Abstract:Computational fluid dynamics is a method for simulating fluid flows that has been widely used in engineering for decades, and which also has applications for studying function and ecology in fossil taxa. However, despite the possible benefits of this approach, computational fluid dynamics has been used only rarely in palaeontology to date. The theoretical basis underlying the technique is outlined and the main steps involved in carrying out computer simulations of fluid flows are detailed. I also describe prev… Show more
“…One key aspect of mesh generation is the geometry of each cell. In Schemes 1 and 4 (Table 1), we employ tetrahedral elements as the base mesh, which is shown to be robust in previous studies for CFD studies and is more appropriate for complex geometry than cube/ hex elements (Adkins and Yan, 2006;Rigby and Tabor, 2006;Shiino et al, 2009;Rahman et al, 2015;Dynowski et al 2016;Rahman, 2017). Scheme 2 applied the ANSYS assembly meshing method, which automatically employs a variety of element types and settings to produce a mesh as a single process.…”
Section: Methodsmentioning
confidence: 99%
“…In all cases, the behavior of these flows are generally governed by the Reynolds-Averaged Navier-Stokes model (Flanagan, 2004;Weymouth et al, 2005;Adkins and Yan, 2006;Rigby and Tabor, 2006;Wilson et al, 2006;Shiino et al, 2009;Hannon, 2011;Dynowski et al 2016;Mossige, 2017;Rahman, 2017). The standard form of the Navier-Stokes equation mathematically approximates laminar flow and general patterns, but does not account for the complexities that arise from flow instability, such as the occurrence and behavior of turbulent eddies (Argyropoulos and Markatos, 2015;Rahman, 2017). Eddies can be simulated by supplementing the Navier-Stokes equation with additional computational algorithms, the options for which vary by software (Iaccarino, 2001;Argyropoulos and Markatos, 2015).…”
Section: Methodsmentioning
confidence: 99%
“…If carefully constructed and verified, a Computational Fluid Dynamics (CFD) model can be used to investigate fluid flow around ammonoids without the logistical challenges of a physical experiment (Cunningham et al, 2014). Long employed in engineering applications, CFD is now increasingly applied in biological and paleontological research (e.g., Adkins and Yan, 2006;Rigby and Tabor, 2006;Shiino et al, 2009;Dynowski et al, 2016;Rahman, 2017). The benefit of these tools is twofold; (1) apart from the cost of the software itself and appropriate hardware to supply the computing power, there is no additional cost to run simulations and iterate models, and (2) numerical methods allow convenient control over experimental param-eters and resolve detailed flow structure within the computational domain.…”
We use three-dimensional (3D) numerical models to examine critical hydrodynamic characteristics of a range of shell shapes found in extinct ammonoid cephalopods. Ammonoids are incredibly abundant in the fossil record and were likely a major component of ancient marine ecosystems. Despite their fossil abundance we lack significant soft body remains, which has made it historically difficult to investigate the potential life modes and ecological roles that these organisms played. By employing numerical tools to study how the morphology of a shell affected an ammonite's hydrodynamics, we can build a foundation for hypothesizing and testing changes in the organism's capabilities through time. To achieve this goal, the study was carried out in two major steps. First, we applied a number of simulation methods to a known problem, the drag coefficient of a half-sphere, to select the most appropriate modeling method that is accurate and efficient. These were further checked against previous experimental results on ammonoid hydrodynamics. Next, we produced 3D models of the ammonoid shells using Blender and Zbrush where each shell model emulated a specific fossil ammonoid, recent Nautilus, or an idealized shell forms created by systematically varying shell inflation and umbilical exposure. We test the hypothesis that both the overall shell inflation and umbilical exposure will increase the drag experienced by a similarly sized ammonoid shell as it moves through water relative to other morphologies. ANSYS FLUENT was employed to execute the study. We further compare our simulation results to published experimental measurements of drag on ammonoid fossil replicas and live Nautilus. The simulation results provide accuracy within an order of magnitude of published values, across the tested range of water flow velocities (1-50 cm/s). The simulated drag measurements demonstrate a first-order sensitivity to shell inflation, with a second-order effect from umbilical exposure. The impact of a larger umbilical exposure (shells that are more evolute) is minimal at low velocities, but substantial at higher velocities. We conclude that the overall shell inflation and umbilical exposure influence an individual shell's drag coefficient, therefore, influence the hydrodynamic efficiency.
“…One key aspect of mesh generation is the geometry of each cell. In Schemes 1 and 4 (Table 1), we employ tetrahedral elements as the base mesh, which is shown to be robust in previous studies for CFD studies and is more appropriate for complex geometry than cube/ hex elements (Adkins and Yan, 2006;Rigby and Tabor, 2006;Shiino et al, 2009;Rahman et al, 2015;Dynowski et al 2016;Rahman, 2017). Scheme 2 applied the ANSYS assembly meshing method, which automatically employs a variety of element types and settings to produce a mesh as a single process.…”
Section: Methodsmentioning
confidence: 99%
“…In all cases, the behavior of these flows are generally governed by the Reynolds-Averaged Navier-Stokes model (Flanagan, 2004;Weymouth et al, 2005;Adkins and Yan, 2006;Rigby and Tabor, 2006;Wilson et al, 2006;Shiino et al, 2009;Hannon, 2011;Dynowski et al 2016;Mossige, 2017;Rahman, 2017). The standard form of the Navier-Stokes equation mathematically approximates laminar flow and general patterns, but does not account for the complexities that arise from flow instability, such as the occurrence and behavior of turbulent eddies (Argyropoulos and Markatos, 2015;Rahman, 2017). Eddies can be simulated by supplementing the Navier-Stokes equation with additional computational algorithms, the options for which vary by software (Iaccarino, 2001;Argyropoulos and Markatos, 2015).…”
Section: Methodsmentioning
confidence: 99%
“…If carefully constructed and verified, a Computational Fluid Dynamics (CFD) model can be used to investigate fluid flow around ammonoids without the logistical challenges of a physical experiment (Cunningham et al, 2014). Long employed in engineering applications, CFD is now increasingly applied in biological and paleontological research (e.g., Adkins and Yan, 2006;Rigby and Tabor, 2006;Shiino et al, 2009;Dynowski et al, 2016;Rahman, 2017). The benefit of these tools is twofold; (1) apart from the cost of the software itself and appropriate hardware to supply the computing power, there is no additional cost to run simulations and iterate models, and (2) numerical methods allow convenient control over experimental param-eters and resolve detailed flow structure within the computational domain.…”
We use three-dimensional (3D) numerical models to examine critical hydrodynamic characteristics of a range of shell shapes found in extinct ammonoid cephalopods. Ammonoids are incredibly abundant in the fossil record and were likely a major component of ancient marine ecosystems. Despite their fossil abundance we lack significant soft body remains, which has made it historically difficult to investigate the potential life modes and ecological roles that these organisms played. By employing numerical tools to study how the morphology of a shell affected an ammonite's hydrodynamics, we can build a foundation for hypothesizing and testing changes in the organism's capabilities through time. To achieve this goal, the study was carried out in two major steps. First, we applied a number of simulation methods to a known problem, the drag coefficient of a half-sphere, to select the most appropriate modeling method that is accurate and efficient. These were further checked against previous experimental results on ammonoid hydrodynamics. Next, we produced 3D models of the ammonoid shells using Blender and Zbrush where each shell model emulated a specific fossil ammonoid, recent Nautilus, or an idealized shell forms created by systematically varying shell inflation and umbilical exposure. We test the hypothesis that both the overall shell inflation and umbilical exposure will increase the drag experienced by a similarly sized ammonoid shell as it moves through water relative to other morphologies. ANSYS FLUENT was employed to execute the study. We further compare our simulation results to published experimental measurements of drag on ammonoid fossil replicas and live Nautilus. The simulation results provide accuracy within an order of magnitude of published values, across the tested range of water flow velocities (1-50 cm/s). The simulated drag measurements demonstrate a first-order sensitivity to shell inflation, with a second-order effect from umbilical exposure. The impact of a larger umbilical exposure (shells that are more evolute) is minimal at low velocities, but substantial at higher velocities. We conclude that the overall shell inflation and umbilical exposure influence an individual shell's drag coefficient, therefore, influence the hydrodynamic efficiency.
“…The taxa selected occupy a wide range of phylogenetic positions and are representative of the main body shapes and sizes of ichthyosaurs, an advance relative to former studies, which focused only on derived forms [6,11]. Using computational fluid dynamics (CFD) [20], a numerical technique for simulating fluid flows, we tested the hypothesis that the derived fish-shaped ichthyosaurs had acquired morphologies that reduced the energy cost of steady swimming. Figure 1.Digital models of the ichthyosaurs analysed in this study shown in their phylogenetic context.…”
Ichthyosaurs are an extinct group of fully marine tetrapods that were well adapted to aquatic locomotion. During their approximately 160 Myr existence, they evolved from elongate and serpentine forms into stockier, fish-like animals, convergent with sharks and dolphins. Here, we use computational fluid dynamics (CFD) to quantify the impact of this transition on the energy demands of ichthyosaur swimming for the first time. We run computational simulations of water flow using three-dimensional digital models of nine ichthyosaurs and an extant functional analogue, a bottlenose dolphin, providing the first quantitative evaluation of ichthyosaur hydrodynamics across phylogeny. Our results show that morphology did not have a major effect on the drag coefficient or the energy cost of steady swimming through geological time. We show that even the early ichthyosaurs produced low levels of drag for a given volume, comparable to those of a modern dolphin, and that deep ‘torpedo-shaped’ bodies did not reduce the cost of locomotion. Our analysis also provides important insight into the choice of scaling parameters for CFD applied to swimming mechanics, and underlines the great influence of body size evolution on ichthyosaur locomotion. A combination of large bodies and efficient swimming modes lowered the cost of steady swimming as ichthyosaurs became increasingly adapted to a pelagic existence.
“…This process is very sensitive and dependent on the material properties such as bone density and mineralization. Subsequently, the virtual model of the object is generated and can be subject to different evolutionary studies using 3D geometric morphometrics (GMM) for ecomorphology (Drake, 2011), finite element analysis for biomechanics (Racicot, 2017;Tseng et al, 2017), or computational fluid dynamics to decipher the behavior of extinct animals in fluid environments (e.g., Rahman, 2017). In addition, such models can be printed out using rapid prototyping to have a physical replica of the object under study and therefore improving the anatomical understanding and opening the possibility of using these models for teaching or public engagement.…”
This article focuses on new virtual advances to solve technical problems usually encountered by paleontologists when using X-ray computed tomography (XCT), such as (i) the limited scanning envelope (i.e., field of view of CT systems/machines) to acquire data on large structures; (ii) the use in the same study of biological objects acquired with different types of computed tomography systems (medical and laboratory XCTs and laboratory high-resolution XµCT) and therefore different resolutions; and (iii) matrix removal within the fossil (e.g., cranial cavities, intratrabecular cavities, among other cavities). All these problems are very common in paleontology, and therefore, solving them is important to save effort and the time invested in data processing. In this article, we propose various solutions to tackle these issues, based on new technical advances focused on improving and processing the images obtained from XCT. Other aspects include image filtering and histogram calibration to remove background noise and artifacts. Such artifacts can result from dense mineral inclusion occurring during the fossilization process or derived from anthropogenic restoration of the sample. Accordingly, here, we provide a protocol to acquire data on samples with size that exceed the scanning envelope of the X-ray tomography machine, joining the parts with enough accuracy, and we propose the use of the interpolation "bicubic" method. Moreover, using this method, it is possible to use medical/laboratory XCT data together with XµCT data and therefore opening new ways to manipulate the acquired data within the image stack. Another advantage is the use of plugins for quantitative analysis, which require data with isometric voxels, such as the plugin BoneJ of the software ImageJ. We also deal with the problem of removing the exogenous material that usually fills the internal cavities of fossils by means of using filters based on edge detection by gradient. Applying this method, it is possible to segment the non-bony matrix parts more quickly and efficiently. All of this is exemplified using five fossil skulls belonging to the cave bear group (Ursus spelaeus sensu lato), an iconic fossil species from the Pleistocene of Eurasia.
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