user's manual for corhyd: an internal diffuser hydraulics model - IfH

3.1.4 Automatic implementation of loss formulations - additional losses
CorHyd automatically applies the necessary local loss formulations for the user given inputs.
For special configurations, which need more detailed specifications of geometries additional
input is necessary for the calculations.
If for example the port is mounted perpendicular onto the riser, this local bending loss is not
included but can be added as a known loss. If a riser has more than one port, it is assumed,
that the discharge flowing through the riser with T-shape including this additional loss and is
distributed evenly among all ports (i.e. for two ports, both would have half the discharge).
The formulations for local losses applied in CorHyd assume reasonable high Reynolds
numbers (above 10 4 ) and reasonable geometrical distance (above 3 times the diameter)
between geometrical changes to avoid interaction of losses. Modifications of the listed
formulations can be found in Idelchik (1986) for special geometries and some limited ranges
of Reynolds numbers, but have not been implemented in CorHyd.
3.2 Governing Equations
The governing equations are continuity equations at each flow division and the work-energy
equation along pipe segments with constant or known flowrate (Fig. 13). Required input data
are the geometry of the discharge structure with sets of diffuser pipe segment locations x,
y, z, riser/port segment geometries (i.e. cross-sections A, riser/port number and allocation, and
roughness k s ). Pipe lengths L and pipe joint configurations are calculated automatically out of
these parameters. Used indices are ‘d’ for diffuser pipe sections, ‘r’ for riser sections, ‘p’ for
port sections and ‘j’ for jet properties at the vena contracta of the discharging jet. The
ambient is described by its density ρ a and the average water level elevation H resulting in
different external hydrostatic pressures p a,i at the vertical location of the jet centreline at the
vena contracta at each i position along the diffuser pipe, where risers or ports are attached.
The effluent is described by its fluid density ρ e and either the total flow rate Q or the total
available water level at the headworks (total head H t ).
Additional input fields allow to specify more detailed information on local losses, T- or Y-
shaped diffuser configurations or the denomination of clogged or temporary closed ports.
Implemented local losses are those from chapter 2.4. Herefore ζ p,i,j , ζ r,i,j , ζ d,i,j denote the local
loss coefficients for each j-component of the total number n p,i of losses in a port, n r,i in a riser
or n d,i in the diffuser pipe with pipe cross-sectional areas A p,i,j , A r,i,j and A d,i,j respectively. λ p,i,j
, λ r,i,j and λ d,i,j denote the friction coefficients for related pipe components with length L p,i,j ,
L r,i,j and L d,i,j diameter D p,i,j , D r,i,j D d,i,j equivalent pipe roughness k sp,i,j , k sr,i,j , k sd,i,j respectively
for either port, riser or diffuser component j. For each port or riser, the local and friction loss
coefficients are determined iteratively, since they depend on the discharge.
Institut für Hydromechanik, Universität Karlsruhe 28