Mean Flow Field Research Articles

Large Eddy Simulation of Self-Excited Oscillation Pulsed Jet (SEOPJ) Induced by a Helmholtz Oscillator in Underground Mining

Pulsed waterjet can break rocks effectively by taking advantage of the water hammer effect, and is thus widely used in mining, petroleum, and natural gas fields. With the aim to further clarify the flow field characteristics of pulsed jets induced by a Helmholtz oscillator, large eddy simulation was conducted under different operating pressures. The velocity distribution, mean flow field, and the coherent structure were examined using the oscillators of different cavity lengths and diameters. The results clearly showed that the major frequency of jet pulsation gradually increased with the increase of operating pressure. A stable periodic velocity core was formed at the outlet of the Helmholtz oscillator, while the external flow field was subjected to periodic impact. As a result, the ambient fluid was strongly entrained into the jet beam. With the increase of the cavity length, the length of the core segment decreased while the energy loss caused by the cavity increased, which was also accompanied by a rapid attenuation of the axial velocity at the jet outlet. The coherent structure of the jet in the oscillator with small cavity diameter was more disordered near the nozzle outlet, and the vortex scale was larger. The effect of cavity diameter can be reflected in the feedback modulation of the jet in the cavity. Compared with the conical nozzle, the length of the core section of the jet was shorter, but the jet had better bunching, a smaller diffusion angle, and better mixing performance. These results provide a further understanding of the characteristics of pulsed water jet for better utilizations in the fields of energy exploitation.

On a momentum interpolation scheme for collocated meshes with improved discrete kinetic energy conservation

In this study, we investigate the effects of momentum interpolation (MI) schemes for collocated meshes on DNS and LES with relatively coarse meshes. Based on this, the primary objective is to present how a MI scheme with reduced errors in mass and discrete kinetic energy (DKE) conservation affects the quality of the simulation results. From an existing MI scheme used widely, it is shown that the continuity equation has a first-order error in time based on the CV-centered velocity. With a specific choice of the pressure variable of the order of the pressure change for interpolating the face velocity, we derive a MI scheme with temporally second-order for the continuity equation. It is noted that this scheme drives the continuity and DKE errors to zero for a steady flow or very small time step. When applied to DNS and LES of a turbulent channel flow and a turbulent flow around an airfoil, the suggested MI scheme with reduced error results in more accurate prediction of mean and RMS flow fields. In order to examine the effects of the MI schemes on the turbulent pressure field, energy and power spectra of pressure fluctuations are examined. The pressure spectra with the revised MI scheme show no clear sign of pressure wiggles at high frequencies and more accurate prediction of small-to-large scale fluctuations, which shows effectiveness of the revised scheme and importance of the mass and DKE conservation.

Impingement of propeller jet on a vertical quay wall

This study experimentally investigates the mean and turbulent flow fields of a propeller jet impinging on a vertical quay wall. Four impingement distances, namely, wall clearances (= longitudinal distance between the propeller and vertical wall), were used to examine their influence on the flow behaviors. In order to investigate the characteristics of the three-dimensional impinging jet, both the streamwise (jet central plane) and transverse (impingement plane) flow fields were measured for each impingement distance using the particle image velocimetry (PIV) technique. Based on the wall clearance, three regions are identified, namely free, impingement and wall jet regions. Additionally, the results show that the evolution of the impinging jet is governed by two mechanisms: jet diffusion and wall obstruction. Their relative importance under varying wall clearances was interpreted in terms of the mean flow patterns and energy dissipation. Moreover, the proper orthogonal decomposition (POD) method is employed to identify the dominant flow structures associated with these two mechanisms in terms of the POD modes and their corresponding dominant frequency, which in turn provides a quantitative means to single out the individual flow mechanism.

Effect of grid sensitivity on the performance of wall adapting SGS models for LES of swirling and separating–reattaching flows

The present study assesses the performance of the Wall Adapting SGS models along with the Dynamic Smagorinsky model for flows involving separation, reattachment and swirl. Due to the simple geometry and wide application in a variety of engineering systems, the Backward-Facing Step (BFS) geometry and Confined Swirling Flow (CSF) geometry are invoked in the present case. The calculation of the SGS stresses employs three models, namely, the Dynamic Smagorinsky model, the Wall Adapting Local Eddy viscosity (WALE) model and the Dynamic WALE model. For studying the effect of the grid sensitivity, the simulations are performed over two sets of grids with different resolutions based on the non-dimensional wall distance parameter ( y+ ). Grids corresponding to y+= 70 and y+= 20 are employed for the subsonic flow over the BFS while grids corresponding to y+= 40 and y+= 20 are employed for supersonic flow over the BFS and for confined swirling flow geometry. The validation against the experimental results includes the mean flow fields and the turbulent stresses obtained for each case. The results reveal that for the fine grid (y+= 20), the near wall eddy viscosity profile for the WALE model is better than both the Dynamic WALE and the Dynamic Smagorinsky model. The difference between the predictions of the coarse and fine grids for Dynamic Smagorinsky and the WALE model is high whereas, the Dynamic WALE model is almost insensitive to the grid resolutions considered for the present case. The mean velocity and pressure values as well as the turbulent quantities predicted by the Dynamic WALE model are closest to the experimental values for all the cases.

POD characterisation of extreme wake patterns of turbulent wind fields past rectangular buildings

The turbulent wind fields around three different rectangular building models in two types of simulated atmospheric boundary layer are measured using particle image velocimetry. Proper orthogonal decomposition (POD) is then applied to recognize and extract the coherent structures of large energy of fluctuating velocities. The extreme flow patterns of the first two POD modes are identified from the instants of occurrence of peak POD coefficients. The way how these extreme patterns influence the instantaneous flow fields is discussed. The results demonstrate that these extreme patterns can contribute to the instantaneous building wake flow in completely different manners but similar influence patterns can be summarized as described from the wake flow data of different rectangular building models. In the broad sense, one extreme wake pattern strengths the time-averaged mean flow field of the wake such as a recirculating bubble behind the building on the vertical planes and two symmetric counter-rotating vortices on the horizontal planes. However, the other extreme wake pattern causes air to flow largely in the opposite directions as the main flow. On the longitudinal vertical planes behind the building, a momentary fluid source formed at some point in the wake drives air to flow upwards with some flow backwards toward the building. On the horizontal planes, one extreme pattern reveals a pair of asymmetric vortices attached to the building leeward wall. The instantaneous peak flow characteristics influenced by the extreme POD modal patterns, apparently reported for the first time, could have important implications in building wake effect assessment especially for hazardous situations.

Large eddy simulation of transverse single/double jet in supersonic crossflow

In this paper, large eddy simulation of transverse sonic single/double hydrogen jets into supersonic Mach 2 crossflow have been carried out to investigate the complex flow structures and the mixing performance. Detailed turbulence characteristics, in terms of the instantaneous and mean flow fields, the vortex structures and their evolutions, the turbulence kinetic energy and the Reynolds shear stress distributions, the maximum hydrogen mass fraction and jet penetration, have been provided. Results of the two-dimensional and three-dimensional streamlines illustrate that the trailing counter-rotating vortex pairs (TCVP), the secondary TCVP of primary jet and the horseshoe vortex can merge and form a new horseshoe vortex. Three counter-rotating vortex pairs (CVP) are formed in the downstream of secondary jet: the CVP-B due to interactions between the supersonic crossflow and secondary jet; the CVP-C due to interactions between the supersonic crossflow, primary and secondary jets; and the CVP-D due to interactions of the supersonic crossflow and primary jet. The presence of primary jet flow alters the Reynolds shear stress distributions after the secondary injection with the influence of these large-scale structures. In addition, the two-stage jet injection system is proved to yield a better mixing performance than the single jet system.

Flow structure between freight train containers with implications for aerodynamic drag

Predictions from embedded-LES are presented of a model of a section of a double-stacked freight wagon subjected to different local loading configurations. In total, 15 different upstream (Gfront) and downstream (Gbase) gap spacings were simulated to characterise the change in the flow topology.The mean flow fields indicate that the inter-wagon flow undergoes a significant topology change over the range of Gfront=1.77W–3.23W (W= wagon width). For Gfront≤1.77W, the mean recirculating flow in the gap covers its entire length. In contrast, for Gfront≳3.23W, the complete wake closure for the upstream wagon occurs enabling the upstream shear layers to impinge on the entire downstream surface, in turn, increasing the rate of change of drag force as Gfront is increased. The change in the wake shedding frequency, directly affecting the base pressure and consequently the drag, due to the variation in Gfront and Gbase, is presented.

The three-dimensional structure of the Leeuwin Current System in density coordinates in an eddy-resolving OGCM

The Leeuwin Current System (LCS) consists of the Leeuwin Current (LC), a surface, poleward current along the west coast of Australia; the Leeuwin Undercurrent (LUC), a subsurface, equatorward current on the continental slope beneath the LC; and zonal flows in the interior ocean that interact with the LC and LUC. To understand the three-dimensional structure of the LCS circulation, we construct a mean flow over twenty years in z coordinates and density coordinates from three-day snapshots of an eddy-resolving ocean general circulation model (OGCM) and carry out a “leak-free” volume budget analysis on the mean flow field in both coordinate systems. The mean flow in z coordinates forms a zonal and a meridional overturning, where a near-surface eastward flow enters the LC, flows poleward and at the same time sinks to the LUC depths, flows equatorward, and finally moves westward out of the LCS, as found in a previous study. On the other hand, the mean flow in density coordinates is mostly isopycnic, except that the upper part of the LC becomes denser as it flows poleward partly owing to sea-surface cooling. The lower part of the LC becomes denser, not because of cooling but because denser water joins the LC from the interior ocean. The LUC becomes lighter as it flows equatorward because its lower part flows westward out of the LCS and its top part is joined by eastward flows from the interior. The mean downwelling in z coordinates is therefore isopycnic and is likely a result of temporal variability.

Flow field dynamics of large-scale experimentally produced downburst flows

This study characterizes the mean and turbulent flow fields resulting from several large-scale downbursts simulated in the Wind Engineering, Energy and Environment (WindEEE) Dome at Western University. Detailed three-component velocity Cobra probe measurements are conducted for several Reynolds numbers and downburst height to diameter ratios. The wind speed records at a comprehensive number of heights and radial distances are analyzed using a moving average approach similarly employed in some full-scale campaigns. A reasonable averaging time is determined and the analysis of the turbulent flow is carried out using first and second order statistics and the similarities with full-scale data is presented. Moreover, Particle Image Velocimetry (PIV) measurements are carried out in order to investigate the dynamics of downburst vortices for the same Reynolds numbers and the same downburst height to diameter ratios as in the Cobra probe measurements. The structure and evolution of the primary downburst vortex from PIV are compared with existing full-scale data.

Installation: numerical investigation

Acoustic installation effects are considered as scattering problem. Two methods to investigate them are presented. First, a fast multipole method boundary element method (FMM-BEM) which can solve the Helmholtz wave equation for full scale aircraft configurations at frequencies of some kHz. There, low Mach number potential mean flow fields can be taken into account by a so-called Taylor transformation. Second, a discontinuous Galerkin method (DGM) which solves acoustic perturbation equations (APE) for realistic mean flow fields is presented. DGM calculations are very expensive and can be performed for full scale aircrafts only at low frequencies. Its main purpose so far is to assess the accuracy of the FMM for selected cases. The Taylor-transformed Helmholtz equation is derived and the fundamentals of the FMM are introduced. Some details of the DLR FMM code FMCAS are given. The basic DGM equations are derived for the APE and some implementation details of the DLR DGM code DISCO++ are discussed. For generic geometries results of the FMM and DGM are compared and the limits of the Taylor transformation are shown. Finally, scattering results for a 1 kHz Monopole at a full scale aircraft geometry will be presented.

Examination of the physical assumptions of a quasi-steady vector model using the integral momentum equation

Quasi-Steady (QS) vector models have served as a convenient and effective tool for wind load estimations for low-rise buildings in the wind engineering community. In order to understand the applicability for practice, the physical assumptions of a QS vector model are investigated in this paper. The derivation is done through algebraic manipulation of the time-averaged integral momentum equation, which is used to relate mean, area-averaged, roof surface pressures to the mean flow and turbulence field above a roof. The two main assumptions of the QS model are revealed through this process: (i) The streamlines of an instantaneous flow near the roof are assumed to be the mean streamlines so that the instantaneous direction of the flow measured at the reference point is equivalent to the mean direction; (ii) The magnitude of the instantaneous flow is obtained by amplifying the magnitude of the mean flow at a spatially uniform rate such that the amplified magnitude of mean velocity is equivalent to the instantaneous magnitude measured at the reference point. Missing terms in the QS model are used to develop correction terms to improve QS model performance.

Delayed detached eddy simulation of pedestrian-level wind around a building array – The potential to save computing resources

The appropriate selection of a turbulence model directly affects the prediction of pedestrian-level wind (PLW) around buildings. Delayed detached eddy simulation (DDES) model, has been reported to be able to predict airflow around a building as good as large eddy simulation (LES) does, but with a lower mesh requirement and much less computing time. This study aims to see if DDES model can perform similarly when simulating the wind flow around a building array. This hypothesis is tested by comparing wind velocities of DDES, LES, and a benchmark wind tunnel experiment. Sensitivity assessments of DDES model are conducted, including the mesh resolution and the choice of an unsteady Reynolds Averaged Navier-Stokes (URANS) model used in conjunction. The normalized minimal grid sizes (0.005 for the building array's windward side and 0.0025 for the lateral and leeward sides) and the unsteady k−ω shear stress transport (SST) model are the most economical and effective. Simulated results are further quantified using four validation indices. Specifically, the correlation coefficient R between the predicted mean velocities using DDES and LES is 0.90, which basically proves our hypothesis in the mean flow field; but DDES only takes 80.3% of the computing time using LES. The time histories and spectrums of instantaneous velocities are also analyzed, indicating that DDES performs the similar predictions as LES of the unsteady flow fluctuations, while it has the potential to save computing time and mesh numbers.

Experimental investigation of flow structure and energy separation of Ranque–Hilsch vortex tube with LDV measurement

In this study, transparent vortex tubes of diameter 30 mm were designed for the main tube visualisation and a 2D laser Doppler velocimetry (LDV) measurement was adopted to investigate the mean flow field on the meridian plane. The distributions of the axial and radial velocities, and particularly the reverse flow boundary, were obtained for understanding the characteristics of large-scale vortex structures. Various operation conditions with different cold mass fractions (0.1–0.9), tube lengths (360 mm, 600 mm, and 900 mm), and inlet pressures (0.1 bar and 0.2 bar) were studied to reveal how the reverse flow boundary affects the energy separation performance. The LDV results show that the mean axial velocity distribution present good axial symmetry, and increasing the cold mass fraction results in an expansion of the reverse flow boundary as reported for previous numerical calculations. A deterioration in the energy separation performance due to an excessively short or long tube was revealed, and the proposed tube optimization criteria were proven.

Importance of variability in initial soil moisture and rainfalls on slope stability

A first-order moment analysis is developed to investigate the temporal and spatial propagation of uncertainty of slope stability during rainfall, considering spatial variabilities in initial soil water pressure and soil hydraulic properties, and temporal variability of rainfall. Results of the analysis indicate that the uncertainties resulting from variabilities in initial soil pore water pressure distributions and rainfalls are comparable with that from the variability in soil hydraulic properties. Further, the evolution of slope stability uncertainty is driven by the mean flow field, and a localized large-uncertainty zone along the slope profile could form, leading to a localized low-reliability zone, which may lead to the failure of the slope. In particular, when the slope is close to saturation, the reliability of the stability analysis of any elevation of the slope is low even at early rainfall times. On the other hand, when the slope is unsaturated and heavy rainfalls occur, the low-reliability zone exists at shallow parts of the slope at early times. The results also show that greater unreliability exists at shallow depths at early times when the rainfall has a descending trend in comparison with uniform and increasing trend. Lastly, the low-reliability zone is always near the impermeable bedrock if rainfall persists.

Data assimilation and resolvent analysis of turbulent flow behind a wall-proximity rib

This study aims to detect the unsteady features of the turbulent flow behind a wall-proximity rib using resolvent analysis, based on the mean flow field determined using an adjoint-based data assimilation (ABDA) model. The rib is located at gap ratios G/d = 0.25 and 0.50 with a flow Reynolds number Re = 7600 based on the rib size (d = 10 mm) and the free-stream velocity U0. The split fiber measurements at x/d = −0.25, 1.25, 4.25, and 9.25 are solely used as observational data, while the temperature sensitive paint and particle image velocimetry (PIV) results are used as the complement for the analysis and validation. First, the mean flows at both gap ratios are reproduced with the ABDA model using the streamwise velocity constraint of the observational data. It is shown that the global fields are accurately recovered, including the wall jet originating from the gap, which is absent from the PIV results. This finding indicates substantial heat transfer enhancement immediately behind the rib. Subsequently, the resolvent modes at Strouhal numbers St = 0.02, 0.05, 0.15, and 0.30 are obtained from the mean flows using a stochastic approach instead of performing the singular value decomposition directly on the resolvent operator, due to the large matrix size. With the help of the power spectral density of the split fiber measurement, the resolvent analysis identifies the large-scale flapping motion and the wall-jet fine scales that enhance the heat transfer in the case of G/d = 0.25, in addition to the Karman vortex shedding, which makes little contribution to the wall heat transfer in the case of G/d = 0.50. The flow dynamical features in both cases are reconstructed using the leading five resolvent modes at St = 0.15, showing good agreement with the proper orthogonal decomposition modes.

Effect of von Karman length scale in scale adaptive simulation approach on the prediction of supersonic turbulent flow

Numerical investigations of the supersonic axisymmetric base flow at Mach number 2.46 and Reynolds number 2.858×106 are carried out using the scale-adaptive simulation (SAS) approach. To achieve SAS computation, three mathematical forms of von Karman length scale are utilized. The first one is calculated from the strain rate tensor and second derivative of the velocity field (this SAS can be marked as “SAS-1”). Computation of the second one is employed using the vorticity and its first derivative (this SAS can be denoted as “SAS-2”). The third one is computed from the vorticity and the second derivative of the velocity field (this SAS can be named as “SAS-3”). Their effects on the quantitative predictions are assessed. Two inflow conditions are also investigated, i.e., inflow condition with/without turbulent-boundary-layer profiles. Results show that the inflow conditions have the significant effects on the base-pressure and streamwise velocity distributions, and the predicted results at the inflow condition with profiles show better agreement with experimental data than that at the inflow condition without profiles. The inflow conditions and von Karman length scales only have the relatively slight effects on the radial velocity distributions. Similarly, at the inflow condition with profiles, the base-pressure distributions are also not sensitive to mathematical forms of von Karman length scale. More comparisons reveal that the best predictions can be obtained by SAS-2 and SAS-3. It may be associated with the vortex stretching effects explicitly considered in the von Karman length scales of SAS-2 and SAS-3. Although the mean flow field predicted by SAS-2 is slightly better than that obtained by SAS-3. However, SAS-3 can give the slightly better predictions for the Reynolds stresses than SAS-2.

An Exponential Decay Model for the Deterministic Correlations in Axial Compressors

The unsteady blade row interaction (UBRI) is inherent and usually has a large effect on performance in multistage axial compressors. The effect could be considered by using the average-passage equation system (APES) in steady-state environment by introducing the deterministic correlations (DC). How to model the DC is the key in APES method. The primary purpose of this study is to develop a DC model for compressor routine design. The APES technique is investigated by using a 3D viscous unsteady and time-averaging Computational fluid dynamics (CFD) flow solver developed in our previous studies. Based on DC characteristics and its effects on time-averaged flow, an exponential decay DC model is proposed and implemented into the developed time-averaging solver. Steady, unsteady, and time-averaging simulations are conducted on the investigation of the UBRI and the DC model in the first transonic stage of NASA 67 and the first two stages of a multistage compressor. The DC distributions and mean flow fields from the DC model are compared with the unsteady simulations. The comparison indicates that the proposed model can take into account the major part of UBRI and provide significant improvements for predicting compressor characteristics and spanwise distributions of flow properties in axial compressors, compared with the steady mixing plane method.

Data-Driven, Physics-Based Feature Extraction from Fluid Flow Fields Using Convolutional Neural Networks

Feature identification is an important task in many fluid dynamics applications and diverse methods have been developed for this purpose. These methods are based on a physical understanding of the underlying behavior of the flow in the vicinity of the feature. Particularly, they rely on definition of suitable criteria (i.e. point-based or neighborhood-based derived properties) and proper selection of thresholds. For instance, among other techniques, vortex identification can be done through computing the Q-criterion or by considering the center of looping streamlines. However, these methods rely on creative visualization of physical idiosyncrasies of specific features and flow regimes, making them non-universal and requiring significant effort to develop. Here we present a physics-based, data-driven method capable of identifying any flow feature it is trained to. We use convolutional neural networks, a machine learning approach developed for image recognition, and adapt it to the problem of identifying flow features. The method was tested using mean flow fields from numerical simulations, where the recirculation region and boundary layer were identified in a two-dimensional flow through a convergent-divergent channel, and the horseshoe vortex was identified in three-dimensional flow over a wing-body junction. The novelty of the method is its ability to identify any type of feature, even distinguish between similar ones, without the need to explicitly define the physics (i.e. through development of suitable criterion and tunning of threshold). This provides a general method and removes the large burden placed on identifying new features. We expect this method can supplement existing techniques and allow for more automatic and discerning feature detection. The method can be easily extended to time-dependent flows, where it could be particularly impactful.

Influences of Domain Symmetry on Supersonic Combustion Modeling

High-fidelity Improved Delayed Detached Eddy Simulation modeling is applied to examine the influence of the symmetry plane on the supersonic flow and combustion characteristics in a round-to-elliptic–transition scramjet combustor. A quarterly split domain and the full domain are modeled by using up to 0.14 billion cells and a third-order scale-selective discretization scheme. The combustion chemistry is described by the finite-rate partially stirred reactor model based on multicomponent diffusion and a skeletal kerosene mechanism with 19 species/53 reactions. Time-averaged pressure, temperature, Mach number, and heat release rate are compared to examine the influence of the symmetry assumption on the mean flow fields. The exchanges of mass, momentum, and energy across the symmetry planes are analyzed. Considerable increases in the combustion efficiency and total pressure loss occur when applying the full domain, although with the similar mixing efficiency. Turbulence spectrum analysis confirms the power-law for supersonic flows, and the inertial subrange is found to be shorter in the quarter-domain modeling. A comparison of the Borghi’s diagrams shows that the data points shift from the flamelet mode to the thin reaction zone mode when using the full domain, and at least of them cannot be described by fast-chemistry combustion models.

Prediction of four concentration moments of an airborne material released from a point source in an urban environment

Ιn case of the dispersion of an airborne material from a point source in an urban environment the reliable prediction of the concentration statistical distribution by a numerical dispersion model presupposes the capability of the model to predict at least four statistical moments (mean, variance, skewness and kurtosis). In the present study, the beta distribution, the selection of which is justified based on a previous study, is incorporated in the Reynolds Averaged Navier Stokes (RANS) methodology. The shape parameters of the beta distribution are calculated using the numerical results of the mean, variance and maximum concentration. The latest is calculated through a deterministic model which uses also the numerical results of the mean and variance concentration as well as a hydrodynamic time scale. The validation of the new hybrid model “RANS-beta” is performed using the experimental dataset of the MUST wind tunnel experiment. The performance of the “RANS-beta” model for the skewness is very good (FAC2 = 0.811) while for the kurtosis it is acceptable (FAC2 = 0.557). The discrepancies are observed mainly at the edges of the plume. Future research will be focused on the optimization of the mean flow field, turbulent quantities (Reynolds stresses, turbulent kinetic energy) and on new parameterizations for the turbulent diffusion term.