Turbulence, entrainment and low-order description of a transitional variable-density jet

Abstract

Geophysical flows occur over a large range of scales, with Reynolds numbers and Richardson numbers varying over several orders of magnitude. For this study, jets of different densities were ejected vertically into a large ambient region, considering conditions relevant to some geophysical phenomena. Using particle image velocimetry, the velocity fields were measured for three different gases exhausting into air – specifically helium, air and argon. Measurements focused on both the jet core and the entrained ambient. Experiments considered relatively low Reynolds numbers from approximately 1500 to 10 000 with Richardson numbers near 0.001 in magnitude. These included a variety of flow responses, notably a nearly laminar jet, turbulent jets and a transitioning jet in between. Several features were studied, including the jet development, the local entrainment ratio, the turbulent Reynolds stresses and the eddy strength. Compared to a fully turbulent jet, the transitioning jet showed up to 50 % higher local entrainment and more significant turbulent fluctuations. For this condition, the eddies were non-axisymmetric and larger than the exit radius. For turbulent jets, the eddies were initially smaller and axisymmetric while growing with the shear layer. At lower turbulent Reynolds number, the turbulent stresses were more than 50 % higher than at higher turbulent Reynolds number. In either case, the low-density jet developed faster than a comparable non-buoyant jet. Quadrant analysis and proper orthogonal decomposition were also utilized for insight into the entrainment of the jet, as well as to assess the energy distribution with respect to the number of eigenmodes. Reynolds shear stresses were dominant in Q1 and Q3 and exhibited negligible contributions from the remaining two quadrants. Both analysis techniques showed that the development of stresses downstream was dependent on the Reynolds number while the spanwise location of the stresses depended on the Richardson number.

Entrainment and its implications on microclimate ventilation systems: Scaling the velocity and temperature field of a round free jet

“…This can be related to findings by Ricou and Spalding who reported that entrainment rate in near exit positions was higher for Re <10 4 . Likewise, Viggiano et al found that turbulent jets at lower Reynold numbers exhibit higher entrainment and velocity fluctuations than experienced at Re >8000 due to smaller eddies that develop along with the shear layer.…”

“…The common method of determining entrainment flow is applying the integral solution (Equation 1) of streamwise velocity profiles at various downstream distances . The entrainment flow rate ( Q e ) up to a point x downstream can be determined by the relationship.…”

“…There are other methods that involve velocity measurements, like the quadrant analysis method that fragment fluctuating velocity components into four events to determine entrainment. This method is outside the scope of this paper but details for interested readers can be found in Wallace and Viggiano et al…”

Schlieren Flow Visualization and Analysis of Synthetic Jets

“…Year Frequency Jet Type Study Type (Hz) Kercher et al [6] 2003 1-1000 synthetic Travnicek and Tesar [8] 2003 106-692 synthetic smoke Smith and Swift [1] 2003 synthetic and Schlieren continuous Pavlova et al [9] 2006 420-1200 synthetic Arik [10] 2008 4500 synthetic Chaudhari et al [11] 2009 100-350 synthetic Bazdidi-Tehrani et al [12] 2011 16-400 synthetic Biden et al [13] 2012 unforced jet POD in crossflow Biden et al [14] 2012 forced jet POD in crossflow Ghaffari et al [15] 2016 20,000 ultrasonic microblower Ghadi et al [16] 2016 pulsed smoke impinging jet Albright and Solovitz [17] 2016 variable-diameter synthetic jet Firdaus et al [18] 2018 300-700 synthetic Solovitz et al [19] 2018 350-2000 synthetic PIV Viggiano et al [20] 2018 variable-density POD and PIV jet Kristo et al [21] 2021 crossflow jets POD and PIV Present work 2021 20-100 synthetic POD, smoke, Schlieren Pavlova et al [9] found that high-frequency jets removed heat more effectively, but that lower-frequency jets were better for larger separation distances. Many authors found that the optimal frequency for heat transfer was the resonance frequency for the device or the diaphragm [11,18,19].…”

Quantification of Preferential Contribution of Reynolds Shear Stresses and Flux of Mean Kinetic Energy Via Conditional Sampling in a Wind Turbine Array

“…Conditional sampling technique has been applied to particle image velocimetry (PIV) data for a number of different applications. Examples include the spatial mapping of flow events in conjunction with proper orthogonal decomposition [6,7], the study of similarity of Reynolds stress profiles in turbulent boundary layers over rough walls [8][9][10], Blowing-snow transport [11], air-sea interaction aerodynamics [12], and characterization of flow over plant canopies by means of quadrant hole analysis [13]. Longo and Losada [14] used quadrant analysis on PIV data to study the structure of the boundary layer at the air-water interface of wind induced water waves.…”