Pipe (IL)
Rigid pipeline for liquid flow in isothermal liquid systems.
blockType: AcausalFoundation.IsothermalLiquid.Elements.Pipe
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Description
Block Pipe (IL) simulates the dynamics of isothermal fluid flow in a pipe. The unit takes into account losses due to viscous friction, and can also take into account the dynamic compressibility and inertia of the fluid.
The pipe contains a constant volume of liquid. Pressure losses occur due to viscous friction and are described by the Darcy–Weisbach equation.
The set of block parameters varies depending on the parameters Fluid dynamic compressibility and Fluid Inertia.
Pipe Effects
This block allows you to enable the effects of dynamic compressibility and inertia of the fluid. Including each of these effects can increase the accuracy of the model at the cost of complicating the equations and potentially increasing simulation time.:
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When the option that takes into account the dynamic compressibility of the liquid is turned off, it is assumed that the liquid passes through the pipe in a short period of time, so there is no accumulation of mass in the pipe, and the inflow of mass is equal to its outflow. This is the simplest option. It is suitable when the mass of liquid in the pipe is a negligible fraction of the total mass of liquid in the system.
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When the option that takes into account the dynamic compressibility of the liquid is enabled, an imbalance in the inflow and outflow of mass can lead to an increase or decrease in the amount of liquid in the pipe. As a result, the pressure in the pipe can rise and fall, which will ensure a certain pliability of the system and lead to rapid pressure changes. This option is enabled by default.
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If the option that takes into account the dynamic compressibility of the liquid is enabled, then you can also enable the option that takes into account the inertia of the liquid. This effect leads to additional hydraulic resistance, in addition to resistance due to friction. This additional resistance is proportional to the rate of change of the mass flow rate. Accounting for fluid inertia slows down rapid flow changes, but it can also lead to spikes and fluctuations in flow. This option is suitable for a very long pipe. Turn on the option that takes into account the inertia of the liquid and connect several segments of the pipe in series to simulate the propagation of pressure waves along the pipe, as, for example, in the case of a water hammer.
Conservation of mass
The mass conservation equation for a pipe has the form:
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where:
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— bulk charges via ports A and B.
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— the volume of liquid in the pipe.
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— pressure inside the pipe.
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— the density of the liquid inside the pipe.
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— the volumetric modulus of elasticity of the liquid inside the pipe.
The liquid can be a mixture of pure liquid and a small amount of air, which is set by the Liquid Properties (IL) unit connected to the mains. Equations used to calculate and , as well as the densities at the ends of the pipe and The Darcy–Weisbach equations for each half of the pipe depend on the selected isothermal fluid model.
Momentum Balance
Momentum conservation equations for each half of the pipe:
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For half of the pipe adjacent to port A
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For half of the pipe adjacent to port B
where:
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and — the pressure of the liquid at the ends of the pipe A and B, respectively.
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and — pressure loss due to viscous friction between the center of the pipe and ports A and B.
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— pipe length.
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— the cross-sectional area of the pipe.
Pressure losses due to viscous friction
Viscous friction pressure loss equations for each half of the pipe:
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For half of the pipe adjacent to port A
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For half of the pipe adjacent to port B
where:
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— the pipe shape coefficient used to calculate the Darcy friction coefficient in the laminar flow regime.
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— dynamic viscosity of the liquid in the pipe.
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— the total equivalent length of the local pipe resistances.
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— the hydraulic diameter of the pipe.
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and — the Darcy friction coefficients in the pipe halves adjacent to ports A and B.
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and — the Reynolds numbers on ports A and B.
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— the Reynolds number, when exceeded, the flow goes into a turbulent flow mode.
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— the Reynolds number, below which the flow enters the laminar flow mode.
When the Reynolds number is between and The flow is in a transitional state between laminar and turbulent flow modes. Pressure losses due to viscous friction in the transition region smoothly between losses in the laminar flow regime and losses in the turbulent flow regime.
The block calculates the Reynolds numbers on ports A and B based on the mass flow through the corresponding port:
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The Darcy friction coefficients follow from the Haaland approximation for the turbulent flow regime:
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where:
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— Darcy’s coefficient of friction.
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— roughness of the pipe surface.
Ports
Non-directional
A — inlet or outlet
isothermal liquid
The port of the isothermal fluid corresponds to the inlet or outlet of the pipe. This block has no internal orientation.
B — inlet or outlet
isothermal liquid
The port of the isothermal fluid corresponds to the inlet or outlet of the pipe. This block has no internal orientation.
Parameters
Pipe length — pipe length
5.0 m (default)
The length of the pipe along the flow direction.
Cross-sectional area — the cross-sectional area of the pipe
0.01 m2 (default)
The cross-sectional area of the pipe perpendicular to the flow direction.
Hydraulic diameter is the diameter of an equivalent cylindrical pipe with the same cross—sectional area
0.1128 m (default)
The diameter of an equivalent cylindrical tube with the same cross-sectional area.
Friction
Aggregate equivalent length of local resistances — the total length of all local resistances present in the pass pipe:q[<br>] 1.0 m (default)
The total length of all local resistances present in the pipe. Local resistances include bends, fittings, fittings, pipe entrances and exits. The effect of local resistances is to increase the effective length of the pipe section. This length is added to the geometric length of the pipe only for friction calculations. The volume of liquid inside the pipe depends only on the geometric length of the pipe, determined by the Pipe length parameter.
Internal surface absolute roughness — the average depth of all surface defects on the inner surface of the pipe
15e−6M (default)
The average depth of all surface defects on the inner surface of the pipe that affect pressure losses in the turbulent flow regime.
Laminar flow upper Reynolds number limit — the Reynolds number above which the flow begins to transition from laminar to turbulent flow mode
2000 (default)
The Reynolds number, above which the flow begins to transition from a laminar to a turbulent flow regime. This number is equal to the maximum Reynolds number corresponding to a stationary laminar flow.
Turbulent flow lower Reynolds number limit — the Reynolds number below which the flow begins to transition from turbulent to laminar flow mode
4000 (default)
The Reynolds number, below which the flow begins to transition from a turbulent to a laminar flow regime. This number is equal to the minimum Reynolds number corresponding to a stationary turbulent flow.
Laminar friction constant for Darcy friction factor — coefficient of hydraulic friction in laminar flow mode for the coefficient of friction of Darcy
64.0 (default)
A dimensionless coefficient that determines the effect of the geometry of the pipe cross-section on viscous friction losses in the laminar flow regime. Typical values: 64.0 for circular cross-section, 57.0 for a square section, 62.0 for a rectangular section with an aspect ratio 2 and 96.0 for a thin annular section.
Effects and Initial Conditions
Fluid dynamic compressibility — accounting for the dynamic compressibility of a liquid
enabled (by default) | turned off
Determines whether the dynamic compressibility of the fluid will be taken into account. Dynamic compressibility makes the density of the liquid dependent on pressure, which affects the transient response of the system over short periods of time.
Fluid inertia — accounting for fluid inertia
disabled (by default) | enabled
Determines whether the inertia of the fluid flow will be taken into account. The inertia of the flow resists the change in mass flow.
Dependencies
To use this option, check the box for the Fluid dynamic compressibility option.
Initial liquid pressure — liquid pressure at zero time
0.101325 MPa (default)
The pressure of the liquid in the pipe at the initial time.
Dependencies
To use this option, check the box for the Fluid dynamic compressibility option.
Initial mass flow rate from port A to port B — mass flow rate at zero time
0.0 (default)
The mass flow rate from port A to port B at the initial time.
Dependencies
To use this option, check the box for the Fluid inertia option.