Orifice Element

Orifice General Description

Orifice element provides a way of modelling a pressure loss between two chambers within a system, where the only purpose of the element is to model a flow restriction with losses within the system (for example a simple aperture, coolers, strainers, fittings, leakages or sudden changes in cross-section). The orifice may be fixed in space or rotating about the engine centerline and each may be positioned at any angle relative to the coordinate system. Orifice elements uses an input of Orifice mechanical Area/Diameter & Loss parameters with a standard isentropic flow relationship to calculate the element flow rates. Loss Parameter can be Cd (Coefficient of discharge) or Incompressible Loss Coefficient (K). This element does not model any fluid inertia.

Quick Guide for Orifice Element Creation in the GUI

There are different subtypes of Orifices elements available in FlowSimulator. All the orifice elements can be used in Compressible (e.g. gas systems) and Incompressible (e.g. hydraulic and non-hydraulic systems) analysis. The various subtypes are

Conventional Orifice

Conventional orifice is a standard orifice element where you need to provide mandatory inputs Cross sectional Area or Diameter and CD or K value. User can convert the conventional orifice to Nozzle by providing the Nozzle efficiency. Cd (discharge coefficient) for an Orifice element can be between any value between 0+ and 1.0 as input. The Users can also provide Incompressible Loss coefficient (K) as input. Allowable Kloss Values are from 0 to 10. The discharge coefficient is calculated by the incompressible relationship,

Heater Cooler

Heater Cooler is same as Conventional Orifice, but a specific subtype is created for the ease of distinction if the users need to model Flow Restrictions with Heat Addition/Removal across the restriction. All the mandate inputs remain same as like Convention orifice (Area, Loss Coefficient) along with Heat Addition mode & its required inputs. There are 4 different heat mode users can apply, they are

1. Heat Addition: Specify Heat Input, (+) Input models Heat Addition & (-) Input model Heat Removal
2. Heat Addition per Mass Flow: Specify Heat Input per Mass Flow.
3. Fluid Delta Tt: Specify Delta Total temperature rise across orifice. (+) Input models Heat Addition & (-) Input model Heat Removal
4. Fixed Fluid Tt Exit: Specify Exit Temperature of the orifice

Discrete Loss

Discreet Loss is another subtype of Conventional orifice & users will have an additional option to specify Delta Total pressure loss (Pt1-Pt2) across the restrictions directly to model restriction losses in addition to Loss Parameters option (Cd or K). Mandatory inputs Cross sectional Area or Diameter and CD or K or Delta.P (Pt1-Pt2) value. Cd (discharge coefficient) for a Discrete loss element can be between any value between 0+ and 1.0 as input. There is no input restriction on upper limit of Kloss Values for discrete loss element.

Swirl Carryover Orifice

The tangential velocity calculation for the swirl carryover orifice element is the only difference from the conventional orifice. The swirl carryover is a fraction of upstream tangential velocity that is carried over to the downstream.

Orifice Element Inputs

Table of the inputs for the Orifice Element.

Orifice Theory Manual

The isentropic flow function written to define the flow through an orifice restriction in terms of upstream total pressure, upstream total temperature, downstream static pressure and cross-sectional flow area. Since the flow function is derived with the assumption of isentropic flow, some sort of empirical correction is required to account for the irreversible losses encountered in the Orifices. This is usually contained in form of a discharge coefficient or Loss coefficient, included in the working definition of flow function and represents the ratio of actual (empirical) to ideal (isentropic) flow rates.

Calculation of Flow Rate and Vena Contracta Mach Number

Conventional Orifice, Heater Cooler & Discrete Loss:

For Compressible Flow Equation:

The element flow is then calculated using theequation:

For Incompressible Flow Equation:

Calculation of Orifice Exit Conditions

The flow is first expanded from the vena contracta throat to the exit conditions before any effect of heat addition, QIN, is considered. it is assumed that the flow is expanded adiabatically (limited to Mach number = 1.0) to the mechanical area of the orifice at the exit static pressure, . The static pressure exit flow parameter, exit Mach number and adiabatic exit velocity is calculated as:

The effect of heat addition specified as QIN is added next, assuming that only the exit temperature and velocity, and not the exit Mach number, are affected. The temperature rise (or drop if QIN is negative) is calculated using an average value of specific heat (Cp)

Cp_avg: Specific heat at the average of TTS and TEX, pressure PSEX, and secondary fluid mass fraction FS(IC)

A new exit velocity is next calculated as:

If 0 values are input for each of the exit head loss variables (KEZ, KEU and KER), the element exit velocity, VEX, is set to VX, and the relative radial and tangential flow angles at the exit plane (THTA and PH) are taken to be the values specified for the input variables THTELX and PHIELX respectively. If any of these exit head loss variables are input as non-zero values, the exit velocity components are recomputed as:

Swirl Carryover Orifice Element Tangential Velocity

For long holes (L/D > 1) the swirl carryover is low (often near 0). This means the swirl from upstream of the restriction does not affect the swirl exiting the restriction (the rotation of the hole itself is what determines the swirl exiting the restriction).

Additional Momentum Loss

For Additional Momentum loss, Portion of Upstream Dynamic Head loss, Exit K Loss refer Solver General theory section.

Orifice Element Outputs

The following listing provides details about conventional orifice output variables.