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where @ has a value of 7.67 and v is the vertical velocity (y-direction). Although both schemes perform well in predicting the vertical velocity profiles, the results from the k-e€ scheme are slightly better. Figs. 8 and 9 show the profiles of kinetic energy per unit mass at x/2b)=50 obtained using k—€ and RNG schemes, respectively. These profiles are compared with the physical model data of Heskestad (1965) at the same location. The results from the k—-€ scheme do not conform with the experimental data near the centerline of the jet, while the RNG scheme predicts a slightly higher 4 value throughout. i, ef i, ee: an: ee ee ne; i eS Se: om

Figure 6 where @ has a value of 7.67 and v is the vertical velocity (y-direction). Although both schemes perform well in predicting the vertical velocity profiles, the results from the k-e€ scheme are slightly better. Figs. 8 and 9 show the profiles of kinetic energy per unit mass at x/2b)=50 obtained using k—€ and RNG schemes, respectively. These profiles are compared with the physical model data of Heskestad (1965) at the same location. The results from the k—-€ scheme do not conform with the experimental data near the centerline of the jet, while the RNG scheme predicts a slightly higher 4 value throughout. i, ef i, ee: an: ee ee ne; i eS Se: om

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where P,; and P,¢ are Prandtl numbers for & and € respectively, S represents the mean rate of strain, and veg is given by viscosity. At some point in this scale, the energy dissipation is equal to the energy production. This scale, referred to as the inertial scale, can be used to describe all the scales. Applying the renormalization technique produces a model that is statistically equivalent to the original Navier-Stokes equations but only describes the inertial scale of turbulence. This scale is of an order that can be efficiently handled by current computer technology. The RNG scheme uses different & and € equations. These equations as given by Bischof, Bucker and Rasch (2004) are
where P,; and P,¢ are Prandtl numbers for & and € respectively, S represents the mean rate of strain, and veg is given by viscosity. At some point in this scale, the energy dissipation is equal to the energy production. This scale, referred to as the inertial scale, can be used to describe all the scales. Applying the renormalization technique produces a model that is statistically equivalent to the original Navier-Stokes equations but only describes the inertial scale of turbulence. This scale is of an order that can be efficiently handled by current computer technology. The RNG scheme uses different & and € equations. These equations as given by Bischof, Bucker and Rasch (2004) are
Fig. 1 Definition sketch of free turbulent jets. velocity at any position x (distance along the jet) is given by wu,»,. The velocity varies from the centerline value, u,, to zero at the edge of the jet. For linear scale and growth of jets, length b is commonly used. Distance b is measured along y or r (for plane turbulent or circular turbulent jet, respectively) coordinate direction to a point where u=0.5u,,. The growth rates of the free plane and circular jets are given by
Fig. 1 Definition sketch of free turbulent jets. velocity at any position x (distance along the jet) is given by wu,»,. The velocity varies from the centerline value, u,, to zero at the edge of the jet. For linear scale and growth of jets, length b is commonly used. Distance b is measured along y or r (for plane turbulent or circular turbulent jet, respectively) coordinate direction to a point where u=0.5u,,. The growth rates of the free plane and circular jets are given by
Figs. 2 and 3 show the decay of the centerline longitudinal velocity along the jet using k-e and RNG schemes, respectively. For reference, the For the plane jet, growth rate, decay of the centerline longitudinal velocity, longitudinal and vertical velocity profiles across the jet, and turbulent kinetic energy profile are compared with experimental data and accepted empirical equations. The growth rates of the plane turbulent jet based on k-e and RNG schemes are found to be 0.11 and 0.12, respectively, and compare well with the value given by Eq. (lla). The virtual origin for k—-€ and RNG schemes are found to be 5.965, and 1.32b,, respectively.
Figs. 2 and 3 show the decay of the centerline longitudinal velocity along the jet using k-e and RNG schemes, respectively. For reference, the For the plane jet, growth rate, decay of the centerline longitudinal velocity, longitudinal and vertical velocity profiles across the jet, and turbulent kinetic energy profile are compared with experimental data and accepted empirical equations. The growth rates of the plane turbulent jet based on k-e and RNG schemes are found to be 0.11 and 0.12, respectively, and compare well with the value given by Eq. (lla). The virtual origin for k—-€ and RNG schemes are found to be 5.965, and 1.32b,, respectively.
ee eee The similarity of longitudinal velocity profiles across the jet at different locations is tested by comparing the predicted velocity profiles with Eq. (13). The velocity profiles obtained using the k-e and RNG schemes are shown in Figs. 4 and 5, respectively, along with Eq. (13). The velocity profile immediately after the potential core is poorly predicted by both schemes, however, more so by the RNG scheme. The velocity profiles further away from the potential core follow the Gaussian curve well. The vertical velocity profiles across the jet predicted by the k-e€ and RNG schemes are compared to Goertler’s solution (Abramovich,
ee eee The similarity of longitudinal velocity profiles across the jet at different locations is tested by comparing the predicted velocity profiles with Eq. (13). The velocity profiles obtained using the k-e and RNG schemes are shown in Figs. 4 and 5, respectively, along with Eq. (13). The velocity profile immediately after the potential core is poorly predicted by both schemes, however, more so by the RNG scheme. The velocity profiles further away from the potential core follow the Gaussian curve well. The vertical velocity profiles across the jet predicted by the k-e€ and RNG schemes are compared to Goertler’s solution (Abramovich,
6. SIMULATION RESULTS FOR CIRCULAR TURBULENT JET
6. SIMULATION RESULTS FOR CIRCULAR TURBULENT JET
Fig. 15 Similarity of vertical velocity of circular jet (RNG scheme).
Fig. 15 Similarity of vertical velocity of circular jet (RNG scheme).
Fig. 11 Centerline velocity decay of circular jet (RNG scheme).
Fig. 11 Centerline velocity decay of circular jet (RNG scheme).
Fig. 13 Similarity of longitudinal velocity of circular jet (RNG scheme).
Fig. 13 Similarity of longitudinal velocity of circular jet (RNG scheme).
Fig. 18 Layout of the field application. surface velocity of less than 0.05 m/s and oscillates back and forth. For numerical simulation, the flow through the river reach is ignored (jet discharging in a still ambient reservoir). The low and high water levels in the river, based on the historical records, are 30.2m and 31.3m. Stormwater outflows of 9.7cms and 5.1 cms are considered for design purposes. The river reach is used extensively for recreational purposes and surface velocity in excess of 0.52 m/s (1 knot) is considered detrimental for recreational use of the river reach. It is required that the zone of surface velocity in excess of 0.52 m/s needs to be delineated with warning signs.
Fig. 18 Layout of the field application. surface velocity of less than 0.05 m/s and oscillates back and forth. For numerical simulation, the flow through the river reach is ignored (jet discharging in a still ambient reservoir). The low and high water levels in the river, based on the historical records, are 30.2m and 31.3m. Stormwater outflows of 9.7cms and 5.1 cms are considered for design purposes. The river reach is used extensively for recreational purposes and surface velocity in excess of 0.52 m/s (1 knot) is considered detrimental for recreational use of the river reach. It is required that the zone of surface velocity in excess of 0.52 m/s needs to be delineated with warning signs.
Fig. 17 Profile of turbulent kinetic energy of circular jet (RNG scheme).
Fig. 17 Profile of turbulent kinetic energy of circular jet (RNG scheme).
Table 1 Length of the 0.52 velocity zone.
Table 1 Length of the 0.52 velocity zone.
Fig. 19 Flow pattern near the surface of the box culvert outlet.
Fig. 19 Flow pattern near the surface of the box culvert outlet.
Fig. 20 Flow pattern near the surface of the diffuser outlet.
Fig. 20 Flow pattern near the surface of the diffuser outlet.
Related topics:
Computational Fluid MechanicsTurbulent Jets
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