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Research Papers: Flows in Complex Systems

# Water Level Rise Upstream a Permeable Barrier in Subcritical Flow: Experiment and Modeling

[+] Author and Article Information
R. Martino

CONICET – Grupo de Medios Porosos,
Univ. de Buenos Aires,
Paseo Colón 850 (1063), Argentina
e-mail: rmartino@fi.uba.ar

A. Paterson

Departamento de Hidráulica,
Univ. de Buenos Aires,
Paseo Colón 850 (1063), Argentina
e-mail: apaters@fi.uba.ar

M. Piva

Grupo de Medios Porosos,
Univ. de Buenos Aires,
Paseo Colón 850 (1063), Argentina
e-mail: mpiva@fi.uba.ar

Contributed by the Fluids Engineering Division of ASME for publication in the JOURNAL OF FLUIDS ENGINEERING. Manuscript received July 2, 2013; final manuscript received December 14, 2013; published online February 28, 2014. Assoc. Editor: Mark R. Duignan.

J. Fluids Eng 136(4), 041103 (Feb 28, 2014) (9 pages) Paper No: FE-13-1407; doi: 10.1115/1.4026356 History: Received July 02, 2013; Revised December 14, 2013

## Abstract

This work addresses the dependence of water depth upstream a permeable barrier, $h1$, with discharge per unit channel width, $Q/W$, in sub-critical flow regime. The barrier, that extends over the entire width of the channel, is composed by smooth cylinders of small aspect ratio vertically mounted on the bottom in a staggered pattern and fully submerged in the flow. The height of the cylinders above the bottom was kept constant for all runs. Several configurations were considered by varying systematically the cylinders diameter, $dv$, the number of cylinders per unit area of the bed, or density, $m$, and the length of the barrier in the stream direction, $Lv$. A one-dimensional model was developed to predict the observed values of $h1$ and to obtain a sound basis taking into account the incidence of $Q/W$, $m$, $dv$ and $Lv$. This model is based on fluid mechanics equations applied on a finite control volume for the flow in the test section, and it was deduced under simplifying assumptions physically-based. Finally, and based on the experimental results and the model predictions, the mechanical energy losses of the flow are analyzed. The main role played by a dimensionless number $R$, that takes into account the barrier's resistance to the flow, is highlighted.

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## Figures

Fig. 1

Scheme of the small horizontal channel and the equipment used for driving and controlling the flow, together with the main dimensions and geometrical variables (not drawn to scale)

Fig. 2

Plan view of the main geometrical variables for to define the staggered distribution of cylinders (not drawn to scale)

Fig. 3

Two snapshots of the flow at the test section (from left to right), with Q = 5000 l/h in both cases, showing the differences between the base flow (with no cylinders), in the upper snapshot, and the flow when a barrier is present, with m = 0.513cyls/cm2, dv = 0.502cm, and Lv = 16.5cm, in the lower snapshot

Fig. 4

After analyzing the snapshots showed in Fig. 3 with an ImageJ macro, it is obtained the free surface profile at the test section for both the base flow (no barrier) and for the flow when a barrier is present

Fig. 5

Effect of cylinders diameter, dv, on flow water depth h1 against discharge per unit channel width, Q/W, for: □ Run A1: dv = 0.308cm with m = 0.513cyls/cm2 and Lv = 16.5cm, ○ Run A2: dv = 0.699cm with m = 0.513cyls/cm2 and Lv = 16.5cm, and ▪ base flow (no barrier)

Fig. 6

Effect of barrier density, m, on flow water depth h1 against discharge per unit channel width, Q/W, for: □ Run B1: m = 0.057cyls/cm2 with dv = 0.502cm and Lv = 15.0cm, ○ Run B2: m = 0.513cyls/cm2 with dv = 0.502cm and Lv = 16.5cm, and ▪ base flow (no barrier)

Fig. 7

Effect of barrier length, Lv, on flow water depth h1 against discharge per unit channel width, Q/W, for: □ Run C1: Lv = 3.5cm with m = 0.513cyls/cm2 and dv = 0.502cm, ○ Run C2: Lv = 23.0cm with m = 0.513cyls/cm2 and dv = 0.502cm, and ▪ base flow (no barrier)

Fig. 8

Comparison between measured (□, repeated) and computed (- - -, Eq. (6)) h1 against Q/W, for two cylinder diameters, dv: Run A1: dv = 0.308cm with m = 0.513cyls/cm2 and Lv = 16.5cm; and Run A2: dv = 0.699cm with m = 0.513cyls/cm2 and Lv = 16.5cm

Fig. 9

Comparison between measured (□, repeated) and computed (- - -, Eq. (6)) h1 against Q/W, for two barrier densities, m: Run B1: m = 0.057cyls/cm2 with dv = 0.502cm and Lv = 15.0cm; and Run B2: ○m = 0.513cyls/cm2 with dv = 0.502cm and Lv = 16.5cm

Fig. 10

Comparison between measured (□, repeated) and computed (- - -, Eq. (6)) h1 against Q/W, for two barrier lengths, Lv: Run C1: Lv = 3.5cm with m = 0.513cyls/cm2 and dv = 0.502cm; and Run C2: Lv = 23.0cm with m = 0.513cyls/cm2 and dv = 0.502cm

Fig. 11

Direct comparison between measurements, h1meas, and the corresponding predicted value from Eq. (6), h1pred, for the new set of measurements D1 to D7 (see Table 2). Continuous line shows perfect agreement.

Fig. 12

The dimensionless flow depth η = h1/h3 as a function of the resistance parameter R = (γCd'/2)mdvLvhv/h3, for all the downstream Froude numbers, F3, Runs A1 to D7. Continuous line corresponds to the average value F3 = 0.77, with standard deviation ΔF3 = 0.09.

Fig. 13

Specific mechanical energy losses, H/(ρQ), against discharge per unit channel width, Q/W: (a) influence of cylinder diameter, dv, for m = 0.513cyls/cm2 and Lv = 16.5cm, □ dv = 0.308cm, and ○dv = 0.699cm; (b) influence of barrier density,  m, for dv = 0.502cm and Lv = 15.0cm, □ m = 0.057cyls/cm2 and ○m = 0.513cyls/cm2; (c) influence of barrier length, Lv, for m=0.513cyls/cm2 and dv = 0.502cm, □ Lv = 3.5cm and ○Lv = 23.0cm. ▪ base flow, mdvLv = 0cm. Uncertainties bars for H/(ρQ) are of the order of data fluctuations and are not plotted for clarity.

Fig. 14

Dependence of H* with R (for γ = 1 and Cd' = 0.68)

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