Browsing by Subject "Large eddy simulation"

Now showing 1 - 6 of 6
  • Thumbnail Image
    Item
    High-fidelity unstructured overset simulation of complex turbulent flows
    (2023-05) Morse, Nicholas
    The goal of this dissertation is to provide insight into the underlying physics of two sets of complex flows: (i) the axisymmetric and appended DARPA SUBOFF and (ii) tabbed jets in crossflow. The accurate simulation of the flow around marine vessels such as the DARPA SUBOFF is critical for maneuvering predictions, which are inherently challenging due to the characteristically large Reynolds numbers, the complex geometries of the hull, appendages, and propeller, and the unsteady flow-fields, which consist of turbulent boundary layers with pressure gradients, curvature, junction flows, and separations. The understanding of jets in crossflow (JICFs) is important for a variety of applications, and there has been significant interest in designing passive devices to control the mixing and penetration characteristics of the jet, although the specific effects of these devices are not well understood. The unstructured overset method of Horne and Mahesh [1,2] provides the flexibility to perform large-eddy simulations (LES) and direct numerical simulations (DNS) to extract valuable physical insights from these flows.First, wall-resolved LES is performed to study flow about the axisymmetric DARPA SUBOFF hull at a Reynolds number of 1.1×10^6 based on the hull length and free stream velocity. To gain an understanding of the streamline curvature and pressure gradient effects of the hull’s turbulent boundary layer (TBL), the axisymmetric Reynolds-averaged Navier-Stokes equations are derived in an orthogonal coordinate system aligned with streamlines, streamline-normal lines, and the plane of symmetry. Analysis in this frame of reference provides a new perspective on curved TBLs, and has numerous practical benefits, including the orthogonality of the streamline-normal coordinate to the hull surface and to the free stream velocity far from the body, which is critical for studying bodies with concave streamwise curvature. In the potential flow outside the boundary layer, the momentum equations in the streamline coordinate frame naturally reduce to the differential form of Bernoulli’s equation and the s-n Euler equation for curved streamlines. In the curved laminar boundary layer at the front of the hull, the streamline momentum equation represents a balance of the streamwise advection, streamwise pressure gradient, and viscous stress, while the streamline-normal equation is a balance between the streamline-normal pressure gradient and centripetal acceleration. At the mid-hull TBL, the curvature terms and streamwise pressure gradient are negligible, and the results conform to traditional analysis of flat plate boundary layers. Finally, the thick stern TBL causes the curvature and streamwise pressure gradient terms to reappear to balance the turbulent and viscous stresses. This balance is used to explain the characteristic variation of static pressure observed for thick boundary layers at the tails of axisymmetric bodies. Next, trip-resolved LES of the DARPA SUBOFF is performed to investigate the extent to which the details of tripping affect the development of TBLs in model-scale studies, which are limited to moderate Reynolds number TBLs. In particular, four cases are studied at length-based Reynolds numbers of 1.1×10^6 and 1.2×10^6: the bare hull and appended SUBOFF with a resolved experimental trip wire geometry, and the same cases tripped using a simple numerical trip (wall-normal blowing), which serves as an example of artificial computational tripping methods often used in practice. When the trip wire height exceeds the laminar boundary layer thickness, LES reveals that shedding from the trip wire initiates transition, and the near field is characterized by an elevation of the wall-normal Reynolds stress and a modification of the turbulence anisotropy and mean momentum balance. This trip height also induces a large jump in the boundary layer thickness, which affects the rate at which the TBL grows and how it responds to pressure gradients and curvature. In contrast, a trip wire height shorter than the laminar boundary layer thickness is shown to initiate transition at the reattachment point of the trip-induced recirculation bubble. The artificial trip reasonably replicates the resolved trip wire behavior. For each case, the inner layer collapses rapidly in terms of the mean profile, Reynolds stresses, and mean momentum balance. This is followed by the collapse of the Reynolds stresses in coordinates normalized by the local momentum thickness, which proves to be a more robust outer scale than the 99% thickness due to its lower sensitivity to the over-tripped wake at the edge of the boundary layer. The importance of tripping the model appendages is also highlighted, due to their lower Reynolds numbers and susceptibility to laminar separations. Finally, DNS of a JICF with a triangular tab at two positions are performed at jet-to- crossflow velocity ratios of R = 2 and 4 with a jet Reynolds number of 2000 based on the jet’s bulk velocity and exit diameter. DNS and dynamic mode decomposition reveal that a tab on the upstream side of the jet produces Lambda-shaped streamwise vortices in the upstream shear layer (USL), while a tab placed 45 degrees from the upstream side produces a tertiary vortex for R = 4, which is not present at R = 2. For the upstream tab, the presence of streamwise vortices curled around the spanwise USL vortices provides an explanation for the improvements in mixing and spreading associated with an upstream tab. This streamwise vortex structure shows remarkable similarities to the ‘strain- oriented vortex tubes’ observed for disturbed plane shear layers. In contrast, the tab placed 45 degrees from the upstream position produces significantly different effects. At R = 4, the jet cross-section is significantly skewed away from the tab and a tertiary vortex is formed, as observed in past experiments on round JICFs at relatively high R and low Reynolds numbers. The 45 degree tab produces asymmetric effects in the wake of the jet at R = 2, but the effect on the jet cross-section is much smaller, highlighting the sensitivity of jets at high R to asymmetric perturbations.
  • Thumbnail Image
    Item
    Input-output analysis of high-speed turbulent jet noise
    (2018-06) Jeun, Jin Ah
    We use input-output analysis to predict and understand the aeroacoustics of high-speed turbulent jets. We consider linear perturbations about Reynolds-averaged Navier-Stokes (RANS) solutions of ideally expanded, axisymmetric, compressible turbulent jets under various operating conditions. For jet noise, a key aspect of our method is the ability to spatially separate near-field input forcing (driven by nonlinear turbulence) from far-field acoustic output. Precisely the same idea, namely the separation of sources and outputs, forms the basis of traditional acoustic analogies. Different from the usual statistical descriptions of the acoustic source terms, input-output analysis provides a dynamical description based on modes correlated over significant distances within the flow. Specifically, we compute optimal and sub-optimal harmonic forcing functions and their corresponding linear responses governed either by the linearized Euler equations (LEE) or by the linearized Navier-Stokes (LNS) equations, using singular value decomposition of the resolvent operator. For supersonic jets, the optimal response closely resembles a wavepacket in both the near-field and the far-field such as those obtained by the parabolized stability equations (PSE), and this mode dominates the response. For subsonic jets, however, the singular values indicate that the contributions of sub-optimal modes to noise generation are nearly equal to that of the optimal mode, explaining why the PSE do not fully capture the far-field sound in this case. Furthermore, we utilize a high-fidelity large-eddy simulation (LES) data to assess the prevalence of sub-optimal modes in the unsteady data. By projecting the LES source term data onto input modes and the LES acoustic far-field onto output modes, respectively, we demonstrate that sub-optimal modes of both types are physically relevant. Far-field acoustics generated from turbulent jets are further modeled, using a Ffowcs Williams-Hawkings (FW-H) solver implemented directly within linear input-output analysis framework. Our hybrid input-output/FW-H method efficiently connects input fluctuations embedded in the jet turbulence to pressure outputs in the far-field, and recovers a significant portion of the LES acoustic energy. By repeating input-output analysis over a wide range of frequencies, we find that the far-field acoustic spectra broaden with increasing the radiation angles, as observed in experiments. To distill acoustically relevant sources, input forcings are further restricted by introducing a new weighting matrix, which selects forcing functions only in the region that contains high turbulent kinetic energy (TKE). We then find that input modes correspond exactly to wavepackets with asymmetric pseudo-Gaussian envelope functions. Furthermore, wavepackets obtained by input-output analysis collapse to a single shape when scaled by $St^{-0.5}$, where $St$ is the jet Strouhal number. This explains the success of recent theoretical models based on stochastic similarity wavepackets.
  • Thumbnail Image
    Item
    Large Eddy Simulation of complex flow over submerged bodies
    (2018-02) Kumar, Praveen
    Predicting the complex flow over a submerged marine vessel in maneuver has two major challenges: the hull boundary layer and the flow due to the propeller. Large eddy simulation (LES) using the dynamic Smagorinsky model (DSM) (Germano \textit{et al.} 1991, Lilly 1992) and discrete kinetic energy conserving numerical method of Mahesh \textit{et al.} (2004) has successfully predicted complex flows in the past. This dissertation discusses four advancements towards reliably using LES to predict and understand the complex flows encountered during maneuvers of submerged marine vessels: (1) understanding skin-friction in axisymmetric boundary layers evolving under pressure gradients, (2) simulating attached flow over axisymmetric hulls and wake evolution, (3) assessing the dependence of the stern flow and axisymmetric wake on hull boundary layer characteristics, and (4) simulating flow through a propeller at design operating condition. Axisymmetric boundary layers are studied using integral analysis of the governing equations for axial flow over a circular cylinder. The analysis includes the effect of pressure gradient and focuses on the effect of transverse curvature on boundary layer parameters such as shape factor ($H$) and skin-friction coefficient ($C_f$), defined as $H = \delta^*/\theta$ and $C_f = \tau_w/(0.5\rho U_e^2)$ respectively, where $\delta^*$ is displacement thickness, $\theta$ is momentum thickness, $\tau_w$ is the shear stress at the wall, $\rho$ is density and $U_e$ is the streamwise velocity at the edge of the boundary layer. Useful relations are obtained relating the mean wall-normal velocity at the edge of the boundary layer ($V_e$) and $C_f$ to the boundary layer and pressure gradient parameters. The analytical relations reduce to established results for planar boundary layers in the limit of infinite radius of curvature. The relations are used to obtain $C_f$ which shows good agreement with the data reported in the literature. The analytical results are used to discuss different flow regimes of axisymmetric boundary layers in the presence of pressure gradients. Wall-resolved LES is used to simulate flow over an axisymmetric body of revolution at a Reynolds number, $Re=1.1 \times 10^6$, based on freestream velocity and the length of the body. The geometry used in the present work is an idealized submarine hull (DARPA SUBOFF without appendages) at zero angle of pitch and yaw. The computational domain is chosen to avoid confinement effects and capture the wake up to fifteen diameters downstream of the body. The unstructured computational grid is designed to capture the fine near-wall structures as well as the wake. LES results show good agreement with the available experimental data. The axisymmetric turbulent boundary layer has higher skin-friction and higher radial decay of turbulence away from the wall, compared to a planar turbulent boundary layer under similar conditions. The mean streamwise velocity exhibits self-similarity, but the turbulent intensities are not self-similar over the length of the simulated wake, consistent with previous studies reported in the literature. The axisymmetric wake transitions from high-$Re$ to low-$Re$ equilibrium self-similar solutions, as theoretically proposed and observed for axisymmetric wakes in the past. The recycle-rescale method of \citet{Lund} is first implemented for unstructured grids and massively parallel platforms and then extended to spatially developing thin axisymmetric turbulent boundary layers. LES of flow over the stern portion of the hull is performed with a prescribed turbulent inflow at a momentum thickness $\theta/a=0.078$ and a momentum thickness-based Reynolds number $Re_{\theta}=2000$, where $a$ is the radius of curvature, to understand the dependence of the flow field in the stern region and the wake, on hull boundary layer characteristics. Additional simulations are performed to study the effect of $Re_\theta$ and $\theta/a$ at the inflow. The turbulent inflows needed for the simulations are generated from auxiliary simulations employing the recycle-rescale methodology. Results are compared to past studies, and used to describe the effect of incoming TBL on the overall flow field. The pressure coefficient on the body is largely insensitive to the incoming boundary layer characteristics, except in the vicinity of flow separation, where it is more sensitive to $\theta/a$. Skin-friction on the other hand, is very sensitive to the boundary layer characteristics. The boundary layer characteristics determine the location of flow separation and hence, the flow field in the stern region and the wake. The wake of the body is more sensitive to $Re_{\theta}$ compared to $\theta/a$. The wake of a five-bladed marine propeller at design operating condition is studied using LES. The mean loads and phase-averaged flow field show good agreement with experiments. Phase-averaged and azimuthal-averaged flow fields are analyzed in detail to examine the mechanisms of wake instability. The propeller wake consisting of tip and hub vortices undergoes streamtube contraction, which is followed by the onset of instabilities as evident from the oscillations of the tip vortices. Simulation results reveal a mutual induction mechanism of instability where instead of the tip vortices interacting among themselves, they interact with the smaller vortices generated by the roll-up of the blade trailing edge wake in the near wake. It is argued that although the mutual-inductance mode is the dominant mode of instability in propellers, the actual mechanism depends on the propeller geometry and the operating conditions. The axial evolution of the propeller wake from near to far field is discussed. Once the propeller wake becomes unstable, the coherent vortical structures break up and evolve into the far wake composed of a fluid mass swirling around an oscillating hub vortex. The hub vortex remains coherent over the length of the computational domain.
  • Thumbnail Image
    Item
    Large Eddy simulation of high Reynolds number complex flows
    (2012-09) Verma, Aman
    Marine configurations are subject to a variety of complex hydrodynamic phenomena affecting the overall performance of the vessel. The turbulent flow affects the hydrodynamic drag, propulsor performance and structural integrity, control-surface effectiveness, and acoustic signature of the marine vessel. Due to advances in massively parallel computers and numerical techniques, an unsteady numerical simulation methodology such as Large Eddy Simulation (LES) is well suited to study such complex turbulent flows whose Reynolds numbers (Re) are typically on the order of 10^6. LES also promises increased accuracy over RANS based methods in predicting unsteady phenomena such as cavitation and noise production. This dissertation develops the capability to enable LES of high Re flows in complex geometries (e.g. a marine vessel) on unstructured grids and provide physical insight into the turbulent flow. LES is performed to investigate the geometry induced separated flow past a marine propeller attached to a hull, in an off-design condition called crashback. LES shows good quantitative agreement with experiments and provides a physical mechanism to explain the increase in side-force on the propeller blades below an advance ratio of J=-0.7. Fundamental developments in the dynamic subgrid-scale model for LES are pursued to improve the LES predictions, especially for complex flows on unstructured grids. A dynamic procedure is proposed to estimate a Lagrangian time scale based on a surrogate correlation without any adjustable parameter. The proposed model is applied to turbulent channel, cylinder and marine propeller flows and predicts improved results over other model variants due to a physically consistent Lagrangian time scale. A wall model is proposed for application to LES of high Reynolds number wall-bounded flows. The wall model is formulated as the minimization of a generalized constraint in the dynamic model for LES and applied to LES of turbulent channel flow at various Reynolds numbers upto Re_tau=10000 and coarse grid resolutions to obtain significant improvement.
  • Thumbnail Image
    Item
    Numerical modeling and simulation of cavitating flows in different regimes
    (2023-03) Brandao, Filipe
    The objective of this dissertation is to develop numerical methodologies for large eddysimulation (LES) of multiphase cavitating flows over different cavitation regimes. Unstructured grids are considered to enable complex geometries to be considered. The dissertation has the following major components: (i) a compressible homogeneous approach for a mixture of water–vapor–gas is developed to study the effect of non–condensable gas on bluff–body cavitation. (ii) Incipient cavitation in the shear layer of a backstep is studied using incompressible simulations of the flow field coupled with a continuum equation for vapor volume fraction. (iii) The inception model is extended to account for multiple groups of bubbles of different sizes and used to investigate the effects of water quality on tip vortex inception. A numerical method based on the homogeneous mixture model, fully compressible formulation and finite rate mass transfer developed by Gnanaskandan and Mahesh [1] is extended to include the effects of non–condensable gas (NCG). We then investigate cavitation over a circular cylinder at two different Reynolds numbers (Re = 200 and 3900 based on cylinder diameter and free–stream velocity) and different cavitation numbers. Two different cavitation regimes are observed depending on free–stream pressure: cyclic and transitional. In the cyclic regime, the cavitated shear layer rolls up into vortices, which are then shed from the cylinder, forming the K´arm´an vortex street, similar to a single phase flow. In the transitional regime, a cavity is formed behind the cylinder, and is only detached after the passage of a condensation shock. As a consequence, there is a drastic drop in shedding frequency. Dynamic mode decomposition (DMD) is performed to explain this change in behavior. DMD reveals that cavitation delays the first transition of the Karman vortex street. The effects of the non–condensable gases on this flow is discussed for both regimes, and it is found that the gas decreases the strength of the condensation shock. It is observed that vapor and gas uniformly introduced in the free–stream, distributed themselves differently in the wake of cylinder depending upon local flow conditions, particularly at lower cavitation numbers as the pressure in the wake dropped below vapor pressure. Vapor and NCG distribution in the boundary layer suggest that cavitation as a mass transfer process only occurs inside a fine layer in the near–wall region, while the remaining boundary layer only undergoes expansion of both vapor and gas. The levels of free–stream void fraction are found to have an impact on the boundary–layer separation point. Vortex stretching and baroclinic torque are greatly reduced in the transitional regime compared to the cyclic regime. Next, the development of a method to simulate cavitation in the incipient regime is presented. The main idea is that since inception is a stochastic process that generates small amounts of vapor for short periods of time, the effects of these small regions of vapor on the liquid density and dynamics can be neglected. Therefore, vapor is treated as a passive scalar in an incompressible liquid. Thus, the equations solved are the incompressible Navier–Stokes equation along with a advection–diffusion equation with source terms for the transport of vapor. The scalar field, however, is advanced in time with a different time step than the one used to advance the velocity field. The model is used to investigate inception in the shear layer of a backward–facing step at Reτ = 1500 (based on skin friction velocity and boundary layer thickness). Statistics are computed for both pressure and vapor volume fraction, and the likelihood of inception is determined. The locations of the preferred sites for cavitation are compared to experimental results and good agreement is achieved. The effects of finite rate evaporation and condensation are revealed by the probability density functions of pressure and volume fraction. The flow topology is investigated and inception is found to occur in the core of the stretched tubular vortical structures with a rotation rate four times higher than the stretching rate. These cavitating tubular structures are elongated two to three times more in their most extensive principal direction than in their intermediate principal direction, and are most likely aligned with the streamwise direction. The model developed for cavitation inception is extended to account for multiple groups of bubbles of different sizes, effectively making it a polydisperse model. This allows us to investigate the effects of water quality on inception. The model is used to simulate inception in a tip vortex of an elliptic hydrofoil at 12 degrees angle of attack and Reynolds numbers of 9 × 105 and 1.4 × 106 based on root chord length and free–stream velocity. It was found that inception is strongly dependent on the amounts of nuclei in the freestream. When the flow is depleted of nuclei, inception is an intermittent event confined to a position very close to the hydrofoils tip. However, when the flow is rich in nuclei, a larger portion of the tip vortex cavitates, as well as part of the suction side very close to the leading edge of the hydrofoil. Probability density functions reveal that cavitation occurs in any region experiencing a pressure field lower than vapor pressure when the flow is rich in nuclei, while extremely low values of pressure (usually kPa of tension) are required to make a flow deplete of nuclei cavitate. The topology of a flow poor in nuclei was investigated and inception was found to occur in regions dominated by irrotational straining with high stretching rates. Particles were released from the hydrofoil tip and tracked. It is seen that at the higher Reynolds number, the particles are more likely to experience low pressures. However, the amount of time they are subject to very low pressures is shorter at the higher Reynolds number.
  • Thumbnail Image
    Item
    Numerical modeling of turbulent flows in arbitrarily complex natural streams.
    (2010-08) Kang, Seok Koo
    An efficient and versatile numerical model is developed for carrying out high-resolution simulations of turbulent flows in natural meandering streams with arbitrarily complex, albeit fixed, bathymetry and instream hydraulic structures. The numerical model solves the three-dimensional, unsteady, incompressible Navier-Stokes and continuity equations in generalized curvilinear coordinates. This model can handle the arbitrary geometric complexity of natural streams by using the sharp-interface curvilinear immersed boundary (CURVIB) method. To enable efficient simulations on grids with tens of millions of nodes in long and shallow domains typical of natural streams, the algebraic multigrid method (AMG) is used to solve the Poisson equation for pressure. Free-surface is treated either with the rigid-lid approach or modeled using a two-phase flow approach implemented using level-sets. Depending on the desired level of resolution and available computational resources, the numerical model can either simulate turbulence via direct numerical simulation (DNS), large-eddy simulation (LES) or unsteady Reynolds-averaged Navier-Stokes (URANS) simulation. The numerical model is validated by simulating several test cases for which good quality laboratory data or benchmark simulations are available in the literature. The potential of the model as a powerful tool for simulating energetic coherent structures in turbulent flows in natural river reaches is demonstrated by applying it to carry out LES and URANS simulations in a field scale natural-like meandering stream, Outdoor StreamLab, at resolution sufficiently fine to capture vortex shedding from cm-scale roughness elements on the bed. Comparisons between the simulated mean velocity and turbulence kinetic energy fields with field-scale measurements are reported and show that the numerical model can capture all features of the measured flow with high accuracy. Furthermore, the simulated flowfields are analyzed to elucidate the multi-faceted physics of the flow in a natural stream with pool-riffle sequences and to uncover the underlying physical mechanisms. The simulations provide new insights into the role of large-scale roughness in flow through riffles and elucidate the three-dimensional structure, interactions and governing mechanisms of the inner and outer bank secondary flow cells and recirculation zones in the pools. Moreover, the simulations underscore the role of turbulence anisotropy throughout the stream and suggest important links between stream hydrodynamics and morphodynamics. Calculations are also carried out for the same meandering stream with an instream structure installed along its outer bank to demonstrate the utility of the model as a powerful tool for developing science-based design guidelines for stream restoration.