functiondp_SplitterWyeType1_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 I (Fig. 1) as f(w_c,w_b,w_s, alpha, rho). (Currently not yet available)

where:

• 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]

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 = A' * zeta'_cb

• A': coefficient of velocity ratio w_b/w_c
• zeta_cb': uncorrected pressure loss coefficient

According to Idel'chik while w_relbc = w_b/w_c <= 0.8, A'= 1 and if w_relbc > 0.8 then A' = 0.8. Since the velocity ratio may change during simulations, the discontinuity in A' is circumvented by the stepsmoother function used in region 0.8 < w_relbc < 1.05.

The uncorrected pressure loss coefficient zeta'_cb is determined by the formula:

zeta'_cb = 1 + w_relbc^2 - 2*cos(alpha)

The pressure loss coefficient at the straight channel for all brnaching angles is described as:

zeta_cs = 0.4*(1-w_relsc)^2

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

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

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