.ThermofluidStream.Processes.Pipes.BaseClasses.PressureLoss.Diffuser.dp_conicalDiffuserOverall_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 conical diffuser as f(m_flow, F_0, F_1, alpha, Delta, rho,mu) where:

• m_flow: mass flow rate [kg/s]
• F_0: cross sectional of narrow section [m^2]
• F_1: cross sectional of wide section [m^2]
• alpha: central divergence angle [rad]
• Delta: relative wall roughness [-]
• rho: density [kg/m^3]
• mu: dynamic viscosity [Pa.s]

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

dp = rho/2 * zeta_dif * c_0^2

with the total pressure loss coefficient of the diffuser zeta_dif:

zeta_dif = k_1* zeta_exp + zeta_fr

• k_1 = 1 coefficient characterizing the state of the boundary layer (uniform velocity profil k_1 = 1)

The local resistance due to diffuser enlargement zeta_exp is diveded in 2 regions and a transition region blending both forumlas using a cubic hermite spline. In the first region (alpha < 40°) the function provided by Idelchik is used:

zeta_exp = k_2 * tan(alpha/2) * (tan(alpha/2))^1/4 * (1 - n_0)^2

• k_2 = 3.2 coefficient characterizing the shape of the diffuser cross section (circular k_2 = 3.2)
• n_0 = F_0/F_1 area ratio of diffuser

In the second region (60 < alpha < 180) a 2nd degree polynomial is fitted to the data given by Idelchik.

zeta_exp = p_1 * alpha^2 + p_2 * alpha + p_3

where the polynomial coefficients a described as functions of n_0:

p_1 = 0.0001116 * n_0^3 - 0.0001112 * n_0^2 + 1.931e-6 + n_0 + 5.91e-6 n_0
p_2 = -0.0292 * n_0^3 + 0.02792 * n_0^2 - 0.002995 * n_0 - 0.002489
p_3 = 1.012 * n_0^2 - 2.428 * n_0 + 1.29

The following figure Fig.1, the data and fitted polynomial coefficients are shown. (Currently not yet available)

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

Interface

function dp_conicalDiffuserOverall_DP
  extends Modelica.Icons.Function;
  import c_spline = ThermofluidStream.Processes.Pipes.Internal.Utilities.cubicHermite;
  input SI.MassFlowRate m_flow "Mass flow rate";
  input SI.Area A_0 "Inlet area";
  input SI.Area A_1 "Outlet area";
  input SI.Angle alpha "Central divergence angle";
  input SI.Length Delta(min = 0) "Relative roughness of diffuser walls";
  input SI.Density rho "Density";
  input SI.DynamicViscosity mu "Dynamic viscosity";
  output SI.Pressure dp "Pressure loss (>0)";
  output Internal.Types.PressureLossCoefficient zeta_dif "Pressure loss coefficient of diffuser";
  output Internal.Types.PressureLossCoefficient zeta_exp "Pressure loss coefficient due to diffuser enlargement";
  output Internal.Types.PressureLossCoefficient zeta_fr "Pressure loss coefficient due to wall friciton";
  output Real alpha_deg = alpha*180/pi "Central divergence angle (in degree)";
end dp_conicalDiffuserOverall_DP;