Engee documentation

Pipe (TL)

Rigid pipework for liquid supply in thermal liquid systems.

pipe (tl)

Description

A Pipe (TL) unit is a pipe segment with a fixed volume of fluid. The fluid experiences pressure loss due to viscous friction and heat transfer due to convection between the fluid and the pipe wall. The viscous friction follows from the Darcy-Weisbach equation and the heat transfer coefficient follows from the Nusselt number relationship.

Hydraulic effects in the pipe

The Pipe (TL) block allows you to include the effects of dynamic compressibility and fluid inertia. The inclusion of each of these effects can increase the accuracy of the model at the cost of increased complexity of the equations and potentially increased modelling resources:

  • When dynamic compressibility is turned off, the fluid is assumed to spend negligible time in the pipe volume. Therefore, there is no mass accumulation in the pipe and the inflow of mass is equal to the outflow of mass. 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.

  • With dynamic compressibility, an imbalance of mass inflow and mass outflow can result in the accumulation or reduction of fluid in the pipe. As a result, the pressure in the pipe volume can rise and fall dynamically, providing a degree of system pliability and modulating rapid pressure changes. This option is used by default.

  • If dynamic compressibility is enabled, fluid inertia can also be enabled. This effect results in additional resistance to flow, on top of the resistance due to friction. This additional resistance is proportional to the rate of change in mass flow rate. Accounting for fluid inertia slows down rapid changes in flow rate, but can also lead to overestimation and fluctuations in flow rate. This option is suitable for a very long pipe. Include fluid inertia and connect several pipe segments in series to simulate the propagation of pressure waves along the pipe, such as in a water hammer.

Conservation of mass

The mass conservation equation for a pipe is as follows:

еслидинамическаясжимаемостьжидкостиотключенаеслидинамическаясжимаемостьжидкостивключена

where

  • - is the mass flow rate through port A;

  • - is the mass flow rate through port B;

  • - is the volume of liquid in the pipe;

  • - temperature-dependent density of the liquid in the pipe;

  • - isothermal bulk modulus of elasticity in the pipe;

  • - isobaric thermal expansion coefficient in the tube;

  • - temperature-dependent density of the liquid in the pipe;

  • - temperature of the coolant in the pipe.

Conservation of momentum

The table shows the conservation of momentum equations for each half pipe.

For the half-pipe adjacent to the port A

еслиинерцияжидкостиотключенаеслиинерцияжидкостивключена

For half of the pipe adjacent to the port B

еслиинерцияжидкостиотключенаеслиинерцияжидкостивключена

In Eqs:

  • - cross-sectional area of the pipe;

  • - liquid pressure in the pipe;

  • - fluid pressure at the port inlet A;

  • - fluid pressure at the port inlet B;

  • - viscous friction pressure loss between the centre of the pipe volume and the port A;

  • - pressure loss due to viscous friction between the centre of the pipe volume and port B.

Pressure losses at viscous friction

The table shows the viscous friction pressure loss equations for each half of the pipe.

For the half of the pipe adjacent to the port A

еслиесли

For half of the pipe adjacent to the port B

еслиесли

In Eqs:

  • λ - pipe shape factor;

  • ν - kinematic viscosity of thermal liquid in the pipe;

  • - cumulative equivalent length of local losses of the pipe;

  • - hydraulic diameter of the pipe;

  • - Darcy friction coefficient in the half of the pipe adjacent to the port A;

  • - Darcy friction coefficient in the half of the pipe adjacent to the port B;

  • and - Reynolds numbers for ports A and B respectively;

  • - Reynolds number, above which the flow becomes turbulent;

  • - Reynolds number, below which the flow changes to laminar.

Darcy friction coefficients follow from the Haaland approximation for the turbulent regime:

where

  • - Darcy friction coefficient;

  • - roughness of the pipe surface.

Conservation of energy

The energy conservation equation for the pipe is as follows:

ρ

where

  • and are the energy flow into the pipe through ports A and B, respectively;

  • - is the heat flux entering the pipe through the pipe wall.

Heat flux through the wall

The heat flux between the thermal liquid and the pipe wall is:

where

  • - is the heat flux through the pipe wall;

  • - the part of heat flux due to convection at non-zero flow rate;

  • - thermal conductivity of thermal liquid in the pipe;

  • - surface area of the pipe wall, the product of the perimeter and length of the pipe;

  • - temperature at the pipe wall.

Assuming an exponential temperature distribution along the pipe, the convective heat transfer is as follows

where

  • - is the average mass flow rate through port A to port B;

  • - is the specific heat at mean temperature;

  • - inlet temperature as a function of flow direction.

The heat transfer coefficient, , depends on the Nusselt number:

where is the thermal conductivity at mean temperature.

Nusselt number depends on the flow regime.

Nusselt number in laminar flow regime is constant and is equal to the value of parameters Nusselt number for laminar flow heat transfer.

Nusselt number in turbulent flow regime is calculated by Gnelinsky’s relation:

where is the Darcy friction coefficient at mean Reynolds number, , and is the Prandtl number calculated at mean temperature.

The average Reynolds number is calculated as:

where μ is the dynamic viscosity estimated at mean temperature.

When the mean Reynolds number is between the parameters Laminar flow upper Reynolds number limit and Turbulent flow lower Reynolds number limit, the Nusselt number follows a smooth transition between laminar and turbulent Nusselt number values.

Assumptions and limitations

  • Pipe wall is rigid.

  • Fully developed flow.

  • The influence of gravity is negligible.

Ports

Non-directional

A - pipe inlet or outlet
thermal liquid

Thermal liquid port, corresponds to the inlet or outlet of the pipe. This port has no directionality of its own.

B - pipe inlet or outlet
thermal liquid

Thermal liquid port, corresponds to the inlet or outlet of the pipe. This port has no directionality of its own.

H is the temperature of the pipe wall
heat

Port associated with the temperature of the pipe wall. This temperature may be different from the temperature of the thermal liquid inside the pipe.

Parameters

Geometry

Pipe length - pipe length
5 m (By default)

Pipe length along the flow direction.

Cross-sectional area - cross-sectional area
0.01 m^2 (by default)

The cross-sectional area of the pipe normal to the direction of flow.

Hydraulic diameter - hydraulic diameter
`0.1128 m (by default).

The diameter of an equivalent cylindrical pipe with the same cross-sectional area.

Friction and Heat Transfer

Aggregate equivalent length of local resistances - total length of all local resistances present in the pipe
1 m (By default)

Total equivalent length of all local resistances present in the pipe.

Local resistances include bends, fittings, fittings, and pipe inlets and outlets. 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 for friction calculations only.

The volume of fluid inside the pipe depends only on the geometric length of the pipe, defined by the Pipe length parameters.

Internal surface absolute roughness - absolute roughness of the internal surface of the pipe
15e-6 m (By default).

Average depth of all surface defects on the internal surface of the pipe that affect the pressure loss in turbulent flow regime.

Laminar flow upper Reynolds number limit - Reynolds number above which the flow starts to change from laminar to turbulent flow mode
2000 (By default)

Reynolds number above which the flow starts to change from laminar to turbulent.

This number is equal to the maximum Reynolds number corresponding to fully developed laminar flow.

Turbulent flow lower Reynolds number limit - Reynolds number below which the flow starts to change from turbulent to laminar flow
`4000 (by default).

Reynolds number below which the flow starts to change from turbulent to laminar.

This number is equal to the minimum Reynolds number corresponding to fully developed turbulent flow.

Shape factor for laminar flow viscous friction - shape factor for viscous friction in laminar flow
64 (By default).

Dimensionless coefficient reflecting the effect of pipe cross-section geometry on viscous friction losses in laminar flow regime.

Typical values: 64 for circular cross section, 57 for square cross section, 62 for rectangular cross section with aspect ratio 2 and 96 for thin annular cross section.

Nusselt number for laminar flow heat transfer - Nusselt number for laminar flow heat transfer
`3.66 (By default).

The ratio of convective to conductive heat transfer in laminar flow regime. Its value depends on the geometry of the pipe cross-section and thermal boundary conditions at the pipe wall, such as constant temperature or constant heat flux.

A typical value is 3.66 for a circular cross section with constant wall temperature.

Effects and Initial Conditions

Fluid dynamic compressibility - Fluid dynamic compressibility
On (By default) | Off

Select the checkbox for this parameter to include fluid dynamic compressibility in the simulation.

Dynamic compressibility makes the fluid density pressure and temperature dependent, which affects the transient response of the system on small time scales.

Fluid inertia - fluid inertia
off (by default) | on

Select the checkbox for this parameter to include fluid inertia in the simulation.

Flow inertia gives the fluid resistance to changes in mass flow rate.

Dependencies

To enable fluid inertia, select the checkbox for the Fluid dynamic compressibility parameters.

Initial liquid pressure is the liquid pressure at zero point in time
`0.101325 MPa (by default).

Liquid pressure in the pipe at the beginning of the simulation.

Dependencies

To enable fluid pressure at zero time, select the checkbox for the Fluid dynamic compressibility parameters.

The Initial liquid temperature is the temperature of the liquid at zero point in time
`293.15 K (By default).

Liquid temperature in the pipe at the beginning of the simulation.

Initial mass flow rate from port A to port B - mass flow rate at zero moment of time
0 kg/s (By default)

Mass flow rate from port A to port B at time zero.

Dependencies

To enable mass flow at zero time, select the checkbox for the Fluid inertia parameters.