Previous publications show that **Computational** **Fluid** **Dynamics** (CFD) can be readily used for the flow prediction and analysis of screw compressors. Several case studies are presented in this paper to show the scope and applicability of such methods. These include solid-**fluid** interaction in screw compressors, prediction of flow generated noise in screw machines, cavitation modelling in gear pumps, and flow in multiphase pumps for oil and gas industry. Numerical grids for all these cases were generated by us of an in-house grid generator, while the CFD calculations were performed with a variety of commercially available CFD codes. In order to validate the accuracy of the CFD calculations, an extended test programme was carried out using Laser Dopler Velocimetry (LDV) to measure the mean and fluctuating velocity distribution in screw compressor flow domains. The measurement results are then compared with the CFD simulations. The results confirm the viability of the developed techniques.

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Almost all engineered objects are immersed in either air or water (or both), or make use of some working **fluid** in their operation. This is particularly true of machines for energy generation and conversion, such as engines, turbines, and renewable energy devices such as wind turbines or wave-energy converters. The ability to model such devices is therefore a key enabling technology, and **Computational** **Fluid** **Dynamics** (CFD) is thus a key element of Digital Engineering. However, the situation is highly complex. As we show below, the basic equations are non-linear, which presents serious challenges; only the most straightforward cases are capable of algebraic solution, hence the development of **computational** methods. Although CFD could loosely be used to denote any **computational** solution of **fluid** flow problems, the subject is commonly understood to refer to the solution of the Euler or the Navier–Stokes equations, or equations derived from these, in two or three spatial dimensions. Moreover, other physical effects are often included, either out of interest or necessity. Turbulence is a state of **fluid** motion characterised by complex, transient, pseudo-random motion, and is almost ubiquitous in energy engineering; its modelling presents severe challenges in CFD. Other physical effects are often also included, such as chemical reaction and combustion, multiphase flow, free surface flow, etc. The challenges are both numerical and physical, and there are a number of reviews keyed towards specific industrial applications or areas of physics [1–5]. One of the key challenges though is the simulation of physical processes across a range of scales from the macro scales, which are well described by the Navier–Stokes equations of **fluid** flow, and thus accessible to conventional CFD simulation, right down to micro scales at which the continuum approximation no longer holds and for which kinetic equations for the system need to be solved. Many systems therefore require a holistic approach integrating different simulation approaches across a range of

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A lot of research has been reported in the field of greenhouse dryers. Solar PV operated fan as an auxiliary attachment to provide forced circulation of air inside the greenhouse dryer has been suggested to achieve higher drying rates. For obtaining better drying rate of dryer, analysis of greenhouse dryer in design stage has proposed using **Computational** **Fluid** **Dynamics**. Local parameters which are very hard to find out experimentally can be easily obtained using CFD.

Today’s reform rhetoric has revived the area of stretching sheet as represented the essence of **computational** **fluid** **dynamics**. The study of laminar flow of a thin liquid film over a stretching sheet is currently attracting the attention of a growing number of researchers because of its immense potential to be used as a technological tool in many engineering applications, with applications in industries such as extrusion, melt-spinning, the hot rolling, wire drawing, glass– fiber production, manufacture of plastic and rubber sheets, cooling of a large metallic plate in a bath, which may be an electrolyte, etc. In industry, polymer sheets and filaments are manufactured by continuous extrusion of the polymer from a die to a windup roller, which is located at a finite distance away. Other applications can be found in food processing, transpiration cooling, reactor fluidization, the aerodynamic extrusion of plastic sheets, the boundary layer along a liquid film in condensation process, the cooling of metallic plate in a cooling bath and last but not the least in present context is use of **Computational** **Fluid** **Dynamics** 1 (CFD) flow modeling in such a manner that that it will provide visible benefits to the wide range of renewable energy applications like wind, wave, tidal and hydro projects.

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In a 1986 report from the National Research Council on “Current Capabilities and Future Directions in **Computational** **Fluid** **Dynamics**”, it was stated “**computational** **fluid** **dynamics** is capable of simulating flow in complex geometries with simple physics or flow with simple geometries with more complex physics”. This is not true anymore thanks to progress in computers and algorithm developments. 3D Euler calculations of flows for complex geometries that were “state of the art” in 1986 for both the hardware and software requirements can now be carried out on laptops. CFD is widely accepted as a key tool for aerodynamic design. Reynolds Average Navier-Stokes (RANS) solutions are a common tool, and methodologies like Large Eddy Simulation (LES) that were once confined to simple canonical flows (isotropic turbulence in a box, channel flow), are moving to complex engineering applications. For example, the Center for Integrated Turbulence Simulations here at Stanford is using LES to simulate the reacting flow in a real combustor chamber of a jet engine.

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In the new era of direct stability assessment (DSA) for ship survivability in intact and damaged conditions, direct and accurate evaluation of the safety level achieved by the design plays a vital role. Two are the most popular methods for DSA namely, time domain numerical simulation (TDNS) and **Computational** **Fluid** **Dynamics** (CFD). Both can be used for the evaluation of the safety level of a ship post casualties, following collision or a grounding incidents. It is common practice for the TDNS methods to have as a core a hydraulic model for capturing the propagation of the floodwater and its **dynamics** in order to reduce the **computational** cost. However, more recently, CFD methods have matured enough to provide a credible alternative, particularly concerning the investigation of complex **fluid** **dynamics** problems. The catch, however, is higher computation costs and this is where ingenuity helps. This paper proposes and demonstrates the feasibility of using high fidelity **computational** **fluid** **dynamics** tools for direct damage stability assessment of ships.

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In order to predict the parameters in two-phase flows and there multidimensional distri- butions, a **Computational** **Fluid** **Dynamics** (CFD) methodology is used in this study. The CFD methodology allows one to obtain approximate numerical solutions of **fluid** flows through discretization. Discretization is replacing the set of coupled differential equations describing the flow by a set of algebraic equations which can be solved by the use of a computer. The CFD methodology became more and more important with the increase of **computational** power and it now represents an significant engineering tool that allows one to not have to rely on the usage of experimental studies and empirical correlations for modeling **fluid** flow but, instead substituting them with more generally applicable methods. It is also a much cheaper way of solving some engineering problems. However, CFD models still require to be validated against experimental data before their usage can be defended and this is one of the purposes behind the work of this thesis.

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There is reason to believe that the lift enhancing effects of the Weis-Fogh mechanism could increase with decreasing Re. Using two-dimensional **computational** **fluid** **dynamics**, we have determined that the lift coefficients generated during translation are lower for Re<32 than for Re>64 (Miller and Peskin, 2004). Wu and Sun (2004) also found that lift coefficients were greatly reduced for Re<100 in three- dimensional simulations without clap and fling. This drop in lift corresponds to a change in the behavior of the vortex wake. For Re=64 and above, a leading edge vortex is formed and at least initially remains attached to the wing. The trailing edge vortex is formed and shed from the wing. The stability of the attached leading edge vortex appears to vary with several factors, one of which is the dimensionality of the flow. In two dimensions, leading and trailing edge vortices are alternately shed forming the von Karman vortex street (Dickinson and Götz, 1993; Birch et al., 2004; Miller and Peskin, 2004). The real situation of insect flight differs from the two-dimensional model in at least two ways: the insect wing has finite span, and its motion involves rotation about the dorsal–ventral axis of the insect. In the three-dimensional rotating motion, the leading edge vortex appears to remain attached for all time (Usherwood and Ellington, 2002). Birch et al. (2004) also observed a stable attached leading edge vortex for Re=120 and Re=1400 using a dynamically scaled robotic insect. For Re=32 and below, both leading and trailing edge vortices are formed and remain attached to the wing (Miller and Peskin, 2004), and the leading edge vortex is more diffuse than the higher Re case (Wu and Sun, 2004). The drop in lift for lower Re is related to a loss of asymmetry in the vortical pattern behind the wing. A similar transition has been observed for thrust generation in flapping flight (Childress and Dudley, 2004; Vandenberghe et al., 2004).

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Abstract Due to recent advances in fast iterative solvers in the field of **computational** **fluid** **dynamics**, more complex problems which were previously beyond the scope of standard techniques can be tackled. In this paper, we describe one such situation, namely, modelling the interaction of flow and molecular orientation in a complex **fluid** such as a liquid crystal. Specifically, we consider a nematic liquid crystal in a spatially inhomogeneous flow situation where the orientational order is described by a second rank alignment tensor. The evolution is determined by two coupled equations: a generalised Navier–Stokes equation for flow in which the divergence of the stress tensor also depends on the alignment tensor and its time derivative, and a convection- diffusion type equation with non-linear terms that stem from a Landau-Ginzburg- DeGennes potential for the alignment. In this paper, we use a specific model with three viscosity coefficients that allows the contribution of the orientation to the viscous stress to be cast in the form of an orientation-dependent force. This effectively decouples the flow and orientation, with each appearing only on the right-hand side of the other equation. In this way, difficulties associated with solving the fully coupled problem are circumvented and a stand-alone fast solver, such as the state-of-the-art preconditioned iterative solver implemented here, can be used for the flow equation. A time-discretised strategy for solving the flow-orientation problem is illustrated using the example of Stokes flow in a lid-driven cavity.

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are constructed for the desired **fluid** properties (using, for example, fitted polyno- mials) which are then used in the CFD model. The behaviour of this CFD model ultimately depends on these functional relationships, and this choice requires some experience or needs to form part of an iterative approach . For the cases considered in this thesis, we adopt the following: for pressure, p = p(ρ); for dynamic viscosity, µ = µ(ρ); surface displacement, δ = δ(ρ); and slip length ξ = ξ(ρ, γ ˙ ), where ρ is the bulk **fluid** density and ˙ γ is the strain rate in the shear zone. This dependence on den- sity would normally imply a high-speed high-Mach number flow, but in nano-scale internal flows it is possible to have substantial **fluid** compressibility at extremely low Mach numbers due to viscous-related pressure losses (see [43] for a discussion of this). For this reason, capturing the influence of density on **fluid** properties is critical to the accurate prediction of nano-scale flows. For all of the examples considered, the influence of strain rate can be safely ignored, but we consider its effect on slip length for demonstration purposes. The fluids we consider are therefore Newtonian in the bulk; a non-Newtonian **fluid**, for example, would at least require µ = µ(ρ, γ ˙ ). Note that for the simulation of well-understood fluids it would not be necessary to extract all of these properties from MD pre-simulations.

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Across multiple simulations, we obtain the bulk pres- sure, a viscosity coefficient, the slip length, and the surface displacement, for a range of combinations of bulk density and applied shear stress. In the MD simulations, the applied shear stress and bulk density are varied by modifying the body force and by adding/removing molecules, respec- tively, using the FADE algorithm (Borg et al. 2014). Finally, once all data are collected over the expected range of density and shear stress, 1 functional relationships are constructed for the desired **fluid** properties (using, for example, fitted polynomials), which are then used in the CFD model. The behaviour of this CFD model ultimately depends on these functional relationships, and this choice requires some experience or needs to form part of an iterative approach (this is discussed in Sect. 5). For the cases considered in this paper, we adopt the following: for pressure, p ¼ pðqÞ; for dynamic viscosity, l ¼ lðqÞ; sur- face displacement, d ¼ dðqÞ; and slip length n ¼ nðq; cÞ, _ where q is the bulk **fluid** density and c _ is the strain rate in the shear zone. This dependence on density would nor- mally imply a high-speed high-Mach number flow, but in nanoscale internal flows, it is possible to have substantial **fluid** compressibility at extremely low Mach numbers due to viscous-related pressure losses [see Gad-el Hak (2010) for a discussion of this]. For this reason, capturing the influence of density on **fluid** properties is critical to the accurate prediction of nanoscale flows. For all of the examples considered in this paper, the influence of strain rate can be safely ignored, but we consider its effect on slip length for demonstration purposes. The fluids we consider are therefore Newtonian in the bulk; a non-Newtonian **fluid**, for example, would at least require l ¼ lðq; cÞ. Note _ that for the simulation of well-understood fluids, it would not be necessary to extract all of these properties from MD pre-simulations.

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Across multiple simulations, we obtain the bulk pres- sure, a viscosity coefficient, the slip length, and the surface displacement, for a range of combinations of bulk density and applied shear stress. In the MD simulations, the applied shear stress and bulk density are varied by modifying the body force and by adding/removing molecules, respec- tively, using the FADE algorithm (Borg et al. 2014). Finally, once all data are collected over the expected range of density and shear stress, 1 functional relationships are constructed for the desired **fluid** properties (using, for example, fitted polynomials), which are then used in the CFD model. The behaviour of this CFD model ultimately depends on these functional relationships, and this choice requires some experience or needs to form part of an iterative approach (this is discussed in Sect. 5). For the cases considered in this paper, we adopt the following: for pressure, p ¼ pðqÞ; for dynamic viscosity, l ¼ lðqÞ; sur- face displacement, d ¼ dðqÞ; and slip length n ¼ nðq; cÞ, _ where q is the bulk **fluid** density and c _ is the strain rate in the shear zone. This dependence on density would nor- mally imply a high-speed high-Mach number flow, but in nanoscale internal flows, it is possible to have substantial **fluid** compressibility at extremely low Mach numbers due to viscous-related pressure losses [see Gad-el Hak (2010) for a discussion of this]. For this reason, capturing the influence of density on **fluid** properties is critical to the accurate prediction of nanoscale flows. For all of the examples considered in this paper, the influence of strain rate can be safely ignored, but we consider its effect on slip length for demonstration purposes. The fluids we consider are therefore Newtonian in the bulk; a non-Newtonian **fluid**, for example, would at least require l ¼ lðq; cÞ. Note _ that for the simulation of well-understood fluids, it would not be necessary to extract all of these properties from MD pre-simulations.

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Figure 8 considers the later stages of drop for- mation when the dimensionless drop length, L, is equal to 4 and 6. The times from the previous droplet break-up taken for the simulations to reach these conditions for both CFX and FLOW-3D are shown above the corresponding figures. Although the agree- ment is reasonably good in all cases, with CFX show- ing the better qualitative agreement in terms of interface shape with reference [16], FLOW-3D shows slightly better quantitative agreement in the time taken to reach this point and is only 8 per cent greater than that of reference [16] compared with the 11 per cent overprediction by CFX. Also of interest, from the practical engineering viewpoint, is the **computational** resource needed to obtain the CFD results. Although there is little to choose between the predictions, the **computational** costs incurred in running simulations to droplet break- up are massively different: 2000 CPU seconds for FLOW-3D as opposed to 433 000 CPU seconds (over 5 days) for CFX on a R10 000, 195 MHz MIPS pro- cessor. Clearly for practical engineering compu- tations, where several simulations on fine meshes may be required, FLOW-3D is the more viable option. For this reason, the latter has been used to obtain all subsequent CFD results. A more detailed comparison between the capabilities of CFX and FLOW-3D is given by Fawehinmi [28].

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The main goal of this work is double. Firstly, we were interested in studying the simulation of the blood flow in thoracic aorta, by using some imported recent tridimensional magnetic resonance imaging data of a real healthy aorta and a real aorta in presence of coarctation, provided by “Laboratoire d’Imagerie Médicale-Un- iversité de Pierre et Marie Curie” (LIB-UPMC), in the context of a specific CFD software (ANSYS-ICEM-CFX), to build a meshing and elaborate an adapted geometry, and to examine the obtained results of the realized com- putational simulation. Secondly, we compared these results with those obtained from a **computational** simulation using the same software on a geometrical model of a healthy aorta proposed in [14], and another geometrical model of stenosis applied to coarctation developed in [15]. In all these cases, we examine the **computational** re- sults concerning the blood flow velocity field as well as pressure and the WSS.

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In the Bassaire cabinet (section 5.2.2.1) CFD studies conducted in this thesis have provided a new theory for the disparity in sampling efficiencies obtained during experiments. In the Sharpies room (section 6.2.2.1) CFD has suggested a reason why the sampling regime failed to detect any release during operation of the centrifuge. These are examples of CFD proposing a scenario which had not previously considered but which, with hindsight, was plausible. This ability to indicate alternative **fluid** flow behaviour was made prominent following the fire at Kings Cross underground station in November 1987. During the Kings Cross fire it was reported that the fire changed from a small blaze within the escalator tunnel to a serious conflagration within minutes. CFD predictions indicated a possible mechanism for this flashover, the so called trench effect where the hot gases stayed near the floor of the tunnel, that was entirely unexpected, but which was subsequently proved to be possible in practice In this case, as in many others, CFD offered an alternative explanation for the phenomena which proved to be correct. The trench effect is now an accepted mechanism in fire studies.

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For that investigations the **computational** ﬂuid **dynamics** (CFD) is used. Cavitation is founded by three dimensional (3D) eﬀects. Therefore the simulations are realised with the 3D-CFD-Code OpenFOAM. This is a excellent tool due to the free availability and the open solver code. The advantage of the numerical simulation is that every detail of the ﬂow can be obtained. Experiments cannot oﬀer this diversity. On the other hand an experiment is necessary to validate the numerical results. One step at the preparation of the simulation is the grid generation. Therefore special

lastic studies of limit cycle oscillations [55, 56]. The extension into the area of stability and control was considered in [57]. Two test cases were evaluated, a NACA 0012 airfoil and a X-31 aircraft model. The Volterra kernels were identified from a set of Gaus- sian shaped impulses, and the accuracy of the prediction model for different pitching motions was assessed. The applications were limited to linear cases, and a good agree- ment of the Volterra reduced-order modeling was observed when compared to time- accurate CFD simulations in the linear aerodynamic range. With weakly non-linear characteristics, the performance of the prediction model quickly degraded. As stated in the review [56], an important issue is the excitation of multiple degrees of freedom to properly identify non-linear cross-coupling of the degrees of freedom, and because of the non-linear nature of the aerodynamic system the principle of superposition is invalid. A method for the inclusion of Volterra cross-kernels applied to a transonic two-dimensional airfoil undergoing forced pitch and plunge harmonic oscillations was investigated [58]. The prediction model was compared to time-accurate CFD solutions, and the improvement in accuracy over approaches that ignore the cross-kernels was demonstrated. Addressing the convergence issue of the Volterra series and the need for the inclusion of higher-order kernels, an alternative formulation was presented [59]. The pruned Volterra series, with a simplified parametric structure of the kernels, was tested for a two-dimensional transonic airfoil undergoing forced sinusoidal pitch oscillations for two AGARD test cases. The identification of kernels up to fourth order demon- strated a feasible undertaking and a good agreement compared to the time-accurate CFD solution was achieved. The formulation of the pruned Volterra series was then used to approximate the flutter boundary and limit-cycle oscillation amplitudes of the NACA 0012 benchmark model [60]. Showing favourable results, a **computational** saving of several orders of magnitude compared to full-order CFD simulations was achieved.

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