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Motivation
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Definition
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и с учетом:
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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 surrounding media.
Definition
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Given
- space coordinates are
- inflow pipeline coordinates
| LaTeX Math Inline |
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| body | \{ x_s = 0, \, y_s = 0, \, z_s = 0 \} |
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- pipeline trajectory
| LaTeX Math Inline |
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| body | \{ x_w(l), \, y_w(l), \, z_w(l) \} |
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, where | LaTeX Math Inline |
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| body | 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 |
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, is pipeline length from inflow point | LaTeX Math Inline |
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| body | \{ x_s = 0, \, y_s = 0, \, z_s = 0 \} |
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- pipeline cross-section area
- inflow temperature , inflow pressure , inflow rate
- pvt properties of water ,
- temperature , thermal diffusivity , thermal conductivity of surrounding media
- heat exchange coefficient based on pipeline schematics
Simulate
- flow temperature , pressure and inflow rate at any moment in time and any location of the pipleine trajectory
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В общем случае задача представляет собой систему уравнений на давление и температуру и решается численными методами, а по результатам рассчитывается профиль скорости и расхода воды.
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