Confusor / Area Change (IH)#

block — Block appearance in REPEAT VISION#

The Confusor / Area Change (IH) unit describes the appropriate types of local resistance in the isothermal liquid piping.

For a Confuser, as fluid moves from the inlet to the outlet, the cross-sectional area of the flow narrows and the velocity of the fluid increases; when moving back, it expands; for a Diffuser, it’s vice versa.

Hint

The cross-sectional area can be specified by conditions - in this case the block will operate as a local resistance of constant diameter.

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

If calculated based on empirical data:

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

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

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

For compression from 45 to 180 degrees (not inclusive) (2):

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

For 180-degree compression (3):

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

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

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

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

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

In the case of calculations using tabular data, the vectors of loss coefficients during compression and expansion are assigned to the vector of Reynolds numbers. All three vectors are specified by the user as model parameters.
The total hydraulic loss factor for the diffuser pipe section 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 on the entry port, [kg/s];

\(\dot m_{th}\) - threshold mass flow, [kg/s], at which a change in the direction of movement of the liquid occurs, associated with a critical Reynolds (7):number:

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

where:

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

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

\(\bar ρ\) - liquid density, [kg/m\(^3\)];

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

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

The pressure differential across the diffuser pipe section 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)#\[\Delta p_{loss}\:=\:\frac{K}{2\:\cdot \:\bar \rho\:\cdot \:A_{R}^2}\:\cdot \:\dot m_{A}\:\cdot \:\sqrt{\dot m_{A}^2+ \dot m_{th}^2}\]

1. Properties#

Property	Default value	Description	Units of measurement
Coefficient calc method: Empirical; Table	Empirical	-	-
Contraction loss coefficient, available when `Coefficient calc method` - `Empirical`	1.0	-	-
Expansion loss coefficient, available when `Coefficient calc method` - `Empirical`	1.0	-	-
Critical Reynolds number, available when `Coefficient calc method` - `Empirical`	150.0	The Reynolds number at which the transition from laminar to turbulent flow occurs	-
Angle, available when `Coefficient calc method` - `Empirical`	30.0	-	degrees
Bigger area (port A)	0.02	-	m\(^2\)
Smaller area (port B)	0.01	-	m\(^2\)
Reynolds number Vector, available when `Coefficient calc method` - `Table`	{10,20,30,40,50,100,200,500,1000,2000}	-	-
Contraction loss coefficient vector, available when `Coefficient calc method` - `Table`	{5,2.7,1.8,1.46,1.3,.9,.65,.42,.3,.2}	-	-
Expansion loss coefficient vector, available when `Coefficient calc 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	-	-	Isothermal hydraulics
Output	Output	-	-	Isothermal hydraulics

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