Effects of Mean Flow Profiles on the Instability of a Low-Density Gas Jet Injected Into a High-Density Gas

The effects of the mean velocity profiles on the instability characteristics in the near-injector region of axisymmetric low-density gas jets injected vertically upwards into a high-density gas medium were investigated using linear inviscid stability analysis. The flow was assumed to be isothermal and locally parallel. Three velocity profiles, signifying different changes in the mean velocity in the shear layer, were used in the analysis. The effects of the inhomogeneous shear layer and the Froude number (signifying the effects of gravity) on the instability for each set of mean profiles were delineated. At a large Froude number (negligible gravity), a critical density ratio was found for the three profiles at which the jet became absolutely unstable. The critical density ratio for each velocity profile was increased as the Froude number was reduced. A critical Froude number was found for the three sets of profiles, below which the jet was absolutely unstable for all the density ratios less than unity, which demarcated the jet flow into the momentum-driven regime and the buoyancy-driven regime.

The structure of a highly decelerated axisymmetric turbulent boundary layer

10.1017/jfm.2021.845 ◽

2021 ◽

Vol 929 ◽

Author(s):

N. Agastya Balantrapu ◽

Christopher Hickling ◽

W. Nathan Alexander ◽

William Devenport

Keyword(s):

Boundary Layer ◽

Pressure Gradient ◽

Shear Layer ◽

Layer Thickness ◽

Boundary Layer Thickness ◽

Large Scale ◽

Convection Velocity ◽

Mean Flow ◽

Mean Velocity ◽

Experiments were performed over a body of revolution at a length-based Reynolds number of 1.9 million. While the lateral curvature parameters are moderate ( $\delta /r_s < 2, r_s^+>500$ , where $\delta$ is the boundary layer thickness and r s is the radius of curvature), the pressure gradient is increasingly adverse ( $\beta _{C} \in [5 \text {--} 18]$ where $\beta_{C}$ is Clauser’s pressure gradient parameter), representative of vehicle-relevant conditions. The mean flow in the outer regions of this fully attached boundary layer displays some properties of a free-shear layer, with the mean-velocity and turbulence intensity profiles attaining self-similarity with the ‘embedded shear layer’ scaling (Schatzman & Thomas, J. Fluid Mech., vol. 815, 2017, pp. 592–642). Spectral analysis of the streamwise turbulence revealed that, as the mean flow decelerates, the large-scale motions energize across the boundary layer, growing proportionally with the boundary layer thickness. When scaled with the shear layer parameters, the distribution of the energy in the low-frequency region is approximately self-similar, emphasizing the role of the embedded shear layer in the large-scale motions. The correlation structure of the boundary layer is discussed at length to supply information towards the development of turbulence and aeroacoustic models. One major finding is that the estimation of integral turbulence length scales from single-point measurements, via Taylor's hypothesis, requires significant corrections to the convection velocity in the inner 50 % of the boundary layer. The apparent convection velocity (estimated from the ratio of integral length scale to the time scale), is approximately 40 % greater than the local mean velocity, suggesting the turbulence is convected much faster than previously thought. Closer to the wall even higher corrections are required.

On the stability of an inviscid shear layer which is periodic in space and time

10.1017/s0022112067002538 ◽

1967 ◽

Vol 27 (4) ◽

pp. 657-689 ◽

Cited By ~ 137

Author(s):

R. E. Kelly

Keyword(s):

Growth Rate ◽

Shear Layer ◽

Finite Amplitude ◽

Periodic Component ◽

Periodic Flow ◽

Flow Profile ◽

Mean Flow ◽

Mean Velocity ◽

The Mean ◽

The Stability

In experiments concerning the instability of free shear layers, oscillations have been observed in the downstream flow which have a frequency exactly half that of the dominant oscillation closer to the origin of the layer. The present analysis indicates that the phenomenon is due to a secondary instability associated with the nearly periodic flow which arises from the finite-amplitude growth of the fundamental disturbance.At first, however, the stability of inviscid shear flows, consisting of a non-zero mean component, together with a component periodic in the direction of flow and with time, is investigated fairly generally. It is found that the periodic component can serve as a means by which waves with twice the wavelength of the periodic component can be reinforced. The dependence of the growth rate of the subharmonic wave upon the amplitude of the periodic component is found for the case when the mean flow profile is of the hyperbolic-tangent type. In order that the subharmonic growth rate may exceed that of the most unstable disturbance associated with the mean flow, the amplitude of the streamwise component of the periodic flow is required to be about 12 % of the mean velocity difference across the shear layer. This represents order-of-magnitude agreement with experiment.Other possibilities of interaction between disturbances and the periodic flow are discussed, and the concluding section contains a discussion of the interactions on the basis of the energy equation.

Experimental Study of Mean Flow Characteristics in the Near Field of Wedge-Shaped Swirling Jets

European Journal of Engineering Research and Science ◽

10.24018/ejers.2020.5.10.2176 ◽

2020 ◽

Vol 5 (10) ◽

pp. 1199-1203

Author(s):

Md. Mosharrof Hossain ◽

Muhammed Hasnain Kabir Nayeem ◽

Dr. Md Abu Taher Ali

Keyword(s):

Flow Field ◽

Near Field ◽

Flow Characteristics ◽

Velocity Profiles ◽

Mean Flow ◽

Mean Velocity ◽

Potential Core ◽

Swirling Jets ◽

The Mean ◽

Sinusoidal Flow

In this investigation experiment was carried out in 80 mm diameter swirling pipe jet, where swirl was generated by attaching wedge-shaped helixes in the pipe. All measurements were taken at Re 5.3e4. In the plain pipe jet the potential core was found to exist up to x/D=5 but in the swirling jet there was no existence of potential core. The mean velocity profiles were found to be influenced by the presence of wedge-shaped helixes in the pipe. The velocity profiles indicated the presence of sinusoidal flow field in the radial direction existed only in the near field of the jet. This flow field died out after x/D=3 and the existence of jet flow diminished after x/D=5.

Evolution and structure of sink-flow turbulent boundary layers

10.1017/s0022112000002597 ◽

2001 ◽

Vol 428 ◽

pp. 1-27 ◽

Cited By ~ 73

Author(s):

M. B. JONES ◽

IVAN MARUSIC ◽

A. E. PERRY

Keyword(s):

Boundary Layers ◽

Velocity Profiles ◽

Turbulent Boundary Layers ◽

Reynolds Stresses ◽

Mean Flow ◽

Mean Velocity ◽

Flow Measurements ◽

Law Of The Wall ◽

The Mean ◽

Logarithmic Law

An experimental and theoretical investigation of turbulent boundary layers developing in a sink-flow pressure gradient was undertaken. Three flow cases were studied, corresponding to different acceleration strengths. Mean-flow measurements were taken for all three cases, while Reynolds stresses and spectra measurements were made for two of the flow cases. In this study attention was focused on the evolution of the layers to an equilibrium turbulent state. All the layers were found to attain a state very close to precise equilibrium. This gave equilibrium sink flow data at higher Reynolds numbers than in previous experiments. The mean velocity profiles were found to collapse onto the conventional logarithmic law of the wall. However, for profiles measured with the Pitot tube, a slight ‘kick-up’ from the logarithmic law was observed near the buffer region, whereas the mean velocity profiles measured with a normal hot wire did not exhibit this deviation from the logarithmic law. As the layers approached equilibrium, the mean velocity profiles were found to approach the pure wall profile and for the highest level of acceleration Π was very close to zero, where Π is the Coles wake factor. This supports the proposition of Coles (1957), that the equilibrium sink flow corresponds to pure wall flow. Particular interest was also given to the evolutionary stages of the boundary layers, in order to test and further develop the closure hypothesis of Perry, Marusic & Li (1994). Improved quantitative agreement with the experimental results was found after slight modification of their original closure equation.

PIV Study of Separated and Reattached Open Channel Flow Over Surface Mounted Blocks

Journal of Fluids Engineering ◽

10.1115/1.2911677 ◽

2008 ◽

Vol 130 (6) ◽

Cited By ~ 22

Author(s):

Martin Agelinchaab ◽

Mark F. Tachie

Keyword(s):

Boundary Layer ◽

Shear Layer ◽

Channel Flow ◽

Open Channel ◽

Open Channel Flow ◽

Reynolds Stresses ◽

Mean Flow ◽

Mean Velocity ◽

High Background ◽

A particle image velocimetry is used to study the mean and turbulent fields of separated and redeveloping flow over square, rectangular, and semicircular blocks fixed to the bottom wall of an open channel. The open channel flow is characterized by high background turbulence level, and the ratio of the upstream boundary layer thickness to block height is considerably higher than in prior experiments. The variation of the Reynolds stresses along the dividing streamlines is discussed within the context of vortex stretching, longitudinal strain rate, and wall damping. It appears that wall damping is a more dominant mechanism in the vicinity of reattachment. In the recirculation and reattachment regions, profiles of the mean velocity, turbulent quantities, and transport terms are used to document the salient features of block geometry on the flow. The flow characteristics in these regions strongly depend on block geometry. Downstream of reattachment, a new shear layer is formed, and the redevelopment of the shear layer toward the upstream open channel boundary layer is studied using the boundary layer parameters and Reynolds stresses. The results show that the mean flow rapidly redeveloped so that the Clauser parameter recovered to its upstream value at 90 step heights downstream of reattachment. However, the rate of development close to reattachment strongly depends on block geometry.

Experimental investigation of turbulent shear flow with quadratic mean-velocity profiles

10.1017/s0022112076001316 ◽

1976 ◽

Vol 73 (1) ◽

pp. 165-188 ◽

Cited By ~ 7

Author(s):

H. K. Richards ◽

J. B. Morton

Keyword(s):

Flow Direction ◽

Correlation Coefficients ◽

Velocity Profiles ◽

Turbulent Shear ◽

Turbulent Shear Flow ◽

Reynolds Stresses ◽

Mean Flow ◽

Mean Velocity ◽

Quadratic Mean ◽

Three turbulent shear flows with quadratic mean-velocity profiles are generated by using an appropriately designed honeycomb and parallel-rod grids with adjustable rod spacing. The details of two of the flow fields, with quadratic mean-velocity profiles with constant positive mean-shear gradients ($\partial^2\overline{U}_1/\partial X^2_2 >0$), are obtained, and include, in the mean flow direction, the development and distribution of mean velocities, fluctuating velocities, Reynolds stresses, microscales, integral scales, energy spectra, shear correlation coefficients and two-point spatial velocity correlation coefficients. A third flow field is generated with a quadratic mean velocity profile with constant negative mean-shear gradient ($\partial^2\overline{U}_1/\partial X^2_2 < 0$), to investigate in the mean flow direction the effect of the change in sign on the resulting field. An open-return wind tunnel with a 2 × 2 × 20 ft test-section is used.

Assessment of Predictive Capabilities of Detached Eddy Simulation to Simulate Flow and Mass Transport Past Open Cavities

Journal of Fluids Engineering ◽

10.1115/1.2786529 ◽

2007 ◽

Vol 129 (11) ◽

pp. 1372-1383 ◽

Cited By ~ 45

Author(s):

Kyoungsik Chang ◽

George Constantinescu ◽

Seung-O Park

Keyword(s):

Reynolds Number ◽

Shear Layer ◽

Transport Model ◽

Detached Eddy Simulation ◽

Reynolds Stresses ◽

Mean Flow ◽

Mean Velocity ◽

Eddy Simulation ◽

Fine Mesh ◽

The three-dimensional (3D) incompressible flow past an open cavity in a channel is predicted using the Spalart–Almaras (SA) and the shear-stress-transport model (SST) based versions of detached eddy simulation (DES). The flow upstream of the cavity is fully turbulent. In the baseline case the length to depth (L∕D) ratio of the cavity is 2 and the Reynolds number ReD=3360. Unsteady RANS (URANS) is performed to better estimate the performance of DES using the same code and meshes employed in DES. The capabilities of DES and URANS to predict the mean flow, velocity spectra, Reynolds stresses, and the temporal decay of the mass of a passive contaminant introduced instantaneously inside the cavity are assessed based on comparisons with results from a well resolved large eddy simulation (LES) simulation of the same flow conducted on a very fine mesh and with experimental data. It is found that the SA-DES simulation with turbulent fluctuations at the inlet gives the best overall predictions for the flow statistics and mass exchange coefficient characterizing the decay of scalar mass inside the cavity. The presence of inflow fluctuations in DES is found to break the large coherence of the vortices shed in the separated shear layer that are present in the simulations with steady inflow conditions and to generate a wider range of 3D eddies inside the cavity, similar to LES. The predictions of the mean velocity field from URANS and DES are similar. However, URANS predictions show poorer agreement with LES and experiment compared to DES for the turbulence quantities. Additionally, simulations with a higher Reynolds number (ReD=33,600) and with a larger length to depth ratio (L∕D=4) are conducted to study the changes in the flow and shear-layer characteristics, and their influence on the ejection of the passive contaminant from the cavity.

Velocity profiles assessment in natural channels during high floods

Hydrology Research ◽

10.2166/nh.2011.064 ◽

2011 ◽

Vol 42 (2-3) ◽

pp. 162-170 ◽

Cited By ~ 19

Author(s):

Tommaso Moramarco ◽

Carla Saltalippi ◽

Vijay P. Singh

Keyword(s):

Flow Velocity ◽

Maximum Flow ◽

Velocity Profiles ◽

Mean Flow ◽

Velocity Measurements ◽

Mean Velocity ◽

Flow Area ◽

The Mean ◽

Logarithmic Law ◽

Maximum Flow Velocity

The accuracy of three different approaches for velocity profiles assessment during high floods, when the velocity points sampling is carried out only in the upper portion of the flow area, has been investigated. The first two methods assume the classical logarithmic law with additional terms, to take account of the dip-phenomenon in the velocity profile. The third one is based on the entropy theory and uses the maximum flow velocity occurring in the flow area. A sample of velocity measurements carried out at Pontelagoscuro gauged section (Po River, Italy), has been considered for the analysis. Six flood events have been selected and the accuracy of the investigated methods has been evaluated in terms of mean error in estimating both the mean velocity along each sampled vertical and the mean flow velocity. For high floods, the logarithmic law and the entropic approach were found quite accurate; however, the ability of the latter in reproducing the velocity profiles only by sampling the maximum flow velocity has been shown. Therefore, a procedure for velocity measurements based on the entropic approach has been proposed. The procedure allows one to both to shorten remarkably the time of the velocity sampling and to quickly estimate the discharge.

Measurements and Characterization of Turbulence in the Tip Region of an Axial Compressor Rotor

Journal of Turbomachinery ◽

10.1115/1.4037773 ◽

2017 ◽

Vol 139 (12) ◽

Cited By ~ 4

Author(s):

Yuanchao Li ◽

Huang Chen ◽

Joseph Katz

Keyword(s):

Strain Rate ◽

Shear Layer ◽

Turbulent Flows ◽

Reynolds Stress ◽

Suction Side ◽

Stress And Strain ◽

Spatial And Temporal Variability ◽

Mean Flow ◽

The Mean ◽

Stress And Strain Rate

Modeling of turbulent flows in axial turbomachines is challenging due to the high spatial and temporal variability in the distribution of the strain rate components, especially in the tip region of rotor blades. High-resolution stereo-particle image velocimetry (SPIV) measurements performed in a refractive index-matched facility in a series of closely spaced planes provide a comprehensive database for determining all the terms in the Reynolds stress and strain rate tensors. Results are also used for calculating the turbulent kinetic energy (TKE) production rate and transport terms by mean flow and turbulence. They elucidate some but not all of the observed phenomena, such as the high anisotropy, high turbulence levels in the vicinity of the tip leakage vortex (TLV) center, and in the shear layer connecting it to the blade suction side (SS) tip corner. The applicability of popular Reynolds stress models based on eddy viscosity is also evaluated by calculating it from the ratio between stress and strain rate components. Results vary substantially, depending on which components are involved, ranging from very large positive to negative values. In some areas, e.g., in the tip gap and around the TLV, the local stresses and strain rates do not appear to be correlated at all. In terms of effect on the mean flow, for most of the tip region, the mean advection terms are much higher than the Reynolds stress spatial gradients, i.e., the flow dynamics is dominated by pressure-driven transport. However, they are of similar magnitude in the shear layer, where modeling would be particularly challenging.

Measurement of the Mean Flow Field in a Smooth Rotating Channel With Coriolis and Buoyancy Effects

Volume 5A: Heat Transfer ◽

10.1115/gt2017-63123 ◽

2017 ◽

Author(s):

Ruquan You ◽

Haiwang Li ◽

Zhi Tao ◽

Kuan Wei

Keyword(s):

Flow Field ◽

Coriolis Force ◽

Indium Tin Oxide ◽

Buoyancy Force ◽

Flow Direction ◽

Density Ratio ◽

Mean Flow ◽

The Mean ◽

Static Conditions ◽

Rotating Channel

The mean flow field in a smooth rotating channel was measured by particle image velocimetry under the effect of buoyancy force. In the experiments, the Reynolds number, based on the channel hydraulic diameter (D) and the bulk mean velocity (Um), is 10000, and the rotation numbers are 0, 0.13, 0.26, 0.39, 0.52, respectively. The four channel walls are heated with Indium Tin Oxide (ITO) heater glass, making the density ratio (d.r.) about 0.1 and the maximum value of buoyancy number up to 0.27. The mean flow field was simulated on a 3D reconstruction at the position of 3.5<X/D<6.5, where X is along the mean flow direction. The effect of Coriolis force and buoyancy force on the mean flow was taken into consideration in the current work. The results show that the Coriolis force pushes the mean flow to the trailing side, making the asymmetry of the mean flow with that in the static conditions. On the leading surface, due to the effect of buoyancy force, the mean flow field changes considerably. Comparing with the case without buoyancy force, separated flow was captured by PIV on the leading side in the case with buoyancy force. More details of the flow field will be presented in this work.