.ThermofluidStream.Processes.Pipes.BaseClasses.PressureLoss.Splitter.dp_SplitterWyeType2_DP

Information

The implementation of the function is based on "Handbook of Hydraulic Resistance" in its first translated Version from 1960! The book has been republished in several updated versions since then!

Function calculating the pressure loss of a Y-shaped splitter of type II (Fig. 1) as f(w_c,w_b,w_s, alpha, rho, k, K'_b). (Currently not yet available)

• w_c: velocity at common channel [m/s]
• w_b: velocity at branching channel [m/s]
• w_s: velocity at straight channel [m/s]
• alpha: branching angle [rad]
• rho: density [kg/m^3]
• k: scaling factor for area ratio dependency at alpha = 90° [-]
• K'_b: correction factor for branching angle dependency [-]

Calculation according to Idelchik (1960). The pressure loss is calculated as:

• in branch: dp_b = rho/2 * zeta_cb * w_c^2
• in straight channel: dp_s = rho/2 * zeta_cs * w_c^2

As you can see above both pressure loss calculation are with respect to the velocity at the common branch. The pressure loss coefficient of the branch zeta_cb is calculated as:

zeta_cb =1 + (w_relbc)^2 - 2*w_relbc *cos(alpha) - K'_b * (w_relbc)^2

Idel'chik provides table data for the coefficient K'_b. Since no sufficiently precise approximation equation can be defined for this factor, a table is also used for implementation. A cubic spline is used to interpolate between the control points. To control the limit behavior at table boundaries control points at alpha = 0° and alpha = 105° are added

Notice: In more recent editions Idelchik gives the same approximation formula, but the diagram and data sets show a limit value against which the friction coefficients of all angles converge. Adjustments using a C-spline have not yet been made. For calculation of the pressure loss coefficient of th straight channel zeta_cs there is no aproximation formula by Idel'chik. Therefore an own aproximation on basis of the data from Idel'chik has to be found. The given table data suggest a basis function, which is transformed into a set of curves by the scaling factor k taking the area ratio dependency at alpha = 90° into account.

A 4th order polynomial is selected as the basis function and fitted to the data set:

zeta_cs_base = 0.5345*w_relsc^4 - 1.124+w_relsc^3 + 1.73*w_relsc^2 - 2.146*w_relsc + 1.005

In order to obtain a set of curves. the basis function is expanded by the scaling factor k.

zeta_cs = k*0.5345*w_relsc^4 - k*1.124+w_relsc^3 + k*1.73*w_relsc^2 - 2.146*w_relsc + 1.005

As befor since no rational approximation has been found the scaling factor is implemented using a look-up table.

The following figure Fig.2, pressure loss coefficients of the branching channel are shown. (Currently not yet available)

[P. Jordan; HTWG Konstanz; 01/24]

Interface

function dp_SplitterWyeType2_DP
  extends Modelica.Icons.Function;
  input SI.Velocity w_c "Splitter inlet velocity";
  input SI.Velocity w_b "Branching pipe velocity";
  input SI.Velocity w_s "Straight pipe velocity";
  input SI.Angle alpha "Branching angle";
  input SI.Density rho "Medium density";
  input Real k "Scaling factor for family of curves at alpha = 90°";
  input Real K_b_prime "Correction factor for branching angle alpha";
  input SI.Velocity eps "To avoid division by zero";
  output SI.Pressure dp_b "Pressure loss of branching pipe";
  output SI.Pressure dp_s "Pressure loss of straight pipe";
  output Internal.Types.PressureLossCoefficient zeta_cb "Pressure loss coefficient of branching pipe w.r.t. inlet velocity";
  output Internal.Types.PressureLossCoefficient zeta_cs "Pressure loss coefficient of straight pipe w.r.t. inlet velocity";
end dp_SplitterWyeType2_DP;