The free jet of a cooling lubricant nozzle

Liquid jets can be classified in the category of free jets. In the case of free jets, a distinction is made between laminar and turbulent free jets. The exit velocity of the cooling lubricant within the grinding technology is high. A resulting parameter of the high exit velocity is a Reynolds number greater than 2300. Therefore, cooling lubricant jets are always turbulent free jets. The turbulent free jet is a typical flow process of a nozzle. [1,2,3]

In addition to the turbulence of the free jet, a distinction is made between the type of flow phenomenon. Since the surrounding medium of a cooling lubricant nozzle is still air, the free jet can be classified in the group of free turbulence. Figure 1 shows the principle structure of a free jet with its characteristic areas. [1,2,3]


Figure 1: Schematic representation of a turbulent free jet and its characteristic regions [4].

The free jet divides into several areas depending on the distance and position relative to the nozzle outlet. The following areas are distinguished:

  • Primary fluid
  • Secondary fluid
  • Core
  • Mixing zone

The basic formation of a free jet can be divided into several points. First, the primary fluid (cooling lubricant) flows out of an opening into a secondary fluid (air) at a velocity c0.

The secondary fluid (air) is a stationary ambient medium without a sharp boundary surface. To be distinguished from this is wall turbulence where the environment is a fixed boundary without exchange. [1,2,3]

A relative motion occurs between the primary fluid and the stationary secondary fluid, since the two media have different velocities. The boundary surface is called the boundary layer. Friction between the boundary zone of the primary fluid and the boundary zone of the secondary fluid ensures that the secondary fluid is entrained. As a result, the boundary zone of the primary fluid mixes and becomes enriched with the secondary fluid. [1,2,3]

The core area is characterized by the fact that it consists of an undisturbed flow. With increasing distance to the outlet opening, the core area decreases in a conical shape. The influence of the secondary fluid increases with increasing distance from the outlet and mixes with the core area. The length of the core area has no fixed relationship to the outlet geometry, but depends to a large extent on the internal design of the nozzle. Immediately downstream of the nozzle exit, the velocity of the primary fluid is constant. [1,2,3]

In the mixing zone, or transition zone, the secondary fluid increasingly mixes with the primary fluid of the nozzle. The velocity decreases hyperbolically with increasing distance from the outlet opening in the x-direction (see Figure 2). The decrease in velocity is caused by the internal friction of the fluid mixture. [1,2,3]

In the y-direction of the free jet, a velocity profile is formed according to a Gaussian normal distribution. The edge zone of the free jet has zero velocity and thus equals the velocity of the secondary fluid. Throughout the free jet, the pressure is ambient. [1,2,3]

The radiation decay of a cooling lubricant nozzle

Immediately after the free jet flows out of the nozzle at a defined velocity, it begins to decay. The fluid decay depends on several factors. These include:

  • the internal shape of the nozzle
  • the material data of the fluid and the surrounding medium
  • the relative velocity between fluid and environmentdie innere Gestalt der Düse

These influencing variables determine the degree of atomization and thus the size distribution of the resulting droplets. In addition, the characteristic length of the core area is determined by these variables.

Mechanisms of disintegration of the cooling lubricant free jet

In the publication one distinguishes different decay mechanisms of the free beam.

These decay mechanisms have been experimentally recognized and defined. A distinction is made between the following:

  • Droplets (Rayleigh decay)
  • Decay
    - first wind induced region
    - second wind induced region
  • Atomization

The previously mentioned decay mechanisms are shown schematically (left) and experimentally (right) in Figure 2.

Figure 2: Types of radiation decay. On the left the schematic representation [5,7] and on the right experimentally determined.

Cooling lubricant jet droplets

The fluid cylinder exiting the nozzle is unstable and eventually leads to the pinching off of individual droplets due to axially symmetrical oscillations of the fluid surface. This decay mechanism is also called Rayleigh decay and occurs at very low flow velocities. The detached droplets are larger than the original jet diameter. The jet decay length Lz, i.e., the length relative to the nozzle exit from which the droplet detaches, is the longest of all decay mechanisms and decreases with increasing flow velocity. [5,6]

Waving of the cooling lubricant jet

First wind-induced area

If the flow velocity out of the nozzle is increased, the Rayleigh decay is accelerated by axially symmetrical oscillations. The droplets detach earlier from the fluid jet, resulting in smaller droplets of the size of the original jet diameter. Due to the earlier detachment of the droplets, the jet decay length Lz decreases. [5,6]


Second wind-induced area

If the flow velocity is increased further, the Rayleigh decay is amplified and with it the axially symmetric oscillations. This leads to droplets that are smaller than the original jet diameter. The jet decay length Lz shifts further toward the nozzle exit. [5,6]

Atomization of the cooling lubricant jet

The droplet separation starts immediately after leaving the nozzle outlet. A spray of small droplets is formed. The size of the droplet size distribution varies greatly and is much smaller than the original jet diameter. Depending on the nozzle geometry, there may be a core area of free jet. [5,6]


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[1] Oertel jr., Herbert (Hrsg.): Prandtl - Führer durch die Strömungslehre: Grundlagen und Phänomene, 14. Aufl. 2017, Wiesbaden, s.l., Springer Fachmedien Wiesbaden, 2017 (Springer Reference Technik).
[2] Schlichting, Hermann; Gersten, Klaus; Krause, Egon: Grenzschicht-Theorie: Mit 22 Tabellen, 10., überarbeitete Auflage, Berlin, Heidelberg, Springer-Verlag Berlin Heidelberg, 2006.
[3] Glazik, Günter; Kraatz, Willi; Kranawettreiser, Jörg; Martin, Helmut; Wagner, Harold: Technische Hydromechanik, 2., vollständig überarbeitete Auflage, Aigner, Detlef (Hrsg.); Carstensen, Dirk (Hrsg.), Berlin, Wien, Zürich, Beuth Verlag GmbH, 2015.
[4] Kümmel, Wolfgang, Technische Strömumgsmechanik, Theorie und Praxis, B.G. Teubner Verlag / GWV Fachverlage GmbH, Wiesbaden 2007.
[5] Pfeifer, Christian: Experimentelle Untersuchungen von Einflußfaktoren auf die Selbstzündung von gasförmigen und flüssigen Brennstofffreistrahlen. Zugl.: Karlsruhe, Inst. für Technologie, Diss., 2010, Karlsruhe, KIT Scientific Publ, 2010 (KIT scientific reports 7555).
[6] Gesellschaft Verfahrenstechnik und Chemieingenieurwesen: VDI-Wärmeatlas: Mit 320 Tabellen, 11., bearb. und erw. Aufl., Berlin, Springer Vieweg, 2013.
[7] Geilert, P.; Kolkwitz, B.; Eckebrecht, J.; Heinzel, C.: Einfluss der Kühlschmierstoffzufuhrbedingung auf die Energieeffizienz und die Leistungsfähigkeit von Schleifprozessen, 2016.

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