Motivation
One of the key problems in designing the pipelines and controlling the pipeline fluid transport is to predict the temperature and pressure losses during the stationary fluid transport.
Pipeline flow simulator is addressing this problem. It should account for the varying pipeline trajectory, gravity effects, fluid friction with pipeline walls and varying heat exchange with surroundings.
Definition
Given
- space coordinates are
\{ x, \, y, \, z \} with
z-ccordinate facing down to the Earth Centre
- inflow pipeline coordinates
\{ x_s = 0, \, y_s = 0, \, z_s = 0 \}
- pipeline trajectory
\{ x_w(l), \, y_w(l), \, z_w(l) \}, where
l = \int_0^l \sqrt{dx^2 + dy^2 + dz^2} = \int_0^l \sqrt{\dot x^2 + \dot y^2 + \dot z^2} dl, is pipeline length from inflow point
\{ x_s = 0, \, y_s = 0, \, z_s = 0 \}
- pipeline cross-section area
A(l)
- earth gravity vector
{\bf g} = (0, \, 0, \, g) where
g = 9.81 \ \rm m/s^2
- inflow temperature
T_s, inflow pressure
p_s, inflow rate
q_s
- PVT properties of water
\rho(T, p),
\mu(T, p)
- surroundings initial temperature
T_g(l), thermal diffusivity
a_e(l), thermal conductivity
\lambda_e(l) of surrounding media
- heat exchange coefficient
U(l) based on pipeline schematics
Simulate
- along-pipe distribution of stabilized pressure
p(l), flow rate
q(l) and average flow velocity
u(l)
- along-pipe distribution of fluid flow temperature
T(t, l) after a flow period of time
t when the flow stabilization achieved
References
https://en.wikipedia.org/wiki/Darcy_friction_factor_formulae
https://neutrium.net/fluid_flow/pressure-loss-in-pipe/
H. J. Ramey, Wellbore Heat Transmission - SPE-96-PA - 1992
R. Shankar, Pipe Flow Calculations, Clarkson University
solverbook.com – Коэффициент теплоотдачи