.ThermofluidStream.Processes.Pipes.BaseClasses.PressureLoss.Junction.dp_JunctionWyeType1_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 junction of type I (Fig. 1, currently not yet available) as f(F_c, F_b, w_c, w_b, w_s, alpha, rho, k, A), where:

• F_c: cross sectional area of common channel [m^2]
• F_b: cross sectional area of branch [m^2]
• 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: coefficient of branching angle dependency [-]
• A: coefficient of area ratio 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 for case 1 (alpha <= 60°) as: zeta_cb = 1 + w_relbc^2 - 2*(1-*Q_relbc)^2 * k * F_relcb*(Q_relbc)^2

• w_relbc = w_b/w_c: velocity ratio
• Q_relbc = Q_b/Q_c: volume flow ratio
• F_relbc = F_b/F_c area ratio

With coefficient k taking the branching angle depedency into account. k is approximated using a 3rd order polynomial:

k(alpha°) = -0.0001766 * alpha^2 - 0.007536 * alpha + 2.1043

For case 2 (alpha = 90°): zeta_cb = A * [A + w_relbc^2 - 2*(1 - Q_relbc)^2] = A * zeta'_cb, with coefficient A scaling zeta'_cb with respect to the given area ratio F_relbc. Since no rational approimation of A = f(F_relbc) has been found, the coefficient is implemented as a table with cubic spline interpolation between the control points.

For case 3 (60° < alpha <90°): Since there is no aproximation formula nor data available in this case zeta_cb is interpolated linear between the function of case 1 and 2. The pressure loss coefficient of the straight channel zeta_cs is calculated as:

• case 1 (alpha <= 60°): zeta_cs = 1 - (1 - Q_relbc)^2 - k * F_relbc * Q_relbc^2, where k is the same coefficient discribed above.
• case 2 (alpha = 90°): zeta_cs = 1.55 * Q_relbc - Q_relbc^2
• case 3 (60° < alpha <90°): As before linear interpolation between the function at alpha <= 60 and alpha = 90 is used to determine the pressure loss in case 3.

The following figures, pressure loss coefficients of the branching channel Fig.2 and straight channel Fig.3 at alpha = 30° are shown. (Currently not yet available)

The following figures pressure loss coefficients of the branching channel Fig.4 and straight channel Fig.5 at alpha = 45° are shown. (Currently not yet available)

The following figures pressure loss coefficients of the branching channel Fig.6 and straight channel Fig.7 at alpha = 60°are shown. (Currently not yet available)

The following figures pressure loss coefficients of the branching channel Fig.8 and straight channel Fig.9 at alpha = 90° are shown. (Currently not yet available)

The following figures pressure loss coefficients of the branching channel Fig.10 and straight channel Fig.11 at alpha = 75° are shown. (Currently not yet available)

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

Interface

function dp_JunctionWyeType1_DP
  extends Modelica.Icons.Function;
  import SMOOTH = ThermofluidStream.Processes.Pipes.Internal.Utilities.Stepsmoother;
  input SI.Area F_c "Cross-sectional area of (common) outlet";
  input SI.Area F_b "Cross-sectional area of branching inlet";
  input SI.Velocity w_c "Velocity at (common) outlet";
  input SI.Velocity w_b "Velocity at branching inlet";
  input SI.Velocity w_s "Velocity at straight inlet";
  input SI.Angle alpha_deg "Branching angle in degree";
  input Real A "Correction factor at alpha = 90°";
  input SI.Density rho_c "Density of fluid at (common) outlet";
  input SI.Velocity eps "To avoid division by zero";
  output SI.Pressure dp_b "Pressure loss at branching inlet";
  output SI.Pressure dp_s "Pressure loss at straight inlet";
  output ThermofluidStream.Processes.Pipes.Internal.Types.PressureLossCoefficient zeta_cb "Pressure loss coefficient of branching inlet w.r.t. outlet velocity";
  output ThermofluidStream.Processes.Pipes.Internal.Types.PressureLossCoefficient zeta_cs "Pressure loss coefficient of straight inlet w.r.t. outlet velocity";
end dp_JunctionWyeType1_DP;