 .4 63.2 /8.7 37.4 0.30 C2.0 0-77 3.5 206.5 2.6 50 8 655 ,4^/5 7740 (64) i i 45 .2 967.5 /7 Ö 2 8 7 5 O ¡ 545,000 950 1626 /28.0 (2.8 6.3 92.5 1070 43.5 o.% 910 0.E5 7 2 2343 22 ! 53 5 645 PROCTER (64) /2D/.5 . 7 6 9 . 6 32.5 1 1 2 2 0 432,000 5 2 0 831 63.0 (3.0 3.1 470 5¡.0 27.8 0.82 43.0 0-8 5 3.6 /56-0 3.0 45 (O 62 / Allegheny (¿3) / 370.0 i 2 3 0 .0 740.0 m s .o (40.0CC 2 0 4 6 8 7 10 4 .0 6.7 7.0 5/0 63.0 Z4.5 0-81 48.0 0-76 7-0 178.3 28 52 // 6// REDMOND (Oí) /0 7 4 .5 1 0 4 2 .5 32.0 í0 0 0 .0 577,000 6.4.4 870 61.0 //.O 3.2 42.5 48.0 251 0.89 3.9 141.0 2.9 : 16 /z 605 Sí ó BEND (EZ) i 4 2 3 0 /3 79.0 44.0 (32 o.o 390,000 31 (> (0 3 6 7 1 .0 14.5 3.3 590 61.0 312 0.?7 54.0 0.89 4 ./ 194.0 3.2 14 U) t3 575 EUPAULA (41) (,0 4 7 51677 S3.0 4 ¿0 .0 4c0,000 510 8 8 5 89 0 (0.0 4P) 56 7 670 29.0 o.g5 53o 0.77 5.7 168 0 2.5_ S3 ¡4- 568 CAZLYLE (Cl) 4¿¿._9 A á 4 ,S _ _22.4_ AOQ.O 160,000 179 8 9 3 5 4 0 (6.0 2.4 44.5 47.0 29.2 0-95 47.0 0.8? 2.8 (42.0 So 45" 15 555 KEYSTOUE (¿0) '?&*>. O ' 6 8 3 . 83.0 ¿ z s .o 939.000 8 5 6 JO 95 <%.o 12.7 4 .3 58-0 7/0 33.5 P,82. 540 ,P_J6 4 .6 174.0 2.5 55 /6 564 TABLE Kock (59) 94-1 ■ O 7 7 5 -2 765 6 6 9 2 .0 5 6 9 0 0 0 52 2 J 0 9 0 íí 7.0 9 3 6.6 83.2. _89_0 33.3^ 0.$4 9.0 253,0 2.9 58 17 43/ GAtl&SOÑ (56) '(350 .0 'T i o l i o * 7 5 8 0 (¿ 2 0 .0 848,000 _ goo _ 1 0 6 0 J/54) 9 2 ¿.7 ¡81.0 82 0 32.7 O.99 76.0 0.93 8 . a , £¿>0.0 2.4 // 18 4o4 QAiTV5PDVT(55} /Z Z 3 .5 / 7 76.3 4 7 2 II 23.0 ¿26,000 664 '9 4 3 72.5 13.6 ‘ 3 .6 53.3 60.0 3o.2 0,86 A,L 223.0 '3.6 , 14 IS 263 WHITNEY (4SI 975.0 4 9 7 .0 75.6 422.0 660,000 8 2 4 8 0 2 90.6 8.9 5 4 75.6 6(1.0 Z7.1 (,Í83 47Ö p-74 8.5 1/26 0 2.0 50 20 240 DSTkO.'T (0-8) /570-4- 7 2 2 8 O 342.4 77 70 .0 1 3 7 ,6 0 0 2 9 4 3 3 5 15/.0 3 5 14 2* 5S.0 68.6 Z0.7 0.85 55.0 D.SO (6.6 2SO.O 3.6 53 2/ 243 &LU£STOfJ¿ (48) /52Ö. 0 1 4 /5 .0 ÍOS.O 1370.0 4 3 0 ,0 0 0 7 9 0 54 5 91.5 6.0 £>.£> 45.0 52 6 21.1 0-S5 7-5 52.33 Í.O3 4 5 22 236 HABLAN CT. (47) Z974.5 78 9 9 .5 75.0 I8 & L 0 4 6 2 ,0 0 0 9 5 6 5 4 0 79.3] 6.8 5.4 37.5 p .o 20.9 0.77 5.5 líl.O 3 3 58 Maximum 342.4 9 5 0 1626 /5/.0 19.0 (4.2 92.0 ¡ 07.0 43.5 0.99 0.93 253.0 3,6 M inim um Z2.4- 156 5 3 5 54.0 3.5 £.4 37.5 4.70 20.7 0.77 Ö.74 / (5 .5 2.0 M e a n . 94.4 4 5 7 9 S 3 85.9 l í r t 4 ,5 59.6 61.1 30.8 0.87 O.SI /S4 0 275 BHL 23 3 /-/,TcE HAZöOR (65) 4 4 0 .5 3 7 5 .0 70.9 3 0 4 .0 _850,oúd S^Q (442 85-3 16.9 3.7 J 71.6 79.5 40. í 0.90 09.0 Q «7 4 .2 /74 .0 2.2 55 24 55-/ D A LLE S (M) / 8 2 3 732.0 5 0 .3 5 5 .0 22 90 ,0 0 0 (55 0 1697 7¿.5 2 /6 3 .0 77.0 é z .r 44.7 0.84 70.0 o.?5 3-6 n o o 2. ( 45 3.3 2 $ 2 h í McÜQfíY (6/) 3 5 6 .5 3 0 3 . 0 53.5 ZZS.Ö 22 00,0 00 13/0 1680 79.0 2(3 3.0 75.0 81.0 44.4 003. J!2lO o.$? .JA 270.0 4 5 /.S7 26 65-/ SoUNEYíLLE1 (58) 7 5 .5 2 3 5 .0 a1 40.5 - 75.0 t¿ o o 000 1070 1(22 65.0 IJ.3 1 2.8 50.0 59.5 o.$4 2.9 87.0 30 17 CHIEF JOí>. (56) 955 5 325.1 730.4 743:0.. 7250. OOO 922 I35& ¡07.8 JZA 5.4 82.1 90.7 38.5 0.9/ 6.S ZZo.o 2.4 55 26127-/ DOAEUfí (33) 8 5 9 9 74 9.2 UO.7 773. Oz 97. 500 200 4 8 7 t 902 5.4 6 .8 36. Z A3, i (9.5 6-74 4-7 154.0 •3.Í 55 3 M a x im u m ^ Í3 0 A )3SO /6 9 7 /078 21.6 6 .8 82.1 90-7 44-7 0.94 270.0 3.3 M in im u m , 4 0 .5 2 0 0 487 65.0 5.4 2 . 8 36. Z 49./ /a ? o.% ¡540 ¿ 4 M eant 7¿-/ 9 0 7 1459 84.3 (5.8 4 J C33 73.7 37.9 OM 0.$7 m s 2.6 / fíev i sed model test * £s tima- te d ^Omitted from /metan i *
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f F / <3 U R £ J - Définitions
5 TABLE 2 Col No ______Explanation of Headings in Table I______1 All- projects are listed in chronological order and given a number for easy reference.
2 This is the Corps of Engineers Technical Report Number. Example: EUFAULA is T.R. 2-575. 3 The name most commonly associated with each project. The date in parenthesis is the year the report was published and not necessarily the date of model tests.
4 Maximum reservoir elevation above mean sea level as determined from tests after all approach modifications were, completed and when passing the spillway design flood. 5 Maximum tailwater elevation above mean sea level as estimated when passing the design flood.
6 Maximum fall from reservoir to tailwater generally indicating the height of structure.
7 The elevation above mean sea level of the stilling basin floor ahead of the end sill.
8 Spillway design flood. In some cases it includes outlet-works flow. The total maximum flow passing through the stilling basin. 9 Average width of rectangular stilling basin. In some cases where slight batter exists, width shown is estimate of average width. 10 Maximum discharge per unit width of stilling basin 11 Average velocity at base of spillway at entrance section of hydraulic jump. Values are estimates using approximately 10 percent energy loss from reservoir to toe of jump.
12 Depth at entrance section of hydraulic jump. Depends on estimate of since d^ = q/V^.
13 Inlet Froude number at entrance section. Here again the values shown depend upon the initial estimate of V,. Vi 1 F^ = x 14 Depth of tailwater determined by subtracting balin floor elevation from tailwater elevation.
15 Conjugate or sequent depth computed from the Belanger equation for free
hydraulic jump. ^ - 1)
16 Critical depth computed from d^ = ^q2/g g " acceleration of gravity. 17 Tailwater depth ratio dxw/d2
6 TABLE 2 - Continued Col N o ______Explanation of Headings in Table I______18 Lowest depth of tailwater before toe of jump begins to move away from toe of chute. Sometimes called sweep-out depth. 19 Sweepout ratio d /d„. so 2 20 Tailwater ratio with inlet depth d^/d^. 21 Length of stilling basin. The distance from the point of intersection (P.I.) of the toe radius to the front face of the end sill. 22 Basin length ratio Lc,t>/d0, OD Z 23 Slope of spillway chute at entrance to stilling basin. The angle is measured from the horizontal. 24 Type of baffle block used. Abbreviations as follows: STD - standard WES block shape — STEP - block is stepped into flow CÀVIT - streamlined, "cavitation free" shape BONN - shape used for Bonneville Project 25 The number of distinctly different types of stilling basins tested as reported in the Technical Reports. Each type involved some change in baffle block or end sill geometry. 26 The horizontal distance from the point of intersection (P.I.) of the toe radius tangents to the front face (at the floor) of the baffle block. Four commonly used block location ratios.
The height of baffle block. Distance from floor to top of block. Baffle block height ratios h h d.. d 1 c ♦ 34 The baffle block width normal to flow measured at base of block. 35] Baffle block width ratios. w w 36] h d 1 37 The baffle block spacing normal to flow measured at base of block. 38 Baffle spacing ratio w/s. -- 39 The blockage ratio. Ratio of block frontal area normal to flow to the total area across basin, i.e. Blockage = w/ w + s The number of rows of baffle blocks Row spacing, Distance from front face of first block row to front face of second.
Block row spacing ratios r r d, h TABLE 2 (Continued)
______Explanation of Headings in Table I______
Type of end sill used. All are solid across the basin width. STEP = Stepped SLOPE * sloped VERT = vertical The vertical height of the end sill above the basin floor. Sill height ratios hs hs
Slope of exit channel downstream of the end sill. L = Level W = Second weir D = Drop V = slope varies Horsepower available at entrance to stilling basin per unit width of basin. is shown in Column 6 of Table 1. If the extreme maximum (342 ft Detroit) afad minimum (22,4 ft Carlyle) values were not used an average of 85.2 ft in drop from reservoir to tailwater would be obtained.
9. The size of the floods that occurred on the large run-of-river projects in the Pacific northwest and model tested at Bonneville Hydraulic
Laboratory (BHL) is shown in Column 8. This resulted in the average unit discharge for WES tested projects being approximately 500 cfs/ft less than those tested at BHL Column 10. There is also a slight indication that recent designs are for higher unit flow rates than in the past (Fig. 2).
10. In the U. S. Bureau of Reclamation’s (USBR) Monograph No. 25, 2 ’’Hydraulic Design of Stilling Basins and Energy Dissipators” , results similar to Table 1 were presented (pps. 21-22). It is interesting to note that the average unit flow rate for these USBR tests is only 265 cfs/ft, and that the maximum (760 cfs/ft) is only slightly higher than the minimum (535 cfs/ft) ever tested at WES. It should also be pointed out that the USBR Type III basin incorporating baffle blocks, and other appurtenances is limited to a maximum of 200 cfs/ft for the design unit flow rate. This factor is undoubtedly the primary reason for the significant difference in design considerations between the WES and USBR which will be discussed in* greater length later in the report.
11. Inlet velocities have been as high as approximately 151 fps and average about 85 ft/sec for the Corps’ designs (Column 11). By contrast
USBR Type III basins limit the entrance velocity to 50 or 60 ft/sec. The previously mentioned trend to narrower basins (higher unit flow rates) also is evident in slightly higher inlet depths, d^ (Column 12) than in earlier designs. stuns>/j
f t sÎ \ £
\ _ ; \ \
\ 12. From considerations of the energy and continuity equations, the inlet velocity and depth (hence F^) are completely dependent upon the fall height and discharge. However, as Fig. 3 illustrates, F^ was almost entirely dependent on the fall height. Consequently, the relationship between inlet depth and F^ is shown in Fig. 4 for all combinations of flow rate and fall height. This interdependence between d^ and F^ can lead to possibilities of 3 spurious correlations between F- and those length scales such as X«, h, w, r, h , etc., that are made dimensionless by dividing by cL . Therefore, other s 1 * length scales are also tabulated where practical.
Tailwater Depths
13. The next six columns involve tailwater relationships. Column 14, shows the range of expected maximum tailwater for the final stilling basin designs for each project while the next Column (15) indicates what the conjugate or sequent depth would be if a free hydraulic jump were allowed to form. Therefore, as shown in Column 17, on the average, the stilling basin floor was set at an elevation which resulted in only 87 percent of the required -tailwater depth being available to form the jump. The baffle blocks
♦ and end sill were relied upon to supply the remaining downstream force to hold the jump in equilibrium in the basin. Although not a strict design requirement, in general, most baffled basins are designed so that the beginning (toe) of the jump is just held at the front of the basin by the given tailwater for the spillway design flood. Lowering the tailwater reduces the back pressure force holding the jump in equilibrium and causes the jump toe to move down the basin. Column 18 indicates how much the tailwater was
11 .3 / E 3 RE U F/G FALL - vs~ 2P
■À F igure 4
S* finally lowered before the jump toe reached the baffle blocks or "swept-out"
of the basin. The average ratio of sweep-out depth to conjugage depth was
0.81 as indicated in Column 19. Thus an average factor of safety against the
jump sweeping out of the stilling basin of approximately 6 percent was
indicated. Note that in the case of Amis tad Dam only 1.5 ft less tailwater
caused the jump to move out of the basin. The inconsistencies in this design
aspect were undoubtedly due to variations in downstream river channel material;
baffle block and end sill design; and design philosophy of the local Corps
District Offices. Current WES practice is to set the basin elevation so that
tailwater depth is 0.85 when conditions are favorable.. By way of contrast
the USER conservatively recommends full conjugate depth (1.0 d^) for both
their Type II and Type III basin designs.
v 14* Figure 5 shows the relationship of d— /d- as a function of inlet IW I Froude number. One important criteria of baffle block and end sill performance
is tailwater reduction. The theoretical limit of tailwater reduction is
the critical depth (Column 16) which is also shown on Fig. 5. Practical
limitations such as excessive downstream waves, cavitation damage to
baffle blocks and increased average exit bottom velocities prevent
appurtenance designs from approaching this limit. Therefore as shown on
Fig. 5 most designs are for d^/d^ greater than about 0.75. The appurtenance
design which gives the lowest tailwater required to hold the toe of the jump stationary at the spillway toe and still gives acceptable waviness,
cavitation and bottom velocity performance is the most economic since it
allows the basin floor to be set at the highest elevation for a given safety
factor with accompanied decrease in rock excavation.
14 GR F 2^-Vf F /GURE F
6 S /O F r o u d e N u m b e r F/ 15. The most interesting statistic of these general data, however, is
given m Column 13, the inlet Froude number, Of the 28 projects tested
at both laboratories since 1947, 27 of them were designed for F^< 7.0.
Using the four distinct classes of hydraulic jumps established by the USBR in
Monograph 25, the breakdown for each distinct jump form is as follows:
1 Description WES BHL TOTAL 1.7-2.5 Pre-jump-low energy loss 1 0 1 2.5-4.5 Transition - rough water surface 10 4 14 4.5-9.0 Good jump - little tailwater effects 10 2 12 9.0 Rough jump - but effective 1 0 1
16. Apparently then, over one-half of the projects designed in this
period were in the transition range where pulsating jump action occurs. The
jet below the roller action oscillates from top to bottom in this range
causing large waves of irregular period downstream. Only 20-45 percent energy
dissipation occurs with these jumps. The correct use of appurtenances and
need for hydraulic model studies for this class of jumps is therefore most
important. *
Basin Length
17. The length of the hydraulic jump remains one of the most difficult
laboratory measurements to make. Usually taken as the distance from the toe
to the point «here the surface profile becomes horizontal, the length is also defined (among others) as the section where a normal open channel velocity profile is reestablished. For the range of ^ investigated, the free jump is
16 approximately 5 to 6 d2 in length(2). Baffle blocks and sills placed in
the jump shorten its length by causing the bottom jet beneath the surface
roller to be deflected upward decreasing the length required for the normal
diffusion process to take place.
18. For all those stilling basins tested at WES the average basin length
was 184 ft which resulted in an average LSB/d2 ratio of about 2.75 (Columns 21
and 22).. West Point and Bluestone data were purposely omitted because their
extremely short lengths were due to site considerations. Basin lengths did
vary from a minimum of 2d2 (Whitney) to a maximum of 3.6d2 (Detroit and Gavins
Pt.). In all cases therefore the basin was considerably shorter than a free
hydraulic jump. The appurtenances were used to shorten the jump lengths and
to reduce bottom velocities at the end of the basin.
19. Column 23 is included for completeness. Most chute slopes were
45° or greater.
Baffle Blocks
20. General. The next nineteen Columns (24-42) of Table 1 involve baffle block geometry. Many of the apparently similar block ratios were • tabulated because none appeared to be solely accepted in the literature.
21. Four distinctly different block shapes have been used over the years.
(See sketches in Table II). As Column 24 indicated, however, the Standard (STD)
WES shape is most common. Column 25 is of historical interest. Over the _ - years an average of 12 individual basin types involving various baffle and sill geometries were tested for each project. This resulted in around
340 tests. Some duplication must have occurred. 22. Location. One of the most important factors affecting performance
of the baffled jump is baffle location. Since most spillway chutes have toe
radii, the distance from the point of intersection (PI) of the radius to the
front face of the block was used for the block location, Xg (Column 26).
Placing the baffles too close to the toe radius left them susceptible to
cavitation damage and caused waviness downstream. Baffles located too far
into the jump left them ineffective for reducing jump lengths and also
caused local bottom velocity disturbances. The final location shown was the best attainable for the time and model funds available at the time of tests.
23. The next four Columns (27, 28, 29, 30) show non-dimensional ratios involving Xg. As mentioned previously} due to the relationship between d^ and
F^, Fig* 6 shows Xg/d^ increasing with increasing F^. Other length scales
LSB* ^2 ant* 51 use<* to non-diraensionalize Xg result in ratios with widely scattered variation with F^. Hence averages are more useful indicators in these cases. Column 28 results show that, on the average, the blocks were placed slightly more than half-way down the stilling basin. Column 29 revealed that this location was approximately 1.5d2 or that Xg was about 10 times the block height (Column 30). For the smaller unit, flow rates and entrance velocities of the USBR Type III basin, X_ was 0.8d„. B 2 24. Much has been written about the cavitation damage on the Bluestone
(4) (5) and Bonneville (6) (7) prototype baffle blocks. Columns 27 through ^
30 reveal why. They simply are placed too close to the toe of the jump where velocities are so high that corresponding pressures reach cavitation potential.
The prototype results for these two early projects have obviously left their
18 G\
ÍM»* I s I mark on later designs. They were not included in the averages. West Point
ratios for Xg/d^ Xg/h and XB/d1 were also excluded for reasons previously
mentioned.
25• Baffle block height is equally important in affecting
jump performance. For a given optimum location if the blocks are too high,
poor jump action with resultant waviness downstream will occur. If too small,
no appreciable difference over a free hydraulic jump occurs. Block heights
are recorded in Column 31. The h ^ ratio is shown in Column 32 and plotted
in Fig. 7 against F ^ The Detroit data make a significant difference in the
curve slope. The USBR Type III basin design curve (Monograph 25) is shown
for comparison. Of significance is the similarity in curve slopes. Because
of the relations between d.^ and F^ previously mentioned, of more significance
is Fig. 8 which reveals the relationship between h/d (Column 33) and F C 1 The scatter is relatively small about a mean value of h/dc equal to 0.33.
Although not tabulated h/<^ mean was about 0.16 .
26. Width. Also important are the block width (Column 34) and spacing
( olumn 37). As the blocks become wider the spacing between them decreases until the block acts as a solid end sill. They must be placed further downstream into the jump in this case to prevent undue waviness and poor jump action and as a result are not as effective in producing shorter jumps with low bottom velocities at exit. The mean w/h ratio (Column 35) is about 0.80^ for the WES tests. Bonneville labs used slightly wider blocks. The w/d^ ratio (not plotted) is given in Column 36.
27. Spacing. As shown in Column 38 many spacings between blocks were less than one block width. The mean w/s ratio was 0.84 at WES (Bluestone data
20 F i a UR E ?ì
Oa
I 5*% ( omitted). The s/d^ mean was about 1,2 (not tabulated).
28. From the block width and spacing data given for each project the
ratio of the total block width to stilling basin width (Column 39)can be
calculated. This ratio sometimes called the blockage ranged from a maximum of
0.50 (West Point) to a minimum of 0.42 (Eufaula) (Column 39). The mean for
the WES data was 0.45. Recommended blockages of 40-50 percent have been
mentioned in the literature (g) (9) (10)
Distance Between Rows
29. Of the 28 projects observed, 20 had two block rows (Column 40).
The second row was always staggered, i.e., a block in the second row would be
directly behind a space in the first row. The bottom jet passing between blocks m the first row was deflected upward by the second row. The reason
for using two rows was to obtain more energy dissipation, lower bottom velocities, and less waviness downstream than a single row or solid sill. In some cases the second row was either hydraulically or economically unjusti fiable. The distance between the front faces of the blocks in each row is called the row spacing (Column 41). Locating the back row too close to the first will produce the detrimental effects (waviness, diving jets, high bottom velocities) of a solid sill. The average distance to the second row was 2.6 block heights (Column 42). Fig. 9 shows what happens if d i s used to non-dimensionalize r and r/d^ is plotted against F^. The scatter is- surprisingly small. Although not tabulated, the r/d2 ratio came out to about 0,40 on the average.
23 F igure
Cd
c o* I End Sill
30, In all cases, solid end sills were used as opposed to the Rehbock end I 'ü sill which resembles a row of baffle blocks. In some instances, however, the ■wi front face was sloped up away from the flow. The main purpose of the end sill
'‘i was to deflect any high velocity jets remaining after passing through the
baffle blocks up away from the channel bottom to eliminate erosion at the end of
the stilling basin. These sills are therefore different than those solely used
to control the hydraulic jump and studied by Forster and Skrinde^. Sill
heights ranged from 4.0 ft to 18 ft (Column 45) and averaged about 0.14d2
(Column 46). Once again, when d^ is used to calculate a sill height ratio
h /d- (Column 47) and plotted against F- the ratio increased with F- as shown in si I ■ . Fig. 10. This result is far from the average h^/d^ ratio of 0.5 recommended by
WES design criteria.
31. For completeness the exit channel slope beyond the end sill is given
in Column 48.
32. Also of possible interest is the amount of horsepower per unit width
of stilling basin that had to be dissipated. Fig. 11 was prepared to illustrate
the widely scattered designs. Interestingly, the damaged stilling basins of
Bluestone and Bonneville Dams were among the low energy basins.
Comparison with Current WES Design Criteria
33. Over the years, laboratory personnel in the Hydraulics Division of the
WES have developed general "rules-of-thumb" for baffled stilling basin designs.
This criteria was sometimes used for the initial model study jlf none was
t available. It was felt to produce the shortest basin at the highest elevation
when the downstream channel was of good material. The basin geometry is based on
the inlet depth, d^, and conjugate depth d2 and is shown in Fig. 12(a).
The corresponding dimensions using averages obtained in Table 1
25 FIGURE. ¡O f-Jú f-Jú /( / . £ R U
i F t s u r e /2(a) C u r r e n t d e s ig n c r it e r ia
F i g u r e /zCt>) M e a n Va l u e s f r o m t a b l e t >/ WALL
1.5 —0- 4dj
■2.75 ¿z
*A LL VALUES VARV W lT^ Fj
28
^(»4«#>ipÿPiWWyWBy of this study for WES data only are shown in Fig. 12(b) for comparison purposes. The results are in fair agreement for those parameters involving
¿2 * However, as demonstrated repeatedly throughout this paper those ratios involving d^ increase with increasing Froude number. Averages of these ratios can be extremely misleading. For example, although h/d^ average was
0.94 and fairly close to the "rule-of-thumb" value of 1.0, the maximum used was 1.72 (Detroit where d^ was only 3.5 ft) and the minimum was only 0.50
(Carlyle where d^ = 16.0 ft). Clearly Fig. 6 shows that even without the
Detroit data at = 14.2, a least squares trend results in the ratio h/d^ increasing with increasing F^. Fig. 12(a) is apparently an oversimplification of the relationships. The use of d^-ratio relationships with F^; complete
use of d2 ~ratios; or perhaps utilization of d^ as the characteristic length scale would in all cases provide more meaningful trends.
Conclusions
34. Keeping the object of this study in mind, that is, to summarize previous Corps’ designs, the following general conclusions can be drawn for those tabulated model tests.
a. Spillways designed were much larger with a higher unit flow 4 rate than USBR Type II and Type III designs.
b. Trends in recent years were to higher unit flow rates, i.e., narrower stilling basins.
c. All but one of twenty-eight projects had inlet Froude numbers less than 7. And over half of these were in the so-called "Transition" range where troublesome pulsating jump action occurs.
29 d. As the inlet Froude No. , increased the inlet depth decreased
almost independently of the flowrate. Therefore any geometry parameter made
dimensionless by d^^ and plotted against F^ is subject to some possibility
of spurious correlation effects.
e. On the average, stilling basin floors were set 13 percent higher (d^ = 0.87d2> than required for full conjugate depth. The baffle blocks and end sill were counted upon to provide the remaining pressure force to
retain momentum equilibrium and hold the jump in the basin.
f. Also on a mean basis, baffled stilling basins were only about one-half as long as similar free hydraulic jumps. (L = 5 to 6d2 for free jump whereas LgB = 2.75d2 on average for forced jump).
g. The WES standard block shape was most prevalent and it took about 12 model tests for each project to determine the optimum basin geometry.
h. ' The average location of the blocks was slightly more than one-half the basin length from the toe or about 1.5d2>
i. The block height ratio, h/d^, varies considerably with F^.
Attempts to use average h/d1 values for all F^ as "rule-of-thumb" design criteria can be grossly misleading. * j. The mean block width was about 0.8 the block height.
k. Blocks were spaced at about 1.2 block widths on the average.
l. Two block rows were used over 80 percent of the time. The __- second row was always staggered and consisted of identical blocks approximately
2.6 block heights from the first row.
m. Solid end sills were always used at the end of the basin and were about 0.14d2 in height on the average.
30 n. The apparent primary reason for the cavitation troubles on the baffle blocks at the Blues tone and Bonneville projects was their proximity to the toe of the jump. The prototype experience of these early designs apparently had a pronounced influence on the shape and location of baffle blocks in later designs.
4
31 REFERENCES
Station,Station1 VVicksburg, i r S 11Cati0nS-°f-the Mississippi, U‘dated S* Anny1 January EnSineer 1967. Waterways Experiment
i. sr
4. A Laboratory Development of Cavitation - Free Raffle P-ie^.. m Dam, New River, West Virginia 1M No - II wilt l Bluestone Vicksburg, Mississippi, 1947.’ ’ rways xperiment Station,
e^*SS2SS5iS5r» pp 2-i24?1±C StrUCtUreS ‘ A » Transactions, ASCE, sB££r«? “““ a«s.«3.TR.- -
2~srsi S i.'siriitrrs .“ **■ ”
32
wm w w - p u r w y » *** w * p w * * ^ ' ™ ^ * w w ”"'* s *'