Flood Routine Analysis of Diversion Tunnels

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Outline of Flood Routine Analysis

Actual programing

iUD=1        # Assume reservoir water level increase
dh=0.0005    # Water level increment for searching equilibrium point
eps=0.001    # Convergence criteria
itmax=int(1.0/dh)*100
for i in range(0,nd-1):
    dt=ti[i+1]-ti[i]             # Time interval
    Qin=0.5*(q_in[i]+q_in[i+1])  # Average inflow rate during dt
    hh=0.0                       # Zero set of water level increment
    k=0
    j=0
    while 1:
        k=k+1
        j=j+1;
        hh=hh+float(iUD)*dh      # Update waler level increment
        elv=EL;    q1=OFC(elv,elof,qof,no)+outlet
        elv=EL+hh; q2=OFC(elv,elof,qof,no)+outlet
        Qout=0.5*(q1+q2)         # Average outflow rate during dt
        dS=(Qin-Qout)*dt*3600.0  # Storage accumulated during dt
        R=VOL+dS                 # Total reservoir volume
        elv=RET_H(nr,rh,rv,R)    # Reservoir water level at reservoir volume R
        if iUD==1 and j==10:  # 10 times trial assuming reservoir water level increase
            if EL+hh>elv:     # if reservoir water level is less than assumed water level,
                iUD=-1        # assume water level decrease
                hh=0.0
                j=0
        if iUD==-1 and j==10: # 10 times trial assuming reservoir water level decrease
            if EL+hh<elv:     # if reservoir water level is greater than assumed water level,
                iUD=1         # assume water level decrease
                hh=0.0
                j=0
        if np.abs(EL+hh-elv)<eps: break  # Judgement of convergence
        if itmax<k: break
    VOL=R    # Cumulative volume
    EL=EL+hh # Elevation
    q_out=q2 # Outflow
    print(i+1,iUD,ti[i+1],EL,EL-elv,VOL,q_in[i+1],q_out,file=fout)
    pEL[i]=EL
    pQo[i]=q_out
    sys.stdout.write('\r%d / %d' % (i+1,nd-1))
    sys.stdout.flush()

Programs and Script

Usage of programs

# Make inflow time history data (hydrograph)
python py_hydro.py  Qmax  dt  >  fnameW.txt

# Make outflow characteristics data
python py_TNHQ.py  D  dh  frameW.txt

# Flood routine analysis
python py_eng_floodrT.py  fnameR1.txt  fnameR2.txt  fnameR3.txt  fnameW.txt

# Draw the graph from calculation result
python py_eng_fig_floodrT.py  fnameR.txt  fnameF.png

Related program

# Draw the basic tunnel shape
python py_fig_tunnel.py
convert -trim fig_tunnel.png -bordercolor 'white' -border 10x10 fig_tunnel.png

# Draw the flowchart for flood routine analysis
python py_fig_flowchart.py  flag
convert -trim fig_flowchart.png -bordercolor 'white' -border 20x20 fig_flowchart.png
# flag=0: without axes and grid
# flag=1: with axes and grid

# Draw the table for explanation of symbles in flowchart
python py_fig_table.py  flag
convert -trim fig_table.png -bordercolor 'white' -border 5x5 fig_table.png
# flag=0: without axes and grid
# flag=1: with axes and grid

Information of Diversion Tunnels

Basic data of structures

Basic shape of Diversion Tunnel

Tunnel cross section data Items Description Cross section shape Horseshoe-shaped Internal diameter x lanes (8 cases were considered) D=5.0m (invert width: 3.660m) x 2 lanes D=6.0m (invert width: 4.392m) x 2 lanes D=7.0m (invert width: 5.124m) x 2 lanes D=8.0m (invert width: 5.856m) x 2 lanes D=9.0m (invert width: 6.588m) x 2 lanes D=10.0m (invert width: 7.321m) x 2 lanes D=11.0m (invert width: 8.053m) x 2 lanes D=12.0m (invert width: 8.785m) x 2 lanes Distance between tunnels 30m (from inside tunnel center to outside tunnel center)

Calculation formula of mean velocity of free flow tunnel

where, $v$ is mean velocity of free flow tunnel, $n$ is Manning's roughness coefficient ($n=0.015$), $R$ is hydraulic radius.

Calculation formula of mean velocity of pressure tunnel

where, $v$ is mean velocity of pressured tunnel, $\Delta H$ is difference of water level between tunnel entrance and tunnel exit.

To make outflow characteristic data for analysis, summation of the discharges at the same elevation for each tunnel.

Input data for flood routing

EL(m) V(x10$^6$ m$^3$) 60 0.000 70 2.485 80 21.670 90 88.555 100 223.959 110 446.817 120 778.284 130 1238.519 140 1865.721 150 2375.546 160 3416.319 170 4773.768
Basic Reservoir capacity data (10m level interval)	Reservoir capacity curve by cubic spline interpolation with 1m level interval
Inflow time history (hydrograph) with 1 hour time interval	Outflow characteristics for two diversion tunnels with 0.1m level interval

Calculation results

Design flood Qmax=3130m$^3$/s

Design flood Qmax=1349m$^3$/s

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