Some Solutions of the Plane Turbulent Impinging Jet

1970 ◽  
Vol 92 (4) ◽  
pp. 915-922 ◽  
Author(s):  
M. Wolfshtein
Keyword(s):  
Reasonable Agreement ◽  
Eddy Viscosity ◽  
Order Differential Equation ◽  
Impinging Jet ◽  
Experimental Information ◽  
Length Scale ◽  
Reynolds Stresses ◽  
Finite Difference Technique ◽  
The Mean ◽  
Mean Strain

The impinging jet problem is solved by an iterative finite-difference technique. Reynolds stresses are assumed to be related to the mean strain by a scalar eddy viscosity. The eddy viscosity is assumed to depend on the level of energy fluctuations and a length scale. The level of energy fluctuations is obtained from a second-order differential equation, while the length scale of turbulence is prescribed on the basis of experimental information. The solutions show reasonable agreement with experiment.

The Effects of Upstream Wall Roughness on Separated and Reattached Flows Over a Forward-Facing Step

2020 ◽  
Author(s):  
Sedem Kumahor ◽  
Xingjun Fang ◽  
William Ediger ◽  
Mark F. Tachie
Keyword(s):  
Correlation Coefficient ◽  
Turbulent Flows ◽  
Eddy Viscosity ◽  
Leading Edge ◽  
Step Height ◽  
Stream Velocity ◽  
Reynolds Stresses ◽  
Third Order ◽  
The Mean ◽  
Forward Facing Step

Abstract Separating and reattaching turbulent flows induced by a forward-facing step submerged in thick oncoming turbulent boundary layers developed over smooth and rough walls were investigated using time-resolved particle image velocimetry. Both smooth and fully rough upstream bottom wall conditions were examined and the resultant oncoming boundary layer thickness were 4.3 and 6.7 times the step height, respectively. The Reynolds number based on the step height and free-stream velocity was 7800. The mean velocities, Reynolds stresses analyzed in both Cartesian and curvilinear coordinate systems, eddy viscosity, correlation coefficient and third order moments are discussed. The results indicate that, due to the enhanced turbulence intensity and shear rate in the fully rough case, distinct elevated regions of vertical and shear Reynolds stresses are consistent upstream of the leading edge of the step while the magnitude of the Reynolds stresses are consistently higher than observed in the smooth case. The correlation coefficient, eddy viscosity and third order moments also show distinct elevated regions upstream of the leading edge of the step in the fully rough case. Above the step, distinct elevated regions of the Reynolds stresses, eddy viscosity and correlation coefficient are observed in both cases with the peak values at a vertical location corresponding to the maximum elevation of the mean separating streamline.

scholarly journals Scaling Turbulent Combustion Fields in Explosions

2020 ◽  
Vol 10 (23) ◽  
pp. 8577
Author(s):  
Allen Kuhl ◽  
David Grote ◽  
John Bell
Keyword(s):  
Turbulent Combustion ◽  
Scaling Laws ◽  
High Explosive ◽  
Length Scale ◽  
Roundoff Error ◽  
Reynolds Stresses ◽  
Phase 3 ◽  
Three Phase ◽  
The Mean ◽  
Thermodynamic Variables

We considered the topic of explosions from spherical high-explosive (HE) charges. We studied how the turbulent combustion fields scale. On the basis of theories of dimensional analysis by Bridgman and similarity theories of Sedov and Barenblatt, we found that all fields scaled with the explosion length scale r0. This included the blast wave, the mean and root mean squared (RMS) profiles of thermodynamic variables, combustion variables, velocities, vorticity, and turbulent Reynolds stresses. This was a consequence of the formulation of the problem and our numerical method, which both satisfied the similarity conditions of Sedov. We performed numerical simulations of 1 g charges and 1 kg charges; the solutions were identical (within roundoff error) when plotted in scaled variables. We also explored scaling laws related to three-phase pyrotechnic explosions. We show that although the scaling formally broke down, the fireball still essentially scaled with the explosion length scale r0. However, the discrete Lagrange particles (DLP) (phase 2) and the heterogeneous continuum model (HCM) of the DLP wakes (phase 3) did not scale with r0, and mean and RMS profiles could differ by a factor of 10 in some regions. This was because the DLP particles and wakes introduced an additional scale that broke the similarity conditions.

On the Constitutive Relation for the Reynolds Stresses and the Prandtl-Kolmogorov Hypothesis of Effective Viscosity in Axisymmetric Strained Turbulence

1999 ◽  
Vol 122 (1) ◽  
pp. 48-50 ◽  
Author(s):  
J. Jovanovic´ ◽  
I. Otic´
Keyword(s):  
Strain Rate ◽  
Stress Tensor ◽  
Reynolds Stress ◽  
Constitutive Relation ◽  
Effective Viscosity ◽  
Constitutive Relations ◽  
Reynolds Stresses ◽  
Reynolds Stress Tensor ◽  
The Mean ◽  
Mean Strain

The constitutive relation for the Reynolds stress tensor is considered for turbulence developing in axisymmetric strain fields. It is confirmed that the Reynolds stress tensor is aligned linearly with the mean strain rate. In contrast to the Prandtl-Kolmogorov, hypothesis, the effective viscosity is found to grow in proportion to the anisotropy of turbulence and the length scale based on the magnitude of the mean strain rate. Using invariant theory the effective viscosity is determined for the limiting states of turbulence. Additional analysis of the constitutive relations is supplemented for the dissipation and pressure-strain correlations. It is shown that analytical derivations are in excellent agreement with the data obtained from direct numerical simulations. [S0098-2202(00)02801-7]

3D Reynolds Stress Modelling of Turbulent Flow in Linear Turbine Cascade

1997 ◽  
Author(s):  
M. Kanniche ◽  
R. Boudjemadi ◽  
F. Déjean ◽  
F. Archambeau
Keyword(s):  
Reynolds Stress ◽  
Eddy Viscosity ◽  
Strain Tensor ◽  
Secondary Flows ◽  
Turbulence Closure ◽  
Turbine Cascade ◽  
Reynolds Stresses ◽  
Mean Flow ◽  
Principal Axes ◽  
The Mean

The flow in a linear turbine cascade (Gregory-Smith et al. (1990)) is numerically investigated using a Reynolds Stress Turbulence closure. A particular attention is given to secondary flows where the normal Reynolds stresses are expected to play an important role. The most classical turbulence closure, the k-epsilon model uses the Boussinesq Eddy Viscosity concept which assumes an isotropic turbulent viscosity. The Reynolds stresses are then related to local velocity gradients by this isotropic eddy viscosity. Corollary, the principal axes of the Reynolds stress tensor are colinear with those of the mean strain tensor. The advantage of Reynolds Stress Turbulence closure is the calculation of Reynolds stresses by their own individual transport equations. This leads to a more realistic description of the turbulence and of its dependance on the mean flow. The most classical Second Order turbulence model (Launder et al. (1975)) is applied to a linear turbine cascade, and the results are compared to secondary velocity and turbulence measurements at cross-passage planes.

scholarly journals Improved Supersonic Turbulent Flow Characteristics Using Non-Linear Eddy Viscosity Relation in RANS and HPC-Enabled LES

Aerospace ◽  
2021 ◽  
Vol 8 (11) ◽  
pp. 352
Author(s):  
Kalyani Bhide ◽  
Kiran Siddappaji ◽  
Shaaban Abdallah ◽  
Kurt Roberts
Keyword(s):  
Turbulent Flow ◽  
Strain Rate ◽  
Linear Relationship ◽  
Eddy Viscosity ◽  
Flow Behavior ◽  
Preliminary Investigation ◽  
Flow Characteristics ◽  
Reynolds Stresses ◽  
Non Linear ◽  
Mean Strain

A majority of the eddy viscosity models for supersonic turbulent flow are based on linear relationship between Reynolds stresses and mean strain rate. The validity of these models can be improved by introducing non-linearity in relation as RANS models offer advantages in terms of reduced turnaround times typical of industry applications. With these benefits, the present work utilizes quadratic constitutive relation (QCR) with Menter’s k omega SST model to characterize the flowfield of rectangular jets. The sensitivity of this model with QCR, weighted towards diffusion, dissipation, and a combination of both, is addressed. Viscous large eddy simulations (LES) with WALE subgrid scale models are employed for qualitative comparisons using a commercial solver. Massively parallel LES are enabled by the new in-house 1088-core computing cluster at the University of Cincinnati and are also used for benchmarking. The nearfield results are validated with available experimental data and show good agreement in both fidelities. Flow characteristics, including the shear layer profiles, Reynolds stresses, and turbulence kinetic energy (TKE) and its production are compared. LES reveal higher TKE production in the regions with highest Reynolds stresses. It is comparatively lower in QCR RANS. As a special case of TKE analysis in jets, a preliminary investigation of retropropulsion is outlined for rectangular nozzles for the first time. Improved flow behavior by implementation of a non-linear relationship between Reynolds stresses and mean strain rate is demonstrated.

scholarly journals Investigation of Changes in Fatigue Damage Caused by Mean Load under Block Loading Conditions

Materials ◽  
2021 ◽  
Vol 14 (11) ◽  
pp. 2738
Author(s):  
Roland Pawliczek ◽  
Tadeusz Lagoda
Keyword(s):  
Fatigue Life ◽  
Fatigue Damage ◽  
Strain Curve ◽  
Mean Value ◽  
Fatigue Properties ◽  
Stress Strain ◽  
Reference Case ◽  
Block Loading ◽  
The Mean ◽  
Mean Strain

The literature in the area of material fatigue indicates that the fatigue properties may change with the number of cycles. Researchers recommend taking this into account in fatigue life calculation algorithms. The results of simulation research presented in this paper relate to an algorithm for estimating the fatigue life of specimens subjected to block loading with a nonzero mean value. The problem of block loads using a novel calculation model is presented in this paper. The model takes into account the change in stress–strain curve parameters caused by mean strain. Simulation tests were performed for generated triangular waveforms of strains, where load blocks with changed mean strain values were applied. During the analysis, the degree of fatigue damage was compared. The results of calculations obtained for standard values of stress–strain parameters (for symmetric loads) and those determined, taking into account changes in the curve parameters, are compared and presented in this paper. It is shown that by neglecting the effect of the mean strain value on the K′ and n′ parameters and by considering only the parameters of the cyclic deformation curve for εm = 0 (symmetric loads), the ratio of the total degree of fatigue damage varies from 10% for εa = 0.2% to 3.5% for εa = 0.6%. The largest differences in the calculation for ratios of the partial degrees of fatigue damage were observed in relation to the reference case for the sequence of block n3, where εm = 0.4%. The simulation results show that higher mean strains change the properties of the material, and in such cases, it is necessary to take into account the influence of the mean value on the material response under block loads.

scholarly journals Jet Formation and Evolution in Baroclinic Turbulence with Simple Topography

2010 ◽  
Vol 40 (2) ◽  
pp. 257-278 ◽  
Author(s):  
Andrew F. Thompson
Keyword(s):  
Southern Ocean ◽  
Potential Vorticity ◽  
Baroclinic Instability ◽  
Length Scale ◽  
Reynolds Stresses ◽  
Mean Flow ◽  
Jet Formation ◽  
Meridional Transport ◽  
Jet Behavior ◽  
Jet Variability

Abstract Satellite altimetry and high-resolution ocean models indicate that the Southern Ocean comprises an intricate web of narrow, meandering jets that undergo spontaneous formation, merger, and splitting events, as well as rapid latitude shifts over periods of weeks to months. The role of topography in controlling jet variability is explored using over 100 simulations from a doubly periodic, forced-dissipative, two-layer quasigeostrophic model. The system is forced by a baroclinically unstable, vertically sheared mean flow in a domain that is large enough to accommodate multiple jets. The dependence of (i) meridional jet spacing, (ii) jet variability, and (iii) domain-averaged meridional transport on changes in the length scale and steepness of simple sinusoidal topographical features is analyzed. The Rhines scale, ℓβ = 2πVe/β, where Ve is an eddy velocity scale and β is the barotropic potential vorticity gradient, measures the meridional extent of eddy mixing by a single jet. The ratio ℓβ /ℓT, where ℓT is the topographic length scale, governs jet behavior. Multiple, steady jets with fixed meridional spacing are observed when ℓβ ≫ ℓT or when ℓβ ≈ ℓT. When ℓβ < ℓT, a pattern of perpetual jet formation and jet merger dominates the time evolution of the system. Zonal ridges systematically reduce the domain-averaged meridional transport, while two-dimensional, sinusoidal bumps can increase transport by an order of magnitude or more. For certain parameters, bumpy topography gives rise to periodic oscillations in the jet structure between purely zonal and topographically steered states. In these cases, transport is dominated by bursts of mixing associated with the transition between the two regimes. Topography modifies local potential vorticity (PV) gradients and mean flows; this can generate asymmetric Reynolds stresses about the jet core and can feed back on the conversion of potential energy to kinetic energy through baroclinic instability. Both processes contribute to unsteady jet behavior. It is likely that these processes play a role in the dynamic nature of Southern Ocean jets.

Prediction of Confined Coaxial Turbulent Jet Mixing With a Streamwise Differencing Scheme

1991 ◽  
Author(s):  
M. A. R. Sharif ◽  
M. A. Gadalla
Keyword(s):  
Reynolds Stresses ◽  
Low Velocity ◽  
Mean Velocity ◽  
Jet Mixing ◽  
Air Jet ◽  
Air Stream ◽  
Constant Diameter ◽  
Flow Domain ◽  
The Mean ◽  
Secondary Air

Abstract Isothermal turbulent mixing of an axisymmetric primary air jet with a low velocity annular secondary air stream inside a constant diameter cylindrical enclosure is predicted. The flow domain from the inlet to the fully developed downstream locations is considered. The predicted flow field properties include the mean velocity and pressure and the Reynolds stresses. Different velocity and diameter ratios between the primary and the secondary jets have been investigated to characterize the flow in terms of these parameters. A bounded stream-wise differencing scheme is used to minimize numerical diffusion and oscillation errors. Predictions are compared with available experimental data to back up numerical findings.

Hot Wire Measurements at the Exit of a Centrifugal Compressor Impeller

1979 ◽  
Vol 193 (1) ◽  
pp. 341-347
Author(s):  
A. Goulas ◽  
R. C. Baker
Keyword(s):  
Centrifugal Compressor ◽  
Magnetic Tape ◽  
Reynolds Stresses ◽  
Hot Wire ◽  
Mean Velocity ◽  
Isentropic Flow ◽  
Compressor Impeller ◽  
The Mean

Hot wire measurements at the exit of a small centrifugal compressor impeller are reported. Three different hot wire readings were obtained and stored on a magnetic tape for each point by gating the analogue hot wire signal with a pulse which indicated circumferential position. The combination of the three readings yielded the mean velocity and some Reynolds stresses at each point. The measurements show a ‘jet-wake’ profile towards the shroud and ‘isentropic’ flow near the hub.

scholarly journals Hydrodynamic diffusion of a sphere sedimenting through a dilute suspension of neutrally buoyant spheres

1992 ◽  
Vol 236 ◽  
pp. 513-533 ◽  
Author(s):  
Robert H. Davis ◽  
N. A. Hill
Keyword(s):  
Reasonable Agreement ◽  
Trajectory Analysis ◽  
Heavy Particle ◽  
Small Reynolds Number ◽  
Mean Velocity ◽  
Dilute Suspension ◽  
Explicit Formulae ◽  
The Mean ◽  
Neutrally Buoyant ◽  
Large Peclet Number

The motion of a heavy sphere sedimenting through a dilute background suspension of neutrally buoyant spheres is analysed for small Reynolds number and large Péclet number. For this particular problem, it is possible not only to calculate the mean velocity of the heavy particle, but also the variance of the velocity and the coefficient of hydrodynamic diffusivity. Pairwise, hydrodynamic interactions between the heavy sphere and the background sphere are considered exactly using volume integrals and a trajectory analysis. Explicit formulae are given for the two limiting cases when the radius of the heavy sphere is much greater and much less than that of the background spheres, and numerical results are given for moderate size ratios. The mean velocity is relatively insensitive to the ratio of the radius of the background spheres to that of the heavy sphere, unless this ratio is very large, whereas the hydrodynamic diffusivity increases rapidly as the radius ratio is increased. The predictions are in reasonable agreement with the results of falling-ball rheometry experiments.

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