Predictions of the Structure of Turbulent, Highly Underexpanded Jets

1995 ◽  
Vol 117 (4) ◽  
pp. 599-604 ◽  
Author(s):  
P. S. Cumber ◽  
M. Fairweather ◽  
S. A. E. G. Falle ◽  
J. R. Giddings
Keyword(s):  
Turbulence Model ◽  
Near Field ◽  
Integration Scheme ◽  
Mean Flow ◽  
Flow Properties ◽  
Flow Equations ◽  
Underexpanded Jets ◽  
Model Predictions ◽  
Volume Integration ◽  
Grid Algorithm

A mathematical model capable of predicting the shock and flow structure of turbulent, underexpanded jets is described. The model is based on solutions of the fluid flow equations obtained using a second-order accurate, finite-volume integration scheme together with an adaptive grid algorithm. Closure of these equations is achieved using a k-ε turbulence model coupled to the compressible dissipation rate correction proposed by Sarkar et al. (1991a). Extending earlier work which demonstrated the ability of this model to predict the structure of moderately underexpanded jets, the present paper compares model predictions and experimental data, reported in the literature, on a number of highly underexpanded releases. The results obtained demonstrate that the model yields reliable predictions of shock structure in the near field, inviscid region of such jets, while in the far field results derived using the compressibility corrected turbulence model are adequate for predicting mean flow properties, and are superior to those obtained using a standard k-ε approach.

Predictions of the Structure of Turbulent, Moderately Underexpanded Jets

1994 ◽  
Vol 116 (4) ◽  
pp. 707-713 ◽  
Author(s):  
P. S. Cumber ◽  
M. Fairweather ◽  
S. A. E. G. Falle ◽  
J. R. Giddings
Keyword(s):  
Experimental Data ◽  
Mathematical Model ◽  
Dissipation Rate ◽  
Integration Scheme ◽  
Rate Model ◽  
Flow Equations ◽  
Underexpanded Jets ◽  
Model Predictions ◽  
Volume Integration ◽  
Grid Algorithm

A mathematical model capable of predicting the structure of turbulent, underexpanded jets is described. The model is based on solutions of the fluid flow equations obtained using a second-order accurate, finite-volume integration scheme coupled to an adaptive grid algorithm. Turbulence within these jets is modelled using a k-ε approach coupled to the compressible dissipation rate model of Sarkar et al. (1991a). Comparison of model predictions and experimental data, reported in the literature, on a number of moderately underexpanded jets demonstrate significant improvements over results derived using the standard k-ε approach, and the adequacy of the compressibility corrected turbulence model for predicting such jets.

scholarly journals Numerical and experimental investigation of the mean and turbulent characteristics of a wing-tip vortex in the near field

2014 ◽  
Vol 228 (13) ◽  
pp. 2516-2529 ◽  
Author(s):  
Micheál S O’Regan ◽  
Philip C Griffin ◽  
Trevor M Young
Keyword(s):  
Reynolds Stress ◽  
Turbulence Model ◽  
Near Field ◽  
Tip Vortex ◽  
Mean Flow ◽  
Turbulent Characteristics ◽  
The Mean ◽  
Wing Tip Vortex ◽  
Wing Tip ◽  
Good Agreement

The near-field (up to three chord lengths) development of a wing-tip vortex is investigated both numerically and experimentally. The research was conducted in a medium speed wind tunnel on a NACA 0012 square tip half-wing at a Reynolds number of 3.2 × 105. A full Reynolds stress turbulence model with a hybrid unstructured grid was used to compute the wing-tip vortex in the near field while an x-wire anemometer and five-hole probe recorded the experimental results. The mean flow of the computed vortex was in good agreement with experiment as the circulation parameter was within 6% of the experimental value at x/ c = 0 for α = 10° and the crossflow velocity magnitude was within 1% of the experimental value at x/ c = 1 for α = 5°. The trajectory of the computed vortex was also in good agreement as it had moved inboard by the same amount (10% chord) as the experimental vortex at the last measurement location. The axial velocity excess is under predicted for α = 10°, whereas the velocity deficit is in relatively good agreement for α = 5°. The computed Reynolds shear stress component 〈 u′v′〉 is in good agreement with experiment at x/ c = 0 for α = 5°, but is greatly under predicted further downstream and at all locations for α = 10°. It is thought that a lack of local grid refinement in the vortex core and deficiencies in the Reynolds stress turbulence model may have led to errors in the mean flow and turbulence results respectively.

Numerical Investigation of Transonic Compressor Rotor Flow Using an Implicit 3D Flow Solver With One-Equation Spalart-Allmaras Turbulence Model

2001 ◽  
Author(s):  
Fangfei Ning ◽  
L. Xu
Keyword(s):  
Experimental Data ◽  
Turbulence Model ◽  
Model Equation ◽  
Stokes Equations ◽  
Turbulence Closure ◽  
Two Dimensional ◽  
Mean Flow ◽  
Internal Flows ◽  
Flow Equations ◽  
Transonic Compressor

A CFD code for three-dimensional viscous flows, in particular for those in turbomachinery, has been developed based on Favre-averaged compressible Navier-Stokes equations and one-equation Spalart-Allmaras turbulence closure. The model equation of Spalart-Allmaras turbulence closure is converted into conservative form and discretized in the same manner as that for mean flow equations. A two-dimensional transonic diffuser flow and a two-dimensional transonic nozzle flow which feature pressure-gradient induced separation and shock wave/boundary layer interaction respectively are used to validate the code and application of the Spalart-Allmaras model (hereafter the S-A model) in internal flows. It is shown that the S-A model can give fairly good results compared to the experimental data. Some modifications of model equation are introduced for improving the grid insensitivity of the turbulence model. To validate the applicability of the code to the complex flows in transonic turbomachines, flows through two transonic compressor rotors, NASA Rotors 67 and 37 are calculated, and numerical results are compared with the well documented experimental data. The calculated results agree reasonably well with the experiments, and as expected, the S-A model, which is primarily developed for external flows, can also be effectively applied to internal flows. Discrepancies between the experimental data and calculations and the possible causes are also discussed.

Predictions of Impacting Sonic and Supersonic Jets

1997 ◽  
Vol 119 (1) ◽  
pp. 83-89 ◽  
Author(s):  
P. S. Cumber ◽  
M. Fairweather ◽  
S. A. E. G. Falle ◽  
J. R. Giddings
Keyword(s):  
Near Field ◽  
Supersonic Jets ◽  
Wall Jet ◽  
Pressure Oscillations ◽  
Free Jets ◽  
Underexpanded Jets ◽  
Free Jet ◽  
Model Predictions ◽  
Periodic Pressure ◽  
Spatially Periodic

A mathematical model of sonic and supersonic jets, validated previously by the present authors for the prediction of moderately and highly underexpanded free jets, is used to simulate the near field structure of jets which impact a flat surface orthogonally, and its accuracy assessed by comparing model predictions with experimental data available in the literature. For impacting, moderately underexpanded jets, results derived from the model are found to be in close agreement with data on the location of both free jet shocks, and the stand-off shock formed adjacent to the impacted surface. In addition, the model provides reasonable estimates of density within the free jet and stagnation regions of such flows, with the existence, or otherwise, of bubbles being successfully predicted. Measurements of pressure occurring on the surface of the impacted plate, produced by the impingement of both sonic and supersonic jets, are also predicted with reasonable accuracy, although the decaying amplitude of spatially periodic pressure oscillations within the wall jet region of these flows is slightly over predicted in some cases.

Free Turbulent Mixing in Axial Pressure Gradients

1973 ◽  
Vol 40 (2) ◽  
pp. 375-380 ◽  
Author(s):  
G. J. Hokenson ◽  
J. A. Schetz
Keyword(s):  
Flow Field ◽  
Turbulent Mixing ◽  
Eddy Viscosity ◽  
Static Pressure ◽  
Initial Conditions ◽  
Near Field ◽  
Pressure Gradients ◽  
Mean Flow ◽  
Axial Pressure ◽  
Flow Equations

The results of an experimental investigation of the free turbulent mixing of wakes and jets in axial pressure gradients are presented. The data include static pressure and velocity profiles and the turbulent intensity which is presented in terms of the parameter u′cL2¯(Δu)max2. It is hypothesized that the representation of the Reynolds stress by a generalized Clauser eddy viscosity model is scaled by this parameter. The experimentally observed dependence of this turbulence quantity on flow field dimensionality and the imposed pressure gradient places more stringent demands on the form of the eddy viscosity than has been shown before. However, the experimental data reveal some fortuitous behavior which aids in the specification of the spatial dependence of the turbulence parameter, leaving the scaling to be determined primarily by the initial conditions, i.e., the state of the turbulence in the near field. Substantial lateral static pressure gradients were observed in all two-dimensional cases studied. It is shown that the boundary-layer form of the viscous flow equations are inadequate in such cases, and a numerical solution of a system of equations that includes an approximate form of the lateral momentum equation provides predictions in good agreement with the data for the mean flow field.

scholarly journals Analysis of Flow Characteristics and Effects of Turbulence Models for the Butterfly Valve

2021 ◽  
Vol 11 (14) ◽  
pp. 6319
Author(s):  
Sung-Woong Choi ◽  
Hyoung-Seock Seo ◽  
Han-Sang Kim
Keyword(s):  
Turbulence Model ◽  
Dissipation Rate ◽  
Flow Characteristics ◽  
Turbulence Models ◽  
Flow Properties ◽  
Nominal Diameter ◽  
Large Pressure ◽  
Sst Model ◽  
Turbulence Effect ◽  
Valve Opening

In the present study, the flow characteristics of butterfly valves with different sizes DN 80 (nominal diameter: 76.2 mm), DN 262 (nominal diameter: 254 mm), DN 400 (nominal diameter: 406 mm) were numerically investigated under different valve opening percentages. Representative two-equation turbulence models of two-equation k-epsilon model of Launder and Sharma, two-equation k-omega model of Wilcox, and two-equation k-omega SST model of Menter were selected. Flow characteristics of butterfly valves were examined to determine turbulence model effects. It was determined that increasing turbulence effect could cause many discrepancies between turbulence models, especially in areas with large pressure drop and velocity increase. In addition, sensitivity analysis of flow properties was conducted to determine the effect of constants used in each turbulence model. It was observed that the most sensitive flow properties were turbulence dissipation rate (Epsilon) for the k-epsilon turbulence model and turbulence specific dissipation rate (Omega) for the k-omega turbulence model.

scholarly journals Instability wave models for the near-field fluctuations of turbulent jets

2011 ◽  
Vol 689 ◽  
pp. 97-128 ◽  
Author(s):  
K. Gudmundsson ◽  
Tim Colonius
Keyword(s):  
Flow Field ◽  
Large Scale ◽  
Microphone Array ◽  
Near Field ◽  
Turbulent Jets ◽  
Instability Wave ◽  
Mean Flow ◽  
Velocity Fluctuations ◽  
The Mean ◽  
Scale Structures

AbstractPrevious work has shown that aspects of the evolution of large-scale structures, particularly in forced and transitional mixing layers and jets, can be described by linear and nonlinear stability theories. However, questions persist as to the choice of the basic (steady) flow field to perturb, and the extent to which disturbances in natural (unforced), initially turbulent jets may be modelled with the theory. For unforced jets, identification is made difficult by the lack of a phase reference that would permit a portion of the signal associated with the instability wave to be isolated from other, uncorrelated fluctuations. In this paper, we investigate the extent to which pressure and velocity fluctuations in subsonic, turbulent round jets can be described aslinearperturbations to the mean flow field. The disturbances are expanded about the experimentally measured jet mean flow field, and evolved using linear parabolized stability equations (PSE) that account, in an approximate way, for the weakly non-parallel jet mean flow field. We utilize data from an extensive microphone array that measures pressure fluctuations just outside the jet shear layer to show that, up to an unknown initial disturbance spectrum, the phase, wavelength, and amplitude envelope of convecting wavepackets agree well with PSE solutions at frequencies and azimuthal wavenumbers that can be accurately measured with the array. We next apply the proper orthogonal decomposition to near-field velocity fluctuations measured with particle image velocimetry, and show that the structure of the most energetic modes is also similar to eigenfunctions from the linear theory. Importantly, the amplitudes of the modes inferred from the velocity fluctuations are in reasonable agreement with those identified from the microphone array. The results therefore suggest that, to predict, with reasonable accuracy, the evolution of the largest-scale structures that comprise the most energetic portion of the turbulent spectrum of natural jets, nonlinear effects need only be indirectly accounted for by considering perturbations to the mean turbulent flow field, while neglecting any non-zero frequency disturbance interactions.

scholarly journals Computation of Three-Dimensional, Rotational Flow Through Turbomachinery Blade Rows for Improved Aerodynamic Design Studies

1986 ◽  
Author(s):  
S. V. Subramanian ◽  
R. Bozzola ◽  
Louis A. Povinelli
Keyword(s):  
Three Dimensional ◽  
Maximum Flow ◽  
Cost Effective ◽  
Computer Code ◽  
Integration Scheme ◽  
Aerodynamic Design ◽  
Design Studies ◽  
Flow Equations ◽  
Transonic Compressor ◽  
Numerical Predictions

The performance of a three dimensional computer code developed for predicting the flowfield in stationary and rotating turbomachinery blade rows is described in this study. The four stage Runge-Kutta numerical integration scheme is used for solving the governing flow equations and yields solution to the full, three dimensional, unsteady Euler equations in cylindrical coordinates. This method is fully explicit and uses the finite volume, time marching procedure. In order to demonstrate the accuracy and efficiency of the code, steady solutions were obtained for several cascade geometries under widely varying flow conditions. Computed flowfield results are presented for a fully subsonic turbine stator and a low aspect ratio, transonic compressor rotor blade under maximum flow and peak efficiency design conditions. Comparisons with Laser Anemometer measurements and other numerical predictions are also provided to illustrate that the present method predicts important flow features with good accuracy and can be used for cost effective aerodynamic design studies.

Large-scale Structure and Turbulence Transport in the Young Solar Wind – Comparison of Parker Solar Probe Observations with a Global 3D Reynolds-averaged MHD Model

2021 ◽  
Author(s):  
Rohit Chhiber ◽  
Arcadi Usmanov ◽  
William Matthaeus ◽  
Melvyn Goldstein ◽  
Riddhi Bandyopadhyay
Keyword(s):  
Solar Wind ◽  
Large Scale ◽  
Transport Equations ◽  
Turbulence Energy ◽  
Reynolds Stresses ◽  
Mean Flow ◽  
Coulomb Collisions ◽  
Flow Equations ◽  
Simulation Results ◽  
Turbulence Transport

<div>Simulation results from a global <span>magnetohydrodynamic</span> model of the solar corona and the solar wind are compared with Parker Solar <span>Probe's</span> (<span>PSP</span>) observations during its first several orbits. The fully three-dimensional model (<span>Usmanov</span> <span>et</span> <span>al</span>., 2018, <span>ApJ</span>, 865, 25) is based on Reynolds-averaged mean-flow equations coupled with turbulence transport equations. The model accounts for effects of electron heat conduction, Coulomb collisions, Reynolds stresses, and heating of protons and electrons via nonlinear turbulent cascade. Turbulence transport equations for turbulence energy, cross <span>helicity</span>, and correlation length are solved concurrently with the mean-flow equations. We specify boundary conditions at the coronal base using solar synoptic <span>magnetograms</span> and calculate plasma, magnetic field, and turbulence parameters along the <span>PSP</span> trajectory. We also accumulate data from all orbits considered, to obtain the trends observed as a function of heliocentric distance. Comparison of simulation results with <span>PSP</span> data show general agreement. Finally, we generate synthetic fluctuations constrained by the local rms turbulence amplitude given by the model, and compare properties of this synthetic turbulence with PSP observations.</div>

Near-field mean flow dynamics of a cylindrical canopy patch suspended in deep water

2018 ◽  
Vol 858 ◽  
pp. 634-655 ◽  
Author(s):  
Jian Zhou ◽  
Subhas K. Venayagamoorthy
Keyword(s):  
Deep Water ◽  
Near Field ◽  
Flow Dynamics ◽  
Flow Diversion ◽  
Circular Cylinders ◽  
Published Data ◽  
Global Flow ◽  
Mean Flow ◽  
Near Wake ◽  
Local Flow

The time-averaged flow dynamics of a suspended cylindrical canopy patch with a bulk diameter of $D$ is investigated using large-eddy simulations (LES). The patch consists of $N_{c}$ constituent solid circular cylinders of height $h$ and diameter $d$, mimicking patchy vegetation suspended in deep water ($H/h\gg 1$, where $H$ is the total flow depth). After validation against published data, LES of a uniform incident flow impinging on the canopy patch was conducted to study the effects of canopy density ($0.16\leqslant \unicode[STIX]{x1D719}=N_{c}(d/D)^{2}\leqslant 1$, by varying $N_{c}$) and bulk aspect ratio ($0.25\leqslant AR=h/D\leqslant 1$, by varying $h$) on the near-wake structure and adjustment of flow pathways. The relationships between patch geometry, local flow bleeding (three-dimensional redistribution of flow entering the patch) and global flow diversion (streamwise redistribution of upstream undisturbed flow) are identified. An increase in either $\unicode[STIX]{x1D719}$ or $AR$ decreases/increases/increases bleeding velocities through the patch surface area along the streamwise/lateral/vertical directions, respectively. However, a volumetric flux budget shows that a larger $AR$ causes a smaller proportion of the flow rate entering the patch to bleed out vertically. The global flow diversion is found to be determined by both the patch geometrical dimensions and the local bleeding which modifies the sizes of the patch-scale near wake. While loss of flow penetrating the patch increases monotonically with increasing $\unicode[STIX]{x1D719}$, its partition into flow diversion around and beneath the patch shows a non-monotonic dependence. The spatial extents of the wake, the flow-diversion dynamics and the bulk drag coefficients of the patch jointly reveal the fundamental differences of flow responses between suspended porous patches and their solid counterparts.

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