TY - GEN
T1 - On Boussinesq and Coriolis coefficients and implications for the Joukowsky equation
AU - Vardy, Alan E.
AU - Tijsseling, Arris S.
N1 - Copyright:
© TU/ e 2023 Pressure Surges 14
PY - 2023
Y1 - 2023
N2 - The purpose of this paper is to show how derivatives of the Boussinesq and Coriolis coefficients, /J and o., can be handled formally in 1-D analyses of unsteady flow. In the case of low Mach number flows typical of liquid flows in many pipes, it is usual to disregard differences between these coefficients and unity, thereby simplifying expressions such as the Joukowsky equation. When this is deemed to be unacceptable - e.g. in moderate and high Mach number flows -a different approach is usually followed, namely allowing for the actual values of the coefficients, but disregarding derivatives of them. It is shown herein that this approach is not only unnecessary, but is actually less accurate than disregarding the coefficients altogether (i.e. using plug-flow approximations). Mathematically, the new result is obtained by deriving expressions that relate derivatives of /J and o. to derivatives of the principal flow parameters (pressure p, density p and mean velocity U). Because these relationships involve derivatives, they do not enable actual values of /J and o. to be deduced. However, it is shown rigorously that inertial waves do not change the product p2 U2(/J-1) and so, if /J is known a priori before a wave-induced velocity change, its value after the change can be deduced.
AB - The purpose of this paper is to show how derivatives of the Boussinesq and Coriolis coefficients, /J and o., can be handled formally in 1-D analyses of unsteady flow. In the case of low Mach number flows typical of liquid flows in many pipes, it is usual to disregard differences between these coefficients and unity, thereby simplifying expressions such as the Joukowsky equation. When this is deemed to be unacceptable - e.g. in moderate and high Mach number flows -a different approach is usually followed, namely allowing for the actual values of the coefficients, but disregarding derivatives of them. It is shown herein that this approach is not only unnecessary, but is actually less accurate than disregarding the coefficients altogether (i.e. using plug-flow approximations). Mathematically, the new result is obtained by deriving expressions that relate derivatives of /J and o. to derivatives of the principal flow parameters (pressure p, density p and mean velocity U). Because these relationships involve derivatives, they do not enable actual values of /J and o. to be deduced. However, it is shown rigorously that inertial waves do not change the product p2 U2(/J-1) and so, if /J is known a priori before a wave-induced velocity change, its value after the change can be deduced.
KW - one-dimensional
KW - unsteady
KW - compressible pipe-flow
KW - momentum correction factor
KW - energy correction factor
M3 - Conference contribution
SN - 9789038657103
SP - 223
EP - 338
BT - Proceedings of the 14th International Conference on Pressure Surges
A2 - Jones, Sarah E. L.
PB - Eindhoven University of Technology
CY - Eindhoven
T2 - 14th International Conference on Pressure Surges
Y2 - 12 April 2023 through 14 April 2023
ER -