Nonisothermal jet

To characterize the relationship between the buoyancy forces and momentum flux in different cross-sections of a nonisothermal jet at some distance x, Grimitlyn proposed a local Archimedes number ... 

Introduction of the local Archimedes criterion helped to clarify nonisothermal jet design procedure. Grimitlyn suggested critical local Archimedes number values, Ar , below which a jet can be considered unaffected by buoyancy forces (moderate nonisothermal jet) Ar, 0.1 for a compact jet, Ar, < 0.15 for a linear jet. 

A Prandtl number of 0.7 has been suggested for nonisothermal jets by Not-tage fro Porstall and Shapiro,Corrsin and Uberoi, - and Grimitlyn. Abramovich suggested a Prandtl number for a compact jet of 0.75, and for a linear jet, 0.5. 

The centerline temperature differential within the zone of fully established turbulent flow (Zone 3) of a nonisothermal jet can be derived using equations of momentum (Eq. (7.39)) and excessive heat conservation along the jet <. S... 

For practical use the influence of buoyancy forces on temperature and velocity decay in vertical nonisothermal jets, as proposed by Grimitlyn, can be accounted for by the coefficient of nonisothermality. For compact jets,... 

The analytical method of jet trajectory study developed by Shepelev allows the derivation of several other useful features and is worth describing. On the schematic of a nonisothermal jet supplied at some angle to the horizon (Fig. 7.25), 5 is the jet s axis, X is the horizontal axis, and Z is the vertical axis. The ordinate of the trajectory of this jet can be described as z = xtga a- Az, where Az is the jet s rise due to buoyancy forces. To evaluate Az, the elementary volume dW with a mass equal to dm dV on the jet s trajectory was considered. The buoyancy force influencing this volume can be described as dP — g(p -Pj). Vertical acceleration of the volume under the consideration is j — dP / dm — -p,)/ g T,-T / T. Vertical... 

The ratio to z depends only on (gag-, zjx, = 2/3 tga.g, and the ratio of x, /Xq has a constant value equal to 0.578. To clarify the trajectory equation of inclined jets for the cases of air supply through different types of nozzles and grills, a series of experiments were conducted. The trajectory coordinates were defined as the points where the mean values of the temperatures and velocities reached their maximum in the vertical cross-sections of the jet. It is important to mention that, in such experiments, one meets with a number of problems, such as deformation of temperature and velocity profiles and fluctuation of the air jet trajectory, which reduce the accuracy in the results. The mean value of the coefficient E obtained from experimental data (Fig. 7.25) is 0.47 0.06. Thus the trajectory of the nonisothermal jet supplied through different types of outlets can be calculated from... 

FIGURE 7.47 Nonisothermal jet trajectory in a room. Reproduced from Regescheit. 

The current Archimedes number for the resulting jet grows along the jet as it does in any nonisothermal jet. However, the consequent momentum additions by directing jets increases the inertial forces in rhe resulting jet and thus at a certain cros.s-section the current Archimedes number falls. The number of directing jets after which Ar reaches the peak can be calculated using... 

Nosovitsky,. 4., and V. Posokhin. 1966. Inclined fountains of heated and chilled air, created by nonisothermal jet.s supply. In Heat, Gas Supply and Ventilation. Budivelnik, Kiev. 

Isothermal jets are not influenced much by small changes in flow rate the size of the influence can be seen from the different equations. Nonisothermal jets could be changed substantially by small differences in both outlet velocity (flow rate) and/or temperature. 

The theoretical analysis could also be valid for nonisothermal jets assuming that the buoyancy is negligible. Grimitlyn, as reported by Hagstrom, suggests a local Archimedes number defined as ... 

According to Abramovich,Regenscheit, " and Shepelev, the relation between the velocity distribution and the temperature distribution in the cross-section of nonisothermal compact, linear, or radial jets within Zone 3 can be expressed as... 

Buoyancy forces influence the trajectory of horizontally projected air jets or air jets supplied at some angle to the horizontal plane (Fig. 7.24). Most nonisothermal air jet studies were devoted to horizontally projected compact air jets. Based on the analytical studies, 42,77-80 trajectory axis of inclined jets can be described by a polynomial function... 

As was shown by Zhivov, the main difference in most of the equations for the jet trajectory is the value of the coefficient i)i. The differences in experimental data obtained by different authors are mainly due to the difficulties in the measurements of nonisothermal air jets supplied with low initial velocities (2-10 m/s). There is also a different understanding of the term air jet trajectory. Some authors mean the points with maximum velocity values, while others mean the centers of gravity of the cross-sections of the jet. 

Other experimental and analytical studies of nonisothermal inclined jets in confined spaces were carried out by Zhivov. Experimental studies were conducted on the physical models. The ratio of the model dimensions L x B x H was changed so that the value H/B was from 0.3 to 3.0 and L/ B xH) = 2.4-4.9. 

Studies of nonisothermal mam stream and horizontal directing jet mterac-non were conducted to evaluate the maximum heat load that can be eltectively supplied by such HVAC systems. To summarize experimental data both in free and confined conditions, it was suggested that the above limiting condition is achieved when the current Archimedes number Ar ratio of rhe buoyancy forces over ineiTia forces along the resulting jet axis) does not exceed s[Pg.502]

In the case of a nonisothermal directing jet, the above assumptions are true, except that the momentum vector component along the Y axis changes due to the buoyancy force ... 

Based on the above assumptions, the following equations were derived to calculate the velocity and temperature decay along the nonisothermal directing jet ... 

Fully developed nonisothermal flow may also be similar at different Reynolds numbers, Prandtl numbers, and Schmidt numbers. The Archimedes number will, on the other hand, always be an important parameter. Figure 12.30 shows a number of model experiments performed in three geometrically identical models with the heights 0.53 m, 1.60 m, and 4.75 m." Sixteen experiments carried out in the rotxms at different Archimedes numbers and Reynolds numbers show that the general flow pattern (jet trajectory of a cold jet from a circular opening in the wall) is a function of the Archimedes number but independent of the Reynolds number. The characteristic length and velocity in Fig. 12.30 are defined as = 4WH/ 2W + IH) and u = where W is... 

Jet, nonisothermal An air jet of a different temperature from that of the space it is entering. 

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