Confuser / Area Change (TL)#

The Confuser / Area Change (TL) block describes the corresponding types of local resistances in a pipeline for a thermal-hydraulic system.

For a confuser, when fluid moves from the inlet port to the outlet port, the cross-sectional area of the flow narrows, and the fluid velocity increases; for reverse flow, it expands. For an area change (diffuser), the opposite occurs.

Hint

The cross-sectional areas can be set equal—in this case, the block will function as a local resistance with a constant diameter.

The loss coefficients for the block can be set empirically or via a tabular method.

For calculation based on empirical data:

For gradual conical contraction in the range of 0 to 45 degrees, the friction coefficient is calculated as (1):

(1)#\[K_{con}\:=\:0.8\cdot C_{con}\cdot sin(\frac{\theta}{2})\cdot (1-R)\]

where R - is the ratio of the smaller port area to the larger port area.

For contraction from 45 to 180 degrees (exclusive) (2):

(2)#\[K_{con}\:=\:0.5\cdot C_{con}\cdot \sqrt{sin(\frac{\theta}{2})}\cdot (1-R)\]

For contraction at 180 degrees (3):

(3)#\[K_{con}\:=\:\frac{C_{con}}{2}\cdot (1-R)\]

For gradual conical expansion in the range of 0 to 45 degrees, the friction coefficient is calculated as (4):

(4)#\[K_{exp}\:=\:2.6\cdot C_{exp}\cdot sin(\frac{\theta}{2})\cdot (1-R)^2\]

For expansion from 45 to 180 degrees (inclusive) (5):

(5)#\[K_{exp}\:=\:C_{exp}\cdot (1-R)^2\]

For calculation based on tabular data, vectors of loss coefficients for contraction and expansion are assigned in accordance with the Reynolds number vector. All three vectors are set by the user as model parameters.
The total hydraulic loss coefficient for a pipe section with a diffuser is calculated as (6):

(6)#\[K\:=\:K_{exp}+\frac{K_{con}-K_{exp}}{2}\cdot (\tanh{(\frac{3\:\cdot \:\dot m_{A}}{\dot m_{th}})+1})\]

where:

\(\dot m_{A}\) - mass flow rate at the inlet port, [kg/s];

\(\dot m_{th}\) - threshold mass flow rate, [kg/s], at which a change in fluid flow direction occurs, related to the critical Reynolds number (7):

(7)#\[\dot m_{th}\:=\:\frac{Re_{crit}\cdot A_{R}\:\cdot \:\nu\:\cdot\:\bar\rho}{D_{h}}\]

where:

\(A_{R}\) - area of the smaller of the two cross-sections, [m\(^2\)];

\(ν\) - kinematic viscosity of the fluid, [m/s\(^2\)];

\(\barρ\) - average fluid density, [kg/m\(^3\)];

\(D_{h}\) - diameter corresponding to the smallest cross-sectional area \(A_{R}\), calculated as (8):

(8)#\[D_{h}\:=\:\sqrt{\frac{4\cdot A_{R}}{\pi}}\]

The pressure drop across the pipe section with a diffuser is calculated as follows (9):

(9)#\[p_{A}-P_B\:=\:\frac{\dot m^2\:}{2\cdot \bar\rho \cdot A_{R}^2}\:\cdot \:(1-R^2)+\Delta p_{loss}\]

where (10):

(10)#\[\Delta p_{loss}\:=\:\frac{K}{2\:\cdot \:\bar\rho\:\cdot \:A_{R}^2}\:\cdot \:\dot m_{A}\:\cdot \:\sqrt{\dot m_{A}^2+ \dot m_{th}^2}\]

Law of Conservation of Mass (11):

(11)#\[\dot m_A+\dot m_B=0\]

Law of conservation of energy (12):

(12)#\[\phi_A+\phi_B=0\]

where:

\(\phi_A\) - energy flow at the input, [W];

\(\phi_B\) - energy flow at the output, [W].

1. Properties#

Property	Default Value	Description	Units of measurement
Calculation method: Empirical; Table	Empirical	-	-
Contraction loss coefficient, available when selecting `Calculation method` - `Empirical`	1.0	-	-
Expansion loss coefficient, available when selecting `Calculation method` - `Empirical`	1.0	-	-
Critical Reynolds number, available when selecting `Calculation method` - `Empirical`	150.0	The Reynolds number at which the transition from laminar to turbulent flow occurs	-
Angle, available when selecting `Calculation method` - `Empirical`	30.0	-	deg
Bigger area (port A)	0.02	-	m\(^2\)
Smaller area (port B)	0.01	-	m\(^2\)
Reynolds numbers vector, available when selecting `Calculation method` - `Table`	{10,20,30,40,50,100,200,500,1000,2000}	-	-
Contraction coefficient vector, available when selecting `Calculation method` - `Table`	{5,2.7,1.8,1.46,1.3,.9,.65,.42,.3,.2}	-	-
Expansion loss coefficient vector, available when selecting `Calculation method` - `Table`	{3.1,2.3,1.65,1.35,1.15,.9,.75,.65,.55,.45}	-	-

2. Inputs and outputs#

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

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