Enhanced Physically Based Models for Pressure Characteristics at Plunge Pool Bottoms

Predicting the characteristics of the dynamic pressures at plunge pool bottoms due to the impact of plunging jets is essential in designing and assessing the stability of lined or unlined plunge pool bottoms. In this article, by developing a large-scale physical model, the generated dynamic pressures at plunge pool bottoms are measured in different plunging jet conditions and pool water depths. The validity of the existing empirical formulations in predicting the dynamic pressure mean ($C_P$) and pressure fluctuations ($C_P^{\prime }$) is assessed based on the experimental data. The comparison of the predicted results through existing empirical models with the observed experimental data indicates that the recently developed models have acceptable accuracy in predicting the $C_P$ coefficient, but not the $C_P^{\prime }$ coefficient. By running a parametric analysis through dimensional analysis, the dimensionless parameter of plunge pool Froude number [$F{r}_P=V_j/{(gY)}^{0.5}$, where, $V_j$ = jet velocity at pool surface, $g$ = acceleration due to gravity, and $Y$ = plunge pool water depth] is introduced as an alternative to $Y/D_j$, (where, $D_j$ is jet diameter at pool surface) to simultaneously consider the effects of pool water depth and jet velocity. The results indicate that at $F{r}_P\le 2$, the $C_P^{\prime }$ coefficient is negligible and = 0.10. At $2<F{r}_P<4$, increasing the $F{r}_P$ leads to an increase in the $C_P$ and $C_P^{\prime }$ coefficients, whereas at $F{r}_P\ge 4$, plunging jet acts on the pool bottom in the form of a core jet; the $C_P$ and $C_P^{\prime }$ coefficients are independent of the $F{r}_P$ parameter. In this circumstance, these coefficients are constant of 0.86 and 0.31, respectively. The nonlinear regression analysis is applied to develop empirical models of the $C_P$ and $C_P^{\prime }$ coefficients based on the $F{r}_P$ parameter in the effective ranges of $F{r}_P$. The results indicate that the $F{r}_P$ by considering two effective variables of jet velocity and pool water depth is more effective than the $Y/D_j$ ratio in describing the characteristics of dynamic pressure generated at the pool bottom. The extent to which the results are applied in practice is addressed.

It is essential to predict the characteristics of the dynamic pressures at plunge pool bottoms due to the impact of plunging jets, to design and evaluate the stability of lined or unlined plunge pool bottoms. In this article, by developing a large-scale physical model, the dynamic pressures generated at the plunge pool bottoms are measured. The dimensionless parameter of plunge pool Froude number [$F{r}_P=V_j/{(gY)}^{0.5}$, where $V_j$ = jet velocity at pool surface, $g$ = acceleration due to gravity, and $Y$ = plunge pool water depth] is introduced to predict the dynamic pressure mean ($C_P$) and pressure fluctuations ($C_P^{\prime }$). Empirical models are introduced to predict the $C_P$ and $C_P^{\prime }$ coefficients based on the $F{r}_P$ parameter. The results indicate that the $F{r}_P$, by considering two effective variables of jet velocity and pool water depth, is more effective than the $Y/D_j$ ratio in describing the characteristics of dynamic pressure generated at pool bottom.