.ThermofluidStream.Processes.Pipes.BaseClasses.PressureLoss.Junction.dp_JunctionWyeType2_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 II (Fig. 1, currently not yet available) as f(F_c, F_b, w_c, w_b, w_s, alpha, rho, k, K_b, K_s), 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 [-]
• K_b: free term correction of area ratio dependency at branch [-]
• K_s: free term correction of area ratio dependency at straight channel [-]

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:

case 1 (alpha <= 60°): zeta_cb = 1 + w_relbc^2 - 2*F_relcs*(1 - Q_relbc)^2 - k * F_relcb*(Q_relbc)^2 + K_b

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

and with free term correction K_b as f(alpha, F_relbc). Since there are few data points a defining a approximation formula is not useful, table interpolation is used instead. As shown K_b is a function of 2 variables a 2-dimensional tables is used. Furthermore the table is using vector in- and output as this data is requierd for interpolation at region 60<alpha<90. The interpolation is done by linear segments since "CombiTable2Dv" does not perform cubic spline interpolation.

For case 2 (alpha = 90°): zeta_cb = 1 + w_relbc^2 - 2*F_relcs*(1 - Q_relbc)^2 + K_b

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 + F_relcs^2 * (1-Q_relbc)^2 - k * F_relcb * Q_relbc^2 + K_s, where k is the same coefficient discribed above and K_s the free term correction of the area ratio. As befor K_s is implemented using table interpolation of 2-dimensional table and vector in- and output.

case 2 (alpha = 90°): Since Idel'chik does not provied a approximation formula for alpha = 90° an approximation of the given date has to be definied. Because there is only a small amount of data available, the approximation shuold be understood as an estimate, especially for small area ratios: zeta_cs = A * [1 + F_relcs^2 * (1 - Q_relbc)^2 - 2 * B * F_relcs * (1 - Q_relbc)^2 - F_rel_cb * Q_relbc^2] + K_s with the coefficients A and B approximated with the formulas:

A = 0.242 * log(F_relbc) + 1.048
B = 3.02 * (Frelbc)^2 - 2.278 * F_relbc + 1.582

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 figure Fig.2 pressure loss coefficients of the branching channel and straight channel at alpha = 15° are shown. (Currently not yet available)

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

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

The following figure Fig.5 pressure loss coefficients of the branching channel and straight channel at alpha = 60° are shown. (Currently not yet available)

The following figure Fig.6 pressure loss coefficients of the branching channel and straight channel at alpha = 90° are shown. (Currently not yet available)

The following figures pressure loss coefficients of the branching channel Fig.7 and straight channel Fig.8 at alpha = 75° are shown. (Currently not yet available)

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

Interface

function dp_JunctionWyeType2_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.Area F_s "Cross sectional area of straight 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 K_s[3] "Free term correction for straight inlet";
  input Real K_b[3] "Free term correction for branching inlet";
  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. (common) outlet velocity";
  output ThermofluidStream.Processes.Pipes.Internal.Types.PressureLossCoefficient zeta_cs "Pressure loss coefficient of straight inlet w.r.t. (common) outlet velocity";
end dp_JunctionWyeType2_DP;