Browsing by Author "Julien, Pierre Y., committee member"

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Open Access
Advanced Bayesian framework for uncertainty estimation of sediment transport models
(Colorado State University. Libraries, 2018) Jung, Jeffrey Youngjai, author; Niemann, Jeffrey D., advisor; Greimann, Blair P., committee member; Julien, Pierre Y., committee member; Wang, Haonan, committee member
Numerical sediment transport models are widely used to forecast the potential changes in rivers that might result from natural and/or human influences. Unfortunately, predictions from those models always possess uncertainty, so that engineers interpret the model results very conservatively, which can lead to expensive over-design of projects. The Bayesian inference paradigm provides a formal way to evaluate the uncertainty in model forecasts originating from uncertain model elements. However, existing Bayesian methods have rarely been used for sediment transport models because they often have large computational times. In addition, past research has not sufficiently addressed ways to treat the uncertainty associated with diverse sediment transport variables. To resolve those limitations, this study establishes a formal and efficient Bayesian framework to assess uncertainty in the predictions from sediment transport models. Throughout this dissertation, new methodologies are developed to represent each of three main uncertainty sources including poorly specified model parameter values, measurement errors contained in the model input data, and imperfect sediment transport equations used in the model structure. The new methods characterize how those uncertain elements affect the model predictions. First, a new algorithm is developed to estimate the parameter uncertainty and its contribution to prediction uncertainty using fewer model simulations. Second, the uncertainties of various input data are described using simple error equations and evaluated within the parameter estimation framework. Lastly, an existing method that can assess the uncertainty related to the selection and application of a transport equation is modified to enable consideration of multiple model output variables. The new methodologies are tested with a one-dimensional sediment transport model that simulates flume experiments and a natural river. Overall, the results show that the new approaches can reduce the computational time about 16% to 55% and produce more accurate estimates (e.g., prediction ranges can cover about 6% to 46% more of the available observations) compared to existing Bayesian methods. Thus, this research enhances the applicability of Bayesian inference for sediment transport modeling. In addition, this study provides several avenues to improve the reliability of the uncertainty estimates, which can help guide interpretation of model results and strategies to reduce prediction uncertainty.
Open Access
Dynamics and parameterization of stably stratified turbulence: implications for estimates of mixing in geophysical flows
(Colorado State University. Libraries, 2014) Mater, Benjamin D., author; Venayagamoorthy, Subhas K., advisor; Bledsoe, Brian P., committee member; Dasi, Lakshmi P., committee member; Julien, Pierre Y., committee member
This research focuses on the relationship between the observed length scales of overturns in stably-stratified shear-flow turbulence and the fundamental length scales constructed from dimensional analysis of basic physical quantities. In geophysical flows such as the ocean, overturns are relatively easy to observe while the basic quantities are not. As such, overturns provide a means of inferring basic quantities if the relationship between the observed and fundamental scales are known. In turn, inferred values of the basic quantities, namely the the turbulent kinetic energy k, and the dissipation rate of turbulent kinetic energy ϵ, can be used to estimate diapycnal diffusivity (i.e. turbulent mixing). Most commonly, the observed Thorpe length scale, LT, is assumed to scale linearly with the fundamental Ozmidov scale, LO =(ϵ/N3)1/2, so that inferred values of ϵ can be obtained and used to estimate mixing from the Osborn formulation for diapycnal diffusivity. A major goal of this research is to re-examine this and other possible scalings using dimensional analysis, direct numerical simulation (DNS), laboratory data, and field observations. The preliminary chapters constitute a fresh approach at dimensional analysis that presents the fundamental length scales, time scales, and dimensionless parameters relevant to the problem. The relationship between LT and the fundamental length scales is then examined for the simple case of homogeneously stratified turbulence (without shear) using DNS. A key finding is that the common practice of inferring ϵ from LT ~ LO, is valid at the transition between a buoyancy-dominated regime and an inertia-dominated regime where the time scale of the buoyancy oscillations, N-1, roughly matches that of the inertial motions, TL = k/ϵ. Regime definition is made possible using a non-dimensional buoyancy strength parameter NTL = Nk/ϵ. Next, the problem is generalized to consider mean shear, and thus, a shear strength parameter, STL = Sk/ϵ, and the gradient Richardson number, Ri = N2/S2, are considered along with NTL to define three regimes available to high Reynolds number stratified shear-flow turbulence: a buoyancy-dominated regime (NTL ≳ 1.7, Ri ≳ 0.25), a shear-dominated regime (STL ≳ 3.3, Ri ≲ 0.25), and an inertia-dominated regime (NTL ≲ 1.7, STL ≲ 3.3). The regimes constitute a multi-dimensional parameter space which elucidates the independent influences that shear and stratification have on the turbulence. Using a large database of DNS and laboratory results, overturns are shown to have unique scalings in the various regimes. Specifically, LT ~ k1/2N-1, LT ~ k1/2S-1, and LT ~ k3/2ϵ-1 in the buoyancy-, shear-, and inertia-dominated regimes, respectively. LT ~ LO is found only for the case of NTL = O(1) and STL ≲ 3.3, or for NTL = O(100), STL ≈ 3.3 and Ri ≈ 0.25 when shear is present. In all three regimes, LT is found to generally indicate k rather than ϵ. An alternative parameterization of turbulent diffusivity is developed based on inferred values of k with a practical eye toward field applications. When tested with DNS and laboratory data, the new model is shown to be more accurate than estimates based on inferred values of ϵ. The multi-parameter framework is broadened with consideration for the turbulent Reynolds number, ReL, thus allowing for an evaluation of existing parameterizations of diapycnal mixing efficiency, R*f. Select DNS and laboratory data sets are used in the analysis. A key finding is that descriptions of R*f based on a single-parameter are generally insufficient. It is found that Ri is an accurate parameter in the shear-dominated regime but fails in the inertia-dominated regime where turbulence is generated by external forcing (rather than mean shear). In contrast, the turbulent Froude number, FrT = (LO/LT)2/3, is an accurate parameter in the inertia-dominated regime but loses accuracy in the shear-dominated regime. Neither Ri or FrT sufficiently describe R*f in the buoyancy-dominated regime where additional consideration for ReL is needed. Another key finding is that the popular buoyancy Reynolds number, Reb = ReL(NTL)-2, is a particularly misleading parameter for describing R*f because it fails to distinguish between (i) a low-Reynolds number, weakly stratified regime of low efficiency (low ReL, low NTL, low R*f) typical of DNS flows and (ii) a high-Reynolds number, strongly stratified regime of high efficiency (high ReL, high NTL, high R*f) typical of geophysical flows. Finally, oceanic observations from Luzon Strait and the Brazil Basin are featured to examine the relationship between LT and LO in geophysical flows where turbulence is driven by overturns that are very large by open ocean standards. LT is found to increase with respect to LO as a function of the normalized overturn size LT = LTN1/2ν-1/2. When large overturns are present, dissipation rates inferred from LT ~ LO are generally larger than measured values on average. The overestimation is quantified over a spring tidal period at Luzon Strait where depth- and time-integration of inferred and measured values show that inferred energy dissipation is four times too large.
Open Access
Dynamics and structure of stably stratified turbulence
(Colorado State University. Libraries, 2012) Schaad, Simon, author; Venayagamoorthy, Subhas Karan, advisor; Julien, Pierre Y., committee member; Dasi, Lakshmi Prasad, committee member
The dynamics and turbulent structures of stably stratified turbulence are explored via direct numerical simulations (DNS). The structural features of stratified turbulence and its relationship to the flow dynamics has been the subject of many recent investigations. In strongly stratified turbulent flows, the formation of large-scale quasi-horizontal vortices in layers with strong vertical variability has been observed in laboratory experiments. Enstrophy isosurfaces of strongly stable flows indicate the emergence of randomly distributed 'pancake'-like structures with near horizontal orientation at later times. The strongly stratified simulations are diffusive and dominated by linear internal waves. The results suggest a decoupling between horizontal and vertical dynamics as the vertical dynamics can be described using rapid-distortion theory (RDT) while horizontal dynamics continue to be dominated by non-linear effects not captured by RDT. The integral flux Richardson number for decaying turbulence is the ratio of background potential energy gain to turbulent kinetic energy loss. The traditional flux-based formulation converges upon this ratio only when integrations are performed over an entire event, while the irreversible formulation converges rapidly without error from reversible effects. Mixing efficiency is a property of the flow for energetic flow but becomes a property of the fluid for diffusive flows and subject to Prandtl number effects. RDT models predict the flux Richardson number scales as the inverse Prandtl number at the diffusive limit when the Prandtl number is greater than unity. Mixing efficiency comparisons between DNS and physical grid-tow experiments reveal a large discrepancy for strong stratification, which is attributed in part to the low Reynolds numbers attained in both DNS and grid-tow experiments. Overturns are unstable conditions where heavier fluid resides above lighter fluid. The collapse of these local instabilities produce additional patches of turbulence and mixing making overturns an important mechanism in stratified turbulence. The overturning structures in strongly stratified flow resemble the quasi-horizontal vorticity structures and were found to be correlated with increased horizontal vorticity. The Thorpe scale, a measure of overturning structure height, and the Ozmidov scale equate only at the critical condition where inertial and buoyancy effects are equal (i.e. the turbulent Froude number is unity). The error of inferred dissipation rates from equating the Thorpe and Ozmidov scales was found to be up to two orders of magnitude.
Open Access
Dynamics of flow in river bends
(Colorado State University. Libraries, 2018) Aseperi, Oladapo, author; Venayagamoorthy, Subhas K., advisor; Julien, Pierre Y., committee member; Ramirez, Jorge A., committee member; Barnes, Elizabeth, committee member
Water is indispensable to life and the means by which it is conveyed is equally important. Natural rivers and manmade channels play a critical role in this respect because they are vital for water supply, navigation, transport of sediments, pollutants and nutrients. Most natural rivers typically have meandering (curved) geometries which make a direct study of their flow dynamics cumbersome. In order to reduce this complexity, natural rivers are usually idealized as open channel bends with rigid boundaries in order to gain insights into the flow dynamics. As such, this research examines the dynamics of flow in open channel bends with rigid boundaries, using computational fluid dynamics (CFD). The particular computational fluid dynamics code used in this research, discretizes the equations of fluid motion (i.e. the Navier-Stokes equations) using a finite volume scheme while tracking the free surface with the volume of fluid method. Turbulence was incorporated into the solution of the equations using large eddy simulation techniques. Even though the general aim is to improve current understanding of natural river bend physics, the specific aims of this research are threefold. These are: (1) to study the effects of radius of curvature on the flow physics of an idealized river bend; (2) to study in detail the effect of a variation in curvature length on the flow structure and dynamics of an open channel bend; and (3) examine in detail the effect of inertial forces on the flow dynamics of an idealized river bend by varying the inflow Froude number. While some of the findings in this research confirm some of the results that has already appeared in literature, a significant amount of results highlight new insights into dynamic events in an open channel bend. As a concrete example on the effect of curvature on the flow structure, simulation results show that the maximum bed and wall shear stress are exerted on the inner wall at the entrance to the curve regardless of curvature. However, further into the bend, the maximum shear stress shifts to the outer bend and wall region. Furthermore, the angular distance into the bend at which this occurs is found to depend on the curvature of the channel. Thus, for a mild channel, the maximum shear stress shifts to the outer bend and wall region a short angular distance from the entrance. This distance increases with a decrease in radius of curvature (i.e. as the channel gets tighter) with the maximum shear stress in the tightest channel (that was simulated in this study) always occurring on the inner side of the bend for the entire channel length. Another key finding comes from an investigation of the effect of the variation of curvature length on the flow structure and dynamics of open channel bends. It was found that the flow circulation pattern depends on the curvature length. Simulation results showed that shorter channel bends reached fully developed vortical states faster than similar channels with longer lengths. Furthermore, new results from this study provide a clear explanation for the emergence of a three-cell circulation structure in tight channel bends that occurs as a result of the splitting of the main cell circulation due to the enhanced vorticity in tight bends. Finally, the study on the effects of Froude number on flow structure clearly shows that an increase in the inertia of the fluid does not affect the radial pressure gradient force (a very important force that plays a critical role in shaping the bend channel dynamics) in a mild channel. Remarkably in the tight channels, there seems to be a positive correlation between the magnitudes of the fluid inertia (as measured by the velocity) and the radial pressure gradient force. This finding has important implications for the modeling of river bends since geometric factors are not sufficient to adequately parameterize the flow structure under certain circumstances in reduced order models. These and more results not mentioned in this abstract are detailed in this dissertation. The overall aim of this research is to provide better insights into bend channel flow dynamics so as to enable engineers to carry out more accurate river modeling and training works.
Open Access
Flow dynamics and scalar transport in drinking water contact tanks
(Colorado State University. Libraries, 2013) Barnett, Taylor C., author; Venayagamoorthy, Subhas Karan, advisor; Julien, Pierre Y., committee member; Sakurai, Hiroshi, committee member
The research and studies presented in this thesis focus on ways to improve the internal hydraulics of chlorine contact tanks used in drinking water disinfection systems. This was accomplished through the use of computational fluid dynamics (CFD) and physical tracer studies of a number of different systems. Three primary tank modifications were investigated in these studies: internal baffling; inlet modifications; and random packing material. The findings from these studies were then applied in a case study of the Jamestown chlorine contact tank. All of the studies presented in this thesis use the baffle factor (BF) designation as defined by the United States Environmental Protection Agency as the primary indicator of a system's disinfection efficiency. The CFD models used for the internal baffling study were first validated using a laboratory scale study of the Embsay chlorine contact tank in Yorkshire, England. This tank footprint was then modified to replicate a precast concrete tank that was installed in the Hydraulics Laboratory located at the Engineering Research Center (ERC) at Colorado State University. This concrete tank was used as the footprint for a parametric study in which the number and length of internal baffles were modeled in various configurations. The internal hydraulics of this baffle tank were optimized using only two dimensionless relationships namely: the baffle opening ratio L* and the baffle opening to channel width ratio Lbo/Wch. The resulting tank geometry from these two relationships yielded a BF of 0.80 and also maximized the length to width ratio of each channel within the concrete tank. The inlet modification study was performed to investigate how the BF of a 400-gallon doorway storage tank could be improved. Three different inlet types with two inlet sizes were modeled and simulated for six different flow rates. Three of these CFD simulations were then physically tested using both saline and lithium tracers to validate the computer models. Key findings from this study show that the size of the inlet and its orientation play a dominant role in the internal hydraulics of the system. For the random packing material study, three different packing material sizes, two tank sizes, and two different flow rates were tested. CFD models were not feasible due to the randomness of how the packing material would settle in these contact tanks. Over 64 saline tracer studies and 6 lithium tracer studies were conducted to complete this study. Key findings show that the initial BF of the system and the volume of the tank filled with the packing material were the dominant variables in the study. The tank size, flow rate, and packing material size had little to no impact on the performance. The Jamestown case study presented in this thesis used findings from both the internal baffle study and the inlet modification study. The BF of the contact tank would fluctuate annually between 0.52 and 0.63 due to a shift in flow regimes caused by a change in the system's flow rate. This turbulent to laminar flow regime change was validated with the use of CFD models coupled with physical tracer studies. Several inlet modifications were investigated using CFD to determine what modifications, if any, the plant operators should implement. Key findings from the CFD models showed that with the proper inlet modification, the BF of the system could be stabilized at 0.63 during both the high flow summer months and low flow winter months.
Open Access
Hydraulic effects of biofilms on the design and operation of wastewater forcemains
(Colorado State University. Libraries, 2016) Michalos, Christopher T., author; Thornton, Christopher I., advisor; Grigg, Neil S., committee member; Julien, Pierre Y., committee member; Williams, John D., committee member
The impact of biofouling on wastewater forcemains is generally not accounted for in current design practice and little information is available in literature regarding the effect of wastewater biofilms on forcemain hydraulics. In practice, many engineers select a clean water, new pipe roughness factor, to perform hydraulic calculations which may lead to under-sizing wastewater lift station pumps. Forcemains have to cope with a particularly challenging task; they have to ensure that solids contained in the wastewater (sand, gravel, organics) are readily transported along with the wastewater. Forcemain design standards generally recommend a velocity of 2.0 ft/s (0.6 m/s) to prevent deposition of solids and a velocity of 3.5 ft/s (1.1 m/s) to re-suspend solids that may have settled. To further complicate forcemain design and operation; wastewater lift station pumps generally operate intermittently which requires remobilization of any material that may have settled while the pumps remain idle. Therefore, forcemains must be designed to be self-cleaning in order to prevent solids deposition which could cause increased sulfide production leading to corrosion and odor issues; loss of capacity through a reduction of cross sectional area; or even blockage at low points, or at the toe of an adversely sloped pipe leading to costly removal. The goal of this research is to identify short-comings in current forcemain design practice by 1) evaluating the hydraulic effect of biofilms on the absolute roughness (ks) of forcemains; 2) evaluating the hydraulic effect of biofilms on Hazen-Williams C factor; and 3) determine critical velocity required for sediment transport, air clearing, self-cleansing, and optimal diameter of forcemains, which are not identified in forcemain design standards. Operational data were collected and evaluated for 20 municipal wastewater forcemains located in the United States. Data from previous studies, academic research, reports, and published papers were used to supplement and support research findings. A total of 415 data points obtained from 68 forcemain systems ranging from 3- to 66 inches in diameter were evaluated as part of this research. Results of the hydraulic analysis determined that 44% of the systems evaluated were operating at velocities between 2- and 3.5 ft/s and 16% of systems were operating at velocities less than 2 ft/s; indicating that these systems are over designed and do not provide sufficient velocity to re-suspend solids promoting sedimentation. The hydraulic effect of biofilms on forcemain flow resistance was evaluated and determined that ks and C factor varied with forcemain velocity. Calculated values of ks ranged from approximately 35 mm to 0.01 mm, with larger values occurring at velocities less than 1 m/s (3.3 ft/s). The upper range of ks values are orders of magnitude larger than the standard clean water, new pipe ks value found in literature. C factor results ranged from approximately 30 to 150; approximately 60% of forcemain systems evaluated are operating at C factors less than 100, which is much lower than the recommended values of 130 – 150, depending on pipe material. Results suggest that biofilms effect forcemains in a similar manner regardless of pipe diameter, material, or age. Although velocity was determined to be the principle factor affecting ks and C factor; a comparison of the C factor results to ks results show that C factor is dependent upon both velocity and diameter. Equations were developed to estimate ks and C factor and should be utilized along with the Colebrook-White / Darcy-Weisbach and Hazen-Williams equations to estimate the friction headloss for forcemains. The required design velocity for self-cleansing, sediment transport, air clearing, and economical diameter ranges from approximately 4- to 11 ft/s, depending on diameter. Selecting a design velocity between 2 ft/s (0.6 m/s) and 3.5 ft/s (1.1 m/s) may not be appropriate and the minimum design velocity should be selected upon either the self-cleansing velocity or economical pipe sizing. Although each system should be evaluated to determine the correct minimum design velocity based upon the proposed system properties, these results indicate that the minimum forcemain design velocity should be at least 5 ft/s (1.5 m/s).
Open Access
Insights and methodologies in wall-bounded turbulent channel flows
(Colorado State University. Libraries, 2024) Mishra, Harshit, author; Venayagamoorthy, Subhas Karan, advisor; Gates, Timothy K., committee member; Julien, Pierre Y., committee member; Barnes, Elizabeth, committee member
Wall-bounded channel flows are of massive interest to civil and environmental engineers due to their immense application for water supply and management. This dissertation addresses five key aspects of turbulent channel flows relevant to practicing engineers, laboratory researchers, fluid scientists, and consultants leveraging computational fluid dynamics for modeling turbulent flows. In the first study, a device was developed and tested to enable Particle Image Velocimetry (PIV) for free surface flows. Measuring flows reliably requires that illumination provided by the laser sheet remains undisturbed. In open channel flows, introducing the laser sheet from the free surface can be necessary as the bed may be optically opaque. An oscillating free surface can further complicate maintaining an undisturbed laser sheet. This research has shown that the disturbance of the laser sheet, when introduced from the free surface, can be mitigated by introducing an improvised device called an optical coupler. The effect of the coupler on the measured velocity field was systematically studied using independent Laser Doppler Anemometer (LDA) measurements. The effect of the coupler on the measured velocity field was confined to its vicinity near the surface of the flow. The mean flow profile remains largely unaffected. Additionally, appropriate material for fabricating the coupler has been recommended by studying the relative performance of a glass and acrylic coupler. While the glass coupler measurements were closer to the undisturbed flow profile, the durability and ease of handling an acrylic coupler make it a viable alternative. The second study is focused on ensuring fully developed flow in short laboratory flumes. Ensuring a fully developed flow is essential for any experimental or modeling study that involves wall-bounded flows. Flow development in pipes has been extensively studied, and empirical relationships have been widely published. Recently, similar studies on open channels have revealed that the entrance length in laboratory flume is ≈ 100h, where h is the depth of the flow. Such a prescription renders most laboratories unfit for experimental work. Further, the inlet configuration in the flume can also hamper flow development, even after the length requirements are met. In this study, we develop a methodology to obtain developed flow in short channels by modifying the inlet and tripping the boundary layer. Further, we also provide a robust, rapid test to confirm if the flow is fully developed using Direct Numerical Simulation (DNS) datasets. The proposed method is validated using flume experiments for flows with friction Reynolds number Reτ ∼ 1500−3000. Against the current prescription, we show that it is possible to obtain fully developed profiles within a distance of ≈ 20h from the inlet. In the next (third) study, we leverage the DNS data for closed channel flow for a range of friction Reynolds Number (Reτ ∼ 180 − 5000) to develop a new One Point Friction Velocity Method (OPFVM) to calculate friction velocity U∗ in terms of free-surface velocity Um, flow depth h and kinematic viscosity ν for smooth wall-bounded flows. In contrast to prevalent methods that require several cumbersome near-boundary measurements to obtain friction velocity, the OPFVM relies on a single easy-to-measure free-surface velocity measurement. The formulation obtains friction velocity for a closed channel flow (CCF) DNS regime with Reτ = 10049 and on four open channel flow (OCF) DNS regimes with Reτ ∼ 180 − 2000. The same formulation was then experimentally verified in our laboratory. To avoid being prescriptive, a sensitivity analysis was performed to determine the permissible variation in Um to restrict the error in estimated U∗ to 2%. The relationship between the depth-averaged velocity Ub and the maximum free-stream velocity Um is also explored using the DNS datasets and an approximate relationship between Ub and Um is proposed. With advances in remote sensing technology that enables free-stream velocity measurements, this method extends the potential to measure even the friction velocity remotely. Computational Fluid Dynamics (CFD) is an essential tool for analyzing fluid flows. The k − ϵ model is a turbulence model used in Raynold-Averaged Navier-Stokes simulations to close the Reynolds stress terms. The empirical constants used in k − ϵ model were obtained using experiments conducted at low Reynolds numbers several decades ago. In this study, we revisit the turbulent viscosity parameter Cµ, based on the stress-intensity ratio c2 = |uw|k. Here, |uw| and k are the absolute values of the Reynolds stress and turbulent kinetic energy, respectively. Through a-priori comparisons, we find that the widely accepted value of Cµ = 0.09, does not agree with the latest DNS and experimental datasets of wall-bounded turbulent planar flows. Therefore, a new value is suggested by averaging c2 in the equilibrium region, where the production (P) of k is within 10% of the dissipation rate(ϵ), and consequently, c4 ≈ Cµ. We evaluate flows up to friction Reynolds number Reτ ≈ 10000 and find that with increasing Reτ, Cµ approaches a value of 0.06, which is 50% lower than the prevalent value of 0.09. Finally, we perform an a-priori test with the new (proposed) value of Cµ = 0.06 to show that the estimated turbulent viscosity νT for wall-bounded flows is in much closer agreement with the exact (DNS) values than when νT is estimated using Cµ = 0.09. The final study develops a new scaling law for wall-bounded turbulent flows. This formulation eliminates all arbitrary constants and depends only on physical parameters, namely, the free-stream velocity Um, the friction velocity U∗, the kinematic viscosity ν, and the distance from the wall z. This is a significant step towards describing the velocity profile using these pertinent parameters.
Open Access
Methodology for calculating shear stress in a meandering channel
(Colorado State University. Libraries, 2010) Sin, Kyung-Seop, author; Thornton, Christopher I., advisor; Julien, Pierre Y., committee member; Wohl, Ellen E., 1962-, committee member
Shear stress in meandering channels is the key parameter to predict bank erosion and bend migration. A representative study reach of the Rio Grande River in central New Mexico has been modeled in the Hydraulics Laboratory at CSU. To determine the shear stress distribution in a meandering channel, the large scale (1:12) physical modeling study was conducted in the following phases: 1) model construction 2) data collection 3) data analysis, and 4) conclusion and technical recommendations. Data of flow depth, flow velocity in three velocity components (Vx, Vy and Vz) and bed shear stress using a Preston tube were collected in the laboratory. According to the laboratory data analysis, shear stress from a Preston tube is the most appropriate shear stress calculation method. In case of the Preston tube, data collection was performed directly on the surface of the channel. Other shear stress calculation methods were based on ADV (Acoustic Doppler Velocity) data that were not collected directly on the bed surface. Therefore, the shear stress determined from ADV measurements was underestimated. Additionally, Kb (the ratio of maximum shear stress to average shear stress) plots were generated. Finally, the envelope equation for Kb from the Preston tube measurements was selected as the most appropriate equation to design meandering channels.
Open Access
Mixing and transport of passive scalars around obstacles in environmental flows
(Colorado State University. Libraries, 2011) Ku, Hyeyun, author; Venayagamoorthy, Subhas K., advisor; Bledsoe, Brian P., committee member; Julien, Pierre Y., committee member; Ito, Takamitsu, committee member
To view the abstract, please see the full text of the document.
Open Access
Mixing in stably stratified turbulent flows: improved parameterizations of diapycnal mixing in oceanic flows
(Colorado State University. Libraries, 2018) Garanaik, Amrapalli, author; Venayagamoorthy, Subhas Karan, advisor; Bienkiewicz, Bogusz, committee member; Barnes, Elizabeth, committee member; Julien, Pierre Y., committee member
Mixing of fluid with different properties across a gravitationally stable density interface, due to background turbulence is an ubiquitous phenomenon in both natural and engineered flows. Fundamental understanding and quantitative prediction of turbulent mixing in stratified flows is a challenging problem, with a broad range of applications including (but not limited to) prediction of climate, ocean thermohaline circulation, global heat and mass budget, pollutant and nutrients transport, etc. Large scale geophysical flows such as in the ocean and atmosphere are usually stably stratified i.e. the density increases in the direction of gravitational force. The stabilizing nature of the density layers has a tendency to inhibit the vertical motion. In such flows, diapycnal mixing, i.e. mixing of fluid across the isopycnal surfaces of constant density, plays a crucial role in the flow dynamics. In numerical models of large scale flows, turbulent mixing is inherently a small scale phenomenon that is difficult to resolve and is therefore generally parameterized using known bulk parameters of the flow. In oceans, the mixing of water masses is typically represented through a turbulent (eddy) diffusivity of mass Kρ. A widely used formulation for Kρ in oceanic flows is given as Kρ = Γϵ/N2, ϵ is the rate of dissipation of turbulent kinetic energy, N = √(-g/ρ)(∂ρ/∂z) is the buoyancy frequency of the background stratification, ρ is the density, Γ = Rƒ/(1 - Rƒ) is a mixing coefficient and Rƒ is the mixing efficiency, that is widely (but questionably) assumed to be constant or sometimes parameterized. However, a robust and universal parameterization for the mixing efficiency remains elusive to date despite numerous studies on this topic. This research focuses on improved parameterizations of diapycnal mixing through an integration of theoretical knowledge with observational and high resolution numerical simulation data. The main objectives are: (1) to provide a better assessment of field microstructure data and methodology for data analysis in order to develop/test appropriate parameterization of the mixing efficiency, (2) to determine the relevant length and velocity scales for diapycnal mixing, (3) to provide improved parameterization(s) of diapycnal mixing grounded on physical reasoning and scaling analysis, (4) to provide a practical field method to identify the dynamic state of turbulence in stably stratified flows from measurable length scales in the ocean. First, an analysis of field microstructure data collected from different locations in the ocean was performed to verify existing parameterizations. A key finding is that the mixing efficiency, Rƒ does not scale with buoyancy Reynolds number, Rℓb, as been proposed previously by others. Rather, Rƒ depends on the strength of background stratification. In a strongly stratified thermocline, a constant value for the mixing efficiency is found to be reasonable while for weakly stratified conditions (e.g. near boundaries) a parameterization is required. A discussion on different methods to estimate the background shear and stratification from field data is provided. Furthermore, the present state-of-the-art microstructure instruments measure the small scale dissipation rate of turbulent kinetic energy ϵ from one dimensional components by invoking the small scale isotropy assumption that is strictly valid for high Reynolds number flows. A quantitative assessment of the departure from isotropy in stably stratified flows is performed and a pragmatic method is proposed to estimate the true three dimensional dissipation (ϵ3D) from one dimensional dissipation (ϵ1D) obtained from microstructure profilers in the ocean. Next, a scaling analysis for strongly stratified flow is presented to show that, the true diapycnal length scale Ld and diapycnal velocity scale wd can be estimated from the measurable Ellison length scale, LE and a measurable root mean square vertical velocity, w´, using a turbulent Froude number defined as Fr = ϵ/Nk, where k is the turbulent kinetic energy. It is shown that the eddy diffusivity Kρ can be then directly inferred from LE and w´. For weakly stratified flow regimes, Fr > O(1), Kρ ~ w´LE and for strongly stratified flow regimes, Fr < O(1), Kρ ~ w´LE x Fr. This finding is confirmed with direct numerical simulation (DNS) data for decaying as well as sheared stratified turbulence. This result indicates that Fr is a relevant non-dimensional parameter to identify strength of stratification in stably stratified turbulent flows. DNS with particle tracking is performed to separate isopycnal and diapycnal displacements of fluid particles, an analysis that is not possible from an Eulerian approach or from standard field measurements. The Lagrangian analysis show that LE is indeed an isopycnal length scale. Furthermore, having established that Fr is the signature parameter which can describe the state of stratified turbulence, a parameterization of mixing coefficient, Γ (or Rƒ) as a function of turbulent Froude number Fr is developed using scaling arguments of energetics of the flow. Proposed parameterization is then verified using DNS data of decaying, sheared and forced stratified turbulence. It is shown that for Fr << O(1), Γ ~ Fr0, for Fr ~ O(1), Γ ~ Fr-1 and for Fr >> O(1), Γ ~ Fr-2. Finally, a practically useful method to identify the dynamic state of turbulence in stably stratified flows is developed. Two commonly measurable length scales in the ocean are the Thorpe overturning length scale, LT and the dimensionally constructed Ozmidov length scale, LO. From scaling analysis and DNS data of decaying, sheared and forced stratified turbulence a new relation between Fr and the ratio of the length scales, LT/LO is derived. The new scaling is, for LT/LO > O(1), Fr ~ (LT/LO)-2 and for LT/LO < O(1), Fr ~ (LT/LO)-2/3.
Open Access
Numerical modeling of reservoir sedimentation and flushing processes
(Colorado State University. Libraries, 2011) Ahn, Jungkyu, author; Yang, Chih Ted, advisor; Julien, Pierre Y., committee member; Thornton, Christopher I., committee member; Wohl, Ellen E., committee member
As rivers flow into reservoirs, part of the transported sediment will be deposited. Sedimentation in the reservoir may significantly reduce reservoir storage capacity. Reservoir capacity can be recovered by removing deposited sediment by dredging or flushing. Generally speaking, the latter is preferable to the former. An accurate estimation sedimentation volume and its removal are required for the development of a long term operation plan in the design stage. One-dimensional, 1D, models are more suitable for a long term simulation of channel cross section change of a long study reach than two or three dimensional models. A 1D model, GSTARS3, was considered, because this study focuses on sedimentation and flushing in the entire reservoir over several years and GSTARS3 can predict channel geometry in a semi-two dimensional manner by using the stream tube concept. However, like all 1D numerical models, GSTARS3 is based on some simplified assumptions. One of the major assumptions made for GSTARS3 is steady or quasi-steady flow condition, which is valid for most reservoir operation. If there is no significant flow change in a reservoir, such as rapid water surface drop during flushing, steady model can be applied. However, unsteady effect due to the flushing may not be ignored and should be considered for the numerical modeling of flushing processes. Not only flow characteristics but also properties of bed materials in reservoir regime may be different from those in a river regime. Both reservoir and river regimes should be considered for a drawdown flushing study. Flow in the upper part of a reservoir may become river flow during a drawdown flushing operation. A new model, GSTARS4 (Yang and Ahn, 2011) was developed for reservoir sedimentation and flushing simulations in this study. It has the capabilities of simulating unsteady flow and coexistence of river and reservoir regimes in the study area. GSTARS4 was applied to the Xiaolangdi Reservoir, located on the main stream of the Yellow River. The sediment concentration in the reservoir is very high, 10 ~ 100 kg/m3 for common operation and 100 ~ 300 kg/m3 for flushing operation, with very fine materials about 20 ~ 70 % of clay. Stability criteria for computing sediment transport and channel geometric changes by using GSTARS4 model was derived and verified for the Xiaolangdi Reservoir sedimentation and flushing computations. Han's (1980) non-equilibrium sediment transport equation and the modified unit stream power equation for hyper-concentrated sediment flows by Yang et al. (1996) were used. Both unsteady and quasi-steady simulations were conducted for 3.5 years with calibrated site-specific coefficients of the Xiaolangdi Reservoir. The computed thalweg elevation, channel cross section, bed material size, volume of reservoir sedimentation, and gradation of flushed sediments were compared with the measured results. The unsteady computation results are closer to the measurements than those of the steady flow simulation results.
Open Access
Numerical simulations on patterns of alluviation in mixed bedrock-alluvial channels
(Colorado State University. Libraries, 2023) Cho, Jongseok, author; Nelson, Peter A., advisor; Julien, Pierre Y., committee member; Ettema, Robert, committee member; Wohl, Ellen E., committee member
Mixed bedrock-alluvial rivers can exhibit partial alluvial cover, which may play an important role in controlling bedrock erosion rates and landscape evolution. However, numerical morphodynamic models generally are unable to predict the pattern of alluviation in these channels. Hence we present a new two-dimensional depth-averaged morphodynamic model that can be applied to both fully alluvial and mixed bedrock-alluvial channels, and we use the model to gain insight into the mechanisms responsible for the development of sediment patches and patterns of bedrock alluviation. The model computes hydrodynamics, sediment transport, and bed evolution, using a roughness partitioning that accounts for differential roughness of sediment and bedrock, roughness due to sediment transport, and form drag. The model successfully replicates observations of bar development and migration from a fully alluvial flume experiment, and it models persistent sediment patches observed in a mixed bedrock-alluvial flume experiment. Numerical experiments in which the form drag, sediment transport roughness, and ripple factor were neglected did not successfully reproduce the observed persistent sediment cover in the mixed bedrock-alluvial case, suggesting that accounting for these different roughness components is critical to successfully model sediment dynamics in bedrock channels. Understanding the development and spatial distribution of alluvial patches in mixed bedrock-alluvial rivers is necessary to predict the mechanisms of the interactions between sediment transport, alluvial cover, and bedrock erosion. This study aims to analyze patterns of bedrock alluviation using a 2D morphodynamic model, and to use the model results to better understand the mechanisms responsible for alluvial patterns that have been observed experimentally. A series of simulations are conducted to explore how alluvial patterns in mixed bedrock-alluvial channels form and evolve for different channel slopes and antecedent sediment layer thicknesses. In initially bare bedrock low-slope channels, the model predicts a linear relationship between sediment cover and sediment supply because areas of subcritical flow enable sediment deposition, while in steep-slope channels the flow remains fully supercritical and the model predicts so-called runaway alluviation in which the bedrock remains fully exposed at all sediment supplies below a threshold. For channels that are initially covered with sediment, the model predicts a slope-dependent sediment supply threshold above which a linear relationship between bedrock expo-sure and sediment supply develops, and below which the bedrock becomes fully exposed. For a given sediment supply, the fraction of bedrock exposure and average alluvial thickness converge toward the equilibrium value regardless of the initial cover thickness so long as it exceeds a minimum threshold. Steep channels are able to maintain a continuous strip of sediment under sub-capacity sediment supply conditions by achieving the balance between increased form drag as bedforms develop and reduced surface roughness as the portion of alluvial cover decreases. In lower-slope channels, alluvial patches are distributed sporadically in regions of the subcritical flow.
Open Access
Physics of environmental flows interacting with obstacles
(Colorado State University. Libraries, 2017) Zhou, Jian, author; Venayagamoorthy, Subhas K., advisor; Julien, Pierre Y., committee member; Bledsoe, Brian P., committee member; Sakurai, Hiroshi, committee member
The effects of natural and man-made obstacles on their surrounding environmental flows such as rivers, lakes, estuaries, oceans and the atmosphere has been the subject of numerous studies for many decades. The flow-obstacle interaction can lead to the generation of turbulence which determines local flow dynamics and even large-scale circulations. The characteristic chaotic and enhanced mixing properties of turbulence in conjunction with other environmental conditions such as the clustering of multiple obstacles and density variations raise a number of interesting problems pertaining to both fundamental fluid dynamics and practical engineering applications. Insights into these processes is of fundamental importance for many applications, such as determining the fate of deep water-masses formed in the abyssal ocean, optimizing the productivity and environmental impact of marine farms, predicting the amount of power that a group of turbines can generate, estimating carbon dioxide exchange between the forests and the atmosphere or modeling flood routing in vegetated rivers. The main aim of this dissertation is to use high-resolution numerical simulations to study environmental flows of different forcing mechanisms interacting with obstacles of different geometries. The objectives are multi-fold: (i) To gain insights into the three-dimensional hydrodynamics of constant-density flows interacting with a finite canopy; (ii) To develop an unambiguous geometrical framework for characterizing canopy planar geometry; (iii) To explore the fundamental differences in the flow dynamics between porous canopies and their solid counterpart; and (iv) To investigate the effect of ambient density stratification on flow-obstacle interactions. The first part of this dissertation focuses on the mean three-dimensional hydrodynamics in the vicinity of a suspended cylindrical canopy patch with a bulk diameter of D. The patch was made of Nc constituent solid circular cylinders with h in height and d in diameter, and was suspended in deep water (H/h ≫ 1 where H is the total flow depth). After the validation against published experimental data, large eddy simulations (LES) were conducted to study the effects of patch density (0.16 ≤ φ = Nc(d/D)2 ≤ 1, by varying Nc) and patch aspect ratio (0.25 ≤ AR = h/D ≤ 1, by varying h) on the near-field flow properties. It was observed qualitatively and quantitatively that an increase in either φ or AR decreases bleeding velocity along the streamwise direction but increases bleeding velocities along the lateral and vertical directions, respectively. A close examination at the flow inside the patch reveals that despite the similar dependence of vertical bleeding on φ and AR, the underlying physics are different. However, in contrast to the bleeding velocity, a flow-rate budget shows that the proportion of the vertical bleeding flow leaving the patch with respect to the total flow entering the patch (i.e. relative vertical bleeding) decreases with increasing AR. Finally, the interlinks between patch geometry, flow bleeding and flow diversion are identified: the patch influences the flow diversion not only directly by its real geometrical dimensions, but also indirectly by modifying flow bleeding which enlarges the size of the near-wake. While loss of flow penetrating the patch increases monotonically with increasing φ, its partition into flow diversion around and beneath the patch shows a non-monotonic dependence, highlighting the fundamental differences in the flow dynamics between porous patches and their solid counterpart. Next, the propagation of full-depth lock-exchange bottom gravity currents over a submerged array of circular cylinders is investigated using laboratory experiments and LES. Firstly, to investigate the front velocity of gravity currents across the whole range of array density φ, the array is densified from a flat-bed (φ = 0) towards a solid-slab (φ = 1) under a particular submergence ratio H/h, where H is the flow depth and h is the array height. The time-averaged front velocity in the slumping phase of the gravity current is found to first decrease and then increase with increasing φ. Next, a new geometrical framework consisting of a streamwise array density μx = d/sx and a spanwise array density μy = d/sy is proposed to account for organized but nonequidistant arrays (μx 6 ≠ μy), where sx and sy are the streamwise and spanwise cylinder spacings, respectively, and d is the cylinder diameter. It is argued that this two-dimensional parameter space can provide a more quantitative and unambiguous description of the current-array interaction compared with the array density given by φ = (π/4) μxμy. Both in-line and staggered arrays are investigated. Four dynamically different flow regimes are identified: (i) through-flow propagating in the array interior subject to individual cylinder wakes (μx: small for in-line array and arbitrary for staggered array; μy: small); (ii) over-flow propagating on the top of the array subject to vertical convective instability (μx: large; μy: large); (iii) plunging-flow climbing sparse close-to-impermeable rows of cylinders with minor streamwise intrusion (μx: small; μy: large); and (iv) skimming-flow channelized by an in-line array into several sub-currents with strong wake sheltering (μx: large; μy: small).Finally, the flow dynamics of intrusive gravity currents past a bottom-mounted obstacle in a continuously stratified ambient was numerically investigated, highlighting the effect of ambient stratification which is not considered in the previous sections. The propagation dynamics of a classic intrusive gravity current was first simulated in order to validate the numerical model with previous laboratory experiments. A bottom-mounted obstacle with a varying non-dimensional height of ˜D = D/H, where D is the obstacle height and H is the total flow depth, was then added to the problem in order to study the downstream flow pattern of the intrusive gravity current. For short obstacles, the intrusion re-established itself downstream without much distortion. However, for tall obstacles, the downstream flow was found to be a joint effect of horizontal advection, overshoot-spring back phenomenon, and associated Kelvin-Helmholtz instabilities. Analysis of the numerical results show that the relationship between the downstream propagation speed and the obstacle height can be subdivided into three regimes: a retarding regime (˜D ≈ 0 ∼ 0.3), an impounding regime (˜D ≈ 0.3 ∼ 0.6), and a choking regime (˜D ≈ 0.6 ∼ 1.0).Overall, at a fundamental level, this dissertation aims to contribute to an improved understanding of the physics associated with environmental flows interacting with obstacles. Moreover, the results from this research are expected to facilitate better parameterizations of this important class of flows.
Open Access
Quasi-equilibrium conditions of urban gravel-bed stream channels in southern Ontario, Canada, and their implications for urban-stream restoration
(Colorado State University. Libraries, 2010) Annable, William Kenneth, 1965-, author; Watson, Chester C., advisor; Bledsoe, Brian P., committee member; Fischenich, J. Craig, 1962-, committee member; Julien, Pierre Y., committee member
Urban gravel-bed stream channels in southern Ontario, Canada, identified to be in a state of quasi-equilibrium have been studied over the past 15 years and compared against rural gravel-bed stream channels of the same hydrophysiographic region. Bankfull width and depth versus bankfull discharge were not found to increase as a function of increasing urbanization as has been found in many other studies. The observed annual frequency of bankfull discharge was typically less than a 1-year return period with many sites ranging between two to eighteen bankfull events per year with higher intensity and shorter duration urban flood responses. The cumulative volume of bankfull and larger flood events from the urban-stream channels were very similar to the same annual event volumes in the rural comparison study reaches. Bed-material supply was found to decrease with increasing urbanization and the reduction in bed-material supply appears to be offset by the smaller bankfull channel width, depth, and access to floodplains during large flood events. Field evidence may also suggest an even greater reduction in channel width trajectory, relative to the rural setting, with floodplains to maintain quasi-equilibrium conditions as bed-material supply continues to decrease with increased anthropogenic activity. Compared to surrounding rural watersheds, urban belt widths were found to decrease, while meander wave lengths and radii of curvature were found to increase as a function of bankfull width. The stream-wise elongation of meander wave lengths (and thus increase in radii of curvature) are a result of increased flood flow frequency and volume in the urban environments combined with reductions in bed-material supply. An increased frequency in riffles and pools was also observed along each reach. Additional pools appeared along straight sections between bends, although they were shallower than pools on bends. The changes in bedforms result from brief but frequent discharge events that exceed critical shear values, resulting in sediment pulsing and the frequent placement of keystone clasts that create frequent riffle (and pool) development. Field observations of standing wave patterns in flood flows also support the role of `dune-like' formations as a means of maximizing flow resistance. Several methods of estimating channel-forming discharge were also evaluated to test their applicability in the urban condition. Bankfull stage was identified at a series of locations along each study reach and it was found that the most consistent observations of bankfull discharge occurred during flood conditions where bankfull stage was identified at the top of point bars along the convex arc of bends. The largest errors in estimation occurred at gauge stations where cross-sectional geometry had been altered to conform to bridges or culverts rather than the channel morphology. Independent evaluations of channel-forming discharge were conducted by eleven practitioners ranging from 10 to 43 years of experience with similar findings and errors. Various methods of relating frequency return periods were evaluated using annual peak series discharge observations and continuous 15-minute systematic discharge records using partial duration series analysis. No specific correlations were identified between frequency return periods and land-use change. However, based upon the findings of this study, the applicability of employing annual series peak discharge data to evaluate bankfull frequency return in urban-stream channels is highly discouraged.
Open Access
The effects of sediment supply, width variations, and unsteady flow on riffle-pool dynamics
(Colorado State University. Libraries, 2018) Morgan, Jacob A., author; Nelson, Peter A., advisor; Bledsoe, Brian P., committee member; Julien, Pierre Y., committee member; Wohl, Ellen, committee member
Channel geometry, water discharge, and sediment supply work together to influence gravel-bed morphodynamics. How these forcings change and interact affects instream meso-scale geomorphic units, such as riffles and pools, which are often important habitat areas for aquatic organisms. Riffles and pools, defined as vertical undulations in the longitudinal bed profile, are often co-located with variations in channel width and their maintenance in natural systems is often attributed to unsteady flow effects. However, little work has been done to investigate the interaction between unsteady flow and the periodic width variations that often accompany riffle-pool morphology. Surficial sediment sorting, which is largely dependent on sediment supply, is also invoked as an important factor for riffle-pool maintenance. However, there is a lack of studies exploring how riffles and pools respond, or are maintained, in the case of increased sediment supply, such as might be experienced due to dam removal. In general, little is known about how constriction-forced riffles and pools interact with unsteady flow and changes to sediment supply. This dissertation investigates the interplay between channel geometry, discharge, and sediment supply using numerical methods, laboratory experiments, and field exploration. Chapter 2 presents a one-dimensional morphodynamic model which was used to investigate the controls on sediment pulse evolution in coarse-bed rivers. The model uses the standard step backwater method to compute hydrodynamics, calculates bedload, and simulates elevation changes. A stratigraphy submodel retains data related to vertical grain size sorting in the channel subsurface. The results suggest that sediment pulses move downstream with a greater degree of translation with smaller pulse sizes, longer pulse feed times, finer pulse grain sizes, and prolonged higher discharges. In Chapter 3, a two-dimensional morphodynamic model was used to systematically investigate the influence of width variations, unsteady flow, and changing sediment supply rates on equilibrium morphodynamics. Multiple channels with various amplitudes and wavelengths of sinusoidal width variations were modeled under conditions of steady and unsteady discharge and different sediment supply rates. Results suggest that the amplitude of width variations exerts a primary control on riffle-pool relief and that under cycled hydrographs a reversal in the location of maximum shear stress occurs providing a riffle-pool maintenance mechanism. Complementary flume experiments are presented in Chapter 4, where two geometries (constant- and variable-width) were subjected to the same sequential phases of steady flow and constant sediment supply, unsteady flow and constant sediment supply, and unsteady flow and increased sediment supply. Results show that the variable-width channel adjusts to an increased sediment supply by reducing the elevation relief between adjacent riffles and pools and decreased cross-sectional elevation variability, effectively reducing the form drag, rather than increasing the overall bed slope. Finally, Chapter 5 presents a field investigation of the Elwha River downstream of the former Glines Canyon Dam site, using the dam removal as a natural experiment. Three annual topographic surveys were conducted along with hydrodynamic modeling to investigate the impact of increased sediment supply to a natural channel with riffle-pool morphology. Results show aggradation and channel widening have resulted in shallower, slower flows. Field surveys were complemented with historical aerial image analysis which suggests that channel widening and lateral migration rates have increased substantially since dam removal.
Open Access
Three-dimensional computational modeling of curved channel flow
(Colorado State University. Libraries, 2014) Sin, Kyung-Seop, author; Venayagamoorthy, Subhas K., advisor; Thornton, Christopher I., advisor; Abt, Steven R., committee member; Julien, Pierre Y., committee member; Dasi, Lakshmi P., committee member
Investigating flow dynamics in curved channels is a challenging problem due to its complex three-dimensional flow structure. Despite the numerous investigations that have been performed on this important topic over the last several decades, there remains much to be understood. The focus of this dissertation is on flow around curved channel bends with an emphasis on the use of three-dimensional numerical simulations to provide insights on the flow dynamics in channel bends. In particular, the answers to the following two main questions are sought: 1) when is it appropriate to use the rigid lid assumption for simulating flow around bends?; and 2) what is (are) the most relevant parameters for quantifying the enhanced shear stress in channel bends from a practical standpoint? A computational fluid dynamics framework was developed using the ANSYS Fluent code and validated using experimental flume data. Following the validation study, a total of 26 simulations were performed and the results analysed in an attempt to answer the two main questions. In an attempt to answer the first question, a broad parametric study was conducted using both free surface resolving simulations as well as simulations that make use of the rigid lid assumption. It is shown that the two main parameters that appear to control the flow dynamics in a bend are the maximum bend angle, expressed as the ratio of the length of the channel bend Lc to its radius of curvature Rc, and the upstream Froude number. Analysis reveal when that Lc/Rc ≥ π/2, the curvature effects begin to dominate the dynamics and the error between the free surface model and the rigid lid model dramatically increases regardless of the value of the Froude number. The study calls for caution to be used when using the rigid lid assumption and indicates that this assumption should not be used for simulating flows when Lc/Rc ≥ π/2, especially for sharply curved channels with a radius of curvature to top width ratio Rc/Tw < 2. The increase in shear stress is commonly expressed as a Kb value, which is simply the ratio of shear stress in a bend of the channel to the averaged approach shear stress in a straight channel. The results from the parametric study show that the conventional approach for parameterizing Kb as a function of Rc/Tw, where Rc is the radius of curvature and Tw is the channel top width, appears to be inadequate because the distributions in the Kb values exhibit significant scatter for small changes in Rc/Tw i.e. for flow around sharply curved bends. Dimensional analysis reveals that for a given channel cross-section, constant flow rate, bed slope and channel bed roughness, Kb depends on both Lc/Rc and Rc/Tw. In this study, the combined effects of these two parameters were investigated. It is shown from the parametric study that the magnitude of the shear stress increases as a function of Lc/Rc and reaches an asymptotic limit as Lc/Rc > π/2, for Rc/Tw < 2. The study also highlights that the location of the maximum shear stress occurs in the inner (convex) side of the bend for Rc/Tw < 2 but shifts towards the outer bend for Rc/Tw > 2. While the emphasis (and in a sense a limitation) of this study has been mainly on sharp curved bends (Rc/Tw < 2), the analysis can be readily extended to curved bends with Rc/Tw > 2. It is envisaged that such an analysis will lead to a framework for parameterizing Kb in a comprehensive manner that would be useful for practical design guidelines.
Open Access
Turbulence modeling of stably stratified wall-bounded flows
(Colorado State University. Libraries, 2014) Karimpour, Farid, author; Venayagamoorthy, Subhas K., advisor; Birner, Thomas, committee member; Bledsoe, Brian P., committee member; Julien, Pierre Y., committee member
The subject of wall-bounded flows has been a matter of discussion and has received considerable attention in the past few decades. This is mainly attributed to the fact that the presence of the solid wall has profound effects on the turbulence and hence results in anomalous mixing and transport of momentum, scalar and heat in environmental flows. This is much more intense in the vicinity of the solid wall commonly known as the near-wall region compared to regions away from the wall. This effect will be more complicated in the presence of density stratification which has a strong influence on the development of turbulence. Therefore, numerous field, laboratory, numerical and theoretical studies are performed in a quest to gain a better understanding of wall-bounded flows especially in the presence of stratification. However, there is still a lack of a clear picture on the near-wall flow properties, the onset of turbulence and the resulting mixing in wall-bounded flows. The aim of this dissertation is to employ both theory and numerical simulations to revisit mixing in wall-bounded flows, especially in the near-wall region. The main objectives are: • To investigate the unstratified near-wall turbulence and revisit the turbulent (eddy) viscosity (νt) formulation in unstratified wall-bounded flows. This will be followed by derivation of a novel proposition for the appropriate velocity, length and time scales in unstratified wall-bounded flows. • To revisit the fundamentals of common Reynolds-averaged Navier-Stokes (RANS) closure schemes such as the standard k-ε model and investigate their capability to model near-wall turbulence. • To investigate the turbulent mixing in stably stratified wall-bounded flows. The mixing of momentum, scalar and the efficiency of the mixing are evaluated. • To study wall-bounded turbulent flows in the presence of stable stratification by performing one-dimensional RANS simulations. In particular, this includes introduction of a modified turbulent Prandtl number (Prt) for wall-bounded flows and calibration of the standard k-ε model. In this dissertation, a novel formulation for the turbulent (eddy) viscosity given by ν=ε/(S2) is derived by assuming equilibrium between the turbulent kinetic energy production rate P and the dissipation rate of the turbulent kinetic energy (ε), where S is the mean shear rate. Also, the relevant scales of length and velocity are derived. The propositions are tested with the direct numerical simulation (DNS) data of unstratified turbulent channel flow of Hoyas & Jiménez (2006) and unstratified turbulent boundary layer flow of Sillero et al. (2013). The comparisons of the propositions with the exact computations from the DNS data are excellent. Furthermore, the suitability of the equilibrium assumption (i.e. P ≈ ε) for modeling near-wall turbulence is revisited. This is important as most widely used turbulent viscosities such as the formulation of the standard k-ε model are developed by using the equilibrium assumption. It is analytically shown that such νt formulations are not suitable for modeling near-wall turbulence. Also, the turbulent mixing in stably stratified wall-bounded flows is studied by employing analytical arguments. 'A priori' tests are performed by using highly resolved stably stratified channel flow DNS data of García-Villalba & del Álamo (2011). It is shown that in such flows assuming P ≈ ε + εPE, where εPE is the dissipation rate of the turbulent potential energy, holds in a big fraction of the flow depth. Also, the results show that an irreversible flux Richardson number as R*f = εPE/(ε + εPE) can properly predict the flux Richardson number (Rf =-B/P), where B is the buoyancy flux. It is also shown that neglecting the transport rate of εPE and assuming equilibrium as -B ≈ εPE is not a suitable assumption. Furthermore, the ideas discussed are utilized to perform 'a posteriori' tests and to simulate stably stratified wall-bounded flows by using RANS numerical models. To do this, first a simple one-dimensional zero-equation as well as two-equation k-ε RANS models are developed. It is shown that turbulent Prandtl numbers based on the homogeneous assumption are not capable of providing a good estimation of the mixing and therefore an inhomogeneity correction must be introduced. It is analytically shown that commonly used homogeneous turbulent Prandtl numbers should be modified for a wall-bounded flow using a correction as (1-z/D), where D is the total flow depth. This work is extended by revisiting the buoyancy parameter (Cε3) in the standard k-ε closure scheme. Analytical arguments are used to show that Cε3 ≈ 0. RANS results show the suitability of the propositions for modeling of stably stratified turbulent channel flows. The ultimate goal of this research is to enhance understanding of the fundamental aspects of wall-bounded environmental flows and develop appropriate turbulence models that can capture the physics of stably stratified wall-bounded turbulent flows.
Open Access
Turbulence parameterizations for numerical simulations of stably stratified environmental flows
(Colorado State University. Libraries, 2011) Elliott, Zachary, author; Venayagamoorthy, Subhas Karan, advisor; Julien, Pierre Y., committee member; Dasi, Lakshmi Prasad, committee member
Almost all environmental and geophysical flows such as lakes, reservoirs, estuaries, and the atmosphere are turbulent and are also often characterized by stable density stratification. The presence of buoyancy forces due to stratification has a substantial effect on the flow development and turbulent mixing processes, influencing the distribution of pollutants and suspended matter in these flows. Mathematical and computer models can be used to simulate and produce numerical solutions to these flows, providing results that would otherwise not be feasibly attainable in a laboratory setting and that can be used for engineering prediction, design, and analysis purposes. Turbulence models use computational procedures to close the system of mean flow equations and account for the effects of turbulence and stratification through the specification of parameters that characterize the behavior of the flow. In this research, an attempt is made to assess and improve turbulence parameterizations for stably stratified environmental flows. An important parameter describing the transfer of momentum and scalar fluxes in stratified turbulent flows is the turbulent Prandtl number Prt. Specifically, four different formulations of the turbulent Prandtl number Prt are evaluated for stably stratified flows. All four formulations of Prt are strictly functions of the gradient Richardson number Ri, a parameter that provides a measure of the strength of the stratification. A zero-equation turbulence model for the turbulent viscosity νt in a one-dimensional turbulent channel flow is considered to assess the behavior of the different formulations of Prt. Both uni-directional and oscillatory flows are considered to simulate conditions representative of practical flow problems, such as atmospheric boundary layer flows and tidally-driven estuarine flows, to quantify the behavior of each of the four formulations of Prt. It is discussed as to which of the models of Prt allow for a higher rate of turbulent mixing and which models significantly inhibit turbulent mixing in the presence of buoyancy forces resulting from fixed continuous stratification as well as fixed two-layer stratification. The basis underlying the formulation of each model in conjunction with the simulation results are used to highlight the importance of choosing an appropriate parameterization of Prt, given a model for νt in stably stratified flows. Other more complete and dynamic models rely on additional parameters that allow stratified turbulent flow to be modeled as a function of local turbulence quantities rather than mean global properties of the flow. This research also focuses on implementing and testing proposed changes that explicitly account for buoyancy effects in two-equation Reynolds-averaged Navier-Stokes (RANS) turbulence models. Direct numerical simulation (DNS) data of stably stratified homogeneous turbulence are used to study the parameters in two-equation RANS turbulence models such as the buoyancy parameter Cε3 and the turbulent Prandtl number Prt in the k-ε model. Both the gradient Richardson number Ri and the turbulent Froude number Frk are used as correlating parameters to characterize stratification in the k-ε model. It is shown that it may be more appropriate to use Frk as the parameter of choice for the stratification parameter in the k-ε model since it is based on the local properties of the turbulence as opposed to Ri, which is a mean property of the flow. The proposed modifications and alterations to Cε3 and Prt as functions of Ri and Frk are implemented in a one-dimensional water column model called General Ocean Turbulence Model (GOTM) and used to simulate stably stratified channel flows. The results from numerical simulations using the modified versions of the k-ε model are compared to stably stratified channel flow DNS data to assess their efficacy.