Area Change (P)#

block — Block appearance in REPEAT VISION#

The Area Change (P) unit simulates changes in energy and pressure of the fluid as it passes the corresponding element of the pneumatic system.

When liquid moves from the inlet port to the outlet port, the cross-sectional area narrows, and when the liquid moves back, it expands. The cross-sectional areas can be set equal.

With reverse Area Change (P) unit operates as a confuser - liquid flow in the forward direction is from a port with a smaller cross-sectional area to a larger one.

Loss factors can be set empirically or in a tabular manner.

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

For expansion 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 expansion (3):

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

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 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 smallest of two sections, [m\(^2\)];

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

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

Mass conservation law (11):

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

Energy conservation law (12):

(12)#\[\phi_А+\phi_В=0\]

where:

\(\phi_А\) - input energy flow, [W];

\(\phi_В\) - output energy flow, [W].

1. Properties#

Property	Default value	Description	Units of measurement
Calculation method: Emperical; Table	Emperical	-	-
Contraction loss coefficient, available when `Calculation method` - `Emperical`	1.0	-	-
Expansion loss coefficient, available when `Calculation method` - `Emperical`	1.0	-	-
Angle, available when `Calculation method` - `Emperical`	30.0	-	deg
Bigger area (port A)	0.02	-	m\(^2\)
Smaller area (port B)	0.01	-	m\(^2\)
Reynolds numbers vector, available when `Calculation method` - `Table`	{10,20,30,40,50,100,200,500,1000,2000}	-	-
Contraction coefficient vector, available when `Calculation method` - `Table`	{5.0,2.7,1.8,1.46,1.3,0.9,0.65,0.42,0.3,0.2}	-	-
Expansion loss coefficient vector, available when `Calculation method` - `Table`	{3.1,2.3,1.65,1.35,1.15,0.9,0.75,0.65,0.55,0.45}	-	-
Laminar flow pressure ratio	0.999	-	-

2. Inputs and outputs#

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

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