Nozzle Theory
The Nozzle feature is used to release a spray of liquid droplets, as if they were released from a nozzle. It computes the initial size and velocity of the released droplets using the so-called Blob model (Ref. 31). This model requires the following assumptions:
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The inlet is circular and produces a round liquid jet of density ρp (SI unit: kg/m3).
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The gas in the adjacent domain is incompressible and initially quiescent, vg,0 = 0.
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The liquid velocity vl (SI unit: m/s) is constant inside the jet.
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Both the injection pressure pinj (SI unit: Pa) and the ambient pressure pamb (SI unit: Pa) are constant.
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The initial parent drop radius is constant and equal to the injector radius r0 (SI unit: m).
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The maximum cone angle Θ (SI unit: rad) is constant and stays constant as the injection progresses.
The following discussion uses several dimensionless variables. Their definitions are listed in Table 5-3 in the Droplet Breakup Theory section.
The initial speed of the released droplets is
where cd (dimensionless) is the discharge coefficient and (SI unit: kg/s) is the mass flow rate.
The droplets are released in a cone with maximum spray angle Θ. The spray angle can be specified directly, or it can be estimated from Kelvin–Helmholtz instability theory:
where Λ (SI unit: m) and Ω (SI unit: 1/s) are, respectively, the wavelength and growth rate of the fastest-growing disturbance on the surface of a liquid jet:
The number multiplication factor n, activated by the Enable macroparticles check box in the physics interface Additional Variables section, is a dimensionless quantity that indicates the number of droplets that are represented by each model particle.
Suppose the range of specified release times is , where Nt is the number of release times.
The droplets that are released at time ti are assigned initial multiplication factor ni:
where N0 is the number of model particles per release and the time intervals Δti are defined as
where N is the number of release times. Note that, based on the previous expressions,
where Np = N × N0 is the total number of released model particles. That is, the sum of the masses of all released droplets, scaled by their multiplication factors, equals the total mass released by the nozzle, assuming that the mass flow rate is constant between the initial and final release times and zero otherwise.