296
Y. Kumar et al.
The main focus of the analysis is based on simulation of water depth calculated
by MacCormack scheme and experimental result and variation of water depth with
respect to nodal points and variation of water velocity and water depth with respect
to time and nodal points located along the length of the flume.
7 Conclusions
The findings of the study may be summarized as follows:
1. The plots of the experimental observations and simulated values using numerical
scheme follow approximately similar trends, within experimental error.
2. Unsteady flow conditions can be successfully simulated by numerical schemes
like the finite difference method although the physical parameters like the channel
roughness has to be carefully evaluated through standard physical experimental
measurements under steady state conditions.
3. Electronic pressure sensors can be used to capture the transient conditions accurately but this has to be supplemented with accurate calibration charts relating
electric voltage outputs from the sensors and the water pressure depths found out
experimentally.
4. The results of this simulation conform that the technique may be used to predict
numerically the transients which occur in open hydropower channels conveying
water to hydroelectric stations, where load rejection may cause turbines to shut
down resulting in surges traveling up along the channel.
References
1. Barré de Saint-Venant AJC (1871) Théorie et equations générales dumouvement nonpermanent des eauxcourantes. Comptes Rendus des séances de l’Académie des Sciences, Paris,
Séance 17 July 1871, 73:147–154 (in French)
2. Benjamin TB, Lighthill MJ (1954) On cnoidal waves and bores. Proc Roy Soc Lond A Math
Phys Sci 224(1159):448–460
3. Boussinesq JV (1877) Essai sur la théorie des eaux courantes. (Essay on the theory of water
flow). Mémoires presents par divers savants à l’Académie des Sciences, Paris, vol 23, Série 3,
No. 1, suppl 24, pp 1–680 (in French)
4. Chaudhry MH (2008) Open channel flow, Springer, New York, USA
5. Chaudhry MH, Gharangik AM (1991) Numerical simulation of hydraulic jumps. J Hydraul
Eng ASCE 117(9):1995–2010
6. Favre H (1935) Etude théorique et expérimentale des ondes de translation dans les canaux
découverts (Theoretical and experimental study of travelling surges in open channels). Dunod,
Paris (in French)
7. Garcia-Navarro P, Saviron JM (2010) McCormack’s method for the numerical simulation of
one-dimensional discontinuous unsteady open channel flow. J Hydraul Res 30(1):95–105
8. Gualtieri C, Chanson H (2012) Experimental study of a positive surge. Part 1: basic flow
patterns and wave attenuation. Environ Fluid Mech 12(2):145–159
Y. Kumar et al.
The main focus of the analysis is based on simulation of water depth calculated
by MacCormack scheme and experimental result and variation of water depth with
respect to nodal points and variation of water velocity and water depth with respect
to time and nodal points located along the length of the flume.
7 Conclusions
The findings of the study may be summarized as follows:
1. The plots of the experimental observations and simulated values using numerical
scheme follow approximately similar trends, within experimental error.
2. Unsteady flow conditions can be successfully simulated by numerical schemes
like the finite difference method although the physical parameters like the channel
roughness has to be carefully evaluated through standard physical experimental
measurements under steady state conditions.
3. Electronic pressure sensors can be used to capture the transient conditions accurately but this has to be supplemented with accurate calibration charts relating
electric voltage outputs from the sensors and the water pressure depths found out
experimentally.
4. The results of this simulation conform that the technique may be used to predict
numerically the transients which occur in open hydropower channels conveying
water to hydroelectric stations, where load rejection may cause turbines to shut
down resulting in surges traveling up along the channel.
References
1. Barré de Saint-Venant AJC (1871) Théorie et equations générales dumouvement nonpermanent des eauxcourantes. Comptes Rendus des séances de l’Académie des Sciences, Paris,
Séance 17 July 1871, 73:147–154 (in French)
2. Benjamin TB, Lighthill MJ (1954) On cnoidal waves and bores. Proc Roy Soc Lond A Math
Phys Sci 224(1159):448–460
3. Boussinesq JV (1877) Essai sur la théorie des eaux courantes. (Essay on the theory of water
flow). Mémoires presents par divers savants à l’Académie des Sciences, Paris, vol 23, Série 3,
No. 1, suppl 24, pp 1–680 (in French)
4. Chaudhry MH (2008) Open channel flow, Springer, New York, USA
5. Chaudhry MH, Gharangik AM (1991) Numerical simulation of hydraulic jumps. J Hydraul
Eng ASCE 117(9):1995–2010
6. Favre H (1935) Etude théorique et expérimentale des ondes de translation dans les canaux
découverts (Theoretical and experimental study of travelling surges in open channels). Dunod,
Paris (in French)
7. Garcia-Navarro P, Saviron JM (2010) McCormack’s method for the numerical simulation of
one-dimensional discontinuous unsteady open channel flow. J Hydraul Res 30(1):95–105
8. Gualtieri C, Chanson H (2012) Experimental study of a positive surge. Part 1: basic flow
patterns and wave attenuation. Environ Fluid Mech 12(2):145–159