SUPERCRITICAL JUNCTION FLOW IN SEWER MANHOLES

Giuseppe Del Giudice

Dip. Ingegneria Idraulica ed Ambientale, Università di Napoli,

I-80125 Napoli, Italy.

Tel: +39 0817683435, Fax: +39 0815938936, E-mail: delgiudi@cds.unina.it

 Willi H. Hager

VAW, ETH-Zentrum, CH-8092 Zurich, Switzerland

Tel: +41 1 632 4149, Fax: +41 1 632 1192, E-mail: hager@vaw.baug.ethz.ch 

Abstract: The hydraulics of supercritical junction flow in a 45° junction manhole as applied in sewer systems are explored. Based on an experimental approach and previously collected evidence on supercritical flow in wastewater hydraulics, the main hydraulic features of this standard structure, with the manhole extension added, are determined. First, the governing wave system including waves A through D is described. Then, the various flow types are presented in a diagram relating to seven regimes. Further, the heights of waves B and C, as also the swell at the manhole end are specified, and the discharge capacities for flows in either one branch, or both branches are given. Finally, it is outlined that under otherwise equal conditions, the capacity of junction manholes is at least 20% larger than in the bend manhole. The present indications allow a direct application. 

Keywords: junction flow, sewer, shock wave, supercritical flow, wastewater hydraulics

1    INTRODUCTION

Junction manholes in sewers are a standard structure. In steeper catchments, the flow in the upstream branches is often supercritical, and this configuration may give rise to complex two-phase flow features. So far, no systematic hydraulic research seems to exist on supercritical flow in junction manholes, and this project was considered based on a collaboration between Università di Napoli, and ETH Zurich. The hydraulic experiments were conducted at the latter Versuchsanstalt, and the detailed observations were submitted elsewhere (Del Giudice and Hager 2001). The purpose of the present note is to highlight the main features of junction flow in a junction manhole, and to summarize the findings for direct engineering application.

Based on previous work of, e.g. Schwalt (1994), who considered supercritical junction flow in open rectangular channels, it was obvious that a hydraulic approach was highly complex, given the cumbersome expressions for the geometrical parameters in the U-shaped and the circular sewer sections. Therefore, based on past results with supercritical flow in general, and using a dimensional analysis, it was decided to follow mainly an experimental approach and correlating the results using the Froude similarity law. It was observed that the resulting expressions become so simple that it is worthwhile to follow such a simplified approach. As will be demonstrated, supercritical junction flow can be described with relations that agree with simple physical arguments and their application to practice is straightforward.

The junction structure considered is a simplification of reality. The so-called simple junction structure has a straight-through line between the upstream and the downstream branches, connected to a lateral branch, with a junction angle of 45°. Further, all three branches had equal diameter, corresponding to a minimum arrangement for the downstream diameter. The centerline radius of curvature from the lateral to the downstream branches was 3D, with D as the internal sewer diameter. In practise, junction manholes may be designed with various branch angles, branch diameters, radii of rounding, slope and roughness and even small drops from the lateral into the main branches. The effect of roughness in a manhole is negligible because the local flow features. As was demonstrated for other supercritical flows, the horizontal case determines sewer design (Hager 1999). Bottom drops may be justified for subcritical flow, whereas they definitely disturb any supercritical flow.

For supercritical flow in a transition manhole, such as expansion, bend, drop or even junction manholes, having a typical length of some sewer diameters, one may assume an essentially constant velocity field, except for separation zones, such as along the inner wall of a bend. This assumption was verified experimentally (Del Giudice et al. 2000) and simplifies the hydraulic design of these structures. In addition, the main features of the free flow surface are of relevance, such as the extreme of the shock waves. An additional relevant feature is the capacity discharge of the structure for free surface flow to exist: Once the discharge is larger than the capacity discharge, the flow chokes and stratified flow with water below air flows transforms in two-phase air-water flow, that behaves significantly different and does not corresponds to a standard hydraulic design of sewers.

Of particular importance for sewer design is the so-called geysering. Once the sewer chokes, an air-water pressurized flow establishes in the manhole, similar to surge tank flow. If the oscillations are too large, the manhole cover may be lifted and sewage flows on public roads. This highly uncontrolled scenario must be inhibited under all circumstances, both from hygienic and public safety reasons. Design equations will be given for the capacity discharge, together with the most important relations describing supercritical 45° junction flow. In the first part, the experimental study is described and the experimental results are presented in the second part. In the third part, the design feats of a junction manhole are highlighted.

2    EXPERIMENTS

Test facilities

The experiments were conducted with a horizontal sewer containing a 45° junction manhole. The internal sewer diameter was D=0.240 m, which corresponded also to the diameter of the U-shaped junction cross-sectional profile. The benches had a height of 1.5D, but the entire manhole was not considered to allow for hydraulic experimentation. Based on a previous recommendation of Gisonni and Hager (2001), the so-called manhole extension was applied consisting of an addition of 2D downstream of the bend end to improve the intake flow into the downstream sewer. Given that the bend and the junction manholes have a similar hydraulic behaviour, with a large standing wave along the outer manhole wall due to the lateral branch flow, the wave may reduce in height along the manhole extension, resulting in a considerably larger discharge capacity. Figure 1 shows a definition sketch of the junction manhole as considered for the present work. The average radius of curvature was R_a=3D, and 1% bottom slope resulted approximately in a compensation between wall friction and gravity. The flows in the upstream and lateral branches were generated with jet-boxes that resulted in a flow without velocity concentrations, shock waves and excessive air entrainment. The details of the experimental apparatus are described elsewhere (Del Giudice and Hager 2001).

In the following only fully supercritical flow along the entire junction manhole is described. Del Giudice and Hager (2001) also referred to the mixed flow conditions, with subcritical flow in either of the two branches. Space limitations do not allow here to describe these complex features. Subcritical flow in all branches was not considered at all in this project.

Flow features

Junction hydraulics may be described with various standing waves that result from the supercritical flow in the three branches. One may distinguish between:

Wave A  mainly for flow in the upstream branch only, because of lateral expansion of flow in the manhole, and impinging on the inner junction wall. For small discharges in the lateral branch, wave A normally is suppressed.

Wave B   corresponding to the main wave for both bend and junction manholes, located        along the outer manhole wall, due to flow impingement from the lateral branch.

Wave C  because of flow combination from the lateral and the upstream branches at the junction point. Wave C was described by Greated (1968) in rectangular channels

Fig. 1     Definition of flow in 45° junction manhole (a) plan, (b) section, with standing waves A to C.

In the following, expressions for the wave heights of waves A, B, and C are presented, then aspects like discharge capacity are discussed and practical considerations are indicated then.

3    EXPERIMENTAL RESULTS

General

Junction flow as supercritical free surface flows in general are governed by Froude similarity. In a circular channel, the Froude number may be approximated simply as F=Q/(gDh⁴)^1/2, with Q=discharge, g=gravitational acceleration, and h= flow depth (Hager 1999). The similarity with the Froude number in a rectangular channel is obvious. The flows in the upstream (subscript o) and lateral (subscript L) branches may be characterized with the corresponding Froude numbers as also the filling ratios y_o=h_o/D and y_L=h_L/D, respectively. From momentum considerations, one may demonstrate that the junction angle f is relevant, and the normalized dynamic momentum is equal to yFcosf. For the through branch, this simplifies to y_oF_o.

Flow regions

In two-phase flow various flow types characterise the governing flow features. For the present problem, seven flow regions were distinguished (Fig.2):

(1) Subcritical flow, for both small y_oF_o and y_LF_Lcosf.

(2) Upstream branch supercritical, lateral branch subcritical, for large y_oF_o and small y_LF_Lcosf.

(3) Transition from sub- to supercritical flows in both branches.

(4) Both branches with supercritical flow for large y_oF_o and y_LF_Lcosf.

(5) Choking pipe flow in either the upstream or the lateral branches.

(6) Main branch subcritical, lateral supercritical for small y_oF_o and large y_LF_Lcosf.

(7) Choking in downstream pipe due to off-capacity for very large y_oF_o or y_LF_Lcosf.

The significance of Fig.2 was established using the experiments, to determine the governing flow type in a 45° junction manhole. Past problems are attributed to a wrong identification of the governing flow type, and the resulting consequences for the hydraulic design.

Fig. 2    Flow types in 45° junction manhole. Notation see main text

Wave B

A junction manhole is dominated by the flow in the lateral branch, which also dictates the features of wave B. For flow only in the lateral branch, the relative wave height Y_B=(h_B/h_L)-1 may be expressed with C_B=1 as (Del Giudice and Hager 2001)

       Y_B = C(F_L - 1).                                (1)

For supercritical flow in both the upstream and the lateral branches, (1) applies with C=C_B=8/7. This result demonstrates the simplicity of the present approach, once the correct hydraulic parameters are selected. Except for filling ratios below 20%, for which scale effects apply, the data follow (1) with a scatter of ±10%. Wave B is located about 3D downstream of the junction point, corresponding roughly at the beginning of the manhole extension (Fig.1). Clearly, without the manhole extension, the maximum flow depth would coincide with the intake section, and resulted in choking of the downstream intake sewer. This was the reason to include this simple element also for the present study, to increase significantly the discharge capacity. From (1) the filling ratio of the upstream branch has practically no effect on the height of wave B, underlining thus the importance of the lateral branch hydraulics.

Wave C

Wave C is generated only for flows in both branches. The previous approach can be maintained to result for the dimensionless wave height Y_C=(h_C/h_L)-1 in (1) with C=C_C=1. For supercritical flow in both branches, wave B is thus by 15% higher than wave C, due to impingement on the outer manhole wall. This is in agreement with Schwalt (1994). Wave B thus determines the freeboard of the manhole structure. Wave C needs no special attention for the hydraulic design, therefore, but is a unique and highly attractive feature of junction flow.

Swell height

In addition to waves A through C, a maximum surface elevation at the intake section may be observed, provided the flow impinges onto the manhole end wall. This height fluctuated considerably, because of turbulence and spray generated in the flow, and the data scatter accordingly. The relative swell (subscript S) height Y_S=(h_S/h_L)-1 may be described with (1) using C=C_S=1. Therefore, both the swell and wave C have the same height. Depending on the lateral flow features h_L and F_L one may easily realize that the downstream sewer chokes, starting when h_S>D/2, and definitely when h_S>D because of the transition from the U-shaped to the circular profile at the manhole end wall.

Discharge capacity

For capacity discharge, the downstream pipe has full filling, i.e. y=1, at the transition from the manhole to the downstream sewer. Indeed, the downstream sewer had always free surface flow provided downstream submergence due to a backwater effect is excluded. The situation considered corresponds to gate type flow as observed with culvert structures. The governing capacity Froude number F_C=Q/(gD⁵)^1/2 corresponds to the pipe Froude number (subscript C).

For only one branch in operation, the data follow the expression

F_C = 2.2 y_m                               (2)

where y_m=y_o for upstream branch flow, and y_m=y_L cosf for lateral branch flow.

For both branches in operation, the capacity Froude number varies with the mixed parameter y_o y_L^1/2, indicating that the lateral branch effect on discharge is small as compared to the through branch. The data may be approximated with (Del Giudice and Hager 2001)

       F_C = 5.5 y_o y_L^1/2                                (3)

The discharge capacity thus depends exclusively on the filling ratios. Once mainly y_L is too large, choking occurs and the supercritical flow structure breaks down.

The maximum discharge (subscript M) is of relevance because it involves a free surface flow from the upstream branches into the downstream sewer:

For upstream branch operation only, the maximum capacity Froude number is F_M=1.4,

For lateral branch operation only, the maximum capacity Froude number is F_C=0.6,             thus much reduced as compared to the previous case,

For both branches in operation, the maximum capacity Froude number is between the   two previous cases, and may attain a value of F_C=1.2 at the maximum. Without         the manhole extension, F_C would be significantly reduced here.

These limitations constitute the main design equations for 45° junction manholes. Note the simple approach for a complex flow configuration, due to the proper selection of relevant variables.

4    COMPARISON WITH BEND MANHOLE

Bend and junction manholes behave hydraulically similar, as was previously mentioned. For bend manholes, wave B corresponds to the main positive shock wave along the outer bend wall. Based on a comparison of results, it may be stated that for otherwise equal hydraulic conditions, wave B in the bend manhole is significantly larger than wave B in the junction manhole, at least for Froude numbers in the approach branches larger than F=1.5.

For equal filling ratios in both branches, the discharge capacity according to (3) is larger than for the corresponding bend manhole. Whereas the maximum discharge was determined to F_C=1.2 in the present case, it is about F_C»1 for the bend manhole, thus reduced by at least 20%. The flow in the upstream branch reduces the height of wave B by generating a component of through-flow across the structure. For a total discharge Q=Q_o+Q_L, the capacity of the junction is a maximum for Q=Q_o, and a minimum for Q=Q_L. Bend manholes are more prone to choking, two-phase pressurized flow and geysering, therefore.

5    CONCLUSIONS

Junction manholes may be investigated with systematic hydraulic modelling, provided the governing hydraulic parameters are correctly selected. A theoretical approach is principally amenable, but would need information on the complex pressure distributions along the manhole walls as also the local distribution of air concentration.

The present approach followed previous research activities and involved a simplified definition of Froude number in circular sewers. Expressions were determined for the maximum wave heights due to the presence of waves B and C, as also the swell at the manhole end wall. It was realized that the maximum wave height occurs along the outer manhole wall due to wave B, at the beginning of the manhole extension. This recently improved manhole design thus is able to significantly increase the manhole discharge capacity by at least 20% compare to the corresponding bend manhole. The maximum capacity of a junction manhole expressed by the capacity Froude number is 0.6 for flow in the lateral branch only, 1.2 for both branches in operation, to a maximum of 1.4 for the upstream branch in operation only. A hydraulic design of the 45° junction manhole is amenable.

Acknowledgements

The present project was a team work between Università di Napoli, and VAW, ETH Zurich. We would like to acknowledge support of Abwassertechnische Vereinigung ATV/DVWK and of Ufficio Scambi Internazionali of Università di Napoli as also constant interest of Prof. G. Rasulo, Napoli, and Prof. Dr. H.-E. Minor, Zurich.

References

Del Giudice, G., Gisonni, C., Hager, W.H. (1999). Supercritical flow in bend manhole. Journal of Irrigation and Drainage Engineering 126(1): 48-56.

Del Giudice, G., Hager, W.H. (2001). Supercritical flow in 45° junction manhole. Journal of Irrigation and Drainage Engineering submitted.

Gisonni, C., Hager, W.H. (2001). Supercritical flow in manholes with a bend extension. Municipal Engineering submitted.

Greated, C.A. (1968). Supercritical flow through junctions. La Houille Blanche 23(8): 693-695.

Hager, W.H. (2000). Wastewater hydraulics. Springer: Berlin, New York.

Schwalt, M. (1994). Vereinigung schiessender Abflüsse und ihre Optimierung durch die Deckplatte. Versuchsanstalt für Wasserbau, Hydrologie und Glaziologie Mitteilung        129. ETH: Zurich (in German).