Pipe (TL)#

The block:

Describes the flow of fluid through a section of pipe;
Takes into account pressure losses during friction against the rough wall of the pipe and temperature change during the passage of liquid through the pipe.

Note

Optionally, the block can take into account fluid compression and inertia.

Pressure losses due to friction:

If the Reynolds number of the flow is less than the upper limit of the Reynolds number for the laminar flow, then the pressure losses are calculated by the formula (1):

(1)#\[ \Delta P_{fric} = \frac{\nu\lambda}{2D^2S} L \ \dot{m} \]

where:

\( u\) – kinematic viscosity, [m\(^2\)/s];

\(\lambda\) – Darcy friction coefficient, which is equal to 64;

\(L\) – pipe length, [m];

\(D\) – pipe diameter, [m];

\(S\) – pipe cross-section area, [m\(^2\)];

\(\dot{m}\) – mass flow rate of liquid, [kg/s].

If the Reynolds number of the flow is greater than the lower limit of the Reynolds number for the turbulent flow, then the pressure losses are calculated by the formula (2):

(2)#\[ \Delta P_{fric} = \frac{f}{2\rho S^2} \frac{L}{D} \mid \dot{m} \mid \dot{m} \]

\(f = \{-1.8 \ log_{10}[\frac{6.9}{Re} + (\frac{\varepsilon}{3.7D_h})^{1.11}] \}^{-2}\)

\( ho\) – fluid density, [kg/m\(^3\)];

\(S\) – pipe cross-section area, [m\(^2\)];

\(L\) – pipe length, [m];

\(D\) – pipe diameter, [m];

\(\dot{m}\) – mass flow rate of liquid, [kg/s];

\(Re\) – Reynolds number;

\(\varepsilon\) – pipe roughness;

\(D_h\) – pipe hydraulic diameter, [m].

If the Reynolds number corresponds to a transient process, then the resistance coefficient is linear interpolation between the boundary points of the turbulent and laminar flow mode.

Law of conservation of mass:

If the liquid is incompressible, then the flow rate at the inlet and outlet of the pipeline is the same.
If the compressibility mode is selected, then the pipeline section is divided into three parts - two pipes connected by a capacitive assembly. The law of conservation of mass in the capacitive assemble is determined by the ratio (3):

(3)#\[ \dot{m_A} + \dot{m_B} = (\frac{1}{\beta_{n}}\frac{dp_{n}}{dt} -\alpha_{n}\frac{dT_{n}}{dt})\rho_{n} V \]

where:

\(\dot{m_A}\) – mass flow rate of liquid in the “left” pipe, [kg/s];

\(\dot{m_B}\) – mass flow rate of liquid in the “right” pipe, [kg/s];

\(α_n\) - isobaric thermal expansion coefficient of the liquid in the capacitive assembly, [1/К];

\(β_n\) - volumetric modulus of elasticity of the liquid in the capacitive assembly, [Pa];

\(p_n\) – pressure in the capacitive assembly, [Pa];

\( ho_n\) – density of liquid in the capacitive assembly, [kg/m\(^3\)];

\(V\) – pipe segment volume, [m\(^3\)].

Law of conservation of energy (4)

(4)#\[ Ф_{A} + Ф_{B} + Q\:=\: \left[(\frac{h_{n}}{\beta_{n}}-\frac{T\alpha_{n}}{\rho_{n}})\frac{dp_{n}}{dt} + (c_{p}-h_{n} \alpha_{n})\frac{dT_{n}}{dt}\right]\rho_{n} V + \dot{m_{ср}} \Delta z g \]

where:

\(Q\) - heat flux through the heat port, [W];

\(h_n\) - enthalpy of the medium in the capacitive assemble, [J];

\(c_{pn}\) - specific isobaric heat capacity of the liquid in the capacitive assembly, [J/(kg\(\cdot\)К)];

\(\phi_A\) - energy flow in the “left” pipe, [W];

\(\phi_B\) - energy flows in the “right” pipe, [W].

Law of conservation of momentum:

The total pressure differential between the pipe ends is determined by friction losses and difference in elevations (5):

(5)#\[ \Delta P = \Delta P_{fric} + \rho \Delta z g \]

where:

\(P_{fric}\) – friction pressure losses, [Pa];

\( ho\) – fluid density, [kg/m\(^3\)];

\(\Delta z\) – elevation difference, [m];

\(g\) – free fall acceleration, [m/s\(^2\)];

If fluid inertia is taken into account, then the full pressure differential is determined by the formula (6):

(6)#\[ \Delta P = \Delta P_{fric} + \rho \Delta z g + \ddot{m} \frac{L}{2S} \]

where:

\(L\) – pipe length, [m];

\(S\) – pipe cross-section area, [m\(^2\)].

Inclined Pipeline:

To model an inclined pipeline, use the Elevation gain from port A to port B property. The height difference reflects the difference in geometric heads at the start and end points of the pipeline, so a positive value indicates that the end point is lower than the start point, and a negative value indicates the opposite.

The table below shows various pipeline positions in space:

№	Pipeline Position	Height Difference Value
1	Horizontal pipeline	Height difference is set to zero
2	Vertical pipeline with descending flow (along the fluid movement direction)	Height difference is set positive and equal in magnitude to the pipeline length
3	Vertical pipeline with ascending flow	Height difference is set negative and equal in magnitude to the pipeline length
4	Inclined pipeline with descending flow	Height difference is set positive and smaller in magnitude than the pipeline length
5	Inclined pipeline with ascending flow	Height difference is set negative and smaller in magnitude than the pipeline length

1. Properties#

Property	Default Value	Description	Units of measurement
Fluid dynamic compressibility	Off	-	-
Fluid inertia, available when selecting `Fluid dynamic compressibility` - `On`	Off	-	-
Pipe length	5	-	m
Pipe diameter	0.1	-	m
Elevation gain from port A to port B	0	-	m
Gravitational acceleration	9.81	-	м/с\(^2\)
Internal surface absolute roughness	15e-6	-	m
Laminar flow upper Reynolds number limit	2000	-	-
Turbulent flow lower Reynolds number limit	4000	-	-
Initial liquid temperature in the pipe	20	-	°С
Initial liquid pressure	0	-	Pa
Initial mass flow rate, available when selecting `Fluid inertia` - `On`	0	-	kg/s

2. Inputs and outputs#

Parameters	Input/Output	Description	Units of measurement	Port type
Input	Input	-	-	Thermohydraulics
Heat port	Output	-	-	Heat exchange
Output	Output	-	-	Thermohydraulics

In order to see the connection capabilities of the block, you need to go to page Description of block ports