Orifice (TL)#

The Orifice (TL) block models flow through a local restriction with a constant orifice area. The orifice area is parameterized either linearly or using a lookup table.

The block conserves mass such that (1):

(1)#\[ \dot m_{A}\:+\:\dot m_{B}\:=\:\rho\:\cdot\:\nu_{A}\:\cdot\:A_{A}\:+\: \rho\:\cdot\:\nu_{B}\:\cdot\:A_{B}\:=\:0 \]

This mass balance implies that velocity increases as the area decreases and decreases when the flow discharges into a larger area. According to Bernoulli’s principle, this velocity change results in a region of lower pressure in the orifice and higher pressure in the expansion zone. The resulting pressure increase, referred to as pressure recovery, depends on the pressure recovery loss coefficient and the ratio of the orifice area to the port area.

Mass Flow Calculation

The block calculates mass flow as (2):

(2)#\[ \dot m\:=\:\frac{C_{d}\:\cdot A_{orifice}\:\cdot \:\sqrt{2\:\cdot \:\bar\rho}}{\sqrt{PR_{loss}\:\cdot \:(1-(\frac{A_{orifice}}{A_{port}})^2)}}\:\cdot \:\sqrt{p_{A}-p_{B}}\:\approx\:\frac{C_{d}\cdot A_{orifice}\cdot \:\sqrt{2\cdot \:\rho}}{\sqrt{PR_{loss}\cdot (1-(\frac{A_{orifice}}{A_{port}})^2)}}\cdot \:\frac{p_{A}-p_{B}}{[(p_{A}-p_{B})^2+\:\Delta p_{crit}]^{1/4}} \]

where:

\(C_d\) – discharge coefficient;

\(A_{orifice}\) – orifice area, [m\(^2\)];

\(A_{port}\) — cross-sectional area of ports A and B, [m\(^2\)];

\(\barρ\) – average fluid density, [kg/m\(^3\)].

Pressure Loss

Pressure loss describes the pressure drop in the valve due to the area reduction. The pressure loss, PRloss, is calculated as (3):

(3)#\[ PR_{loss}\:=\:\frac{\sqrt{1-(\frac{A_{orifice}}{A_{port}})^2\cdot (1-C_{d}^2)}-C_{d}\cdot \:\frac{A_{orifice}}{A_{port}}}{\sqrt{1-(\frac{A_{orifice}}{A_{port}})^2\cdot (1-C_{d}^2)}+C_{d}\cdot \:\frac{A_{orifice}}{A_{port}}} \]

Critical Pressure

The critical pressure drop, \(Δp_{crit}\), is the pressure drop associated with the critical Reynolds number, Re\(_{crit}\), which marks the transition between laminar and turbulent flow in the fluid (4):

(4)#\[ \Delta p_{crit}\:=\:\frac{\Pi\:\cdot \:\bar\rho}{8\cdot A_{orifice}}\cdot \:(\frac{\nu\:\cdot Re_{crit}}{C_{d}})^2 \]

Law of conservation of energy (5):

(5)#\[ {\phi}_{A}+{\phi}_{B}=0 \]

1. Procedure for using variable orifice area in the block#

The Orifice (TL) block allows the use of variable orifice area values.

The change in area is controlled by an automation signal (in this scheme from block №14) within the range [0 to 1]. A value of 0 corresponds to the first value in the orifice area vector, while a value of 1 corresponds to the last. Intermediate values are interpolated according to a piecewise function defined by the vector .

Example of a hydraulic orifice with adjustable area:#

2. Properties#

Property	Default Value	Description	Units of measurement
Orifice type: Variable; Constant	Variable	-	-
Port area	0.001	-	m\(^2\)
Orifice area, available when selecting `Orifice type` - `Constant`	1.0E-4	-	m\(^2\)
Orifice area vector, available when selecting `Orifice type` - `Variable`	{1.0E-9; 2.0352E-7; 4.0736E-5; 1.1438E-4; 3.4356E-4;}	-	-
Discharge coefficient	0.64	-	-
Critical Reynolds number	150.0	-	-

3. Inputs and outputs#

Parameters	Input/Output	Description	Units of measurement	Port type
Spool displacement	Input	Available, when `Orifice type` - `Variable`	m	Automation
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