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The purpose of this paper is to review the available reduced order modeling approaches in the literature for predicting the flow and specially temperature fields inside data centers in terms of the involved design parameters.

This paper begins with a motivation for flow/thermal modeling needs for designing an energy‐efficient thermal management system in data centers. Recent studies on air velocity and temperature field simulations in data centers through computational fluid dynamics/heat transfer (CFD/HT) are reviewed. Meta‐modeling and reduced order modeling are tools to generate accurate and rapid surrogate models for a complex system. These tools, with a focus on low‐dimensional models of turbulent flows are reviewed. Reduced order modeling techniques based on turbulent coherent structures identification, in particular the proper orthogonal decomposition (POD) are explained and reviewed in more details. Then, the available approaches for rapid thermal modeling of data centers are reviewed. Finally, recent studies on generating POD‐based reduced order thermal models of data centers are reviewed and representative results are presented and compared for a case study.

It is concluded that low‐dimensional models are needed in order to predict the multi‐parameter dependent thermal behavior of data centers accurately and rapidly for design and control purposes. POD‐based techniques have shown great approximation for multi‐parameter thermal modeling of data centers. It is believed that wavelet‐based techniques due to the their ability to separate between coherent and incoherent structures – something that POD cannot do – can be considered as new promising tools for reduced order thermal modeling of complex electronic systems such as data centers

The paper reviews different numerical methods and provides the reader with some insight for reduced order thermal modeling of complex convective systems such as data centers.

The purpose of this study is to propose a fast method for predicting flow fields with periodic behavior with verification in the context of a radial turbine to meet the urgent requirement to effectively capture the unsteady flow characteristics in turbomachinery. Aiming at meeting the urgent requirement to effectively capture the unsteady flow characteristics in turbomachinery, a fast method for predicting flow fields with periodic behavior is proposed here, with verification in the context of a radial turbine (RT).

Sparsity-promoting dynamic mode decomposition is used to determine the dominant coherent structures of the unsteady flow for mode selection, and for flow-field prediction, the characteristic parameters including amplitude and frequency are predicted using one-dimensional Gaussian fitting with flow rate and two-dimensional triangulation-based cubic interpolation with both flow rate and rotation speed. The flow field can be rebuilt using the predicted characteristic parameters and the chosen model.

Under single flow-rate variation conditions, the turbine flow field can be recovered using the first seven modes and fitted amplitude modulus and frequency with less than 5% error in the pressure field and less than 9.7% error in the velocity field. For the operating conditions with concurrent flow-rate and rotation-speed fluctuations, the relative error in the anticipated pressure field is likewise within an acceptable range. Compared to traditional numerical simulations, the method requires a lot less time while maintaining the accuracy of the prediction.

It would be challenging and interesting work to extend the current method to nonlinear problems.

The method presented herein provides an effective solution for the fast prediction of unsteady flow fields in the design of turbomachinery.

A flow prediction method based on sparsity-promoting dynamic mode decomposition was proposed and applied into a RT to predict the flow field under various operating conditions (both rotation speed and flow rate change) with reasonable prediction accuracy. Compared with numerical calculations or experiments, the proposed method can greatly reduce time and resource consumption for flow field visualization at design stage. Most of the physics information of the unsteady flow was maintained by reconstructing the flow modes in the prediction method, which may contribute to a deeper understanding of physical mechanisms.

The purpose of this study is to investigate the coherent structures of pulsed opposing jets by large eddy simulation (LES) model and proper orthogonal decomposition (POD) snapshot method. Flow pulsation as an active flow control method is considered for the enhancement of transport phenomena in impinging jets. The effect of flow pulsation parameters such as pulsation signal shape and frequency on the vortical coherent structures, the energy content of primary modes and their variation are studied numerically.

In this study, flow field of turbulent pulsating opposing jets has been simulated using LES. The result of the simulation in different time steps (snapshots) are stored and POD is applied on the snapshots. In this study, the POD method and calculation of spatial modes has been done using OpenFOAM, and time coefficients have been calculated using a MATLAB code.

The results of this study show that the flow excitation has a great effect on the coherent structure formation and the energy containment of fundamental modes of the flow. When the flow was excited by a harmonic sinusoidal or step function, the turbulent kinetic energy accumulated in the set of primary modes. On the other hand, the pulsed opposing jets had more regularity compared to the steady jets. The shapes, patterns and energy values of dominant modes depended on the inlet pulsation signal. An increase in pulsation frequency leads to an augmentation in energy content of the primary modes.

The predictions may be extended to include various pulsation conditions such as: various amplitudes, Reynolds number and aspect ratio.

The results of this study are a valuable source of information for active control of transport phenomena in opposing jet configurations which is used in different industrial applications such as cooling, combustion, reactors, heating and drying processes.

In this study, the coherent structures and energy content of primary modes was studied for the first time by LES model and POD snapshot method and a comprehensive discussion on numerical results is provided.

The study aims to display the bubbles' evolution in the shear layer and their relationship with the pressure fluctuations. Furthermore, the coherent structures of the first six modes are extracted, in order to provide insight into their temporal and spatial evolution and determine the relationship between cavitating bubbles and coherent structures.

In the present study, numerical simulations of submerged jet cavitating flow were carried out at a cavitation inception condition inside an axisymmetric cavity using the large eddy simulation (LES) turbulence model and the Schnerr–Sauer (S–S) cavitation model. Based on snapshots produced by the numerical simulation, dynamic mode decomposition (DMD) was performed to extract the three-dimensional coherent structures of the first six modes in the shear layer.

The cavitating bubbles in the shear layer are deformed to elongated ellipsoid shapes by shear forces. The significant pressure fluctuations are induced by the collapse of the biggest bubble in the group. The first mode illustrates the mean characteristics of the flow field. The flow in the peripheral region of the shear layer is mainly dominated by large-scale coherent structures revealed by the second and third modes, while different small-scale coherent structures are contained in the central region. The cavitating bubbles are associated with small size coherent structures as the sixth or higher modes.

This work demonstrates the feasibility of LES for high Reynolds number shear layer flow. The dynamic mode decomposition method is a novel method to extract coherent structures and obtain their dynamic information that will help us to optimize and control the flow.

(1) This paper first displays the three-dimensional coherent structures and their characteristics in the shear layer of confined jet flow. (2) The relationship of bubbles shape and pressure fluctuations is illustrated. (3) The visualization of coherent structures benefits the understanding of the mixing process and cavitation inception in jet shear layers.

The purpose of this paper is to present a full three-dimensional (3D) computational fluid dynamics (CFD) analysis of a rectangular asymmetric 3D diffuser utilizing seven turbulence models frequently used in engineering to assess the predictive capabilities of the turbulence models for separated flows in internal flows.

The structured computational grids are generated by means of the mesh generation tool IGG software package. The computational grids are imported into the commercial CFD code Fluent. The performance of the different turbulence models adopted has been systematically assessed by comparing the numerical results with the available experimental and direct numerical simulation/large eddy simulations data.

The comparisons show that the Reynolds stress model (RSM) evidently performs better than the other turbulence models for predicting wall pressure, velocity, and vorticity fields. Moreover, only the RSM can predict the separation bubble region around the top right corner, which is consistent with the experiment. It is found that the RSM can well predict Prandtl’s secondary flow of the second kind for considering turbulence anisotropy, whereas the other models cannot.

The paper utilizes seven turbulence models frequently used in engineering in detailed numerical investigations of a real 3D diffuser to expand the scope of application for various turbulence models. The studies are valuable for the proper use of the turbulence models, allowing the designers to understand the numerical results further and contributing to the modification of the turbulence models for 3D flows.

To achieve a full understanding of the role of marketing from plan to profit requires a knowledge of the basic building blocks. This textbook introduces the key concepts in the art or science of marketing to practising managers. Understanding your customers and consumers, the 4 Ps (Product, Place, Price and Promotion) provides the basic tools for effective marketing. Deploying your resources and informing your managerial decision making is dealt with in Unit VII introducing marketing intelligence, competition, budgeting and organisational issues. The logical conclusion of this effort is achieving sales and the particular techniques involved are explored in the final section.

This paper aims to demonstrate the capabilities of a diffuse interface free energy lattice Boltzmann method to perform direct numerical simulations of liquid–liquid dispersions in a well-controlled turbulent environment. The goal of this research study is to develop numerical techniques that can visualize and quantify drop interaction with the turbulent vortices. The obtained information will be used for the development of sub-models of drop breakup for multi-scale simulations.

A pure binary liquid system is considered that is subject to fully developed statistically stationary turbulent flow field in a cubic fully periodic box with the edge size of 300 lattice units. Three turbulent flow fields with varying energy input are examined and their coherent structures are visualized using a normalized Q-criterion. The evolution of the liquid–liquid interface is tracked as a function of time. The detailed explanation of the numerical method is provided with a highlight on a choice of the numerical parameters.

Drop breakup mechanisms differ depending on energy input. Drops break due to interaction with the vortices. Quantification of turbulent structures shows that the size of vortices increases with the decrease of energy input. Drop interacts simultaneously with multiple vortices of the size comparable to or smaller than the drop size. Vortices of the size smaller than the drop size disturb drop interface and pinch off the satellites. Vortices of the size comparable to the drop size tend to elongate the drop and tear it apart producing daughter drops and satellites. Addition of the second phase enhances turbulent dissipation at the high wavenumbers. To obtain physically realistic two-phase energy spectra, the multiple-relaxation-time collision operator should be used.

Detailed information of drop breakup in the turbulent flow field is crucial for the development of drop breakup sub-models that are necessary for multi-scale numerical simulations. The improvement of numerical methods that can provide these data and produce reliable results is important. This work made one step towards a better understanding of how drops interact with the turbulent vortices.

This chapter undertakes one re-evaluation of Louis Althusser’s philosophical legacy for modern Marxism. While Althusser self-consciously undertook to defend the scientific character of Marxism and so permanently establish it on a firm footing, many of his closest followers eventually exited the Marxian paradigm for a post-structuralism post-Marxism. We will argue that this development was rooted in Althusser’s initial procedure as he attempted to ground Marxism’s scientificity in an epistemological argument whose main referent was Marxism itself. This initiated a circularity which was ultimately to prove fatal to Althusser’s project. Less remarked upon, however, is a further legacy of the Althusserian oeuvre, the critical realist conception of Marxism initiated by Roy Bhaskar. Bhaskar found part of his inspiration in Althusser’s successful posing of the question of Marx’s science. On the one hand, Althusser’s work can legitimately be seen as a bridge into the post-modern challenge to Marxism. On the other hand, it can be seen as clearing the ground and establishing some of the foundation for critical realism’s successful recuperation of the scientific character of Marxism.